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ioptnjoifih. 

DrrftboiH  i-O'kng, 
I'  Ohffbofh  f'-nfhfif. 


Civil  engineers'  pocket  hook 


Albert  Irvin  Frye 


d  by  Google 


d  by  Google 


d  by  Google 


d  by  Google 


d  by  Google 


CIVIL  ENGINEERS' 
POCKET-BOOK  - 

A    REFERENCE-BOOK   FOR  ENGINEERS 

CONTRACTORS     AND     STUDENTS 

CONTAINING   RULES,   DATA 

METHODS,   FORMULAS 

AND   TABLES  /  ^ 


ALBERT  I.   FRYE,  S.  B. 

Member  Amenean  Sodety  of  Citil  Enffineera 


NEW  YORK: 
D.    VAN   NOSTRAND   COMPANY 

LONDON; 
CONSTABLE  AND   COMPANY,  LTD. 

1918  Digitized  by  Google 


TA^-'^ 


Copyright,  1913, 

BY 

ALBERT  I.  FRYE 

AU  riohU  reserved 


L 


Wbstbrn  Nbwspapbr  Union.  Chicago, 
Electrotypbrs. 

F.  H.  OiLSON  Company,  Boston 
Printers 

Gborgb  McKibbin  and  Son,  Nbw  York, 

B''*°»'^«-  Dgtized  by  Google 


PREFACE. 

The  preparation  of  notes  for  this  volume  was  begun  several 
years  ago,  while  chief  engineer  of  the  Hoffman  &  Bates  Bridge 
and  Construction  Company,  and  has  been  continued  systematic- 
ally up  to  the  present  time. 

Tbxee  separate  systems  of  note-keeping  have  been  employed, 
namely:  (1)  Two  blank-books,  size  eight  by  twelve  and  one-half 
inches,  with  quadrangular  ruling  and  marginal  index,  were 
started,  one  for  mathematical  and  structural  data  and  the  other 
for  general  construction  notes,  each  book  containing  five  hA- 
dred  pages  in  flexible  leather  binding.  (2)  Note  books  of  the 
same  general  style,  but  of  pocket  size,  were  classified — ^for 
bridges,  buildings,  water-works,  sewers,  surveys,  etc. — and  kept 
at  hand  for  general  reference  and  memoranda.  (3)  The  loose- 
leaf  method  was  inaugurated  and  found  to  be  specially  useful  in 
consulting  practice.  The  last  named  is  explained  in  an  article 
prepared  for  the  ''Engineering  Record"  and  published  in  the 
issue  of  January  21,  1911. 

In  1904,  the  present  system  was  outlined — arranging  the 
matter  logically  in  numbered  Sections  for  convenient  reference. 
Prom  that  time  up  to  the  present,  the  work  has  gradually  been 
crystallized  and  brought  up  to  date. 

^)ecial  attention  is  invited  to  the  vast  number  of  tables,  their 
completeness  and  arrangement.  Although  most  of  thqp  have 
never  before  appeared  in  print — at  least  in  their  present  form — 
yet  nearly  all  of  them  have  been  subjected  to  the  test  of  more 
or  less  constant  use  for  a  number  of  years,  in  connection  with 
practical  work.  All  of  them  have  been  thoroughly  checked — 
the  proofs  of  all  were  checked  twice  before  electrotjrping,  and  the 
proofs  of  the  most  important  ones  were  checked  again  after 
electrotyping. 

The  logarithmic  tables  comprise  both  the  common  and 
hyperbolic  systems,  side  by  side,  the  latter  being  useful  in  cer- 
tain bridge  calculations  and  in  steam  engineering.  Both  the 
logarithmic  and  trigonometric  tables  are  carried  out  to  five 
decimal  places,  a  sufficient  refinement  for  most  engineering  opera- 

JJI  Digitized  by  VjOOQ  IC 


lY  PREFACE, 

tions,  being  much  more  exact  than  actual  measurements  in  shop 
or  field. 

The  tables  of  cubes  and  squares,  in  Section  33,  will  be  found 
useful  to  structural  detailers.  They  were  calculated  by  the 
incremental  additive  method,  which  is  self -checking. 

The  text  is  so  arranged  that  all  general  data  may  be  foimd 
readily  from  the  Table  of  Contents,  which  should  be  consulted 
as  frequently  as  the  Index,  the  latter  being  necessary  for  more 
specific  reference.  The  number  and  title  of  each  Section  appear 
as  even-page  captions  throughout  the  work.  The  tables  and 
illustrations  are  numbered  fi-om  one  upward  for  each  Section. 
It  has  been  the  aim  to  begin  each  subject  and  paragraph  with 
the  leading  or  key  word,  as  a  supplementary  page  index. 

At  the  end  of  most  of  the  S«:tions  will  be  found  references 
to  valuable  data  in  leading  technical  publications,  which  should 
be  in  the  library  of  every  engineer.  The  reader  is  advised  to 
supplement  this  data  with  his  own  lists,  perhaps  in  a  separate 
note  book,  under  the  respective  Section  ntunbers. 

Acknowledgments  are  due  to  Mr.  Paul  D.  Pord,  for  his 
kindness  in  volimteering  to  read  over  portions  of  the  manuscript 
while  in  preparation,  and  making  many  valuable  suggestions; 
also  to  Professor  C.  H.  Peabody,  for  permission  to  use  the  steam 
tables  and  other  material  in  Section  69;  and  to  many  others 
whose  names  appear  in  the  body  of  the  work,  where  specific 
credit  is  given. 

The  Publishers,  Electrotypers  and  Printers  are  to.  be  con- 
gratulated on  the  neat  appearance  of  the  book,  and  the  author 
desires  to  thank  Mr.  Jacob  Wemli  for  his  excellent  work  in 
preparing  the  illustrations. 

ALBERT  I.  FRYE. 

N0W  York,  D0c0mber,  1912, 


d  by  Google 


CONTENTS. 

(Page  nttmbera  are  given.     For  Alphabetical  Index,  see  page  1539.) 

Introduction XXIX 

Signs  and  Abbreviations XXXVII 

SEC  I.— ELEMENTARY  ARITHMETIC. 

Xumben — ^Roman  System,  Arabic  System 1 

Primes,  Multiples  and  Factors.  2;  Table 3 

Greatest  Common  Factor;  Least  Common  Multiple 6 

Fractiona,  7:  Reduced  to  Decimals.  Tables 9 

Decimals.  10;  Repeating  Decimals 11 

Short  Methods  of  Multiplication — Fractions  and  Decimals 11 

Caoccllation 13 

SEC  2.— POWERS,  ROOTS  AND  RECIPROCALS. 
A. — Engineers'  Tables. 

Square  Root.  14;  Square  Roots  (and  Squares)  of  Numbers,  Tables 16 

Cube  Root,  30;  Cube  Roots  (and  Cubes)  of  Numbers.  Tables 21 

Square  Roots  of  Fifth  Powers  of  Numbers.  Table 26 

Fifth  Powers  (and  Fifth  Roots)  of  Numbers.  Table 26 

Reciprocals  of  Numbers.  30;  Table 28 

B.— Arithmetical  or  Common  Tables. 

Squares,  Cubes,  Square  Roots.  Cube  Roots  of  Numbers  1-1600,  Table. .  31 

Square  Roots  and  Cube  Roots  of  Numbers  1600-3200,  Table 44 

Reciprocals  of  Numbers  1-1000,  Table * 51 

SEC  3^-PRACTICAL  ARITHMETIC 

Proportion.  66;  Permutation.  0>mbination,  66;  Allegation,  Progression  67 

Percentage^  Interest.  Discount,  68;  Simple  Interest  Table 60 

Table  for  Fmding  Number  of  Days  Between  Any  Two  Dates 61 

Equation  of  Payments,  61 :  Compound  Interest  Table 62 

Partial  Payments.  AnnuiUes.  Sinking  Fimd.  63;  Tables 64.  66 

SEC  4.— MEASURES,  WEIGHTS  AND  MONEY. 
Fnndamental  Units. 

Meter— Length,  Area,  Volume 66 

Litei^— Capacity  (Liquid  and  Dry) 66 

Gram— Mass  (Weight) 67 

General  Tables. 

Approximate  Equivalents — ^Mftric  and  English 68 

EngH^  Measxares,  Metric  Equivalents — Long.  Surveyors',  Mariners'.  .  .  68 

Lengths — Inches  and  Millimeters 69  ,70 

Lengths — ^Metric  Table-  Metric  and  English,  Equivalents  (1-9) 70 

Lengths — Feet  and  Inches  to  Meters.  71:  Meters  to  Feet 75 

Areas— Metric  Table:  Metric  and  English,  Eouivalents  (1-9) 79.  80 

Areas — English  Land  Measure,  Texas  Land  Measure 81 

Measures  and  Weights  of  the  Philippines,  English  Equivalents 81 

Volumes — Metric  Table;  Metric  and  English,  Equivalents  (1-9) 81.  82 

Volumes — English  Cubic  Measure.  Metric  Equivalents 82 

Capacities  (Liquid) — ^Metric  Table:  Metric  and  English,  Equiv.  (1-9)..  82.  83 

(^aiMbcities  (Liquia) — ^Liquid  and  Apothecaries'  Measures 83 

Capacities  (Dry) — ^Metric  Table:  Metric  and  English.  Equivalents  (1-9)  84 

Capacities  (Dry) — ^English  Dry  Measure,  Metric  Equivalents 84 

Weights — ^Metric  Table;  Metric  and  English,  Equivalents  (1-9) 86 

Weights — ^Apothecaries,  Troy,  Avoirdupois — ^Metric  Equivalents 86 

Weights — ^Various  Tons  and  Pounds,  Equivalents  (1-9) 87 

Simple  and  Compound  Units  in  Conimon  Use.  Equivalents 88 

Electrical,  Mechanical  and  Heat  Units — Equivalents 91 

Foreign  Weights  and  Measures,  American  Equivalents 92 

Numbexs— Abstract,  Duodecimo.  Paper— Tables ^ 95 


V 


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VI  CONTENTS. 

Money — Domestic  and  Foreign 95 

Money — Value  of  Foreisn  Coins,  American  Equivalents 96 

Prices — Comparison  of  German  for  Metric;  British;  and  American  ....  98 

Time  Measure;  Circular  Measure 99 

SEC  5.~ALQEBRA. 

Exponents JOD 

Binomial  Formula,  101;  Completing  the  Square 102 

Simultaneous  Equations [ .  103 

SEC.  6.— LOOARITHMS  OF  NUMBER& 

Common  System — Described,  104;  Operations,  105;  Table 108 

Naperian  System — ^Described,  104;  Operations.  106;  Table 108 

Sliae  Rules 126 

SEC.  7— PLANE  QEOMETRV. 

Angles  and  Lines;  Triangles;  Ouadrilaterals 128 

Polygons  (General) ;  Regular  Polygons;  Circle   129 

Problems  in  Construction  of  Figures 130 

iSEC.  8— SOLID  GEOMETRY. 

Planes,  Angles  and  Lines:  Polyhedrons 132 

Prisms  and  Pyramids 1 33 

Cylinders,  Cones  and  Spheres I34 

SEC.  9r-PLANE  TRIGONOMETRY. 

Trigonometric  Pimctions — Formulas 1 36 

Values  of  Trigonometric  Functions  in  the  Four  Quadrants I37 

Natural  Functions  of  Angles  in  the  Four  Quadrants 1 33 

Functions  of  Complement,  Supplement,  etc.,  of  any  angle  x 139 

Functions  of  the  bum  and  Difference  ot  Two  Angles,  x  and  y [  139 

Functions  of  one-half  x,2x.  Sat  and  4x 146 

Inverse  Trigonometric  Functions 140 

Solution  of  Right  Angle  Triangles 141 

Solution  of  any  Triangle. — Circular  Measure 142 

Cubic  Equations I43 

Table  of  Nattiral  Sines,  Tangents,  Cotangents,  Cosines,  etc 144 

Table  of  Natural  Secants,  Cosecants.  Exsecants  and  Coexsecants 167 

Table  of  Logarithmic  Sines.  Tangents.  Cotangents,  Cosines,  etc 1 76 

Table  for  Finding  the  Logarithmic  Sines  and  Tangents  of  Small  Angles  198 

SEC.  10.— SPHERICAL  TRIGONOMETRY. 

Functions;  Ri^ht  Spherical  Triangles.  Formulas 190 

Oblique  Spherical  Triangles — Formulas  and  Rules 200 

Distance  Between  Two  Points  on  the  Earth's  Surface 201 

The  Celestial  Sphere,  201;  Astronomical  Time,  Tables 202 

SEC.  II.— MENSURATION. 
A. — Plane  Surfaces,  Lines,  etc. 

Triangle  and  Quadrilateral 208 

Regular  Polygon,  and  Table:  Circle 204 

Tabular  Values  of  Combinations  of  ».  with  Logs 206 

Arc  and  Chord  of  Circle,  207;  Lengths  of  Circular  Arcs -208 

Lengths  of  Circular  Arcs  for  Radius  1,  Table 209 

Lengths  of  Circular  Arcs  for  Chord  1,  Table 210 

Flat  Circular  Arc,  Formulas  and  Tables 211 

Circular  Segments— Formulas,  214.  215;  Tables 216-218 

Circular  Ring  and  Circular  Zone.  Properties  of 219 

Circular  Lune;  Circular  Segtor;  Circle  and  Square,  Relations  of 220 

Table  of  Relations  of  Circle  and  Square 221 

Decimals  of  a  Foot  for  Each  ^  of  an  Inch.  Table 22^ 

Table  of  Circles — Circumferences  for  Given  Diameters.  Decimals 225 

Table  of  Circles — Circumferences  for  Diameters  in  Feet  or  Inches 226 

Table  of  Circles — ^Areas  for  Given  Diameters  in  Inches  and  Fractions . .  230 

Table  of  Circles — ^Areas  for  Given  Diameters.  Decimals 282 

Table  of  Circles— Areas  (Sq.  Ft.)  for  Given  Diameters  (Ft.,  Ins.) 284 

Cycloid 236 

Parabola,  Parabolic  Segment,  Parnb'c  Half-Segment,  Parab'c Spandrel.  237 


CONTENTS.  VII 

i    Lengths  of  Parabolic  Arcs  for  Chord  (Base)  1,  Table 238 

ElHpse,  238;  Formulas  for  Circumference  of  Ellipse 239 

,   Lengths  of  Semi-Elliptic  Arcs,  Table 241 

f  Segment  and  Chord  of  Ellipse 242 

B.— Solids. 

I   Papptn's  Theorem. — ^Prismoidal  Formula 243 

The  Five  Regular  Polyhedrons,  Table 243 

Prisms  and  Cylinders;  Frustums  of  Prisms  and   Cylinders 244 

Circular  Cylindric  Wedges  and  Half-Wedges 245 

Properties  of  Hollow  Cyl's  (Pipes,  Tanks,  Wells),  One  Foot  Long.  Table  246 

Pyraniids  and  Cones;  Frustums  of  Pyramids  and  Cones 248 

Conic  Wedge  and  Frustum;  Wedge;  Sphere 249 

Areas  of  the  Surfaces  of  Spheres,  Table 261 

Volumes  of  Spheres.  Table 252 

Spherical  Segment,  252;  Spherical  Zone 253 

Hollow  Sphere;  Circular  Segmental  Ring 253 

Regular  Circular  Ring;  Circular  Spindle 253 

Parabolic  Spindle;  Cycloidal  Spindle;  Paraboloid 254 

EDipaoid 255 

SEC  12.— ANALYTIC  QEOMETRY. 

Straight  Line 256 

Circle;  Parabola 257 

ElKpse 268 

Hypcibola,  269;  Equilateral  Hyperbola 260 

Cvdoid;  Spiral  of  Archimedes;  Logarithmic  Spiral 260 

HypeiboKc  Spiral'  Lcmniscate  of  Bemouilli 260 

Hekx  (w  Screw;  Common  Spiral 260 

SEC.  13.— DESCRIPTIVE  QEOIWETRY. 

Perspective;  Cabinet-,  Isometric-.  Orthographic  Projection 261 

Revolved  Planes;  Projection  of  the  Point 262 

Proicction  of  the  Right  Line;  Projection  of  Two  Lines 262 

Projection  of  the  Plane;  Problems  of  Construction 263 

SEC.  14.— THE  CALCULUS. 
A.— Differential  Calculus. 

Differentiation  and  Differential  Coefhcient.  Defined 266 

Tangent  and  Normal;  Rules  for  Differentiation 267 

\fa-rtfny  and  Minima,  with  Problems 268  ,269 

Differentiation  of  Logarithmic  and  Exponential  Functions 270 

Differentiation  of  Trigonometric  Fimctions 270 

Differentiation  of  Inverse  Trigonometric  Ftmctions 271 

Expansion  of  Functions — By  Division,  Successive  DilTercnliation 271 

Uaclauren's  Theorem 271 

Taylor's  Theorem 272 

B. — Integral  Calculus. 

Integiation  as  a  Summation,  Defined 272 

Definite  Integration  a  Method  of  Limits 273 

Formulas  for  Integration 274 

Areas  and  Lengths  of  Plane  Cxirves,  Problems 275 

Aiea^of  Curved  Surfaces.  Problem 276 

Volumes,  or  Planes  of  Revolution 277 

SEC.  15.— MECHANICS. 

Fnadamental  Equations  of  Motion  and  Force 278 

Motion  Formulas. 

Unif(»m  Motion,  No  Acceleration 279 

Ui^ormly  Accelerated  Motion,  No  Initial  Velocity 279 

t^aiformly  Accelerated  Motion  with  Positive  Initial  Velocity 280 

:  Ilaifbrmly  Accelerated  Motion  with  Negative  Initial  Velocity 282 

;  Table  of  Palling  Bodies  ISee,  also,  Table  on  page  1156] 283 

koimary  of  Preceding  Motion  Formulas 284 

the  Resultant  of  Two  Constant  Velocities 284 

httbolic  Motion— Path  of  Projectile 286 

Chcttlar  Motion— Fly-Wheel (^vsA(tlV>  ^**® 

Digitized  by  V^OOQ  Ic 


VIII  CONTENTS. 

Motion  on  Inclined  Plane 280 

Motion  on  Cycloidal  Curve 286 

Simple  and  Compound  Circular  Pendulums 287 

Simple  Cycloidal  Pendtdum 287 

Dynamic  Formulas. 

Force — Fundamental  Relations. — ^Atwood's  Machine 288 

Force — General  Relations,  Distance  Included 289 

Work — Hoisting-Rope  Problem 290 

Power — ^Locomotive  Problem 291 

Leverage — Simple  Lever 291 

Compovmd  Lever;  Inclined  Plane;  Wedge 292 

Screw;  Pulley,  Simple  and  Compound 292 

Toggle. — Imptklsc  and  Momentum. — Energy 298 

Composition  and  Resolution  of  Forces 294 

Principles  of  Equilibrium 294 

Polygon  of  Forces;  Moments  and  Reactions 295 

Center  of  Gravity  and  Resultant  of  a  System  of  Parallel  Forces 296 

Resultant  of  a  Distributed  Force — ^Problem 296 

Centrifugal  Force — Fly-Wheel  Problem 297 

Centrifugal  Force — ^Elevation  of  Outer  Rail  on  Curve 298 

Forces  Acting  on  Plane  Surfaces. 

Bending  Moment  and  Resisting  Moment 298 

Resisting  Moment  and  Moment  of  Inertia 299 

Moment  of  Inertia  and  Radius  of  Gyration 299 

Radius  of  Gyration  and  Moment  of  Inertia 300 

Resistance  of  Rectangular  and  Circular  Beams  Compared 301 

Forces  Acting  on  Solids. 

Moment  of  Inertia  of  Solid  Body,  Defined 802 

Moments  of  Inertia  of  Regular  Solids,  Table 302 

Radius  of  Gyration  of  Solids 302 

Center  of  Gravity  of  Solids 303 

Center  of  Oscillation—  Center  of  Percussion 303 

Impact  or  Collision,  303;  Formulas 304 

SEC  16.— THEORY  OP  STRESSES  IN  STRUCTURES. 

Outer  and  Inner  Forces — Loads,  Reactions,  Stresses 806 

Principles  of  Static  Equilibrium 305 

Methods  of  Calculation — By  Moments,  Shears,  Graphics 806 

Loads  and  Reactions  Vertical. 

Pratt  Truss  Calculation— Dead  Load  Stresses 806 

Reaction  at  Left  Support;  Lengths  of  Members 307 

Trigonometric  Ratios  for  Calculating  Chord  and  Web  Stresses 807 

Stresses  in  Chord  Members  by  Method  of  Moments — Rules 807 

Stresses  in  Web  Members  by  Method  of  Shears — Rules 308 

Static  Equilibrium  of  Inner  and  Outer  Forces  at  Joints 309 

Bow's  Notation  in  Graphical  Statics 309 

Graphical  Method 310 

General  Rules  for  Stress  Diagrams 810 

Order  of  Considering  Joints 311 

Graphical  Solution  of  Pratt  Truss,  with — 312 

Loads  at  Top  Joints;  Loads  at  Top  and  Bottom  Joints 313 

Reactions  in  Any  Direction. 

Roof  Truss.  Both  Ends  Fixed,  Wind  on  One  Side 814 

Roof  Truss,  One  Roller  End,  Wind  on  Either  Side 814 

Three-Hinged  Arch,  Vertical  Loads 815 

SEC.  17.— NATURAL  HISTORY  OF  MATERIALS. 
A.— Chemical. 

Composition  of  Matter. — ^The  Old  Atomic  Theory 816 

Recent  Discoveries. — ^The  Corpuscular  Theory 816 

The  Electronic  Theory, — ^The  Chemical  Elements 817 

Table  of  the  Chemical  ElemenU 318 

Compounds. — Simple  Combinations 321 

Acids,  Bases  and  Salts;  Oxides  and  Hydroxides. . .  .^ i 321 

Acid  Combinations lyzed by.VwjO.OglC 321 


CONTENTS.  IX 

Periodic  Law.  322;  Natural  System  of  the  ElemenU 823 

Chemical  Substances  and  their  Common  Names 324 

B.— Miaeralofical. 

Minerals — Hardness  and  Other  Physical  Characteristics 824 

Classification  of  Important  Mineral  Species 326-828 

Native  Elements;  Sulphides;  Chlorides,  Bromides.  Iodides 325 

Oxygen  Compounds — Oxides.  Silicates 326 

Oxygen  Compotmds — Phosphates.  Borates,  Sulphates,  Carbonates .....  327 

Hyarocarbons — Petroleum.  Naphthalin,  Asphaltimi.  Coal 328 

Blowpipe  Characteristics  of  Minerals 328 

328 

328 

329 

329 

330 

1 330 

on 330 

331 

t 331 

rth 331 

331 

331 

332 

c 334 

339 

C— BoCanicaL 

Acreage  of  Timber  Land  in  the  United  States 340 

Claisihcation  of  Important  Trees,  Table — 34i-346 

Trees — Soft  Pines,  Pitch  Pines,  Larches,  Spruces 341 

Trees — Spruces.  Hemlocks,  Firs.  Redwoods,  Cedars,  Cypresses ........  342 

Trees— Cypresses,  Walnuts,  Hickories,  Poplars 343 

Trees — Poplars,  Willows,  Birches,  Beeches,  Chestnuts.  White  Oaks! .    .  344 

Trees— White  Oaks.  Black  Oaks,  Ehns.  Sweet  Gums 345 

Trees — Maples.  Ashes 34g 

Tree  Data — Tallest,  Best,  Ages,  Growth.  Important  Products .'..'.  346 

D.— Zoolofical. 

Animal  S{>ecies  and  their  Uses  to  Man 347 

Classification  of  Animals,  Table '  347-349 

SEC.  18.— EXPLOSIVES. 

(a).— Mechankal  Mixttiras. 

Nitrate  Mixtures,  Gunpowder,  Blasting  Powder 850 

Weight  of  Powder  in  a  Hole  One  Foot  Deep,  Table 35O 

Chlorate  Explosive  Mixtures \[[\  35I 

(b). — Chemical  Compounds. 

Nitro  Substitution  Explosives;  Nitric -Acid  Compounds;  Guncotton.  361 

Detonation;  Smokeless  Powders;  Nitroglycerin;  Dynamite '.".  362 

Unmixed  Explosives;  Percussion  Caps ' '  *  ]  353 

The  Handling  and  Use  of  Dynamite 363 

Some  of  the  Most  Common  Commercial  Dynamites 354 

List  of  Permissible  Explosives  for  Use  in  Coal  Mines ...........'.  354 

SEC.  19.— PRESERVATIVES. 
Paints. 

Kgincnta — ^Lead,  Zinc.  Lampblack.  Boneblack,  Graphite,  Iron,  etc 355 

V  daclesh^Linseed  Oil 855 ,  366 

Dnera;  Solvents — ^Turpentme 356 

House  Paints — Mixtures — Colors.  Table '/,'/,  866 

Special  Paints — Altunintun \\  356 

Special  Paints — Bronze,  Copper 357 

Varnishes,  Lacquers,  etc 

Viamishing;  Laquering;  Japanning 857 

Qalvanizing  and  Tinning. 

Galvanizing;  Tinning — ^Tin  Plate,  Teme  Plate A~f .  i . .  367 

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X  CONTENTS. 

Electro-PUtinf. 

BlectroX^hexnittry:  Electrolysis;  Electro-Metalluivy 857 

Electro-Plating--Gold,  Silver,  Copper,  Nickel,  etc 358 

pTMcrvatioo  of  Stod  and  Iroo. 

Oiling.  Painting,  Asphalting;  Removing  Mill  Scale 858 

Preservatioo  of  Timber. 

Sources  of  Decay — ^Wet  Rot,  Fermentation,  Dry  Rot,  Insect  Larvae. .. .  350 

Piling;  Creosoting;  Bumettizing;  Miscellaneous  Notes 360 

Seasoning — Distribution  of  Water  in  Timber 361 

Seasoning — Relation  of  Water  to  Decay*  What  Seasoning  Is 362 

Seasoning — Preservative  Treatment;  Advantages;  Methods 363 

Seasoning — Conclusions  and  Recommendations 865 

Creosote  In  Well-Preserved  Timbccs. 

Manufacture  and  Coznposition  of  Creosote. — Coal  Tar 865 

Analyses  of  Creosote  Extracted  From  Wcll-Preserved  Timber 867 

Results  of  Analyses  of  Extxacted  Oils,  Table 868 

Excerpts  ud  References. 

Protection  of  Ferric  Structures  from  Corrosion 372 

Painting  and  Sand-Blast  Cleaning  of  Steel, Bridges.  Costs 373 

Creosoting  Wooden  Poles  for  Electric  Line-Work,  Costs 373 

Corrosion  of  Steel  in  Reinforced  Cinder  Concrete 874 

Cleaning  Steelwork  by  Sand-Blast.  Painting  by  Compressed  Air.  Costs.  874 

Compaxuon  of  Various  Processes  of  Preserving  Timber.  Costs 876 

SEC.  20.— LUMBER  AND  LUMBERINQ. 

Stumpage  in  the  United  States,  Tables 876 

Range  of  Limiber  Prices  for  Twenty  Years 877 

Logging — ^Trees.  Time  for  Cutting.  Volimie  of  Standing  Timber 378 

Logging — ^Transportation  of  Logs,  378;  Scaling  Logs 379 

Lumber — Sawing,  Sizing.  Planing,  Seasoning,  Board  Measure 879 

Table  of  Feet  Board  Measxire  of  Lumber 380-387 

Grading  of  Lumber 387 

Classification  and  Inspection  of  Yellow  Pine  Ltimber 387 

Rules  for  Grading  Fir,  Spnice.  Cedar  and  Hemlock  Lumber 388 

Shingles — Grades  and  Specifications 390 

Graphical  Comparison  of  Various  Log  Rules 391 

Commercial  Shipping  Weights  of  Various  Kinds  of  Lumber 391 

SEC.  21.— METALLUROV. 

Iron  Ore;  Pig  Iron;  Cast  Iron 392 

Cast  Steel;  Malleable  Castings;  Wrought  Iron 393 

Steel — Various  Processes — ^Acid-Bessemer 394 

Steel — Basic  Bessemer,  Add  Open  Hearth,  Basic  Open  Hearth 395 

Steel— Cementation  Process;  Shear  Steel;  Crucible  Cast  Steel 395 

Steel — Open  Hearth  Cast-.  Harveyiaed-,  Vanadium-, 396 

Steel — Chrome-,  Nickel-.  Tungsten- 896 

Alloys  of  Variotis  Metals — 396 

Bronze — Phosphor-.Manganese-,  Aluminimi-,  Silicon- 397 

Brass — Copper-Zinc  Alloys.  Table 397 

Tin-base  Alloys;  Lead-base  Alloys;  Alzene 398 

Bialleable  Cast  Iron;  Nickel  Steel,  Properties 898 

Vanadium  Steel — Structural — ^Alloys 899 

SEC.  22.— BUILDING  STONES  AND  CEMENTS. 
Natural  Building  Stones. 

Granite.  Basalt^  ^'^R*  Greenstone,  Limestone 400 

Carbonate  of  Lime.  Dolomite.  Hydraulic  Limestone 401 

Marl,  Travertine.  Marble  (Domestic  and  Foreign) 401 

Sandstone  (Berea,  Medina.  Potsdam,  Conn.  Val.,  N.J.) 401 

Sandstone,  Frost  Test;  Flagstone;  Slate 401 

Cements  (MlsceOaneous). 

Materials  with  Cementing  Properties 40* 

Cements — Boiler,  Coppersmith's.  Fireproof,  Flour,  Gas  Fitters' 402 

Cements — Iron,  Glue,  Steam-Pipe 402 

Cements — Keene's  Marble 40S 


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I                                                   CONTENTS.  XI 

Cements  (Builders). 

iOJcimn,  Lime,  Common  Lime,  Lime  Mortar.  Lime  Plaster 403 

knaster  of  Paris,  Hydraulic  Lime 404 

^HTdraulic  Cement— Natural,  Portland,  Slag 404 

Bittunen,  Asphalt 404 

Manufacture  of  Portland  Cement — ^Wet  and  Dry  Processes 405 

Cakxnation — ^Rotary  Kiln;  Grinding  the  Clinker 406 

*  'ites  of  a  Cement  in  Cement  Testing 406 

of  Testing  Cement— A.  S.  C.  E.  and  A.  S.  T.  M.— 407 

n  of  Sample.  Specific  Gravitv,  Fineness 407 

.  Consistency — Vicat  Needle  Test 408 

itaoe  of  Water  for  Standard  Sand  Mortars 409 

,  of  Setting;  Standard  Sand 409 

form  of  Briqt^tte;  Molds;  Mixing 410 

Holding-  Storage  of  the  Test  Pieces 410 

Itesile  Strength;  Constancy  of  Volume 411 

Specifications  for  Cement— A.  S.  T.  M.— 411 

"Bpecifications — Natural  Cement,  Portland  Cement 412 

Specifications  for  Cement— Engrs.  U.  S.  A. — 413 

I  ftecifications — American  Portland  Cement 413 

'Ipwifications — ^Natural  Cement  Puzzolan  Cement 414 

Artificial  Building  Stones. 

Bri(*— Common.  Pace.  Glazed,  Vitrified,  Terra  Cotta 416 

Fire  Brick,  Paving  Brick.  Sewer  Brick 416 

Concrete — ^Kinds,  Mixture,  Proportions,  Voids,  Economy 416 

Concrete — Cement-Sand  Mix,  Cement-Sand -Stone  Mix 417 

Concrete — Size  of  Broken  Stone 417 

Block  Stone — Beton-Coignet,  Sand  Bricks,  Portland  Stone 417 

Blodc  Stone — McMurtrie  Stone.  Ransome  Stone.  Sorel  Stone 417 

Miscellaneous  Data. 

Lates  and  Cements  Useful  to  Engineers — 418 

Compositions— Water-Proof,  Oil-Proof.  Acid-Prcwf,  etc 418 

Cost  of  Portland  Cement 418 

A  Cement  which  is  Proof  Against  Sea-Water 418 

SEC.  23.— QUARRVINO. 

Susd,  Gravel,  Rip-rap.  Stone — Hand  Tools,  Channeling  Machines 410 

Wei^t  and  Specifications  of  Sullivan  Channelers,  Table 421 

Explosives;  Rock  Drills — Hammer,  Chum,  Percussion 422 

Quarrying  by  Direct  Use  of  Compressed  Air 423 

tost  at  OuarryingRubble  and  Dimension  Stone 423 

Dimensions  and  Weights  of  Rand  Percussion  Rock  Drills.  Table 424 

SEC.  24.— STONE  CUTTINQ. 

Stones  Classified  According  to  Finish. — ^Tools  Employed 426 

Ucsquared  Stones. — Hand  Hammer,  Plug  and  Feathers,  etc 426 

Squared  S.;  Quarry-Faced  S. — Face  Hammer;  Cavil 427 

Pitched-Faced  S.;  Drafted  S.— Chisel;  Pitching  C;  Tooth  C 427 

Cut  Stones. — Mallet.  Pick,  Point,  Crandall 428 

Cut  Stones. — ^Ax,  Pean  Hammer,  Patent  Hammer,  Tooth  Ax 429 

Cut  Stones. — Biish  Hammer,  Machine  Tools 430 

SEC  25.— MASONRY. 

Snds  of  Masonry;  Classification  of  Railroad  Masonry.  Table 431 

I. — ^Stone  Masonry. 

Definitions  of  Parts  of  Wall 431 

Definitions  of  Kinds  of  Masonry 432 

Specifications  for  Stone  Masonry,  General 433 

Specifications  for  Bridge  and  Retaining  Wall  Masonry 434 

Specificatkms  for  Arch  Masonry,  Culvert  M..  Dry  M 436 

Oosntities  of  Masonry  in  Raihxiad  Abutments,  Table 436 

■»ble  for  Finding  Weights  of  Quantities  in  Preceding  Table 437 

II. — Brick  Masonry. 

Bonds— English.  Flemish,  etc.;  Brickwork 437 

Hortar  Us^  in  Brickwork;  Table  of  Quantities 438 

III.— Concrete  Masonry.         '  ^^ ^T^.„« 

Koi^Cnishen:  Concrete  Mixers— Gravity,  MechanicaldtBtot^*i)3.00g.l€439 


XII  CONTENTS. 

Concrete— Proportions  of  Cement,  Sand  and  Stone — ^Mixtng 440 

Concete — Placing,  Spreading  and  Ramming;  Subaqueous  C 440 

Concrete,  Subaqueous — ^Depositing  by  Tubes,  Buckets,  Bags. 441 

Sub-Foundations — Prepared  by  Dreoging,  Cement  Grout 442 

German  Specifications  tor  Concrete 442 

IV. — Reinforced  Concrete. 

Uses  of  Reinforced  Concrete 443 

The  Preservative  Qualities  of  Cement 444 

The  Fire-Resisting  Qualities  of  Concrete 444 

The  Proportions  Used  in  Mixing  Concrete 444 

Calculations  of  Reinforced  Concrete  Beams — 444 

Formulas;  Values  of  /  for  Three  Standard  Mixes 445 

Properties  of  Reinforced  Concrete  Beams  1  Inch  Wide,  Table 446 

Formulas  for  Reinforced  Concrete  Construction — A.  S.  C.  E 446 

V. — Mixed  Masoniy. 

Description — ^Weakness  of  Bond 449 

VI.— Concret^Block  Masonry. 

Solid  Concrete  Blocks;  Hollow  Concrete  Blocks 450 

Specifications  for  Hollow  Concrete  Building  Blocks .*  •  •  •  ^^ 

Miscellaneoas  Data. 

Permeability  of  Concrete  Under  High  Water  Pressure 453 

Waterproofing  Data — Concrete  in  Government  Fortifications 453 

The  Efficiency  of  Concrete-Mixing  Machines 453 

Method  of  Finishing  the  Concrete  Surfaces  of  Bridges 454 

Concrete  Bridge — Materials  Required  for  Different  Mixes 454 

Expansion  Toints  in  Concrete  Structures — Reservoirs,  Drydocks 454 

Oil-Mixed  Concrete  as  a  Waterproofixig  Material 455 

Specifications  for  Scrubbed  Concrete  Surface 455 

SEC.  26.— STEREOTOMV. 

Wall  of  Building.— Stone  Arch 457 

SEC.  27.— WEIQHTS  AND  SPECIFIC  QRAVITIES  OF  MATERIALS. 
Definitions. 

Mass,  Unit  of  Mass.  Gravity  Acceleration,  Weight 450 

Volume,  Density,  Specific  Gravity 460 

Methods  for  Determining  Specific  Oravity. 

Solids  Heavier  than  Water;  Solids  Lighter  than  Water 460 

Displacement  Method;  Porous  Substances 460 

Granular  Substances:  Liquids — 461 

Beaum^'s  Hydrometer,  Tweddell's  H.;  Rousseau's  Densimeter 461 

Nicholson's  and  Fahrenheit's  Hydrometers;  Refinements 462 

Gases— Standard  Pressure,  Temperature,  Substance 462  | 

Oases. 

Weight  of  a  Cubic  Foot  of  Dry  Air  at  Various  Temperatures,  Table. . . .  463 

Weights  and  Specific  Gravities  of  Gases,  Table 464 

Uquids. 

Weight  of  a  Cubic  Foot  of  Water  at  Various  Temperatures,  Table 465 

Eqwvalents  of  Centigrade  and  Fahrenheit  Scales,  Table 465 

Weights  and  Specific  Gravities  of  Liquids,  Tables 468  .469 

Solids  and  Miscellaneous. 

Weights  and  Specific  Gravities  of  Woods,  Tables 470-478 

Weights  and  Specific  Gravities  of  Building  Stones,  Masonry  and 

Cements.  Table 474-477 

General  Table  of  Weights  and  Specific  Gravities  of  Materials,  Table  478-482 

Weights  of  Produce  (U.  S.  Law),  Table 482 

Redaction  Tables. 

Weight  Equivalent  for  Any  Specific  Gravity 483 

Weight  of  Sheets,  Bars,  Wire,  for  any  Specific  Gravity 484 

Weight  for  Cubic  Yard  for  Any  Specific  Gravity 484 

Comparison  of  Various  Weights,  Capacities  and  Volumes 485 

SECw  28.— STRENOTH  AND  RESISTANCE  OF  MATERIALS. 
-  I. — Qeneral  Principles. 

Stress.— Strain.—Modulus  of  Elasticity ni?eTi^;GoOgk- 486 


CONTENTS.  XIII 

Bhstic  Limit. — Yield  Point.— Ultimate  Strength  or  Stress 487 

Static  Stress. — ^Repeated  Stresses. — ^Alternating  Stresses 487 

Working  Stress  and  Factor  of  Safety 487 

Resilience  or  Work  of  Materials  Under  Stress — Pormtilas,  Table 488 

Effect  of  Sadden  Loading,  and  Impact 489 

II.— Tables  of  Strength  of  Materials. 
A. — Woods. 

Compression  (End)  Tests  of  Timber,  12%  and  16%  Moisture 490 

Strength  Factors  for  Reducing  Moisture  from  15%  to  12% 491 

Compression  (End)  Tests  of  (Treen  Timbers — Above  40%  Moisture. . . .   491 

Bending  TesU  of  Timber  at  Rupture 492 

Bending  Tests  of  Timber  at  Relative  Elastic  Limit 493 

(Compression  Tests  of  Timber  Across  Grain 494 

Shearing  TcsU  of  Timber  With  Grain 494 

Relation  Between  Weight  and  Strength  of  Timber 494 

Timber  in  Tension,  (Compression,  Bearing.  Bending  and  Shear 495 

Remarics  on  Preceding  Table. — Formula  tor  Longitudinal  Shear 496 

B. — Metals. 

496-507 

'  in  Electric  Transmission    496 
•Bronze  Wire  to  (Copper. .  497 

» 498 

tructures 499 

500 

id  Rivet  Steel 501 

8S 503 

504 

506 

C. — Building  Stonbs,  Cbmbnts,  btc. 

(Compression,  Tension,  Bending,  etc 507-512 

TesU  of  Bluestone  and  Brick;  Rattler  Test  for  Bricks 507 

Tests  of  Cements:  Natural  and  Portland  (Compared 508 

Tests  of  (Concrete;  Formula  Deduced  from  Tests 508 

Modulus  of  Elasticity  and  (Coefficient  of  Expansion  of  Concrete 510 

Cinder  (Concrete — Watertown  Arsenal  Tests 610 

(Compressive  Strength  of  Granite,  Marble  and  Masonry 611 

(Compressive  Strength  of  Sandstone,  Slate  and  Terra  (>>tta 512 

D. — Miscellaneous  Materials. 

Stxength  of  (Canvas,  Cotton,  Flax,  Glass,  Ice.  etc 512 

III.— Heat  Effects  on  Various  Substances. 
Definitions — ^A  Gas,  Liquid,  Solid ^  Critical  Point,  Critical  Temperature.  512 
Definitkms— Critical  Pressure,  Boiling  Point,  Latent  Heat  of  Vaporiz'n.  513 

Definitkma — Melting  Point,  Latent  Heat  of  Fusion 613 

Liquefaction  of  Gases — Four  Methods;  Absolute  Zero  of  Temperature..  513 

Bcniing  Point.  Freezing  Point,  etc.,  of  Gases  and  Liquids.  Table 614 

Boiling  Point  of  Substances  at  Atmospheric  Pressure,  Table 614 

Meltinff  Fonts  of  Various  Substances,  Table 616 

(Coefficients  of  Expansion — Formulas  and  Table 516 

IV.—Frictional  Resistance  of  Materials. 

Coefficient  of  Friction  of  Revolving  Journals 617 

Friction  of  Plane  Surfaces  Which  Have  Been  Some  Time  in  Contact. .  .617 

Friction  of  Plane  Surfaces  in  Motion  Upon  Each  Other 519 

Friction  of  Journals  in  Motion  Upon  Their  Pillows 520 

(CocfficienU  of  Friction  and  Angles  of  Repose  or  Friction 621 

Rolling  Friction  (Dry) — Formula 621 

v.— Miscellaneous  Data. 

Crushing  TesU  of  Brick  and  Terra  Cotta  Piers,  Tables 622 

The  EiTect  of  Fire  on  Building  Materials 623 

(gypsum  as  a  Fireproofing  Material 523 

Some  Testa  of  Old  Timber,  (Compared  With  New 623 

fBC  29-— PROPERTIES  AND  TABLES  OP  PLANE  SURFACES. 
1. — Qeometrical  Figures. 

Any  Figure  :  Axis  through  c.  of  gr.  Axis  at  Base;  Parallel  Axis 624 

Triangle  :  Axis  through  Center  of  (5ravity J*J 

Tdangle  :  Axis  at  Base;  Axis  through  Apex ^^^.^ byGoOgk* 


XIV  CONTENTS. 

Triangle,  Rectangle,  Hollow  Rectangle,  Square,  Hollow  Sqtiare....  525 

Parallelogram,  Rhomboid 526 

Square,  Hollow  Souare,  Trapezoid,  Regular  Hexagon 526 

Hollow  Hexagon,  Regular  Octagon.  Hollow  Octagon 527 

Circle,  Hollow  C,  Semicircle,  Circular  Sector,  Circular  Half-Segment  . .  528 

Ellipse,  Hollow  £..  Parabolic  Half-Segment*  Parabolic  Spandrel 529 

2.— Skeleton  Figures  With  Thin  Lines. 

Vertical  Web  Plate;  Straight  Line  about  Parallel  Axis 529 

Angle.  Tee.  Cross.  H-Section.  Rectangular  Cell.  Channel,  I-Beam 530 

I-Beam,  Inclined  Lines,  Angles.  Triangular  Cell,  Circular  Cell 531 

Circular  and  Semi-Circular  Arcs — Five  Cases 531 .632 

CoiTugated  Sheets— Cycloidal  and  Screw-Thread  Shaped 532 

3.— Bloclc  Shapes. 

Flanges.  Cross,  I-Beam,  Z-Bar,  Tec,  Angle,  Channel 538 

I-Bcam,  Channel,  Z^Bar,  Tee  with  Tapered  Stem 534 

4.— Rolled. 

Moments  of  Inertia  Abotit  Inclined  Axis,  Formulas 635 

Moment  of  Inertia  About  Inclined  Axis,  Problem 537 

Max.  and  Min.  Values  of  /  About  Inclined  Axis,  Formulas 537 

Properties  of  T-Beam;  Properties  of  Channel 537 

Properties  of  Tee,  Z-Bar.  Angle 538 

Moments  of  Inertia  of  Rectangles.  Table 539  ,540 

SEC.  30.-PROPERTIES  AND  TABLES  OF  STEEL  SHAPES. 

List  of  Tables  and  Relevant  Tables  in  All  Sections 541 

Steel  Rods,  Square  and  Round — Weights  and  Areas,  Table 542 

Steel  Plates— Weights  and  Areas,  Table 544 

Steel  Angles,  Unequal  Legs — Properties  of.  Table 548 

Steel  Angles,  Equal  Legs — Properties  of.  Table 562 

Steel  I-Beams— Properties  of,  Table 664 

Steel  Channels— Properties  of,  Table 566 

Steel  Z-Bars— Properties  of.  Table 567 

Steel  T-Shapes;— Properties  of.  Table 568 

Steel  Rail  Sections — Dimensions  and  Properties,  Table 500 

References:  Steel  H-Shapes,  Corrugated  Sheeting,  Memoranda 501 

SEC.  31.— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS. 
Working  Stress,  Load,  Moment.  Slope  and  Deflection  of  Beams — Formulas  502 

Practical  Examples  in  Use  of  Preceding  Formulas 564 

Span  and  Deflection  for  Plastered  Ceiling — Examples 504 

Longitudinal  Shear  in  Beams — Formulas  and  Problem 565 

Safe  Uniform  Loads  on  Rectangular  Beams,  Table 566 

Examples  in  Use  of  Preceding  Table 607 

Steel  Beam  Box  Girders — Properties  of.  Table,  Problem 568  .569 

Steel  Plate-Girders.  Complete — Properties  of.  Table 670 .671 

Flange  Angles  of  Plate-Girders— Properties  of.  Table 572-574 

Web  Plates  of  Plate-Girders— Properties  of.  Table 576-579 

Flange  Plates  of  Plate-Girders— Properties  of.  Table 580-682 

Bethlehem  Girder  (Single  I)  Beams,  Table 683 

Bethlehem  Special  I-Beams,  Table 584 

Reinforced  Concrete  Beams — Working  Stresses 585 

Computing  the  Strength  of  Reinforced  Concrete  Beams 585 

Various  Referencesr--Concrete  Beams  and  Slabs,  etc 586 

SEC.  32.— PROPERTIES  AND  TABLES  OF  COLUMNS. 

General  Stresses. — Shearing  Effect 587 

Notation  for  Column  Formulas — Various  End  Conditions 587 

Formulas— Short  Strut — Eccentric  Loading — Long  Columns 688 

Ritter's  Formula  for  Columns 589 

Author's  Formula  for  Columns 590 

Gordon's  Formula  for  Columns 592 

C.  Shaler  Smith's  Formula  for  Wooden  Columns 593 

Straight-Line  Column  Formulas — ^Tablc 593 

Safe  Loads  for  Wooden  Columns,  Pin  Bearing — Table 694 

Steel  Columns — Secondary  Stresses — Useful  Sections 696 

Channel  Coltunns — ^Table  of  Standard  Dimensions 696 

Ultimate  Strength  of  Steel  Columns— General  Table 697 

Z-Bar  Columns.  Without  Side  Plates— Table 598  .699 

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CONTENTS.  XV 

Z-Bar  Coltimns  (14-Indi).  ^th  Side  Plates—Table 600 

CaiBnnel  Columns  (6-Inch).  With  Plat  Ends— Table 601 

Ghaimel  Columns  (a-Inch),  With  Plat  Ends— Table 602 

Gfaaixnel  Columns  (10-Inch).  With  Plat  Ends— Table 603 

Fbcenix  Steel  Columns — ^Table  of  Dimensions.  Loads,  etc 604 

Cast  Iron  Columns.  Rectangular  and  Round — Table  of  Strengths  . .  606 .607 

Rolled  Steel  H-Columns  (8^to  14")— Tables 608 

Reinforced  Concrete  Colxunns — ^Working  Stresses 609 

Carbon-Steel  and  Nickel-Steel  Coltimns — ^Tests  and  Formulas 609 

Tests  of  Plain  and  Reinforced  Concrete  Columns 610 


SEC  33.— STRUCTURAL  DETAILS. 


..  611 
..  612 
..  612 
..  613 
..  614 
..  615 
..  616 
..  617 
..  618 
..  619 
..  620 
..  621 
..  621 
..  622 
..  622 
..  623 
..  624 
..  625 
..  626 
..  627 
..  628 
..  629 
..  629 
..  630 
..  631 
..  632 
..  633 
..  634 
'Is  634 
..  635 
..  635 
..  636 
..  637 
..  637 
..  638 
..  639 
..  640 
41 .642 
43.644 
45-650 
51-664 
..  665 
..    665 


SEC  34.— METAL  QAQES. 


8tandanl  Metal  Gages— B.  W.  G.,  B.  &  S.,  etc.— Table 666 

U  S.  Standard  Gage  for  Sheet  and  Plate  Iron  and  Steel,  Table 667 

SEC  35.— CORDAQE.  WIRE  AND  CABLES. 

Technical  Cordage  Terms— ^Make-Up  (In  Manufactiu^) 668 

Rooe — ^Techntad  Terms  in  Manufacture  and  Use 668 

RSpe=^Knots.  Hitches.  Bends.  Splices,  etc       ,      668  .669 

--  •^-    «  —     *» *--* —  c*.— ^I;j  a^jjjj  Weight oO» 

- -Tables 670 

-Tables 671 

rawe  ol  ±Toperixe»  oi  x^^ocoums  ^i-^^*  "  "V  t^'t^"". ^  Metric. . . 672 

Wire  Rope-^ianufacture,  Use.  Strength.  Lubncatic^.^  .^.QQ^Jgl^-  •  •   e78 


XVI  CONTENTS, 

Roebling  Round  '^^^re-Rgpe — ^Table  or  Properties 674 

Wire  Rope  Pastenuin — Details 675 

Telephone  Cable  in  St.  Gothard  Tunnel— Description 676 

SEC.  36.— PIPES  AND  TUBES. 

Wrought  Iron  Welded  Steam,  Gas  and  Water  Pipe— Tables 677  »678 

Lead  and  Tin  Lined  Lead  Pipe  and  Tubing.  Tables 679 

Weight  of  Lead.  Sheet  Lead  and  Cast  Tin 679 

Spiral  Riveted  Steel  Pipe  and  Specials,  Table 680 .681 

Spiml  Riveted  Steel  Pipe  Details 682 

SEC.  37.— BRIDGES. 

Economic  Lengths  of  Spans  for  River  Crossing,  Pormtila 683 

Economic  Depth  of  Plate  Girders  and  Trusses,  Formulas ....  684 

Estimating  Weights  of  Bridges 685 

Formula  for  Additional  Length  of  Eye-Bars  to  Form  Heads 686 

Formulas  for  Weights  of  Steel  Bridges  and  Trestles .  . . .  T 686 

Formula  for  Finding  Bending  Stresses  in  Eye-Bars 686 

SEC.  38.— RAILROAD  BRIDGES. 

Moments  and  Shears — Beams  or  Girders — ^Distributed  Loads 688 

Easy  Method  of  Drawing  a  Moment  Parabola 688 

Moments  and  Shears— Concentrated  (Axle,  Wheels,  etc.)  Loads 690 

Engine  I>iagrams,  Axle  Loads,  with  Table 690 

Typical  Moment  Diagram  of  Special  Locomotive 691 

Bending  Moments  and  Shears  from  Special  Locomotive.  Table 692 

Moments  and  Shears — Spans  with  Floorbeams 693 

Concentrated  Load»— Maximum  Floorbeam  Reactions 694 

Concentrated  Loads — Positions  for  Maximum  Moment 695 

Chord  Stresses  in  Pratt  Truss  from  Concentrated  Loads,  Problem 695 

Chord  Stresses  in  Warren  Truss  from  Concentrated  Loads 696 

Concentrated  Loads — Positions  for  Maximum  Shear 696 

Lateral  Bracing — Wind  and  Curve  Pressure 697 

Portal  and  Intermediate  Vertical  Bracing,  Formulas 698 

General  Specifications  for  Steel  Railroad  Bridges — 699 

General  Description — Material.  Types  of  Bridges,  Clearance 699 

Trusses.  Girdere,  Floorbeams,  Stringers,  Wooden  Floor,  Guards 700 

Loads — ^Dead  Load,  Live  Load 700 

Effect  of  Impact,  Formula. — Engine  Diagrams 701 

Wind  Pressiure-  Momentum  of  Train;  Centrifugal  Force 702 

Proportion  of  Parts — Least  Thickness  of  Material 702 

Permissible  Tensile  and  Compressive  Stresses 702  ,708 

Alternate  Stresses;  Combined  Stresses 704 

Transverse  Loading  of  Tension  or  Compression  Members 704 

Shearing  and  Beanng  Stresses . . .  \ 704 

Bending  Stress  on  Pins. — Plate  Girders 704 

Provision  for  Future  Increase  of  Live  Load 705 

Details  of  Construction — Camber;  Adjustable  Members 705 

Truss  Bridges;  Lateral  and  Sway  Bracing 705 

Diagonal  Bracing;  Gusset  Plates;  Temperature 705 

Bolsters  and  Expansion  Rollers;  Bed  Plates 705 

Rivete;  Tie  Plates;  Lacing;  Pin  Plates 705 ,705 

Workmanship — ^Riveted  Work;  Planing  and  Reaming 705 

Woricmanship— Eye-Bars;  Machine  Work 706 

Steel — ^Manxitacture;  Properties;  Pins;  Castings 706 

Cooper's  Standard  Loading — Axle  Loads — Table 707 

Moments,  Shears  and  Fl.-Bm.  Reac. — Cooper's  Loading — ^Table 708 

Coefficients  of  Impact — Formula  and  Table 709 

Permissible  Compressive  Stresses — Soft  and  Med.  Steel — Table 710 

Approx.  Weight  of  Steel  in  Railroad  Bridges — Formula,  Tables 710 

Plans  and  Details  of  Howe  Truss 71 1 

Reinforced  Concrete  Bridges 712 

Safe  Unit  Stresses  in  Structural  Timber,  Table 718 

SEC.  39.— ELECTRIC  RAILWAY  BRIDGES. 

Typical  Loadings— "L"  and  "K" 71fl 

Momente.  Shears  and  Fl.-Bm.  Reac. — "L  24"  Loading--Table 717 

Moments  and  Fl.-Bm.  Reactions — "K  25"  Loading— -Table 718 

udmum  End  Shears  from  "K  25"  Loading— Table. ^.^.^^i.^ 719 

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CONTENTS.  XVII 

SEC  40.— HIGHWAY  BRIDOES. 

Unit  Stress  Sheets  for  Various  Types  of  Trusses — ^Tables 720-726 

CaktUation  of  Stresses  by  Graphics 725 

Cue  oi  Cutting  Fcrnr  Active  Members 726 

Typical  Loading  for  Highway  Bridges — ^Table 727 . 

Live-Load  Data  for  Floor  Systems  and  Spans  Under  60  Ft 728 

Majdmum  Moments  and  End  Shears  for  "L"  Loadings — ^Table 728 

Uniform  Live  Loads  for  Trusses  of  Spans  Over  60  Ft. — Table 729 

Details  cA  Combination  Bridge,  290-Pt.  Span 729-730 

Nickel-Steel  and  Carbon-Steel  Spans— Costs.  Specifications— Table .  737 ,738 
Reinforced  Concrete  Bridges — Cost  Data 738 ,739 

SEC  41.— CANTILEVER  BRIDOES. 

Reactions  by  Formulas  and  Influence  Diagrams 74O 

Deck  Cantilever  Bridges;  Camber 741 

SEC  42.— MOVABLE  BRIDOES. 

Types — Swing,  Traversing.  Basctde,  Lift,  Pontoon 742 

Swmg  Briclges — Drawbridges — Rim-Bearing,  Center-Bearing 742 

Rim-Bearing  Draw — Fo\ir  Supports — Reactions — Formulas 743 

Continuous  Girder — Fo\ir  Supports — Formulas 743 

Rim-BearingDraw — Fo\ir  Supports — Reactions — ^Table 744 

Rim-Bcar'g  Draw — Reactions  and  Moments  for  Balanced  L'ds — Table.  746 

Calculation  of  316  Ft.  Drawbridge — Graphical  Solution 746 

Center-Bearing  Draw — ^Three  Supports — Mom.  and  Reac. — Formulas . .   746 

Continuous  Girder — ^Three  Supports — Formulas 740 

Center-Bearing  Draw — ^Three  Supports — Mom.  and  Reac. — ^Table 747 

Deck  Drawbridge — Center-Bearing — Hints  for  Calculation 748 

Formulas  for  Weight  of  Steel  in  Swing  Bridges 748 

Cotmterweight  Jack-Knif  e  Drawbridge 748 

Steel  Bascule  Bridges 749 

SEC  43.— SUSPENSION  BRIDOES. 

Theoretical — Curve  of  Main  Cables— The  Parabolic  Cable 750 

The  Catenarian  Cable — Formxxlas  and  Tables 761 ,762 

Linear  or  Skeleton  Arch. — Graphical  Solution  of  Catenary 763 

The  Transformed  Catenary 763 

Practical — Cables  or  Chains;  Towers  and  Backstays 764 

Anchorages. — Cable  Wrappings 766 

Manhattan  Bridge  Details — Description — Live  Loads 766 

Manhattan  Bridge— Specifications — Material,  Allowable  Stresses 768 

Longitudinal  Section  of  Anchorage 760 

Weight  of  Materials  in  Manhattan  Bridge,  Table 760 

Economic  Considerations 760 

SEC  44.— ARCHES. 


761 
763 
764 
764 

18 

766 
766 
767 
767 

768-770 

770 

773 

s 

778 

s 

774 

S 

778 

c 

782 

S 

es 

782 

F 

783 

T 

783 

C 

VCA^  49. —  iict:aiL.c9* 

784 

Pile 

Trestles.  Timber  Trestles— Plans  and  Dimensions. . 

787 

Pil^  ««r«  TirT.Ki.r  TtwutlMi — A-    T-  &  S    P_  R    R.  Plan  . . 

790 

Digitized  by  Google 

XVIII  CONTENTS. 

Wooden  Stringen — Allowable  Bending  Moments,  Table 791 

Steel  Trettle8.~£levated  Railroad  Trestles 791 .702 

Reinforced  Concrete  Trestles  ^ 792 

Cost  of  Railroad  Trestles— Timbers,  Steel,  and  Rein.-Conc 793 

Reinforced  Concrete  Trestles  Actually  Built,  Described 798 

SEC.  44^— ROOFS. 

Wind  Pressure — Velocities;  Direct  Pressure,  Formulas 794 

Direct  Normal  Wind  Pressures.  Table 796 

Effect  of  Wind  Suction  or  Tension 796 

Normal  and  Component  Wind  Pressures.  Formulas 795 

Normal  Wind  Presstu-es  on  Inclined  Surtaces,  Table 976 

Wind  Pressure  on  Pitched  Roofs,  Table 797 

Wind  Pressures  in  Open  Sheds,  and  on  Cylinders  and  Spheres 797 

Snow  Loads  on  Roou — ^Latitude-Altitude  Diagram 797 ,798 

Roof  Coverings 798 

Shingle  Roofing;  Weight  of  Shingles  Laid  on  Roofs,  Table 799 

Slate  Roofing;  Number  of  Slates  Laid  on  Roofs,  Table 799 

Weight  of  Slate:  Total  Weight  oer  Square  of  Roof ;— Tables 799 ,800 

TileKoofing — Kinds  and  Spedncations 800 

Tin  Roofing— Roofing  Tin— Plates 800 

Steel  Sheet  Roofing;  Corrugated  Steel  R.,  Formula;  Tar-Gravel  Roof..  801 

Cement-Gravel  R.,  Asphalt-Gravel  R.;  Slag  R.;  Patented  R 802 

Weight  of  .Roofing  Materials,  Table 802 

Common  Types  of  Roof  Trusses;  Stress  Diagrams 803 ,804 

Unit  Stresses  in  Pratt  Roof  Trusses.  Table 804 

Unit  Deductions  for  Half  Truss  (Lean-to) 806 

Unit  Stresses  in  Fan  and  Fink  Tniases,  Table 806 

Unit  Deductions  for  Half  Truss  (Lean-to) 806 

Design  for  Combination  Roof  Trusses — Spacing  of  Jack-Rafters 806 

Design  of  Sheathing  and  Jack-Rafters 807 

Design  of  Purlins  and  Trusses 808 

Table  of  Stress<».  and  Stress  Sheet,  of  Roof  Truss 809 

Details  of  Roof -Truss  Design — Chord  Splice,  Chord  Block,  Keys,  etc. . .  810 

Weight  of  Steel  Obstruction  in  Roofs,  Formulas 810 

Steel  Roofs — ^Approximate  Weight  of  Trusses  and  Parlins — ^Table 811 

SEC  47.— BUILDINQS. 

Plastering. — Lathing. — ^Partitions 812 

Wooden  Partitions;  Hollow  Tile  Partitions;  Other  Partitions 813 

Expanded  Metal  Partitions  and  Lathes 814 

Floors,  Oilinss.  etc. — Live  and  Dead  Loads 814 

Live  Loads— Mmimum  for  Floors  and  Roofs — ^Ten  Cities — ^Table 815 

Maximum  Live  Load  Possible  from  People 815 

Loads  from  Safes,  with  Problem 816 ,817 

Table  of  Weights  and  Dimensions  of  Heavy  Safes 816 

Examples  of  Floor  and  Ceiling  Construction 817  ,818 

New  York  City  Building  Code — Digest — 819-823 

Qtiality  of  Materials. — Excavations  and  Foimdations 819 

Wooden  Beams,  Girders  and  Columns. — Fireproof  Buildings 819 

Iron  and  Steel  Construction. — ^Floor  Loads 820 

Calculations. — Strength  of  Materials 821 

Reinforced  Concrete  Omstruction 822,  823 

Allowable  Stresses  for  Steel  and  Concrete,  Table 823 

Chicago  Building  Ordinance — Digest— 823,  824 

Reinforced  Concrete — Ratio  of  Moduli  of  Elasticity 823 

Reinforced  Concrete — Adhesion — Bond 824 

Philadelphia  Building  Laws  and  Ordinances — Digest — 824  ,826 

Live  Loads  for  Floors  and  Roofs 824 

Calculations. — Ultimate  and  Working  Stresses 824 

Allowable  Pressures. — Reinforced  Concrete  Construction 825 

Boston  Building  Law— Digest — 826-827 

Materials — ^Allowable  Fiber  Stresses 826 

Omcrete  and  Reinforced  (Concrete  (Construction 826 

Buffalo  Bxailding  Laws — Digest — 828 ,829 

Omcrete  and  Reinforced  (Concrete  (Construction 828 

Hollow  Omcrete  Blocks 829 

Reinforced  (Concrete  Btiilding — Formxxlas  for  Unit  Stresses 831 

einforced  Concrete — Standard  Building  Regulations.  .^ 831 

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CONTENTS.  XIX 

Cutting  Stroctural  Steel  Work  with  Oxy-Acetylcne  FUune 838 

Wind  Loads  on  Mill  Buildings 833 

SEC.  48— RETAINING  WALLS. 

Theory  of  Earth  Pressure.  835;  Rankine's  Theory 839 

Cubic  Yards  of  Masonry  in  Retaining  Walls.  Table   841 

Comparative  Sections  of  Thirty  Retaining  Walls,  Table 842 

SEC.  49^DAMS. 

Comnxm  Fixed  Types,  Described 844 

Stability  of  Gravity  Dams. — Hydrostatic  Pressure    845 

Center  of  Pressure — Formulas 846 

Center  of  Gravity  cf  Trapezoid — ^AnalyticaUy  and  Graphically 847 

The  Triangular  Dam 847 

Prosure  on  Foundations,  Formulas 848 

Factor  of  Safety  Against  Overturning.— Shear 850 

Pressure  on  Foundations.  Table 851 

Masonry  Gravity  Dam — Calcxilations  and  Design 852-854 

Effect  of  Profile  on  Gravity  Dams 854 

Dimensiona  and  Quantities  for  Masonry  Dams.  Tables 856 .856 

Dimensions  and  Quantities  for  Rock-Pill  Dams,  Table 857 

Dimensions  and  Quantities  for  Earth  Dams.  Table 858 

H^  Blasonry  Dams — ^Table  of  Dimensions 859 

Comparative  Cross-Sections  of  High  Earth  Dams , 859 

Rubble-Concrete  Dam — Cyclopean  Masonry 860 

The  Eastwood  Multiple-Arch  Dam,  Described 860 

SEC.  50.— FOUNDATIONS. 

Foundation  Beds— Rock,  Gravel,  etc 863 

Actual  Bearing  Pressures  on  Bed  Rock,  Table 864 

Actual  Bearing  Pressures  on  Sand.  Table 864 

Actual  Bearing  Pressures  on  Gravel.  Table . . .  ^ 865 

Actual  Bearing  Pressures  on  Clay  and  Sand,  Table 865 

SoQs — Practical  Test.  Selection  of  Site,  Examination 865 

Borings  in  Scdl. — Estimating  Loads  on  Foundations 866 

Bearing  Power  of  Soils,  from  Variotis  City  Codes — ^Table 867 

Foundations  for  Machines.  Dynamos,  etc 867 

Types  of  Foundation  Footings 867 

Stc«l  I-Beam  Footing  for  Independent  Piera 868 

Coffer-Dams— Types  Described. 868 

Sheet  Piling— Types— Timber  and  Steel 869 ,870 

Pile  Foundationfl— Supporting  Power  of  Piles 871 

Pile-Driving  Formulas  lor  Drop  Hammer  and  Steam  Hammer 871 

Safe  B^ixina  Power  of  Piles,  Table 872 

The  Drop  Hammer  and  Steam  Hammer,  Described 872 

PDe  Drivezs — Derrick.  Power  and  Water-Jet 873 

Pile  Shoes;  Pile  Foundations;  Splicing  Piles;  Cutting  Off  Piles 874 

Pilea— Dead-Men  Piles;  Iron  Piles;  Screw  Piles;  Disk  Piles 874 

Pilea— Sand  Piles-  Concrete  Piles;  Water- Jet  Concrete  Piles 875 

Piles— Metal  Shell  Concrete  Piles;  Reinforced  Concrete  Piles 875 

Open  Caissons 876 

Crib  Piers;  Pile  Piers;  Tubular  Piers 877 

Cvahiag  Pic« 878 

Platform  Cylinder  Piers. — Pneumatic  Cylinder  Piers  and  Process 879 

Pneumatic  Foundations — Caisson  and  Crib 880 

Coffer-Dam. — Freezing  Pro6ess 882 

Masonry  Piert.  Design 888 

Contents  of  Piers  by  Pnsmoidal  Formula 889 

SEC  51.— WHARVES,  PIERS  AND  DOCKS. 

Definitions.- — ^Foundations 892 

Pierhead  and  Bulkhead  Lines. — Construction  Methods 892 

Piers. — Ferry  Slips  and  Bridge  Aprons 893 

Plans  of  Ferry  Crib,  Dolphin  and  Bridge ^•*'2SS 

Reinforced  Concrete  Wharf  Construction 900 

SEC,  52  —BREAKWATERS. 

Q^lities  and  Cost^  Lki.*  Ft.  of  Br^kWater;  TableV.  :^:  Gx)Dgk* '   ®^^ 


XX  CONTENTS, 

SUtistics  of  Noteble  Breakwaters,  Table 903 

Materials  for  Concrete  in  Buffalo  Breakwater 004 

SEC  53.-^ETTIES. 

Jetty  Construction. — Fascines ©06 

SEC  54.— EARTHWORK. 

Uncertain  Cost. — Kind  and  Quality  of  Material 906 

Approved  Methods  of  Handling. — Clearing  and  Grubbing 906 

Loosening  Earth. — ^Loading  and  Conveying 907 

Superintendence. — Labor 908 

Earth  Empankment. — Shrinkage  of  Earth 909 

Experiments  on  Shrinkage  of  Earth 913 

Shrinkage  in  Volume  and  Vertical  Shrinkage 915 

Performance  of  Work — Methods  and  Costs 915 

Diamond  Drill  Borings,  Deep  Waterwajrs  Survey,  Table 917 

Railroad  Grading  with  Wheeled  Scrapers,  Costs 917 

Trenching  and  Backfilling  for  Sewer  Pipe.  Costs 918 

Earthwoik  Classification — Solid  Rock,  Loose  Rock,  etc 919 

References  to  Earthworic  and  Especially  to  Shrinkage 920 

Machine  for  Excavation  in  Frozen  Ground,  Cost  Data 921 

SEC  55.— ROCK  EXCAVATION. 

Open  Rock  Cuts— Drills.  Drilling,  etc 922 

Trenching  in  Rock,  Methods;  Chicago  Drainage  Canal 928 

Chicago  Drainage  Canal — Methods  and  Costs,  Tables 924 

Performance  of  Work — Methods  and  Costs 925 

Use  of  Well  Driller  for  Drilling  Blasting  Holes,  Costs 926 

SEC.  56.— DREDOINa 

Methods  of  Measuring  Material. — Dredges,  Tjrpes 927 

Elevator  (Bucket)  Dredge. — Hvdraulic  Dredge 928 

BlastingUnder  Water--l)redging  Detroit  River 929 

Detroit  River— Dredging,  Drilling,  Scows— Cost  Tables 980 

Gold  Dredging  in  California 980 .989 

Performance  of  Work — Methods  and  Costs 981 

Large  Elevator  Dredge  for  Work  in  Boston  Harbor,  Described 982 

SEC.  57.— TUNNELINa 

Definitions. — Kinds  of  Timnels 983 

Methods  of  Tunneling — Open  Cut — "Heading"'vs.  "Drift" 933 

Drilling  and  Blasting. — ^Timbering. — Lining 934 

Alinemcnt  and  Grade. — ^Ventilation 936 

Shield  Method. — Dredging  Method. — Caisson  Method 936 

Performance  of  Work — Methods  and  Costs 937 

Some  Notable  Tunnels  that  Have  Been  Built.  Data 987 

Some  Detail  Tunnel  Costs,  Los  Angeles  Aqueduct 939 

SEC  58— SURVEYING,  MAPPINQ  AND  LEVELING. 

Care  of  Instruments. — ^To  Adjust  the  Level 041 

To  Adjust  the  Transit,  942,  The  Solar  Attachment 944 

The  Solar  Instrument — Description  and  Use 944 

To  Adjust  the  Solar  Attachment 947 

Solar  Observations  with  Transit  Alone— Calculations 947 

To  Determine  the  Meridian  from  the  North  Star 948 

Polar  Distance  of  Polaris  for  Lat.  0**.  and  Any  Latitude 949 

Arimuth  of  Polaris  at  Elongation  Jan.  1.  Table 960 

Observations  of  Polaris  at  Elonflation,  or  at  Any  Hour  Angle 961 

Time— Civil,  Astronomical  and  Railway 962 

Local  Mean  Time  of  Upper  Culmination  of  Polaris.  Table 963 

Azimuth  of  Polaris  for  Use  of  Land  Surveyors,  Table 964 

Polaris  Tables  for  the  Year  1912 966a-96ftf 

Tapes. — ^Temperature  Corrections,  Table 966 

Sag  and  Stretch  of  Tapes — ^To  Correct 967 

Table  of  Eqtiivalents  of  Feet  and  Chains 068 

Methods  of  Plotting  Angles.— Table  of  Chords 069 

Farm  Stirveying — Equipment  and  Method — Adjustment  of  the  Traverse  964 

Office  Plan  and  Finished  Map. — City  Lot  Surveying 066 

Government  Land  Surveying. — Acts  of  Congress j^ _ 967 

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CONTENTS,  XXI 

Geoenl  Roles  from  the  Poregoinff  Acts 968 

To  Restore  Lost  or  Obliterated  Coraers — ^Rules 060 

Rukt  for  Subdivision  of  Sections 070 

Useful  Tables  in  Public  Land  Surveys — ^Meridians  and  Base  Lines 071 

Azimuths  of  the  Secant,  and  Offsets  to  the  Parallel — ^Table 078 

Aiimuths  of  the  Tangent  to  the  Parallel,  Table 074 

Offsets  from  Tangent  to  Parallel,  Table 076 

Correction  of  Randoms,  Table 076 

Convcigency  of  Meridians — ^Table  and  Examples 077,  078 

Lengths  of  a  Degree  of  Latitude  to  Minutes,  Table '  070 

Lengths  of  a  Degree  of  Longitude  to  Minutes,  Table  081 

The  Stadia. — Stadia  Reduction  Table 083 .984 

Leveling  Correction  for  Curvature  and  Refraction *087 

Correction  for  Earth's  Curvature,  and  Refraction — ^Table 088 

Allowable  Errors  in  LevelixiA,  Table  and  Formula 080 

Description  of  Four  Stadia  Surveys  and  Their  Cost 090 

sea  59.— RAILROADS. 
A. — Qeneral  Diacitssion. 

Existing  Mileage,  etc. — Economic  Principles 091 

Tractive  Force  of  a  Locomotive — Grades — Formulas 002 

Tractive  Force  of  Engines  on  Various  Grades,  Table 004 

Allowable  Expense  for  Grade  Reduction    .• 005 

Cost  of  Haul  on  Various  Grades.  Table 006 

Economic  Considerations  of  Curvature  and  Distance 007 

B. — Reconnoissaiice  Survey. 

Aneroid  Barometer — Formula,  etc 098 

Table  of  Barometric  Elevations. — Barometric  Correction  Table 099 

C. — Preliniiiiary  Survey. 

Field  Operations — ^Locating  Engineer  and  Transitman 1000 

Table  of  Grade»— Ft.  per  100  Ft.  to  Ft.  per  Mile.  Equivalents 1001 

Table  of  Stations  Corresponding  to  Distance  in  Miles 1001 

Table  of  Grades — Angles  for  Rates  of  Grades.  Equivalents 1002 

Table  of  Grade»— Ft.  per  Mile  to  Ft.  per  100  Ft..  Eqiiivalcnts 1003 

Table  of  Grades — Angles  for  Ft.  per  Mile,  Equivalents 1003 

Duties  of  Levelman  and  Topographer. — Mapping 1004 

D. — Location  Survey. 

Prc^les  and  Grades 1004 

Parabolic  Vertical  Curves. — Horizontal  Circular  Curves 1006 

Table  of  Radii  of  Curves — English  and  Metric 1007 

Table  of  Tangents  and  Externals  to  1^  Curve — English  and  Metric 1009 

Minutes  and  Seconds  to  Decimals  of  Degree  or  Hour.  Table 1010 

Various  Problems  in  Simple  Curves. — Compound  Curves 1011 

Solution  erf  Compound  Curve  Problems — ^Table  of  Formulas 1012 

Reversed  Curves — Formulas 1012 

Cubic  Parabola. — Spiral  Curve. — Easement  Curves 1013 

E.--Riglit  of  Way. 

Fmoe  the  Location 1013 

PtDchase  and  Condemnation 1014 

Table  for  Finding  Widths  of  R.-of-W.  for  Cuts  and  Fills 1014 

Tables  for  Finding  Acreage  of  Right  of  Way 1016 

F.— Constmction. 

Methods  of  Calculation  of  Earthwork 1016 

Lost  and  Description  of  E^hwork  Tables,  with  Page  No 1017 

Multiplication  Tables  for  Earthwork  Calculation. .' 1018-1020 

Slope-Staking  and  Ecuthwork  Computation 1066 

The  Prismoidal  Formula  and  Prismoidal  Correction  Formula 1065 

TaUes  of  Prismoidal  Corrections 1066-1068 

Earthwork  Correction  for  Curvature. — Haul. — Roadbed 1060 

Rails  and  Fastenings— Standards 1060 

Standard  Dimensions  of  Rails  and  Fastenings,  Table 1061 

Weisht  of  Rails  Reduced  to  Tons  per  Mile  of  Track,  Table 1003 

Middle  Ordinates  for  Curving  Rails.  Formulas 1063 

BGddle  Ordinates  for  Curving  Rails,  Tables 1064-1067 

Choid  Lengths  of  Curved  Rails.  Takes 1066  .1067 

To  Find  the  D^ree  of  Curve  of  Laid  Track,  Formulas 1066 

Track  Spikes—^ble.— RaU  Joints 'n;<r\'r^v} 

Digitized  by  V^OOQIC 


XXII  CONTENTS. 

Formula  for  Thickness  of  Shims  in  Tracklayizis 1069 

Cross  Tics. — ^Table  of  Cubic  Feet  in  Wooden  Ties 1069 

Table  of  Feet  Board  Measure  in  Wooden  Ties 1070 

Bills  of  Switch  Tics  for  Nos.  6  and  8  Frogs,  Tables 1070 

Cross  Ties — Best  Kinds,  Life,  and  Time  to  Cut 1071 

Tie  Plates — ^Types,  and  Advantages. — Rail  Braces 1071 

Steel  Ties.— Concrete  Steel  Ties 1072 

Ballast — Kinds,  and  Amount  Required 1073 

Track  Gage. — Wheel  Ga^e,  M.  C.  B.  Standard 1073 

Increase  of  Gage  for  Vanous  Curves.  Table 1073 

Gages  and  Half -Gages  of  Track,  with  Log  Values — ^Table 1074 

Various  Track  Gages  in  Use. — Best  Standard  Gage 1074 

Turnouts  and  Switches. — Fro^. — Frog  Numbers ]  1075 

Manganese  Steel  Frogs. — Spring  Rail  Frogs 1075 

Properties  of  Frog  Angles  and  Half  Frog  Angles,  Table 1076 

Movable-Point  Frogs 1076  ,1077 

Crossing  Frogs. — Stub  Switches 1078 

Table  for  Laying  Out  Switches  in  the  Field 1078 

Table  of  Theoretical  or  Stub  Switches 1079 

Table  of  Radii  of  Theoretical  Turnout  Curves 1081 

Table  of  Theoretical  Switches  for  Any  Gage 1082 

Turnout  Curves  for  Stub  Switches,  Formulas 1083 

Formulas  for  Double  Turnout  Ciirves 1084 

Turnout  Curves  from  Curved  Main  Trade,  Formulas 1084 

Split  Switches 1084 

TiuTiouts  for  Split  Switches  and  Sirring  Frogs,  Table. ..^ 1085 

Three-Throw  Turnouts,  Split  Switches — ^Table 1086 

Turnouts  from  Straight  Track,  Split  Switches — ^Table 1087 

Formulas  for  Split  Switches 1087 

Wharton  Switch 1088 

Ladder  Tracks — Spacing  of  Frog»— Table 1089 

Crossovers — Spacing  of  Frogs — Table 1090 

Standards  of  Track  Construction  on  American  Railways 1003 

Street  Railway  Track  Construction  and  Paving 1004 

SEC.  «>— HIGHWAYS. 
A. — Traction. 

Power  of  a  Horse. — Effect  of  Road  Surfaces  on  Traction 1097 

Effect  of  Grades  on  Traction — Formulas,  Tests,  Problem 1 007 

B.— Roads  and  Streets. 

Definitions. — ^Dirt  Roads. — Corduroy  Roads 1008 

Plank  Roads. — Gravel  Roads  and  Walks 1008 

Broken-Stone  Pavement. — Hydraulic  Cement  Pavement 1099 

Cement  Sidewalks 1009 

Wood-Block  Pavements. — Cobblestone  Pavement 1009 

Belgian  Block  Pavement. — Granite  Block  Pavement 1 100 

Brick  Pavement. — ^Asphalt  Pavement 1 100 

Asphalt  Paving  Blodcs. — Bituminous-Rock  Pavement 11 00 

C. — Pavement  Specifications. 

Allegheny  County ^a.: — Road  Specifications 1 101 

Boston:— -Granite  Block  Pavement — Brick  Sidewalk 1 102 

Wood  Block  Pavement — Brick  Sidewalk 1 108 

Asphalt  Pavement. — Bitulithic  Pavement 1 104  , 1 106 

Macadam  Roadway — Crushed  Stone  Sidewalk 1 105 

The  Proper  Construetion  of  Brick  Pavements. — (W.  P.  Blair) 1 106 

Cincinnati: — Boulder  Pavement 1 107 

Detroit: — General. — Brick  Pavement,  Concrete  Foundations 1108  ,1109 

Sheet  Asphalt  Pavement  on  Concrete  Fotmdations 1110 

Cedar  Block  Pavement  on  Concrete  Foundations 1 1 10 

Easton,  Pa.: — Macadam  and  Telford  Roads 1111 

Concrete  Curbs,  Gutters  and  Sidewalks 1111 

Reinforced  Concrete  Fotmdations — Reference 11  li 

El  Paso,  Tex.: — Petrolithic  Pavement 1 1  li 

Los  Angeles: — Gravelled  Streets 11  tl 

Bituminized  Brick  Gutters 1 1 1| 

Maryland  State  Highway: — Macadam  Construction 1 1  ll 

NatU  Association  Cement  Users: — Portland  Cement  Sidewalk 1111 


CONTENTS.  ^ 

Manhattan  (N.  Y.  City):— Oranitc  Block  Pavement 

Wood  Block  Pavement 

Richmond  (N.  Y.  City): — Iron  Slag  Bk)ck  Pavement 

Vhrified  Brick  Pavement 

Asphalt  Block  Pavement.— Curb  on  Concrete  Foundation 

Rkhmond,  Ind.: — Street  Crowning,  Table 

Syiacwe.  N.  Y.:—Oeneral.— Vitrified  Brick  Pavement 

Sandstone  Block  Pavement 

A^)halt  Sheet  Pavement 

Ctoowted  Wood  Block  Pavement. — Bitulithic  Pavement 

Toronto.  Ont.: — Grading 

Cedar  Block  Pavement. — Concrete. — ^Asphalt  Pavement 

Brick  Pavement. — Macadam  Roadway. — Concrete  Walk 

D.— Care  of  Road  Surfaces. 

Dust  Preventives:— Classification 

Tars,  their  Manufacture  and  Properties — Coal  Tars 

Water-Gas  Tar. — Composition  ol  Tars 

Application  of  Tars  to  Finished  Road  Surfaces 

Lae  of  Tar  in  Road  Construction 

Oils,  their  Classification  and  Properties 

Ap{]4ication  of  Heavy  Oils  to  Surfaces,  and  Roads 

Spcdficatkms  for  Coal  Tars 

Experiments  with  Dust  Preventives: — 

Tar  Experiments — Miscellaneous  and  Cost  Data.  Tables 

Cost  of  Applying  Calcitmi  Chloride 

Rock  AsrOialt  and  Oil  Experiments— Cost  Data 1138- 

Asphalt  and  Bituminous  Rock  Deposits  of  the  U.  S 

E. — Miacellaneoiis. 

Paving  a  Country  Road  with  Brick 

Inverted  Macadam  Road  Construction 

Vitrified  Clay  Curbing  for  Streets  and  Roads 

Sidewalk  and  Paving  Practice  in  Chicago,  Cost  Data 

Experience  in  Dust  Suppression  on  N .  1.  Roads.  Cost  Data 

Tests  d  Vaxious  Road  Surfacing  Materials,  Table 

SEC.  61.— HYDROSTATICS. 

Definitkms. — Atmospheric  Pressure. — Air. — Water 

Hydrostatic  Pressure — Units  and  Formulas 

Hydrostatic  Head  and  Pressure,  Equivalents  (1-10),  Tables , 

Head  in  Feet  for  Given  Pressures  per  Square  Inch,  Table 

Pressure  for  Square  Inch  for  Given  Heads  in  Feet,  Tabic 

Pressure  for  Sqtiare  Foot  for  Given  Heads  in  Feet,  Table 

Center  of  Presmare  on  Submerged  Surfaces,  Formulas 

Center  of  Pressure  on  Orifices,  Weirs,  etc..  Table 

Preanire  on  Pipes,  Tanks,  etc. — Flotation. — Buoyancy 

Metacenter. — ^Laws  of  Equilibritun 

SEC.  62.— HYDRAULICS. 

Definitions. — ^Theory  of  Flow — Formulas 

Velocity  and  Discharge,  Formulas 1 155 

Theoretic  Vekxdties  for  Various  Heads,  Table (283) 

Areas  of  Pipes  in  Sq.  Ft.  for  Diameter  in  Ft.  and  Ins.,  Table 

Velocity  in  Pipes  or  Varying  Cross-Section,  Formulas 

Losses  During  Plow  Through  Pipes.  Formulas 

HydrauJic  Grade  Line. — Velocity  of  Approach 

Total  Head. — Loss  of  Head  due  to  Friction 

Hydranlic  Notation  and  Formulas 

Economic  Sections  of  (Conduits — Maximimi  Velocity 

Cbezy'B  Hydraulic  Formula. — Kutter's  Formula 

Values  of  n  (and  c)  in  Kutter's  Formula 1108 

CocflBcicnts  c  in  Kutter's  Formula,  Table 1170- 

Practical  Examples  in  Use  of  Kutter's  Formula 

The  Vcnturi  Meter — 

Meter  Roister;  Manometer;  Piezometer  Tubes 

Orifices,  Tubes,  Nozzles  and  Jets — Formulas  and  Tables 

Weiis — Standard  Weir— Theoretic  Discharge,  Formulas 

Prancis'  Weir  Formulas ^^ 

Baxin's  Weir  Formula;  and  Value  of  m.  Table. ^6^ byV^jOO^le-  -^^78 


XXIV  CONTENTS. 

Ptelcy  and  Stearns*  Weir  Ponnulas 1180 

Parmley's  Weir  Formula;  and  Values  of  C  and  K,  Tables 11 80    I 

Triangtilar  and  Trapezoidal  Weirs 1 181     I 

The  Submerged  Weir:— 1181     | 

Pteley  and  Steams'  Formula;  and  Values  of  m.  Table 1181 

HerBchcl's  Formula;  and  Values  of  c.  Table 1181 ,1182     1 

Hydraulic  Measurements — ^Tank.  Venturi,  Weir,  etc 1182 

Hook  GaRe. — Pilot  Tube  Meter. — Floats 1183 

Current  Meters — Rating  and  Use.— Meter  Register 1185  .1186 

Depth  of  Thread  of  Mean  Velocity  in  Rivers 1187 

Values  of  n  in  Kutter's  Formula  Determined  for  Earth  Canals 1187 

Durability  of  Wood  Stave  Pipe  Actually  Laid 1187 

Values  of  c  and  n  in  Kutter's  Formula — Experiments,  Table 1188 

Bazin's  Hydraulic  Formula 1189 

Friction  of  Air  in  Small  Pipes.  Formula 1189 

SEC.  63.— WATER  SUPPLY. 

Source. — Rainfall — Distribution. — Artesian  Nomenclature 1190 

Average  Monthly  Precipitation  in  the  U.  S.,  Table 1191 

Percentage  of  Rainfall  to  Average  Rainfall,  Table 1 195 

High  Intensities  of  Rainfall,  Notation 1 195 

Maximum  Intensity  of  Downpour,  Formulas. — Rain  Gage 1 196 

Maximum  Rates  of  Rainfall  by  Preceding  Formulas,  Table 1197 

Rimoff. — Measuring  Stream  Discharge 1 197 

Rimoff  Formulas. — Eflfect  of  Slope 1198 

Evaporation  from  Ice,  Snow,  Water  Siirface,  etc 11 99 

Monthly  Evaporation  from  Water  Surfaces  in  the  U.  S.,  Table 1199 

Seepage  and  Evaporation  in  Canals,  etc 1200 

SEC.  64.— WATER  WORKS. 
A. — Consumption  of  Water. 

Water  Meters,  and  Waste  of  Water 1202 

Population  in  17  Cities  of  the  U.  S..  from  1860  to  1906— Table 1202 

Water  Consumption  in  17  Cities  of  the  U.  S..  from  1860  to  1906— Tab.  1203 
B.— Purification  of  Water. 

Screening. — Sedimentation.— Slow  Sand  Filtration 1204 

Rapid  Sand  Filtration — Mechanical. — Copper  Sulphate 1204 

C. — Reservoirs. 

Storage  Reservoirs. — ^Distributing  Reservoirs 1205 

Reservoir  Linings. — Stand  Pipes — Formulas  for  Design 1206 

D. — Conduits. 

Canals. — ^Flimies. — Bored  Wooden  Pipe.— Salt  Glazed  Pipe 1207 

Masonry  Aqueducts — Reinforced  Concrete 1208 

Bored  Wooden  Pipe,  Banded. — Wood  Stave  Pipe,  Details 1208 

Wood  Stave  Pipe  and  Details,  Table 1210-1213 

Notes  on  Preceding  Table — Bands  and  Shoes  1214 

Discharge  in  Gallons  through  Wood  Stave  Pipe,  Table     1214 

'^       '        ""  1214 

:ast  Iron  Pipe 1215 

lell  and  Spigot  Joint  Pipe — 1216 

with  Lead  and  Hemp  Data— Table 1216 

Cast  Iron  Pipe,  Table 1217.1218 

eding  Table 1219 

id  Taking  Up  Laid  Pipe 1219 

of  C.  L  Pipe  and  Specials.  Tables 1219-1267 

ipe 1220  .1222  ,1223 ,1243-1246 

ngs 1221,1223 

es 1224,  1248.  1249 

Cast  Iron  Pipe  Branchesr— L's,  Ts,  Crosses 1226-1227,1260-1264 

Cast  Iron  Pipe  Branches— Ys 1227  ,1228  ,1266  ,1266 

Cast  Iron  Pipe  Hydrant  Branches 1229 

Cast  Iron  Pipe  Blow-Off  Branches 1230  .1231 ,1267  ,1268 

Cast  Iron  Pipe  Sleeves 1232  ,1266 

Cast  Iron  Pipe  Increasers  and  Reducers 1233 ,1269-1264 

Cast  Iron  Pipe  Caps 1234  ,1266 

Cast  Iron  Pipe  Lugs 1247 

Cast  Iron  Pipe  Offsets o^^ed  b^C^OOgle.  •  1235  .1240 


CONTENTS.  XXV 

...1234  4267 
...1232.1259 

1239 

1236 

1236 

1236 

1238 

1268 

1268 

1269 

1269 

1269 

1270 

1271 

:.1272 

1273 

...1247.1276 
...1276-1279 
1280 

1280 

1281 

1282 

1283 

1284 

1284 

1286 

...1286.1287 

1288 

1288 

1289 

1290 

r. — in  I8(;eiuineuu5  i/buu 

Costs  of  Slow  and  Rapid  Sand  Filtration : 1291 

Efficiencies  of  Riveted  Pipe  Joints. 1291 

Water  Purification  in  Reservoirs,  Cost  Data 1292 

Steel  Pipes  for  Water  Works— Economic. 1292 

Pneumatic  Calking  of  Mains  with  Lead  Wool 1293 

Waterproofing  the  New  Ulm  Reservoir 1293 

SEC  65.— SANITATION. 

The  Disposal  of  Refuse. — House  Drainage 1296 

Cesspools. — Sewers— Size  and  Grade .^ 1296 

'"        '  "      "  1297 

Table 1298 

1298 

1299 

1300 

1301 

lulas 1302 

1303 

as 1304 

1306 

1306 

indations 1306 

1306 

»ipc.  Tables 1307 

1307 

1308 

1309 

1310 

1310 

1310 

SEC.  66.— IRRIGATION. 

General  Discussion. — Irrigation  Units 1313 

Miner's  Inch — Equivalents  of  Discharge — ^Table 1313 

EquivalenU  of  Discharge  of  One  Cu.  Ft.  per  Sec.  Table.  .^^ 1314 

tizedbyUOOgle 


XXVI  CONTENTS. 

Units  of  Volume — ^Acre-Foot  and  Acre-Inch 1314 

Rates  of  Discharge  for  One  Acre-Foot  per  Day,  Table 1314 

Rates  of  Discharge  for  One  Acre-Foot  per  Month,  Table 1815 

Duty  of  Water  in  Irrigation 1315 

Duty  of  Water — ^Meastu^ments  at  Different  Points — Tables ! ! . ! !  1316 

Duty  of  Water — Losses  in  Main  Canal  Included — ^Table 1316 

Duration  of  Irrigation  Period  on  Some  Canals.  Table 1316 

Duty  of  One  Cu.  Ft.  per  Sec.,  and  Inches  in  10  days — ^Table .'.  1317 

Canals. — Data  on  Some  Perennial  Canals,  Table 131 7 

Conduits  and  Flumes 1317 

Field  Location  of  Irrigation  Ditches  and  Canals ]  1318 

Cost  Date  on  Drainage  of  Irrigated  Lands I319 

SEC.  67.— WATERWAYS. 

Suez  Canal. — Cronstadt  and  St.  Pertersbuxg  Canal 1320 

Corinth  Canal. — ^Manchester  Ship  Canal 1320 

Traffic  Data  on  Suez  Canal.  Table ! !  1 321 

Kaiser  Wilhelm  Canal. — Elbe  and  Trave  Canal '.  .1322 

Welland  Canal. — Sault  Ste.  Marie  Canals 1322 

Canadian  Canal  Systems. — ^Lake  Borgue  Canal 1323 

Chicago  Drainage  Canal. — ^Proposed  Am.  Isthmian  Canal 1324 

Distance  Data  via  Panama  and  Nicaragua  Routes 1328 

Harlem  River  Canal. — Cost  of  Maintenance  of  Canals 1329 

Principal  Commercial  Canals  of  the  U.  S. — ^Table 1329 ,1330 

SEC  68.— WATER  POWER. 

Definitions  and  Formulas. — Economic  Design  of  Penstock 1332 

Horsepower  per  Cubic  Foot  of  Flow  per  Second,  Table I333 

Horsepower-Hours  from  Storage  of  One  Million  Cu.  Ft.,  Table 1334 

Horsepower-Hours  from  Storage  of  One  Acre-Foot,  Table I335 

Water  Motors — ^Wheels — Current,  Undershot,  Breast,  Overshot 1336 

Impulse  Water  Wheels 1330 

Single  Nozzle  Pelton  Water  Wheel  Data,  Table 1338 

Ouintex  Nozzk  Pelton  Water  Wheel  Data.Table 1342 

Turbine  Water  Wheels — Nomenclature  of  Terms 1342 

Losses  of  Energy  in  Turbines;  Efficiencies  of  Turbines I343 

Theoretic  Horsepower  of  Tiu-bines. — Transmission  of  Power 1344 

Important  Designs  for  Reference I345 

SEC.  69.— STEAM  AND  QAS  POWER. 
A.— Heat 

Matter  and  Energy;  Kinds,  Forms  and  Transformation  of  Energy 1346 

Thermal  Energy. — First  Law  of  Thermodynamics I347 

Thermal  Units — British,  French,  British-French I347 

Mechanical  Equivalent  of  Heat,  J I347 

Thermal-Units — Equivalents  (1-10).  Mechanical  Work — Table 1348 

British  Thermal  Units,  Power  and  Work — ^Equivalents  (1-9) — ^Table  ..1349 

Examples  in  Use  of  Preceding  Table I35O 

B.— FueL 

Heating  Power  of  Fuels — ^Methods  of  Determination 1350 

Chemical  Analysis. — Coals  Classified  by  Carbon  and  Volatiles.  Table. .  .1360 

Proximate  Analysis  and  Heating  Values  of  U.  S.  Coals,  Table 1361 

Ultimate  Analysis  of  Fuel,  Defined 1 351 

Chemical  Analysis  of  Several  Kinds  of  Solid  Fuels.  Table 1352 

Calculation  of  Heat  of  Combustion — Formulas;  Calorimeter 1352 

Pmctical  Boiler  Tests— Coal  as  Fuel — ^Table 1363 

C— Steam. 

General  Discussion — Kinds  of  Steam 1364 

Superheated  Steam  and  Saturated  Steam,  Formulas 1 356 

Saturated  Steam  Tables,  Described;  Heat  of  Vaporization,  Formula. .  .1356 

Saturated  Steam  Tables— Old 1357  .1358 

Saturated  Steam  Tables — Revised 1359  .1 360 

Flow  of  Steam  Through  Pipes — Formula  and  Table 1361 

Steam  Boilers — Efficiency  and  Ojmmercial  Horsepower  Rating 1361 

Consumption  of  Coal  per  Boiler  Horsepower-Hour 1362 

Kinds  of  Steam  Boilers;  Boiler  Settings 1362 

Steam  Engines;  Engine  Horsepower,  Problem 1363 

Coal  Consxunption  per  Horsepower  per  Hour 1362 

Digitized  by  VjOOQ  IC 


CONTENTS,  XXVII 

Value  of  Wood  as  Fuel;  Principle  of  the  Steam  Engine 1363 

Steam  Bnsixie  Cylinder  and  Double  Indicator  DiagxEun 1304 

Uean  Effective  Pressure— Table,  Formulas  and  Problem 1365 

Bcooocoic  Performance  of  Steam  Engines — ^Non-Condensing  Engines. .  .1366 
Boon.  Perf .  of  Steam  Engines — Condensing,  and  Compound  Engines . .  .1366 

Effect  of  Load  Upon  Economy  of  Steam  Engines 1366 

Steam  Pumps — Duplex.  Centrifugal  and  Rotary 1366, 1367 

Duty  of  Pumps — ^Formula 1367 

D.— Heat  (Intemal-Combiistioa)  Engines. 

Tests  of  Heat  Engines  on  Alcohol  Fuel 1368 

CoocltttioRS  Drawn  from  Above  Tests 1 369 

Properties  of  Liquid  Fuels — Gasoline,  Kerosene.  Alcohol 1370 

Heat  of  Combustion  of  Petroleiun  Oils  and  Alcohol 1370 

Air  Necessary  for  Combustion  of  Liquid  Fuels 1371 

Vaporization  of  Liquid  Fuels 1371 

Avagadro's  Law  of  Gases. 1372 

Vapor  Pressure  of  Saturation  for  Various  Liquids.  Table 1373 

Methods  of  Testing  Heat  Engines;  Brake  Horsepower,  Formula 1374 

Indicated  Horsepower,  Formula 1375 

Fuels  Used  in  Testing  Heat  Enrfnes— Properties 1375 

Fx^ctiooal  Distillation  of  Gasolme.  Table 1376 

E. — Miscellancotis  Data. 

Heat  Conductance  and  Resistance  of  Various  Materials.  Table 1377 

Solution  of  Steam  Problems  by  Entropy  Diagrams — (Ref.) 1378 

Unique  Direct-Acting  Explosion  Piunp — (Ret.) 1378 

SEC  70.— ELECTRIC  POWER  AND  LIOHTINQ. 

Electricity  as  a  Form  of  Energy 1379 

Electric  Power  Units — ^Watt;  Kilowatt  or  Electric  Horsepower 1370 

Steam-Electric  and  Hydro-Electric  Problems;  D3mamos,  Defined 1379 

Transformers,  Converters  and  Boosters,  Defined 1380 

Principles  of  Electricity  and  Magnetism. — ^What  Electricity  Is 1380 

Ether  ;  Ether  Waves;  Electrid^^  and  Magnetism;  Magnetic  Field 1380 

The  Electro-Magnet. — Induced  Currents  or  Induction 1381 

Parraday's  Ring;  The  Horse-Shoe  Magnet;  Permanent  Magnets 1382 

Prixiciple  of  the  Alternate-Current  Dynamo 1382 

Claaaincation  of  Alternate-Current  Dynamos 1383 

Principle  of  the  Conttnuous-Currcnt  Dynamo 1384 

Claasincation  of  ContinuotJS-Currcnt  Dynamos .* f..  1384 

Electric  Transmission  of  Power. — Steam  and  Water  Power  Compared.  .1385 

Alternating  Current  vs.  Continuous  Current 1386 

Long-Distance  Transmission 1386 

The  Transmission  Line — ^Aluminum  vs.  Copper 1386 

Tiansmisnon  Line— Sise  of  Conductors;  Problems 1387 

Copper  Wire  Table  for  Electrical  Calculations 1388-1391 

National  Elbctric  Codb — General  Outline  of  Plan 1393 

Ctess  A- — Stations  and  Dynamo  Rooms — Generators;  Conductors 1394 

Switchboards;  Resistance  Boxes  and  Equalizers 1 395 

Lightning  Arresters;  Care  and  Attendance;  Insulation  Resistance 1396 

Motors,  f397;  Railway  Power  Plants 1398 

Storage  or  Primary  Batteries*  Transformers 1398 

ClassB. — Outside  Woric,  All  Systems  and  Voltages— Wires 1399 

Constant-Potential  Pole  Lines,  Over  5,000  Volts 1400 

Transformers:  Grounding  Low-Potential  Circuits 1401 

Oaas  C. — Inside  WorkTAll  Systems  and  Voltages— Wires 1403 

Undefnound  Conductors;  Table  of  Carrying  Capacities  of  Wires 1404 

Inside  Woric,  Constant-Current  Systems — ^Wires;  Series  Arc  Lamps 1405 

Incandescent  Lamps  in  Series  Circuits 1406 

Inside  W<»k.  Constant-Potential  Systems — ^Automatic  Cut-Outs 1406 

Switch«i:  Electric  Heaters 1407 

Inside  Work,  Constant  Low-Potential  Systems— Wires 1408 

Armored  Cables 1411 

Interior  Conduits;  Metal  Moldings 1412 

Pizturvs;  Sockets;  Flexible  Cord. 1413 

Arc  Lamps  on  Constant-Potential  Circuits:  Economy  Coils 1414 

Decorative  Lighting  System;  Theater  Wiring 1414 

Car  Wiring  and  Equipment  of  Cars 4,v:      v^ /  •  \\\l 

Car  Houses,  1421;  Lighting  and  Power  from  Rail^a^g  ^iresQ^^^J^  1422 


XXVin  CONTENTS, 

Inside  Work,  Constant  High-Potential  Systems— Wiret 1422 

Transformeis,  1422;  Series  Lamps 1423 

Inside  Work,  Constant  Extra-High-Potcntial  Systems— Wires. 1423 

Class  D. — Fittings,  Materials  and  Details  of  Construction 1423 

Insulated  Wires— General  Rules 1423 

Rubber-Covered  Wires,  1424;  Slow-Burning  Weatherproof  Wire 1426 

Slow-Burning  Wire;  Weatherproof  Wire 1425 

Flexible  Corf,  1426;  Fixture  Wire,  Conduit  Wire 1427 

Armored  Cable,  1427;  Interior  Conduits 1428 

Switch  and  Outlet  Boxes;  Moldings 142» 

Tubes  and  Bushings;  Cleats 1430 

Flexible  Tubing;  Switches 1431 

Cut-Outs  and  Circuit  Breakers 1434 

Fuses,  1436;  Standard  Cartridge  Enclosed  Fuses,  Table 1433 

Tablet  and  Panel  Boards;  Cut-Out  Cabinets;  Rosettes 1439 

Sockets,  1440;  Hanger-Boards  for  Series  Arc  Lamps 1442 

Arc  Lamps;  Spark  Arresters;  Insulating  Joints;  Rheostats 1442 

Reactive  Coils  and  Condensers;  Transformers;  Lightning  Arres.  1443,1444 

Class  E. — Miscellaneous — Signaling  Systems 1444 

Electric  Gas  Lighting;  Moving  Picture  Machines 1446 

Insulation  Resistance;  Soldering  Fluid 1447 

Class  F. — Marine  Work— Generators,  Wires 1447 

Portable  Conductors;  Bell  or  Other  Wires;  Table  of  Capacity  of  Wires  1448 

Switchboards;  Resistance  Boxes;  Switches 1440 

Cut-Outs:  Fixtures-  Sockets;  Wooden  Moldings 1449  1450 

Interior  Conduits;  Signal  Lights;  Motors;  Insulation  Resistance....       1450 

Electrical  Standardization  Rules  of  A.  I.  E.  E  — Definitions 1451 

Definitions — Currents;  Rotating  Machines;  Stationarv  Indue.  Appara.1451 

General  Classification  of  Apparatus;  Motors — Speed  Classification 1452 

Definition  and  Explanation  of  Electrical  Terms — 1453 

Load  Factor;  Non- Inductive  Load  and  Inductive  Load 1453 

Power-Factor  and  Reactive-Factor,  Equations 1453 

Saturation-Factor;  Variation  and  Pulsation 1468 

Performance  Specifications  and  Tests — 1454 

Rating;  Wave  Shape;  Efficiency 1454  .1456 

Regulation — Definitions,  and  Conditions  for  Tests 1461  ,1462 

Insulation  Resistance;  Dielectric  Strength 1462  ,1468 

Conductivity. — Rise  of  Temperature 1466 

OverloJta  Capacities 1469 

Voltages  and  Frequencies 1470 

General  Recommendations — Name  Plate,  Rheostat  Data,  etc  1470 

Electrical  Notation;  Railway  Motore 1471 

Photometry  and  Lcunpe — Candle-Power,  Ccmdle-Lumen,  etc     1473 

Sparking  Distances  in  Air,  Table  1474 

Temperature  Coefficients  of  Resistivity  of  Copper — Formulas,  Table  . .  1475 

Miscellaneous  Data — Properties  of  Various  Kinds  of  Wire 1476 

Reinforced  Concrete  Telegraph  Poles,  Described 1477 

Cost  of  Constructing  Steam-Driven  Electric  Power  Plants 1477 

Cost  of  Large  Steam  Plants.  Table;  also  Smaller  Plants 1478 

Rates  for  Electric  Current  Charged  by  Pasadena  Plant,  Table 1478 

Cost  of  Overhead  Trolley  Systems,  Table 1479 

SEC.  71.— MISCELLANEOUS  DATA  AND  ILLUSTRATIONS. 

References — ^Derricks  and  Cranes,  Chimneys 1480 

References — Mechanism  and  Gearing;  Marine  Engineering 1480 

References — Cableways  and  Conveyors;  Revetments. 1481 

References — Well  Boring;  Machines;  Btmkers  and  Bins 1481 

References — Compressed  Air;  Heating  and  Ventilation 1482 

References — ^Telephones;  Mining 1482 

New  Helical  Spring  Formulas 1482 

Tests  of  Steel  Springs,  Table 1484 

References — Solar  Power;  Valuations  and  Reports;  Contracts 1484 

Metal  Hoisting  Chains — Oval,  Open-Link — Formulas  . . 1484 

QLOSSAR  V 1 485- 1 5  38 

INDEX  1530-1611 


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INTRODUCTION. 

QmcnU  Diaciisiioii« — The  young  engineer  or  student  should  realize  that, 
although  engineering  is  not  an  exact  science  itself,  it  is,  in  its  entire  field, 
founded  on  the  exact  sciences,  supplemented  with  experimental  data.  As 
he  becomes  more  proficient  in  his  work  he  will  discern  certain  broad,  under- 
lying principles  which  he  will  begin  to  use  instead  of  mere  methods  or  rules, 
formerly  employed.  It  should  be  his  aim  to  master  these  principles  thor- 
oughly. 

MATHEMATICS. 

The  various  branches  of  mathematics  as  taught  in  our  common  schools 
are  based  on  methods  of  operation  rather  than  on  mathematical  principles, 
for  when  viewed  from  the  latter  standpoint  they  overlap  each  other  to 
such  an  extent  that  the  dividing  lines  are  not  always  clearly  marked.  For 
instance,  the  science  of  number,  space,  quantity,  position,  motion,  mass, 
force  and  ittertia  cannot  be  taught  in  logioal  sequence  from  out  text-books 
as  now  arranged. 

In  view  of  the  above,  and  of  the  fact  that  an  attempt  has  been  made 
in  the  body  of  this  work  to  classify  the  subject  matter  of  mathematics 
under  the  usual  headings — Arithmetic,  Algebra,  Geometfy,  etc., — it  is 
deemed  pertinent  here  to  mtroduce  a  discussion  of  the  more  abstract  science 
of  number,  sface,  quantity,  etc..  as  preliminary  to  the  main  text,  recognizing 
here  none  <^  the  divisions,  as  such,  which  are  contained  in  the  latter. 

NUMBBR.* 

The  science  of  Arithmetic  involves  the  principles  of  Algebra;  these 
principles  in  turn  having  been  deduced  from  the  theory  of  number,  and 
so  on. 


Nninber  is  independeot  of  the  order  of  countiiif . 

—In  cotmting  any  number  of  things,  the  counting  of 
the  last  one  contains  the  numeral  word  which  desig- 
nates the  total  number,  no  matter  in  what  order 
they  are  coimted.  In  the  illustration,  for  exam- 
ple, there  are  five  dots  in  each  case. 


12      3      4     4 


4      5      I 


A  Sniii  is  independent  of  the  order  of  adding. — 

In  finding  the  sum  of  two  or  more  groups  of  things,  ^ 
it  naatters  not  in  what  order  they  are  added;  as 
Sadded  to  6  equals  6  added  to  3,  equals  8;  or,  8+  6—  « 

6+3-8.    3  plus  5  plus  4-6+3+4-  4+6+3; 

etc,-12. 

Using  shorthand  characters  or  letters  to  represent 
numbers  the  same  law  holds  true:  as,  a+b^b  +  a; 
a+6+c—6+a  +  c;  etc. 

A  Product  is  independent  of  tlie  order  of  mtiitl- 


4  3's-4  times  3-4X3-12;  or,  aX6-ai- 12. 

3  4's- 3  tiroes  4-3x4-12;  or,  &Xa-&a- 12.      m 

Similarly.  4X3X6-(4X3)X6-4X  (3  X6)-3X   i 
(4X6)  —  60.    And  using  shorthand,  in  which  the  let-  *" 
ter  a  — 4,  6— 8,  and  c— 6:  aXbXc'^  abc  "  acb  "  bac 
—  bca  -mcab  —  c6a— 60. 

Note  the  6  (1 X  2X3)  different  ways  of  arranging 
the51etters. 


Fig.  1. 


3 
•5 


Fig.  2. 
q«4 


I 

Z 

3 

4 

z 

3 

Fig.  3. 


•  See.  also,  Clifford's  "Common  Sense  of  the  Exact  Science^^'j^ 
XXIX 


XXX 


INTRODUCTION-, 


12      3      4      5      6      7 

Z 

3       .       . 

4 

6       • 


C-6 
Fig.  4. 


d-l 


A  Product  it  inilepenileiit  of  the  parting  of  its  factorf^^Thus,  7X5* 
(7X3) +  (7X2)  -  21  +  14-36.  or.  by  a-7 

shorthand.  a6—a#+a/— a(#+/).  Again, 
7X6-(6+l)  (8+2)  -  6(3+2)  +  lX 
(3+2)  -  80+6-36  or,  a6-  (c  +  d) 
X(#+/)-c(#+/)+d(#+/)-#(c+(i)+' 
/(c+d). 

A  l\>wer  is    indepeodent  of  the 
parting  of  the  index. — 

The  iirsi  powtr  of  a  number  is  the  num- 

ber  itself:  as  a^  —  a. 
The  squartoi  6-6«— 6X6;  of  a-o«— 

aa\  in  which  2  is  the  indtx. 
Th^cvbe  of  7-7»-7»X7«-7i+«-7X7» 

„ 71+1+1- 7X7X7;  of  6-6»-66» 

-666. 

The  fourth  powtr  of  a-a*-a>+»-o«+«— o»a-ao»-a^*-o*-'v/or  _ 

The /»/<Apow»r  of  2-2»-2X2X 2X2X2-2(2X2X2X2) -(2X2)  (2X2X2)- 

or,  2»-  2«+*-  2«+»-  2X2<-  2>X  ».  

Thtsquartroot  of  the  fifth  power  of  4  -  vl*  -  V4*+«  -  V4*X4  -  v^X 

vT-  4«vT-  16VT-  16X2  -  32:  orV4»  -  4* -_^*_-  4«  X4'- 

4X4**  -  4X4X4*  -  32;  or.  vl*  -  V¥x^  "^  V4«X4«X4  -  n/4«X 

>/4?X  vT-  4X4X2  -  32. 

Prom  the  above  it  will  be  seen  that  o^- 1,  for  a  *«"-" —"^  —  !• 

^ c 

Square  of  (a +1)  is  a  special  case  of  (a  +  6)>. 
(4+  1)1-  (4+  1)  (4+ 1)  - 4(4+  1)  +  1  (4+  1)  - 16  + 

4+4+1-26. 
(a+ 1)«-  (a+ 1)  (a+ 1)  -o  (a+ 1)  + 1  (a+  1)  -o«+ 

2a+l.  •« 

(a+6)«-(a+6)(a+6)-a(a+6)+6(o+6)-a«+    • 

2a6+6>.  0 

Again:(a-l)«-a«-2a+l;  and  (a-6)«-a«~2a6 

+^- 
Practical  application:  (21)«-(20+l)«  -  (20)«+2  - 

X  20+ 1-400+ 40+1 -441:  ^ 

also.  (19)*-(20-1)»-(20)«-(2X20)  +  1-400- 

40+1-361.  Fig.  6. 

Note. — By  making  6  extremely  small  compared  with  a,  in  the  case  of 
(0+6)',  it  will  be  seen  that  the  third  term  6*.  as  6  approach  zero,  can  be 
omitted,  as  it  will  be  the  sqtiare  of  an  infinitely  small  decimal  or  fraction. 
Hence,  the  limit  of  (a +6)*  as  6  approaches  zero,  is  o>+2a6,  or.  in  other 
words,  the  actual  increase  of  (a +  6)'  over  a\  where  6  is  infinitely  small,  is 
(a«+2a6)-a«-2a6. 

This  is  an  elementary  principle  of  the  Differential  Calculus — the  method 
of  limits. 


(a»-l)-(a+l)  (a-1)  is  a  special  case  of 
((j«-6»)-(o+6)  (a-6). 
(4«- 1)  - (4+  1)  (4- 1)  -  4  (4-  1)  +  1(4-  1)  - 

4X8+1X3-12+3-16. 
o«-l  -  (a+1)  (a-1)  -  a(a-l)  +  l  (a-1)  -  t 

a«-a+a-l-a«-l.  • 

a«-6«-  (a+6)  (a-6)  -  a  (a-6)  +  6  (a-6)  -    ^ 

a»-a6+6a-6«-a»-6«. 
Practical  application*  41 X  39- (40+ 1)  (40-1) 

-40»-f- 1600- 1-1699. 
Prom  a*''(a+ 1)  (o- 1)  + 1.  we  have  39«-  40X 

88+1-1620+1-1621. 


a-4  b- 


-^ 

♦  I 

1 

^ 

o«4 

Fig.  6. 

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INTRODUCTION. 


XXXI 


Spacb. 

Aa  Object  is  composed  of  layenand  boimded  by  •  surface. — ^The  surjac9 
q£  ea  object  has  a  definite  area,  but  as  it  has  no  thickness, 
ID  itaeH;  it  occupies  no  space.  On  the  other  hand,  the  layers 
fomposmg  the  object,  no  matter  how  thin  we  may  assume 
them  theoretically,  must  occupy  space  and  have  thickness. 
In  theory  we  assume  such  shapes  as  cones,  cylinders,  spheres, 
etc,  to  be  composed  of  an  infinite  number  of  layers  of 
an  infinitesimal  thickness,  U 

A  Suface  is  an  area  with  or  without  lineal  boundary. — 

The  surface  of  the  Barth,  of  a  chair,  of  a  cube,  or  of  any 
wlvJlr  object  can  have  no  lineal  boundary:    but  the  surface 
of  part  of  an  object,  as  of  a  continent,  of  one  face  of  a  cube.       „.     _ 
or  of  the  top  of  a  table  is  bounded  by  lines  along  the  edges       *^**  '• 
o€  the  siirface.    Neither  the  surface  nor  its  bounding  lines  can  have  thick- 
ness nor  occupy  space. 

The  surface  of  an  object  is  its  shape. 

A  Line  is  a  boundary,  division,  or  an  intersection,  of  surfaces. — ^The 
btmndary  of  a  surface  is  a  ctirved  or  broken  line  of  definite  length,  and  con- 
tinuousi  that  is,  without  terminal  points.  A  good  illustration  of  this  is  a 
traverse  survey,  as  arotmd  a  farm.  If  the  field  notes  do  not  "close"  they 
are  made  to  close  by  "adjustment." 

A  plant  surface  can  be  divided  bv  a  straight  line,  of  definite  length  only, 
that  is,  with  terminal  points  at  its  boundaries;  but  it  can  be  divided  also 
by  a  ammi  or  broken  contintious  line,  as  for  instance  by  a  circle,  entirely 
within  its  boundaries. 


Pig.  8. 


Ss 


Pig.  9. 


Pig.  10.  Pig.  11. 

The  intersections  of  the  surfaces  of  the  cube  furnish  the  right  angle  and 
the  5Quar€\  the  intersections  of  the  surfaces  of  the  wedge  furnish  the  triangle 
and  the  rectangle',  and,  similarly,  the  pyramid,  in  its  various  forms,  furnishes 
the  numerotis  polygons. 

By  cutting  surfaces,  the  cone  furnishes  the  point,  p,  the  straight  line,  p  s, 
the  truMngle,  pst,the  circle,  C,  the  ellipse,  E,  the  parabola,  P,  the  hyperbola, 
H,  etc.  Its  properties  embrace  such  a  wide  range  in  Analytic  Geometry 
that  the  subject  is  often  termed  Conic  Sections. 

The  boundary  of  a  surface  is  its  shape. 

Quantity. 

Quantity  is  a  summation  of  units,  of  one,  two  or  ttiree  dimensions. — 

The  first  involves  continuity,  length,  or  number;  as  time,  angles, 
vei^ts.  lengths,  money  and  numerals. 

The  second  involves  length  and  breadth,  or  area;   as  surface  measures. 

The  third  involves  length,  breadth  and  depth,  or  contents;  as  measures 
of  volume.  Digitized  by  GoOg le 


XXXII 


INTRODUCTION, 


Area  ii  •  summation  of  one  or  more  products  of  two  factors  each.^- 

If  we  divide  the  surface  of  the  right  _cl. 
triangle,  Fig.  12.  into  txtremely  thin 
strips  of  length  y,  and  thickness  /. 
and  then  move  the  apex  to  one  side. 
as  in  Pig.  18,  allowing  the  thin  strips 
to  slide  on  one  another,  their  ends  will 
still  form  straight  lines  from  the  apex. 
a,  to  the  base  of  the  triangle,  and  its 
height  and  area  will  remain  the  same. 
The  area  of  the  triangle  is  the  sum- 
mation of  the  areas  (yXt)  of  all  the 
thin  strips.    The  above  illustrates  two 


.        Fig.  12.  Fig.  13. 

principles,  namely,  simple  proportion  and  the  equation   of  the   straight 
line,  a§;  thus — 


Simple  proportion:  —  ■■  -r-. 


Equation  of  the  straight  line,  ae:  y— r-*.* 

The  straight  line  is  sometimes  called  a  curve  of  the  first  degree. 

The   same   law    holds   true  in  the  case  of  any  a 

figure,  as  Fig.  14  where  the  boundary  line  a#  is  a 
curve  of  the  second  degree:  for  it  is  necessary  only 
to  find  the  equation  ot  the  curve  in  terms  of  x  and 
y  so  that  for  each  value  of  x  we  may  know  the 
value  of  y.  In  either  case  we  derive  the  area  from 
the  summation  of  all  the  infinitesimal  strips  yt  be- 
tween the  limits  «— A  and  «— 0.  This  maybe  per- 
formed accurately  by  the  method  of  the  Calculus, 
by  assuming  an  infinite  number  of  infinitesimal 
strips. 

If  we  consider  Fig.  12  to  be  an  elastic  layer  of 
definite  thickness,  having  the  surface  as  shown,  and 
apply  a  lateral  pressure  at  the  apex,  a,  to  change  its  shape  to  Fig.  13.  we 
conceive  in  Mechanics  the  terms  forc$,  tlasticUy,  stress,  strain  and  shear. 


Fig.  14. 


'^ 

"1 

B 

Pig.  15. 


Length  is  a  summation  of  the  square  roots  of  the  sums  of  squares^ 

It  is  an  elementary  problem  to  prove  that  the  square  ^  \ 

H  (hypothenuse^  is  eciual  to  the  square  B  (base^  plus 
the  square  P  (perpendicular*),  by  the  proposition  that  H 
is  composed  of  two  rectangles  B'  and  P*  eaual  in  area  to 
B  and  P,  respectively.  From  this  principle  the  length 
of  any  cxirve  may  be  obtained  by  the  summation  of  its 
infinitesimal  parts. 

Thus,  required  (Fig.  16)  to  find  the  length  S  of  the 
curve  ac  between  the  limits  a;  =  c'  and  ic  — o'.    We  have 
here,  to  find  the  summation  of  the  infinitesimal  tangent 
lengths  ds  in  terms  of  dy  and  dx  for  every  change  of 
position  of  the  tangent    as   the  values  of  x  and  v 
change.    It  is  evident  that  each  infinitesimal  length 
ds  -■  Vrfx* + (i.v*.  hence  if  we  find  the  values  of  dx'^ 
and  dy'from  the  equation  of  the  curve,  by  the  Calcu- 
lus, we  can  get  the  value  of  ds  in  general  terms.    It 
only  remains  to  find  the  summation  of  all  the  values 
of  ds,  that  is,  S,  and  this  may  be  obtained  by  inte- 
gration, subtracting   the   result  obtained  by  mak- ' 
ing  xo-o',  from  the    result    obtained    by    making 

The  ratio  of  the  circumference  of  a  circle  to  its 
diameter  -  3. 1 4 1 592  + .  called  k.  Fig.  1 6. 

Volume  is  a  summation  of  layers ;  or  area  times  thickness. — If  a  beam 
of  homogeneous  material  and  of  rectangular    cross-section    be    loaded  so 

*  The  general  equation  of  the  straight  line  is  y  — mur  +  c,  in  iwhich  m  is  the 
tangent  of  the  angle,  and  c  is  a  constant.    In  the  above,  c— 0. 


INTRODUCTION, 


XXXIII 


thjit  it  deflects,  as  in  Pig.  17.  there  will  be  a  plane  s—s  throtigh  the  middle 
of  the  beam  which  will  not  change  from  its  original  length ;  that  is,  there 
vrill  be  no  stretching  or  shortening  of  the  fibers  along  this  plane,  which 
may  be  called  the  neutral  axis  of  the  beam.    If  now  the  be^  be  turned 


..p::: 


^ 


Pig.  17. 
cm  its  aide  and  again  deflected,  a  new  plane,  s*  —  s*t  at  right  angle  to  the 
first,  will  become  a  new  neutral  axis.  In  either  case  the  fibres  at  the  top 
of  the  beam  will  be  compressed  and  the  fibers  at  the  bottom  of  the  beam 
stretched,  equally.  Also,  the  stretching  or  compression  of  any  fibre  in 
the  beam  wiU  be  proportional  to  its  distance  from  the  neutral  axis.  In 
other  words,  while  the  beam  loses  in  voliune  above  the  neutral  axis  it 
gains  an  eqtial  amount  below.  The  intersection  of  the  neutral  axes  will 
also  be  found  to  be  at  the  center  of  gravity,  c.  g.,  of  the  section. 
The  center  of  gravity  may  be  defined  as  the  point  of  inter- 
section of  all  possible  neutral  axes,  for  no  matter  which  way  the 
beun  may  mst,  on  its  comer* or  otherwise,  the  neutral  axis 
wiQ  pa»  through  the  center  of  gravity  of  the  section. 

The  center  of  gravity  of  any  ngular  section,  as  a  square.    Pig.  18. 
rectangle,  parallelogram,  equilateral  triangle,  circle  orreg-     j- 
ular  polygon  is  in  the  center  of  the  figure.    (Pig.  18.)  i 

The  center  of  gravity  of  a  triangular  section  is  one-third 
the  height  from  cither  base.     (Pig.  19.) 

These  principles  furnish  the  rules  for  finding  the 
contents  of  the  cylinder,  circular  ring,  cone,  paraboloid, 
ellipsoid,  or  any  similarly  curved  bodies.* 

(kmsider  any  section  lying  wholly  on  one  side  of  the  axis 
of  revolution,  or  center  of  curvature:  multiply  the  area  of 
the  section  bv  the  distance  traversed  bv  its  center  of  grav- 
ity. The  product  will  be  the  volume  ox  revolution  of  that 
section. 

Por  example,  the  volume  of  a  cone  is  equal  to  the  area 
of  the  triuigle  of  revolution  X\  the  base  X  2k 


2^3 


-r—  ■■■:;•  X  area  of  base, 
o         o 

Position. 


(Pig.  20.) 


Pig.  20. 


The  Relative  Position  of  an  object  may  be  determined  by  ofu,  two  or 
ffcrw  quantities,  according  as  it  is  on  a  known  line,  surface  or  in  space.  The 
third  dimension  problem  can  be  reduced  to  the  second  by  passing  a  known 
sorface  or  plane  through  the  point  in  space;  and  this  can  be  reduced  to  the 
first  by  passing  a  known  line  throtigh  the  point  on  the  surface  or  plane. 
A  distance  along  the  line,  measured  to  the  object  in  question,  will  fix  its 
exact  position. 

TIm  Fodtiofl  of  a  Point  on  a  Plane. — 

The  polar  co-ordinates,  angle  oc  and  distance  D,  locate  the  point  P 
from  A.  Polar  co-ordinates  may  be  reduced  to  rectangular  co-ordtnaies,  x 
and  y.  Pig.  21. 


Pig.  21. 


Pig.  22. 


•  See  also  Pappus's  Theorems  for  surfaces  and  solids,  page  24^1e 


XXXIV  INTRODUCTION. 

A  point  P.  Pig.  22.  may  be  located  from  a  fixed  point  i4  by  a  diitance 
D,  and  from  a  fixed  line  r  —  K  by  a  distance  x.  li  D  and  x  are  allowed 
to  increase  and  decrease  with  constant  ratio,  the  point  P  will  trace  (1) 
the  parabola,  if  the  ratio  of  D  to  x  is  unity;  (2)  the  hyperbola,  if  the 
ratio  of  D  to  X  is  greater  than  unity;  and  (3)  the  ellipse,  if  the  ratio  of  D 
to  x'vt  less  than  unity. 


Fig.  23.  Fig.  24. 

A  point  P.  Fig.  23,  may  be  located  from  two  fixed  points:  A,  by 
distance  D,  and  B,  by  distance  d.  If  the  ratio  of  D  to  d  is  allowed  to  in- 
crease and  decrease,  but  so  their  sum  will  remain  constant,  the  point  P 
will  trace  an  ellipse. 

The  results  of  experiments  are  conveniently  platted  on  cross-section 
paper,  and  a  curve  drawn  as  nearly  regular  as  possible  through  the  aver- 
age position  of  the  points.    The  curve  then  serves  as  a  formula  for  future 


Pig.  2ft. 

If  the  curve  is  of  the  second  degree  it  can  be  represented  by  a  straight 
line  if  logarithmic  cross-section  paper.  Pig.  26,  is  used.  Hydraulic  formu- 
las and  experiments  are  often  platted  on  -  this  kind  of  paper,  for  sim- 
plicity. ^         •:  ^ 

Digitized  by  VjOOQ  IC 


INTRODUCTION,  XXXV 

Motion. 

A  man  starts  \o  row  a  boat,  at  a  constant  rate  of  speed,  directly  across 
the  stx«am  irom  A  Xo  B,  not  allowing  for  any 
cnxrent.  On  reaching  the  east  bank*  he  finds 
he  has  landed  at  D.  If  the  current  was  uniform 
in  all  parts  of  the  stream  his  course  was  the 
straight  line  AoD,  and  his  motion  down  stream 
uuxfarm  in  passing  from  the  west  to  the  east 
bank.  If  the  current  was  very  strong  at  the 
west  bank  and  gradually  lessened  toward  the 
east  bank  his  course  was  the  line  AcD  and  his 
mouon  down  stream  a  retarded  one — uniform- 
ly retarded  if   the   current   at  any  point   was 


"^C 


(uxectly  proportional  to  its   distance    from   the 
'.  bank.     If  the   current  gradually 


^ ^    increased 

toward  the  east  bank  his  course  was  the  line 
AbD  and  his  motion  down  stream  an  accelerated 
one — uniformly  accelerated  if  the  current  at 
any  point  was  directional  proportional  to  its 
dirtancr  from  the  west  bank. 

The  averagf  vehcity   of  the  (surface  of  the) 
stream  is  the  same  for  all  three  cases  above  pj^  26 

cited  if  the  boat  lands  at  the  same  point,  D.  ^'      ' 

Umiform  velocity  or  motion  may  be  represented  by  a  straight  line,  i.  e., 
curve  of  the  first  dM(ree;  uniformly  accelerated  or  retarded  velocity  or 
motion,  by  a  curve  of  the  second  degree. 

The  accfkratdon  per  second  of  time  due  to  the  gravity  of  the  earth  on 
any  body  falling  in  vacuo  is  practically  constant.  It  is  designated  by  the 
letter  c.  and  its  value  is  about  32.16  ft.  per  sec.  It  vanes  somewhat 
with  the  elevation  above  sea  level  and  with  the  lattitude  of  the  place. 

Mass  (Matter).  Porcb  and  Inertia. 

These  are  convenient  terms  used  in  Applied  Mechanics  to  express  certain 
oo-relative  ideas. 

We  may  consider  mass  as  matter,  or  that  property  which  cannot  be 
destroyed,  because  matter  is  indestructible,  although  the  body  of  which 
it  is  composed  may  change  its  form  or  apparently  disappear.  Mass  is 
pcoportiooal  to  weight,  and  the  unit  of  weight  is  one  pound.     The  mass 

W 
of  a  body  is  its  weight.  W,  divided  by  gravity  acceleration.  «.  as  Af — — ; 

or.  the  mass  of  a  body  is  measured  by  a  force,  F,  which  will  produce  an 
acceleration,  a,  as  Af — .      The  acceleration  in  either  case  is  the  velocity 

attsined  at  the  end  of  the  first  second  of  time. 

Forct  is  a  shorthand  expression  of  stating  the  value  of  one  mass  acting 
OQ  another,  by  pressure  or  impact.  Force— mass  X  acceleration.  F— Afa. 
Its  onit  is  one  pound. 

Inertia  is  a  negative  term  implying  inherent  inactivit^r  in  a  relative 
nsnaen  the  tendency  which  a  oody  has  to  continue  doing  what  it  is 
alresdir  doing — if  at  rest  to  remain  at  rest,  and  if  in  motion  to  continue 
in  motion  in  the  same  direction  and  at  the  same  velocity. 

EXPERIMENTATION. 

Several  years  ago  the  late  Professor  Toseph  L.  LeConte»  in  a  very  elabor- 
ate scientific  discussion,  "proved  conclusively"  that  the  heavier-than-air 
fiying-machine  was  an  absolute  impossibility;  and  yet,  today,  aerial  flights 
in  such  machines  are  attracting  but  passing  interest. 

Our  collie  professors  are  daily  teaching  the  maxim:  "There  is  no  con- 
fflct  between  theory  and  practice."  This  should  be  restated  as  follows: 
"There  can  be  no  conflict  between  correct  theory  and  perfect  practice,  but 
neither  can  always  be  attained."  The  theory  of  Professor  LeConte  was  in- 
correct—but nevertheless  a  theory — and  the  first  experiments  in  flying,  by 
Octave  Chanute.  were  simply  imperfect  ones.  ^  g  tized  by  GoOglc 


XXXVl  INTRODUCTION, 

Joseph  H.  Choate,  the  able  lurist.  in  an  address  before  a  society  of  engi- 
neers,  a  tew  years  ajso,  exposed  nimself  to  criticism  in  statins  that  engineer- 
ing was  an  exact  science — a  statement  that  is  very  far  from  the  truth. 

The  great  advance  in  the  whole  field  of  engineering— quite  phenomenal 
during  the  post  decade,  especially— is  due  almost  wholly  to  experimental 
work,  scientifically  conducted. 

Manasement. 

Scientific  management  is  becoming  a  potent  factor  in  the  industrial 
world,  and  is  destined  to  possess  an  increasing  sphere  of  influence  in  the 
future.  It  simply  means  inielligent  cooperation:  distinctly  opposed  to  the 
old  S3mtem  of  bo^tsm,  which  is  more  or  less  militant  and  invites  toadyism^ 
a  qualification  distasteful  to  every  honest  workman. 


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SIGNS  AND  ABBREVIATIONS. 


Abbreviatioiu. — ^The  following  abbreviations,  and  others  not 
listed  here,  are  used  constantly  thoughout  this  volume  in  order  to  conserve 
space.  In  general,  they  appear  in  the  text  after  the  full  word  has  been  used 
so  there  can  be  no  doubt  as  to  the  meaning: 


abut 

—  abutment. 

covers 

-co-versed  sine. 

Bccel 

—  acceleration. 

=  (hyp  -  perp)  +hyp. 

ans 

—answer. 

exsec 

—  exsecant. 

approz 

—  approximate. 

—  (hyp  -  base)  +  base. 

cen 

—center. 

coexsec 

— co-exsecant. 

orcum 

-  (hyp  -  perp) -•- perp 

diag 

—  diagonal. 

sec,  8. 

—  seconds. 

diam 

—  diameter. 

min,  m. 

—  minutes. 

dist 

—  distance. 

hrs.h. 

—hours. 

^^ 

z^''- 

d. 
mos. 

—  days. 

—  months. 

hor 

—horizontal. 

yrs. 

^  years. 

— lor  instance. 

ht 

-height. 

e.g. 

hyp,h]rpoth  —  hypothenuse. 

i.c. 

-that  is. 

hyp  log 

— hyperbohc  log. 

etc. 

—and  so  forth. 

log 

— et.  cetera. 

perp 

—perpendicular. 

e.g. 

—center  of  gravity. 

prw 

^pressure. 

ms. 

—  inches. 

Pt 

—  point. 

ft. 

-feet. 

rad 

—  raditis. 

r^ 

—  yards. 

tang 

—  tangent. 

—  pounds. 

vd,veloc 

-velocity. 
—  vertical. 

pte. 

—  pints. 

vert 

qts. 

—  quarts. 

vol 

—  volume. 

e 

-gallons, 
-bushels. 

mrt 

—wrought. 

wt 

-weight. 

bbls. 

—barrels. 

ttn 

—  sine  —  perp  -»- hyp. 

lin. 

-lineal. 

008 

— cosine  —  base -»- hyp. 

sq. 

—  square. 

tan 

—  tangent  —  perp  -t-  base. 

cu. 

—  cubic. 

cot.cotan 

—  cotangent. 

B.M. 

—  board  measure. 

-base -4- perp. 

M..  B.  M. 

-thousand  ft.  B.  M. 

sec 

—secant. 

H.P. 

—horse- power. 

— hyp  +  baae. 

A.  W.  G. 

—  American  wire  gauge 

—  Birmingham  wTG. 

C3C.C0SCC 

—  cosecant. 

B.  W.  G. 

-  hyp  ■<- perp. 

r.  p.  s. 

-revolutions  per  sec. 

rtn 

"■versed  sine. 

-  (hyp  -  base)  -t-hyp. 

r.  p.  m. 

-revolutions  per  min. 

XXXVII 


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XXXVIII 


SIG.VS  AND  ABBREVIATIONS, 


Qreek  Alphabet. — Greek  letters  are  used  in  the  sciences  to  designate 
certain  properties,  as  angles,  latitude,  temperature,  etc. 


English 
Equiva- 
lents. 

Greek  Letters. 

Used  to  designate. 

Name. 

Capital 

SmaU 

A 
B 
G 
D 

E 

Z 

E 
Th 

L 
M 
N 
X 

o 
P 

R 

S 

T 

6 

Alpha 
Beta 
Gamma 
DelU 

Eptilon 

Zeta 
Eta 
Theta 
Iota 

Lambda 

Mu 

Nu 

Xi 

Omicron 

Pi 

Rho 
Sigma 

Tau 
Upsikm 

Chi 
Psi 
Omega 

A 
B 

r 
d 

E 

z 

B 
0 
I 
K 
A 
M 
N 
S 
0 

n 

p 
I 

T 

r 

# 
J 
r 
a 

a 
0 

r 
d 

€ 

( 
C 

X 

/» 

V 
0 

r 

P 
o,  S 

X 

« 

Angles  and  coefficients. 
Angles  and  coefficients. 
Angles,  coefficients,  and  specific  gravity. 

density. 
Eccentricity;  base  of  natural  logarithms  — 

2.7182818:  strain. 
Coefficients,  co-ordinates. 
Coefficients. 
Angles  and  coefficients. 

Coefficients. 

Latitude,  angles  and  coefficients. 

Angles  and  co-efficients. 

Coefficients,  co-ordinates. 

n  signifies  continued   product,   as    77  8    ■• 

1X2X8. 
ir- 3.14169+ -ratio  of  circum  to  dia.     — 

180*»of  arc. 
Rad  of  gyration;  rad  of  curvature;  ratio. 
I  signifies  summation:    as  IW  means  the 

summation  of  all  the  weights  W*,  W", 

W",  etc.,  in  any  system.   In  the  Calculus 

it  is  replaced  by  the  symbol  1 . 

0  is  used  as  a  coefficient;  stress. 
Coefficients;  temperature,  time. 

Angles  and  coefficients. 
Coefficients;  angular  velocities. 

a,  6,  c, 

---  x,y,$. 


± 

=F 

X 

a.b 


MATHEMATICAL  SYMBOLS. 

Represent  known  or  constant  quantities. 

Represent  unknown  or  variable  quantities. 

Equals,  is  equal  to. 

Plus,  as  3+2—6;  positive,  as  +  J— +.6;  extension,  as  ^  — 

.14286+. 
Minus,  as  6~ 3—  2;  negative,  as  —  i—  —  .6;  contraction,  as  i— ^ 

Plus  or  minus,  as  \/4  —  ±  2. 

Minus  or  plus. 

Times,  multiplied  by;  as  3X2  — 6;  aXb''a.b''ab. 

"oXb'^ab. 

Divided  by;  as  8+2-4;  8:2-4;  8/2-4;  |  -4. 


r-    Divided  by. 
o 

a/b    Divided  by. 


d  by  Google 


COMMON,    GREEK.    MATHEMATICAL,  XXXIX 

::    :  Proportion;  as  2:3::4:6;  means  }—  «;  reads  "as  2  is  to  8  so  it 

4  to  6."  ® 

4.3  ->4t),-4^.etc. 

>  Is  greater  than,  as  4  >  3;  reads  "4  is  greater  than  8." 

<  Is  less  than,  as  3<  4;  reads  "  3  is  less  than  4." 

7  Is  equal  to  or  greater  than;  as,  a 7 4. 

^  Is  equal  to  or  less  than;  as,  4Ta. 

/.  Therefore,  hence. 

*.*  Because. 

oo  Infinity;  as,  ^r  ->  oo. 

oc  Is  proportional  to,  varies  directly  with;  also,  angle  alpha. 

I  Bar 

—  Vinculum 

( )  Parenthesis 

[  ]  Bracket 


II 


a+6Xc-<r(a+6)-ac+o6. 
Abbreviation;  2Ca(6  +  r)  +  it]  -  2o(6 + c)  +  2«. 

ered  or  enclosed  —  2o  [o (6  + 1)  4- x\-\- ad 

n«i/«.  must  be  "taken  -2a«(6  +  c)  +  2ajc+ad 

""**  together."  -2a«i+2a«c+2a«  +  ad. 

>/    Radical  sign,  square  root.    Thus  s/a  —  >/a — ai— — r- 

V    Cube  root. 

^    fif^  root. 

cfl    The  square  or  second  power  of  a,  as  a Xa.  or  aa, 

X*    The  i«til  power  of  «.  ««»-  — -;  «»-«;  sfi"  1. 

a        </    Continuation.    Thus,  a.  6.  c.  d.   (Either  dots  or  dashes  may  be 
used.) 
a*,  h",  x"'    Primes,  to  distinguish  letters ;  as  a  —  prime  ,h  —  2  —  prime  or  A — 
second,  x—Z  —  prime  or  « — third. 
%.  Os.  A«    Subs,  to  distinguish  letters;  x  sub  1.  a  sub  2.  A  sub  4. 

^    Inverted   caret   indicates  repeating  decimal;    as,   0.016''6— 

0.0166666 . 

/—    Number,  as  #2— nimibcr  2. 

—  #    Pound,  or  pounds,  as  4#>-i 4  pounds  or  4  lbs.  in  weight. 
6'  —  3*    Feet  and  inches  (linear  measure) ;  as  6  feet  3  inches,  or  6  ft.  8  ins. 
(P-IS'-IS*    Degrees,  minutes  and  seconds  (of  arc) ;  as  0  dcg.,  18  min..  15  sec. 
or  18m.  156. 
O    Round,  diameter.     6'*  — 6  ft.  diameter-  6'  dia.     3*"  — 3  ins. 

diameter  —  3*  dia. 
D    Square.    2'a-2  ft.  sq.;  3^-3  ins.  sq.     4°'- 4  sq.  ft.;  9°*- 

9  sq.  ins. 
H   Cube.  2«-2  ft.  cubed;  4'»- 4  ins.  cubed.    27^-27  cubicft 
A  Z    Angle;  A  angles. 
L    Right  angle. 
JL    Perpendicular  to. 
II     Parallel  with. 
®   Circle. 
/^    Triangle. 
^    Right  angle  triangle, 
a    Square. 
CZD    Rectangle. 


Parallelogram. 

Digitized 


by  Google 


XL 


SIGNS  AND  ABBREVIATIONS. 


T^     n  •  < .  A  circumference      ,    .    ,  ,  «aa     « 

Pi  — 3.1416— —  -  J. ,_ of  circle;  or,   —180*  of  arc 


180* 


diameter 
-  67.2968*  nearly. 


«  — Base  of  Naperian.  hyperbolic,  or  natural  logarithms  — 
2.7182818+ . 


sin  a     Sine  of  the  angle  a. 
tin~*  a     Inverse  on  anti-sine  of  a;  the  angle  whose  sine  is  a.    It  is  net 
1 
sin  a' 
sin  a-*    —  (sin  a)  -*  —  • 


see  below. 
1 
sina* 

d    Differential  (in  Calculus) ;     d  (;r^  —  2xdx, 
I   Sigma,  summation. 
A   Delta,  difference;  usually  considered  as  a  very  small  quantity. 


/: 


Integral  (in  Calculus) :  the  reverse  of  differentiation 


Intergral  between  limits  h  and  k 


2xdx^h*-k^, 


;  J2xdx^s 


MECHANICAL  SYMBOLS. 


L  or  1  —  length. 
M  or  m  —  mass. 
T  ort  =-time. 
V  —  velocity. 

a  —acceleration,  a  —  r?. 

g  -gravity  acceleration, 

-  ^-32.16  ft.  per  sec. 
^  per  sec. 

Wor  w==work,  or  weight. 
P  =  power. 

F  =  force, 

ft.-lbs.   =  foot-p>otmds. 
I  —moment  of  inertia. 

E  —  modulus  of  elasticity. 

D  —  diameter. 


r  —  radius. 

H.  P.      =  horse-power. 

B.H.P.   —  brake  norse-powcr. 

I.  H.  P.  —indicated  horse-power. 

M.  E.  P.  —  mean  effective  pressure. 

r.  p  m.  —revolutions  per  minute. 

C.  G.  S.  —centimeter-gram-seconds 

(system). 
A.W.G.  —American  wire  gauge. 
B.W.G.  =  Birmingham  wire  gauge. 
B.  T.  U.  -  British  thermal  unit 

—  p>ound -degree- Fahr. 
cal.          =calorie  (French). 

—  kilogram -degree-Cent, 
lb. -cal.    =  pound-calorie. 

—  pound-degree-Cent. 


ELECTRICAL  SYMBOLS. 


E.. 
P. 
C 
R 


E.M.F. —electro-motive  force. 
D.  —  potential  difference. 

—current. 

=  resistance. 

—  specific  resistance. 
-■  quantity. 

«=  capacity. 

—  inductance. 
M.           —ampere  meter. 
M.           —volt  meter. 

M.  —field  magnet. 

—  positive  pole. 

—  negative  pole. 


6 


Galvanometer.        Ammeter. 


•"0_ 
-•I    m\- 


—  volt,  potential. 

—  ampere. 

—  megohm. 

.  =»  British  Association  units. 

—  microfared. 

—  Henry, 

—  Joule. 

—  kilowatt. 

=  complete  period 
(alt.  current). 

—  dynamo. 

—  battery. 


-©-         -^ 


Voltmeter.  /^Wattmeter. 

Digitized  by  VjOC 


MATHEMATICAL,    MECHANICAL.    ELECTRICAL,      XH 


! 

Of 

verpcr 
ilvcr. 

i 

1 

1 

O 

milligrams  of  sil 

ard  Dmniel  Cell, 

milligrams  of  s 
U.  S.  cable. 

a 
1  i 

1 

1      . 

§1 

1.118 

stand 

1.118 
oiD. 

S     o 

2.2 

eposits 
second. 
26  of  a 

eposits 
6  knots 

§    -5 

-H          00 

'^13 

D       CO 

^ 

Q    *    Q«           « 

D       CM 

T1 

lO    _ 

ISI 

h 

s.    &    &&       gg    §    1 

1 

_u_ 

•4 

^     ^     ^^ 

_ 

V 

H 

1 

!• 

o 

1 

H  ' 

c 

1 

S 

dI 

3 

1 

^  1 

8 

1 

< 

•s 

« 

3' 

1 

I 

i-d 

" 

K 

i 
1 

.s 

*?; 

jj 

rrcnt 

sctromo- 
ive  force.. 

lantity 

pacity. . . . 

0 

c 

1 

ii 

(S 

U     W     OO          ;{ 

s  1 

1 

Pfi 

O     W    OW        :  ( 

s:  i 

>. 

CO 

:     :     :  !      -d 

S 

1 

E 

Ampere.. 

Volt 

Coulomb. 
Farad... 

Microfara 

s  1 

V^ 


-^   s^   ^  ^  a 


J^  I   D     I   a   II   B 

o     •-   S     3  0-8  5? 


S,2 
c 


sa 
a 


B 


D    B     I    I    g    I 


^3B  i^ 


«1 


O  0>«      P^      W      ^H^S 


H    H  H  H  , 


I  I     0     I   D 

iis  8.  8.    -a 

I  •o's    I 

S  g    g  Xti 

8  +  +  •  s  5 

I  -g  g  si 

I  I  I  II  I 

«M«M  O      «M        9 

o  o  a  o  «  V 

>>Q  u    >«    u  g 


XLII 


SIGNS  AND  ABBREVIATIONS, 


MAQNETIC  SYMBOLS. 


N  —  north  pole. 
S  —south  pole. 
tn  —  strength  of  pole. 

B- magnetic  force  (C.  G.  S.). 
—  magnetic  inductance 
(C.G.S.). 
I    —intensity  of  magnetization. 


u  —magnetic  permeability. 
k  —  ma^etic  susceptibility. 
H  —horizontal  intensity  oiearth'i 

magnetism. 
Z  —reluctance. 


MEDICAL  SIGNS  AND  ABBREVIATIONS. 

R  (Lat.  Recipe},take:  aa.  of  each;  tb.  pound;  8.  oimce;  5.  drachm: 
3,  scruple;  V\,  mmim,  or  drop;  O  or  o,  pmt;  f  ^,  fluid  ounce;  f  3,  fluid 
drachm;  as,  8  ss,  half  an  ounce;  Si*  one  ounce;  l^ias,  one  otmce  and  a  half; 
Sij.  two  ounces;  gr.,  grain;  Q.  b..  as  much  as  sufficient:  Ft.  Mist.,  let  a 
mixttire  be  made;  Ft.  liaust.,  let  a  draught  be  made;  Ad.,  add  to;  Ad. 
lib.,  at  pleasure;  Aq..  water;  M.,  mix:  Mac.,  macerate;  Pulv.,  powder;  Pil.. 
pill;  Solv..  dissolve;  St.,  let  it  stand;  Sum.,  to  be  taken;  D.,  dose;  Dil., 
dilute;  Pilt.,  filter;  Lot.,  a  wash;  Gaig.,  a  gargle;  Hor.,  Decub.,  at  bed 
time:  Inject.,  injection;  Gtt.,  drops;  ss,  one-half;  Ess.,  essence. 


SURVEYING  SYMBOLS. 

(U.  S.  Public  Lands  Surveys.) 
The  following  contractions  are  authorized  to  be  used  in  the  preparation 
of  field  notes,  transcripts,  inspection  reports  and  similar  records,  and  no 
others  should  be  introduced: 


A. 

a.  m. 
A.  M.  C. 

asc. 

astron. 

bdy. 

bdrs. 

bet. 

B.O. 

B.T. 

C.C. 

chs. 

cor.,  cors. 

corr. 

decL 

dep. 

desc 

dia. 

diff. 

dist. 

D.S. 

E. 

elong. 

frac. 

ft. 

G.  M. 

h.,  hrs. 

ins. 

lat. 

L.C. 

Iks. 

1.  m.t, 

long. 

m. 


for  acres. 

^t    ' 

"  forenoon. 

"  aux.  meander  comer. 

mer. 

**  ascend. 

mkd. 

"  astronomical. 

N. 

"  boundary. 

NE. 

"  boundaries. 

NW. 

'*  between. 

obs. 

"  bearing  object. 

obsn. 

"  bearing  tree. 

g-or 

**  closing  comer. 

"  chains. 

Pr.  Mer. 

Pt.of  Tr. 

**  correction. 

isec. 
R..  Rs. 
red. 

"  declination. 

"  departure. 

"  descend. 

S. 

"  diameter. 

S.C. 

*'  difference. 

SE. 

••  distance. 

sec.,  sees. 

*'  deputy  survejror. 

S.  M.  C. 

••  east. 

sq. 

"  elongation. 

St.  Par. 

*•  fractional. 

SW. 

"  foot,  feet.     ^ 

T..orTp. 

"  guide  meridian. 
"  hour,  hours. 

Ts.  otTps. 

temp. 
U.C. 

*'  inches. 

'*  latitude. 

var. 

"  lower  culmination. 

W. 

"  links. 

w.c. 

"  local  mean  time. 

w.  corr. 

"  longitude. 

W.  P. 

"  minutes. 

w.t. 

for  magnetic 
'  meander  corder. 
'  meridian. 
'  marked. 
'  north. 
'  northeast. 
'  northwest. 
'  observe. 

observation. 

afternoon. 

Polaris. 

principal  meridian. 

point  of  triangulation. 

quarter  section. 

range,  ranges. 

reduce,  reduction. 

south. 

standard  comer. 

southeast. 

section,  sections. 

special  meander  comer. 

square. 

standard  parfdleL 

southwest. 

township. 

townships. 

temporary. 

upper  culmination. 

variation. 
'  west. 

'  witness  comer. 
I  watch  correction. 

witness  point. 
'  watch  t'me. 


For  ordinary  surveying  abbrevations  see  general  text  on  Surveying. 
Section  58. 


d  by  Google 


1.— ELEMENTARY  ARITHMETIC. 

NUMBERS. 
Ronuui  System. — ^This  system  is  nsed  in  the  arts,  for  dates,  for  number' 
ing  chapters  in  Uterature,  and  for  distinctive  numbering  where  the  Arabic 
Dumerals  will  not  suffice.    It  employs  seven  letters,  corresponding  with  the 
Arabic  numbers,  as  follows: 


Roman... 

.  I 

V 

X 

L 

C 

D 

M 

Arabic... 

.   1 

5 

10 

50 

100 

500 

1000 

Higher  basic  denominations  are  sometimes  represented  by  the  letters 
C,  D  and  M.  inverted,  but  they  are  not  in  general  use.  The  following  table 
wiU  be  foimd  useful  in  expressing  any  number  by  a  combination  of  these 
letters. 

1. — Roman  Numbrals. 


Roman 

Arabic 

Units. 

Thousands. 

Htmdreds. 

Tens. 

Units. 

II 

C 

X 

I 

CC 

XX 

II 

ccc 

XXX 

III 

3     ^ 

CD 

XL 

IV 

D 

L 

V 

DC 

LX 

VI 

DCC 

LXX 

VII 

DCCC 

LXXX 

VIII 

DCCCC 

XC 

IX 

To  write  any  number  in  Roman  system:  Begin  with  the  highest  de- 
nomination of  the  number — tens,  hundreds,  thousands,  etc. — ^and  pick  out 
the  letter  or  letters  in  the  Roman  colxmin.  corresponding  with  that  denomi- 
natioo  and  opponte  the  proper  figure  in  the  Arabic  column;  then  proceed 
in  the  same  manner  with  each  figure  of  lower  denomination.  Thus,  3—  III; 
34-XXX  IV  -  XXXrV:  648  -  DC  XL  VIII  -  DCXLVIII:  1799  - 
H  DCC  XC  IX  -  MDCC^dClX;  1900  -  MDCCCC  (preferred)  -  MCM. 

Arabic  System. 


w  H  P 


li 


0.000.087,054.32     1.123.456 


0  0  0 


This  number  is  read  thus:  "Nine  himdred  eighty-seven  million,  six 
hundred  fifty-four  thousand,  three  hundred  twenty-one  .  .  .  and  one  hundred 
twenty-three  thousand,  four  hundred  fifty-six,  millionths."  By  moving  the 
decimal  point  to  the  right  or  left,  the  number  is  respectively  muHiplted  or 
iind^d  by  ten,  times  the  number  of  places  moved. 


.    Digitized 


by  Google 


J 


(a.: 

(6) 


2  l.-^ELEM£i^TARY  ARITHMETIC. 

'  '  Primes,  Miittiples  'and  l^acfors. — A  i^rime  number  differs  from  a  mul- 
tiple m  thaf  it  cannot  bfe  t&ctOred;  that  is,  it  is  not  exactly  divisible  by  any 
other  number,  except  1.  There  is  no  known  positive  rule  for  detecting  ali 
prime  numbers;  tentative  rules  have  been  framed  from  time  to  time  only 
to  fail  high  up  in  the  scale.  But  negative  rules,  universal  in  their  appli- 
cation, may  be  stated  as  follows: 

\a.)  No  even  number  (2  excepted)  is  a  prime,  because  divisible  by  2. 
'6).  No  number  (3  excepted),  the  sum  of  whose  digits  is  divisible  by  3,  is 
a  prime,  because  itself  divisible  by  8.    Example:   171  (1  +  7-1-1  —  ») 
is  not  a  prime  number,  because  9  is  divisible  by  3. 
(c.)    No  number  (5  excepted)*  endins  in  5  or  0,  is  a  prime,  because  divisible 

by  6.    Examples:    16.  30,  125.  are  divisible  by  5. 
(d.)  No  number  composed  of  prime  factors  can  have  more  than  one  set  of 
prime  factors.    Example:    1001  —  7X11X13;   and  7,  11  and    13  is 
the  only  set  of  prime  factors. 
From  the  above  we  rightly  conclude  that  all  numbers,  excepting  2  and  6, 
which  end  in  2,  4,  5.  6,  8  and  0,  are  multiple  or  composite;   that  a  multiple 
may  end  in  any  figure;   and  that  the  ending  of  prime  numbers  is  limited 
strictly  to  the  digits  1.  3,  7  and  9.     Furthermore,  we  may  examine  any 
number  ending  in  1,  3,  7  or  9  to  see  if  the  sum  of  the  digits  is  a  multiple 
of  3;  if  so,  the  number  is  composite  and  divisible  by  3;  but  if  not,  it  may 
be  either  prime  or  composite. 

Table  2.  following,  contains  a  list  of  numbers  up  to  9600,  which,  by  the 
preceding  rules  and  analysis,  cannot  be  detected  as  prime  or  composite. 
The  numbers  are  composed  of  hundreds  at  the  left  oi  the  lines,  and  tens 
and  units  at  the  top  ot  the  columns.  At  the  intersection  of  the  respective 
line  and  column  of  a  niunber  will  be  fotmd  the  smallest  prime  factor  (above 
unity)  of  that  numbet.  K  the  niunbcr  is  prime,  the  intersection  will  be 
represented  by  two  dots. 

Tile  elimination,  by  Rule  (6),  of  numbers  ending  in  1.  3.  7  and  9  which 
may  be  factored  by  3,  makes  it  convenient  to  separate  the  table  into  three 
parts  by  steps  of  300,  in  order  to  condense  it.    The  arrangement  is  as  fol- 
lows: 
Sn  +  0.    This  part  (1)  contains  hundreds  beginning  with  0,  as  000.  300,  600, 

900.  etc.    Example :    2400 -(3x8-1-0)  hundreds. 
Sn-¥l.    This  part  (2)  contains  hundreds  beginning  with  100,  as  100,  400. 

700,  1000.  etc.    Example:    6200=  (3 X  17  +  /)  hundreds. 
3n+2.    This  part  (3)  contains  hundreds  beginning  with  SOO,  as  200,  600. 
800.  1100.  etc.    Example:    3600- (3 X  11 +f)  hundreds. 
Example.— What  kind  of  a  number  is  27,489? 

Solution. — ^The  sum  of  its  digits  is  30,  hence  3  is  a  factor.  3  )  274S9 

From  part  2  (Si  -5»  +  ;)  of  table,  the  smallest  factor  of  9163  is  7.  7  )  9163 
From  part  2  (/5-5n  +  /)  of  table,  the  smallest  factor  of  1309  is  7.  7  )  1309 
From  part  2  (/-5n  +  /)  of  table,  the  smallest  factor  of  187  is  11.  11  )  187 
From  part  1  (0— 5m  +  0)  of  table.  17  is  foimd  to  be  a  prime.  17 

Answer. — 27489  is  found  to  be  a  multiple  or  composite  number  whose 
prime  factors  are  3.  7,  7,  11  and  17;  and  from  Rule  (a)  we  learn  that  these 
are  its  only  prime  factors. 


d  by  Google 


NUMBERS. 


2. — Primes,*  Multiplbs  and  Factors. 
Part  1.— (5n-»-0)  Hnndrtds. 


Tens  and  Units. 


JV 

01  07  11  13  17 

19  23 

29  31  37  41  43  47  49 

63  59  61  67  71  73 

77  79  83  89  91  97 

000 

7 

7 7  .. 

3« 

7 

11  17 

7  ..  ..  11  7  ..  .. 

..  ..  19  ..  7  .. 

13 17  .. 

«ao  ..  ..  13  ..  .. 

9t»    17  ..  ..  11  7 

..  7 
..  13 

17  ..  7 11 

..  7  ....  23  ..  13 

23  11  .. 

..  7  31  ..  ..  7 

..  7  ..  13  ..  17 
..  11  ..  23  ..  .. 

I2W  ..17  7  ..  .. 

23 

17  11  29  .. 

7  ..  13  7  31  19 

• 

..  ..  7  ..  ..  11 
17  11 

I5«  It  11  ..  17  37 
IBOO  ..  13  ..  7  23 

7  .. 
17  .. 

11  ..  29  23  ..  7  .. 
31  ..  11  7  19  ..  43 

19  ..  ..  7  37  .. 
....  7  ..  31  7 

ZlOvl  11  7  ....  29 
24«'  7  29  . .  19  . . 

13  11 
41  .. 

19  7 

7  11  ..  ..  7  ..  31 

..  17  ..  11  13  41 
11  ..  23  ..  7  .. 

7  .  37  11  7  13 
..  37  13  19  47  11 

2700;  37 11 

1 

..  7 

....  7  ..  13  41  .. 

..  31  11  ..  17  47 

..  7  11  

JOOOj  ..  31  ..  23  7 
33«j  ....  7  ..  31 

13  7  ..  ..  17  11  .. 

....  47  13  ....  17 

43  7  ....  37  7 
7  ..  ..  7  ..  .. 

17 11  19 

11  31  17  ....  43 

2S4» 

3900 

4^ 

13  ..  23  ..  .. 

47  ..  ..  7  .. 

7  .. 

19  ....  11  ..  7  41 
..  ..  31  7  ..  ..  11 

13  ..  7  19  ..  .. 
59  37  17  ..  11  29 

17  ..  .. 

. .  13  29  7  . .  . . 
41  23  7  ..  13  7 

1 

'..  7  ..  11  .. 

..  41 

..  ..  19  ..  ..  31  7 

7  11  ..  ..  7  .. 

4509 

4aoo 

7    13  ..  .. 

7  23  13  19  7  ..  .. 
11  ..  7  47  29  37  13 

29  47  ... .  717 
23  43  ..  31  ..  11 

23  19  ..  13  ..  .. 

,  ..  11  17  ..  .. 

61  7 

..  7  19  ..  67  59 

5100  .  ..  19  ..  7 
MOO  11  ..  7  ..  .. 

..  47 
..  11 

23  7  11  53  37  ,.  19 
61 13  .. 

..  7  13  ..  ..  7 
7  53  43  7  ..  13 

31  ..  71  ..  29  .. 
11  17  23 

570O  ..  13  ..  29  .. 

7  69 

17  11 7  .. 

11  13  7  73  29  23 

63  ..  ..  7  .11 

«IGO  17  .  ..  7  11 

«300|  ..  7  ..  69  .. 

13  19 
71  .. 

..  37  ..  7  ....  23 
..  13  ..  17  ..  11  7 

..  73  11  ..  13  .. 
23  .. 

59  ..  7  ..  ..  7 
7  ..  13  ..  7  .. 

«00'  7  ..  11  17  13 

0900.  67  ..  .  31  .. 

..  37 
11  7 

7  19  ..  29  7  17  61 
13  29  7  11  53  ..  .. 

59  7  .. 

17 19 

11  ..  41  ..  ..  37 
..  7  ..  29  ..  .. 

72891  19 7 

..  31 

..  7  ,.  13  ..  ..  11 

..  7  53  13  11  7 

19  29  . .  37  23  . . 

TSaol  13  ..  7  1!.. 
TWO  29  37  73  13  . . 

73  .. 

7 

..  17  ..  ..  19  ..  .. 
..  41  17  ..  11  7  47 

7  . .  . .  7  67  . . 
..29  7  ..  17  .. 

..  11 71 

7  13  53 

?10o!  ..  1!  ..  7  .. 
^M  31  7  13  47  19 

23  .. 

11  47  79  7  17  ..  29 
..  ..  11  23  ..  ..  7 

31  41 11 

79  11  ..  ..  43  37 

..  19  ..  11  7  31 

13  ..  7  19  ..  7 
7  61  17  13  7  29 

reo'  7  ..  31  ..  23 

..11 

7 7  ..  13 

67  ....  11  59  19 

M90 71 

im   71  41  ..  67  7 

29  7 

..  11  7  ....  83  .. 
19  7 13  .. 

11  ..  13  ..  47  43 
47  7  11  17  ..  7 

29  7  31  61  ..  11 
..  83  11  41  ..  .. 

The  smallest  prime  factors  of  multiple  numbers  are  given.     Prime  num- 
bers are  indicated  by  dots. 

Example:  To  find  the  prime  factors  of  2413:  The  smallest  prime  factor, 
from  above  table,  is  19;  then,  2413+19=127.  Now,  from  Part  2.  on  the 
following  page,  127  is  found  to  be  a  prime  number.  Hence,  the  prime 
facto™  of  2413  are  19  and  127.  „g,,3,  by  GoOglc 


L—ELEMENTARY  ARITHMETIC. 


2. — Primbs.*  Multiplbs  and  FAcroRS.^-Continued. 
Part  2.—{3n-\-l)  Hundrtds. 


+  -0 

^1 

' 

Tens  and  Units. 

N 

01  03  07  09  13 

19  21 

27  31  33  37  39  43  49 

51  57  61  63  67  69  73 

79  81  87  91  93  97  9« 

100 

7 

11 

..  ..  7  ..  ..  11  . 
7  ....  19  

..  ..  7  ....  13 
11 7 

11  . 

400 

..  13  11  ..  7 

11 

..  13  ..  ..  17  7  .. 

700 

..19  7  ..  23 

..  17  ..  11  ..  ..  7 

7  13  .. 

19  11  ..  7  13  ..  17 

1000 
1300 

7  17  19  ..  .. 
7  13 

13  ....  17  ..  7  .. 
..  11  31  7  13  17  19 

.   7  ..  ..  11  .. 
7  23  . .  29  . .  37 

29 

13  23 7 

7  ..  19  13  7  11  .. 

HOO 

..  7 

7  23    11  31  17 

13  ..  11  

..  19  37  13  7  11 

7 

23  41  7  19  .  . 

1900 

..  11  ..23  .. 

19 

17 

41  ....  13  7  29  .. 

..  7  ..  11  

2200 

31  ....  47  .. 

7 

17  23  7 13 

. .  37  7  81.... 

43  ..  ..  29  ..  ..  11 

2500 

41  ..  23  13  13 
....  7  63  29 

11 

7  ..  17  43  

...  13  11  17  7 

31 

13 

..  29  13  ..  ..  7  23 

2800 

11  19  ....  17  ..  7 

7  47  19 

..  43  ..  7  11  ..  13 

3100 
3400 

7  29  13  ..  11 

19  41  ..  7  .. 

13 

ii 

53  31  13  ..  43  7  47 
23  47  ..  7  19  11  .. 

23  7  29 

7 

19 
23 

11 31  23  : 

7  69  11  ..  7  13  .. 

3700 

..  7  11  ..  47 

61 

. .  7  . .  37  . .  19  23 

11  13  ..  53  ..  .. 

7 

..19  7  17  ....  2f 

4000 

19  .. 

n  13  59  31  19 

'7 

29 

..  29  37  11  7  13  .. 

..  31  17  7  13 

7  61  ..  ..  17 

4300 

.61  7  ....  43  .. 

19  ..  7  ..  11  17 

29  13  41  . .  23  . .  53 

4600 

43  ..  17  11  7 
13  ..  7  ..  17 

7  11  41  ..  13 

7  37 

..  7  ..  37  .. 

..  17  31  41  .. 
37  19  43  13  11 

31  .. 
..  7 

17  23 

7  11  41  

..  ..  59  ..  13  7 

. .  31  43  . .  13  7  37 

4900 

13 11  ..  7 

13  7  29 

..  ..  11  7  29  23  31 

11  7  ..  .. 

13  17  ..  7  ..  19 

5200 

59  7  ..  19  23  11 

7  ..  67  ..  19  .. 
11  ..  .. 

...  17  11  67  ..  7 

n-MK) 

'7 

7    37    7  29  11 

5800 

11 

29 

7 

..  7  19  13  

...  7  43  71  ..  17 

6100 
6400 

11  ..  ..  17  7  ..  11 
..59  7  41  47  17  .. 

..  47  61  ..  7  31 
.11  7  23  29  .. 

37  7  23  41  II  ..  .. 
11  ..  13  ..  43  73  67 

6700 

..  ..  19  ..  7 

11 

7  53  ..  ..  23  11  17 

43  29  ....  67  7 

13 

..  ..  11  ..  ..  7  13 

7000 
7300 

. .  47  7  43  . 
7  67  ....  71 

is 

7 

..  79  13  31  ..  ..  7 
17  ..  ..  11  41  7  .. 

11  .  23  7  37  .. 
..  7  17  37  53  .. 

11 
73 

..  73  19  7  41  47  31 
47  11  83  19  ..  13  7 

7600 
7900 

11  ....  7  23 
..  7  ..  11  41 

19 

89 

29  13  17  7  

..  7  ..  ..  17  13  .. 

7  13  47  79  11  .. 
..  73  19  ..  31  13 

"7 

7 7  43  . . 

79  23  7  61  ..  11  19 

8200 

59  13  29  ..  43 

19 7  ..  73 

37  23  11  ..  7  .. 

17  7 43 

8500 
8800 

..  11  47  67  .. 
13  ....  23  7 

7 

..19  7 83 

7  ..  11  ..  ..  37  .. 

17  43  7  .  13  11 
53  17 7 

i9 

23  ..  31  11  13  ..  .. 
13  83  ..  17  ..  7  11 

9100 
9400 

19  ..  7  ..  13 
7  . .  23  97  . . 

11 

7 

..  23  ....  13  41  7 
11 7  11 

7  89  53 

13  7 17 

67  ....  7  29  17  .. 
..  19  53  ..  11  ..  7 

*The  smallest  prime  factors  of  multiple  numbers  are  given.    Prime  num- 
bers are  indicated  by  dots. 

Example:  To  find  the  prime  factors  of  1001:  The  smallest  prime  factor. 
from  above  table,  is  7;  then,  1001+7—143.  the  smallest  prime  factor  of 
which  is  11;  then,  143-1-11—13,  a  prime  number.  Hence,  the  prime  factors 
of  1001  are  7.  11  and  13.  Digitized  by  GoOglc 


NUMBERS, 

2. — ^PRDfBS,*  MuLTiPLBS  AKD  FACTORS. — Concluded. 
Part  8.— (5n+je)  Hundreds. 


"1 

H 

Tens  and  Units. 

N 

93  99  11  17  21  23 

27  29  33  39  41  47 

61  53  67  59  63  69  71 

77  Ql  83  87  89  93  99 

2m 

7  11  ..  7  13  .. 

13 

..  11  ..  7  

7  17  ..  13 

199 

..  ..  7  11  ..  .. 
11  ..  ..  19  ..  .. 

17  2J13  7  ..  .. 
....  7  ..  29  7 

19  7  ..  18  

..  7  11  ..  19  ..  .. 

8M 

28 11  13 

..  ..  13  19  ..  7  .. 
....  31  ..  7  13  .. 

7  19  29 

1199 
1499 

..  ..  11  ..  19  .. 
23  .  17  13  7  .. 

7  ..  11  17  7  31 
H  .. 

11  ..  7  ..  29  ..  11 
7 

1799 

13  ..  29  17  ..  .. 

11  7  ..  37  ..  .. 

17  ..  7  ..  41  29  7 

..  13 11  7 

2999 
23IW 

..  7  ....  43  7 
7  ..  ..  7  11  23 

19  ..  7  ....  43 
..  ..  41  ..  23  37 

..  ..  19  ..  13  23 
13  17 

7  .Til  29  ....  19 
..  13  ..  7  17  23  .. 

31 7  .. 

7 

2699 

37  11  ..  7  19  .. 
..29  7  ..  17  7 

11  7 17  .. 

13  ..  ..  11  

..  7 

2909 

13  11  19  29  7  41  .. 

2299 

..  ..  13  ..  ..  11 

7  ..  53  41  7  17 

13  7  .. 

29  17  7  19  11  37  .. 

2509 

3899 

31  11  ..  ..  7  13 
..  13  37  11  ..  .. 

43  7  '.'.'ii  23  V. 

53  11  ..  ..  7  43  .. 
..  ..  7  17  ..  53  7 

7  ..  ..  17  37  ..  59 
....  11  13  ..  17  7 

4109 
4499 

11  7  ..  23  13  7 
7  ..  11  7  ..  .. 

4111 

19  43  11  23  ..  .. 

7 23  11  43 

..  61  ..  7  ..  41  17 

..  37  47  53  69  7  13 
11  ..  ..  7  67  ..  11 

4799 

..17  7  53  ..  .. 

29  ..  .. 

..  ..  47  13  17  .. 

29  ..  ..  7  11  47 

11  47  7  ..  71  7 
7  73  ..  19  7  .. 

..  7  67  ..  11  19  13 

..  31  13  ..  61  37  11 
..  53  11  23  31  7  41 

17  7 

1999 
1399 

..  ..  18  ..  7  11  .. 
19  ..  7  ..  17  ..  .. 

M9e 

13  71  31  41  7  .. 
..  19  23  61  31  .. 

17  13  43  

7  ..  53 

7  13  ..  11  ....  41 

9999 

..  7  17  ..  13  19 

11  ..  7  69  67  47  7 

43  ..  81  ..  53  13  7 

009 

..  7 7 

7  23  n    7  ..  11 
..  11  7  17  19  .. 

13  ..  23  17  79  .. 

61  ..  47  18  31  .. 
7  ..  41 

7  13  ..  11  

..  11  61  ..  19  7  .. 

151^ 

...  79  7  

....  29  7  11  19  .. 

1899 

13  7  ..  19  

13  7  ..  71  83  61  .. 

7199 
7490 

..  ..  13  11  ..  17 
11  31  ..  ..  41  13 

..  ..  7  11  37  7 
7  17  ..  43  7  11 

..  23  17  ..  13  67  71 
..  29  ..  ..  17  7  31 

,.  43  11  ..  7  ..  23 
..  ..  7  ....  59  .. 

7799 

..  13  11  ..  7  .. 

..  99  11  71  ..  61 

23 7  17  19 

7  31  43  13  ..  ..  11 

9090 
9390 

51 13  71 

19  7  ....  53  7 

23  7  29  ..  11  13 
11  ..  13  31  19  n 

83  ..  7  ..  11  ..  7 
7  ..  61  13  ..  ..  11 

41  ..  69 7 

..  17  83  ..  ..  7  37 

9M0 
M90 

7  ..  79  7  37  .. 
29  69  7  37  11  .. 

..  ..  89  63  ..  .. 
79  ..  .  7  ..  23 

41  17  11  7  ....  13 
..  7  13  17  

..  ..  19  7  

47  7  13  11  89  17  .. 

tm 

..  ..  ft  13  ..  23 

..  U  7  ..  ..  7 

11  19  ..  47  59  13  73 

37  7  ..  17 

1599 

13  37  ..  81  ..  89 

7  13  ....  7  .. 

..  41  19  11  73  7  17 

61  11  7  ..  43  53  29 

•The  smalkst  prime  factors  of  multiple  numbers  are  given.    Prime  num- 
bers are  indicated  by  dots. 

Example:  To  find  the  prime  factors  of  3211:  The  smallest  prime  factor, 
from  above  table,  is  18;  then,  3211  +  18-247.  the  smallest  prime  factor  of 
which  is  13;  then,  247-*-13— 1».  a  prime  number.  Hence,  the  prime  factors 
o£3211aro  18.  13and  19.  ogtizedbyGoOglc 


U— ELEMENTARY  ARITHMETIC, 


Oreatest  Common  Factor. — ^The  G.  C.  F.  of  two  or  more  numbers  is 
the  greatest  factor  common  to  all  of  them.    It  will  be: 
Ist.     A  factor  of  all  the  numbers,  therefore  no  greater  than  the  least  num- 
ber; 
2nd.    A  factor  of  all  the  differences  and  successive  differences  except  0, 

therefore  no  greater  than  the  least  difference; 
And  can  be  obtained  (1)  by  differences,  (2)  by  factoring,  and  (3)  by  divi- 
sion. 
Example:   Find  the  G.  C.  F.  of  84,  126.  210  and  231. 
1st  Method.^— By  differences. 


^^ 


1st 

Numbers,  diff. 
231 


S^ 


Pig.  1. 


210 
126 

84 


21 

84 


Ans. — ^The  least  difference,  21. 
is  obviously  the  G.  C.  F.  as 
it  is  the  greatest  common 
factor  of  the  least  number 
and  of  all  the  differences. 


42 


Snd  Method. — By  factoring, 
(a.) — ^Finding  all  the  prime       (6.)- 


-Finding  all  the 


2)84 

factors. 

2)126   2)210 

3)63   3)106 

3)21     6)36 

7           7 

3)231 

7)77 
11 

common  prime  factors. 
3)84     126  210  231 

2)42 
3)21 

7 

7)28     42     70     77 
4       6     10     11 

(c.) — Finding  the 
common  factors. 
21)84  126  210  231 
4       6     10     11 


3  and  7  arc  common 
to  all— 21. 


8  and  7  are  common  to  all — 21.  to  all — 21.  By  inspection — 21. 

Srd  Method. — By  division  (this  is  simply  another  form  of  differences), 
84  and  126  210  231 

84)i26(l  .  42)210(5  42)231(6 

_84  210  210 

42)84(2  21)42(2 

84  42 

Rule. — Start  with  any  two  of  the  numbers.  Divide  the  greater  by  the 
less  and  if  there  is  a  remainder  use  this  remainder  as  a  divisor  of  the  previous 
divisor,  and  continue  until  there  is  no  remainder.  The  last  divisor  will 
be  the  greatest  common  divisor  or  G.  C.  F.  of  the  two  ntunbers.  Use  this 
G.  C.  F.  so  obtained  with  the  next  number  for  a  new  G.  C.  F.,  and  so  on 
until  all  the  numbers  are  exhausted.  The  last  divisor  without  a  remainder 
will  be  the  G.  C.  F.  of  all  the  numbers. 

Least  Common  Multiple. — ^The  L.  C.  M.  of  two  or  more  numbers  is  the 
least  number  that  can  be  divided  exactly  by  each  of  them. 

I^ule  for  finding  the  L.  C.  M. — Divide  the  given  numbers  by  the  greatest 
(or  any)  factor  common  to  most  of  them,  and  if  divisible,  set  down  the 
quotients  in  the  line  below;  but  if  not  divisible,  bring  down  the  numbers 
themselves.  Divide  the  new  line  of  numbers  in  a  similar  manner,  and  also 
each  successive  line,  until  no  two  numbers  have  a  common  factor  except  1. 
The  L.  C.  M.  will  be  the  product  of  all  the  factors  and  the  last  line  of  num- 
bers. During  the  process,  if  any  number  is  a  factor  of  any  other  number 
in  the  same  line  it  can  be  cancelled. 

Example  1.  Example  2. 

Find  the  L.C.M.  of  7.  24.  1 68  and  264.     Find  the  L.  C.  Af .  of  1 3. 28, 52  and  84. 


4 

7 

24 

168 

264 

6 

7 

« 

42 

66 

7 

7 

7 

11 

13 


$t       H 


n 


13 


21 


11 


Note. — 13  is  a  factor  of  13,  and 
7  of  21 

Ans.-~4X13X21-1092. 


Ans.— 4X6X7X11-1848. 

Note  that  the  first  line  in  each  example  above  could  have  been  divided 
by  2.  and  then  again  by  2,  instead  of  by  4;  and  that  the  second  line  in 
Example  1  could  ha\'e  been  divided  by  2  and  then  by  3,  instead  of  by  6, 


FRACTIONS. 


The  L.C. 


Example  3. 
Find  the  L  C.  M.  of  126  and  462. 


126 


21 


M.  of  two  numbers  is  obviously  a  special  case  of  the  above 
in  which  the  product  of  the 
factors  is  the  G.  C.  F.,  and  the 
last  line  of  numbers  are  quo- 
tients obtained  by  dividing  the 
respective  numbers  by  their 
G.  C.  T.  Thus,  in  Example  3. 
the  L.  C.  M,  of  126  and  462  is 
their  G.  C.  F.(-42)  multiplied 
by  the  product  of  their  respective 

quotients.  ^-  3.  and^=  11. 


462 


77 


3  11 

L— (6X7)  X  3  X  11  -  1386. 


FRACTIONS. 


Kinds  of  Fractions. 

fProper.-f,  |. 
Stmplf^    < 

I  Improper.— §,  J. 

Mixed. -2f,  51- 


g     Compound.  — i  of  4,  ]  of  3^. 
^    |Complcx.-i    i    |A 


.    .  f  Pure. -.26.   .625. 

6  *  f 


^^1 


Mixed. -1.26.    4.876 


Equivalent  values. 

1  -  ?5  -  ?^?  -  A  -  6         Bothtcrm* 
bemui- 


bn      5X2 


may  t 

tiplled  or  di- 
vided by  the 
same  num- 
ber without 
affening  its 
value. 

|of3JHX3*»|x«-±l.|xl4»2i 


S+i  -  Y. 


f|-2K3i. 


-^9        J  X  7       »■ 


2        2 


.26- 


.25 


2^ 
10  ' 


100 


100      10 
400  "■  40  "  *• 


4.875  -  4AVo  -  45888  -  4J. 


To  reduce  to  lowest  terms. — Divide  both  terms  of  the  fraction  by  their 
greatest  common  factor;  or  factor  them  as  in  finding  their  G.  C.  F.    Thus, 


12 


12-i-J 
30-t-6' 


?-         \1       L      L 
6  •  ^"^  30  "  16  "  6  • 


To  reduce  to  a  common  denominator. — Reduce  the  fractions  (generally) 
to  their  lowest  terms  and  find  the  least  common  multiple  of  their  denomi- 
nators for  a  common  denominator.  Then  expand  both  terms  of  each 
fraction  proportionately  so  that  their  denominators  will  be  equal  to  the 
comnx>n  denominator.     Thus,  i,  5,  |  and  iV  —  i.  J.  t  and  i.     The  L.  C.  M . 


o(  their  denominators  —  72.    Hence,  i  — 


1X36       36 
72     "  72'  *  ' 


»X5      45        .  ,        24X1 
—  =-..  and  J  -  ■ 


72         72* 


72 


24 
72* 


8X7      56  . 
72    "  72'  *  "^ 


To  Chance — 

(a).  An  improper  fraction  to  a  mixed  number. 


177 
32 


=  ?       Ans.  5i?, 


Rule. — Divide  the  numerator  by  the  denomi- 
nator. The  quotient  is  the  whole  number, 
and  the  remainder  the  new  nimierator. 


Process: 
32)177(6 
160 

d  by  Google 


8  I.— ELEMENTARY  ARITHMETIC, 

131 
(6.)  A  mixed  number  to  an  improper  fraction.  14|  —  ?    Ans.  -r-. 

Rule. — Multiply  the   integral    part  by  the  de-        Process. 
nominator,  add  the  numerator,  and  place  the  14 

sum  over  the  denominator.  9 

126-1-6-131. 

?  90 

(c.)   A  whole  number  to  an  improper  fraction.  *  "  Tfi         ^"^^  fi  • 

Rule. — Multiply    the    whole    number    by    the  Process. 

given  denominator  for  the  required  numer*         6  X  15  —  90. 
ator. 

(d.)  A  compound  to  a  simple  fraction.  I  of  f  *  ?      Ans.    A* 

Rule. — Proceed    as    in    multiplication.     ("Of"  Process. 

means  "times.")     Place  the  product  of  the  ^  v  '^       A 

numerators  over  the  product  of  the  denomi>  8       •  "  12* 

nators,  and  reduce  to  lowest  terms.     Cancel,  4 
generally,  before  multiplying. 

2i 

(#.)   A  complex  to  a  simple  fraction.  ai "  ^         ^****  ^• 

Rule. — Reduce  the  numerator  and  denominator  Process. 

each  to  simple  fractions;    then  multiply  the    2 J     J_     ^w  2        ^ 
numerator  by  the  denominator  inverted.  3j"i~37  "'* 

CftocelUtion. — In  practical  operations  where  the  multiplication  of  vari- 
ous kinds  of  numbers,  including  fractions,  is  expressed,  the  process  may 
often  be  shortened  by  cancellation.  Thus,  let  it  be  required  to  find  the 
product  of  ]i8,  ^  and  (.  Clearly,  we  may  place  the  product  of  the 
numerators  over  the  product  of  the  denominators  for  a  simple  fraction  ex- 
pressing the  result,  or  we  may  go  to  the  other  extreme  and  cancel  as 
long  as  factors  will  cancel  each  other.  There  is.  however,  a  medium 
point  where  cancellation  may  sometimes  cease  for  simplicity  of  operation. 
86 

'^"*'  4Mx26xS  "  T^*     ^"^  denominator  is  a  power  of  10.) 

Addition  of  Fractioiis. — Reduce  to  the  smallest  common  denominator 
and  add  the  new  numerators.  Thus,  i-H  J-l-H  J-l  -  U;  It-t-f-J-l-l- 
V-U;  U+16i-V+Y-l!  +  SV-\Y-17il;  or.  m-16i -IG-hf-l-f- 
ie-t-H-hU- 16|J- 17iJ. 

Subtraction  of  Fractions. — Reduce  to  the  smallest  common  denominator 
and  find  the  difference  of  the  new  numerators.  Thus,  11— t"l|  — A"- A; 
8i-3A-8A-3r.-7M-3A-4li. 

Mnltiplication  of  Fractions. — If  necessary,  change  to  simple  fractions: 
cancel  where  advisable,  and  place  the  product  of  the  numerators  over  the 
product  of  the  denominators;    reduce  to  required  form.     Thus,  J XI  — A; 
6 

2ixf  X  m  -jXyX^-f"**- 

Division  of  Fractions. — If  necessary,  change  to  simple  fractions:   invert 

29 

the  divisor  and  multiply.    Thus.  82|  +  6i-^^-i-^-^x|=-T-*l. 

To  reduce  a  fraction  to  a  reciprocal. — Divide  the  denominator  by-the 
numerator,  writing  the  quotient  in  decimal  form.    Thus,  the  reciprocal  of 

A  —  V  —       g'g  "  '  •  2.      Hence,  instead  of  dividing  a  number  by  A  we  may 
multiply  it  by  3.2. 

To  reduce  a  common  fraction  to  a  decimal. — Divide  the  numerator  by 
the  denominator,  writing  the  quotient  in  decimal  form.    Thus, 


•3^*        Digitized  by  Google 


FRACTIONS  REDUCED  TO  DECIMALS.  9 

8.— Fractions  (7th8)  Rbducbd  to  Decimals. 

NoTB. — These  decimals  are  all  repeating  decimals,  that  is.  they  contaio 

figures  or  groups  of  figures  that  may  be  repeated  or  annexed  indefinitely. 

Thus.  J  -  .14285r'14286ri4286ri -.14&r'l.  the  inverted  caret  D  sig- 

m'fying  that  the  figure  following  is  the  first  of  the  repeating  group.     Ex- 
amples:  J -.n -.1111^1 -.11111111...;  i-.rs-aa^a-.assss^a.^tc. 


Fractions. 

Equivalent 
Decimals. 

Jp^ctions.;  Eq^y^-lent 

'Fractions. 

Equivalent 
Decimals. 

\ 

.14285ri 
.285714-2 

i         1      .428571-4 
\         '      .571428-6 

'     1 

.714286-7 
.867142-8 

4. — Fractions  (9ths)  Reduced 

to  Decimals. 

Prac- 
tiona. 

Equiv.  , 
Deci-     1 
mals. 

Frac- 
tions. 

Equiv. 
Deci- 
mals. 

Frac- 
tions. 

Equiv. 
Deci- 
mals. 

Frac- 
tions. 

Equiv. 
Deci- 
mals. 

1 

.1-1 
.2-2 

i 

.3-3 
.4-4 

8 

f 

6-6 

.6-6 

1 

.8-8 

Not«.— I -.222222...;  |- .6566 ;  etc. 

6. — Fractions  (IIths)  Reduced  to  Decimals. 


• 

Equiv. 
Deci- 
mals. 

pi 

u 

b 

Equiv. 
Deci- 
mals. 

Equiv. 
Deci- 
mals. 

fa** 

III 

i! 

.09-0 
.18-1 

S 

.27-2 
.36-3 

p. 

.46-4 
.64-5 

i 

.63-6 
.72-7 

ft 

.81-8 
.90-9 

Note.— ,»x-.  272727....;   fi- .686868. .. .;  etc. 

6. — Fractions  (12ths)  Reduced  to  Decimals. 


Frac- 
tions. 

Equiv. 
Deci- 
mals. 

Frac- 
tions. 

Equiv. 
Deci- 
mals. 

Frac- 
tions. 

Equiv. 
Deci- 
mals. 

4 

.083-3 
.166-6 
.25 

i 

.833-3 
.416-6 
.50 

.683-3 
.666-6 
.75 

11 

.833-3 
.916-6 

Note.— A -.083333...;  A- .416666 ;  etc. 

7. — Fractions  (13ths)  Reduced  to  Decimals. 


Fiactions. 


Equivalent  > 
Decimals. 


.070023-0 
.153846-1 
.330769-2 
.307002-3 


Fractions. 


A 
A 


1?e"SS.'  l'F'-"°-- 


.304616-3 
.461638-4 
.638461-6 
.616384-6 


A 

w 


Equivalent 
Decimals. 


.602307-0 
.760230-7 
.846153-8 
.923076-9 


Note. — These  are  repeating  decimals,  as  above.    tizedbyCjOOglC 


10 


I.— ELEMENTARY  ARITHMETIC. 


8. — Fractions  (64ths)  Rboucbd  to  Decimals. 


i 

1 

J3 

1 

'2 

1 

1 

J2   1 

i 

1 

1 

s 

&. 

Q 

i 

PL4 

Q   ,|  S 

Q 

i  b. 

Q 

1 

.015635 

17 

.265625  !  33 

.515625 

49 

.766826 

2 

^i 

.03125 

18 

/« 

.28125 

34 

u 

.63125 

50 

it 

.78125 

3 

.046876 

10 

.296875 

35 

.646875 

51 

.796875 

4 

1-16 

.0625 

20 

5-16 

.3125 

36 

^16 

.5626 

62 

13-16 

.8126 

6 

.078125 

21 

.328125 

37 

.678126 

63 

.828126 

6 

^* 

.00376 

22 

ih 

.34375 

38 

i! 

.59375 

54 

i: 

.84376 

7 

.109375 

23 

.350376 

39 

.609376 

65 

.859376 

8 

/-5 

.126 

24 

SS 

.375 

40 

&S 

.626 

60 

7-8 

.876 

0 

.140626 

25 

.390625 

41 

.640626 

57 

.890626 

10 

A 

.15625 

26 

11 

.40626 

42 

il 

.66626 

58 

51 

.90625 

11 

.171876 

27 

.421875 

43 

.671875 

69 

.021875 

12 

3-16 

.1875 

28 

7-16 

.4375    44 

11-16 

.6875 

60 

15-16 

.9375 

13 

203125 

29 

.453125 

45 

703125 

61 

.953125 

14 

s'a 

.21875 

30 

i! 

.46875 

46 

if 

.71876 

62 

U 

.96875 

15 

.234375 

31 

.484375 

47 

.734376 

63 

.964375 

16 

i-4 

.25 

32 

1-2 

.6 

48 

3-4 

.75 

64 

1 

1. 

DECIMALS. 

Addition  of    Decimals. — Have  the  decimal 
p/'iints  "in  column"  before  adding. 


Subtraction  of    Decimals. — Have  the  decimal 
points  "in  column"  before  subtracting. 


Multiplication  of  Decimals. — Multiply  as  with 
whole  numbers:    the  product  to  have  as 
many  decimal  places  as  the  factors  com- 
bined.   Thus,  2. 8X  .06X7. 22-. 83030- 
.8303. 

Division  of  Decimals. — Multiply  or  divide  the 
divisor  and  dividend  by  some  power  ot  10 
that  will  make  the  divisior  a  whole  number 
of  significant  figures,  marking  the  new 
decimal  point  in  tne  dividend  by  a  caret  (^). 
The  quotient  will  then  contam  as  many 
decimal  places  as  the  new  dividend. 
Example:    Divide  17.34  by  600? 


Example: 


Example: 


Example: 


Example: 


2.0625 
316.25 

.0375 
317.3500 

15  125 
3.71825 
11.40675 
6.75 

2700 
1350. 
16.200 


.0289 


Ans. 


Example:    Divide  17.34  by  .006? 
MQ)  17.340. 

2890.  Ans. 


Divide  3573.2  by  2.376. 
Ans.  1504.505  + 

1504.505  + 
2.375)3573.200^ 
2375 
li982 
11875 
10700 
9500 
12000 
11875 
12500 
11875 


To  reduce  a  decimal  to  a  common  fraction. 

a.)  Exact  decimals. — For  the  numerator  of  the  fraction,  use  the  significant 
figures  of  the  decimal,  the  denominator  being  1  with  as  many  ciphers 
annexed  as  there  are  decimal  places  in  the  decimal;  reduce  to  lowest 

terms. 

TKu.  .75  -  ^„  -  ,:   .0072  -  ^„Vo  "  I^.^GoOglc 


DECIMALS  AND  FRACTION S^SHORT  METHODS. 


11 


(&.)  R§p€atimt  decimals. — ^Treat  the  non-repgaiing  and  the  first  repgaiing 
gronps  as  a  whole  number;  subtract  from  this  the  non-repeating 
group  treated  as  a  whole  ntunber;  the  difference  will  be  the  numerator 
of  the  fraction.  The  denominator  will  be  composed  of  as  many  9's  as 
there  are  repeating  figures  in  a  group,  followed  by  as  many  O's  as  there 
are  non-repeating  figures.    Reduce  to  lowest  terms. 

Bxample:  Reduce  .3  3  to  a  fraction.  Example:  Reduce    467^6  to  a  fraction. 

numer._3  ^  .       .  num.      463    . 

denom.  9  *"  demon.  990 

ADDITION. 

The  following  examples  serve  to  illustrate  approved  methods: 


~ 

Same  by 

Add: 

columns: 

257.83 

24 

986.97 

33 

456.73 

29 

523.82 

25 

857.19 

23 

2582  54      . 

.     2582.54 

Add: 

153f 
251 
16i 


Reduced  to 
eighths: 


Reduced  to 
decimals: 

.      .875 
.      .75 
.      .5 


Ans.    2582  54     ..     2582.54  Ans.   196i     .    .       V 

Carried   t$  JZ 

Fractions:     l  +  *-|  +  l-!-li  311+l|-32f. 

Decimals:    .75+5  -1.25.    81.25+1.126-32.375. 

Mechanical  adding  machines  are  used  by  accountants. 
SUBTRACTION. 


2.125 


Subtract: 
153f 
_25| 
Ans.  1271 


Accurate: 
12.64 
6.74 


Reduced  to 

eighths: 
.       8  +  6     . 
7_    . 

i     . 


Reduced  to 

decimals: 

1+.75 

.875 

.875 


MULTIPLICATION. 

Sufficiently 


5056 
8848 
7584 


Accurate: 
12.64 

6J4 

50  .. 
885  . 
7584 


3f  X  21 


i-  J-  i-i-  1 

.76 -.5  -.25. 

Reduce  the  fraction 
to  a  common  denomi- 
nator, for  addition  or 
subtraction. 

1_X_3       , 
2X4"'- 

4    ^  3       *^- 


Ass.     85.1936: 


3.75  X  2J  -  7.5  +  1.25-  8.75. 
.2  X  .3  -  .06  .111 

85.19  ^3 

.0333 
A  few  short  methods  of  multiplication  will  be  fotmd  useful: 
(1).  By  reducing  <A#  muUipUer*  to  an  intproper  fraction  with  a  simple 
meraior  and  denominator.     Where  the  numerator  becomes   1,    10,   100. 
1000,  etc..  it  is  known  as  the  reciprocal  method.     In  the  following,  let  n  rep- 


resent the  number  to  be  multiplied: 


n  X 


*  H  the  multiplier  is 


is    U.add  \. 
\Z\,    "     I  ar 


and  multiply  by  10. 
"         -^  100. 


d  by  Google 


12  I.— ELEMENTARY  ARITHMETIC, 

(2).  When  tk§  sum  of  the  unit  figures  equals  10;  and  baiance  of  ntmbiri 
are  identical: 

11  12  15  24  48  96  124  243 

J9  _18  _15  ^  _42  _»4  126  _247 

209  216  225  624  2016  9024  15624  60021 

Rule. — ^Mvdfiply  the  unit  figures  together,  occuoying  two  places  (sec 
first  example  above) ;  and  prefix  the  product  of  the  oatance  of  either  num- 
ber bv  (itself  +  1). 

(o.)  Special  Case. — When  the  last  figure  is  S  the  last  two  figures  of  the 
product  will  be  eS'.    thus.    25*  -  625,   95«  -  9025.    145«  -  21025, 
245*  —  60025;  all  performed  mentally. 
(6.)   Special  C^ase. — When  the  last  figure  in  each  number  is  a  decimal,  and 
their  sum  is  xmity,  the  whole  numbers  being  identical;   thus, 
1.1  X  1.9  -  2.09.     2.4  X  2.6  -  6.24,     24.3  X  24.7  -  600.21 
(c.)    Special  Case. — When  the  whole  numbers  are  identical  and  the  iftimbers 
contain  fractions  (instead  of  decimals,  as  above)  whose  sum  is  unity; 
thus, 

l^  X  \i%  -  2,8o.  U  X  U  -  2J,  121  X  12f  -  15641. 
(3).    The  product  of  any  two  numbers  each  ending  vnth  the  fraction  i,  or 
with  the  decimal  .5: 

9J   X     3i    -9X3+  ^-y-?  +   i    -  33J. 

7.5X11.5-      77+9      +.25-86.25. 
Rule. — *The  product  of  the  whole  numbers  +  half  their  sum  +   i. 
(a.)   Special  Case. — When  the  numbers  are  whole  numbers  ending  with  5". 
95  X     85  -  100  (  27  +     6  +  .26)  -  3325. 
75  X  115  -  100  (   77  +     9  +  .25)  -  8625. 
185  X  305  -  100  (540  +  24  +  .26)  -  56425. 
Rule. — ^Apply  the  general  rule  above,  considering  each  number  divided 
by  10.  and  mtiltiply  the  result  by  100. 

(4.)  ^The  product  of  any  two  numbers  is  equal  to  the  square  of  their  m*an, 
minus  the  square  of  half  their  difference: 

24  X  26  =  252  -  1  -  624.       136  X  144  -  140>  -  16  -  19581 
87  X  93  -  90«  -  9  -  8091.     244  X  256  -  250»  -  36  -  62464. 
(5.)   ^The  converse  of  (4),  of  course,  holds  true  and  may  be  applied 
readily  in  finding  the  squares  of  numbers — considering  them  as  means: 
89»  -  38  X  40  +  1  -  1521.     68«  -  66  X  70  +  2«  -  4624. 
Note. — Use  for  a  base,  any  multiple  of  10  nearest  the  number  to  be 
squared. 

(6.)   XThe  square  of  any  number  is  equal  to  the  square  of  ( itself  ±1), 
called  the  base,  T     the  sum  of  the  base  and  the  number: 

39»  -  40«  -  79  -  1621.   71«  -  70«  +  141  -  5041. 

(7.)   Miscellaneous  MethodsA  

a.)  To  multiply  any  number  «  by  11.  n  —  870^ 687 

Note. — Imagine  the  number,  and  its  product  by  10, 

arranged  thus:      879687  -        - ....  -r --.  .^, 

879687    'o*"  addition  Ans.    9,676,557 


(6.)  To  multiply  a  number  n  by  any  number  from  12  n—      73  64    * 

to  19,  inclusive:  wX  7-  +   51  S48 

Example:   Multilpy  7364  by  17.  Ans.         125,188. 

Note. — When  the  unit  figtu^  of  the  multiplier  is  1,  7  864 

the  same  principle  of  course  holds  true;  as.  for  instance,  +  515  48 

7364  X  71  -522,844. 

(c.)   To  multiply  a  number  n  by  any  number  from  92  lOOn  — 736  400 

to  99,  inclusive:  -  2»       14  728 


Example:   Multiply  7364  by  98.  Ans.      721.672 

d.)  When  the  multiplier  contains  simple  factors.  987 

it  may  be  quicker  to  use  the  factors:  nX  8—   7896 

Example:    Multiply  987  by  64.  mX 8X8- 63168.  Ans. 

*  From  Algebra:    (a  +  c)  (6  +  c)  -  o6  +  c  (a  +  6)  +  c«. 

t  From  Algebra:     (x  +  y)  (x  —  y)  —  x*—y*. 

i  From  Algebra:     (x  ±  1)«  -  ««  ±  2  ar  +  1. 

1  These  illustrations  may  be  expanded  almost  indefinitely. 


Accurate: 

2.64 

674.82)  1783.16^88 
1849  64 

433  528 
404  892 
28  6368 
26  9928 

DECIMALS  AND  FRACTIONS— SHORT  METHODS.  18 

DIVISION. 

Sufficiently  accxarate: 

2.64 
674.84)1783.17^ 
1349  64 
433  63 
404  88 

28  65 

There  are  short  special  methods  of  dixnsioii,  but  they  are  usually  not 
bfoad  enough  in  their  application  to  record  for  general  use. 
(fl.)  Factor  the  divisor:  4  )_972 

Example:   Divide  972  by  16.  4  ).  243 

60f  Ans. 
(b.)  Multiply  by  the  reciprocal:  43.2 

Bzample:  Divide  43.2  by  2.5  _.4_ 

17.28  Ans. 
(c)  To  divide  by  a  fraction^  invert  it  and  multiply,  but  reducing  it  to  a 
simple  decimal  or  reciprocal  if  possible: 

*+l-*X|-f.       66  +  #-56X.8-  44.8. 

UDCnc^t^:     ||-^;|-^-2f.  An.. 


^ 


d  by  Google 


2.— POWERS,  ROOTS  AND  RECIPROCALS. 

The  processes  of  mtiltiplication  and  divisioni  and  of  finding  the  powers 
roots  and  reciprocals  of  numbers  may  be  performed  by  arithmetic  (and 
a^bra);  by  the  use  of  tables;  by  logarithms;*  or  by  the  logarithmiL 
shde  rule.t 

A.    ENGINEERS*   TABLES. 

Under  the  present  heading  will  be  found  Engineers*  Tables  of  powersv 
roots  and  reciprocals  of  numbers  arranged  in  form  similar  to  logarithmic 
tables,  so  that  the  above  properties  of  any  number  can  be  obtained  by 
manipulating  the  decimal  point,  and  by  the  use  of  the  proportional  parts 
(P.  P.)  columns,  as  in  finding  the  logarithms  of  ntmibers.  These  tables 
may  also  be  used  inversely  in  findmg  the  squares,  cubes,  and  invers* 
reciprocals,  corresponding  respectively  to  the  square,  roots,  cube  roots  and 
reciprocals — the  process  being  similar  to  finding  the  numbers  correspaHdint 
to  given  logarithms.  For  a  more  academic  arrangement  see  Arithmetical 
Tables  9.  10.  and  11,  following. 

Square  Root. — ^Tables  1  and  2,  following,  comprise  a  4-page  table  of  the 
squaie  roots  of  numbers.  The  first  two  pages  (Table  1)  are  for  numbers  with 
an  odd  number  of  figures  to  the  left  ot  the  decimal  point ;  or,  if  it  is  a  ptire  dedmal 
the  first  significant  figure  must  be  an  even  number  of  places  to  the  right  ci 
the  decimal  point.  The  last  two  pages  (Table  2)  are  for  numbers  just  the 
reverse — even  to  the  left  knd  odd  to  the  right.  The  range  of  the  tables  may  b« 
extended  by  remembering  that  "  changing  two  decimal  points  in  the  square 
—one  decimal  point  in  the  root — in  the  same  direction."  The  tables  are 
logarithmic  in  form,  containing  P.  P.  colimins  for  extension  or  interpolatioo. 

Example. — Required  the  square  root  of  907.6. 

Solution. — Three  figures  at  the  left  of  the  decimal  point  calls  for  the 
"odd"  table  (Table  1),  from  which  the  sq.  rt.  of  907-30.116,  and  the  pro- 

Sortional  part  of  the  difference,  1 7,  between  it  and  the  next  higher  number. 
08.  is  found  to  be  10  (10.2)  which,  added  to  30.116-30.126.    Ana. 

The  following  methods  are  given  for  extracting  the  sqtuuie  root  whca 
tables  are  not  accessible,  or  when  great  acciiracy  is  desired,  for  large  num- 
bers: 

By  Algebra.  By  Arithmetic. 

Square  root  of  a*+  2ax  +  x*  ?  Square  root  of  576  ? 

s^+2ax  +  x^{a  +  x.Ans.  2a  =  40     576   (20+4-24.   Ans. 

a* Assume     Jf— _4     400 

2a  +  x)       2ax  +  x*  2o  +  ar-44  )'l76  a-20. 

2ax  +  x*  176  x~   4. 

Example. — Extract  the  square  root  of  46.354.87  ? 

Remarks. — Be-  Process: 

ginning    with     the  .... 

unit    figure,   point  46354.87(215.301 +  .  Ana 

off  two  places  each  oi  =  20 )  _* 

way.     forming    Assume  Xi-    If   .'.  2ai+jri-41)  63  Oo-    2. 

groups  of.  two  fig-  a2-210)  JL_       ai=  »,  x,«L 

SSit°nir?r^°e'^d    Assume  x,-    5}    .-.  2aa+^2-425)2254       ^2-210.  x^-l 

2125 


as  indicated. 


Or,  215X2  =  430: 


2153X2-4306;         430601)      780000 

*  See  table  of  logarithms,  page  108. 

t  For  description  and  use  of  the  slide  rule,  see  page  126. 

14  Digitized  by  Google 


ENGINEERS'  TABLES— SQUARE  ROOTS,  15 

Example. — Extract  the  square  root  of  4.635.4  ? 
Note  that  the  position  of  the  decimal  Process: 

point  affects  the  pointing  off  and,  conse-  .    . 

qtwntly,  the  entire  character  of  there-  4635.40   (68.08+    Ans. 

ailt.  36 

128  TiMS 
1024 
13608  )     114000 
108864 


d  by  Google 


le 


2.-'P0WERS,  ROOTS  AND  RECIPROCALS, 


Odd.  Even. 

1. -Square  Roots  (and  Squares *)  of  Numbers — 


.    .    .        Note. — ^The  souart  must  contain  an  odd 

P.P. 

90  48  44  44  43 

60301 .  020406    number  of  figxir^  to  the  left  of  the  decimal 

1 

5    5    5    4    4 

ODD    EVEN    point.    If  the  square  is  a  ^rv  (i«c«ma/ — less 

2 

10  10    9    9    8 

than  imity — the  first  siimificant  fiaure  must 

3 

15  14  14  13  13 

be  an  nten  number  of  places  to  the  right  of  the  decimal  point.  1 

4 

20  19  18  18  17 

See 

page  14  for  explanation  of  table. 

5 

26  24  23  22  21 

6 

30  29  28  26  25 

7 

35  34  32  31  29 

-     ,      _     ■       -    . 

8 

40  38  37  86  34 

8q. 

n/0  1      1         -    '      -    « 

2 

3 

4 

5 

6 

7 

8 

9 

9 

45  43  41  40  38 

1.0 

1.0000 

0050 

0100 

0149 

0198 

0247 

0296 

0344 

0392 

0140 

41  40  J9  38  37 
4    4    4    4    4 

8    8    8    8    7 

.1 

0488 

0536 

0583 

0630 

0677 

0724 

0770 

0817 

0863 

0909 

1 

.2 

0954 

1000 

1045 

1091 

1136 

1180 

1225 

1269 
1705 

1314 

1358 

2 

.3 

1402 

1446 

1489 

1533 

1578 

1619 

1662 

1747 

1790 

3 

12  12  12  11  11 

!■:; 

1832 

1874 

1916 

1958 

2000 

2042 

2083 

2124 

2166 

2307 

4 

16  16  16  15  15 

2247 

2288 

2329 

2369 

2410 

2450 

2490 

2530 

2570 

2610 

5 

21  20  20  19  19 

1  :? 

2649 

2689 

2728 

2767 

2806 

2845 

2884 

2923 

2961 

3000 

« 

25  24  23  23  22 

3038 

3077 

3115 

3153 

3191 

3229 

3266 

3304 

3342 

3379 

7 

29  28  27  r  26 

•|3.0 

3418 

3454 

3491 

3528 

3565 

3601 

3638 

3675 

3711 

3748 

8 

33  32  31  30  30 

3784 

3820 

3856 

3892 

3928 

3964 

4000 

4036 

4071 

4107 

9 

37  3<  85  34  33 

4142 

4177 

4213 

4248 

4283 

4318 

4353 

4387 

44«2 

4457 

36  35  34  33  33 

4491 

4526 

4560 

4595 

4629 

4663 

4697 

4731 

4765 

4799 

1 

4    4    8    3     3 

1  i 

4832 

4866 

4900 

4933 

4967 

5000 

5033 

5067 

5100 

5133 

2 

7    7    7    7     6 

5166 

5199 

5232 

5264 

5297 

5330 

5362 

5395 

5427 

5460 

3 

U  11  10  10  10 

•§      .4 

5492 

5524 

5556 

5588 

6620 

5652 

5684 

5716 

5748 

5780 

4 

14  14  14  13  13 

•^  2.S 

5811 

5843 

5875 

6906 

5937 

5969 

6000 

6031 

6062 

6093 

5 

18  18  17  17  16 

7  :? 

6125 

6155 

6186 

6217 

6248 

6279 

6310 

6340 

6371 

6401 

6 

22  21  20  20  19 

6432 

6462 

6492 

6523 

6553 

6583 

6613 

6M3 

6673 

6703 

7 

25  25  24  23  22 

g     .S 

6733 

6763 

6793 

6823 

6852 

6882 

6912 

6041 

6971 

7000 

8 

29  28  27  26  26 

^,1 

7029 

7059 

7088 

7117 

7146 

7176 

7205 

7234 

7263 

7292 

9 

32  82  31  30  29 

7321 

7349 

7378 

7407 

7436 

7464 

7493 

7521 

7650 

7578 

31  30  39  28  37 

1  :J 

7607  >  7635 

7664 

7692 

7720 

7748 

7776 

7804 

7833 

7861 

1 

3    3    3    3     3 

7889 

7916 

7944 

7972 

8000 

8028 

8055 

8083 

8111 

8138 

2 

6    6    6    6     5 

t'-' 

8166 

8193 

8221 

8248 

8276 

8303 

8330 

8358 

8385 

8412 

3 

9    9    9    8     8 

8439 

8466 

8493 

8520 

8547 

8574 

8601 

8628 

8655 

8682 

4 

12  12  12  11   11 

I3.5 

8708 

8736 

8762 

8788 

8815 

8841 

8868 

8894 

8921 

8947 

5 

16  15  15  14   14 

8.  •« 

8974 

9000 

9026 

9053 

9079 

9105 

9131 

9157 

9183 

9209 

6 

19  18  17  17   16 

1   -^ 

8    .9 

9235 

9261 

9287 

9313 

9339 

9365 

9391 

9416 

9442 

9468 

7 

22  21  20  20  19 

9494 

9519 

9545 

9570 

9596 

9621 

9647 

9673 

9698 

9723 

8 

25  24  23  22  22 

9748 

9774 

9799 

9824 

9849 

9875 

9900 

9925 

9950 

9975 

9 

28  27  26  25  24 

•0  4.0 

3.0000 

0025 

0050 

0075 

0100 

0125 

0149 

0174 

0199 

0224 

26  2S  34  33  33 

<N        .1 

0248 

0273 

0298 

0322     0347 

0372     0396 

0421 

0445 

0469 

1 

3    3    2     2     2 

tc      2 

0494 

0518 

0543 

0567  1  0591 

0616 

0640 

0664 

0688 

0712 

2 

5    5    5     5     4 

S      .3 

0736 

0761 

0785 

0809  i  0833 

0857 

0881 

0905 

0928 

0952 

3 

8    8    7     7     7 

i  * 

0976 

1000 

1024 

1048 

1071 

1095 

1119 

1142 

1166 

1190 

4 

10  10  10     9     9 

J  4.5 

1213 

1237 

1260 

1284 

1307 

1331 

1354 

1378 

1401 

1424 

5 

13  13  12  12   11 

0     .6 

1448 

1471 

1494 

1517 

1541  :  1564 

1587 

1610  '  1633 

1656 

6 

16  15  14   14   13 

.7 

1679 

1703 

1726 

1749 

1772  ,  1794 

1817 

1840  1  1863 

1886 

7 

18  18  17  16   15 

.8 

1909 

1932  ;  1954 

1977 

2000     2023 

2045 

2068     2091 

2113 

8 

21  20  19  18   18 

.9 

2136 

2159  1  2181 

2204  1  2226  1  2249 

2271  >  2293  1  2316 

2338 

9 

23  23  23  21   20 

^Square  Roots  are  obtained  directly  as  in  the  logarithmic  tables, 
the  Proportional  Parts  tables  for  interpolation. 
Squares  may  be  obtained  by  inverse  interpolation. 
Example. —SqyiSLTc  root  of  374 . 9  -  19 .  339 

-I-  23 

-19.362  Ans., 


tisins 


d  by  Google 


ENGINEERS'  TABLES^SQUARE  ROOTS. 


17 


Odd.  Even. 

— tPKOM  1  TO  10;  100  TO  1.000;  10.000  to  100.000;  etc. 


Sq. 

v/0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

SJ 

2.2M1 

2383 

2405 

2428 

24f0 

2472 

2494 

2517 

2539 

2561 

23  23  ai  ao 

.1 

2583 

2805 

2627 

2650 

2672 

2694 

2716 

2738 

2760 

2782 

1 

2   2   2   2 

J 

3»4 

2825 

2847 

2869 

2891 

2913 

2935 

2956 

2978 

3000 

2 

5   4   4   4 

3032 

3043 

3065 

3087 

3108 

3130 

3152 

3173 

3195 

3216 

3 

7   7   6   6 

3238 

3350 

3281 

8302 

3324 

3345 

3367 

3388 

3409 

8431 

4 

9   9  8   8 

i.9 

3452 

34n 

3495 

3516 

3537 

3558 

3580 

3601 

3623 

8643 

5 

12  U  11  10 

.< 

3<6I 

3885 

3707 

3728 

3749 

3770 

3791 

3812 

3833 

3854 

6 

14  13  13  12 

.7 

3875 

3898 

3917 

3937 

3958 

3979 

4000 

4021 

4042 

4062 

7 

16  15  15  14 

.8 

4883 

4104 

4125 

4145 

4166 

4187 

4207 

4228 

4249 

4269 

8 

18  18  17  16 

i.: 

4290 

4310 

4331 

4352 

4373 

4393 

4413 

4434 

4454 

4474 

9 

21  20  19  18 

4495 

4515 

4538 

4556 

4576 

4597 

4617 

4637 

4658 

4678 

21  20  19 

S  .1 

4898 

4718 

4739 

4759 

4779 

4799 

4819 

4839 

4860 

4880 

1 

2.1  2.0  1.9 

3   .2 

4900 

4920 

4940 

4960 

4980 

5000 

5020 

5040 

5060 

5080 

2 

4.2  4.0  3.8 

P 

5100 

5120 

5140 

5159 

5179 

6199 

5219 

5239 

5259 

6278 

3 

6.3  6.0  5.7 

5298 

5318 

5338 

5357 

5377 

5397 

5417 

5436 

5456 

5475 

4 

8.4  8.0  7.6 

^  S.5 

5495 

5615 

5534 

5554 

5673 

6593 

5612 

5632 

5652 

5671 

5 

10.6  10.0  9.5 

5890 

6710 

5729 

5749 

5768 

5788 

5807 

5826 

5846 

5865 

6 

12.6  12.0  11.4 

i  -7 

5884 

5004 

5923 

5942 

5962 

5981 

6000 

6019 

6038 

6058 

7 

14.7  14.0  13.3 

'  J 

8077 

60N 

6115 

6134 

6153 

6173 

6192 

6211 

6230 

6249 

8 

16.8  16.0  15.2 

1,: 

82C8 

6287 

6306 

6325 

6344 

6363 

6382 

6401 

6420 

6439 

9 

18.9  18.0  17.1 

8458 

8478 

8495 

6514 

6533 

6552 

6571 

6589 

6608 

6627 

19  18  17 

I  •' 

8848 

6865 

6683 

6702 

6721 

6739 

6758 

6777 

6796 

6814 

1 

1.9  1.8  1.7 

8833 

8851 

6870 

6889 

6907 

6926 

6944 

6963 

6981 

7000 

2 

3.8  3.6  3.4 

1:3 

7019 

7037 

7055 

7074 

7092 

7111 

7129 

7148 

7166 

7185 

3 

5.7  5.4  5.1 

7203 

7221 

7240 

7258 

7276 

7295 

7313 

7331 

7350 

7368 

4 

7.6  7.2  6.8 

f'» 

7388 

7404 

7423 

7441 

7459 

7477 

7495 

7514 

7532 

7560 

5 

9.5  90  8.5 

2  .( 

7588 

7586 

7604 

7622 

7641 

7659 

7677 

7695 

7713 

7731 

6 

11.4  10.8  10.2 

3   5 

n49 

7767 

7785 

7803 

7821 

7839 

7857 

7876 

7893 

7911 

7 

13.3  12.6  11.9 

B   j 

7928 

7946 

7964 

7982 

8000 

8018 

8036 

8054 

8071 

8089 

8 

15.2  14.4  13.6 

!   • 

8107 

8125 

8142 

8160 

8178 

8196 

8213 

8231 

8249 

8267 

9 

17.1  16.8  15.3 

1-1 

8284 

8302 

8320 

8337 

8355 

8373 

8390 

8408 

8425 

8443 

18  17   16 

8480 

8478 

S496 

8513 

8531 

8548 

8566 

8583 

8601 

8618 

1 

1.8  1.7  1.6 

3  -' 

8838 

8653 

8671 

8688 

8705 

8723 

8740 

8758 

8775 

8792 

2 

3.6  3.4  3.2 

5  .3 

8810 

^27 

8844 

8862 

8879 

8896 

8914 

8931 

8948 

8965 

3 

6.4  5.1  4.8 

s  .4 

8983 

9000 

9017 

9034 

9052 

9069 

9086 

9103 

9120 

9138 

4 

7.2  6.8  6.4 

9155 

9172 

9189 

9206 

9223 

9240 

9257 

9275 

9292 

9309 

5 

9.0  8.5  8.0 

«  .f 

93M 

9343 

9360 

9377 

9394 

9411 

9428 

9445 

9462 

9479 

6 

10.8  10.2  9.6 

?  -7 

9498 

9513 

953(r 

9547 

9563 

9580 

9597 

9614 

9631 

9648 

7 

12.6  11.9  11.2 

3   .1 

9865 

9682 

9698 

9715 

9732 

9749 

9766 

9783 

9799 

9816 

8 

14.4  13.6  12.8 

Ni 

9833 

9650 

9866 

9883 

9900 

9917 

9933 

9950 

9967 

9983 

9 

16.2  15.3  14.4 

limo 

0017 

0033 

0050 

0067 

0083 

0100 

0116 

0133 

0160 

17   16  IS 

0188 

0183 

0199 

0216 

0232 

0249 

0265 

0282 

0299 

0315 

1 

1.7  1.6  1.5 

J 

0332 

0348 

0364 

0381 

0397 

0414 

0430 

0447 

0463 

0480 

2 

3.4  3.2  3.0 

.1 

0498 

0512 

0529 

0545 

0661 

0578 

0594 

0610 

0627 

0643 

3 

5.1  4.8  4.6 

.4 

0859 

0678 

0692 

0708 

0725 

0741 

0757 

0773 

0790 

0806 

4 

6.8  6.4  6.0 

fj 

0622 

0838 

0854 

0671 

0887 

0903 

0919 

0935 

0952 

0968 

5 

8.5  8.0  7.5 

.< 

0984 

1000 

1018 

1033 

1048 

.1064 

1081 

1097 

1113 

1129 

6 

10.2  9.6  9.0 

.' 

1145 

1161 

1177 

1193 

1209 

1225 

1241 

1257 

1273 

1289 

7 

11.9  11.2  10.5 

.1 

1J05 

1321 

1337 

1353 

1369 

1386 

1401 

1417 

1432 

1448 

8 

13.6  12.8  12.0 

.J 

I4C4 

1480 

1496 

1512 

1528 

1544 

1559 

1575 

1591 

1607 

9 

15.3  14.4  13.6 

tForsqamrea  10-100, 1.000-10.000,  etc..  see  following  Uble. 
SMmp/r.—^uare  of  24.64-607.1  Ans.  ^  , 

Digitized  by  VjOOQ IC 


18 


2.— POWERS,  ROOTS  AND  RECIPROCALS. 


Evn.  Odd . 

2. — Square  Roots  (and  Squares*)  of  Numbers— 


Note.  —The  squart  must  contain 

an 

P 

P. 

604020.10306    evtn  number  of  figures  to  the  left  of 

EVEN    ODD    the  decimal  point.    If  the  square  is 

155  150  14«  140  135 

a  pure  decimal — less  than  unity — the 

1 

16 

15 

15 

14     14 

first    significant  figure  must  be  an  odd  number  of 

2 

31 

30 

29 

28     27 

places  to  the  right  of  the  decimal  point. 
See  page  14  for  explanation  of  table. 

3 

47 

45 

44 

42     41 

4 

62 

60 

58 

66     54 

5 

78 

76 

73 

70     68 

• 

Q 

93 

OA 

m 

84     81 

7 

109  105  102 

98    95 

8q. 

V.o 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

8 

124 

120  116 

112  108 

9 

130  135  131 
130  136  133 

126  122 

10. 

3.1623 

1780 

1937 

2094 

2249 

2404 

2558 

2711 

2863 

3015 

118  114 

1. 

3166 

3317 

3466 

3615 

3764 

3912 

4059 

4205 

4351 

im 

1 

13 

13 

12 

12     11 

2. 

4641 

4785 

49» 

5071 

5214 

6355 

5496 

5637 

5777 

6917 

2 

26 

25 

24 

24     23 

^    3. 

6056 

6194 

6332 

6469 

6606 

6742 

6878 

7014 

7148 

7283 

3 

39 

38 

37 

35     34 

O     4. 

7417 

7550 

7683 

7815 

7947 

8079 

8210 

8341 

8471 

8601 

4 

52 

80 

49 

47     46 

8730 

8859 

8987 

9115 

9243 

9370 

9497 

9623 

9749 

9876 

5 

66 

63 

61 

69     57 

4.0000 

0125 

0249 

0373 

0497 

0620 

0743 

0866 

0988 

1110 

6 

78 

76 

73 

70     68 

^     7. 

1231 

1352 

1473 

1593 

1713 

1833 

1952 

2071 

2190 

2308 

7 

91 

88 

85 

83    80 

.S     8. 

2426 

2544 

2661 

2778 

2895 

3012 

3128 

3243 

3359 

3474 

8 

104 

lui 

98 

94     01 

3589 

3704 

3818 

3932 

4045 

4159 

4272 

4385 

4497 

4609 

9 

117  113  110  10«  103 

4721 

4833 

4944 

6055 

5166 

6277 

6387 

6497 

6607 

5717 

110106103 

98    94 

6826 

5935 

6043 

6152 

6260 

6368 

6476 

6583 

6690 

6797 

1 

11 

11 

10 

10      9 

p. 

•S  26. 

6904 

7011 

7117 

7223 

7329 

7434 

7539 

7646 

7749 

7854 

2 

22 

21 

20 

20     19 

7958 

8062 

8166 

8270 

8374 

8477 

8580 

8683 

8785 

8888 

33 

32 

31 

29     28 

8990 

9092 

9193 

9295 

9396 

9497 

9598 

9699 

9800 

9900 

44 

42 

41 

39    38 

5.0000 

0100 

0200 

0299 

0398 

0498 

0696 

0695 

0794 

0892 

56 

63 

61 

49    47 

•H      6. 

0990 

1088 

1186 

1284 

1381 

1478 

1575 

1672 

1769 

1866 

66 

64 

61 

59    66 

II     7. 

1962 

2058 

2154 

2249 

2345 

2440 

2536 

2631 

2726 

2820 

77 

74 

71 

69    66 

£    8. 

2915 

3009 

3104 

3198 

3292 

3385 

3479 

3572 

3666 

3759 

88 

85 

82 

78    75 

1     9. 

3853 

3944 

4037 

4129 

4222 

4314 

4406 

4498 

4689 

4681 

99 

95 

92 

88    85 

§•30. 

4772 

4863 

4955 

5045 

5136 

5227 

5317 

5408 

6498 

6588 

90 

88 

86 

84    83 

ey      1- 

5678 

5767 

5857 

5946 

6036 

6125 

6214 

6303 

6391 

6480 

9 

9 

9 

8      8 

^     2. 

6569 

6657 

6745 

6833 

6921 

7009 

7096 

7184 

7271 

7369 

18 

18 

17 

17     16 

**    3. 

7446 

7533 

7619 

7706 

7793 

7879 

7966 

8062 

8138 

8224 

27 

26 

26 

25    25 

e    4. 

8310 

8395 

8481 

8566 

8652 

8737 

8822 

8907 

8992 

9076 

36 

35 

34 

34    33 

2  36. 

9161 

9245 

9330 

9414 

9498 

0582 

9666 

9749 

9833 

9917 

45 

44 

43 

42    41 

.s  «• 

6.0000 

0083 

0166 

0249 

0332 

0415 

0498 

0581 

0663 

0745 

54 

63 

62 

50    49 

il: 

0828 

0910 

0992 

1074 

1156 

1237 

1319 

1400 

1482 

15Q3 

63 

62 

60 

59    57 

1644 

1725 

1806 

1887 

1968 

2048 

2129 

2209 

2290 

2370 

72 

70 

69 

67    66 

rt  ^• 

2450 

2530 

2610 

2690 

2769 

2849 

2929 

3008 

3087 

3166 

81 

79 

77 

76    74 

■§T' 

3246 

3325 

3403 

3482 

3561 

3640 

3718 

3797 

3875 

3953 

80 

78 

76 

74    72 

4031 

4109 

4187 

4265 

4343 

4420 

4498 

4576 

4653 

4730 

8 

8 

8 

7      7 

ra    2. 

4807 

4885 

4962 

5038 

5115 

5192 

5269 

5345 

5422 

5498 

16 

16 

16 

15    14 

w     3. 

5574 

5651 

5727 

5803 

5879 

5955 

6030 

6106 

6182 

6257 

24 

23 

23 

22    23 

u    4. 

"m  45. 

6332, 

6408 

6483 

6558 

6633 

6708 

6783 

6858 

6933 

7007 

32 

31 

30 

30    29 

7082 

7157 

7231 

7305 

7380 

7454 

7628 

7602 

7676 

7750 

40 

39 

38 

37    36 

S    ^■ 

7823 

7897 

7971 

8044 

8118 

8191 

8264 

8337 

8411 

8484 

48 

47 

46 

44    43 

jQ     7. 

8557 

8629 

8702 

8775 

8848 

8920 

8993 

9065 

9138 

9210 

56 

55 

53 

52    50 

^     8. 

9282 

9354 

9426 

9498 

9570 

9642 

9714 

9785 

9857 

9929 

64 

62 

61 

59    58 

9. 

7.0000 

0071 

0143 

0214 

0285 

0356 

0427 

0498 

0569 

0640 

72 

70 

68 

67    65 

*Square  Roots  are  obtained  directly  as  in  the  logarithmic  tables,  using  the 
Proportional  Parts  column  for  interpolation. 
Squares  may  be  obtained  by  inverse  interpolation^  . 

Digitized  by  VjOOQ  IC 


ENGINEERS'  TABLES— SQUARE  ROOTS. 


19 


Evtn.  Odd. 

— tPROu  10  TO  100;    1,000  to  10,000;  etc. 


8q. 

V.o 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

P.  P. 

80. 

74*711 

0781 

0852 

0922 

0993 

1063 

1134 

1204 

1274 

r344 

71 

70  69 

68  67 

1. 

1414 

1484 

1551 

1624 

1694 

1764 

1833 

1903 

1972 

2042 

1 

7 

7   7 

7   7 

2. 

2111 

2180 

2250 

2319 

2388 

2157 

2526 

2595 

2664 

2732 

2 

14 

14  14 

14  13 

3 

2801 

»70 

2938 

3007 

3075 

3144 

3212 

3280 

3348 

3417 

3 

21 

21  21 

20  20 

1. 

3485 

3553 

3621 

3689 

3756 

3824 

3892 

3959 

4027 

4095 

4 

28 

28  28 

27  27 

» 

4182 

4220 

4297 

4364 

4431 

4498 

4565 

4632 

4699 

4766 

5 

36 

35  35 

34  34 

1. 

4833 

4900 

4967 

5033 

5100 

5166 

5233 

5299 

5366 

5432 

6 

43 

42  41 

41  40 

7. 

M»8 

5565 

5631 

5697 

6763 

5829 

5895 

5961 

6026 

6092 

7 

50 

49  48 

48  47 

8. 

6158 

6223 

6289 

6354 

6420 

6485 

6551 

6616 

6681 

6746 

8 

67 

66  55 

54  54 

6811 

6877 

6942 

7006 

7071 

7136 

7201 

7266 

7330 

7395 

9 

64 

63  62 

61  60 

7480 

7524 

m 

7653 

7717 

7782 

7846 

7910 

7974 

8038 

06 

65  64 

63  62 

ft     1 

8102 

8166 

8294 

8358 

8422 

8486 

8549 

8613 

8677 

1 

7 

7   6 

6   6 

5  2. 

8740 

8804 

8867 

8930 

8994 

9057 

9120 

9183 

9246 

9310 

2 

13 

13  13 

13  12 

c  3 

9373  ,  9436 

9498 

9561 

9624 

9687 

9750 

9812 

9875 

9937 

3 

20 

20  19 

19  19 

-  4 

8.0000 

0062 

0125 

0187 

0250 

0312 

0374 

0436 

0498 

0561 

4 

26 

26  26 

25  25 

11; 

0623 

0685 

0747 

0808 

0870 

0933 

0994 

1056 

1117 

1179 

5 

33 

33  32 

32  31 

1240 

1302 

1363 

1425 

1486 

1548 

1609 

1670 

1731 

1792 

6 

40 

39  38 

38  37 

1=^ 

1854 

1915 

1976 

2037 

2098 

2158 

2219 

2280 

2341 

2401 

7 

46 

46  45 

44  43 

2463 

»23 

2583 

2644 

2704 

2766 

2825 

2885 

2946 

3006 

8 

53 

52  51 

50  50 

3066 

3126 

3187 

3247 

3307 

3367 

3427 

3487 

3546 

3606 

9 

59 

59  58 

57  56 

^70. 

3666 

3726 

3785 

3845 

3905 

3964 

4024 

4083 

4143 

420S 

61 

60  59 

58 

7  1 

4281 

4321 

4380 

4439 

4499 

4558 

4617 

4676 

4735 

4794 

1 

6 

6   6 

6 

I  2. 

4853 

4912 

4971 

5029 

5088 

5147 

5206 

5264 

5323 

5381 

2 

12 

12  12 

12 

e  3- 

5440 

5499 

5557 

5615 

5674 

5732 

5790 

5849 

5907 

5965 

3 

18 

18  18 

17 

§  '■ 

6023 

6081 

6139 

6197 

6256 

6313 

6371 

6429 

6487 

6545 

4 

24 

24  24 

23 

?75. 

6603 

6660 

6718 

6776 

6833 

6891 

6948 

7006 

7063 

7121 

5 

31 

30  30 

29 

1?: 

7178 

7235 

7293 

7350 

7407 

7464 

7521 

7579 

7636 

7693 

6 

37 

36  35 

35 

n50 

7807 

7864 

7920 

7977 

8034 

8091 

8148 

8204 

8261 

7 

43 

42  41 

41 

=  !• 

8318 

8374 

8431 

8487 

8544 

8600 

8657 

8713 

8769 

8826 

8 

49 

48  47 

46 

5  •■ 

6882 

8038 

8994 

8051 

9107 

9163 

9219 

9275 

9331 

9387 

9 

55 

54  53 

52 

=  §•, 

M43 

9499 

9554 

9610 

9666 

9722 

9778 

9833 

9889 

9944 

57 

56  55 

54 

H.  i 

9.BU00 

0056 

0111 

0167 

0222 

0277 

0333 

0388 

0443 

0499 

1 

6 

6   6 

5 

-  2. 

0654 

0609 

0664 

0719 

0774 

0830 

0885 

0940 

0996 

1049 

2 

11 

11  11 

11 

2  3 

1104 

1159 

1214 

1269 

1324 

1378 

1433 

1488 

1542 

1597 

3 

17 

17  17 

16 

C  4. 

1653 

1706 

1761 

1815 

1869 

1924 

1978 

2033 

2087 

2141 

4 

23 

22  22 

22 

2105 

2250 

2304 

2358 

2412 

2466 

2520 

2574 

2628 

2682 

5 

29 

28  28 

27 

«  6- 

2736 

2790 

2844 

2898 

2952 

3005 

3059 

3113 

3167 

3220 

6 

34 

34  33 

32 

«  7. 

ir4 

3327 

3381 

3434 

3488 

3541 

3595 

3648 

3702 

3755 

7 

40 

39  39 

38 

C  S. 

3808 

3862 

3915 

3968 

4021 

4074 

4128 

4181 

4234 

4287 

8 

46 

45  44 

43 

1  ». 

4340 

4393 

4446 

4499 

4552 

4604 

4657 

4710 

4763 

4816 

9 

51 

60  60 

49 

JcM. 

4868 

4921 

4974 

5026 

5079 

5131 

5184 

5237 

5289 

6341 

53 

52  51 

90 

O  I. 

5394 

5446 

5499 

5551 

5603 

5656 

5708 

5760 

5812 

5864 

1 

5 

5   6 

5 

2. 

8017 

5969 

6021 

6073 

6120 

6177 

6229 

6281 

6333 

6385 

2 

11 

10  10 

10 

2 

6437 

6488 

6540 

6592 

6644 

6695 

6747 

6799 

6850 

6902 

3 

16 

16  15 

15 

i. 

6954 

7005 

7057 

7108 

7160 

7211 

7263 

7314 

7365 

7417 

4 

21 

21  20 

20 

fS. 

7468 

7519 

7570 

7622 

7673 

7724 

7776 

7826 

7877 

7929 

5 

27 

26  26 

25 

«. 

7980 

8031 

8082 

8133 

8184 

8234 

8285 

8336 

8387 

8438 

6 

32 

31  31 

30 

7. 

8489 

8539 

8590 

8641 

8691 

8742 

8793 

8843 

8894 

8944 

7 

37 

36  36 

35 

8. 

8995 

9045 

9096 

9146 

9197 

9247 

9298 

9348 

9398 

9448 

8 

42 

42  41 

40 

» 

,  9499 

9549 

9599 

9649 

9700 

9750 

9800 

9850 

9900 

9950 

9 

48 

47  46 

45 

tPor  squares  I  — 10,  10(f— 1,000.  etc.,  see  preceding  table. 

Digitized  by  VjOOQ  IC 


30 


2,— POWERS.  ROOTS  AND  RECIPROCALS. 


Cube  Root. — ^The  cube  roots  of  numbers  may  be  obtained  from  Tables 
3,  4  and  6,  as  follows:  ^ 


Table. 
3 

4 

6 


Whole  Numbers  (cubes). 


1  to  60. 
1000  to  50000.  etc. 

1  to  1000.  etc. 
Any  number. 

1  to.  1.6. 
1000  to  1600.  etc. 


Decimals  (cubes).  Remarks. 

.001  to  .060.  Srecial 

.000001  to  .000060.  etc.  table. 

.001  to  1.  etc.  General 

Any  decimal.  table. 

.001  to  .0016.  Special 

.  000001  to  .  0000016.  etc.  table. 


Note  that,  the  special  tables.  8  and  6.  give  results  more  accurately, 
within  their  limits,  than  does  the  general  table,  4.  The  least  accuracy 
from  these  tables  is  for  numbers  just  above  1.5,  or  just  above  1500;  and 
for  the  cube  roots  of  such  numbers  Table  3  may  be  used,  or  Tables  9  and 
10.  remembering  that  "chantnng  three  decimal  points  in  the  cube— one 
decimal  point  in  the  root — ^in  the  same  direction. 

Table  3"  gives  the  cube  roots  of  numbers  from  1  to  60  :  directly,  ad- 
vancing by  tenths;  and  by  one  interpolation  of  the  P.  P.  table,  advancing 
by  hundreths.  Thus,  the  cube  root  of  24.4  is  2.9004;  of  24.46  is  2.9004  + 
20—2.9024.  the  20  being  obtained  from  the  P.P.  tabib  opposite  6  and 
under  the  difference  40  (-9044-9004). 

By  manipulating  the  decimal  point,  the  cube  root  of  0.02445  is  0.29024; 
of  24450  is  29.024.  etc.  Note  that  if  the  decimal  point  is  changed  only 
one  or  two  places  in  the  cube  the  cube  root  comprises  another  set  of  signifi- 
cant figures,  as.  cube  root  o(  24.4-2.9004;  of  2.44-1.3463;  of  0.244 *» 
0.6249. 

Table  5  is  especially  useful  in  finding  the  cube  roots  of  numbers  from 
1  to  1.6,  or  from  1000  to  1600.  The  cub^  of  ntmibers  with  four  significant 
figures  may  be  obtained  directly  from  the  table,  and  of  numbers  with  five 
significant  figures  may  be  obtained  by  one  interpolation  of  the  P.  P.  table. 
Thus,  cube  root  of  1.146-1.04617;  of  1.1462-1.04628,  the  increment 
being  Vio  of  the  difference  30  (-464f-4617).  Likewise,  the  cube  root  of 
1146.2-10.4623. 

Table  4  is  a  general  table,  with  numbers  from  1  to  1000.  Its  special 
range,  however,  is  for  numbers  from  60  to  1000. 

Cubes  of  nxunbers  may  be  obtained  by  inverse  interpolation. 

For  numbers  beyond  the  accurate  range  of  the  tables  the  following 
methods  are  given  for  extracting  the  cube  root: 


By  Algebra. 
Cube  root  of  o>+ 3a%-f  3ajK«  +  ic»  ? 


By  Arithmetic. 
Cfuberoot  of  12.167? 


a^+ZdH+3axl'+x*(a+x.  Ans.      3a«-1200  12167(20+3-23.  Ans. 

o*       Assume  * -3 :  3aa:-  180  _8000   a+x 

3a«+3<w+x«)     ^hc+2ax*+x*'                        a-'-      9  4167 

3a«x+3cuf>+*»         3o»+3a«'+a:«=1389)  4167 


Example. — Extract  the  cube"root  of  46.354.87  ? 


Remarks. — 
Beginn  i  n  g 
with  the 
unit  figure, 
point  off  3 
places  each 
way,  form- 
ing groups 
of  3  fig- 
ures to  be 
brought 
down  each 
time.  Pro- 
ceed as  in- 
dicated. 


Process: 


Ox -30. 
Assume  ^1—  5: 


3ai«-3(30»)-2700 
3aiT,  =3.30.5-  450 

afi«-       y-     25  J 

3175   )  19354 
15875 


46354.870(35.9+ 
27 


Ans. 


02-260.  3a2*-3(350») -367500 
Assume  ifj- 9:  302*2  =  3.350.9  «•     9460 

xa«-         93- 81 

377031 


3479870 


00-3 
o,  =  30 
02-350 
aj-3590 


3393279 


o^-36fl 
Assume  atj  —  ? 


308» 
303af; 


86591000 


Ready  for  an< 

Digitized  by 


tion. 


ENGINEERS'  TABLES-^UBE  ROOTS.  21 


1  to  50  .001  to  .060 

1.000  to  50.000  .000.001  to  .000.060 

3. — CuBB  Roots  (and  Cubbs*)  of  Numbers  1  to  50. 


•CuA*  RooU  arc  obtained  directly  as  in  the  logarithmic  tables,  iising  the 
Proportional  Parts  tables  for  interpolation. 
Cubts  may  be  obtained  by  inverse  interpolation.    Digged  by  GoOglc 


2.— POWERS,  ROOTS  AND  RECIPROCALS. 

1  to  500  .001  to  .5 

1,000  to  500.000  .000.001  to  .0005 

4. —  CuBB  Roots  (and  Cubes*)  of  Numbers  1  to  1,000 — 


*Cube  Roots  are  obtained  directly  as  in  the  logarithmic  tables,  using  the 
Proportional  Parts  tables  for  interpolation. 
Cubes  may  be  obtained  by  inverse  interpolation. 
The  dash  (-)  is  to  be  supplied  by  figs.  0  to  9  at  the  head  of  the  respective 

^^""™"-  Dgtized  by  Google 


ENGINEERS'  TABLES— CUBE  ROOTS,  23 

800  to  1.000  .6tol 

800.000  to  1.000.000  .0005  to  .001 

—And  Any  Other  Numbers ;  or  Decimals. 


J 

Ex-Cttbe  root  of  887.2  ?  Solution— 9.6082  for  887 

7  for .2 

Ans.     9.6069  for  887.2 
The  dach  (-)  is  to  be  supplied  by  figs.  0  to  9  at  the  head  of  the  respective 

Digitized  by  VjOOQ  IC 


24  2.—P0WERS,  ROOTS  AND  RECIPROCALS: 

1  to  1.6 
1.000  to  1.500  .001  to  .0015 

1.000.000  to  1.500.000  .000001  to  .0000015 

5. — CuBB  Roots  (and  Cubes*)  of  Numbers  1,000  to  1.500. 


Cube 

Vo. 

1. 

2. 

3. 

4. 

6. 

6. 

7. 

8. 

9. 

P.  P. 

1000 

.00-. 

IO.0000 

0033 

0067 

0100 

0133 

0166 

0200 

0233 

0266 

0299 

34  33  3331 

,«1- 

0332 

0365 

0398 

0431 

0466 

0498 

0631 

0563 

0696 

0629 

3  3  3  3 

.02-. 

0662 

0695 

0728 

0761 

0794 

0626 

0669 

0892 

0925 

0957 

7  7  6  6 

.03-. 

0990 

1023 

1056 

1088 

1121 

1153 

1186 

1218 

1251 

1383 

10  10  10  9 

1' 

.04-. 
)50 
.06-. 

1316 

1348 

1381 

1413 

1446 

1478 

1510 

1543 

1576 

1607 

14  13  13  12 

1640 

1672 

1704 

1736 

1769 

1801 

1833 

1865 

1807 

1929 

17  17  16  16 

.06-. 

1961 

1993 

2026 

2057 

2089 

2121 

2153 

2185 

2217 

2249 

20  20  19  19 

.07-. 

2281 

2313 

2346 

2376 

2408 

2440 

2472 

2503 

2536 

2567 

24  23  22  23 

*i 

.08-. 

2599 

2630 

2662 

2693 

2726 

2757 

2788 

2820 

2861 

2883 

27  26  26  25 

.09-. 

00 

.10-. 

2914 

2946 

2977 

3009 

3040 

3071 

3103 

3134 

3165 

3197 

31  30  29  28 

3228 

3259 

3291 

3322 

3363 

8384 

3415 

3447 

3478 

8609 

32  31  30  39 

a 

.11-. 

3540 

3571 

3602 

3633 

3664 

3696 

3726 

3757 

3788 

3819 

3  3  3  3 

C3 

.12-. 

3850 

3881 

3912 

3943 

3973 

4004 

4035 

4066 

4097 

4127 

6  6  6  6 

•S 

.13-. 

4168 

4189 

4219 

4250 

4281 

4311 

4342 

4373 

4404 

4434 

10  9  ft  9 

•S  1 

.14-. 

50 

,15-. 

4464 

4495 

4625 

4656 

4686 

4617 

4647 

4678 

4708 

4739 

13  12  12  12 

s' 

4769 

4799 

4830 

4860 

4890 

4921 

4951 

4981 

5011 

6042 

16  16  15  IS 

1 

.16-. 

6072 

6102 

6132 

5162 

5192 

5223 

5253 

6283 

5313 

6343 

19  19  18  17 

.17-. 

6373 

5403 

6433 

5463 

5493 

5523 

5553 

5583 

6612 

5642 

22  22  21  20 

l.l»-. 

6672 

6702 

6732 

6762 

6791 

5821 

6851 

5881 

6910 

6940 

26  25  24  23 

a 

,19- 

6970 

6000 

6029 

6059 

6088 

6118 

6148 

6177 

6207 

6236 

29  28  27  26 

•o  1 

(00 

,20-. 

6266 

6295 

6326 

6354 

6384 

6413 

6443 

6472 

6601 

66S1 

30  39  38  27 

1 

.21-. 

6560 

6590 

6619 

6648 

6678 

6707 

^36 

6765 

6796 

6824 

3  3  3  8 

1 

.22-. 

6853 

6882 

6911 

6940 

6970 

6999 

7028 

7057 

7086 

7116 

6  6  6  6 

.23-. 

7144 

7173 

7202 

7231 

7260 

7289 

7818 

7347 

7376 

7405 

9  9  8  8 

1" 

,24-. 
850 
.25-. 

7434 

7463 

7491 

7520 

7549 

7580 

7607 

7635 

7664 

7693 

12  12  11  U 

7722 

7760 

7779 

7808 

7837 

7865 

7894 

7922 

7951 

7980 

16  15  14  14 

.5 

,26-. 

8008 

8037 

8066 

8094 

8122 

8051 

8179 

8208 

8236 

8265 

18  17  17  16 

5 
a 

a.: 

.27-. 

8293 

8322 

8350 

8378 

8407 

8436 

8463 

8492 

8520 

8548 

21  20  20  19 

.28-. 

8577 

8605 

8633 

8661 

8690 

8718 

8746 

8774 

8802 

8831 

24  23  22  22 

.29-. 

00 

.30-. 

8859 

8887 

8915 

8943 

8971 

8999 

9027 

9055 

9063 

9111 

27  26  26  24 

9139 

9167 

9195 

9223 

9251 

9279 

9307 

9335 

9363 

9391 

39  38  37  2* 

2 

.31-. 

9418 

9446 

9474 

9502 

9530 

9757 

9685 

9613 

9641 

9668 

3  3  3  3 

.g 

.32-. 

9696 

9724 

9752 

9779 

9807 

9834 

9862 

9890 

9917 

9945 

6  6  5  6 

^ 

,33-. 

9972 

0000 

0028 

0O55 

0083 

0110 

0138 

0165 

0193 

0220 

9  8  8  8 

•§ 

.34-. 

11.0247 

0275 

0302 

0330 

0357 

0384 

0412 

0439 

0466 

0494 

12  U  11  10 

CO  1. 

150 

1 

oS 

.36-. 

0521 

0548 

0575 

0603 

0630 

0667 

0684 

0712 

0739 

0766 

15  14  14  13 

I .36-. 

0793 

0820 

0847 

0875 

0902 

0929 

0956 

0983 

1010 

1037 

17  17  16  16 

1 .37-. 

1064 

1091 

1118 

1145 

1172 

1199 

1226 

1253 

1280 

1307 

20  20  19  18 

1 .38-. 

1334 

1361 

1387 

1414 

1441 

1468 

1496 

1622 

1548 

1676 

23  23  22  21 

s, 

1 .39-. 

100 

1,40-. 

1602 

1629 

1655 

1682 

1709 

1736 

1762 

1789 

1816 

1842 

26  25  24  23 

1869 

1896 

1922 

1949 

1975 

2002 

2028 

2055 

2082 

2108 

27  36  35 

1,41-. 

2136 

2161 

2188 

2214 

2241 

2267 

2293 

2320 

2346 

2373 

3  3  3 

1.42-. 

2399 

2425 

2452 

2478 

2506 

2631 

2557 

2583 

2610 

2636 

6  5  5 

1,43-. 

2662 

2689 

2715 

2741 

2767 

2793 

2820 

2846 

2872 

2898 

8  8  8 

• 

1.44-. 

150 

1.46-. 

2924 

2950 

2977 

8003 

3029 

3055 

3081 

3107 

3133 

8169 

11  10  10 

3185 

3211 

3237 

3263 

3289 

3316 

3341 

3367 

3393 

3419 

14  IS  13 

1,46-. 

8445 

3471 

3496 

3522 

3548 

3574 

360d 

3626 

3652 

3677 

16  16  15 

I.47-. 

3703 

3729 

3755 

3780 

3806 

3832 

3858 

3883 

3909 

3935 

19  18  18 

1,48-. 

3960 

3986 

4012 

4037 

4063 

4089 

4114 

4140 

4166 

4191 

22  21  20 

1 

1  49-. 
SCO 

4206 

4242 

4268 

4293 

4319 

4344 

4370 

4395 

4421 

4446 

24  23  23 

*Ex.— Cube  of  1.07275?  Solution— 1.234   for  1.07260 

.OOOSJor     16 

Ans.     r2345  for  1.07275 
The  dash  (-)  is  to  be  supplied  by  figs.  0  to  9  at  the  head  of  the  r«spectrv« 

Digitized  by  VjOOv  IC 


ENGINEERS  TABLES—SQ.  RTS.  OF  Mi  POWERS. 


2$ 


t— Square  Roots  of  Fifth  Powers  of 

Numbers,  Advancing 

BY  0.26. 

N 

V]7».M 

.26 

.50 

.75 

AT. 

v^».oo 

.25 

.60 

.75 

•. 

Zero. 

.03125 

.17678 

.48714 

50. 

17678. 

17899. 

18123. 

18348. 

1. 

1.0000 

1.7469 

2.7507 

4.0513 

51. 

18576. 

18803. 

19033. 

19265. 

1. 

5.1500 

7.5937 

9.8821 

13.541 

52. 

19499. 

19734. 

19971. 

20210. 

3. 

15.588 

19.042 

22.918 

27.233 

53. 

20450. 

20692. 

20936. 

21181. 

4. 

33.000 

37.237 

42.957 

49.174 

54. 

21428. 

21677. 

21928. 

22180. 

1    ». 

55.902 

63.154 

70.943 

79.281 

65. 

22434. 

22690. 

22947. 

23207. 

\    «. 

88.183 

97.656 

107.72 

118.38 

56. 

23468. 

23731. 

28995. 

24261. 

I    ^- 

129.64 

141.53 

154.05 

167.21 

57. 

24529. 

24799. 

26071. 

25344. 

8. 

181.03 

195.50 

210.64 

226.48 

58. 

25620. 

25896. 

26175. 

26456. 

'    ». 

243.00 

360.33 

278.17 

296.83 

50. 

26738. 

27022. 

27308. 

27596. 

It. 

311.33 

336.36 

357.25 

378.90 

60. 

27886. 

28177. 

28470. 

28765. 

11. 

401.31 

424.50 

448.48 

473.35 

61. 

29062. 

29361. 

29661. 

29963. 

12. 

408.83 

525.22 

552.43 

580.46 

62. 

30268. 

30574. 

30882. 

31191. 

\  »'• 

609.34 

639.06 

669.63 

701.06 

63. 

31503. 

31816. 

32132. 

32449. 

I  14. 

733.30 

766.54 

800.61 

835.56 

64. 

33768. 

33069. 

83413. 

33736. 

■  15. 

871.43 

906.19 

945.87 

984.47 

65. 

34063. 

34392. 

34722. 

35054. 

-  11. 

1034.0 

1064.5 

1105.9 

1148.2 

66. 

36388. 

35724. 

36062. 

36402. 

•  17. 

119l.f 

1235.9 

1281.1 

1327.4 

67. 

36744. 

37088. 

37433. 

37781. 

►  i». 

1374.6 

1423.8 

1472.1 

1522.3 

68. 

38131. 

38482. 

38835. 

39191. 

.  *•• 

1573.6 

1625.8 

1679.1 

1733.5 

69. 

39648. 

39907. 

40268. 

40631. 

i  ^ 

1788.9 

1846.3 

1902.8 

1961.3 

70. 

40996. 

41363. 

41733. 

42103. 

21. 

2020.9 

2081.6 

2143.4 

2206.2 

71. 

42476. 

42851. 

43228. 

43607. 

22. 

2270.2 

2335.3 

2401.4 

2468.7 

72. 

43988. 

44371. 

44755. 

45142. 

L». 

2537.0 

2606.6 

2677.1 

2748.9 

73. 

45531. 

46922. 

46315. 

46709. 

24. 

2S21.8 

2895.9 

2971.1 

3047.5 

74. 

47106. 

47605. 

47906. 

48309. 

|25. 

3135.0 

3303.7 

3283.6 

3364.7 

75. 

48714. 

49121. 

49530. 

49941. 

5  il. 

3446.9 

3530.4 

3615.1 

3700.9 

76. 

50354 

60769. 

51188. 

61606. 

J  27. 

3788.0 

3876.3 

3965.8 

4056.6 

77. 

52027! 

524S0. 

52875. 

63303. 

»»• 

4148.5 

4241.8 

4386.3 

4431.9 

78. 

63732. 

64164. 

54598. 

55033. 

». 

4538.9 

4627.2 

4726.7 

4827.4 

79. 

66471. 

65911. 

56353. 

56797. 

:». 

4929.5 

5032.8 

5137.5 

5243.4 

80. 

67243. 

57692. 

58142. 

58594. 

:  31. 

5350.6 

5450.2 

5569.0 

6680.1 

81. 

59049. 

69964. 

60425. 

a. 

5792.6 

5006.4 

6021.6 

6138.0 

82. 

60888. 

61364! 

61821. 

62290. 

33. 

62558 

6375.0 

6495.5 

6617.4 

83. 

62762. 

63235. 

63711. 

64189. 

M. 

6740.6 

6865.2 

6991.1 

7118.6 

84. 

64669. 

65161. 

65636. 

66122. 

'35. 

7347.3 

7377.3 

7508.8 

7641.7 

85. 

66611. 

67102. 

67595. 

68090. 

3f. 

7n6.0 

7911.7 

8048.8 

8187.3 

86. 

68588. 

69087. 

69589. 

70093. 

17. 

8327.3 

8468.7 

8611.5 

8756.7 

87. 

70599. 

71107. 

71618. 

72130. 

2- 

8901.4 

9048.5 

9197.1 

9347.2 

88. 

72646. 

73162. 

73681. 

74203 

2». 

9496.6 

9651.6 

9806.0 

9961.9 

89. 

74727. 

75252. 

75781. 

76311. 

f^ 

10119. 

10278. 

10438. 

10600. 

90. 

76843. 

77378. 

77915. 

78454. 

41. 

10764. 

10929. 

11095. 

11363. 

91. 

78996. 

79539. 

80085. 

80633. 

pH 

11433. 

11603. 

11775. 

11949. 

92. 

81184. 

81737. 

82291 . 

82849. 

«. 

13125. 

12302. 

12480. 

12660. 

93. 

834U8. 

83970. 

84534. 

85100. 

44. 

138a. 

13025. 

13210. 

13396. 

94. 

86668. 

86239. 

86812. 

87387. 

45, 

I3S64. 

13n4 

13965. 

14157. 

95. 

87965. 

88546. 

89127. 

89711. 

41. 

14351. 

14547. 

14745. 

14044. 

96. 

90298. 

90887. 

91478. 

92072. 

47. 

15144. 

15346. 

15550. 

15766. 

97. 

92668. 

93206. 

93867. 

94470. 

4t. 

15963. 

16171. 

16382. 

16593. 

98. 

95075. 

96682. 

96292 

96904. 

•. 

10807. 

17022. 

17239. 

17458. 

99. 

97519. 

98136. 

98755. 

99376. 

Ml 

17678. 

17899. 

18123. 

18348. 

too. 

100000. 

100626. 

101255. 

101886. 

Note  that  >/lV»  -iV*-N«"*"^-iV«  xiV^-AT'X  >/^.  Hence,  the 
■hove  values  may  be  obtained  by  multiplying  together  the  square  and 
the  square  root  ot  the  respective  numbers. 

Digitized  by  VjOOQ IC 


26 


i.—POWERS,  ROOTS  AND  RECIPROCALS. 


7. — Fifth  Powers*  (and  Fifth  Roots)  of  Nuicbbrs  1  to  10 — 


N 

Ar»    0 

2 

4 

5 

6 

8 

1.00 

Unity 

1.01004 

1.02016 

1.02525 

1.03036 

1.04064 

.01 

1 .05101 

1.06146 

1.07199 

1.07728 

1.08260 

1 .09330 

.02 

1.10408 

1.11495 

1.12590 

1.13141 

1.13694 

1.14806 

.03 

1.15927 

1.17057 

1.18196 

1.18769 

1.19344 

1.20500 

.04 

1.21665 

1.22840 

1.24023 

1 .24618 

1.25216 

1.26417 

1.05 

1.27628 

1.28848 

1.30078 

1.30696 

1.31317 

1.32565 

•       .06 

1.35090 

1 .36367 

1.37009 

1.37653 

1.38949 

:       .07 

1.40255 

1 .41671 

1.42896 

1.43563 

1.44232 

1.45577 

;       .08 

1.46933 

1.48298 

1 .49674 

1.50366 

1.61060 

1.52456 

>       .09 

1.53862 

1 .55279 

1.56706 

1.67424 

1.58144 

1.59592 

I     1.0 

Unity 

1.10408 

1.21665 

1.27628 

1.33823 

1.46933 

?      * 

1.61051 

1.76234 

1 .92541 

2.00136 

2.11034 

2.28775 

^      .2 

2.48832 

2.70271 

2.93163 

3.05176 

3.17580 

3.43697 

:      -3 

3.71293 

4.00746 

4.32040 

4.48403 

4.65259 

5.00490 

»       .4 

5.37824 

5.77353 

6.19174 

6  40973 

6.63383 

7.10082 

!  1.6 

7.69375 

8.11368 

8.66171 

8.94661 

9.23896 

9.84658 

I       .6 

10.4858 

11.1677 

11.8637 

12.2298 

12.6049 

13.3828 

1       -7 

14.1986 

15.0537 

15.9495 

16.4131 

16.8874 

17.8690 

I      .8 

18.8957 

19.9690 

21.0906 

21.6700 

22.2620 

23.4849 

•' 

24.7610 

26.0919 

27.4795 

28.1961 

28.9255 

30.4317 

1     3.0 

32.0000 

33.6323 

35.3306 

36.2051 

37.0968 

38.9329 

^,       •* 

40.8410 

42.8232 

44.8817 

45.9401 

47.0185 

49.2360 

.2 

51.5363 

53.9219 

66.3949 

57.6650 

58.9579 

61.6133 

>       .3 

64.3634 

67.2109 

70.1583 

71.6703 

73.2082 

76.3633 

.4 

79.6262 

82.9998 

86.4867 

88.2735 

90.0898 

93.8130 

*    2.5 

97.6563 

101.626 

105.723 

107.820 

109.951 

114.314 

3       -8 

118.814 

123.454 

128.239 

130.686 

133.171 

138.253 

.     '^ 

143.489 

148.883 

154.438 

157.276 

160.157 

166.044 

I       .8 

172.104 

178.339 

184.753 

188.029 

191.351 

198. 13« 

i      .9 

205.111 

212.283 

219.653 

223.414 

227.226 

235.007 

i    3.0 

243.000 

261 .209 

259.638 

263.936 

268.292 

277.175 

286.292 

295.647 

305.245 

310.136 

315.091 

325.189 

3       !2 

335.544 

346.162 

357.047 

362.591 

368.204 

379.637 

5       .3 

391.354 

403.358 

415.655 

421.914 

428.249 

441.147 

i  •* 

454.354 

467.876 

481.717 

488.760 

495.884 

510.383 

1 

3     3.5 

525.219 

540.398 

555.925 

563.822 

671.808 

588.051 

« 

604.662 

621.646 

639.009 

647.835 

656.758 

674.899 

3        .7 

693.440 

712.385 

731.742 

741.577 

751.517 

771.719 

^       .8 

792.362 

813.424 

834.941 

845.870 

856.913 

879.343 

3        .9 

902.242 

925.615 

949.470 

961.580 

973.814 

998. 6S5 

»    4.0 

1024.00 

1049.86 

1076  23 

1089.62 

1103.14 

1130.58 

2      .1 

1158.56 

1187.10 

1216.19 

1230.95 

1245.85 

1276.09 

?      .2 

1306.91 

1338.33 

1370.34 

1386.58 

1402.97 

1436.21 

«       .3 

1470.08 

1504.59 

1539.74 

1557.57 

1575.55 

1612.02 

3    -^ 

1649.16 

1686.99 

1725.60 

1745.02 

1764.71 

1804.64 

4.5 

1845.28 

1886.65 

1928.77 

1950.10 

1971.62 

2015.24 

.« 

2059.63 

2104.80 

2150.75 

2174.01 

2197.50 

2246.07 

.7 

2293.45 

2342.66 

2392.72 

2418.07 

2443.63 

2495.40 

.8 

2548.04 

2601.57 

2655.99 

2683.54 

2711.32 

2767.57 

.9 

2824.75 

2882.87 

2941.94 

2971.84 

3001.98 

3063.00 

5.0 

3125.00 

3188.00 

32.')2.01 

.3284.41 

3317.05 

3383.13 

♦Powers  (.V")  arc  obtained  directly  as  in  the  logarithmic  tables:  roots  (AT), 
by  inverse  interpolation. 

Note  that  Ar»»-N"  +  »-iV»  X  N=».  Hence,  the  above  values  may  be  ob- 
tained by  multiplying  together  the  square  and  the  cube  of  the  respective 
numbers.  C^r\nin]o 

Digitized  by  VjOOv  IC 


ENGINEERS  TABLES^FIFTH  POWERS.  27 

— ^Am>  Any  Wholb  Nuubbr;  or  Dbcimal. 


- 1 

iV«  0 

2 

4 

5 

6 

8 

5.0 

3125.00 

3188.00 

3252.01 

3284.41 

3317.05 

3383.13 

.1 

3450.25 

3518.44 

3587.70 

3622.73 

3658.04 

3729.49 

J 

3802.04 

3875.72 

3950.54 

3988.38 

4026.61 

4103.64 

.3 

4181.95 

4261 .46 

4342.17 

4382.97 

4424.09 

4607. ». 

.4 

4501.65 

4677.31 

4764.25 

4808.20 

4852.47 

4942.00 

5.5 

5032.84 

5125.02 

5218.54 

5265.81 

6313.42 

5409.67 

.6 

5507.32 

5606.37 

5706.84 

6757.61 

5808.74 

6912.10 

>       .7 

6016.92 

6123.22 

6231.02 

6285.49 

6340.34 

6451.18 

.8 

6563.67 

6677.52 

6793.04 

6851.40 

6910.16 

7028.89 

3      .9 

7149.24 

7271.24 

7394.89 

7457.36 

7620.24 

7647.26 

I     M 

7776.00 

7906.47 

8038.68 

8105.45 

8172.65 

8308.41 

'         J 

8445.96 

8585.33 

8726.54 

8797.83 

8869.59 

9014.62 

I       \t 

9161.33 

9310.05 

9460.69 

9536.74 

9613.28 

9767.83 

D        .3 

9924.37 

10082.9 

10243.5 

10324.5 

10406.0 

10670.7 

3        .4 

10737.4    • 

10906.2 

11077.2 

11163.5 

11260.3 

11426.5 

:     15 

11602.9 

11782.5 

11964.3 

12066.1 

12148.4 

12334.7 

•         C 

12523.3 

12714.2 

12907.5 

13004.9 

13103.0 

13300.9 

3     -7 

13301.3 

13704.0 

13900.1 

14012.6 

14116.7 

14326.8 

i     .8 

14539.3 

14754  4 

14972.0 

15081.8 

15192.2 

15414.9 

-    .» 

15640.3 

15868.3 

16098.9 

16215.3 

16332.2 

16668.3 

\   7^ 

16807.0 

17048.5 

17292.7 

17415.9 

17539.8 

17789.6 

IS042.3 

18297.8 

18556.3 

18686.6 

18817.6 

19081.9 

i    :1 

19349.2 

19619.4 

19892.7 

20030.4 

20168.9 

20448.3 

I        .3 

20730.7 

21016.3 

21305.0 

21450.6 

21696.8 

21891.8 

»        .4 

22190.1 

22491.5 

22796.3 

22949.9 

23104.4 

23415.7 

:    7.5 

23730.5 

24048.6 

24370.1 

24532.1 

24695.0 

26023.4 

.       .6 

25355.3 

25690.6 

26029.6 

26200  3 

26372.1 

26718.1 

5       .7 

27067.8 

27421.2 

27778.3 

27958.2 

28139.0 

28503.5 

5        .8 

28871.7 

29243.8 

29619.7 

29809.1 

29999.4 

30383.0 

3        .9 

30770.6 

31162.1 

31567.5 

31756.7 

31957.0 

32360.4 

'     &0 

32768.0 

33179.7 

33595.4 

33804.9 

34015.4 

34439.5 

.1 

34867.8 

35300.4 

35737.3 

35957.4 

36178.6 

36624.1 

.1 

37074.0 

37528.3 

37987.1 

38218.1 

38450.3 

38918.1 

.3 

39390.4 

39867.3 

40348.8 

40691 .3 

40834.9 

41325.7 

.4 

41821.2 

42321.4 

42826.4 

43080.8 

43336.3 

43851.0 

•      8.5 

44370.5 

44895.0 

45424.4 

45691.0 

46958.8 

46498.2 

.6 

47042.7 

47592.3 

48146.9 

48426.2 

48706.8 

49271.8 

.7 

49842.1 

50417.6 

50998.5 

51290.9 

61584.7 

52176.2 

.8 

52773.1 

63375.6 

53983.6 

54289.6 

64597 .0 

65216.0 

.9 

55840.6 

56470.9 

57106.8 

67428.9 

67748.4 

68396.8 

f     f.O 

B0049.0 

59706.0 

60372.9 

60707.6 

61043.7 

61720.4 

.1 

62403.2 

63092.0 

63786.8 

64136.6 

64487.8 

66194.9 

}         2 

65908.2 

66627.6 

67353.6 

67718.7 

68085.6 

68824.0 

.3 

69568.8 

70320.1 

71077.9 

71469.2 

71842.1 

72612.9 

A 

73390.4 

74174.5 

74966.3 

76363.1 

75762.7 

76567.0 

9.9 

77378.1 

78196.0 

79020.9 

79436.9 

79852.7 

80691.4 

.6 

81537.3 

82390.2 

83250.1 

83682.9 

84117.3 

84991.8 

.7 

85873.4 

86762.4 

87658.7 

88109.6 

88562.3 

89473.5 

.8 

90392.1 

91318.2 

92261.9 

92721.6 

93193.3 

94142.2 

.9 

95099.0 

96063.5 

97036.8 

97524.9 

98016.9 

99004.0 

l&O 

100000 

Examples:— 5th  root  of  7B00 - 6.954- .007  -  6.967. 
5th  root  of  0.76 -.944. 


d  by  Google 


28 


lto5. 


2.— POWERS,  ROOTS  AND  RECIPROCALS. 


8. — Rbciprocals  of  Numbbrs — 


N 

I* 

i 

LOO 

Unity 

f 

.01 

O.9901 

.02 

9804 

.03 

9709 

.04 

9615 

5 

1.05 

0.9624 

.s 

.06 

9434 

12 

.07 

9346 

O 

.08 

9259 

•^ 

.09 

9174 

•Xj 

1.0 

Unity 

1 

1 

0.9091 

.2 

8333 

.3 

7692 

.4 

7143 

o 

1.5 

0.6667 

1 

.6 

6250 

.7 

6882 

.s 

.8 

5556 

.9 

5263 

2.0 

O.5000 

.1 

4762 

.2 

4545 

.3 

4348 

1 

.4 

4167 

^ 

2.5 

0.4000 

g 

.6 

3846 

3 

.7 

3704 

(3 

.8 

3571 

2 

.9 

3448 

:S 

a 

3.0 

0.3333 

.1 

3226 

CO 

.2 

3125 

1 

.3 

3030 

.4 

2941 

a 

^ 

3.5 

0.2857 

.6 

2778 

*» 

.7 

2703 

.2 

.8 

2632 

S. 

.9 

2564 

73 

4.0 

O.2500 

g 

.1 

2439 

1 

.2 

2381 

.3 

2326 

.4 

2273 

5 

4.5 

0.2222 

3 

.6 

2174 

.7 

2128 

'1 

.8 

2083 

•' 

2041 

U5.0 

O.20O0 

9990 

.9980 

.9970 

.9960 

.9950 

.9940 

9891 

9881 

9872 

9862 

9852 

9843 

9794 

9785 

9775 

9766 

9756 

9747 

9699 

9690 

9681 

9671 

9662 

9653 

9606 

9597 

9588 

9579 

9669 

9860 

9515 

.9506 

.9497 

.9488 

.9479 

.9470 

9425 

9416 

9407 

9398 

9390 

9381 

9337 

9328 

9320 

9311 

9302 

9294 

9251 

9242 

9234 

9225 

9217 

9208 

9166 

9158 

9149 

9141 

9132 

9124 

9901 

.9804 

.9700 

.9615 

.9524 

.9434 

9009 

8929 

8850 

8772 

8696 

8621 

8264 

8197 

8130 

8066 

8000 

7937 

7634 

7576 

7519 

7463 

7407 

7353 

7092 

7042 

6993 

6944 

6897 

6849 

6623 

.6579 

.6536 

.6494 

.6452 

.6410 

6211 

6173 

6135 

6098 

6061 

6024 

5848 

5814 

5780 

6747 

5714 

5682 

5525 

5495 

5464 

5435 

6405 

5376 

5236 

5208 

6181 

5155 

5128 

5102 

4975 

.4950 

.4926 

.4902 

.4878 

.4864 

4739 

4717 

4696 

4673 

4651 

4630 

4525 

4505 

4484 

4464 

4444 

4425 

4329 

4310 

4292 

4274 

4255 

4237 

4149 

4132 

4115 

4098 

4082 

4065 

3984 

.3968 

.3963 

.3937 

.3922 

.3906 

3831 

3817 

3802 

3788 

3774 

3759 

3690 

3676 

3663 

3650 

3636 

3623 

3569 

3546 

3534 

3521 

3509 

3497 

3436 

3425 

3413 

3401 

3390 

3378 

3322 

.^n 

.3300 

.3289 

.3279 

.3268 

3215 

3205 

3195 

3185 

3175 

3165 

3115 

3106 

3096 

3086 

3077 

3067 

3021 

3012 

3003 

2994 

2985 

2976 

2933 

2924 

2915 

2907 

2899 

2890 

.2849 

.2841 

.2833 

.2825 

.2817 

.2809 

2770 

2762 

2755 

2747 

2740 

2732 

2695 

2688 

2681 

2674 

2667 

2660 

2625 

2618 

2611 

2604 

2597 

2591 

2558 

2551 

2545 

2538 

2532 

2525 

.2494 

.2488 

.2481 

.2475 

.2469 

.2463 

2433 

2427 

2421 

2415 

2410 

2404 

2375 

2370 

2364 

2358 

2353 

2347 

2320 

2315 

2309 

2304 

2299 

2294 

2268 

2262 

2257 

2252 

2247 

2242 

.2217 

.2212 

.2208 

.2203 

.2198 

.2193 

2169 

2165 

2160 

2155 

2151 

2146 

2123 

2119 

2114 

2110 

2105 

2101 

2079 

2075 

2070 

2066 

2062 

2058 

2037 

2033 

2028 

2024 

2020 

2016 

.1996 

.1992 

.1998 

.1984 

.1980 

.1976 

.9930 
9833 
9737 
9643 
9651 

.9461 
9372 
9285 
9200 
9H6 

,9346 
8547 
7874 
7299 


.6369 
5988 
5650 
6348 
6076 

.4831 
4608 
4405 
4219 
4049 


3746 
3610 
3484 
3367 

3267 
3155 
3058 
2967 


.2801 
2725 
2653 
2584 
2519 

.2467 


2237 

2188 
2141 
2096 
2053 
2012 

1972 


.9921 
9823 
9728 
9634 
9542 

.9452 
9363 
9276 
9191 
9107 

.9259 
8475 
7813 
7246 
6757 

.6329 
S952 
5618 
6319 
6051 

.4808 
4587 
4386 
4202 
4032 

.3876 
3731 
3597 
3472 
3356 

.3247 
3145 
3049 
2959 
2874 

.2793 
2717 
2646 
2577 
2513 

.2451 
2392 
2336 
2283 
2232 

.2183 
2137 
2092 
2049 
2008 

.1969 


(Subtract  tbedtL) 
9  P.  p. 


9911 
9814 
9718 
9625 
9533 

9443 
9365 
9268 
9183 
9099 


7752 
7194 
67^1 

.6289 
5917 
5587 
5291 
5025 

.4786 
4566 
4367 
4184 
4016 

.3861 
3717 
3584 
3460 
3344 

.3236 
3135 
3040 
2950 
2865 

.2786 
2710 
2639 
2571 
2506 

.2445 
2387 
2331 
2278 
2227 

.2179 
3132 
2088 
2046 
2004 

.1965 


^Reciprocals  to  four  decimal  places  on  this  page. 
Ex.— Find  reciprocal  of  2.743?  Solution— 0.3650 

-4 
Reciprocal  of  27.43-0.03646;  of  0.2743-3.646;  etc.  Q.dim    Ans. 

Digitized  by  VjOOQ IC 


ENGINEERS'  TABLES— RECIPROCALS  OF  NUMBERS.       29 


5  to  10. 


— ^Wholr  and  Decimal. 


I   1^ 
-V    aTo 


c    $^. 


ai 


.IA.I  »608 

2i  ♦231 

.3;  8S€8 

.4  8519 

S.5«.l  8182 

-it    7857 
.7    7544 

.9;    7241 

-» 


r 


M87 

a»3 

.2|  C128 
€.  .3|  5673 
^  .4    5625 

•  f.sloLl  5386 

f   .it    BI52 

-  .71    4925 

-  -8    4706 
.9    4483 


1    7.0  9. 


».l  4286 
4065 


3699 
3514 


7.5^1  8333 
2158 
2987 
2821 
2658 


£    a4>{0.l  2500 


>    8.5*. 


S  9.6{a.i  nil 


2346 
2199 
2048 

1906 

I  1765 
1628 
1494 
1364 
1236 


0870 
0753 
0638 


9  SiO.1  0 

«|  0417 

.7  fl 

.6  0204 

.9  0101 


9194 
8832 
8484 

8149 
78» 
7513 
7212 
6920 


6367 
6103 
5848 
5601 

5361 
5129 
4903 


3495 

3316 
3141 
2970 
2804 
3642 

2484 
2330 
2180 
2034 
1881 

1751 
1614 
1481 
1351 
1223 

1089 
0877 
0858 
0741 
0637 


0515 


0194 
0081 


9920 
9531 
9157 
8797 
8450 

8116 
7794 
7483 
7182 
6892 

6611 
6340 
6077 
5823 

6576 

5337 
5106 
4881 
4663 
4461 

4245 
4045 
3850 
3661 
3477 

3298 
3123 
2953 
2788 
2626 

2469 
2315 
2165 
2019 
1876 

1737 
1601 
1468 
1338 
1211 

1086 
0965 
0846 
0730 
0616 

0604 
0895 
0288 
0183 
0081 


9881 
9493 
9120 
8762 
8416 

8083 
7762 
7452 
7153 
6863 

6584 
6313 
6051 
5798 
5562 

5314 
5083 

4859 
4641 
4430 

4225 
4025 
8831 
3643 
3459 

3280 
3106 
2937 
2771 
2610 

2453 
2300 
2151 
2005 
1862 

1723 
1587 
1455 
1325 
1198 

1074 
0953 
0834 
0718 


0493 
0384 
0277 
0173 
0070 


9841 
9455 
9084 
8727 


8061 
7731 
7422 
7123 


6566 

6387 
6026 
6773 
5638 

5291 
5060 
4837 
4620 
4409 

4205 
4006 
3812 
3624 
3441 

3363 
3089 
2920 
2755 
2594 

2438 
2285 
2136 
1990 
1848 

1710 
1574 
1442 
1312 
1186 

1062 
0941 
0823 
0707 


0482 
0373 
0267 
0163 
0060 


8692 
8349 

8018 
7699 
7391 
7094 
6807 

6529 
6260 
6000 
5748 
5504 

5267 
5038 
4816 
4599 
4388 

4184 
3986 
3793 
3605 
3423 

3245 
3072 
2903 
2739 
2579 

2422 
2270 
2121 
1976 
1834 

1696 
1561 
1429 
1299 
1173 

1060 
0929 
0811 
0695 
0582 

0471 
0363 
0256 
0152 
0050 


9763 
9380 
9011 
8657 
8315 

7986 
7668 
7361 
7065 
6779 

6502 
6234 
5974 
5723 
5480 

5244 
5015 
4793 

4577 
4368 

4164 
3966 
3774 
3587 
3405 

3228 
3055 
2887 
2723 
2563 

2407 

2255 
2107 
1962 
1820 

1682 
1547 
1416 
1287 
1161 

1038 
0917 
0799 


0460 


0246 
0142 


9724 
9342 
8975 
8622 
8282 

7863 
7617 
7881 
7036 
6750 

6474 
6207 
5949 
5699 
5456 

5221 
4993 

4771 
4556 
4347 

4144 

3947 
3755 
3569 
3387 

3210 
3038 
2870 
2706 
2547 

2392 
2240 
2092 
1947 
1806 

1669 
1534 
1403 
1274 
1148 

1025 
0905 
0787 
0672 
0560 

0440 
0341 
0235 
0132 
0030 


9685 
9306 
8939 
8587 
8248 

7921 
7606 
7301 
7007 
6722 

6447 
6181 
5924 
5674 
5432 

5198 
4970 
4749 
4535 
4327 

4124 
3928 
3736 
3550 
3369 

3193 
3021 
2853 
2690 
2531 

2376 
2225 
2077 
1933 
1792 

1655 
1521 
1390 
1261 
1136 


0776 
0661 
0549 

0438 
0331 
0225 
0121 


(Subtract  tbedlt.) 
9  P.  P. 


9646 

9268 
8904 
8553 
8215 

7889 
7525 
7271 
6978 


6420 
6155 
5898 
5649 
5408 

5175 
4948 
4728 
4514 
4306 

4104 
3908 
3717 
3533 
3351 

3175 
3004 
2837 
2674 
2516 

2361 
2210 
2063 
1919 
1779 

1641 
1507 
1377 
1249 
1123 

1001 
0881 
0764 
0650 
0537 

0428 
0320 
0216 
0111 
0010 


-38-3«^34^3 

4  4  3  3 

8  7  7  6 

11  11  10  10 

15  14  14  13 

19  18  17  16 
23  22  20  19 
27  25  24  22 
30  29  27  26 
34  32  31  29 

■28-26-24-23 

3  3  2  2 
6  5  5  4 
8  8  7  7 

11  10  10  9 

14  13  12  11 
17  16  14  13 

20  18  17  16 
22  21  19  18 
25  23  22  20 

-21-19-17-16 

2  2  2  2 

4  4  3  3 
6  6  5  5 
8  8  7  6 

11  10  9  8 

13  11  10  10 

15  13  12  11 
17  15  14  13 
19  17  15  14 

-18-14-13-12 

2  111 

3  3  3  2 

5  4  4  4 

6  6  5  5 


14    13    12    11 

-13 -12-11 -10 

1111 

3  2      2      2 

4  4      3      3 

5  5      4      4 


7  6  6 

8  7  7 

9  8  8 

11  10  9 

12  11  10 


f  Reciprocals  to  five  decimal  places  on  this 
Ex.— Find  reciprocal  ot  1.2388  by 
the  inverse  method. 


page 


Solution — 8.08     for  0.12376 

.005 :J 

8lW5    for  0.12368 
Ans.- 0.8066  for  1.2368 


Digitized 


by  Google 


80  i.^POWERS,  ROOTS  AND  RECIPROCALS. 

Reciprocals. — The  reciprocal  of  a  number  is  1  divided  by  that  number. 
Thus,  the  reciprocal  of  2  77  — .361,  aod  likewise  the  reciprocal  of  .361  is 
2.77;  or  2.77  — V.»i  and  .361  — Van-  Hence,  to  divide  any  quantity  by  a 
number,  as  2.77,  is  equivalent  to  multiplying  it  by  its  reciprocal.  V2.770r.36l. 

As  multiplication  is  usually  performed  more  readily  than  divisjon.  it  is 
convenient  to  multiply  by  the  reciprocal  of  a  nimiber  rather  than  to  divide 
by  the  number  itself. 

Table  8*  comprises  the  reciprocals  of  numbers  from  1  to  10,  advancing 
by  decimals  as  in  logarithmic  tables,  so  as  to  include  a  wide  range  of  num- 
bers. Note  that  changing  the  decimal  point  n  places  in  the  number  equals 
a  change  of  n  places  in  the  opposite  dirtction  in  the  reciprocal;  also  that  the 
differences  between  any  reciprocal  and  the  following  one  is  a  minus  diffennce, 
hence  the  proportional  part  must  be  subtracted. 

Example. — What  is  the  reciprocal  of  79.16? 

Solution. — From  the  table,  the  reciprocal  of  7.91  — .12642;  the  propor- 
tional part  for  5  (under  the  difference,—  16)  is  —8.  Hence,  the  reciprocal 
of  7.915  is  .12634.  and  of  79.15  is  0.012634.    Ans. 

B.  ARITHMETICAL  OR  COMMON  TABLES. 

The  preceding  tables  are  arranged  in  decimal   form,  and  arc  called 
Engineers' Tables;  while  the  arithmetical  tables  are  in  the  form  most  com- 
monly used,  and  are  arranged  as  follows: — 
Table  9 — Sqtiares,  cubes,  square  roots,  cube  roots,  of  numbers,    1   to   1000. 

page  31: 

Nos.    0—130,  page  31.  Nos.   910—1040.  page  38. 


-  130—260, 

^32. 

-  1040—1170. 

^  39. 

-  260—390, 

"  33. 

•  1170—1300. 

-  40. 

-  390—520, 

-  34. 

-  1300—1430. 

-  41. 

-  620—660, 

•  36. 

•  1430—1660, 

-  42. 

-  660—780. 

-  36. 

■  1660—1600, 

-  43. 

-  780—910. 

-  37. 

Table  10 — Square  roots  and  cube  roots  of  numbers  1600  to  3200,  page  44 
Nos.  1600— 1860.  page  44.        Nos.  2640— 2900.  page  48. 

*  1860—2120,     ^    45.  -     2900—3160.      *     49. 

-  2120—2380.      -     46.  -     3160—3200,      "     50. 

•  2380—2640.      "     47. 

Table  11 — Reciprocals  of  numbers  1  to  1000.  page  51: 

Nos.       1—  325,  page  51.        Nos.    650—  975.  page  63. 

-  326—  650.      •     52.  **       97&— 1000.      '     54. 

*  Pages  28  and  29. 


d  by  Google 


COMMON  TABLES— SQUARES,  CUBES,  ROOTS. 


31 


9. — SguARss.  CuBBs.  Square  Roots,  Cubb  Roots,  op  Numbers 
I  to  1600. 


KoJ  Square 

Cube. 

Sq.  Rt. 

Cu.  Rt. 

No. 

Square 

Cube. 

Sq.  Rt. 

Cu.  Rt. 

0 

0.0000000 

65 

42  25 

274  625 

8.0622577 

4.0207256 

1 

1.0000000 

6 

43  56 

287  496 

.1240384 

.0412401 

8 

.2599210 

7 

44  89 

300  763 

.1853528 

.0615480 

27 

.4423496 

8 

46  24 

314  432 

.2462113 

.0816551 

16 

64 

58740U 

9 

47  61 

328  509 

.3066239 

.1015661 

25 

125 

1.7099769 

70 

49  00 

343  000 

8.3666003 

4.1212853 

36 

216 

.8171206 

1 

60  41 

357  911 

.4261498 

.1408178 

49 

343 

.9129312 

2 

61  84 

373  248 

.4852814 

.1601676 

64 

512 

2.0000000 

3 

63  29 

389  017 

.6440037 

.1793392 

81 

729 

.0800637 

4 

64  76 

406  224 

.6023253 

.1983364 

1  00 

1  000 

2.1544347 

75 

66  26 

421  876 

8.6602540 

4.2171633 

1  21 

1  331 

.2239801 

6 

67  76 

438  976 

.7177979 

.2358236 

1  44 

1  728 

.2894286 

7 

69  29 

466  533 

.7749644 

.2543210 

1  69 

2  197 

.3513347 

8 

60  84 

474  662 

.8317609 

.2726586 

1  96 

2  744 

.4101422 

9 

62  41 

493  039 

.8881944 

2908404 

2  25 

3  375 

2.4662121 

80 

64  00 

612  000 

8.9442719 

4.3088695 

2  56 

4096 

0 

.5198421 

1 

65  61 

631  441 

9.0000000 

.3267487 

2  89 

4  913 

.5712816 

2 

67  24 

661  368 

.0663851 

.3444815 

3  24 

5  832 

.6207414 

3 

68  89 

571  787 

.1104336 

.3620707 

3  61 

6859 

.6684016 

4 

70  56 

692  704 

.1651514 

.3795191 

4  00 

8000 

2.7144177 

86 

72  25 

614  125 

9.2195446 

4.3968296 

4  41 

9  261 

'7 

2.7589243 

6 

73  96 

636  056 

.2736186 

.4140049 

4  84 

10  648 

.8020393 

7 

75  69 

668  503 

.3273791 

.4310476 

3;  529 

12  167 

.8438670 

8 

77  44 

681  472 

.3808316 

.4479602 

4I  57C 

13  824 

.8844991 

9 

79  21 

704  969 

.4339811 

.4647451 

25  1  6  25 

15  625 

2.9240177 

90 

81  00 

729  000 

9.4868330 

4.4814047 

e!  67C 

17  576 

.9624960 

1 

82  81 

763  671 

.5393920 

.4979414 

7  29 

19  683 

3.0000000 

a 

84  64 

778  688 

.6916630 

.5143574 

7  84 

21  952 

.0365889 

3 

86  49 

804  357 

.6436508 

.5306549 

8  41 

24  380 

.0723168 

4 

88  36 

830  684 

.6953597 

.5468369 

900 

27  000 

3.1072326 

95 

90  25 

857  376 

9.7467943 

4.5629026 

9  61 

29  791 

.1413806 

6 

92  16 

884  736 

.7979590 

.5788570 

10  24 

32  768 

.1748021 

7 

94  09 

912  673 

.8488578 

.5947009 

10  89 

35  937 

.2075343 

8 

96  04 

941  192 

.8994949 

.6104363 

11  56 

39  304 

.2396118 

9 

98  01 

970  299 

.9498744 

.6260650 

12  25 

42  875 

3.2710663 

100 

1  00  00 

1  000  000 

10.0000000 

4.6415888 

12  96 

46  656 

.3019272 

1 

1  02  01 

1  030  301 

.0498756 

.6570095 

13  69 

50  653 

.3323218 

2 

1  04  04 

1  061  208 

.D995049 

.6723287 

14  44 

64  872 

.3619754 

3 

1  06  09 

1  092  927 

.1488916 

.6875482 

15  21 

60  319 

.3912114 

4 

1  08  16 

1  124  864 

.1980390 

.7026694 

16  00 

64  000 

3.4199519 

106 

1  10  25 

1  157  625 

10.2469508 

4.7176940 

16  81 

68  921 

.4482172 

6 

1  12  36 

1  191  016 

.2956301 

.7326235 

17  64 

74  088 

.4760266 

7 

1  14  49 

1  225  043 

.3440804 

.7474594 

18  49 

79  507 

.5033981 

8 

1  16  64 

1  259  712 

.3923048 

.7622032 

19  36 

85  184 

.6303483 

9 

1  18  81 

1  296  029 

.4403066 

.7768562 

46 

20  25 

91  125 

3.6668933 

110 

1  21  00 

1  331  000 

10.4880885 

4.7914199 

6  ,  21  16 

97  336 

.6830479 

1  23  21 

1  367  631 

.5356538 

.8058955 

7  2209 

103  823 

.6088261 

12 

1  26  44 

1  404  928 

.5830052 

.8202845 

8  23  04 

110  592 

.6342411 

13 

1  27  69 

1  442  897 

.6301458 

.8345881 

9  24  01 

117  649 

.6693057 

14 

1  29  96 

I  481  544 

.6770783 

.8488076 

50  25  00 

126  000 

3.6840314 

115 

1  32  26 

1  520  875 

10.7238053 

4.8629442 

1  26  01 

132  651 

.7084298 

16 

1  34  56 

1  560  896 

7703296 

.8769990 

27  04 

140  608 

.7325111 

17 

1  36  89 

1  601  613 

8166538 

.8909732 

28  09 

148  877 

.7662868 

18 

1  39  24 

1  643  032 

.8627805 

.9048681 

29  If 

157  464 

.7797631 

19 

1  41  61 

1  685  159 

.9087121 

.9186847 

16 

30  25 

166  375 

3.8029626 

120 

1  44  00 

I   728  000 

10.9544512 

4.9324242 

31  36 

175  616 

.8258624 

1 

1  46  41 

1  771  561 

11.0000000 

9460874 

33  49 

186  193 

.8485011 

2 

1  48  84 

1  815  848 

.0453610 

.9596757 

33  64 

195  112 

.8708766 

3 

1  51  29 

1  860  867 

.0905365 

.9731898 

34  81 

206  379 

.8929965 

4 

1  53  76 

1  906  624 

.1355287 

.9866310 

m 

36  00 

216  000 

3.9148676 

125 

1  66  25 

1  953  125 

11.1803399 

5.0000000 

37  21 

236  981 

.9364972 

6 

1  58  76 

2  000  376 

.2249722 

.0132979 

38  44 

238  328 

.9678915 

7 

1  61  29 

2  048  383 

.2694277 

.0266257 

39  69 

260  047 

— ._^J 

.9790571 

8 

1  63  84 

2  097  lf»2 

3137085 

.0396842 

40  »6 

262  144 

8.0000000 

4.0000000 

9 

1  66  41 

2  146  f.h9 

.3578167 

.0527743 

15 

42  25 

274  625 

S.0623577 

4.0207266 

130 

1  69  00 

2  197  000 

11.4017543 

5.0657970 

2.-'P0WERS,  ROOTS  AND  RECIPROCALS. 


9. — Squarbs,  Cubbs,  Squarb  Roots,  Cubb  Roots,  of  Numbers 
1  to  1600 — Continued. 


No. 

Square 

Cube. 

Sq.  Rt. 

Cu.  Rt. 

No. 

Squ&re 

CuUe.       9q.  Rt. 

Ca.Rt. 

"lio" 

169  00 

2  197  000 

11.4017543 

5.0657970 

190 

"sloM 

7  414  875il 3.964240(1 

5.7968109 

17161 

2  248  091 

.4455231 

.0787531 

I 

3  84  16 

7  629  53C 

14.000QO0C 

.8067867 

174  24 

2  299  968 

.4891253 

.0916434 

'i 

388  09 

7  645  373 

.0356688 

.8l8M7f 

176  89 

2  352  637 

.1044687 

3  92  04 

7  762  392 

.0712473 

.8284767 

179  66 

2  406  104 

.5758369 

.1172299 

J 

3  96  01 

7  880  59S 

.1067360 

.8382735 

135 

182  25 

2  460  375 

11.6189500 

5.1299278 

20Q 

400  OQ 

8000  OOC 

14.1421356 

5.8480356 

184  96 

2  615  456 

.6619038 

.1425632 

1 

4  04  01 

8120  601 

.1774469 

.8577660 

187  69 

2  571  353 

.7046999 

.1551367 

2 

408  04 

8  242  408 

.2126704 

.8674643 

190  44 

2  628  072 

.7473401 

.1676493 

3 

4  12  09 

8  365  427 

.2478068 

.8771307 

193  21 

2  685  619 

.7898261 

.1801015 

4 

4  16  16 

8  489  664 

.2828569 

.8887SS3 

140 

196  00 

2744  000 

11.8321596 

5.1924941 

205 

4  20  25 

8  615  125 

14.3178211 

5.8961665 

198  81 

2  803  221 

.8743422 

.2048279 

6 

424  36 

8  741816 

^27001 

.906N06 

2  0164 

2  863  288 

.9163753 

.2171034 

7 

4t8  49 

8  869  743 

.3874946 

J164817 

2  04  49 

2  924  207 

.9582607 

.2293215 

8 

4  32  64 

8  998  912 

.4222051 

.92481X1 

2  07  36 

2985  984 

12.0000000 

.2414828 

9 

4  36  81 

9  129  329 

.4568323 

.9344721 

U5 

2  10  25 

3  048  62S 

12.0415946 

5.2536879 

210 

4  4100 

9  261000 

14.4913767 

5.«43tta) 

2  1316 

3  112  136 

.0830460 

.2656374 

11 

4  45  21 

9  393  931 

.5258390 

J533418 

216  09 

3  176  923 

.1243557 

.2776321 

12 

4  49  44 

9  528128 

.5602198 

.9637810 

2  19  04 

3  241  792 

.1655251 

.2895725 

13 

453  69 

9  663  597 

.5945195 

.9730628 

2  22  01 

3  307  949 

.2065556 

.3014592 

14 

4  57  96 

9  800  344 

.6287388 

.9814240 

15U 

226  00 

3  375  000 

12.2474487 

5.3132928 

215 

4  62  25 

9  938  375 

14.6628783 

5.9967364 

2  28  01 

3  442  951 

.2882057 

.3250740 

16 

466  66 

10  077  696 

.6969385 

6.0000000 

2  3104 

3  511808 

.3288280 

.3368033 

17 

4  70  89 

10  218  313 

.7309199 

.0092450 

2  34  09 

3  581  577 

.3693169 

.3484812 

18 

4  75  24 

10  360  233 

.7648231 

.0184617 

2  37  16 

3  652  264 

.4096736 

.3601084 

19 

4  79  61 

10  503  459 

.7986486 

.0376502 

155 

240  2S 

3  723  875 

12.4498996 

5.3716854 

220 

484  00 

10  648  000 

14.8323970 

6.0368167 

2  43  36 

3  796  416 

.4899960 

.3832126 

1 

4  88  41 

10  793  861 

.8660687 

.0499435 

246  49 

3  869  893 

.629964L    ^46907 

2 

4  92  84 

10  941048 

.8996644 

.O6SO40 

249  64 

3  944  312 

.5698050 

.4061202 

3 

4  97  29 

11089  567 

.9331845 

.0641270 

263  81 

4  019  679 

.6095202 

.4176015 

4 

6  0176 

11239  424 

.9666295 

.0731779 

160 

256  00 

4096  000 

12.6491106 

5.4288352 

225 

506  25 

11390  625 

15.0000000 

6.0632036 

2  59  21 

4  173  281 

.6885775 

.4401218 

6 

6  10  76 

11  643  176 

.0332964 

.0011994 

262  44 

4  251  528 

.7279221 

.4513618 

7 

515  29 

11  697  083 

.0665192 

.1001702 

265  69 

4  330  747 

.7671453 

.4625556 

8 

619  84 

11852  352 

.0996689 

.1091147 

2  68  96 

4  410  944 

.8062485 

.4737037 

9 

6  24  41 

12  008  989     .1327460 

.1180332 

165 

2  72  25 

4  492  125 

12.8452326 

5.4848066 

230 

629  00 

12  167  000^15.1657509 

6.1289357 

2  75  56 

4^4  296 
4  657  463 

.8840987 

.4958647 

1 

5  33  61 

12  326  391 

.1986842 

.1357tM 

2  78  89 

.9228480 

.5068784 

2 

6  38  24 

12  487  168 

.2315462 

.1446337 

382  24 

4  741  632 

.9614814 

.5178484 

3 

642  89 

12  649  337 

.2643375 

.1534495 

2  85  61 

4  826  809 

13.0000000 

.5287748 

4 

5  47  56 

12  812  904 

.2970585 

.1623401 

170 

289  00 

4  913  000 

13.0384048 

5.5396583 

235 

6  52  25 

12  977  875 

15.3297097 

6.17100S8 

2  92  41 

5000  211 

.0766968 

.5504991 

6 

5  56  96 

13  144  256 

.8622916 

.1767466 

2  95  84 

5  088  448 

.1148770 

Ji612978 

7 

5  6169 

13  312  053 

.3948043 

.1884628 

299  29 

6177  717 

.1529464 

.5720546 

8 

5  66  44 

13  481  272 

.4272486 

.197 1M4 

3  02  76 

5  268  024 

.1909060 

.5827702 

9 

6  7121 

13  651  919 

.4596248 

.2068218 

175 

306  25 

5  359  375 

13.2287566 

5.5934447 

240 

5  76  00 

13  824  000 

15.4919334 

6.2144660 

3  09  76 

5  451  776 

.2664992 

.6040787 

1 

580  81 

13  997  521 

.5241747 

.2230043 

3  13  29 

6  645  233 

.3041347 

.6146724 

2 

585  64 

14172  488 

.5563492 

.2316797 

3  16  84 

5  639  752 

.3416641 

.6252263 

3 

6  90  49 

14  348  907 

.5884573 

.2402515 

3  20  41 

5  735  339 

.3790882 

.6357406 

4 

5  95  36 

14  626  784 

.6204994 

.24S70M 

180 

324  00 

5  832  000 

13.4164079 

5.6462162 

245 

6  00  25 

14  706  125 

15.6524758 

6.2573248 

8  27  61 

5  929  741 

.4136240 

.6566528 

6 

6  05  16 

14  886  936 

.6843871 

.2658266 

3  3124 

6  028  568 

.4907376 

.6670511 

7 

6  10  09 

15  069  223 

.7162336 

.2743054 

3  3489 

6128  487 

.527749;* 

.6774114 

8 

6  15  04 

15  252  992 

.7480167 

.2827613 

3  38  56 

6  229  504 

.5646600 

.6877340 

9 

6  20  01 

15  438  249 

.7797338 

.3911646 

185 

3  42  26 

6  331625 

13.6014705 

5.6980192 

250 

6  25  00 

15  625  000 

15.8113883 

6.2996663 

3  46  96 

6  434  856 

.6381817 

.7082675 

1 

6  30  01 

15  813  251 

.8429796 

.3079035 

3  49  69 

6639  203 

.6747943 

.7184791 

2 

6  35  04 

16  003  008 

.8745079 

.3103S96 

3  53  44 

6644  672 

.7113092 

.7286543 

3 

6  40  09 

16  194  277 

.9059737 

.3247035 

3  57  21 

6751  269 

.7477271 

.7387936 

4 

6  45  16 

16  387  064 

.9373775 

190 

3  6100 

6859  000 

13.7840488 

5.7488971 

255 

6  60  25 

16  581  375 

15.9687194 

6!3413357 

3  64  81 

6967  871 

.8202750 

.7589652 

6 

6  55  36 

16  777  216 

16.0000000 

1 606017 

3  68  64 

7  077  888 

.8564065 

.7689982 

7 

6  60  49 

16  974  593 

.0312195 

.3878611 

3  72  49 

7  189  057 

.8934440 

.7789966 

8 

6  65  64 

17  173  512 

.0623784 

.3660966 

4 

3  76  36 

7  301  384 

.9283883 

.7889604 

9 

6  70  81 

17  373  979 

.0934769 

.3743111 

195     3  so  25  1 

7  414  875 

13.9642400 

5.7988900 

260 

6  76  00 

17  576  000 

16.1245165 

6.3825043 

COMMON  TABLES^SQUARES.  CUBES,  ROOTS. 


9. — S0UARB8,  CuBBB,  Squarb  Roots,  Cubb  Roots,  of  Numbers 
1  TO  1500 — Contiiiued. 


No. 

8qi»r« 

Cube. 

8q.Rt. 

CU.RI. 

No. 

Square 

Cube.       8q.  Rt. 

Cu.Rt. 

Ho 

6  76  00 

17  576  000 

16.1245155 

6.3826043 

325 

10  56  26 

34  328  135 

18.0277564 

6.8753443 

6  8121 

17  779  581 

.1554844 

J806766 

6 

10  62  76 

34  646976 

.0654701 

.8823888 

686  44 

17  984  728 

.1864141 

J988279 

7 

10  69  29 

34965  783 

.0831413 

.8804188 

6*160 

18  191  447 

J172747 

.4069585 

8 

10  75  84 

35  287  552 

.1107703 

.8964345 

6NN 

18  899  744 

.2480768 

.4160687 

9 

10  82  41 

35  611289 

.1383571 

.9034369 

SS9 

702  25 

18  608  625 

164788206 

6.4231583 

330 

10  89  00 

85937  000 

15.1659021 

6.9104232 

707  66 

18  821096 

J095064 

.4312276 

1 

10  95  61 

36  264  681 

.1934054 

.9173964 

7  12  89 

18  034  163 

.3401346 

.4392767 

2 

1102  24 

36  594  368 

.2208672 

J243556 

7  18  24 

18  248  832 

J70706S 

.4473057 

3 

1106  89 

36  926  037 

.2482876 

J313008 

7  23  61 

18  465109 

.4012195 

.4553148 

4 

11  15  56 

37  259  704 

.2756669 

.9382321 

00 

729  00 

18  683  000 

16.4316767 

6.4633041 

335 

1122  25 

37  695  376 

18.3030052 

6.9451496 

7  34  41 

19  902  511 

.4620n6 

.4712736 

6 

1128  96 

37  933  066 

.3303028 

.9520533 

739  84 

20123  648 

.4924225 

.4792236 

7 

1135  69 

38  272  753 

.3575598 

.9589434 

74S29 

20346  417 

.5227116 

.4871541 

8 

1142  44 

38  614  472 

.3847763 

.9658198 

7  SO  76 

20  570  824 

.5529454 

.4950653 

9 

1149  21 

38  958  219 

.4119526 

.9726826 

175 

7S6  2S 

20  796  875 

16.5831240 

6.5029572 

340 

1156  00 

39  304  000 

18  4390889 

6.9795321 

7  6176 

21  024  576 

.6132477 

.5106300 

1 

1162  81 

39  651821 

.4661853 

.9863681 

767  29 

21253  933 

.6433170 

.5186839 

2 

1169  64 

40  001688 

.4932420 

.9931906 

7  72  84 

21484  952 

.6733320 

.5265189 

3 

1176  49 

40353  607 

.5202592 

7.0000000 

7  78  41 

21  717  639 

.7082931 

.5343351 

4 

1183  36 

40  707  584 

.5472370 

.0067962 

280 

784  00 

21952  000 

16.7332006 

6.5421326 

346 

1190  25 

41063  625 

18.5741756 

7.0135791 

7  89  61 

22  188  041 

.7630646 

.5499116 

6 

1197  16 

41  421  736 

.6010752 

.0203490 

795  24 

23  425  768 

.7928556 

.5676722 

7 

1204  09 

41  781  923 

.6279360 

.0271058 

800  89 

22  665  187 

J226038 

.6654144 

8 

12  1104 

42  144  192 

.6547581 

.0338497 

806  56 

22  906  804 

.8522995 

.5731385 

9 

12  18  01 

42  508  549 

.6815417 

.0405806 

»9 

8  12  25 

23  149  125 

16.8819430 

6.5808443 

350 

12  25  00 

42  875  000 

18.7082869 

7.0472987 

817  96 

23  383  656 

Jl  15346 

.5885323 

12  32  01 

43  243  551 

.7349940 

.0540041 

823  69 

23  639  903 

.9410743 

.5962023 

2 

12  39  04 

43  614  208 

■7616630 

.0606967 

828  44 

23  887  872 

J705627 

.6038545 

3 

12  46  09 

43  986  977 

.7882942 

.0673767 

838  21 

24187  569 

17.0000000 

.6114890 

4 

12  53  16 

44  361  864 

.8148877 

0740440 

190 

8  4100 

24888  000 

17.0293864 

6.6191060 

355 

12  60  25 

44  738  875 

18.8414437 

7.0806988 

8  46  81 

24  642  171 

.0087221 

.6267054 

6 

12  67  36 

45  118  016 

.8679623 

.0873411 

2 

852  84 

24  897  088 

.0680075 

.6342874 

7 

12  74  49 

45  499  293 

.8944436 

.0939709 

3 

866  49 

25  153  757 

.1172428 

.6418522 

8 

12  8164 

45  882  712 

.9208879 

.1005885 

864  36 

25  412184 

.1464282 

.6493998 

9 

12  88  81 

46  268  279 

.9472953 

.1071937 

M 

8  7026 

25  672  375 

17.1755640 

6.6569302 

360 

1296  00 

46  656  000 

18.9736660 

7.1137866 

8  7616 

25934  836 

2046606 

.6644437 

1 

13  03  21 

47  045  881 

19.0000000 

.1203674 

882  09 

28198  073 

.2336879 

.6719403 

2 

13  10  44 

47  437  928 

.0262976 

.12693(0 

888  04 

28  468  682 

.2626765 

.6794200 

3 

13  17  69 

47  832  147 

.0525589 

.1334925 

884  01 

26  730  899 

.2916165 

.6868831 

4 

13  24  96 

48  228  544 

.0787840 

.1400370 

soo 

900  00 

27  000  000 

17.3205081 

6.6943295 

365 

13  32  25 

48  627  125 

19.1049732 

7.046.5695 

9  06  01 

27  270901 

.3493516 

.7017593 

6 

13  39  56 

49  027  896 

.1311265 

.1530901 

9  12  04 

r54S60e 

.3781472 

.7091729 

7 

13  46  89 

49  430  863 

.1572441 

.1595988 

9  18  09 

27  818  127 

.4068952 

.7165700 

8 

13  54  24 

49  836  032 

.1833261 

.1660957 

9  24  16 

88  084  464 

.4355058 

.7239508 

9 

13  61  61 

50  243  409 

.2093727 

.1725809 

M6 

92825 

28  372  625 

17.4642493 

6.7313156 

370 

13  69  00 

50  653  000 

19.2353841 

7.1790544 

936  36 

28  652  616 

.4928567 

.7386641 

1 

13  76  41 

51064  811 

.2613603 

.1855162 

942  49 

28  934  443 

.6214156 

.7459967 

2 

13  83  84 

51  478  848 

.2873015 

.1919063 

948  64 

28  218  112 

.5499288 

.7533134 

3 

13  9129 

51895117 

.3132079 

.1984050 

9  54  81 

29  503  628 

.5783968 

.7606143 

4 

13  98  76 

52  313  624 

.3390796 

.2048322 

SIO 

96100 

28  791000 

17.6068169 

6.7678995 

375 

14  06  25 

52  734  375 

19.3649167 

7.2112479 

9  67  21 

30  080  231 

.6351921 

.7751690 

6 

14  13  76 

53  157  376 

.3907194 

.2176522 

973  44 

30  371328 

.6635217 

.7824229 

7 

14  2129 

53  582  633 

.4164878 

.2240450 

979  69 

30  664  297 

.6918060 

.7896613 

8 

14  28  84 

54  010  152 

.4422221 

.2304268 

98596 

30959  144 

.7200451 

.7968844 

9 

14  36  41 

54  439  939 

.4679223 

.2367972 

SIS 

992  25 

31255  876 

17.7482393 

6J040921 

380 

14  44  00 

54  872  000 

19.4935887 

7.2431565 

998  56 

31554  496 

.7763888 

J112847 

1 

14  5161 

55  306  341 

.5192213 

.2495045 

1004  88 

81856  013 

.8044938 

.8184620 

2 

14  59  24 

55  742  968 

5448203 

.2558415 

101124 

32157  482 

J82554S 

.8266242 

3 

14  66  89 

56  181  887 

.6703858 

.2621675 

10  17  61 

32  461769 

J8Qi711 

J827714 

4 

14  74  56 

56  623  104 

.5955/179 

.2684824 

no 

10  2400 

32  768  000 

17.8885438 

6.8399037 

385 

14  82  25 

57  066  625 

19  62141C9 

7.2747864 

10  3041 

38  076  161 

.9184729 

.8470213 

6 

14  89  96 

57  512  456 

.6468827 

.2810794 

103684 

33  386  248 

.9443584 

.8541240 

7 

14  97  69 

57  960  603 

.6723156 

.2873617 

10  43  29 

83  898  287 

.9722008 

.8612120 

8 

15  05  44 

58  411072 

.6977156 

.2936330 

10  49  76 

34  012  224 

18.0000000 

.8682855 

9 

1513  21 

58  863  869 

.7230829 

.2998936 

m 

1056  25 

34828125 

18.0277564 

6J753443 

390 

15  2100 

69  319  000 

W.7484177 

Coog 

7.3061436 

tized  by 

e 

84 


2.-'P0WERS,  ROOTS  AND  RECIPROCALS. 


9. — SguARBs,  CuBBs,  Squarb  Roots.  Cubb  Roots,  of  Numbbrs 
1  TO  1600— Continued. 


No.  Square 


Cube.      8q.  Rt.    Co.  Rt.  No.  Sqaare 


Cube.     8q.  Rt.    Ol  RL 


390 

2 

8 
4 

815 
6 
7 
8 
9 

400 
1 
2 
8 
4 

406 
0 
7 
8 
9 

410 
II 
12 
13 
14 

415 
16 
17 
18 
19 

420 


4 

425 

6 

7 

8 

9 

430 

1 

2 

3 

4 

435 

6 

7 


2 

3 

4 

445 

6 
7 
8 
9 
460 

2 
3 

4 


15  2100 
15  28  81 
1536  64 
15  44 
15  52  36 
15  60  25 
15  6816 
15  76  09 
15  84  04 

15  92  01 

16  00 
16  08  01 
16  16  04 
16  24  00 
16  32  16 
16  4025 


59819  000 
69  776  471 
60  236  288 

60  698  457 

61  162  984 
61629  875 
82  099  136 

62  570773 

63  044  792 

63  521199 

64  000  000 
64  481  201 

64  964  808 

65  450  827 

65  939  264 

66  430125 


19.7484177 
.7737199 
.7989899 
.8242276 
.8494332 

19.8746069 
.8997487 


16  48  36  66  923  416 


16  56  49 
16  64  64 
16  72  81 


67  419  143 

67  917  312 

68  417  929 


16  81  00  68  921  000 


16  89  21 

16  97  44 

17  05  69 


17  47  24 
17  55  61 
17  64  00 
17  72  41 
17  80  84 
17  89  29 

17  97  76 

18  06  25 
18  14  76 
18  23  29 
18  3184 
18  40  41 
18  49  00 


69  426  531 

69  934  528 

70  444  997 
17  13  96|  70  957  944 
17  22  25  71  473  875 
17  30  56  71991296 

17  38  89^92  511713 
73  034  632 

73  560  069 

74  088  000 

74  618  461 

75  151  448 

75  686  967 

76  225  024 

76  765  625 

77  308  776 

77  854  483 

78  402  752 

78  953  589 

79  507  000 

18  57  61180  062  991 
18  66  24  80  621  568 
18  74  89  81  182  737 
18  8;5  56  81746  504 

18  92  25  82  312  875 

19  00  96:  82  881  856 
19  09  69'  83  453  453 
19  18  44  84  027  672 
19  27  21' 84  604  519 
19  36  00  85  184  000 
19  44  81  85  766  121 
19  53  64  86  350  868 
19  62  49  86  938  307 
19  71  36!  87  528  384 
19  80  25  88  121  125 
19  89  16  88  716  536 

19  98  09  89  314  623 

20  07  04  89  915  392 


.9499373 
.9749844 

i20. 

.0249844 
.0499377 
.0748599 
.0997512 

20.1246118 
.1494417 
.1742410 
.1990099 
.2237484 

20.2484567 
.2731349 
.2977831 
.3224014 
.3469899 

20.3715488 
.3960781 
•4206779 
,4490483 
,4694895 


7.3061436 
.3123828 
J186114 
.3248295 
.3310369 

7.3372339 
.3434205 
.3495966 
.3657624 
.3619178 

7.3680630 
.3741979 
.3803227 
.3864373 
.3925418 

7.1 
.4047206 
.4107950 
.4168505 
.4229142 

7.4289589 
.4349938 
.4410189 
.4470342 
.4530399 

7.4590356 
.4650223 
.4709991 
.4769664 
.4829242 


20.4939015  7.4888724 


20  16  01 
20  25  00 
2034  01 
20  43  04 
20  52  09 
2061  16 
2070  25 


518  849 
91  125  000 

91  733  851 

92  345  408 

92  959  677 

93  576  664 

94  196  375 


.5182845 
.5426386 
.5669638 
.5912603 

20.6155281 
.6397674 
.6639783 
.6881609 
.7123152 

20.7364414 
.7605395 
.7846097 
.8086520 
.8326667 

20.8566536 
.8806130 
.9045450 
.9284495 
.9523268 

20.9761770 

21.0000000 
.0237960 
.0475652 
.0713075 

21.0950231 
.1187121 
.1423745 
.1660106 
.1896201 

21.2132034 
.2367606 
.2602916 
.2837967 
J072758 

21.3307290 


.4948113 
.5007406 
.5066607 
.5125715 

7.5184730 
.5243652 
.5302482 
.5361221 
.5419867 

7.5478423 
.5536888 
.5595263 
.5653548 
.5711743 

7.5769849 
.5827865 


.5943633 
.6001385 

7.6059049 
.6116626 
.6174116 
.6231519 
.6288837 

7.6346067 
.6403213 
.6460272 
.6517247 
.6574138 

7.6630943 
.6687665 
.6744303 


.6857328 
.6913717 


470 


2070  28 
20  79  81 
208849 
20  97  64 
210681 
2116  00 
2125  21 
2134  44 
2143  69 
2152  96 
2162  25 
217166 
2180  89 
2190  24 
2199  61 


94196  375 
94  818816 
05  443  99S 
96  071912 

96  702  579 

97  336  000 

97  972  181 

98  611128 

99  262  847 
99  897  844 

100  544  625 
101194  696 

101  847  663 

102  603  232 

103  161  709 


22  00  00103  823  000 


22  18  41 
22  27  84 
22  37  29 
22  46  76 
22  56  25 
22  66  76 
22  75  29 
22  84  84 
22  94  41 


101 487  ih 
105  154  048 

105  823  817 

106  496  434 

107  171  876 

107  850  176 

108  531333 

109  215  352 
109  902  239 


23  04  00110  592  000 


23  18  61 
23  23  24 
23  32  89 
23  42  56 


11284  641 
111980168 
112  678  587 
118  379  904 


23  52  25114  084125 


23  6196 
23  7169 
23  8144 
23  9121 


14  791  256 

115  501303 

116  214  272 
116  930169 


24  0100117  649  000 


24  10  81 


118370  771 


24  20  64119  095  488 


3  24  30  49 


119  823157 


4  24  40  36120  563  784 
495  24  50  2512l287S7Ste.2485955 


11.3907290 
.8541565 
.8n5583 
.4009346 
.4242863 

21.4476106 
.4709106 
.4941863 
.6174348 
.6406502 

21.5638587 
.5870331 
.6101828 
.6333077 
.6664078 

21.6794834 
7025344 
,726661C 
,7486622 
,7716411 

21.7944947 
.8174242 
.8403297 
.8632111 
.8860686 

21J089023 
.9317122 
.9544984 
.97726IC 

22.0000000 

22.0227155 
.0454077 
.0680765 
.0907220 
.1133444 

122.1350436 
.1585198 
.1810730 
.2036033 
.2261108 


7.6818717 


.7082388 
.7138448 

7.7194426 
.7250325 
.730C141 
.7361877 
.7417682 

7.74721W 


7.7749611 
.780061 
.7851638 
.7914875 
.7966746 

7.8Q84B8 
.8Qf792S4 
.813I8R 
.8ie846« 
.8242942 

7.82678S3 
.8351688 
.8406019 
.8460124 
.8514244 

7.856B2BI 
.8^2242 
.8676110 
.8728944 
.8783684 


6  24  6016 
24  70  09 
24  80  04 
24  90  01 


25  30  09 
25  40  16 
25  50  25 
25  60  36 
25  70  49 


122  023  936 

122  763  473 

123  505  992 

124  251499 
25  00  00 125  000  000 
25  10  01 125  751  501 
25  20  04126  506  008 

127  263  527 

128  024  064 

128  787  625 

129  554  216 

130  323  843 
25  80  64'131  096  612 

25  90  81,131872  229 
510|  26  01  00132  661  000 

26  11  2i;i33  432  831 
26  21  44  134  217  728 
26  3169135  005  697 
26  4196  135  796  744 
26  52  25136  590  875 
26  62  56  137  388  096 
26  72  89138  188  413 
26  83  24  138  991832 

26  93  611139  798  359 

27  04  00|l40  608  000 


6  93  61  K 

7  04  0dli 


.2710675 
.2934968 
.3159136 
.3383079 

22.3606798 
.3830293 
.4063565 
.4276615 
.4499443 

22.4722061 
.4944438 
.5166605 
.5388553 
.6610283 

22.5831796 
.6053091 
.6274170 
.6495033 
.6715681 

22.6936114 
.7156334 


xigk 


.8897917 
.90612M 

7.910I9M 
.91578U 
.92ie»4 
.9264065 
.9317161 

7.93766B 
.9422921 
.9478739 
.95284n 
.9581144 

7.963374S 
.9686271 
.9788ni 
.9791121 
.9842444 

7.789B6r 
J947883 


.0164683 
&01BM6 
0207194 


.7376340     .0259574 
.7596134 
.7816715 
122.8035085 


COMMON  TABLES— SQUARES.  CUBES.  ROOTS. 


9.— Squakss,  Cubbs,  Squarb  Roots.  Cvbb  Roots,  of  Numbbrs 
1  to  1600— Continued. 


Hojaqnare 

Cube. 

8<|.Rt. 

Cu.Rt. 

Na 

Square 

Cubew 

Sq.Rt. 

Cu.Rt. 

at 

27M0Q 

140608  000 

28.8035085 

8.0414615 

686 

34  22  25200  201626|24.186n3i 

"sJoiiw 

2714  41 

141  420  761 

.8254244 

.0466030 

6 

34  33  96 

201230  066 

.2074369 

J)682095 

27  24S4 

142  236  648 

.8473193 

.0517479 

7 

34  46  69 

202  262  003 

2280829 

.3729668 

27  35  20 

143  055  667 

.8601933 

.0568862 

8 

34  67  44 

203  297  472 

.2487113 

.3777188 

27  4  76 

143  877  824 

.8910463 

.0620180 

9 

34  69  21 

204  336  469 

.2693222 

.3824653 

6S 

27W25 

144  703  126 

22.9128785 

8.0671432 

590 

34  81  00^205  379  000|24.2899I56 

8.3872065 

27«76 

145  531  576 

.9346899 

.0722620 

34  92  81 

206  425  071 

.3104916 

.3919423 

TnUT^ 

146  363  183 

.9564806 

.0773743 

2 

35  04  64 

207  474  688 

.3310601 

.3966729 

27  87M 

147  197  952 

.9782506 

.0824800 

3 

36  16  49 

208  527  857 

.3515913 

.4013981 

27H4I 

148  035  889 

23.0000000 

.0875794 

4 

35  28  36 

209  584  584 

.3721152 

.4061180 

m 

280100 

148  on  000 

23.0217289 

8.0926723 

595 

35  40  25 

210  644  87524.3926218 

8.4108326 

2810  01 

149  721  291 

.0434372 

0977589 

6 

35  62  16 

211708  736 

.4131112 

.4156419 

1 

2830M 

150  568  768 

.0651252 

.1028390 

7 

36  64  09 

212  776  173 

.4335834 

.4202460 

28  40  00 

151  419  437 

.0867928 

.1079128 

8 

36  76  04 

213  847  192 

.4540385 

.4249448 

285150 

152  373  304 

.1084400 

.1129803 

9 

36  88  01 

214  921  799 

.4744765 

.4296383 

m 

28  68  25 

153  130375 

23.1300670 

81180414 

600 

36  00  OOI2I6  000  000!24.494897^ 

8.4343267 

28  7206 

153  990  656 

.1516738 

.1230962 

1 

36  12  01 

217  081  801 

.5153013 

.4390098 

28  83  00 

154  854153 

.1732606 

.1281447 

2 

36  24  04 

218  167  208 

.5356883 

.4436»77 

2894  44 

155  720872 

.1948270 

.1331870 

3 

36  36  09 

219  256  227 

.5560583 

.4483606 

29  06  21 

156  590  819 

.2163736 

.1382230 

4 

36  48  16 

220  348  864 

.5764115 

.4530281 

MO 

2916  00 

157  464  000 

23.2379001 

8.1432629 

605 

36  60  25 

221  446  125 

24.59674781  8.4576906 

29  26  81 

158  340  421 

.2604067 

.1482765 

6 

36  72  36 

222  545  016 

.6170673 

.4623479 

29  37  64 

159  220  088 

.2808936 

.1532939 

7 

36  84  49  223  648  543 

.6373700 

.4670000 

29  48  40 

160103  007 

.3023604 

.1683061 

8 

36  96  64  224  756  712 

.6576560 

.4716471 

29S9  36 

160989  184 

.3238076 

.1633102 

9 

37  08  81  225  866  529 

.6779254 

.4762892 

MS 

29  70  25 

161878  625 

23.3452351 

8.1683092 

610 

37  21  00  226  981  GOO 

24.6981781 

8.4809261 

29  81  16 

162  771336 

.3666429 

.1733020 

11 

37  33  21  228  099  131 

.7184142 

.4855579 

29  98  09 

163  667  323 

.3880311 

.1782888 

12 

37  45  44  229  220  928 

.7386338 

.4901848 

30  03  04 

164566  593 

.4093998 

.1832695 

13 

37  57  69  230  346  397 

.7588368 

.4948066 

30  14  01 

166  460  149 

.4307490 

.1882441 

14 

37  69  96 

231  475  544 

.7790234 

.4994233 

SO 

3025  00 

166  875  000 

23.4520788 

8.1932127 

615 

37  82  25 

232  608  375 

24.7991935 

8.5040350 

3036  01 

167  284  151 

.4733882 

.1981753 

16 

37  94  56 

233  744  896 

.8193473 

.5086417 

3047  04 

168  196  606 

.4946802 

.2031319 

17 

38  06  89 

234  886113 

.8394847 

.5132436 

seuQo 

160  112377 

.5160520 

J080826 

18 

3819  24 

236  029  032 

.8596058 

.5178403 

30  69  16 

170  031  464 

.6372046 

.2130271 

19 

38  3161 

237  176  669 

.8797106 

.5224321 

■s 

30  80  25 

170  953  875 

23.5584380 

8.2179657 

620 

38  44  00 

238  328  000 

24.8997992 

8.5270189 

309136 

171  879  616 

.6796522 

2228985 

1 

38  66  41 

239  483  061 

.9198716 

.5316009 

3102  49 

172  806  693 

.6009474 

.2278254 

2 

38  68  84 

240  641  848 

.9399278 

.5361780 

3113  64 

173  741  112 

.6220236 

.2327463 

3 

38  8129 

241804  367 

.9599679 

5407501 

3184  81 

174  676  879 

.6431808 

.2376614 

4 

38  93  76 

242  970  624 

.9799920 

.5453178 

MB 

8186  00 

175  616  000 

23.6643191 

8.2425706 

626 

39  06  25 

244  140  625 

25.0000000 

8.5498797 

8147  21 

176  558  481 

.6864386 

.2474740 

6 

3918  76 

245  314  376 

.0199920 

.5544372 

3150  44 

177  504  328 

.7066392 

J623716 

7 

39  3129 

246  491  883 

.0399681 

.5589899 

8109  09 

178  453  547 

.7276210 

.2572633 

8 

39  43  84 

247  673  152 

.0599282 

.5635377 

8100  9« 

179  406  144 

.7486842 

J62I492 

9 

39  66  41 

248  858  189 

.0798724 

.5680807 

m 

81«25 

180  362125 

23.7697286 

&2670294 

630 

39  69  00 

250  047  000 

25.0998008 

8.5726189 

S2  03  5« 

181821496 

.7907546 

.2719039 

1 

39  8161 

251  239  591 

.1197134 

.6771523 

38  14  89 

182  284  263 

.8117618 

J767726 

2 

39  94  24 

252  435  968 

.1396102 

.5816809 

33  36  24 

183  250  432 

.83r506 

.2816356 

3 

40  06  89 

253  636  137 

.1594913 

.5862047 

32  87  61 

184  220  009 

J537200 

.2864928 

4 

4019  56 

254  840  104 

.1793566 

.5907238 

m 

38  40  00 

185193  000 

23.8746728 

8.2913444 

636 

40  32  25 

256  047  875 

25.1992063 

8.5952380 

32  60  41 

186169  411 

J956063 

.2961903 

6 

40  44  96 

257  259  456 

.2190404 

.5997476 

33  7184 

187  149  248 

.9166216 

.3010304 

7 

40  57  69 

258  474  853 

.2388589 

.6042526 

32  83  29 

188132  517 

.9374184 

J068651 

8 

40  70  44 

259  694  072 

.2586619 

.6087526 

32  94  70 

189  119  224 

.9582971 

.8106941 

9 

40  83  21 

260  917  119 

.2784493 

.6132480 

m 

33  06  25 

190109  375 

23.9791676 

8.3155175 

640 

40  96  00 

262  144  000 

25.2982213 

8.6177388 

33  17  76 

191  102  976 

24.0000000 

J203353 

1 

4108  81 

263  374  721 

.3179778 

.6222248 

33  29  29 

192  100  033 

.0208243 

.3251476 

2 

412164 

264  609  288 

.3377189 

.6267063 

»40  84 

193  100  562 

.0416306 

.3290542 

3 

41  34  49 

265  847  707 

.3574447 

.6311830 

S52  41 

194  104  539 

.0624188 

.3347653 

4 

4147  36 

267  089  984 

.3771551 

.6356551 

OS 

33  64  00 

196112  000 

24.0631891 

8.3^5609 

645 

41  60  25 

268  336  125 

25.3968502 

8.6401226 

33  75  61 

196122941 

.1039416 

.3443410 

6 

41  73  16 

269  586  136 

.4165301 

.6445855 

83  87  24 

197  137  868 

J246762 

.3491256 

7 

4186  09 

270  840  023 

.4361947 

.6490437 

S3  98  09 

198155  287 

.1463929 

.3639047 

8 

4199  04 

272  097  792 

.4658441 

.6534974 

341056 

199176704 

.1660019 

.3586784 

9 

42  12  01 

273  359  449 

.4754784 

.6579466 

m 

soajs 

200201621 

24.1807732 

8.3634466 

660 

42  26  00 

274  626  000 

25.4950976 

8.6623911 

86 


2.^P0WERS,  ROOTS  AND  RECIPROCALS. 


9. — SguARBs.  CuBBS.  Square  Roots.  Cubb  Roots,  of  Numbbks 
1  TO  1800 — Continued. 


Mo.    Square      Cube.      Sq.  Rt.    Cu.  Rt.  No.  Square    Cube.      Sq.  Rt.    Cu.  Rt. 


No. 

Square 

650 

42  26  0( 

42  38  0] 

42  MM 

42  64  0» 

42  77  le 

42  90  25 

43  03  36 

43  16  4» 

43  29  64 

43  42  81 

43  56  0C 

43  69  21 

43  82  44 

43  95  69 

44  0696 

44  22  25 

44  35  5C 

44  48  8S 

44  62  24 

44  75  61 

44  89  0C 

45  02  41 

4515  84 

46  29  2fl 

45  42  7C 

45  56  21! 

45  69  7« 

45  83  29 

45  96  84 

46  10  41 

46  24  OC 

46  37  61 

46  5124 

46  64  89 

46  78  5« 

46  92  25 

47  05  96 

47  19  69 

47  33  44 

47  47  21 

47  610C 

47  74  81 

47  88  64 

48  02  49 

48  16  3C 

48  30  25 

48  44  U 

48  58  09 

48  72  04 

48  86  01 

49  00  0C 

49  14  01 

49  28  04 

49  42  09 

49  56  16 

49  70  25 

49  84  36 

49  98  49 

6012  64 

50  26  81 

50  410(1 

60  65  21 

50  69  44 

60  83  69 

50  97  96 

51  12  25 

274  625  000 

275  894  451 
277167  806 

278  446  077 

279  726  264 

281  Oil  375 

282  300  416 

283  593  393 

284  890  312 

286  191  179 

287  496  000 

288  804  781 

290  117  528 

291  434  247 

292  754  944 

294  079  625 

295  406  296 

296  740  963 

298  077  632 

299  418  300 

300  763  000 
303111711 

303  464  448 

304  821  217 

306  182  024 

307  546  875 

308  915  776 
310  288  733 
311665  752 

313  046  8:19 

314  432  000 

315  821241 

317  214  568 

318  611987 

320  013  504 

321  419  125 

322  828  856 

324  242  703 

325  660  672 
327  082  769 
828  509  000 
329  939  371 

331  373  888 

332  812  557 

334  255  384 

335  702  375 

337  153  536 

338  608  873 

340  068  392 

341  532  099 

343  000  000 

344  472  101 

345  948  408 

347  428  927 

348  913  664 

350  402  625 

351  895  81G 

353  393  243 

354  894  912 

356  400  829 

357  911000 

359  425  431 

360  944  128 

362  467  097 

363  994  344 
365  525  875 


25.495097C 

".6147016 
.5342907 
.5538647 
.6734237 

25.5029678 
.6124969 
.6320112 
.6515107 
.6709953 

25.6904652 
.9099203 
.7293607 
.7487864 
.7681975 

25.7875939 
.8069758 
.8263431 
J456960 
.8650343 

25.8843582 
.9036677 
.9229628 
.9422435 
.9615100 

25.9807621 

26.0000000 
.0192237 
.0384331 
.0576284 

26.0768096 
.0959767 
.1151297 
.1342687 
.1533937 

26.1725047 
.1916017 
.2106848 
.2297541 
.2488095 

26.2678511 


.3058929 
.3248932 
.3438797 

26.3628527 
.3818119 
.4007576 
.4196896 
.4386081 

26.4575131 
.4764046 
.4952826 
.5141472 
.5329983 

26.5518361 
.5706605 
.5894716 
.6082694 
6270539 

26.6458252 
,6645833 


.7020598 

.7207784 

26.7394839 


8.6623911 
.666831 C 
.6712665 
.6756974 
.6801237 

8.68454M 


.6933759 
.6977843 
.7021882 

8.7065877 
.7109827 
.7153734 
.7197596 
.724141 

8.7285187 
.7328918 
.7372604 
.7416246 
.7459846 

8.7503401 
.7546913 
.7590383 
.7633809 
.7677192 

8.7720532 
.7763830 
.7807084 
.7850296 
.7893466 

8.7936593 
.7979679 
.8022721 
.8065722 
.8108681 

8.8151598 
.8194474 
.8237307 
.8280099 


8.8365659 
.8408227 
.8450654 
.849344( 


J.8678489 


.8705757 
.8748099 
8.879040Q 


.8959204 
8.9001304 
.9043366 
.9085387 
.9127369 
.9169311 
8.921121 
.9253078 
.9294902 
.933668; 
.9378433 
8.942O140 


7  52  85  29 
8 


755 


61  12  25365  525 
6126  56367  061696 
614089368  601813 
5155  24370146  232 
371  694  959 


,7581763 

.n68567 

.7966220 

51  69  61^1  694  959  .8141754 

51  84  00  373  248  000  26.8328157 
5198  41374  805  361  .8514432 
62  12  84  376  367  048  .8700577 
62  27  29377  933  067 

52  4176370  503  424 
52  56  25381078 
52  70  76382  657  176 

384  240583 


.9072481 

1.9258240 

.9443872 

.9629375 

52  99  84^85  828  362^  .9814751 

27.0000000 

000J27.0185122 

.0370117 


54  6121 


54  9081 

55  06  64 

56  2049 
55  3536 
55  50  25 
55  65  16 
55  80  09 

55  95  04 
5610  01 

56  25  00 


56  55-04 
66  70 


87626.7894839 


387  420  489 

53  29  00389  017 

53  43  61 390  617  891 

56  24392  223168 

53  72  89393  832  837 

53  87  56395  446904 
64  02  25397  065 
541696398  688  256 

54  3160400  315  553 
54  46  44401947  272 


403  583  419 


54  76  00405  224  00027. 


406  869  021 
408  518  488 

410  172  407 

411  830  784 
413  493  625 

415  160  936 

416  832  723 
418  508  9#2 
420  189  749 
421876 


56  40  01  423  564  751 


425  259 

426  957  777 

56  85  16,428  661  064 

57  00  25,430368  8752 
67  15  36432  081216 


57  30  49 
57  45  64 
57  60  81 


433  798  093 
435  519  512 
437  245  479 


57  76  00438  976  00027. 


57  91  21 

58  06  44 
58  2169 
5836  96 
58  52  25 
58  67  56 
68  82  89 

58  98  24 

59  13  61 


59  44  41 
59  59  84 
59  75  29 

59  90  76 

60  06  25 
60  21  76 
60  37  29 
60  62  84 
60  68  41 


440  711  081 
442  450  728 

444  194  947 

445  943  744 
447  697  125 
449  455  096 

451  217  663 

452  984  832 
454  756  609 


59  29  00456  533  00027. 


458  314  011 

460  099  648 

461  889  917 
463  684  824 
465  484  375 
467  288  576 

097  433 
470  910952 
472  729  139 


60  84  00474  562 


.0739727 
.0924344 
7.1108834 
.1293199 
.1477439 
.1661564 
.1845644 
7.2029410 
.2213152 
.2396760 
.2580263 
.2763634 

27.29468811 
.3130006! 
.8313007 
.3495887 
.3678644 
.3861279 
.4043792 
.4226184 
.4408455 
.4590604 
.4772633 
.4954542 
.6136330 
.5317998 
.5499546 
6680975 
.5862284 
.6043475 
.6224546 
.6405499 

27.6586334 
.6767050 
.6947648 
.7128129 
7308492 
.7488739 
.7668868 
.7848880 
.8028775 
.8208555 

27.8388218 
.8567766 
.8747197 
.8926514 
.9105715 


8.9420140 
.9461609 
.0503438 
.9546020 
.9566681 

8.9628095 
.9669570 
.9711007 
.9752406 
.9793766 

8.9835069 
.9876373 
.9917620 
.9958829 

9.0000000 

9.0041134 
.0082229 
.0123288 
.0164309 
.0206293 

9.0246S9 
.0287149 
.0328021 


9.0450417 
.0491142 
.0631831 
.0572483 
.0613098 

9.065S6n 
.0694220 
.0734726 
.0776197 
.0816631 

9.0866080 
.0866393 
.0936719 
.0977010 
.1017365 

9.10674^ 
.1007669 
.1137818 
.1177931 
.1218010 

9.1358063 
.1298061 
.1838034 
.1377971 
.1417874 

9.1467742 
.1497576 
.1537375 
.1577139 
.1616889 

9.1666665 
.1696326 
.1736653 
.1776445 
.1816003 

9.1864627 
.1894018 
.1933474 
.1972897 
.2012286 

9.2051641 


COMMON  TABLES—SQUARES,  CUBES,  ROOTS.  37 

f. — Squarbs,  Cubbs.  Squarb  Roots,  Cubb  Roots,  op  Numbbrs 
1  TO  1600— Continued. 


d  by  Google 


88 


2.'-P0WERS,  ROOTS  AND  RECIPROCALS, 


9. — Squarbs,  Cubbs,  Squarb  Roots,  Cubb  Roots,  of  Numbbrs 
1  TO  IMO — Continued. 


No. 

Square 

~iio 

82  8100 

11 

82  99  21 

12 

83  17  44 

13 

83  35  69 

14 

83  53  96 

915 

83  72  25 

16 

83  90  56 

17 

84  08  89 

18 

84  27  24 

19 

84  45  61 

920 

84  64  00 

1 

84  82  41 

2 

85  00  84 

3 

8519  29 

4 

86  37  76 

925 

85  66  25 

6 

85  74  76 

7 

85  93  29 

8 

86  1184 

9 

86  30  41 

930 

86  49  00 

1 

86  67  61 

2 

86  86  24 

3 

87  04  89 

4 

87  23  56 

935 

87  42  25 

6 

87  60  96 

7 

87  79  69 

8 

87  98  44 

9 

88  17  21 

940 

88  36  00 

1 

88  54  81 

2 

88  73  64 

3 

88  92  49 

4 

89  11  36 

945 

89  30  25 

6 

89  49  16 

7 

89  68  09 

8 

89  87  04 

9 

90  06  01 

950 

90  25  00 

90  44  01 

2 

90  63  04 

3 

90  82  09 

4 

9101  16 

955 

9120  25 

6 

91  39  36 

7 

9158  49 

8 

91  77  64 

9 

9196  81 

960 

92  16  00 

1 

92  35  21 

2 

92  54  44 

3 

92  73  69 

4 

92  92  96 

965 

93  12  25 

6 

93  3156 

7 

93  50  89 

8 

93  70  24 

9 

93  89  61 

970 

94  09  00 

1 

94  28  41 

2 

94  47  84 

3 

94  67  29 

4 

94  86  76 

975 

95  06  25 

Cube. 


8q.  Rt. 


Cu.  Rt.  No.  Square. 


Cube. 


8q.  Rt. 


Ca.Rt^ 


753  671 
756  058 
758  550 
761048 
763  551 
766  060 
768  675 
771095 
773  620 
776  151 
778  688 
781229 
783  777 
786  330 
788  889 
791  463 
794  022 
796  597 
799  178 
801765 
804  357 
806  954 
809  557 
812  166 
814  780 
817  400 
820  025 
822  656 
825  293 
827  936 
830  584 
833  237 
835  896 
838  661 
841  232 
843  908 
846  590 
849  278 
851  971 
854  670 
857  375 
860  085 
862  801 
865  523 
868  250 
870  983 
873  722 
876  467 
879  217 
881974 
884  736 
887  503 
890  277 
893  056 
895  841 
898  632 
901  428 
904  231 
907  039 
909  853 
912  673 
915  498 
918  330 
921  167 
924  010 
926 


00030.1662063 


.1827765 
.1993377 
.2158899 
.2324329 


87530.2489669 


.2664919 
.2820079 
.2985148 
.3150128 
00030.3315018 
.3479818 
.3644529 
.3809151 
3973683 


125  30.4138127 


.4302481 
.4466747 
.4630924 
.4795013 
D.4959014 
.5122926 
.6286750 
.5460487 
.5614136 


375^0.5777697 


.5941171 
.6104557 
.626785: 
.6431069 


00030.6594194 
.6757233 
.6920185 
.7083051 
.7245830 


.7571130 
.7733651 
.7896086 
.8058436 
000|30.8220700 


9.6905211 

.6940694 

.6976151 

,7011583 

,7046989 
9.7082369 

,71in23 

.7153051 

.7188354 

.7223631 
9.7258883 

.7294109 

7329309 

.7364484 

.7399634 
9.7434758 

.7469867 

.760493C 

,75399: 

.7576002 
9.7610001 

.764497- 

.7679922 

.7714845 

.7749743 
9.77846IC  1000 1 

.781946^  ]  1 
21 
31 
U 
1 
6|1 

81 

91 

9.8131989110101 


.7923861 
9.7958611 
.7993336 
.8028036 
.8062711 
.8097362 


.8382879 
.8544972 
.8706981 
.8868904 


87530.9030743 


,9192497 
.9354166 
.9515751 
.9677251 

000130.9838668 

31.UO0O00O 

.0161248 

.0322413 

.0483494 

125131.0644491 


,0805405 
.0966236 
.1126984 
.1287648 
31.1448230 
.1608729 
.1769145 
.1929479 
.2089731 


859  37531.2249900 


,8166591 
.8201169 
.8235723 
.8270252 

9.8304757 
.8339238 
.8373695 
.8408127 
.8442536 

9. 

.851128( 
.854561 
.8579929 
.8614218 

9.1 
.868272^ 
.8716941 
.8751135 
.8785305 

9.8819451 

•  .885357 
.8887673 
Ut92l749 
.8955801 

9. 
.9023835 
.905781 
.9091771 
.9125712 

9.9159624 


96  0625 
96  25  76 
95  45  29 
95  64  84 

95  84  41 

96  04  00 
96  23  61 
96  43  24 
96  62  89 

96  82  56 

97  02  25 
97  21  96 
97  41  69 
976144 

97  8121 

98  0100 
98  20  81 
98  40  64 
98  60  49 

98  80  36 

99  00  25 
99  20  16 
99  40  09 
99  60  04 
99  80  01 
00  00  00 
00  20  01 
00  40  04 
00  60  09 

00  80  16 

01  00  25 
01  20  36 
01  40  49 
01  60  64 

01  80 

02  01 


11 

121 

131 

141 

1015,1 

161 

1 

1 


2  01  oai 

2  21211 
2  41  4411 


19 


6169 
8196 
03  02  25  1 
03  22  561 
03  42  89  1 
03  63  241 

03  83  611 

04  04  001 
04  24  41  1 
04  44  84  1 

65  2911 


261 
27  1 
281 
291 
10301 
311 
32 
33 
34 


21 

n 

1 
898983011035.1 
361 
37  1 
381 
39jl 
I040:i 


04  85  76 

05  06  25 
05  26  7t> 
05  47  29 
05  67  84 

05  88  41 1 

oeogwi 

06  29  611 
06  50  24;1 
06  70  89  1 

06  91561 

07  12  25  1 
07  32  96  1 
07  63  69  1 
07  74  44  1 

07  95  21  1 

08  16001 


926  859  37531 
929  714  176 
932  574  833 
935  441  352 
938  313  739 
941  192 
944  076  141 
946  966  168 
949  862  087 
952  763  904 
955  671 
958  585  256 
961504  803 
964  430  272 
967  361  669 
970  299  OOU: 
973  242  271 
976  191H88 
979  146  657 
982  107  784 
985  074  875: 
988  047  936 
991  026  973 
994  Oil  992 
997  002  999 

ooooooooo: 

003  003  001 
006  012  008 
009  027  027 
012  048  064 
015  075  125 
018  106  216 
021  147  343 
024  192  512 
027  243  729 
030.301000! 
033  364  331 
036  433  728 
039  509  197 
042  590  744 
045  678  375: 
048  772  096 
051871913 
054  977  832 
058  089  859 
061208  000: 
064  332  261 
067  462  648 
070  599  167 
073  741  824 
076  890  625; 
080  045  576 
083  206  683 
086  373  952 
089  547  389 
092  727  000: 
095  912  791 
099  104  768 
102  302  937 
105  507  304 
108  717  87 
111  934  656 
115  157  653 
118  386  872 
121622  319 
124  864  000 


.2249900 
.2409987 
.2569992 
.2729915 
.2889767 

000>01.3049517 
.3209195 
.3368792 
.3528308 
.3687743 

625^31.3847097 
.4006369 
.4165561 
.4324673 
.4483704 
.4642654 
.4801525 
.4960315 
.5119025 
.5r7656 
.5436206 
.5594677 
.6753068 
.5911380 
.6069613 
.6227766 
.6385840 
.6543836 
.6701752 
.6859590 
31.7017349 
.7175030 
.7332633 
.7490157 
.7647603 
1.780497 
.7962262 
.8119474 
.8276609 
.8433666 
1.8590646 
.8747549 
.8904374 
.9061123 
.9217794 
1.9374388 
.9530906 
.9687347 
.9843712 
32.0000000 
2.0156212 
.0312348 
.0468407 
.0624391 
.0780298 
!.0936131 
.1091887 
.1247568 
.1403173 
1558704 


87532.1714159 
.1869539 
.2024844 
.2180074 
.3335229 
2.2490310 


9.9159624 
,9193513 
.9227379 
.9261222 
.92950tt 

9.9328839 
.9362613 
.93963t3 
.9430093 
.9463797 

9.9497479 
.9531138 
.966477$ 
.9598389 
.9631961 

9.9665649 
.9699095 
.9733619 
.9766120 
.9799599 

9.9823066 
.9866488 
.9899900 
.9933289 
.9966656 

I0.0O0O0QC 
.0033322 
.0066622 
.0099899 
.0133156 

10.016638S 
.019960] 
.0232791 
.0265951 
.0299104 
1.0332221 
.036533< 
.039841( 
.043146! 
.0464501 

10.0497521 
.053051 
.056348! 
.059643 
.062936 

I0.0662r 
.069515 
.072802 
.076086 
.079368 

10.082648 
.085926 
.089201 
.092475 
.095746 

10.099016 
.102383 
.105546 
.106811 
.112072 

10.115331 
.118588 
.121842 
.125095 
.128345 

10.131594 


210. 


COMMON  TABLES— SQUARES,  CUBES,  ROOTS.  89 

9. — Squakbs,  Cubbs.  Squarb  Roots.  Cubb  Roots,  of  Numbbrb 
1  TO  1600 — Continued. 


d  by  Google 


40 


2.— POWERS.  ROOTS  AND  RECIPROCALS. 


9. — Squares.  Cubes,  Square  Roots,  Cube  Roots,  op  Numbers 
1  to  1600— Continued. 


No.   Sauare       Cube.       Sq.  Rt.   Cu.  Rt.  |Na    Square      Cube.       8q.  Rt.  Cu.  Rt. 

1170 

71 

72 

73 

74 
1175 

761 

77 

78 

79 
11801 

81 

82 

83 

84 
11851 

86 

87 


36  8900 

37  12  41 
37  35  84 
37  59  291 

37  82  76  1 

38  06  25 1 
38  29  76 1 
38  53  29  1 
38  76  84  I 


11901 
91 
92 
93!l 
941 

11951 
961 
97  1 
981 
991 

12001 
II 
21 


2 
3 
4 
12051 
6 
7 


39  00  41 
39  24  00 
39  47  61 
39  71  24 

39  94  89 

40  18  56 
40  42  25 
40  65  96 

40  89  69 

41  13  44 
41  37  21 
4161001 

41  84  81 

42  08  64 
42  32  49 
42  56  36 

42  80  251 

43  04  161 
43  28  09, 
43  52  04  1 
43  76  0111 


Bl 
91 
12101 
111 
121 
131 


44  00  00 
44  24  01 
44  48  04 
44  72  09 

44  96  16 

45  20  25 
1  45  44  36 
145  68  49 


14 
UlS 

16 
17 

18 
19 
1220 
21 
22 
23 
24 


12251 

26 

27 


1230 
31 
32 
33 
34 


12351 


45  92  64 

46  16  811 
46  41  00 1 
46  65  21 1 

46  89  44 1 

47  13  69  1 
47  37  96  1 
47  62  25,1 

47  86  56  1 

48  10  89|1 
48  35  24 


48  59  61 

48  84  00 

49  08  41 
49  32  84 
49  57  29 

49  81  76 

50  06  25 1 
50  30  76 
50  55  29 

50  79  84 

51  04  41 
51  29  00 
51  53  61 

51  78  24 

52  02  89 
52  27  56 
52  52  25 


601  613  000 
606  723  211 
609  840  448 
613  964  717 
618  096  024 
622  234 
626  379  776 
630  532  233 
634  691  752 
638  858  339 
643  032 
647  212  741 
651  400  568 
655  595  487 
659  797  504 
664  006  62534. 
668  222  856 
672  446  203 
676  676  672 
680  914  269 
685  159 
689  410  871 
693  669  888 
697  936  057 
702  209  384 
706  489  8' 
710  777  536 
715  072  373 
719  374  392 
723  683  599 
728  000 
732  323  601 
736  654  408 
740  992  427 
745  337  664 
749  690 
754  049  816 
758  416  743 
762  790  912 
767  172  329 
771561 
775  956  931 
780  360128 
784  770  597 
789  188  344 
793  613  3: 
798  045  696 
802  485  313 
806  932  232 
811386  459 
815  848 
820  316  861 
824  793  048 
829  276  567 
833  767  424 
838  265 
842  771  176 
847  284  083 
851  804  352 
856  331  989 
860  867 
865  409  391 
869  959  168 
874  516  337 
879  080  904 
883  652  875 


34.2052627 
J198773 
.2344855 
.2490875 
.2636834 


10.53728U  1235 


.5402837 
.5432832 
.5462810 
.5492771 


1  52  62  25 1  883  662  875  35.142566ai0.7289112 
jj n r -r^     .^_ 


375  34.2782730 10.652271 5  1240 


2928564 


.3220046 
.3365694 
1.3511281 
.3656805 
.3802268 
.3947670 
.4093011 
,4238289 
.4383507 
.4528663 
.4673759 
.4818793 
1.4963766 
.6108678 
.6253530 
.5398321 
.5543051 
L5687720 
.5832329 
.5976879 
.6121366 
.6265794 
1.6410162 
.6554469 
.6698716 
,6842904 
.6987031 
1.7131099 
.7275107 
.7410055 
.7562944 
.7706773 


.5552642 
.5582552 
.5612445 
.5642322 
).6672181 
.5702024 
.5731849 
.5761658 
.6791449 


41 
42 
43 
44 
12451 
46 
47 
48 
49 


52  76  96 

53  0169 
53  26  44 
53  5121 

53  76  00 

54  00  81 
54  25  64 


1888  232  256 
1  892  819  053 
897  413  272 
1^902  014  919 
1  906  624 
1911240  521 
1915  864  488 


1 

1  54  50  49 1  920  495  907 


10.5821225  1250 


.5850983 
.5880725 
.6910450 
.5940158 


54  75  36 

55  00  25 
55  2516 
55  50  09 

55  75  04 

56  00  01 
56  25  00 
56  50  01 

56  75  04 

57  00  09 
57  2516 


1  925  134  784 
1  929  781 
1  934  434  936 
1  939  096  223 
943  764  992 
1  948  441  249 
1  953  125 
I  957  816  251 
1962  515  008 
I  967  221  277 
1971935  064 


.1567917  .7318062 
.1710108  .7346997 
.1852242    .7375916 

.7404819 
10.7438707 

.7462(^9 
.2420204^  .7491436 
.2562051 


.1994318 
i.2136337 
.2278299 


.7520277 

.2703842^    .7549108 

125^5.2845575 10.7577913 

.2987252    .7606706 

.7635488 


.3128872 

.3270435    .7664253 

.3411941 


.3694784 
.3836120 


.5969850  1255 1  57  50  25 1  976  656  375 

,5999525 

,6029184 


.6088451 


57  75  36 

58  00  49 
58  25  64 

10.611806(112601  58  76  00 


35.4259792 
.4400903 


.6147652 
.6177228 
.620678S 
.6236331 


1  981  385  216 

986  121  593 

1  990  865  512 

1  995  616  979 

2  000  376  00035.4964787 


1  59  01  212  005  142  581 


10.6265857  1265 


00034.7850543 
.7994253 
.8137904 
.8281495 
.8425028 

1.8568501 
.8711915 
.8855271 
.8998567 
.9141805 

1.9284984 
.9428104 
.9571166 
.9714169 
.9857114 


.629536: 
.6324860 
.6354338 
.6383799 
).6413244  1270 
.6442672 
.6472085 
.6501480 
.6530860 


59  26  44  2  009  916  728 
69  51  69  2  014  698  447 

59  76  96  2  019  487  744 

60  02  25'2  024  284 
60  27  56,2  029  089  096 
60  52  89i2  033  901  163 
60  78  24  2  038  720  832 
6103  6112  043  548  109 
6129  002  048  383 


.5246393 
-6387113 
.6527777 
625)35.5668385 
.5806937 
.5949434 
.6089876 
.6230262 


,7693001 

10.7721735 

.7760453 

.7779156 

J97740d    .7807843 

.4118624    .7836SI6 

10.7865173 

.7893815 


4641958  .7922441 
.4682957  .7951063 
.4823900    .7979649 

10.8006230 

610S618  .8036797 
.8065348 
JB093884 
.8122404 
10.8160909 
.8179400 
.8207876 


6154  412  053  225  611 
6179  84  2  058  076  648 
62  05  292  062  933  417 
62  30  762  067  798  824 
10.656022311 275|1  62  56  252  072  671  87535.7071421 
162  81762  077  552  576 


.6589570 
.6618902 
.664821 
.6677616 


63  32  84 

63  58  41 
I0.6706799h280 1  63  84  00 

64  09  61 
64  36  24 


.6736066 
.6765317 
.6794552 
.6823771 
9.6852973 


821 

831 

841 

12851 


00035.6370693 


.6651090 
.6791255 
.6931366 


163  07  292  082  440  933 


.6882160     861 


.6911331  87  165  63  69 

.6940486  88  1  65  89  44 

.6969625  891661521 

625^5.0000000 10.6998748  1290 1  66  41  00 

.0142828     .702785.'!    91166  66  81 

,0428309     .7086023  93  1  67  18  49 

.0570963     .71 15083  94  I  67  44  36 


087  336  952 
2  092  240  639 
2  097  152 
2  102  071  041 
2  106  997  768 
64  60  892  111  932  187 

64  86  562  116  874  304 

65  12  252  121824 
65  37  962  126  781656 


00035.0713558 
.0856096 
.0998575 
.1140997 
.1283361 
35.1425668 


.7027855 
.705694 
.7086023 
.7115083 
9.7144127 
.7173155 
.7202168 
.7231165 
.7260146 
9.7289112 


29a  1 
961 
971 
981 
991 
13001 


68  48  04 

68  74  01 

69  00  00 


2  131  746  903 
2  136  719  872 
2  141  700  569 

146  689 
2  151  686  171 
2  156  689  088 
2  161  700  757 
2  166  720  184 


.8364782 

10.8293213 

.8321629 

.8380030 

.8378416 

.8406788 

ia8435144 

:8463486 

.84918U 

.8520125 

.8548422 

10.6676704 

.860tt72 

.8633221 

.81898941    .6661464 

.8329457     .86896^ 

125135.8468966 10.8717897 

.8608421 


.7211422 
.735136: 
.7491258 
.7631095 
000135.7770676 
.7910603 
.8050276 


.8746091 
.8747822^  .8774271 
.8887169  .8802436 
.9026461  .8830887 
000^35.9166699 10.88G6723 
.9304884  ,8866845 
.9444016     .8914952 


67  70  252  171747 
67  9616  2  176  782 


.9583092 
.9722115 


68  22  09  2  181  825  073 


.89T1I23 

10.8999166 

336^36.0000000^    .9027235 


37535J861084 


2  186  875  592 
2  191  933  899 
2  197  000  OOOt 


.0138862 
.0277671 
.0416426 


XIl 


.9I11»6 


36.0655128 10.91S»87 


COMMON  TABLES— SQUARES,  CUBES,  ROOTS,  41 

i—^UARBS,  CuBBS.  Squarb  Roots,  Cubb  Roots.  of  Numbers 
1  TO  1800 — Continued. 


d  by  Google 


2.- POWERS,  ROOTS  AND  RECIPROCALS. 

9. — Squares.  Cubbs,  Squarb  Roots,  Cubb  Roots,  of  Nuubbrs 
1  to  1600 — Continued. 


No.  Square      Cube.       Sq.  Rt.  Cu.  Rt. 


No.  Square      Cube.       Sq.  Rt.   Cu.  Rt. 


143C  8  04  49  00  2  924  207  000  37.81i 
812  04  77  612  930  345  991  .8285606 
322  05  06  242  936  493  568  .8417759 
332  05  34  892  942  649  737  .8549864 
34  2  05  63  66  2  948  814  504     .8681924 


n.a6623U  1486  2  23  50  25  3  341  362  375  38.6652299 11.4344092 


14352  05  92  252  954  987  87537.8813938 


362  06  20  962  961  169  856 


1 1 .2793473  15002  25  00003375000000  38.7298335 1 1.44714»4 


372  06  49  692  967  360  453     .9077828 

106  78  442  973  559  672 
39)2  07  07  21 2  979  767  519 
1440  2  07  36  00  2  985  984  00037.9473319 


41 1 07  64  81  2  992  209  121 
42  2  07  93  642  998  442  888 
432  08  22  49  3  004  685307 
44  2  08  51363  010  936  384 


1445  2  08  80  253  017  196  12538.0131556 11.3054871 


462  09  09  163  028  464  536 
47  2  09  38  00  3  029  741628 
482  09  67  04  3  036  027  392 
492  09  96  013  042  321849 
1450  2  10  25  00  3  048  625  000  3&0788655 


61 2  10  54  01  3  054  936  851 
622  10  83  04  3  061257  408 
632  11  12  093  067  586  677 
642  1141  163  073  924  664 


14562  11  70  253  080  271 37538.1444622 


562  1199  363  086  626  816 
67  212  28  493  092  990  993 
682  12  57  64  3  099  363  912 
592  12  86  813  105  745  579 


14602  13  16  003  112  136  00038.2099463 


612  13  45  213  118  535181 
622  13  74  443  124  943  128 
63  2  14  03  693  131350  847 
642  14  32  963  137  785  344 


14652  14  62  253  144  219  62538.2753184 


662  14  91  563  150  662  696 
67  2  15  20  893  157  114  56J 
682  15  50  24  3  163  575  232 
9  2  15  79  613  170  044  709 


14702  16  09  003  176  623  00038.3405790 


712  16  38  413  183  010  111 
722  16  67  84  3  189  506  048 
32  16  97293  196010817 
4  2  17  26  763  202  524  424 


14752  17  56  253  209  046  875  38.4057287 


79 
1480 
81 
82 
83 
84 


87 


762  17  85  763  215  578  176 
772  18  15  293  222  118  333 
782  18  44  843  228  667  352 
2  18  74  41  3  235  225  239 
2  19  04  00  3  241792  000 
2  19  33  61  3  248  367  641 
2  19  63  24  3  254  952  168 
2  19  92  893  261  545  587 
2  20  22  563  268  147  904 
14852  20  52  253  274  759  125 
2  20  81  963  281  379  256 
2  21  11  69  3  288  0(^303 
2  21  41  44  3  294  646  272 
892  21  71  213  301  293  169 


.5875627 
1490|2  22  01  003  307  949  000|38.600518i 


912  22  30  813  314  613  771 
922  22  60  643  321  ^7  488 
93  2  22  90  493  327  970  157 
9412  23  20  36  3  334  661  784 
149512  23  50  25i3  341  362  371 


•  I,*   £,0    I.M  J 

i95^2  23  50  2 


.9605058 
.9736751 


.1575681 
.1706693 
.1837662 
.1968585 


.2688573  96|2  23  80  16 
.27I48K  97  2  24  10  09 
.2741047     882  24  40  04 


.276726e 


3  348  071  936 

354  790  473 

3  361  517  992 


992  24  70  013  368  254  499 


.8945906     .281966<       13  2630  013  381754  501  .7427412 

.2845849       22  25  60  043  388  518  008  .7556447 

.9209704^    .2872019       82  25  90  09  3  395  290  527 

.9341535     .2898177       422620  16  8402  072  064  .7814389 

11.2924323  15052  26  50  258  408  862  62538.7943294 

.2950491       62  26  80863  415  662  216  .8072158 

J976579I     7  2  27  10  49  3  422  470  843  .8200978 

82  27  40043  429  288  512  .8329757 

38.00000001    .30287861     92  27  70  813  436  115  229  .8458491 


1610  2  28  01  00  3  442  951  000  38.8587184 


.0263067  .3080944    112  28  31  2l|3  449  795  831  .8715834 

.0394532  .310700(  12  2  28  61443  456  649  728  .8844442 

.0525952  .313305(  132  28  9169  3  463  512  697  .8973006 

.0657326  .3159094  142  29  2196  3  470  384  744  .9101529 
11.8185119  15152  29  52  253  477  265  87538.9230009 

.0919939  .8211132  162  29  82  56  3  484  156  096  .9358447 

.1051 178  .3237134  17  2  30  12  89  3  491  055  413  .9486841 

.1182371  .3263124  182  30  43  243  497  963  833  .9615194 

.1313519  .3289102  19  2  30  73  613  504  881359  .9743505 


.2230297 
.2361065 
.2491829 
.2622529 


.2883794 
.3014360 
.3144881 
.3275358 


.3536178 


.3666522  .3754679 
,3796821  .3780433 
.3927076     .3806178 


.4577691 

38.4707681 

,4837627 


.5227206 
38.5356977 


.5616389 


5p8.( 


.6134691 
.6264158 
.6393582 
,6522962 
,66522i»9 


11.357407S  15302  24  09  003  581  577  00039.115214411.5229S3S 


.3599911 
.362573S 


.36515471    33  2  35  00  89  3  602  686  437     .1535439 
.3677347     34  2  35  31  56  3  609  741  304     .1663120 


11.3703136  15352  35  62  253  616  805  37539.179076011.5354920 


.3728914 


11.383190(  15402  37  16  003  652  264  000  39.2428337 


.4187454     .385762! 

.4317577 

.4447656     .390902^ 


.4967530     .4011695 
.5097390     .4037332 


.4062959     49 


,5486705  .4114177  61 


.4139769  52 


5746030     .4165349     53 


.4190918     54 


.4242022  56 

.4267556  57 

.4293079  58 

.4.il859i  59 


37  2  36  23  69 


38  2  36  54  44  3  638  052  872  .2173431 


39 


2  36  85  21 


.3934712     44 
11.3960384  15452  38  70  2! 
.3986045     462  39  01 


2  37  46  81  3  669  383  421 
2  37  77  64  3  666  512  088 
43  2  38  08  49P  673  650  007 


2  38  39  36P  680  797  184     .2937654 


47 


.6781593 
.6910843 
.7040060 
.7169214 


.4369561 
.4395059 
.4420535 
.4445980 


11.3315067  1520  2  31  04  003  611  806  00038.9871774 11.4977942 


.33410221  21  2  31  34  41  3  518  743  761 39.0000000 

,3366964  22  2  31  64  84  3  525  688  648     .0128184 

.8392894  23  2  3195  29  3  532  642  667     .0256326 

.3416813  242  32  26  763  539  605  824     .0384426 
11.3444719  15252  32  56  253  546  578  12539.0512483 

.34706H  262  32  86  76  3  553  559  576     .0640499 

.3496497  27  2  33  17  29  3  560  650  183     .0768473 

.352236f  28  2  33  47  84  3  567  649  952     .0896406 

.3548227  29  2  33  78  41  3  574  658  889     .1024296 


2  34  39  61  3  588  604  291 


322  34  70  243  595  640  768     .140ni6     .5279722 


362  35  92  96  3  623  878  656     .1918359 


3  630  961  153 


.4496857 
.4622278 
.4547688 
.4673087 
11.459M74 
.4623850 
.4649215 
.4674568 
.4609911 
11.4725243 
4750562 
4775871 
4801169 
4826455 
11.4851731 
.4876996 
.4902249 
.4927491 
.4952722 


.5003151 
.6028348 
.5053535 
.5078711 
11.5103876 
.5129030 
.6154173 
.5179305 
.5304425 


.1279951 


.5254634 


.5304799 
.5329865 


.2045915 


3  645153  819     .2300905 


.2565728 
.2683078 
.2810387 


5379965 
.5404998 
.5430021 
.5455033 
11.5480034 
.5505025 
.5530004 
.5554973 
.5579931 


687  953  62539.3064880 11.5604878 


695  119  336     .3192065 


)  32  09P  702  294  323 


482  39  63  04^709  478  592 


2  39  94  013  716  672  149 


1 M088574  1550  2  40  25  OOb  723  875  000  39.3700394 


2  40  56  01^731087  151 
2  40  87  04^  738  308  608 
2  41  18  09^  745  539  377 
2  41  49  lea  752  779  464 


11.4216476  15552  41  80  25b  760  028  87539.4334883 


2  42  11360  767  287  616 
2  42  42  49Q  774  555 
2  42  73  640  781833  112 
2  43  04  8l«789  119 


11.4344092  15602  43  36  OOb  796  416  00039.4968353 


.3319208 
.3446311 
.3573373 


.3827373 
.3954312 
.4081210 
.4208067 


.4461658 
.4588393 
.4715087 
.4841740 


yGOOgl 


5629816 
5654740 
.5679655 
.5704559 

11.5729453 
.5754SM 
.5T7»208 
.5804069 
.5828919 

11.58537S9 
.5878568 
.5903407 
.5928215 
.5953013 
1.5977791 


COMMON  TABLES— SQUARES,  CUBES.  ROOTS. 


43 


9. — Squa&bs,  Cubes,  SguARB  Roots,  Cubb  Roots,  of  Numbers 
1  TO  1600 — Concluded. 


Ho.  S<iiiaTO       Cube.        Sq.  Rt    Co.  Rt    No.  SqaaK 


Cube. 


Sq.  Rt.    Cu.  Rt. 


ni 


711 

imi 


HI 


43  3<003 
13 €7  lis 
43M443 
44»tt3 
44€09i3 
44»283 
4523  513 
45M8I3 
45K243 
4ft  17  11  3 
46 

41)3 
47  11  MS 
47  43111 

47  74  711 

48  06  29i 
4837  74  3 
4S69»3 

49  00  841 
49  33  411 
49N0n 


796  416  00039.49«83d3 
803  731 
811086 
818  360 


833  037  1 
840  3894 
847  751 S 
855  1224 
863  603C 


I  481 
&328 
)547 
1144 


.5094925 
.52214S7 
.5347948 
.5474399 


.6727179 


1.597779915802 
.6002576  81 2 
.6027342  823 
.6062097  83  2 
.6076841  842 
I.610187B  15852 
.612629S  862 
.6151013  87 
,6178715     882 


.5979797 
_  ,  ^  !6106046     .62004071   89 

lin|3  46  49  00(3  869  813  000^.6232255 11 
.6368424 
.6484552 
.6610640 


877  292 
881701 
892  119 
889  547 
906  984 
914  430 
921887 
929  363 
936  827 
944  312 


6225088  15902 
,6249750  91 2 
.6274420     922 

a 

2 


.629907C     93 
.6323710     94 


375  39.6882696 11.6348339  1595  2 


.7114593 
.7240481 
.7366329 
».7492138lll 


.6372957 


962 
972 
982 


.6471329  160012 


49  64  003 

49  95  61 3 

50  27  243 
50  58  883 
50  90  568 
5122  253 
5153  963 
5186  693 
5217  444 
52  49  21 4 

52  81004 

53  12  81 4 
53  44  644 

53  76  494 

54  08  364 
54  40  264 

54  72  164 

55  04  094 
55  36  044 

55  68  01  4 

56  00  0014 


00039. 


944  312 
951  805  941 
959  309  368 
966  822  287 
974  344  704 
981876 
989  418  056 
996  969  003 
004  529  472 
012  099  469 
019  679 
027  268  071 
034  866  688 
042  474  857 
050  092  584 
057  719 
065  356  736 
073  003  173 
080  659  192 
088  324  799 
096  000 


.749213811 
.7617907 
.7743636 
.7869325 
.7994975 
».8120585U, 
.8246156 
.8371686 
.8497177 


).  87480401 
.8873413 
.8998747 
.9124041 
.9249295 

).9374511 
.9499687 
.9624824 
.9749922 
.9874980 
1.000000(^11 


.6471329 
.6495896 
.6520452 
.6544998 
.6569534 
.6694060 
.6618574 
.6643079 
.6667574 
.6692058 
.6716532 
.6740996 
.6765449 
.6789892 
,6814325 
.6838748 
.6863161 
.6887563 
.6911956 


.6960709 


dbyGoOgk 


44 


2.^POWERS,  ROOTS  AND  RECIPROCALS. 


10. — Squarb  Roots  and  Cubb  Roots  op  Numbb 
1800  to  8200. 


No. 

8q.  Rt. 

Cu.  Rt 

No. 

8q.  Rt. 

Cu.  Rt 

No. 

Sq.  Rt. 

Cu.  Rt. 

No. 

IfOO 

40.0000 

11.6961 

1665 

40.8044 

11.8524 

1730 

41.8933 

12.0046 

1795 

I 

.0125 

.6985 

66 

.8167 

.8547 

81 

.6053 

.0069 

96 

2 

.0250 

.7009 

67 

.8289 

.8571 

32 

.6173 

.0093 

97 

3 

.0375 

.7034 

68 

.8412 

.8596 

33 

.62M 

.0116 

98- 

4 

.0500 

.7056 

69 

.8534 

.8618 

34 

.6413 

.0139 

99 

1605 

40.0625 

11.7082 

1670 

40.8656 

11.8642 

1785 

41.6633 

12.0162 

1800 

6 

.0749 

.7107 

71 

.8779 

.8666 

36 

.6663 

.0186 

1 

7 

.0874 

.7131 

72 

.8901 

.8689 

37 

.6773 

.0206 

2 

8 

.0999 

.7155 

73 

.9023 

.8713 

38 

.6893 

.0231 

3 

9 

.1123 

.7180 

74 

.9145 

.8737 

39 

.7013 

.0254 

4 

1610 

40.1248 

11.7204 

1675 

40.9268 

11.8760 

1740 

41.7123 

12.0277 

1805 

11 

.1373 

.7228 

76 

.9390 

.8784 

41 

.7263 

.0300 

6 

12 

.1497 

.7252 

77 

.9512 

.8808 

42 

.7373 

.0323 

7 

13 

.1622 

.7277 

78 

.9634 

.8831 

43 

.7493 

.0346 

8 

14 

.1746 

.7301 

79 

.9756 

.8855 

44 

.7612 

.0369 

9 

1615 

40.1871 

11.7325 

1680 

40.9878 

11.8878 

1745 

41.7732 

12.0392 

1810 

16 

.1995 

.7350 

81 

41.0000 

.8902 

46 

.7852 

.0416 

11 

17 

.2119 

.7373 

82 

.0122 

.8926 

47 

.7971 

.0438 

12 

18 

.2244 

.7398 

83 

.0244 

.8949 

48 

.8091 

.0461 

13 

19 

.2368 

.7422 

84 

.0366 

.8973 

49 

.8210 

.0484 

14 

1620 

40.2492 

11.7446 

1685 

41.0488 

11.8996 

1750 

41.8330 

12.0507 

1815 

21 

.2616 

.7470 

86 

.0609 

.9020 

51 

.8450 

.0530 

16 

22 

.2741 

.7494 

87 

.0731 

.9043 

52 

.8560 

.0553 

17 

23 

.2865 

.7518 

88 

.0853 

.9067 

53 

.8688 

.0576 

18 

24 

.2989 

.7543 

89 

.0974 

.9090 

54 

.8808 

.0599 

19 

1625 

40.3113 

11.7567 

1690 

41.1096 

11.9114 

1755 

41.8927 

12.0622 

1820 

26 

.3237 

.7591 

91 

.1218 

.9137 

56 

.9047 

.0645 

21 

27 

.3361 

.7615 

92 

.1339 

.9161 

57 

.9166 

.0668 

22 

28 

.3485 

.7639 

93 

.1461 

.9184 

58 

.9285 

.0690 

23 

29 

.3609 

.7663 

94 

.1582 

.9208 

59 

.9404 

.0713 

24 

1630 

40.3733 

11.7687 

1695 

41.1704 

11.9231 

1760 

41.9524 

12.0736 

1825 

31 

.3856 

.7711 

96 

.1825 

.9255 

61 

.9643 

.0759 

26 

32 

.3980 

.7735 

97 

.1947 

.9278 

62 

.9762 

.0782 

27 

33 

.4104 

.7759 

98 

.2068 

.9301 

63 

.9881 

.0605 

28 

34 

.4228 

.7783 

99 

.2189 

.9325 

64 

42.0000 

.0828 

29 

1635 

40.4351 

11.7807 

1700 

41.2311 

11.9348 

1765 

42.0119 

12.0850 

1830 

36 

.4475 

.7831 

1 

.2432 

.9372 

66 

.0238 

.0873 

31 

37 

.4599 

.7855 

3 

.2553 

.9395 

67 

.0357 

.0896 

32 

38 

.4722 

.7879 

3 

.2674 

9418 

68 

.0476 

.0919 

33 

39 

4846 

.7903 

4 

.2795 

.9442 

69 

.0595 

.0942 

34 

1640 

40.4969 

11.7927 

1705 

41.2916 

11.9465 

1770 

42.0714 

12.0964 

1835 

41 

.5093 

.7951 

6 

.3038 

.9489 

71 

.0833 

.0987 

36 

42 

.5216 

.7975 

7 

.3159 

.9512 

72 

.0951 

.1010 

37 

43 

.5339 

.7999 

8 

.3280 

.9535 

73 

.1070 

.1033 

38 

44 

.5463 

.8023 

9 

.3401 

.9559 

74 

.1189 

.1056 

39 

1645 

40.5586 

11.8047 

1710 

41.3521 

11.9582 

1775 

42.1307 

12.1078 

1840 

46 

.5709 

.8071 

11 

.3642 

.9605 

76 

.1426 

.1101 

41 

47 

.5832 

.8095 

12 

.3763 

.9628 

77 

.1545 

.1124 

42 

48 

.5956 

.8119 

13 

.3884 

.9652 

78 

.1663 

.1146 

43 

49 

.6079 

.8143 

14 

.4005 

.9675 

79 

.1782 

.1169 

44 

.9410 

.1^ 

1650 

40.6202 

11.8167 

1715 

41.4126 

11.9698 

1780 

42.1900 

12.1192 

1845 

42.9535 

»^-2S 

51 

.6325 

.8190 

16 

.4246 

.9722 

81 

.2019 

.1215 

46 

.9651 

.»7J 

52 

.6448 

.8214 

17 

.4367 

.9745 

82 

.2137 

.1237 

47 

.9767 

•2!J 

53 

.6571 

.8238 

18 

.4488 

.9768 

83 

.2256 

.1260 

48 

.9884 

.ITU 

64 

.6694 

.8262 

19 

.4608 

.9791 

84 

.2374 

.1283 

49 

43.0000 

.ffM 

1655 

40.6817 

11.8286 

1720 

41.4729 

11.9815 

1785 

42.2493 

12.1305 

1850 

43.0116 

i3.rj 

56 

.6940 

.8310 

21 

.4849 

.9838 

86 

.2611 

.1328 

61 

.0232 

.rfl 

67 

.7063 

.8333 

22 

.4970 

.9861 

87 

.2729 

.1350 

62 

.0349 

.vol 

68 

.7185 

.8357 

28 

.5090 

.9884 

88 

.2847 

.1373 

63 

.0465 

^ 

59 

.7308 

.8381 

24 

.6211 

.9907 

89 

.2966 

.1396 

54 

.0581 

.JMJ 

1660 

40.7431 

11.8405 

1725 

41.6331 

11.9931 

1790 

42.3084 

12.1418 

1855 

43.0697 

ll.gl 

61 

.7554 

.8429 

26 

.6452 

.9954 

91 

.3202 

.1441 

56 

.0813 

.ttfi 

62 

.7676 

.8452 

27 

.6672 

.9977 

92 

3320 

.1464 

57 

.0929 

.291! 

63 

.7799 

.8476 

28 

.6692 

12.0000 

93 

.3438 

.1486 

58 

.1045 

.tfil 

64 

.7922 

.8500 

29 

.6812 

.0023 

94 

.3556 

.1509 

59 

1161 

.»» 

1665 

40.8044 

11.8524 

1730 

41.5933 

12.0046 

1795 

42.3674 

12.1531 

1860 

43.1277 

12.J9W 

COMMON  TABLES— SQUARE  ROOTS.  CUBE  ROOTS. 


45 


10. — Square  Roots  and  Cube  Roots  op  Numbers 
1600  TO  3200 — Continued. 


Na 

9n.R%. 

Co.  Rt. 

No. 

8Q.  Rt 

Cu.  Rt. 

No. 

8q.  Rt. 

Cu.  Rt. 

No.  8Q.  Rt. 

CuRt 

UN 

Q.\m 

12.2961 

1925 

43.8748 

12.4397 

1990 

44.6004 

12.5782 

2055 

45.3321 

12.7137 

61 

.tm 

.2003 

26 

.8862 

.4419 

91 

.6206 

.5803 

56 

.8431 

.7167 

12 

Am 

.8025 

27 

.8976 

.4440 

92 

.6318 

.6824 

57 

.3542 

.7178 

O 

Ata 

.8047 

28 

.9090 

.4462 

93 

.6430 

.6845 

68 

.3652 

.7198 

M 

.1741 

.3069 

29 

.9204 

.4483 

94 

.6542 

.5866 

69 

.3762 

.7219 

ins 

42.18M 

12.3091 

1930 

43.9318 

12.4505 

1995 

44.6654 

12.5887 

2060 

45.3872 

12.7240 

M 

Am 

.8113 

31 

.9431 

.4526 

96 

.6766 

.5608 

61 

.8982 

.7260 

17 

.2N8 

.3186 

32 

.9545 

.4548 

97 

.6878 

.6929 

62 

.4093 

.7281 

« 

.2204 

.3167 

33 

.9659 

.4569 

98 

.6990 

.5950 

63 

.4203 

.7301 

« 

.23lf 

.3179 

34 

.9773 

.4M1 

99 

.7102 

.5971 

64 

.4313 

.7322 

un 

42.2435 

12.3201 

1935 

43.9886 

12.4612 

2000 

44.7214 

12.5092 

2065 

46.4423 

12.7342 

71 

.2961 

.3223 

36 

44.0000 

.4634 

1 

.7325 

.6013 

66 

.4633 

.7368 

72 

.2fM 

.3345 

37 

.0114 

.4655 

2 

.7437 

.6034 

67 

.4643 

.7384 

n 

.2782 

.3287 

28 

.0227 

.4676 

3 

.7549 

.6055 

68 

.4753 

.7404 

74 

.28»7 

.8289 

39 

.0341 

.4698 

4 

.7661 

.6076 

69 

.4863 

.7426 

U7f 

43.2n3 

12.3311 

1940 

44.0454 

12.4719 

2005 

44.7772 

12.6097 

2070 

45.4973 

12.7446 

71 

.2128 

.3333 

41 

.0568 

.4741 

6 

.7884 

.6118 

71 

.6062 

.7466 

77 

.2244 

.3354 

42 

.0681 

.4762 

7 

.7996 

.6139 

72 

.6192 

.7486 

71 

.33» 

.8376 

43 

.0795 

.4784 

8 

.8107 

.6160 

73 

.6302 

.7507 

T» 

.2474 

.8298 

44 

.0908 

.4805 

9 

.8219 

.6181 

74 

.6412 

.7627 

1M43.15M 

12  2420 

1945 

44.1022 

12.4826 

2010 

44.8330 

12.6202 

2076 

a.6622 

11.7646 

11 

.27N 

.2442 

46 

.1135 

.4848 

11 

.8442 

.6223 

76 

.5681 

.7666 

12 

.3820 

.2464 

47 

.1248 

.4869 

12 

.8553 

.6244 

77 

.6741 

.7689 

13 

.2935 

.3486 

48 

.1362 

.4891 

13 

.8665 

.6264 

78 

.6661 

.7600 

14 

.4051 

.2506 

40 

.1475 

.4912 

14 

.8776 

6286 

78 

.6061 

.7630 

IMS 

43.41N 

12.2529 

1950 

44.1588 

12.4933 

2015 

44.8888 

12.6306 

2060 

46.6070 

U.76iO 

m 

.4281 

.2551 

51 

.1701 

.4956 

16 

.8999 

.6327 

81 

.6180 

.7671 

n 

.43N 

.3673 

52 

.1814 

.4976 

17 

.9110 

.6348 

82 

.6289 

.7691 

m 

.4511 

.2585 

53 

.1928 

.4997 

18 

.9222 

.6369 

83 

.6399 

.7711 

m 

.4426 

.3617 

54 

.2041 

.5019 

19 

.9333 

.6390 

84 

.6508 

.7732 

UM 

42.4741 

12.2639 

1955 

44.2154 

12.5040 

2020 

44.9444 

12.6411 

2085 

45.6618 

12.7752 

•1 

.«5I 

.3660 

56 

.2267 

.5061 

21 

.9555 

.6432 

86 

.6727 

.7773 

t2 

.4ri 

.8682 

67 

.2380 

^.5083 

22 

.9667 

.6452 

87 

.6837 

.7793 

n 

.MM 

.3704 

58 

.2493 

.5104 

23 

.9778 

.6473 

88 

.6946 

.7814 

14 

.H81 

.2726 

60 

.2606 

.5125 

24 

.9889 

.6494 

89 

.7056 

.7834 

UM 

43.B16 

12.2747 

1960 

44.2719 

12.5146 

2025 

45.0000 

12.6515 

2096 

45.7165 

12.7854 

M 

.501 

.8789 

61 

.2832 

.5168 

26 

.0111 

.6536 

91 

.7275 

.7875 

« 

.MM 

.8791 

62 

.2945 

.5189 

27 

.0222 

.6657 

92 

.7384 

.7895 

H 

.iMI 

.2813 

a 

.3058 

.5210 

28 

.0333 

.6677 

93 

.7493 

.7915 

M 

-•«"» 

.2884 

64 

.3170 

.5232 

29 

.0444 

.6698 

94 

.7602 

.7936 

itw 

O.MM 

12.2856 

1965 

44.3283 

12.6263 

2030 

45.0665 

12.6619 

2095 

45.7712 

12.7956 

1 

.9m 

.8878 

66 

.3396 

.5274 

31 

.0666 

.6640 

96 

.7821 

.7977 

a 

.8119 

.8800 

67 

.3509 

.6295 

32 

.0777 

.6661 

97 

.7930 

.7997 

8 

.8224 

.2921 

68 

.3621 

.6317 

33 

.0888 

.6681 

98 

.8039 

.8017 

4 

-•»« 

.8843 

69 

.8734 

.5838 

34 

.0999 

.6702 

99 

.8148 

.8038 

UN 

13.8482 

12.8865 

1970 

44.3847 

12.5359 

2035 

45.1110 

12.6723 

2100 

46.8258 

12.8058 

• 

.6878 

.2886 

71 

.3950 

.5380 

36 

.1221 

.6744 

1 

.8367 

.8078 

1 

.6888 

.4008 

72 

.4072 

.5401 

37 

.1331 

.6764 

2 

.8476 

.8099 

1 

.6807 

.4080 

73 

.4186 

.5423 

38 

.1442 

.6785 

3 

.8585 

.8119 

• 

.6821 

.6051 

74 

.4297 

.6444 

39 

.1553 

.6806 

4 

.8694 

.8139 

Ifl* 

0.7N8 

12.4073 

1975 

44.4410 

12.6465 

2040 

45.1664 

12.6827 

2105 

45.8803 

12.8159 

11 

.7158 

.6095 

76 

.4522 

.5486 

41 

.1774 

.6847 

6 

.8912 

.8180 

U 

.7184 

.4116 

77 

.4635' 

.5507 

42 

.1885 

.6868 

7 

.9021 

.8200 

u 

.71ft 

.4188 

78 

.4747 

.5528 

43 

.1996 

.6889 

8 

.9130 

.8220 

J! 

.74M 

.4160 

79 

.4860 

.5650 

44 

.2106 

.6909 

9 

.9238 

.8241 

tiu 

0.7881 

U.4181 

1980 

44.4972 

12.5571 

2045 

45.2217 

12.6930 

2110 

45.9347 

12.8261 

If 

.nil 

.4808 

81 

.5084 

.6592 

46 

.2327 

.6951 

11 

.9456 

.8281 

11 

.im 

.4225 

82 

.5197 

.6613 

47 

.2438 

.6971 

12 

.9666 

.8301 

IS 

,im 

.48a 

83 

.6309 

.5634 

48 

.2548 

.6992 

13 

.9674 

.8322 

t» 

J884 

.4161 

84 

.5421 

.5655 

49 

.2669 

.7013 

14 

.9783 

.8342 

IM 

njun 

12.4188 

1985 

44.6533 

12.5676 

2050 

45.2769 

12.7033 

2115 

45.9891 

12.8362 

n 

Mn 

.4211 

86 

.5646 

.5697 

51 

.2880 

.7054 

16 

46.0000 

.8382 

n 

.84M 

.4332 

87 

.5768 

.6719 

52 

.2990 

.7075 

17 

.0109 

.8403 

» 

.86M 

.4354 

88 

.6870 

.5740 

53 

.3100 

.7095 

18 

.0217 

.8423 

24 

J824 

.4276 

89 

.6082 

.5761 

54 

.3211 

.7116 

19 

.0326 

.8443 

im 

0.8748 

12.4397 

1990 

44.6094 

12.5782 

2055 

45.3321 

12.7137 

2120 

46.0436 

12.8462 

40 


2.— POWERS,  ROOTS  AND  RECIPROCALS. 


10. — Squarb  Roots  and  Cubb  Roots  of  Numbbrs 
1600  to  3200 — Continued. 


No.  Sq.  Rt.  Cu.  Rt.  No.  Sq.  Rt.  Cu.  Rt.  No.  Sq.  Rt.  Cu.  Rt. 


No   8q.  Rt.Ca.  RC 


3120  46.0436 


21 
22 
23 
24 

2125 
26 
27 

28 
29 


.0543 
.0653 
.0760 
.0669 
46.0977 
.1086 
.1194 
.1303 
.1411 


2130  46.1519 


31 
32 
S3 
84 
2135 
36 
37 
38 
39 


.1628 
.1736 
.1844 
1952 
26.2061 
.2169 
.2277 
.2385 
.2493 


2140  46.2601 


41 

42 

43 

44 
2145 

46 

47 

48 

49 
2150 

61 

62 

63 

64 
2155 

56 

67 

68 

59 
2160 

61 

62 

63 

64 
2165 

66 

67 

68 

69 
2170 

71 

72 

73 

74 
2175 

76 

77 

78 

79,  

2180  146.6905 

81  .7012 

82  .7119 

83  .7226 

84  .7333 
2185  46.7440 


.2709 
.2817 
.2925 
.3033 

46.3141 
.3249 
.3357 
.3465 
.3573 

46.3681 
.3789 
.3897 
.4004 
.4112 

46.4220 
.4327 
.4435 
.4543 
.4650 

46.4758 
.4866 
.4973 
.5081 
.5188 

46.5296 
.5403 
.6510 
.5618 
.5725 

46.5833 
5940 
,6047 
6154 
.6262 

16.6369 
.6476 
.6583 
,6690 
.6798 


12.8463 
.8483 
.8504 
.8524 
.8644 

12.8564 
.8584 
.8604 
.8625 
.8645 

12.8665 
.8685 
.8705 
.8725 
.8745 

13.8766 
.8786 
.8806 
.8826 
.8846 

12.8866 
.8886 
.8906 
.8926 
.8946 

12.8966 
8986 
9006 
9026 
9046 

12.9066 
.9086 
.9106 
.9126 
.9146 

12.9166 
.9186 
.9206 
.9226 
.9246 

12.9266 
.9286 
.9306 
.9326 
.9346 

12.9366 
.9386 
.9406 
.9426 

.»4a 

12.9466 
.9485 
.9505 
.9525 
.9545 

12.9565 
.9584 
.9604 
.9624 
.9644 

12.9664 
.9684 
.9703 
.9723 
.9743 

12.9763 


2186 
86 
87 
88 

89 

2190 
91 
92 
93 
94 

2195 
96 
97 
98 
99 

2200 
1 
2 
3 
4 

2205 
6 
7 
8 
9 

2210 
11 
12 
IS 
14 

2215 
16 
17 
18 
19 

2220 
21 
23 
23 
34 

2225 
26 
27 
28 
29 

2230 
31 
32 
33 
34 

2235 
36 
37 
38 
39 

2240 
41 
42 
43 
44 

2245 
46 
47 
48 
49 

2250 


46.7440 
.7647 
.7654 
.7761 
.7868 

46.7974 
.8081 
.8188 
.8295 
.8402 

46.8608 
.8615 
.8722 
.8828 
.8936 

[46.9042 
.9148 
.9255 
.9361 
.9468 

46.9574 
.9681 
.9787 
.9894 

47.0000 

47.0106 
.0213 
.0319 
.0426 
.0532 

.0744 
.0850 
.0956 
.1063 

47.1169 
.1276 
.1381 
.1487 
.1693 

47.1699 
.1805 
.1911 
.2017 
.2123 

47.2229 
.2335 
.2440 
.2546 
.2652 

47.2758 
.2864 
.2969 
.3075 
.3181 

47.3286 
.3392 
.3498 
.3603 
.3709 

47.3814 
.3920 
.4026 
.4131 
.4236 

47.4342 


12.9763- 
.9783 
.9802 
.9822 
.9842 

12.9862 
.9882 
.9901 
.9921 
.9941 

12.9961 
.9980 

13.0000 
.0020 
.0039 

IS. 0059 
.0079 
.0099 
.0118 
.0138 

13.0168 
0177 
0197 
0217 
0236 

13.0256 
0276 
0295 
0316 
0334 

13.0354 
.0374 
.0393 
.0413 
.0432 

13.0452 
.0472- 
.0491 
.0511 
.0530 

13.0550 
.0569 
.0589 
.0609 
.0628 

13.0648 
.0667 
.0687 
.0706 
.0726 

13.0745 
.0765 
.0784 
.0804 
.0823 

13.0843 
.0862 
.0882 
.0901 
.0920 

13.0940 
.0959 
.0979 
.0998 
.1018 

13.1037 


2250 
51 
62 
53 
54 

2255 
66 
57 
68 
59 

2260 
61 
62 
63 
64 

2265 
66 
67 
68 
69 

2270 
71 
72 
73 
74 

2276 
76 
77 
78 
79 

2280 
81 
82 
83 
84 

2285 
86 
87 
88 
89 

2290 
91 
92 
93 
94 

2295 
96 
97 
98 
99 

2300 
1 
2 
8 
4 

2305 
6 
7 
8 
9 

2310 
II 
12 
13 
14 
2315 


47.4342 
.4447 

.4552 
.4658 
.4763 

47.4868 
.4974 
.5079 
.5184 
.5289 

17.6395 
.6500 
.5605 
.5710 
.5815 

47.6920 
.6025 
.6130 
.6235 
.6340 

47.6445 
.6550 
.6655 
.6760 
.6865 

47.6970 
.7074 
.7179 
.7284 
.7389 

47.7493 
.7598 
.7703 
.7807 
.7912 

47.8017 
.8121 
.8226 
.8330 
.8435 

47.8539 
.8644 
.8748 
.8853 
.8957 

47.9062 
.9166 
.9270 
.9375 
.9479 

47.9583 
.9687 
".9792 
.9896 

48.0000 

48.0104 
.0208 
.0312 
.0416 
.0521 

48.0625 
.0729 
.0833 
.0937 

I  .1041 

48.1144 


13.1037 
.1066 
.1076 
.1095 
.1115 

13.1134 
1153 
1173 
1192 
.1212 

13.1231 
.1250 
.1270 
.1285 
.1308 

IS. 1328 
.1347 
.1366 
.1386 
.1405 

IS. 1424 
.1443 
.1463 
.1482 
.1501 

IS. 1621 
.1640 
.1659 
.1678 
.1598 

IS. 1617 
.1636 
.1655 
.1675 
.1694 

13.1713 
.1732 
.1751 
.1771 
.1790 

13.1809 
.1828 
.1847 
.1867 
.1886 

13.1905 
.1924 
.1943 
.1962 
.1981 

13.2001 
.2020 
.2039 
.2058 
.2077 

13.2096 
.2115 
.2134 
.2153 
.2173 

13.2192 
2211 
2230 
2249 
2268 

13.2287 


2315 
16 
17 
18 
19 

2320 
21 
22 
23 
24 

2325 
26 
27 
28 
29 

2330 
31 
32 
33 
34 

2336 
36 
37 
38 
39 

2340 
41 
42 
43 
44 

2345 
46 
47 
48 
49 

2350 
51 
62 
63 
64 

2355 
56 
67 
68 
59 

2360 
61 
62 
63 
64 

2365 
66 
67 
68 
69 


48.1144 
.1348 
.1362 
.1456 
.1560 

48.1664 
.1768 
.1871 
.1976 
.2079 

48.2183 
.2286 
.2390 
.2494 
.2597 

48.2701 
.2804 
.2908 
.3011 
.3116 

48.8218 
.3322 
.3425 
.3529 
.3632 

48.3735 
.3839 
.3942 
.4045 
.4149 

48.4252 
.4356 
.4458 
.4563 
.4666 

48.4768 
.4871 
.4974 
.6677 
.6180 

48.6283 
.6386 
.5489 
.6592 
.6695 

48.6798 
.5901 
.6004 
.6107 
.6310 

48.6313 
.6415 
.6518 
.6631 
.6724 
2370  148.6826 


13.3387 
.3306 
.3335 
.3344 
.3363 

13.3381 
2401 
342« 
3439 
2458 

13.24n 
.2496 
.2515 
.3634 
.3553 

13.3573 
3891 
3610 
3629 
3648 

13.36fr 
.3686 
.3706 
.3714 
.37tt 

1S.3761 
.3780 
.3799 
.3818 

^   .3837 

18.3886 
.3878 
.2894 
.3118 
.3981 

18.1980 


71 
72 
73 
74 

2375 
76 
77 
78 
79 

2380 


.6929 
7032 
7134 
7237 

48.7340 
7443 
7545 
7647 
,7760 

48.7863 


13.8060 

.3063 

.8663 

.3101 

.3130 

13.3130 

3167 

3176 

3105 

^     W14 

13.8381 

1381 

3379 

3389 

8806 

13.18M 


.3601 


.3458 

.3<7« 


13.3814 


COMMON   TABLES-SQUARE  ROOTS,  CUBE  ROOTS. 


10. — Squarb  Roots  and  Cubb  Roots  op  Numbbrs 
1600  to  3200— Contintied. 


Now 

k.K. 

CU-   Rt. 

Ifo. 

Sq.  Rt. 

eu.  Rt 

No. 

Sq.  Rt. 

Cu.  Rt 

No. 

Bq.  Rt. 

Co.  Rt 

2%6 

48.7852 

13.3514 

2445 

48.4469 

13.4718 

2610 

60.0999 

13.5902 

2575 

50.7446 

13.7066 

81 

7955 

46 

.4571 

.4737 

11 

.1099 

.5820 

76 

.7543 

.7063 

61 

.8857 

.3551 

47 

.4672 

.4756 

12 

.1199 

.5938 

77 

.7642 

.7100 

83 

.8169 

.3570 

48 

.4773 

.4773 

12 

.1298 

.5956 

78 

.7740 

.7118 

•4 

2185 

8263 

3588 

49 

.4874 

.4792 

14 

.1398 

.5974 

79 

.7839 

.7138 

48!8365 

13.364»7 

2450 

49.4975 

13.4810 

2515 

50.1498 

13.5092 

2580 

50.7937 

13.7163 

86 

8467 

51 

.5076 

.4828 

16 

.1597 

.6010 

81 

.8035 

.7171 

87 

!SS69 

.3644 

52 

.5177 

.4847 

17 

.1697 

.6028 

82 

.8134 

.7188 

88 

8672 

.3663 

53 

.5278 

.4865 

18 

.1797 

.6046 

83 

.8232 

.7207 

88 
2386 

.'8774 
48.8876 

.3682 

54 

.5379 

.4883 

19 

.1896 

.6064 

84 

.8331 

.7224 

13I37OO 

3455 

49.5480 

12.4902 

3520 

60.1996 

13.6082 

2585 

50.8429 

13.7242 

61 

•2 
•S 
94 

96 

97 

98 
90 

*-? 

2 
3 
4 
S465 
6 
7 
8 

.8979 
.9681 
.9183 
.9285 

48.9387 
.9490 
.9S92 
.9694 
9796 

48.9098 

!0102 
.8204 
.9306 

49.0408 
.0510 
.0612 
.0714 
.6816 

49.0918 
.1019 

3719 

56 

.5580 

.4920 

21 

.2096 

.6100 

86 

.8527 

.7260 

1 3738 

57 

.5681 

.4938 

22 

.2195 

.6118 

87 

.8626 

.7277 

.3756 

58 

.5782 

.4957 

23 

.2295 

.8136 

88 

.8724 

.7296 

'3775 

59 

.5883 

.4975 

24 

.2394 

.6154 

89 

.8822 

.7318 

13*3794 

48.5984 

12.4993 

2525 

50.2494 

13.6172 

2590 

50.8920 

12.7330 

.3812 
.3831 
.3849 
.3868 

U.8887 
.3905 
.3924 
.3942 
.3961 

13.3980 
.3998 
.4017 
.4035 
.4054 

13.4072 
.4991 
.4109 
.4128 
.4146 

tZ    -"5 

12  7 

13  0 

12  J 

13  * 

*^            5 

61 

.6085 

.5011 

26 

.2502 

.6190 

91 

.9019 

.7348 

62 

.6185 

.5030 

27 

.2693 

.6208 

92 

.9117 

.7368 

63 

.6286 

.5048 

28 

.2792 

.6226 

92 

.9215 

.7388 

64 

.6387 

.5066 

29 

.2892 

.6244 

94 

.9313 

.7401 

2465 
66 

49.6488 
.6588 

13.5085 
.5103 

2530 
31 

50.2991 
.3090 

13.6262 
.6280 

2595 
96 

50.9411 
.9510 

13.7419 
.7436 

67 

.6689 

.5121 

32 

.3190 

.6298 

97 

.9608 

.7454 

68 

.6790 

.5139 

33 

.3289 

.6315 

98 

.9706 

.7472 

69 

.6890 

.5158 

34 

.3389 

.6333 

99 

.9804 

.7489 

2470 
71 

49.6991 
.7092 

13.5176 
.5194 

2635 
36 

50.3488 
.3587 

13.6351 
.6369 

2600 

50.9902 
51.0000 

13.7507 
.7525 

72 

.7192 

.5212 

37 

.3686 

.6387 

2 

.0098 

.7542 

73 

.7293 

.6231 

38 

.3786 

.6405 

3 

.0196 

.7660 

74 

.7393 

.6249 

39 

.3885 

.6423 

4 

.0294 

.7677 

9 

1416 

11 

2475 
76 

77 

49.7494 
.7694 
.7695 

12.5267 
.5285 
.5303 

2540 
41 
42 

50.3984 
.4083 
.4183 

13.6441 
.6459 
.6477 

2605 
6 

7 

51.0392 
.0490 
.0588 

13.7586 
.7618 
.7630 

12 

.1121 

78 

.7795 

.5322 

43 

.4282 

.6495 

8 

.0686 

.7648 

13 

.1223 

79 

7896 

.5840 

44 

.4381 

.6512 

9 

.0784 

.7665 

14 

.1325 
49.1426 

2480 

49.7996 

13.5358 

2545 

50.4480 

13.6530 

2610 

51.0882 

13.7683 

Ml  5 

81 

8096 

.6376 

46 

.4579 

.6548 

11 

.0979 

.7701 

14 

.1628 

82 

.8197 

.5394 

47 

.4678 

.6566 

12 

.1077 

.7718 

17 

.1630 

83 

.8297 

.5413 

48 

.4777 

.6584 

13 

.1175 

.7736 

18 

.1732 

84 

.8397 

.5431 

49 

.4876 

.6602 

14 

.1273 

.7763 

19 

.1833 

2485 

48.8498 

13.5449 

2560 

50.4975 

13.6620 

2616 

51.1371 

13.7771 

2120 

49.1935 

86 

.8598 

.5467 

51 

.6074 

.6638 

16 

.1468 

.7788 

21 

.2097 

87 

.8698 

.5485 

52 

.6172 

.6655 

17 

.1566 

.7806 

22 

.2138 

88 

.8799 

.5503 

53 

.6272 

.6673 

18 

.1664 

.7823 

23 

.2249 

89 

.8899 

.5522 

54 

.5371 

.6691 

19 

.1762 

.7841 

24 

.2341 

2490 

48.8999 

13.5540 

2555 

50.6470 

12.6709 

2620 

51.1859 

13.7859 

2I2S 

48.24^ 

91 

.9099 

.5558 

56 

.5669 

.6727 

21 

.1957 

.7876 

26 

.2544 

92 

.9199 

.5576 

57 

.5668 

.6746 

22 

.2055 

.7894 

27 

.2646 

93 

.9300 

.5594 

68 

.W67 

.6762 

23 

.2152 

.7911 

28 

.2747 

94 

.9400 

.5612 

69 

.8666 

.6780 

24 

.2250 

.7929 

28 

.2849 

2495 

49.9500 

13.5630 

2660 

50.6864 

13.6798 

2625 

51.2348 

13.7946 

2428 

49.2960 

96 

.9600 

.5648 

61 

.6063 

.6816 

26 

.2445 

.7964 

21 

.3052 

97 

.9700 

.5667 

62 

.6162 

.6834 

27 

.2543 

.7981 

22 

.3153 

98 

.9800 

.5685 

63 

.6261 

.6851 

28 

.2640 

.7999 

23 

.3254 

99 

.9900 

.5703 

64 

.6360 

.6869 

29 

.2738 

.8016 

24 

.3356 

2500 

50.0000 

13.5721 

2565 

50.6458 

13.6887 

2630 

51.2835 

13.8034 

U25 

49.3457 

1 

.0100 

.5739 

66 

.6557 

.6905 

31 

.2933 

.8051 

21 

.3559 

2 

.0200 

.5767 

67 

.6656 

.6923 

32 

.3030 

.8069 

27 

.3660 

3 

.0300 

.5775 

68 

.6754 

6940 

33 

.3128 

.8086 

28 

.3761 

4 

.0400 

.5793 

69 

.6853 

.6958 

34 

.3225 

.8104 

28 

.3862 

.«« 

50.0500 

13.5811 

2570 

50.6952 

13.6976 

263.-) 

51.3323 

13.8121 

2M6 

».3964 

.0600 

.5829 

71 

.7050 

.6994 

36 

.3420 

.8139 

41 

.4065 

7 

.0700 

.5847 

72 

7149 

.7011 

37 

.3517 

.8156 

42 

.4166 

A 

.0799 

.5865 

73 

.7247 

.7029 

38 

.3615 

.8174 

42 

.4267 

L         9 

.0899 

.5884 

74 

.7346 

.7047 

39 

.3712 

.8191 

44 

.4368 

■     2S10 

50.0989 

13.5902 

2575 

50.7445 

13.7065 

2640 

51.3809 

13.8208 

24tt'|49.4469  | 

13-          • 

■ 

'  r^^^ 

^T^ 

)gic 

48 


2— POWERS,  ROOTS  AND  RECIPROCALS. 


10. — Square  Roots  and  Cubb  Roots  op  Nuubbrs 
1600  to  8200— Continued. 


No. 

8a.  Rtlot  Rt. 

No. 

Sq.   Rt. 

CU-  Rt. 

No.  leq.  Rt. 

Cu.  Rt 

No. 

8q.  Rt. 

Cu.  n 

2640 

51.3809 

13.8206 

2705 

52.0096 

13.9334 

2770 

62.6308 

14.0441 

2835 

53.2447 

14.15a 

41 

.3907 

.8226 

6 

.0192 

.9351 

71 

.6403 

.0458 

36 

.2641 

.IM 

42 

.4004 

.8243 

7 

.0288 

.9368 

72 

.6498 

.0475 

37 

.2635 

.15« 

43 

.4101 

.8261 

8 

.0384 

.9385 

73 

.6593 

.0491 

38 

.2729 

.1981 

44 

.4198 

.8278 

9 

.0481 

.9402 

74 

.6688 

.0608 

39 

.2823 

.im 

2645 

51.4296 

13.8296 

2710 

52.0577 

13.9419 

2775 

52.6783 

14.0525 

2840 

63.2917 

14.161^ 

46 

.4393 

.8313 

11 

.0673 

.9437 

76 

.6878 

.0642 

41 

.3010 

.lOl 

47 

.4490 

.8331 

12 

.0769 

.9454 

77 

.6972 

.0659 

42 

.3104 

.164: 

48 

.4587 

.8348 

13 

.0865 

.9471 

78 

.7067 

.0576 

43 

.3198 

.16t4 

49 

.4684 

.8365 

14 

.0961 

.9488 

79 

.7162 

.0593 

44 

.3292 

.1W( 

2650 

51.4782 

13.8383 

2716 

52.1057 

13.9505 

2780 

52.7257 

14.0610 

3845 

53.3385 

14.1«« 

51 

.4879 

.8400 

16 

.1153 

.9622 

81 

.7352 

.0626 

46 

.3479 

A7U 

52 

.4976 

.8418 

17 

.1249 

.9539 

82 

.7447 

.0643 

47 

.3678 

.1731 

53 

.6073 

.8435 

18 

.1344 

.9666 

83 

.7541 

.0660 

48 

.3667 

.174: 

64 

.5170 

.8452 

19 

.1440 

.9674 

84 

.7636 

.0677 

49 

.3760 

.1762 

2655 

51.5267 

13.8470 

2720 

52.1536 

13.9591 

2786 

52.7731 

14.0694 

2860 

53.3854 

14.1781 

66 

.5364 

.8487 

21 

.1632 

.9608 

86 

.7826 

.0711 

61 

.3948 

.17OT 

67 

.5461 

.8504 

22 

.1728 

.9625 

87 

.7920 

.0728 

52 

.4041 

.1813 

58 

.6658 

.8622 

23 

.1824 

.9642 

88 

.8015 

.0744 

53 

.4135 

.18» 

50 

.6655 

.8539 

24 

.1920 

.9659 

89 

.8110 

.0761 

64 

.4228 

.1841 

2660 

51.6762 

13.8667 

2726 

52.2015 

13.9676 

2790 

62.8205 

14.0778 

2855 

63.4322 

14.1868 

61 

.6849 

.8574 

26 

.2111 

.9693 

91 

.8299 

.0795 

66 

.4416 

.187« 

62 

.6946 

.8591 

27 

.2207 

.9710 

92 

.8394 

.0812 

67 

.4509 

.18»€ 

63 

.6043 

.8609 

28 

.2303 

.9727 

93 

.8488 

.0828 

68 

.4603 

.1913 

64 

.6140 

.8626 

29 

.2398 

.9744 

94 

.8583 

.0845 

69 

.4696 

.itas 

26f5 

51.6236 

13.8643 

2730 

52.2494 

13.9761 

2796 

52.8678 

14.0862 

2860 

53.4790 

14.1»4fl 

66 

.6333 

.8661 

31 

.2690 

.9779 

96 

.8772 

.0879 

61 

.4883 

.1»<2 

67 

.6430 

.8678 

32 

.2685 

.9796 

97 

.8867 

.0896 

62 

.4977 

A9n 

68 

.6527 

.8695 

33 

.2781 

.9813 

98 

.8961 

.0912 

63 

.6070 

.1998 

69 

.6624 

.8713 

34 

.2877 

.9830 

99 

.9056 

.0929 

64 

.6164 

.20M 

2670 

51.6720 

13.8730 

2735 

62.2972 

13.9847 

2800 

52.9150 

14.0946 

2866 

53.5257 

U.20M 

71 

.6817 

.8747 

36 

.3068 

.9864 

I 

.9245 

.0963 

66 

.5350 

.SOU 

72 

.6914 

.8765 

37 

.3163 

.9881 

2 

.9339 

.0980 

67 

.5444 

.2061 

73 

.7011 

.8782 

38 

.3259 

.9898 

3 

.9434 

.0996 

68 

.6637 

.9078 

74 

.7107 

.8799 

39 

.3356 

.9915 

4 

.9528 

.1013 

69 

.5630 

.2094 

2675  51.7204 

13.8817 

2740 

52.3450 

13.9932 

2805 

52.9623 

14.1030 

2870 

53.5724 

^4.3111 

76 

.7301 

.8834 

41 

.3646 

.9949 

6 

.9717 

.1047 

71 

.5817 

.JUT 

77 

.7397 

.8851 

42 

.3641 

.9966 

7 

.9811 

.1063 

72 

.6010 

.1144 

78 

.7494 

.8868 

43 

.3737 

.9983 

8 

.9906 

.1080 

73 

.6004 

.2160 

79 

.7591 

.8886 

44 

.3832 

14.0000 

9 

53.0000 

.1097 

74 

.6097 

.1177 

2680 

51 .7687 

13.8903 

2745 

52.3927 

14.0017 

2810 

53.0094 

14.1114 

2875 

53.6190 

14.2193 

81 

.7784 

.8920 

46 

.4023 

.0034 

11 

.0189 

.1130 

76 

.6284 

.1110 

82 

.7880 

.8938 

47 

.4118 

.0051 

12 

.0283 

.1147 

77 

.6377 

.1226 

83 

.7977 

.8955 

48 

.4214 

.0068 

13 

.0377 

.1164 

78 

.6470 

.2243 

84 

.8073 

.8972 

49 

.4309 

.0085 

14 

.0471 

.1180 

79 

.6663 

2286 

2685 

51.8170 

13.8989 

2750 

52.4404 

14.0102 

2815 

53.0566 

14.1197 

2880 

53.6656 

14.2176 

86 

.8266 

.9007 

51 

.4500 

.0119 

16 

.0660 

.1214 

81 

.6749 

.1391 

87 

.8363 

.9024 

52 

.4595 

.0136 

17 

.0754 

.1231 

82 

.6843 

.1309 

88 

.8469 

.9041 

53 

.4690 

.0163 

18 

.0848 

.1247 

83 

.6936 

.3315 

89 

.8656 

.9058 

54 

.4786 

.0170 

19 

.0943 

.1264 

84 

.7029 

.3343 

2690 

51.8652 

13.9076 

2755 

52.4881 

14.0187 

2820 

53.1037 

14.1281 

2885 

53.7123 

I4.23SB 

91 

.8748 

.9093 

66 

.4976 

.0204 

21 

.1131 

.1297 

86 

.7215 

.1374 

92 

.8845 

.9110 

67 

.5071 

.0221 

22 

.1225 

.1314 

87 

.7308 

.3391 

93 

.8941 

.9127 

68 

.5167 

.0238 

23 

.1319 

.1331 

88 

.7401 

.3407 

94 

.9038 

.9144 

59 

.5262 

.0255 

24 

.1413 

.1348 

89 

.7494 

.3434 

2696 

51.9134 

13.9162 

2760 

52.6357 

14.0272 

2825 

53.1507 

14.1364 

2890 

58.7587 

14.3440 

96 

.9230 

.9179 

61 

.5452 

.0289 

26 

.1601 

.1381 

91 

.7680 

.3457 

97 

.9326 

.9196 

62 

.6647 

.0305 

27 

.1695" 

.1398 

.92 

.7773 

.3473 

98 

.9423 

.9213 

63 

.5642 

.0322 

28 

.1789 

.1414 

93 

.7866 

.3489 

99 

.9519 

.9230 

64 

.5738 

.0339 

29 

.1883 

.1431 

94 

.7959 

.3501 

2700 

51.9615 

13.9248 

2766 

52.5833 

14.0356 

2830 

53.1977 

14.1448 

2895 

53.8052 

14.3533 

1 

.9711 

.9265 

66 

.5928 

.0373 

31 

.2071 

.1464 

96 

.8146 

.1589 

2 

.9808 

.9282 

67 

.6023 

.0390 

32 

.2165 

.1481 

97 

.8238 

.3565 

3- 

.9904 

.9299 

68 

.6118 

.0407 

33 

.2259 

.1498 

98 

.8331 

.3671 

4 

52.0000 

.9316 

69 

.6213 

.0424 

34 

.2353 

.1614 

99 

.8424 

.8689 

2705 

52.0096 

13.9334 

2770 

52.6308 

14.0441 

2835 

53.2447 

14.1531 

2900 

63.8616 

U.36M 

COMMON  TABLES— SQUARE  ROOTS,  CUBE  RQOTS. 


49 


10. — Squarb  Roots  and  Cubb  Roots  of  Numbers 
1600  TO  3200 — Continued. 


Kclsq.  Bt 

Co.  Rt. 

No. 

8q.  Rt. 

C?a.  Rt. 

No. 

8q.  Rt. 

Cu.  Rt, 

No. 

8q.  Rt.'cu.  Rt. 

a»  £3.8916 
if  .8611 
2'    .8711 

16.2604 

2965 

54.4518 

14.3662 

3030 

56.0454 

14.4704 

3095 

55.6327 

14.5732 

.2621 

66 

.4610 

.3678 

31 

.0546 

.4720 

96 

.6417 

.6747 

.2837 

67 

.4702 

.3694 

32 

.0636 

.4736 

97 

.6507 

.6763 

3,    .8795 

.8653 

68 

.4794 

.3710 

33 

.0727 

.4752 

98 

.6507 

.5779 

4,    .8888 

.2670 

69 

.4885 

.3726 

34 

.0618 

.4768 

99 

.6687 

.5794 

2NS 

S3.8881 

14.2686 

2970 

54.4977 

14.3743 

3035 

55.0908 

14.4784 

3100 

55.6776 

14.5810 

f 

.9073 

.2703 

71 

.5060 

.3769 

86 

.0999 

.4800 

.6866 

.5826 

? 

.9166 

.2719 

72 

.6161 

.3775 

37 

.1090 

.4815 

8 

.6956 

.5841 

s 

.9258 

.2735 

73 

.5252 

.3791 

38 

.1181 

.4831 

3 

.7046 

.5857 

9      .1351 

.r52 

74 

.5344 

.3807 

39 

.1271 

.4847 

4 

.7136 

.5873 

BI8  |S.I444 

14.r68 

2975 

54.5436 

14.3823 

3040 

65.1362 

14.4863 

3106 

56.7225 

14.5888 

n      .»SI7 

.2784 

76 

.5527 

.3839 

41 

.1453 

.4879 

6 

.7315 

5904 

12      .N30 

.2801 

77 

.6619 

.3855 

42 

.1543 

.4895 

7 

.7405 

.5920 

13      .1722 

.2817 

78 

.5711 

.3872 

43 

.1634 

.4911 

8 

.7494 

.5935 

14      .$815 

.2833 

79 

.5802 

.3888 

44 

.1725 

.4927 

9 

.7584 

.5951 

ms  53J907 

14.2850 

2980 

54.5894 

14.3904 

3045 

55.1815 

14.4943 

3110 

55.7674 

14.5967 

11  M.OOOO 

.2866 

81 

.5085 

.3920 

46 

.1906 

.4958 

11 

.7763 

.5982 

17      .WW 

.2882 

82 

.6077 

.3936 

47 

.1996 

.4974 

12 

.7853 

.5998 

IS      .0185 

.2899 

83 

.6168 

.3952 

48 

.2087 

.4990 

13 

.7943 

.6014 

1»      .0278 

.2915 

84 

.6260 

.3968 

49 

.2178 

.5006 

14 

.8032 

.6029 

2m  $4.(»70 

14.2931 

2985 

54.6352 

14.3984 

3050 

55.2268 

14.5022 

3115 

55.8122 

14.6045 

21  !    .8463 

.2948 

86 

.6443 

.4000 

51 

.2369 

.5038 

16 

.8211 

.6060 

Jjl    .8555 

.2964 

87 

.6535 

.4016 

52 

.2449 

.5053 

17 

.8301 

.6076 

23  i    .8648 

.2880 

88 

.6626 

.4032 

53 

.2540 

.5069 

18 

.8391 

.6092 

24 

.0740 

.2999 

89 

.6717 

.4048 

54 

.2630 

.5085 

19 

.8480 

.6107 

2R5 

54.8833 

14.3013 

2890 

54.6809 

14.4065 

3055 

65.2721 

14.5101 

3120 

56.8570 

14.6123 

.36 

.0025 

.3029 

91 

.6900 

.4081 

66 

.2811 

.5117 

21 

.8659 

.6138 

r 

.1018 

.3046 

92 

.6992 

.4097 

67 

.2901 

.5133 

22 

.8749 

.6154 

28 

.1110 

.2062 

93 

.7083 

.4113 

58 

.2992 

.5148 

23 

.8838 

.6170 

21 

.1282 

.3078 

94 

.7175 

.4129 

69 

.3082 

.5164 

24 

.8928 

.6185 

2»8 

94.1295 

14.3094 

2895 

54.7266 

14.4145 

3060 

66.3173 

14.5180 

3125 

55.9017 

14.6201 

SI 

.1387 

.3111 

96 

.7357 

.4161 

61 

.3263 

.5196 

26 

.9106 

.6216 

33 

.1479 

.3127 

97 

.7449 

.4177 

62 

.3353 

.5212 

27 

.9196 

.6232 

a 

.1872 

.3143 

98 

.7540 

.4193 

63 

.3444 

.5228 

28 

.9285 

.6248 

14      .1664 

.2169 

99 

.7631 

.4209 

64 

.3534 

.5243 

29 

.9375 

.6263 

B35  54.1736  !u.3I76 

3000 

54.7723 

14.4225 

3065 

56.3624 

14.5259 

3130 

66.9464 

14.6279 

36 

.1849 

.3192 

1 

.7814 

.4241 

66 

.3715 

.5275 

31 

.9553 

.6294 

17 

.1941 

.3206 

2 

.7905 

.4257 

67 

.3805 

.5291 

32 

.9643 

.6310 

38 

.2033 

.3224 

3 

.7096 

.4273 

68 

.3895 

.6307 

33 

9732 

.6326 

38 

.2125 

.8241 

4 

.8088 

.4289 

69 

.3986 

.5322 

34 

.9821 

.6341 

2840  54.2318 

14.3257 

3005 

54.8179 

14.4305 

3070 

65.4076 

14.5338 

3135 

55.9911 

14.6357 

41 

.2310 

.3273 

6 

JJ270' 

.4321 

71 

.4166 

.6354 

36 

56.0000 

.6372 

12 

.2402 

.3289 

7 

.8361 

.4337 

72 

.4256 

.5370 

37 

.0089 

.6388 

12 

.2404 

.3306 

8 

.8462 

.4353 

73 

.4346 

.5385 

38 

.0179 

.6403 

44 

.2966 

.3322 

9 

.8544 

.4369 

74 

.4437 

.5401 

39 

.0268 

.6419 

2M5 

54.2679 

14.3338 

3010 

54.8635 

14.4385 

3075 

55.4527 

14.5417 

3140 

56.0357 

14.6434 

46 

.2771 

,3354 

11 

.8726 

.4401 

76 

.4617 

.6433 

41 

.0446 

.6450 

47 

.280 

.8371 

12 

,  .8817 

.4417 

77 

.4707 

.5448 

42 

.0535 

.6466 

48 

.1995 

.3387 

13 

.8908 

.4433 

78 

.4797 

.5464 

43 

.0625 

.6481 

48 

.3047 

.3403 

14 

.8999 

.4449 

79 

.4887 

.5480 

44 

.0714 

.6497 

2H0 

54J129 

14.3419 

3015 

54.9090 

14.4465 

3080 

56.4977 

14.5496 

3145 

56.0803 

14.6512 

51 

4331 

.3435 

16 

.9181 

.4481 

81 

.6068 

.5511 

46 

.0892 

.6528 

St 

.1323 

.3453 

17 

.9272 

.4497 

82 

5158 

.5527 

47 

,0981 

.6543 

n 

.3415 

.3468 

18 

.9363 

.4513 

83 

.5248 

.6543 

48 

.1070 

.6559 

J! 

.2507 

.3484 

19 

.9454 

.4529 

84 

.5338 

.5559 

49 

.1160 

.6574 

2865 

54.3S09 

14.3500 

3020 

54.9545 

14.4545 

8085 

56.6428 

14.5574 

3150 

56.1249 

14.6590 

16 

.2091 

.3516 

21 

.9636 

.4561 

86 

.5518 

.5590 

51 

.1338 

.6605 

87 

.2783 

.3533 

22 

.9727 

.4577 

87 

.5608 

.5606 

52 

.1427 

.6621 

88 

.2875 

.3549 

23 

.9818 

.4593 

88 

.5698 

.5622. 

53 

.1516 

.6636 

if 

.3967 

.3565 

24 

.9909 

.4609 

89 

.5788 

.6637 

54 

.1605 

.6652 

1860 

54.4059 

14.3581 

3025 

55.0000 

14.4624 

3090 

56.5878 

14.5653 

3155 

56.1694 

14.6667 

61 

.4151 

.3587 

26 

.0091 

.4640 

91 

.5968 

.6669 

56 

.1783 

.6683 

62 

.4243 

.3613 

27 

.0182 

.4656 

92 

.6058 

.6684 

67 

.1872 

.6698 

63 

.4234 

.8630 

28 

.0273 

.4672 

93 

.6147 

.5700 

58 

.1961 

.6714 

J* 

.4426 

.3646 

29 

.0364 

.4688 

94 

.6237 

.5716 

B9 

.ZOM) 

.6729 

2866 

54.4518 

14.3662 

3030 

56.0454 

14.4704 

3095 

56.6327 

14.6732 

3160 

56.2139 

14.6745 

w 


2.T-P0WERS,  ROOTS  AND  RECIPROCALS. 


10. — Squarb  Roots  Ain>  Cubb  Roots  op  IMumbbrs 
1600  to  3200— Concluded. 


Na 

8q.  Rt. 

Cu.  Rt. 

No. 

Sq.  Rt. 

Cu.  Rt 

No. 

Sq.  Rt.  Cu.  Rt 

Na 

8q.Rt.0u.Rt. 

3160 

56.2139 

14.6745 

3170 

56.3028 

14.68M 

3180 

66.3^15 

14.7054 

2190 

56.4801 

U.7208 

61 

.2228 

.6760 

71 

.3116 

.6915 

81 

.4004 

.7069 

91 

.4880 

.7223 

•2 

.2317 

.6776 

72 

.3205 

.6930 

82 

.4092 

.7064 

98 

.4978 

.7288 

63 

.2406 

.6791 

73 

.3294 

.6946 

83 

.4181 

.7100 

93 

.5066 

.7254 

64 

.2494 

.6807 

74 

.3383 

.6961 

84 

.4269 

.7115 

94 

.5155 

.72«f 

8165 

96.2583 

14.6822 

3175 

56.3471 

14.6977 

3185 

56.4358 

14.7131 

3195 

56.5243 

14.7284 

66 

.2672 

.6837 

76 

.3560 

.6992 

86 

.4447 

.7146 

96 

.5332 

.7300 

67 

.2761 

.6853 

77 

.3649 

.7007 

87 

.4535 

.7161 

97 

.5420 

.7315 

68 

.2850 

.6868 

78 

.3738 

.7023 

88 

.4624 

.7177 

98 

.5509 

.7831 

69 

.2939 

.6884 

79 

.3826 

.7038 

89 

.4712 

.7192 

99 

.6697 

.7346 

8170 

56.3028 

14.6899 

3180 

56.3915 

14.7054 

3190 

56.4801 

14.7208 

3300 

56.6685 

14.7861 

Note. — For  square  roots  and  cube  roots  of  numbers  above  3200,  see 
Engineers'  Tables,  preceding. 


d  by  Google 


COMMON  TABLES— RECIPROCALS  OF  NUMBERS. 

11. — ^RBCIPItOCAL»  OF  NUICBBRS  1  TO  1000. 


51 


Koi 

Bedproeml 

No, 

R«9lproaU 

No. 

Reelproe&l 

No. 

Reciprocal 

No. 

Reciprocal 

InftaJte. 

6f 

.01538  4615 

130 

.00760  2308 

195 

.00512  8206 

260 

.00384  6154 

.00000  0000 

.01615  1515 

.00763  3588 

6 

.00510  2041 

1 

.00383  1418 

.soooooooo 

.01492  5373 

.00757  5758 

7 

.00507  6142 

2 

.00381  6794 

.S3S33  3333 

.01470  5882 

.00751  8797 

8 

.00506  0505 

3 

.00380  2281 

.38000  0000 

.01449  2754 

.00746  2687 

9 

.00502  5126 

4 

.00378  7879 

.20000  0000 

.01428  5714 

136 

.00740  7407 

200 

.00500  0000 

265 

.00377  3585 

IMCO  OIO? 

.01408  4507 

.00735  2941 

.00497  5124 

6 

.00375  9398 

.14286  7143 

.01388  8889 

.00729  9270 

2 

.00495  0495 

7 

.00374  5318 

.12500  0000 

.01369  8630 

.00724  6377 

3 

.00492  6108 

8 

.00373  1343 

.11111  1111 

.01351  3514 

.00719  4245 

4 

.00490  1961 

9 

.00371  7472 

.10000  0000 

.01333  3333 

140 

.00714  2857 

205 

.00487  8049 

270 

.00370  3704 

OHOO  9091 

.01315  7895 

.00709  2199 

6 

.00485  4369 

1 

.00369  0037 

68333  3333 

.01298  7013 

.00704  2254 

7 

.00483  0918 

2 

.00367  6471 

.07(92  3077 

.01282  0513 

.00699  3007 

8 

.00480  7692 

3 

.00366  3004 

.07143  8571 

.01266  8228 

.00694  4444 

9 

.00478  4689 

4 

.00364  9635 

U  OMM  6«C7 

.01250  0000 

145 

.00689  6552 

210 

.00476  1905 

275 

.00363  6364 

1<  i  OtZM  0000 

.01234  5679 

.00684  9315 

11 

.00473  9336 

6 

.00362  3188 

17  1.05882  3529 

.01219  5122 

.00680  2721 

12 

.00471  6981 

7 

.00361  0108 

IS  ;  05S56  5566 

.01204  8193 

.00675  6757 

13 

.00469  4836 

8 

.00359  7122 

»  I.052C3  1579 

.01190  4762 

.00671  1409 

14 

.00467  2897 

9 

.00358  4229 

05000  0000 

.01176  4706 

150 

.00666  6667 

215 

.00465  1163 

280 

.00357  1429 

04701  9048 

.01162  7907 

.00662  2517 

16 

.00462  9630 

1 

.00355  8719 

.04545  4545 

.01149  4253 

.00657  8947 

17 

.00460  8295 

2 

.00354  6099 

.04347  8361 

.01136  3636 

.00653  5948 

18 

.00458  7156 

3 

.00353  3569 

4  ..MIM  0067 

.01123  5955 

.00649  3506 

19 

.00456  6210 

4 

.00352  1127 

.01111  nil 

155 

.00645  1613 

220 

.00454  5455 

285 

.00350  8772 

«  .03940  1538 

01098  9011 

.00641  0256 

1 

.00452  4887 

6 

.00349  6603 

7  .03703  7037 

.01086  9565 

.00636  9427 

2 

.00450  4505 

7 

.00348  4321 

8  03571  4236 

.01075  2688 

.00632  9114 

3 

.00448  4305 

8 

.00347  2222 

03448  2759 

.01063  8298 

.00628  9308 

4 

.00446  4286 

9 

.00346  0208 

30 

.03333  3333 

.01052  6316 

160 

.00625  0000 

225 

00444  4444 

290 

.00344  8276 

.03225  8065 

.01041  6667 

.00621  1180 

6 

.00442  4779 

1 

.00343  6426 

2 

.03125  0000 

.01030  9278 

.00617  2840 

7 

.00440  5286 

2 

.00342  4658 

% 

.03010  3030 

.01020  4082 

.00613  4969 

8 

.00438  5965 

a 

.00341  2969 

.62941  1765 

.01010  1010 

.00609  7561 

9 

.00436  6812 

4 

.00340  1361 

35 

.03857  1429 

100 

.01000  0000 

165 

.00606  0606 

230 

.00434  7826 

295 

.00338  9831 

.02777  7778 

.60990  0990 

.00602  4096 

1 

.00432  9004 

6 

.00337  8378 

.02703  7027 

.00980  3922 

.00598  8024 

2 

.00431  0345 

7 

.00336  7003 

.(8631  5789 

.00970  8738 

.00595  2381 

3 

.00429  1845 

8 

.00335  5705 

62964  1026 

.00961  5385 

.00501  7160 

4 

.00427  3504 

9 

.00334  4482 

40 

02500  0000 

105 

.00952  3810 

170 

.00588  2353 

235 

.00425  5319 

300 

.00333  3333 

02439  0244 

.00943  3962 

.00584  7953 

6 

.00423  7288 

1 

.00332  2259 

.02380  9524 

.00934  5794 

.00581  3953 

7 

.00421  9409 

2 

.00331  1258 

02326  5614 

.00925  9259 

.00578  0347 

8 

.00420  1681 

3 

.00330  0330 

02272  7373 

.00917  4312 

.00574  7126 

9 

.00418  4100 

4 

.00328  9474 

45 

02222  2222 

no 

.00909  0909 

175 

.00571  4286 

240 

.00416  6667 

305 

.00327  8689 

.03173  9130 

.00900  9009 

.00568  1818 

1 

.00414  9378 

6 

.00326  7974 

.62127  6600 

.00692  8571 

.00564  9718 

2 

.00413  2231 

7 

.0a{25  7329 

.02063  3333 

.00684  9558 

.00561  7978 

3 

.00411  5226 

8 

.00324  6753 

.03040  8163 

.00677  1930 

.00558  6502 

4 

.00409  8361 

9 

.00323  6246 

10 

.02000  0000 

115 

.00860  5652 

180 

.00555  5556 

245 

.00408  1633 

310 

.00322  5806 

.01960  7843 

.00862  0690 

.00552  4862 

6 

.00406  5041 

•  11 

.00321  6434 

.01923  0769 

.00654  7009 

.00549  4505 

7 

.00404  8583 

12 

.00320  5128 

.01806  7925 

.00847  4576 

.00546  4481 

8 

.00403  2258 

13 

.00319  4888 

.61851  8519 

.00640  8361 

.00543  4783 

9 

.00401  6064 

14 

.00318  4713 

Si 

.01818  1818 

120 

.00633  333J 

186 

.00540  5405 

250 

.00400  0000 

315 

.00317  4603 

.61785  7143 

.00626  4463 

.00537  6344 

1 

.00398  4064 

16 

.00316  4557 

.01754  3860 

.00819  6721 

.00534  7594 

2 

00396  8254 

17 

.00315  4574 

.01734  1379 

.00613  0081 

.00631  9149 

3 

.00395  2569 

18 

.00314  4654 

.01694  9153 

.00606  4616 

.00529  1005 

4 

.0a393  7008 

19 

.00313  4796 

CO 

.01666  6667 

125 

00600  0000 

190 

.00526  3158 

255 

.00392  1569 

320 

.00312  5000 

.01639  3443 

! 00793  6508 

.00523  5602 

6 

.00390  6250 

1 

.00311  5265 

.01613  9032 

.00787  4016 

.00520  8333 

7 

.0a389  1051 

2 

.00310  5590 

61907  3016 

.00781  2500 

.00518  1347 

8 

.00;{87  5969 

3 

.00309  5975 

.01563  5000 

.00775  1938 

00516  4639 

9 

.00.186  1004 

4 

.00:508  6420 

« 

.01538  4615 

130 

.00769  2308 

195 

.00512  8205 

260 

.00384  6154 

325 

.00307  6923 

d  by  Google 


52  2.— POWERS,  ROOTS  AND  RECIPROCALS. 

m 

11. — Rbciprocals  of  Numbers  1  to  1000 — Continued. 


d  by  Google 


COMMON  TABLES^RECIPROCALS  OF  NUMBERS. 
II.— Rbciprocals  op  Numbbrs  1  TO  1000. — Continued. 


68 


J^o-lEedproeall 

Na 

Redproeal 

No. 

Reciprocal 

No. 

Reciprocal 

No. 

Reciprocal 

60 

t8lS3  8482 

TIB 

.00139  8001 

IsT 

.00128  2051 

845 

.00118  3432 

910 

.00109  8901 

I 

-Wa60»8 

.00139  6648 

.00128  0410 

.00118  2033 

11 

.00109  7695 

t 

•8153  3742 

.00139  4700 

.00127  8772 

.00118  0638 

12 

.00109  6491 

8 

ma  1384 

.00139  2758 

.00127  7139 

.00117  9245 

13 

.00109  5290 

4 

«ia8852 

.00139  0821 

.00127  5510 

.00117  7856 

14 

.00109  4092 

«55 

NiaS718 

720 

.00138  8889 

785 

.00127  3885 

850 

.00117  6471 

915 

.00109  2896 

« 

MS  4380 

.00138  0963 

.00127  2265 

.00117  5088 

16 

.00109  1703 

I 

0818  2870 

.00138  5042 

.00127  0648 

.00117  3709 

17 

.00109  0513 

S 

08151  8757 

.00138  3126 

.00126  9036 

.00117  2333 

18 

.00106  9326 

J 

08151  7451 

.00138  1215 

.00126  7427 

.00117  0960 

19 

.00106  8139 

««  Mil  M52  1 

725 

.00137  9310 

790 

.00126  6823 

855 

.00116  9591 

920 

.00108  6957 

I    NIM  28W 

.00137  7410 

.00126  4223 

.00116  8224 

1 

.00106  5776 

2 

08151  8574 

.00137  5516 

.00126  2626 

.00116  6861 

2 

.00108  4599 

3 

08150  8286 

.00137  3626 

.00126  1034 

.00116  6501 

3 

.00108  3424 

4 

08118  8024 

.00137  1742 

.00125  9446 

.00116  4144 

4 

.00108  2251 

m 

00136  37S8 

730 

.00136  9863 

795 

.00125  7862 

860 

.00116  2791 

925 

.00108  1081 

6 

00150  15(12 

.00136  7989 

.00125  6281 

.00116  1440 

6 

.00107  9914 

7 

08149  9250 

.00136  6120 

.00125  4705 

.00116  0093 

7 

.00107  8749 

8 

•8148  7006 

.00136  4266 

.00125  3133 

.00115  8749 

8 

.00107  7586 

9 

08149  4768 

.00136  2898 

.00125  1564 

.00116  7407 

9 

.00107  6426 

RO 

08149  2537 

735 

.00136  0544 

800 

.00125  0000 

866 

.00115  6069 

930 

.00107  5269 

1 

08148  0313 

.00135  8696 

.00124  8439 

.00115  4734 

1 

.00107  4114 

2 

00148  8085 

.00135  6852 

.00124  6883 

.00116  3403 

2 

.00107  2961 

3 

00148  5881 

.00135  5014 

.00124  5330 

.00116  2074 

3 

.00107  1811 

4 

00148  3680 

.00135  3180 

.00124  3781 

.00115  0748 

4 

.00107  0664 

irs 

■00148  1481 

740 

.00136  1361 

805 

.00124  2236 

870 

.00114  9425 

935 

.00106  9519 

6 

m47  92»0 

.00134  9528 

.00124  0695 

.00114  8106 

6 

.00106  8376 

I  .WI47  7185 

.00134  7709 

.00123  9157 

.00114  6789 

7 

.00106  7236 

8  !  01147  4t2« 

.00134  5695 

.00123  7624 

.00114  6475 

8 

.00106  6098 

»  .5147  rw 

.00134  4086 

.00123  6094 

.00114  4165 

9 

.00106  4963 

»    »I47  0588 

745 

.00134  2282 

810 

.00123  4568 

876 

.00114  2857 

940 

.00106  3830 

1  ,  lOm  8429 

.00134  0483 

.00123  3046 

.00114  1553 

I 

.00106  2699 

2 

00146  6276 

.00133  8688 

.00123  1527 

.00114  0251 

2 

.00106  1571 

3 

.00146  4129 

.00133  6898 

.00123  0012 

.00113  8952 

3 

.00106  0445 

4 

00146  1988 

.00133  6113 

.00122  8501 

.00113  7656 

4 

.00105  9322 

I6S 

00145  8854 

750 

.00133  3333 

815 

.00122  6994 

880 

.00113  6364 

945 

.00105  8201 

•  .mmm 

.00133  1658 

.00122  5490 

.00113  5074 

6 

.00105  7082 

7  Mm  5604 

.00132  9787 

.00122  3990 

.00113  3787 

7 

.00105  5966 

6 

88145  3488 

.00133  8021 

00122  2494 

.00113  2503 

8 

.00105  4852 

9 

08145  1379 

.00133  6260 

.00122  1001 

.00113  1222 

9 

.00105  3741 

IW 

88144  9275 

755 

.00132  4503 

820 

.00121  9512 

885 

.00112  9944 

950 

.00105  2632 

1 

jjOm  7178 

.00132  2751 

.00121  8027 

.00112  8668 

1 

.00105  1525 

2 

QO144  50B7 

.00132  1004 

.00121  6545 

.00112  7396 

2 

.00106  0420 

3    W144  3(I01 

.00131  9261 

.00121  5067 

.00112  6126 

3 

.00104  9318 

J    «I44  M22 

.00131  7523 

.00121  3592 

.00112  4859 

4 

.00104  8218 

W    210  884» 

760 

.00131  5789 

825 

.00121  2121 

890 

.00112  3596 

955 

.00104  7120 

*    2«  «7W 

.00131  4060 

.00121  0654 

.00112  2334 

6 

00104  6025 

7    •8143  47M 

.00131  2336 

.00120  9190 

.00112  1076 

7 

.00104  4932 

B 

80143  2865 

.00131  0616 

.00120  7729 

.00111  9821 

8 

.00104  3841 

1 

5143O6I5 

.00130  8901 

.00120  6273 

.00111  8568 

9 

.00104  2753 

M 

0^42  8871 

766 

.00130  7190 

830 

.00120  4819 

895 

.00111  7318 

960 

.00104  1667 

1 

00142  ifi34 

00130  5483 

.00120  3369 

.00111  6071 

1 

.00104  0583 

2 

00142  4601 

.00130  3781 

.00120  1923 

.00111  4827 

2 

.00103  9501 

3 

•0142  2476 

.00130  2063 

.00120  0480 

.00111  3586 

3 

.00103  8422 

4 

2142  0456 

.00130  0390 

.00119  9041 

.00111  2347 

4 

.00103  7344 

K 

•01418440 

no 

.00129  8701 

835 

.00119  7605 

900 

.00111  nil 

965 

.00103  6269 

;   mn  1431 

.00129  7017 

.00119  6172 

.00110  9878 

6 

.00103  5197 

7   .«tt  4427 

.00129  5337 

.00119  4743 

.00110  8647 

7 

.00103  4126 

8  :.«141  2428 

.00129  3661 

.00119  3317 

.00110  7420 

8 

.00103  3058 

9   .M41  M37 

.00129  1990 

.00119  1895 

.00110  6196 

9 

.00103  1992 

0  ,.M48  8451 

775 

.00129  0323 

840 

.00119  0476 

900 

.00110  4972 

970 

.00103  0928 

11    ■••148  8470 

.00128  8660 

.00118  9061 

.00110  3753 

I 

.00102  9866 

U  |.«148  4484 

.00128  7001 

.00118  7648 

.00110  2536 

2 

.00102  8807 

13    .••l48  2S2ft 

.00128  6347 

.00118  6240 

.00110  1322 

3 

.00102  7749 

\i  i.5!48  8060 

.00128  3697 

.00118  4834 

.00110  0110 

4 

.00102  6694 

15  '.••129  8801 

780 

.00128  2051 

845 

.00118  3432 

910 

.00109  8901 

975 

.00102  5641 

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64  2.— POWERS,  ROOTS  AND  RECIPROCALS, 

11. — RsciPROCALS  OF  NuMBBRS  1  TO  1000. — Concluded. 


No. 


• 

Reciprocal 

No. 

.00102  5641 
.00102  4690 
.00102  3541 
.00102  2495 
00102  1450 
.00102  0408 

980 
I 
2 

3 

4 
985 

Rediiroca] 

No. 

.00102  04C8 
.00101  9368 
.00101  8330 
.00101  7294 
.00101  6260 
.00101  5228 

985 
6 
7 
8 
9 

990 

Redproeal 

No. 

.00101  5228 
.00101  4199 
.00101  3171 
.00101  2146 
.00101  1122 
.00101  0101 

990 
1 
2 
3 
4 

995 

Reciprocal 


No. 


Reciprocal 


975 
6 
7 
8 
9 

960 


.00101  0101 
.00100  9082 
.00100  80«5 
00100  7049 
00100  6036 
00100  5025 


995 
6 
7 
8 
0 

hooo 


00100  5025 
.00100  4016 
00100  30O9 
00100  20O4 
00100  1001 
00100  0000 


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3.— PRACTICAL  ARITHMETIC. 

PROPORTION. 

At  Algebra  is  the  shorthand  of  Mathematics  so  is  Proportion  the  key  to 
many  of  its  operations.  Indeed,  all  mathematical  problems  may  be  expressed 
in  proportion. 

Ratio  IS  an  expression  of  the  relative  magnitude  of  two  quantities  in 
the  form  of  a  fraction,  either  term  of  which  may  be  considered  the  tmit 
of  messore.     Thus,  the  ratio  of  the  yard  to  the  foot  may  be  expressed  as 

•p  or  Y  :  F,  ia  which  case,  however,  Y  and  F  must  be  considered  in  the 

tame  unit  of  measure,  yard  or  foot.     Every  ratio  implies  proportion,  as 

1-4-  -ri   F:l  ^  Y:x:  etc. 

Proportion  is  the  eqtxality  of  two  or  more 
ratios,  and  it  may  be  represented  graphically 
by  similar  triangles,  as  m  Fig.  1,  from  which 
may  be  obtained  a  variety  of  expressions,  as 
follows: 

By  proportional  lengths  (also  illustrating  con- 
ttnued  proportion): 

*P  ^    P    ^Pl^  P^Pl  .  P+P         P+Pt  P+P+Pl     ^.^    /«.i„^.r*«^N 

12       9        3        9+3       12+9         12+3        12+  9  +  3     ,     ,      . 
,l6  -  12  -  T  "  lF+7  "  16^12  "  i6+4   "  ltJ+12+4-  **^-  ^^^  »"^^^ted). 

12  9-3        12-9        12-3       12-9-3     .     ,      .       ^   .. 

77  '^jr  ■"  l7  •  ^^^  77  —  T  ""  A^  '"^^  likewise  be  extended  (or  inverted). 

By  proportional  squares  (also  iUustrating  compound  proportion): 
m.h^  :V  ::  P*+iB»  :  p«+6»  :  p»«+ V;  or  ^* :  /h«  -  ^^  :  Pi«  +  6i». 

VP.W:  5»::12«+lfi«:9«+12»:3»+4«;  or   ^ :  5«  -  %X^^  :    3»  +  4*. 

In  the  above  some  of  the  ratios  are  compound  ratios,  hence  the  term 
vowkpoumd  proportion. 

Stepic  Proportioa  or  single  rule  of  three  deals  with  two  simple,  equal 
ratios.    Thus, 

Extreme  mean  mean  extreme 

P         :        B  "         p  :  6 

nads.  ''AsPistoBsois^to  6.'*    The  first  and  last  terms  are  called  the 

^nremes,  and  the  middle  terms  the  means.  In  any  simple  problem  there  will 

♦Pnwi—  --^wehavePfr-pB.whence^- j.or^---  or  ^-^,  etc. 


66 


Digitized 


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66  S.—PRACTICAL  ARITHMETIC. 

be  one  unknown  term  which  can  be  solved  by  applying  the  rule:     Th^ 
product  of  the  means  is  tqual  to  the  product  of  the  extremes. 

Problem. — If  a  train  travels  280  miles  in  7 
hours,  how  far  will  it  travel  in  5  hours? 

Solution. — Prom  similar  triangles  there  is  ob- 
tained. 7:5-  2B0:x 


from  which,  applying  the  above  rule, 
7   «  -  6  X  280 

or    X  -  ^  ^y^^^  -  200  miles.    Ans. 

Meaa  Proportional. — In  any  proportion  where  the  two  means  are  equal 
to  each  other,  they  are  each  said  to  be  a  mean  proportional  between  the 
extremes.  In  the  accompanying  geometrical  figiire,  b,  an  ordinate  to  the 
circumference,  is  a  mean  proportional  between  a  and  c,  com- 
posing the  diameter,  as,  from  similar  triangles  there  will 
obtain  the  proportion 

a  :  6  —  6  :  f 

Fig.  3.  or  4  :  6  -  6  :  9 

whence  6  —  y/i  X  9;  or,  the  mean  —  Vproduct  of  extremes. 

Inverse  Proportion. — This  term  is  tised  in  such  problems  as  those  where 
the  rate  of  spe^  or  velocity  are  compared,  when  the  total  time,  distance, 
amount  of  work,  etc..  are  given;  as,  the  rate  of  work  is  inversely  proportional 
to  the  time  occupied  in  doing  it;  or.  the  speed  of  a  train  is  mversely  pro- 
portional to  the  time  used  in  traveling  a  certain  distance. 

Compound  Proportion  or  double  rule  of  three. — Compound  proportion 
is  merely  simple  proportion  in  which  two  or  more  of  the  ratios  are  com- 
poimded. 

Problem. — If  a  man  saws  18  cords  of  wood  in  12  days  of  9  hours  each, 
how  many  cords  of  wood  can  he  saw  in  15  days  of  8  hours  each? 

Solution.-  ^?i^  -  j/^-g  ;  whence  x  -  ^,^-ff^  -  W  d.^ 

A  little  thought  coupled  with  a  graphical  conception  of  the  problem 
will  always  point  to  a  correct  grouping  of  the  terms. 

PERMUTATION  AND  COMBINATION. 

Permutation. — The  number  of  different  ways  in  which  any  number.  N. 
of  objects  may  be  arranged  in  Une  or  cotmted,  is  equal  to  the  product  of  all 
the  numbers  from  1  to  iV.  Thus,  3  objects  as  a.  6  and  c  may  be  arranged 
1X2X3  —  6  different  ways  in  line — abc,  acb,  bac,  bca,  cab,  cba;  7  objects 
may  be  arranged  1X2x3x4X5X6X7-  5040  different  ways,  and 
so  on. 

Combination. — The  number  of  different  groups  each  composed  of  it 
objects  (no  two  groups  to  be  composed  of  the  same  objects)  which  can  be 
formed  separately  from  any  number  *V,  of  objects,  is  equal  to  the  product 
of  all  the  numbers  from  (A'  —  «  +  1)  to  A^,  divided  by  the  product  of  all 
the  numbers  from  1  to  n.  (It  must  be  remembered  that  the  objects  in  each 
group  arc  not    permuted.)    Thus,  6  objects  as  a,  b,  c,  d,  e  and  /  may  be 

arranged  in  groups  of  2.        iru~o  "15  different  ways;  thus. 
1  X  * 

od.        ac,        ad,       ae,        af, 

be,        bd,       be,        bf, 

cd,        ce,        cf, 

"'  i 

Similarly,  8  objects  may  be  arranged  in  groups  of  4. 

6X6X7X8       -„  ,.^ 

—  70  different 


rx  2  X-3  X-4  -  '°  ^oXTSl^SSgle 


ALUGATION  AND  PROGRESSION,  67 

AIXIQATION. 

The  avera^  cost  of  a  mixture  containixis  various  quantities  of  ingre- 
dieats  at  different  unit  prices  may  be  obtained 

by  dividing  the  total  co»t  of  the  mixture  by  the  u ^r«v ft 

total  quantity.     Let   it  be  required  to  find  the  r f^" ""i    i 

average  cost  of  a  mixture  as  follows:  ''^ ;3  j     f 

10  bbU.  cement  9  $2.00  -   $  20.  S!  4 

20     •*  ••  2.25  -        46.  I ili. 

30    "  "  2.60  -       76.  r i^Pi ^-»? 


.-.60  -   $140.  ?«•*• 

Average  price  per  bbl.  —  W  ■*  W .  83 J.    Ans. 
This  tffoblem  is  analogous  to  finding  the  position  of  the  center  of  gravity 
lad  resultant  of  a  sjrstem  of  concentrated  loads,  in  Mechanics. 

PROQRESSION. 
AritlHBCtical  Progressioa. — An   arithmetical  series  or  progression  con- 
sists of  a  series  of  terms  which  uniformly  increase  or  decrease  by  a  common 
ooQstant  diS^9nc0,  d.    Thus, 
Ascending: 
(«<-(/).-       a,    a  +  d,  a  +  23,  a+3d,  a  +  4<i.  ...; 
(d-J).-        1.        4,       7.  10,         13.     ...; 

rf-i).-    -2.6.-2,  -1.6,      -1,       -.6.    ...; 

Descending: 
(d--d).-     a,a-d,a-2d,a-2d,a-id, 
(d--2).-      7.    6,        3.  1.        -   1. 

(i--i).-     I.    i        0,        -i,        -   i. 
an  arithmetical  series. 

As  the  difference  is  constant,  any  arithmetical  series  may  be  represented 
by  the  equation  of  a  straight  line — 

y  —  m  X  +  c.  in  the  language  of  Analytic  Geometry; 
or  s  «»J(n— l)+a,  in  the  language  of  Arithmetical  Progression; 
in  which  c  —  a  —  the  value  of  the  first  term  (placed  at  axis  Y—  K); 

m  —  J  —  the  common  difference.  +  or  — .  between  adjacent  terms; 
ac  —  «  —  1  —  the  number  of  any  term  considered  from  (not  counting) 

the  first  term; 
f  "^  s  ^  the  value  of  any  term  «  —  «  —  1 : 
■  "■  the  number  of  any  term,  counting  the  first  term. 
Pig.  6  illustrates  an  ascending  series,  &nd  when 
the  first  term  is  a  positive  qtiantity.  The  equation. 
however,  tK>lds  good  for  any  case  by  using  the  quan- 
tities algebraically. 

Problem  1. — ^Find  the  number  of  the  term  whose  ^'c 
value  is  10.  in  a  series  whose  common  difference  is)^-»^-— *■ 
1  and  who63  first  term  is  2.  ' 

Sohitkm. — From      y  "  fnx  +  c  there  is  obtained. 
10  -  i  «  +  2. 
.-.  «  -  24  -  »  -  1.  Fig.  6. 

orn  "•  25.    Ans. 
Problem  2. — Insert  4  terms  between  the  numbers  3  and  28  and  find  the 
oommon  difference. 

Solution. — From      y  «»  m  x  +  c 

28-m5+  3(If4  terms  are  inserted.  28  -  6th  term 
.-.  X  -  6.) 
28—3 
whence    m  ■-  — = —  —  5  —  common  difference.   Ans. 

9 

An  arithmetical  mean  between  two  quantities  »  one-half  their  sum. 

OaoweUlcal  Progressioii. — A  geometrical  series  or  progression  consists 
c^  a  aenes  of  terms  which  increase  or  decrease  by  a  common  constant 
factor,  /.    Thus, 

Ascending:  Decending: 


f'*  r*' 


if^r).—     a^ar,ar*,ar*,ar*,  ...;  v"/'" 

L~  ^-.  ■'•  .••  *^-  2*.  <«.  •  •  •:         (/-«•-  D,«!ed|(5db'^e- •  •' 

M«  geometrical  series.  o 


S8  Z.'^PRACTICAL  ARITHMETIC. 

Any  ^geometrical  progression  may  be  represented  by  a  'curve  wboae 
equation  is — 

y  —  c  /».  in  the  language  of  Analytic  Geometry; 

or  5  —  a  Z^""   ',  in  the  language  of  Geometrical  Progression: 
in  which,    c  —  o  —  the  value  of  the  first  term  (placed  at  axis  K—  K); 
/  —  the  common  factor  or  ratio  between  the  adjacent  terms: 
:r  —  ft  —  1  —  number  of  any  term  considered  from  (not  iscltadii^ 

the  first  term; 
y  —  5  —  the  value  of  any  term  x  «=•  n—\\ 

n  —  the  number  of  any  term,  counting  the  first  term. 

Fig.  6  illustrates  an  increasing  series,  and  wbee 
the  first  term  is  a  pcMiitive  quantity:    but  by  tisiz^ 
the  quantities  algebraically,  Uie  equation  holds  good 
'i  for  any  case. 

!  Problem  1. — Find  the  value  of  the  6th  term  <rf 

1  an  increasing  series  whose  1st  term  is  3,  and  the  com* 

^  nmon  factor  2. 

■*  Solution. — From 

y  «  c  /«,  there  is  obtained, 

y  (-  5)    -  8  X  2»  -  3  X  82.     («  -  w  -  1  —  5.) 
.*.  5  =«  96.     Ans. 

Problem  2. — Insert  3  terms  between  the  numbers  2  and  lOi.  and  find 
the  common  factor. 

Solution. — From      y  "  c  f*  there  is  obtained. 

101  -  2  /*  (If  3  terms  are  inserted,  10|  »   4th  term 
.-.  X  «-  4.) 

.-./  -  1  -  If     Ans. 
Note. — ^The  latter  part  ot  the  above  solution  may  also  be  perfonned  by 
logarithms.    Thus, 

/I  -  1^  -  6.0626     log  6.0625  -   0.704365    (Divide  this  by  4.) 

Ans.  f  —  1.5    0.176091    (Find  number  corresponding.) 
A  geometrical  mean  between  two  numbers  —  the  square  root  of  tiicir 
product  (sec  Fig.  3,  page  56). 

O>mpoimd  interest  is  a  good  illustration  of  geometrical  progression. 

PERCENT AQE,  INTEREST  AND  DISCOUNT. 

Percentage. — Per  cent  means  hundredths,  and  raU  per  cent  means  any 
given  number  of  hundredths.  Thus,  5  per  cent,  or  5%,  means  .06,  or  V^ 
in  which  5  is  the  rate.  It  may  also  be  expressed  m  true  ratio.  5  :  IML 
meaning  5  parts  of  the  100.  both  terms  being  of  the  same  denominatloa. 

To  reduce  any  rate,  expressed  in  two  denominations,  to  a  rate  per  cent, 
one  term  must  first  be  reduced  to  the  denomination  of  the  other  so  that  s  i 
true  ratio  may  be  expressed.     Thus,  a  rate  of  grade  in  feet  per  mile,  as 
52  i"o  feet   per   mile,  may  be  expressed  in  ratio  62  ft    :  5280,  as  there  are 
5280  feet  in  a  mile.    Clearly,  this  is  equal  to  a  Viooi  or  1%  grade. 

Simple  Interest  is  percentage  in  which  the  element  of  /«mr  has  to  be 
considered.  The  sum  placed  at  interest  is  called  the  principal^  and  die 
principal  plus  the  interest  is  called  the  amount.  Simple  interest  difien 
from  compound  interest  in  that  the  principal  is  not  allowed  to  increase  finoin 
time  to  time  by  its  own  interest. 

The  rate  of  interest  is  the  rate  per  cent  for  one  year.    There  are  two 
methods  used  in  calculating  interest: 
(a.)  The  common  method,  in  which  a  year  is  considered  to  be  divided  into 

12  months  of  30  days  each. 
(6.)  The  exact  method,  in  which  the  year  is  divided  into  366  (or  366  if  Inp 
year)  days. 

In  either  case, 

Simple  Interest  -  Principal  (I)  X  Rate  %   X  Time  (years). 

The  Common  Method. — ^Table  1.  page  60,  shows  the  simple  interest  co 
various  principals  ($1. —  $1,000.)  at  various  rates  (3i%  —  7%)  for  time 
in  days  and  months  up  to  one  year.  Clearly,  by  combination  and 
factoring,  the  interest  on  any  principal,  at  any  rate  and  for  any  time,  may 
readily  be  obtained.  Thus,  the  interest  on  $1253.  at  4|%  for  6  nK>atha; 
I  i  days,  is  calculated  as  follows: 


PERCENTAGE,  INTEREST  AND  DISCOUNT.  «« 

5  mos.  lOd.         Id. 


Interest  on  $1000  (1000  X  1)  -18.75  1.25 

200  (  200  X  1)  -   3.75  .25  'g 

50  (     50  X  1)  -      .038  .062  > 

8  -      .056  .004  ^ 


^ 


Therefore,  total  interest  -23.494    +   1.566  +    .157-125.22.     Ana. 

This  may  be  calculated  in  the  ordinary  manner,  as  follows: 
(Principal)      (Rate  %)  (Time) 

Interest  -  1253       X        .045       X       ^"        -     «25.22.        Ans. 

As  the  interest  on  any  amount  is  directly  proportional  to  the  rate, 
some  prefer  to  use  a  round  rate  like  6%.  6  being  a  factor  of  12  (months)  and 
oi  30  (days),  for  a  first  result,  and  then  factor  this  result  for  the  required 
rate.    Thus,  in  the  above. 

(12.53 
Interest  on  11253  at  6%  for   5  mos.    -   1253  X  2i%  -  V  12.53 


(  12.£ 
.{12.5 

'    5  ? 


.265 
10  days    -   1253  X  i%     -       2.089 
1   "        —  A  above  -         .  209 


At  6%  33.62 

Deduct  i  8.40 


At  4}%.  $25.22 

Ans. 

7fc#  Exact  Method. — ^This  is  used  bv  various  large  financial  concerns 
in  deaHng  with  each  other  and  where  large  amoimts  are  involved.  The 
time  is  the  ratio  of  the  number  of  days  for  which  the  principal  has  been 
loaned,  to  the  number  of  days  in  the  jrear.  Thus,  if  the  loan  is  for  21/ 
days  the  time  will  be  "Vsm  of  a  year;  or,  if  the  29th  of  February  is  includea. 
it  will  be  *"/a8s  of  a  year. 

Table  2.  page  61,  gives  the  number  of  days  from  one  date  to  another  cove*-* 
ing  a  period  of  two  ordinary  years  of  365  days  each.  If  one  of  the  vears  is  a 
leap  year  add  one  day  to  each  number  of  days  after  February  28th.  Thus, 
a  the  interest  is  to  be  calculated  from  February  1 5th  of  one  year  to  January 

10th  of  the  following  year,  the    time  would  be ^^ —  =■  -^^^  of  a  year. 

If  the  first  year  is  a  leap  year  the  time  would  be  '•^/aoa  of  a  year,  adding  one 
to  each  term  of  the  ratio.  For  example,  the  interest  on  $450.  from  Feb.  15, 
1908,  Ocap  year)  to  Jan.  10,  1969,  at  5%  -  $450.  X  .05  X  »«/3m- 
120.39.    Ans. 

DiscounL — ^The  fundamental  principle  of  discount  is  "  money  off  for 
ash."  but  most  mercantile  houses  will  discount  their  trade  catalogue  prices 
to  their  regular  customers  on  short  time  payments. 

A  certain  customer  may  be  favored  with  a  discount  of  20%,  which 
means  that  the  cost  to  him  will  be  80%  of  the  catalogue  price;  another 
cn^omer,  more  favored  or  on  account  of  heavier  purchases,  may  receive  a 
discount  of  "20  and  10"%,  making  the  cost  .80  X  .90  -  72%  of  the  list 
prke;  while  a  third  may  receive  a  discotmt  of  **  20,  10  and  5"  which  would 
make  the  cost  .80  X  .90  X  .95  -  68  Vio  %. 

Bank  discount  is  the  equivalent  interest  on  the  face  of  a  note  up  to  the 
time  of  its  maturity. 

True  discount  is  the  equivalent  interest  on  the  present  worth  of  a  note, 

or  principal  which,  at  maturity,  will  amount  to  the  face  of  the  note.    Thus, 

Prcfcent  worth  +  interest  on  same  ( -true  discoimt)       1 1  +  interest  on  same  . 

Amount  (—  face  of  note)  Amoimt  of  $1  and  int.  ' 

rw  ♦     nrth       Face  of  note 

,  prcsea  Amount  of  $1  and  interest,  to  maturity' 

Whence  the  true  discount  —  face  of  note  —  present  worth. 

Conpoitiul  Interest. — ^The  simple  interest  on  any  orincipal  loaned  is  due 
asnoally.  But  by  a  special  agreement  it  may  become  due  semi-annually, 
^juarterfy,  or  for  any  other  period.     If  not  paid,  it  is  added  periodically  to 


Z.—PRACTICAL  ARITHMETIC. 


the  principal  for  a  new  principal  drawing  interest;    hence,   compotmd 
interest.     (See  Table  8.  page  ft2. ) 

The  amotant  (principal  and  interest)  due  at  the  end  of  any  number  of 
years,  fi,  interest  payable  annually,  may  be  expressed  as  follows: 
Amount  -  Principal  (1  +  Rate  %)». 

If  the  number  of  years  is  large  the  restilt  is  easily  obtained  by  the  use 
of  logarithms.  Ptirther,  the  above  formula  may  represent  any  general  case 
by  considering  n  the  number  of  periods  (as  semi-annual  or  qTiarterly 
periods)  of  compounding  —  the  proportiooate  rate  per  cent  to  be  used  for 
that  period. 

1. SiMPLB   InTBRBST  TaBLB.* 


sli-l 

Time. 

M^ 

1 

Year 

6  Mo. 

5  Mo. 

4  Mo. 

3  Mo. 

2  Mo. 

IMo. 

20  d. 

10  d. 

1  d. 

11 

.040 

.0200 

.01666^6 

.018^ 

.01000 

.0066-6 

.00883^3 

.0022^2 

.00111-1 

.0001  If'] 

2 

.080 

.0400 

.03333^3 

026^6 

.02000 

.0133-8 

.00666-6 

.0044-4 

.00222-2 

.000222-2 

3 

.120 

.0600 

.05000 

.040 

.03000 

.0200 

.01000 

.0066-6 

.00333-8 

.000333-3 

4 

.160 

.0800 

.06666^6 

.053^3 

.04000 

.0266-6 

.01333-3 

.0088-8  .00444-4 

.000444-4 

4% 

5 

200 

.1000 

.08333''3 

.066^6 

.05000 

.0333-3 

.01666-6 

OH  1-1  .00555-5 

.000555-9 

« 

.240 

.1200 

.10000 

.080 

.06000 

.0400 

.02000 

. 0133^3  .00666-6 

.000666-6 

7 

.280 

.1400 

.11666^6 

.093"3 

.07000 

.0466-6 

.02333-3 

.0155-5  .00777-7 

.0007m 

8 

.320  ;.i«oo 

.133.33^3 

.106-6 

.08000 

.0533-3 

.02666-6 

.0177-7  .00888-8 

.000888-8 

9 

.360 

.1800 

.15000 

.120 

.09000 

.0600 

.03000 

.0200      .01000 

.001000 

$1 

.045 

.0225 

.01875 

015 

.01126 

.0076 

.00376 

.0025      .00125 

.000125 

2 

.090 

.0450 

.03750 

.030 

02250 

.0150 

.00760 

.0060 

.00250 

.000250 

3 

.135 

.0675 

.05625 

.045 

! 0337 5 

.0226 

01126 

.0075 

.00375 

.000375 

4 

.180 

.0900 

.07500 

.060 

.04500 

.0300 

.01500 

.0100 

.00500 

.000900 

4% 

5 

.225 

.1125 

.09375 

.075 

.05625 

.0375 

.01876 

.0125 

.00625 

.00005 

« 

.270 

.1350 

.11250 

.090 

.06750 

.0450 

.02250 

.0160 

.00750 

.000750 

7 

.315 

.1676 

.13125 

.106 

.07875 

.0625 

.02626 

.0176 

.00875 

OOOBTS 

8 

.360 

.1800 

.15000 

.120 

.09000 

.0600 

.03000 

.0200 

.01000 

.001000 

9 

.405 

2025 

.16875 

.135 

.10125 

0675 

.03376 

.0225 

01125 

.001 12S 

11 

.050 

.0250 

.02083^3 

.016-6 

.01250 

.0083-3 

.00416-6 

.0027-7 

.00138-8 

.000138^ 

2 

.100 

.0500 

.04166^6 

.033-3 

.02500 

.0166-6 

.00833-3 

.0055-6 

.00277-7^.000277-7 
.00416^61.000416^ 

3  1.150 

.0750 

.06250 

.050 

.03750    .0250 

.01250 

0083-3 

4  1.200 

.1000    .08333^3 

.066-6 

.05000   .0333-3 

.01666-6 

.0111-1 

■  00555-51.000555-5 

■  00694-7.  OOOCM-4 

5% 

5  '.250 

.12.')0    .10416^6 

.083-3 

.06250    .04 1 6-6*. 02083-3 

.0138-8 

6 

.300 

.1500  1.12500 

.100 

.07500 

.0500    1.02500 

.0166-6 

.00833-^. ooo«sn 

■00972-2>.000t7r] 

7 

.350 

.1750    .14583^3 

.116-6 

.08750 

.0583-3'.  029 16-6 

.0194-4 

8 

.400 

.2000  1.16666^6 

.  1.33-3 

.10000 

.0666-6 

.03333-3 

0222-2 

.01111-1  .001111-1 

9 

.450 

.2250 

.18750 

.150 

.11250 

.0750 

.03760 

.0250 

.01250      .00129t 

11 

.060 

.0300 

.02500 

.010 

.01500 

.0100 

.00600 

.0033-3 

.00166-6  OOOliTS 

2 

.120 

.0600 

.05000 

.040 

.03000 

.0200 

.01000 

.0066-6 

.00338^3'  0WB23-3 

3 

.180 

0900 

07500 

.060 

.04500 

.0300 

.01600 

.0100 

.00500 

.000000 

4 

.240 

.1200 

.10000 

.080 

.06000 

.0400 

02000 

.0133-3 

.00666^^ 

6% 

5 

.300  1.1500 

.12500 

.100 

.07500 

.0500 

.02500 

.0166-6 

.00833-3 

.000033-3 

6 

.360    .1800 

15000 

.120 

.09000 

.0600 

.03000 

.0200 

.01000 

.001000 

7 

.420  ;.2ioo 

.17500 

.140 

.10500 

.07U0 

.03500 

.0233-3 

.01166^6 

.ooiiort 

8 

.480 

.2400 

.20000 

.160 

.12000 

.0800 

.04000 

.0266-6 

.01333^3 

.001333-3 

9 

.540 

2700 

22500 

.180 

.13600 

.0900 

04500 

.0300 

.01500 

.001501 

11 

.070 

.0350 

.02916^6 

.023-3 

.01750 

.0116-6 

.00583-3 

.0038-8 

.00194^4 

.OOOlfCl 

2    .140 

.0700 

.05833^3 

.046-6 

.03760 

.0233-3 

01166-6 

.0077-7 

.00388^8 

.ooossri 

3 

.210 

.ior.o 

.  OH  7  50 

.070 

.05250 

.0350 

.01750 

.0116-6 

.00583-3 

.000583^3 

4 

.280 

.1400 

.11666''6 

.093-3 

.07000 

.0466-6 

-.02333-3 

.0165-5 

.00777^ 

.ooo7rr'7 

7% 

6 

.350 

.1750 

14583^3 

.116-6 

.08750 

.0583-3 

.02916-6 

.0194-4 

.00972^3 

.000072-1 

6 

.420 

2100 

.17500 

.140 

.10500 

.0700 

03500 

.0233-3 

.01166^6 

.001106-1 

7 

.490 

.2450 

20416^6 

.163-3 

.12250 

.0816-6 

.04083-3 

.0272-2 

.01361>'l 

.OOlMl-1 

8 

560 

.2800 

.23333^3 

.186-6 

.14000 

.0933-3 

.04666-6 

.0311-1 

.01565^5 

.00153r^? 

9 

MO 

.3150 

26250 

.210 

.15750 

.1050 

.05250 

0350 

.01750 

.001750 

the 


*  Note  that  all  repeating  decimals  may  be  extended  indefinitely  Thus, 
uie  interest  on  $1.00  at  4%  for  4  months  is  given  as  .013-3 or  14  cents. 
because  the  decimal  .013-3  =  .01333333. .  .;  hence  the  interest  on  SI  OoC 
000.  at  the  same  rate  and  for  the  same  time,  is  $13,333,331.  Decimals  whSi 
are  not  repeatmg  decimals  are  exact.  ^^ 


EQUATION  OF  PAYMENTS.  61 

Bzample. — Find  the  amount  of  $600.  Solution, 

compounded  at  2%  ■emi-annually  for  6  log.     000.  —  2.7781513 

r^n  (12  periods).  12  X  log.  1.02  -  0.1032024 

Ana.  $760.95  .  .  .    2.8813537 
Clearly,  the  process  of  calculating  compound  interest  is  simply  geomet- 
rical progression,  in  which  1  +  Rate  %  is  a  constant  factor  between  sue- 
oeasive  terms. 

EQUATION  OF  PAYMENTS. 
Like  Alligation,  this  is  a  "center  of  gravity"  problem.     It  consists  in 
finding  the  average  time  when  a  single  payment  can  be  made  to  cancel 
sever^    notes,    bearing    the   same    rate    of   interest,  which   fall    due    on 
different  dates. 

Problem. — A  holds  B's  notes  as  follows:    $600  due  in  1  month;    $700 
due  in  3  months;    $400  due  in  4  months;  and  $300  due  in  5  months—all 
bearing  the  same  rate  of  interest.    At  what  time  can  B  make  a  single  pay- 
ment of  the  whole  amoimt,  $2000.  to  cancel  the  obligation  equitably  r 
Solution. —  600  X    1   -      600. 

700  X  3  -  2100. 
400  X  4  -  1600. 
300  X    6  -   1500. 

2000  X  ^  -   5800. 
.'.  Average  time  x  —  ^Kqq  "   2. 9  months  —  2  m.,  27  d.   Ans. 

2.— Tablx  Por  Pikdino  Numbbr  or  Days  Bbtwbbn  Any  Two  Datbs 

IN  Two  CONSBCUTIVB  YbaRS.* 


d  by  Google 


9S 


n.— PRACTICAL  ARITHMETIC. 


3. — Compound  Intbsbst  Tablb. 
Amount  of  $1.  at  compound  interest  for  periods  1  to  60  at  various  Aperiodic 

rates. 


Periods. 

•Periodte  Rates. 

n. 

2% 

3% 

8i% 

4% 

H% 

5% 

6% 

7% 

1.02000 
1.04040 
1.06121 
1.08243 
1.10406 

1.03000 
1.06090 
1.09273 
1.12551 
1.15927 

1.03500 
1.07123 
1.10872 
1.14752 
1.18769 

1.04000 
1.08160 
1.12486 
1.16986 
1.21665 

1.04500 
1.09203 
1.14117 
1.19252 
1.24618 

1.05000 
1.10250 
1.15763 
1.21551 
1.27628 

1.06000 
1.12360 
1.19102 
1.26348 
1.83823 

1.0700O 
1.14490 
1.22504 
1.3108O 
1.402W 

1.12616 
1.14869 
1.17166 
1.19509 
1.21899 

1.19406 
1.22987 
1.26677 
1.30477 
1.34392 

1.22926 
1.27228 
1.31681 
1.36290 
1.41060 

1.36532 
1.31593 
1.36857 
1.42331 
1.48024 

1.80226 
1.36086 
1.42210 
1.48610 
1.65297 

1.84010 
1.40710 
1.47746 
1.55183 
1.62889 

1.41862 
1.60363 
1.69386 
1.68948 
1.79066 

1.50073 
1.60878 
1.71819 
1.8384C 
1.9671S 

1.24337 
1.26824 
1.29361 
1.31948 
1.34587 

1.88423 
1.42576 
1.46853 
1.51250 
1.56797 

1.45997 
1.51107 
1.56396 
1.61870 
1.67535 

1.53945 
1.60103 
1.66507 
1.73168 
1.80094 

1.62285 
1.69588 
1.77220 
1.85194 
1.93528 

1.71034 
1.79586 
1.88565 
1.97993 
2.07893 

1.89830 
2.01220 
2.13293 
2.26090 
2.89666 

2.10485 
2.25219 
2.4098S 
2.57853 
2.75903 

20 

1.37279 
1.40024 
1.42825 
1.45681 
1.48595 

1.60471 
1.65285 
1.70243 
1.75351 
1.80611 

1.73399 
1.79468 
1.85749 
1 .92250 
1.98979 

1.87298 
1.94790 
2.02582 
2.10685 
2.19112 

2.02237 
2.11338 
2.20848 
2.30786 
2.41171 

2.18287 
2.29202 
2.40662 
2.52695 
2.65330 

2.64036 
2.69277 
2.85434 
3.02560 
8.20714 

2.05216 

3.15882 
3  87993 
3.616S3 
3.86988 

81 

a 

28 
24 

26 

1.51567 
1.54508 
1.67690 
1.60844 
1.64061 

1.86029 
1.91610 
1.97358 
2.03279 
2.09378 

2.05043 
2.13151 
2.20611 
2.28332 
2.36324 

2.27876 
2.36991 
2.46471 
2.56330 
2.66583 

2.52024 
2.63365 
2.75217 
2.87602 
3.00544 

2.78596 
2.92523 
3.07152 
8.22510 
8.88635 

3.39957 
3.60354 
8.81976 
4.04894 
4.29188 

4.14057 
4.43041 

4.74064 
5.07237 
5.42744 

26 

27 
28 

29 
SO 

1.67342 
1.70689 
1.74108 
1.77585 
1.81134 

2.15659 
2.22129 
2.28792 
2.35656 
2.42726 

2.44595 
2.53156 
2.62016 
2.71187 
2.80672 

2.77246 
2.88336 
2.99870 
3.11864 
3.24339 

3.14068 
3.28201 
3.42970 
3.58406 
3.74532 

3.65567 
3.73346 
8.92013 
4.11614 
4.32194 

4.54939 
4.82224 
5.11170 
5.41840 
5.74351 

5.80738 
6.21388 
6.64885 

7.11427 
7.61227 

81 
32 
33 
84 

35 

1.84759 
1.88454 
1.92224 
1.96068 
1.99989 

2.50008 
2.57506 
2.65233 
2.73190 
2.81386 

2.90501 
3.00670 
3.11193 
3.22085 
3.33358 

3.37312 
3.50805 
3.64837 
3.79430 
3.94608 

3.91386 
4.08998 
4.27403 
4.46637 
4.66735 

4.53804 
4.76494 
6.00319 
5.25335 
6.51600 

6.08812 
6.45340 
6.8/061 
7.25116 
7.68811 

8.U61S 
8.71620 
9.82538 
9.9781S 
10.8766 

86 
87 
88 
89 
40 

2.03989 
2.08069 
2.12230 
2.16475 
2.20801 

2.89827 
2.98518 
3.07478 
3.16702 
3.26203 

8.45025 
3.57101 
3.69599 
3.82535 
3.95924 

4.10392 
4.26806 
4.43880 
4.61635 
4.80100 

4.87738 
5.09686 
5.32618 
5.56590 
5.81637 

5.79182 
6.08141 
6.38548 
6.70475 
7.03999 

8.14728 
8.63611 
9.15428 
9.70354 
10.2866 

11.4240 
12.2238 
13.0793 
13.9948 
14.9746 

41 
42 

43 
44 

45 

2.25221 
2.29725 
2.34320 
2.39006 
2.43786 

3.36989 
3.46069 
3.56451 
3.67144 
8.78159 

4.09781 
4.24124 
4.38968 
4.54332 
4.70233 

4.99306 
5.19276 
5.40047 
5.61649 
5.84115 

6.07811 
6.35162 
6.63744 
6.93613 
7.24826 

7.39199 
7.76159 
8.14967 
8.55715 
8.98504 

10.9029 
11.6571 
12.2505 
12.9855 
13.7647 

16.0227 
17.1443 
18.8444 
19.6285 
21.0025 

46 
47 
48 
49 
50 

2.48662 
2.63635 
2.58708 
2.63882 
2.69160 

3.89503 
4.01188 
4.13224 
4.25621 
4.38389 

4.86692 
5.03726 
5.21356 
5.39604 
5.58491 

6.07480 
6.31779 
6.57050 
6.83330 
7.10665 

7.57443 
7.91528 
8.27146 
8.64368 
9.03265 

9.43426 
9.90597 
10.4013 
10.9213 
11.4674 

14.5906 
15.4660 
16.3939 
17.3776 
18.4202 

22.4727 
24.0458 
25.7290 
27.6300 
29.4571 

*  Periods  niay  be  annual,  semi-annual  or  quarterly,  etc.  Periodic  rates 
are  proportioned  to  the  length  of  the  period.  Thus.  4%  annual  -■  2%  aemi* 
■onual  rate.     For  explanation  of  table,  see  top  of  page  fiOi  t 

Digitized  by  VjOOQ  LC 


ANNUITIES— SINKING  FUND.  88 

PARTIAL  PAYMENTS. 

la  caooening  notes  by  partial  pairments  the  following  it  the  rule  in 
Urattd  States  law: 

Whenever  the  payment  or  payments  tqual  or  9xc$€d  the  interest  a  new 
principal  shall  be  formed  by  adding  the  interest  and  deducting  the  pay- 
ment or  payments.  That  is,  the  pnncipal  cannot  be  reduced  without  first 
^•^nrpHrng  the  interest. 

A  common  method,  however,  is  to  consider  the  debt  as  the  original 
psiodpal  together  with  its  accumulated  interest  down  to  the  date  of  settle* 
taeat;  this  to  be  cancelled  by  the  various  payments  (considered  as  separate 
pcmripals)  together  with  their  accumulated  interest,  down  to  the  same 
date. 

ANNUITIES. 
payment  of  money  amounting  to  a  fixed  sum  each  year  is 

an  annuity: — Certain  annuity,  when  payments  extend  over  certain 

definite  periods;  Contingent  annuity,  when  payments  are  contingent  on 
ceftain  events;  Life  annuity,  when  payments  are  for  life  of  one  or  more 
penoos;  Deferrmi  atmuity,  when  payments  begin  at  some  future  time  or 
event. 

The  value  of  an  annuity  may  be  reduced  to  its  — 
Final  Value,  or  amount  of  all  payments  at  compound  interest  to  the  end  of 

the  annuity; 
Initial  valme,  or  equivalent  principal  which,  at  compound  interest  for  the 

life  of  the  annuity,  would  amount  to  its  final  value  j 
Preunt  valme,  or  equivalent  principal  which,  at  compoxmd  mterest  for  the 
tmlance  of  the  life  ot  the  annuity,  would  amotmt  to  the  value  of 
future  payments  at  compound  interest  to  the  end  of  the  annuity. 

TItt  fundamental  equations  which  enter  into  the  conversion  of  annuity 
in  one  form  to  its  eqmvalent  in  another  form,  are  those  of  geometrical 
pftgreasioci,  in  general,  and  compound  interest  in  particular. 

Rnal  Valiw  off  Anflaity. — ^The  final  value  of  an  annuity  is  directly  pro- 
portiona]  to  the  value  of  the  annual  payment.  Hence,  from  a  table  caicu- 
Uted  on  the  basis  of  an  annuity  of  $1,  at  different  rates  of  interest  and  for 
aay  number  of  years,  the  final  value  of  any  annuity  at  the  same  rate  and 
for  the  same  time  may  be  obtained  by  mtutiplying  the  value  in  the  table 
by  the  annuity. 

Table  4,  following,  gives  the  final  values  of  an  annuity  of  $1  at  com- 
pound interest  rates  of  2,  3,  31,  4,  4i,  5,  6  and  7  per  cent  up  to  50  years.  It 
a  calculated  from  the  formula: 

P««l  ^h.^       (1  +  Rate  %)«  -  1. 
Pmal  value ^^^^^ ; 

a  wfaidi  X  —  the  number  of  vears  —  the  ntmiber  of  payments,  the  final 
vahie  being  calculated  up  to  the  time  of  each  payment,  and  also  includes 
that  payment. 

pTfient  or  Initial  Value  of  Annuity. — ^The  present  value  of  an  annuity 
taay  be  considered  the  initial  value  of  that  part  of  the  annuity  comprising 
hitnre  payments,  the  date  beginning  with  the  first  of  these  payments. 
Hence  the  term  "  Present  value'  will  be  used  In  the  broadest  sense.  Fiulher. 
it  is  the  amount  of  capital  or  the  principal  which,  if  placed  at  interest. 
vould  exactly  furnish  the  annuities  for  the  specified  time;  that  is,  the 
principal  wotud  be  depleted  at  the  end  of  that  time. 

For  the  same  time  and  at  the  same  rate  of  interest,  the  present  value 
is  directly  proportional  to  the  annuity  (and  to  the  final  value).  Hence,  in 
Table  5,  oblige  dS,  to  find  the  present  value  of  any  annuity,  as  $1000. 
nmhipty  the  tabular  number  by  that  annuity  ( 1 000) .  The  table  is  calculated 
fmm  the  formula: 

1-        ' 


Pre«nt  value y^'',^^; 

Rate  % 

«  which  X  —  the  number  of  years  to  run  —  the  number  of  payments  to  be 
made,  payments  being  made  at  the  end  of  each  year. 

Staking  Fnnd. — ^An  annuity  may  be  applied  as  a  sinking  fund  to  cancel 
s  debt  payable  at  some  future  time,  as  in  the  case  of  bonds  maturing  in, 
ttF.  20,  30  or  60  years.    A  plant  may  thus  be  made  to  pay  for  itseu  by 


04 


t.— PRACTICAL  ARITHMETIC. 


4. — Final  Valub  of  Annuitt  of  $1  m  From  1  to  50  Ybars  or  Pbriodc. 


Periods. 


Yearly  or  Periodic  Rates. 


2% 


3*% 


4% 


4*% 


5% 


6% 


1 

S 
8 

4 
6 

6 

f 
8 
9 
10 

11 
II 
IS 
14 
15 

16 
17 
18 
19 
20 

21 
22 

23 
24 

25 

26 

r 

28 

29 
80 

81 

82 
83 
34 


36 
87 
88 
39 
40 

41 
42 

43 
44 
45 

46 
47 
48 
49 
50 


2.02000 
3.06040 
4.12161 
5.20404 

6.30812 
7.43428 
8.58297 
9.75463 
10.9497 

12.1687 
13.4121 
14.6803 
15.9739 
17.2934 

18.6393 
20.0121 
21.4123 
22.8406 
24.2974 

25.7833 
27.2990 
28.8450 
30.4219 
82.0303 

33.6709 
35.3443 
37.0513 
38.7923 
40.5682 

42.3796 
44.2272 
46.1117 
48.0340 
49.9947 

51.9945 
54.0344 
56.1151 
58.2374 
60.4023 

62.6103 
64.8625 
67.1598 
69.5030 
71.8930 

74.3309 
76.8176 
79.3540 
81.9411 
84.5800 


2.03000 
3.09090 
4.18363 
5.30913 

6.46840 
7.66245 
8.89232 
10.1591 
11.4638 

12.8078 
14.1920 
15.6178 
17.0863 
18.5989 

20.1569 
21.7616 
23.4144 
25.1168 
26.8708 

28.6765 
30.5368 
32.4529 
34.4265 
36.4592 


40.7096 
42.9309 
45.2188 
47.5753 

50.0026 
52.5026 
55.0777 
57.7300 
60.4619 

63.2758 
66.1740 
69.1592 
72.2340 
75.4010 

78.6630 
82.0229 
85.4836 
89.0481 
92.7195 

96.5012 
100.396 
104.408 
108.540 
112.796 


1. 

2.03500 

3.10623 

4.21495 

5.36247 

6.55016 
7.77942 
9  05170 
10.3685 
11.7313 

13.1419 
14.6019 
16.1129 
17.6769 
19.2956 

20.9709 
22.7049 
24.4996 
26.3571 
28.2795 

30.2693 
32.8287 
84.4602 
36.6663 
88.9497 

41.3129 
43.7589 
46.2904 
48.9106 
51.6224 

54.4291 
57.3341 
60.3408 
63.4528 
66.6736 

70.0072 
73.4574 
77.0284 
80.7244 
84.5498 

88.5090 
92.6069 
96.8481 
101.238 
105.781 

110.483 
115.350 
120.387 
125.601 
130.997 


1. 

2.04000 

3.12160 

4.24646 

5.41632 

6.63297 
7.89829 
9.21422 
10.5828 
12.0061 

13.4868 
15.02.58 
16.6268 
18.2919 
20.0236 

21.8246 
23.6975 
25.6454 
r.67l2 
29.7780 

31.9691 
34.2479 
36.6178 
39.0825 
41.6458 

44.3116 
47.0841 
49.9674 
52.9661 
56.0847 

59.8281 
62.7012 
66.2093 
69.8576 
73.6519 

77.5980 
81.7019 
85.9700 
90.4088 
95.0251 

99.8261 
104.819 
110.012 
115.412 
121.029 

126.870 
132.945 
139.263 
145.833 
152.666 


1. 

2.04500 

8.18703 

4.27820 

5.47072 

6.71690 
8.01916 
9.38002 
10.8021 
12.2882 

13.8412 
15.4640 
17.1599 
18.9321 
20.7840 

22.7193 
24.7417 
26.8551 
29.0636 
81.3714 

88.7831 
86.3034 
38.9370 
41.6892 
44.5652 

47.5706 
50.7113 
53.9933 
57.4230 
61.0071 

64.7524 
68.6663 
72.7663 
77.0303 
81.4967 

86.1641 
91.0414 
96.1383 
101.464 
107.030 

112.846 
118.924 
125.276 
131.914 
138.850 

146.098 
153.672 
161.588 
169.859 
178.503 


1. 

2.05000 

3.15250 

4.31012 

5.52568 

6.80191 
8.14201 
9.54911 
11.0266 
12.6779 

14.2068 
15.9171 
17.7130 
19.5986 
21.5786 

23.6576 
25.8405 
28.1326 
30.5389 
83.0660 

85.7193 
38.5052 
41.4305 
44.5020 
47.7271 

51.1134 
56.6691 
60.4025 
64.8226 
66.4389 

70.7608 
75.2989 
80.0638 
85.0670 
90.3203 

95.8364 
101.628 
107.710 
114.095 
120.800 

127.840 
135.232 
142.994 
151.143 
159.700 

168.685 
178.119 
188.025 
198.426 
209.348 


1. 
2.06000 

8.18860 
4.87462 
5.68710 

6.97538 
8.89385 
9.89748 
11.4918 
13.1806 

14.9716 
16.8700 
18.8822 
21.0151 
23.2760 

25.6726 
28.2129 
80.9067 
88.7601 
86.7867 

89.9927 
48.8923 
46.9960 
50.8157 
54.8647 

59.1565 
63.7060 
68.5282 
78.6400 
79.0584 

84.8019 
90.8900 
97.3434 
104.184 
111.435 

119.121 
127.269 
135.905 
145.050 
154.762 

165.048 
175.950 
187.508 
199.758 
212.743 

226.509 
241.099 
256.565 
272.959 
290.837 


annually  setting  aside  a  certain  amount  of  its  earnings  to  be  placed  at 
compound  interest. 

Table  6,  pase  65,  shows  the  annual  amount  to  be  set  aside  in  order  to 
accumulate  $1000  at  various  rates  of  interest  and  for  various  terms  of  shears, 
compounded  annually.    It  is  calculated  from  the  formula: 


ANNUITIES— SINKING  FUND.  06 

in  yfbkii  x  •—  the  number  of  years  »  the  number  of  annuities,  the  payments 
bdng  made  at  the  end  of  each  year. 

Problem. — ^What  semi-annual  pairments  shall  be  made  to  a  sinking  fund 
to  create  $  1,000,000  in  20  years,  interest  at  4%  ? 

Solution. — In  this  case  there  will  be  40  periods  compounded  at  2%. 
Pnxn  the  table.  40  payments  of  $16,556  will  create  $1,000.    But.  in  order 

to  create  $1,000,000  this  must  be  multiplied  by  1000  (  -   -^^^5^)  • 

Hence  the  semi-azmual  payments  would  be  $16,556  each. 

5. — Prbsbnt  Worth,  Prbsbmt  Valub.or  Capitalization  of  Annuity  of  $1. 


Rate  of  Interest. 

YcarsL 

2% 

8% 

»i% 

4% 

4i% 

6% 

6% 

7% 

5 

4.7134 

4.6796 

4.5150 

4.4518 

4.3899 

4.3294 

4.2124 

4.1002 

10 

8.9824 

8.5301 

8.3165 

8.1108 

7.9127 

7.7217 

7.3602 

7.0236 

15 

12.849 

11.938 

11.517 

11.118 

10.739 

10.380 

9.7123 

9.1079 

20 

16.351 

14.877 

14.212 

13.590 

13.008 

12.462 

11.470 

10.594 

29 

19.524 

17.413 

16.482 

15.622 

14.828 

14.094 

12.783 

11.654 

20 

22.396 

19.600 

18.392 

17.292 

16.289 

15.372 

13.765 

12.409 

95 

24.999 

21.487 

20.000 

18.664 

17.461 

16.374 

14.498 

12.948 

40 

27.355 

23.115 

21.355 

19.793 

18.401 

17.159 

15.046 

13.332 

45 

29.490 

24.519 

22.495 

20.720 

19.156 

17.774 

15.456 

13.606 

90 

31.424 

25.730 

23.456 

21.482 

19.762 

18.256 

15.762 

13.801 

60 

34.761 

27.676 

24.988 

22.623 

20.638 

18.929 

16.161 

14.039 

70 

37.499 

29.123 

26.000 

23.395 

21.202 

19.343 

16.385 

14.160 

80 

39.745 

30.201 

26.749 

23.915 

21.565 

19.596 

16.509 

14.222 

90 

41.587 

31.002 

27.279 

24.267 

21.799 

19.752 

16.579 

14.253 

100 

43.098 

31.599 

27.655 

24.505 

21.949 

19.848 

16.613 

14.269 

6. — Sinking  Fund  Table. 

Annuities  (or  Annual  Saving)  Which  Will  Create  $1,000  in  Given 

Number  of  Years,  x,  at  Various  Rates  of  Interest  Compotmded 

Annually. 


Teanto 

Rate  of  Interest. 

Run. 

X 

2% 

3% 

3i% 

4%  . 

4i% 

6% 

6% 

7% 

$495.05 

$492.61 

$491.42 

$490.20 

$489.00 

$487.80 

$485.44 

$483.09 

326.72 

323.56 

321.94 

320.36 

318.77 

3i7.21 

314.10 

311.05 

242.63 

239.02 

237.26 

235.60 

233.74 

232.01 

228.60 

225.26 

192.16 

188.35 

186.49 

184.63 

182.79 

180.98 

177.39 

173.89 

158.53 

154.61 

152.67 

150.79 

148.88 

147.02 

143.36 

139.80 

134.52 

130.51 

128.57 

126.61 

124.67 

122.82 

119.13 

115.55 

116.51 

112.46 

110.48 

108.53 

106.60 

104.72 

101.03 

97.468 

102.52 

98.434 

96.446 

94.493 

92.575 

90.690 

87.022 

83.487 

10 

91.327 

87.231 

85.242 

83.291 

81.360 

79.505 

75.868 

72.377 

74.660 

70.462 

68.484 

66.552 

64.666 

62.826 

69.277 

55.902 

IB 

57.826 

63.767 

51.825 

49.941 

48.114 

46.342 

42.963 

39.795 

20 

41.157 

37.216 

35.361 

33.682 

31.876 

30.243 

27.184 

24.393 

2S 

31.220 

27.428 

25.674 

24.012 

22.439 

20.952 

18.227 

15.811 

30 

24.650 

21.019 

19.371 

17.830 

16.392 

15.051 

12.649 

10.586 

35 

20.002 

16.539 

14.998 

13.577 

12.270 

11.072 

8.9738 

7.2340 

40 

16.556 

13.262 

11.827 

10.524 

9.3432 

8.2781 

6.4615 

4.9976 

45 

13.910 

10.785 

9.4535 

8.2625 

7.2020 

6.2617 

4.7005 

3.4996 

50 

11.823 

8.8656 

7.6338 

6.5502 

5.6021 

4.7767 

3.4443 

2.4598 

•0 

8.7679 

6.1330 

6.0887 

4.2019 

3.4543 

2.2207 

1.8757 

1.2292 

70 

6.6678 

4.3366 

3.4610 

2.7451 

3.1651 

1.6992 

1.0331 

.61952 

80 

5.1607 

3.1118 

2.3849 

1.8141 

1.3708 

1.0296 

.57254 

.31357 

M 

4.0460 

2.2566 

1.6578 

1.2078 

.87316 

.62711 

.31836 

.15905 

too 

3.2027 

1.6467 

1.1593 

.80801 

.55839 

.38314 

.17735 

.08076 

4.— MEASURES.  WEIGHTS  AND  MONEY. 

FUNDAMENTAL  UNITS. 

The  Metric  System^  on  account  of  its  simplicity,  is  destined  in  all  proba- 
bility to  become  the  mtemational  standard  of  weights  and  measures.  It 
has  been  legalized  by  Great  Britain.  Russia  and  the  United  States;  and 
has  been  adopted  by  all  other  European  nations,  by  Mexico,  and  by  many 
South  American  States. 

Meter. — Length.  Ana,  Volume.  The  international  standard  Meter,  the 
unit  of  len^h.  is  the  distance  between  two  lines  on  a  platinum-iridium  bar, 
at  0°  centigrade,  deposited  at  the  International  Bureau  of  Weights  and 
Measures,  in  Paris.   The  legalized  ratio  of  the  standard  meter  to  the  standard 

yard  by  the  United  States*  is  —-j  -  1.093«11U tl.093dl^l;  henca. 

the  following  equivalents: 

Length. 

1  meter- 1.0936n  yards- 3. 28083'' 3  feet- 39.37  inches. 

lyard-0.914  401  838  80  meter.  Log -9.9611371.  Co-log- 0.0388620 
1  foot -0.304  800  609  60  meter.  "  -9.4840168.  "  -0.5159842 
1  inch  -  0.025  400  050  80  meter.      "    -  8.4048346.         "      - 1.5951«54 

Arba. 

I  iqtiare  meter- 1.195  986  262  35 sq.  yd.- 10.763  867 ^6n  sq.  ft. - 
1549.9969  sq.  ins. 
lsq.yd.-0.836  130  704  628q.met.  Log- 9.9222742.    Co-log- 0.0777258 
Isq.ft.  -0.092  903  411  61  sq.met.     "'-8.9680316.       "       -1.0319684 
Isq.in.  -0.000  645162  588q.met.     "    -6.8096692.       "       -3.1903308 

Volume. 

1  cubic  meter- 1.307  942  771  63 cu.  yd.-  35.314  454  833  91  cu.  ft.- 
61023.377953  cu.  ins. 
leu. yd. -0.764  559 445  33 cu.met.  Log -9.88341 13.    Co-log -0.1 165887 
leu.  ft.  -0.028  317  016  49  cu.met.    "    -8.4520475.       "       -1.5479525 
leu. in.  -0.000 016  387  16 cu.met.     "    -5.2145038.       "      -4.7854962 

Liter. — Capacity  {Liquid  and  Dry).  The  liter,  the  unit  of  capacity,  is 
the  volume  of  one  kilogram  of  pure  water  at  its  maximum  density;  and 
this  is  equal  to  a  cubic  decimeter,  or  a  cube  whose  edge  is  one -tenth  of  a 
meter  =•  3.937  inches.  The  capacity  of  one  liter  is  therefore  „^J,  of  the 
volume  of  a  cubic  meter.    The  toUowing  are  the  United  States!  eqmvalents: 

*In  Great  Britain  the  meter  has  been  legalized  at  39.37079  inches,  but 
the  length  of  39.370432  inches,  as  adopted  by  France,  Germany,  Belgium 
and  Russia,  is  frequently  used. 

t  Logarithm  1.0936n- 0.0388629;   co-logarithm -9.9611 371. 

IThe   Imperial  gallon,  the   British  unit  of  liquid  capacity,  contains 
/     277  274\ 
277.274  cubic  inches,  or  1.200320  (-     ^^^    j  United  States  gallons.    The 

Imperial  bushel,  the  British  unit  of  dry  capacity,  contains  8  Imperial  gal- 


lons or  2218.192  cubic  inches- 1.03151570  (-  2150  42^)    United  States 

ime  denominati 
latter  by  these  1 

66  Digitized  by  Google 


(struck)  bushels.    British  measures  of  the  same  denomination  as  those  of 
the  United  States  are  hence  greater  than  the  latter  by  these  ratios. 


METRIC  UNITS— ENGLISH  EQUIVALENTS. 

VOLUMB. 

i  liter*  1  cubic  decimeter  —  0.001  cubic  meter. 

-0.001  307  942  77  cu.  yd.  Log-7.11«5887 


-0.085  314  454  83  cu.  ft. 

-  01.028  877  953     cu.  ins.  (exact.) 
1  cu.  yd.  -  754.650  445  33  Uters. 
leu.  ft.  -   28.317  016  49  Uters. 
1  CO.  in.  «     0.015  387  15  Uter. 


-8.5479525 
-1.7854952 
-2.8834113 
-1.4520475 
-8.2145088 


57 


Liquid. 

1  fiter     -0.254  170  457  38  U.  S.  gallon.  Log-9.421884S 

- 1.055  581  869  32  quarts.  "  -0.0239442 

-2.113  363  738  64  pints.  "  -0.3249742 

IgaUon -231cu.  ins-0.133  680  5^5cu.ft.  **  -9.1260682 

-0.004  951  131  69  cu.  yd.  "  -7.6947045 

-8.785  434  496  56  liters  or  cubic  dm.  "  -0.5781158 

1  quart  -0.945  858  524  14  Uter.  "  -9.9760558 

Prt. 

1  Uter     - 0.028  877  422  99  U.  S.  bushel.  Log-  8.4529730 

-0.118  509  691  97  peck.  "  -9.0550330 

-0.908  077  535  78  quart.  *'  -9.9581229 

lbafliiel-2150.42cu.in8.-1.2444560185ncu.ft.  "  -0.0949796 

-0.046  090  963  65  cu.  yd.  "  -8.6636158 

-0.035  239  281  60  cubic  meter.  "  -8.5470270 

-  85.239  281  602  15  liters  or  cubic  dm.  "  - 1.5470270 

Ipeck    -8.800  820  400  54  Uters.  "  -0.9449670 

1  quart  -1.101  227  550  07  Uters.  '*  -0.0418771 


Mass. 

1  liter  (—1  cubic  decimeter)  of  pure  water  at  maximum  density  weighs 

1  kilogram  (Idlo). 

1  miffimeter  ( —  1  cubic  centimeter)  of  pure  water  at  maximum  density  weight 
1  gram. 


B. — Mass  (Wgighi).  The  Gram,  the  unit  of  weight,  is  the  weight  of 
s  ctabic  centimeter  (1  milUraeter)  of  pure  water  at  its  maximum  density 
~  n^  of  the  international  kilogram.  The  bureau  of  Standards,  Washington, 
O.  C.  givi     '*^    '  ^ •        '     * 


.  gives  the  fundamental  equivalents: 

1  avoirdupois  pound  —453.592  4277  grams,  and 

1  troy  pound  -  f398  avoir,  pound  -  373.241 769  078  867 142  8^67 

grams,  from  which  are  derived  the  following 

values: 


Log -2. 6666658 
••    -2.5719903 


1  kilogram 


1  gram 


-  2.204  622  341  406  avoir,  pounds. 

-  2.679  228  539  903  troy  pounds. 

-  0.035  278  957  462  6  avoir,  ounce. 

-  0.032  150  742  478  8  troy  ounce. 
- 15.432  356  389  84       grains  (troy). 

1  avoirdupois  ounce-  28.349  526  731  26       grams. 
1  troy  ounce  —31.103  480  756  66       grams. 

I  grain  (troy)  -  0.064  798  918  248     gram,    og^ed 


Log- 0.3433342 
••  -0.4280097 
•'  -8.6474642 
••  -8.6071910 
••  -1.1884323 
"  -1.4626468 
"  -1.4928090 
by  G'6(- 8.8115677 


L^MEASURES,  WEIGHTS  AND  MONEY, 


GENERAL  TABLES. 

1. — ^Approximate  Equivalents — Metric  and  Engush. 

acre —      .40    hectar 4047 

bu«heL -35  liters 85.24 

centimeter —      .39    inch 3837 

cubic  centimeter —      .061  cubic  inch OolO 

cubic  foot —      .025  cubic  meter .  0283 


cubic  inch -»  16 

cubic  meter —  35 

cubic  meter —    1.3 

cubic  yard —      .76 

foot -30 

gallon —  3.5 


grain —      .065  gram 


cubic  ccntimet.     1 6 .  89 

cubic  feet 35.31 

cubic  yards 1 .  308 

cubic  meter 7645 

centimeters 30 .  48 

Uters 3.786 


gram —  15 

nectar —  2.5 

inch —  25 

kilo -  2.2 

kilometer —      .62 

liter -      .91 

liter -    I.I 

meter —  3.3 

mile —    1 .6 

millimeter = 

ounce  (avoirdupois). . .  =28 
ounce  (Troy) =31 


.0648 


peck. 

pint 

pound 

quart  (dry) . . . . 
quart  (liquid) . 
sq.  centimeter. 

sq.  foot 

sq.  inch 

sq.  meter 

sq.  meter 

sq.  yard 

ton  (2,000  lbs.) 
ton  (2.240  lbs.) 
ton  (metric)... 
ton  (metric)... 

yard 

2.- 


grains 15.43 

acres 2.471 

millimeters 25 .  40 

pounds 2.205 

mile 6214 

quart  (dry) 9081 

quarts  (liquid) ...    1 .  057 

feet 3.281 

kitometcrs 1 .  609 

039  inch 0394 

grams 28.36 

grams 81.10 

8.8      liters 8.809 

.  -      .47     Utcr 4782 

.  -      .45    kilo 4636 

.-    I.I       liters 1.101 

.  -      .95     Uter 9464 

.  —      .15     sq.  inch 1660 

.  -      .093  sq.  meter 0929 

.—  6.5      sq.  centimeters . .   6 .  452 

.—    1.2       sq.  yards 1.196 

.-II  sq.  feet 10.76 

.  =      .84     sq.  meter 8361 

.91     metric  ton 9072 

metric  ton 1.017 

I       ton  (2.000  lbs.)..    1.102 
98    ton  (2.240  lbs.)..      .9842 
91     meter 9144 


-    I 
.-    I 


-LoNo  Measure.  English. 

-  1  inch  (in.)  -  0.025400  Metos 

12  inches -  1  /w/  (//.)  -0.304801 

3  feet -lyard(yd.)         -0.914402     " 

Sk  yards  (-16*  ft.) =  lrod  (rd.)  -5.029210     " 

40  rods  ("  220  yds.  -  660  ft.) =  i  furlong  (fur.)    -20L1684     " 

8  furlongs  ( =  320  rods-  1760  yds- 

6280  ft.) =  1  siatui*  miU       - 1609.347     " 

8  miles  ( =  24  furs.  -  960  rds.  -  5280 

yds.  -  15840  ft.) -  1  Uague  -4828.042     " 

3. — Surveyors'  Measure  (lineal). 

7.92  inches -  1  link  -.2011684  Meters 

100  links  (  =  4  rds.- 22yds.  =66  ft.) '-Ichain  -20.11684     ** 

80  chains  (320  rds.  =  1760  yds -5280  ft.)  -1  5/a/u^mi^  -1609.347     " 
4. — ♦Mariners'  Measure. 

6  feet -  1  fathom  - 1.828804  Meters 

120  fathoms  ( -  720  ft.) =1  cabl^  length   -  219.4664      "     , 

[7icable  lengths(  =  880fathoms  -  5280ft.)  =  1  statute  mile   -  1609.347      "     ] 

1.15246  statute  miles  (-6086  ft.)     =  1  miMttca/m*/*- 1864.712      " 

60  nautical  miles  =  1  degree.  360  degrees  =  circumference  of  the  earth. 
*  The  old  nautical  mile  was  given  as  7J  cable  lengths  —  5400  feet,  but  it  is 
now  obsolete.  The  present  nautical  mile  is  not  an  exact  term,  being  equal 
to  about  one  minute  of  longitude  at  the  equator.  The  British  Admiralty 
knot  is  6080  ft.  The  nautical  mile  of  the  U.  S.  Coast  Survey  is  6086.07  ft.  - 
1.162664  statute  or  land  miles.    Three  nautical  miles  —  1  league. 


LENGTHS— ENGUSH  AND  METRIC. 


60 


5.— LiKGTBS— InCHBS  AND  MlLLnfBTBRS.—EgUIVALBNTS  OF  DbCZMAL  AND 

Common  Fractions  of  an  Inch  in  Millimbtbrs. 
From  ^  to  1  Inch. 


:: 

1 

1 

1 

1 

Mmi- 
meters. 

1 

s 

1 

• 

1 

-     .397 

.015625 

33 

-13.097 

.615625 

2 
3 

-  .794 

—  1.191 

.03125 
.046875 

17 

34 
35 

-13.494 
-13.891 

.53125 
.546875 

4 
5 

-  1.588 

-  1.984 

.0625 
.078125 

9 

18 

36 
87 

-14.288 
-14.684 

.5625 
.578125 

6 
7 

«-  2.381 

«  2.778 

.09376 
.109375 

19 

38 
39 

-15.081 
-15.478 

.59375 
.609375 

1 

8 

9 

10 
U 

-  3.175 

-  3.572 

-  3.969 
»  4.36« 

.1250 

.140625 
.15625 
.171875 

6 

10 

20 
21 

40 

41 
42 
43 

-15.876 

-16.272 
-16.669 
-17.066 

.625 

.640625 
.65625 
.671875 

12 

13 

14 
15 

-  4.763 

-  5.159 
«  5.556 

-  5.953 

.1875 

.203125 
.21875 
.234375 

11 

22 
23 

44 

45 
46 
47 

-17.463 

-17.859 
-18.256 
-18.653 

.6875 

.703125 
.71876 
.734375 

1 

2 

16 

17 
18 
19 

->  6.350 

-  6.747 

-  7.144 

-  7.541 

.2500 

.265625 

.28125 

.296875 

3 

6 

12 

24 
25 

48 

49 
60 
51 

-19.050 

-19.447 
-19.844 
-20.241 

.76 

.765625 
.78125 
.796875 

10 

11 

20 

21 
22 

23 

-  7.938 

-  8.334 

-  8.731 

-  9.128 

.3125 

.328125 
.34375 
.359376 

13 

26 

27 

52 

53 
54 

55 

-20.638 

-21.034 
-21.431 
-21.828 

.8125 

.828125 
.84376 
.859375 

3 

13 
13 

24 

25 
2« 

27 

-  9.525 

-  9.922 
-10.319 
-10.716 

.3750 

.390625 
.40625 
.421875 

7 

14 

28 
29 

56 

57 
58 
59 

-22.225 

-22.622 
-23.019 
-23.416 

.875 

.890625 
.90625 
.921875 

14 
15 

28 

29 
30 
31 

-11.113 

-11.509 
-11.906 
-12.303 

.4376 

.453125 
.46875 
.484375 

15 

30 
31 

60 

61 
62 
63 

-23.813 

-24.209 
-24.606 
-25.003 

.9375 

.953125 
.96875 
.984375 

1 

2 

4 

* 

32 

-12.700 

.8 

1 

1 

2 

4 

8 

16 

82 

64 

-25.400 

1.000 

-Lbngths — Hundredths  op  an  Inch  to  Millimbtbrs. 
From  1  to  100  Hundredths. 


u 

in 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

0 

0 

.254 

.508 

.762 

1.016 

1.270 

1.524 

1.778 

2.032 

2.286 

10 

2.540 

2.794 

3.048 

3.302 

3.556 

3.810 

4.064 

4.318 

4.572 

4.826 

20 

5.080 

5.334 

6.588 

5.842 

6.096 

6.350 

6.604 

6.858 

7.112 

7.366 

30 

7.020 

7.874 

8.128 

8.382 

8.636 

8.89fl 

9.144 

9.398 

9.652 

9.906 

40 

10.160 

10.414 

10.668 

10.922 

11.176 

11.430 

11.684 

11.938 

12.192 

12.446 

50 

12.700 

12.954 

13.208 

13.462 

13.716 

13.970 

14.224 

14.478 

14.732 

14.986 

H 

15.240 

15.494 

16.748 

16.002 

16.256 

16.510 

16.764 

17.018 

17.272 

17.526 

70 

17.780 

18.034 

18.288 

18.542 

18.796 

19.050 

19.304 

19.558 

19.812 

20.066 

80 

20.320 

20.574 

20.828 

21.082 

21.336 

21.59C 

21.844 

22.098 

22.352 

22.606 

90 

22.860 

23.114 

23.368 

23.622 

23.876 

24.130 

24.384 

24.638 

24.892 

25.146 

Example.— 21  htmdredths  of  an  inch— 5.334  millimeters. 


70 


i.^MEASURES.  WEIGHTS  AND  MONEY. 


7. LbNOTHS MiLLIMBTBRS  TO    DbCIMALS  OF  AN  InCH. 

From  1  to  100  Units, 


sl 

0 

1 

3 

3 

4 

5 

6 

7 

8 

9 

0 

0 

.03937 

.07874 

.11811 

.15748 

.19685 

.23622 

.2755^ 

.31496 

.35433 

10 

.3937C 

.43307 

.47244 

.51181 

.551U 

.62992 

.66929 

.70866 

.74803 

30 

.7874C 

.82677 

.86614 

.90551 

.9448{ 

1.02362 

1.06299 

1.10236 

1.14173 

30 

1.18110 

1.22047 

1.25984 

1.29921 

1.3385J 

1 .37795 

1.41732 

1.456691.4960611.63543 

40 

1.57480 

1.61417 

1.65864 

1.69291 

1.73228 

1.77165 

1.81102 

1.86039 

1.88976 

1.92913 

50 

1.96850 

2.00787 

2.04724 

2.08661 

2.12598 

2.1653H  2.20472 

2.24409 

2.28346 

2.32283 

60 

2.36220 

2.40157 

2.44094 

2.48031 

2.5196{ 

2.55909 

2.69842 

2.637792.67716 

2.71653 

70 

2.7559C 

2.79527 

2.83464 

2.87401 

2.9133« 

2.95275 

2.99212 

3.031493.070863.11023 

80 

3.1496C 

3.18897 

3.22834 

3.26771 

3.30708 

3.34643 

3.38582 

3.425193.46456 

3.50398 

90 

3.54330 

3.68267 
1 

3.62204 

3.66131 

3.70078 

3.74015 

3.77952 

3.818893.858263.89763 

Example. — ^21  millimeters— 0.82677  inch. 
8. — Lbngths. 


Inches 

Feet. 

Yards. 

MUes. 

1  millimeter  (m  m)      - 

.03937 

.0032808 

.0010936 

10  millimeters  (  —  i Jo  meter)  — 

.3937 

.0328083 

.0109361 

10  centimeters    ( —  A  meter)  — 

1  decxmeUr  (d  m)         -> 

3.937 

.328083^2 

.109361^1 

10  decimeters  — 

1  msUr                        - 

39.37 

3.28088^2 

1.0936n 

.0000213 

10  meters  — 

1  dekameUr  (Dm)       - 

393.7 

32.8083^3 

I0.936n 

.0062137 

10  dekametcTs  ( -  100  meters}  - 

i  heciomeUr  (Hm)       - 

3937 

328.083^3 

109.861^1 

.062137 

10  hectometers  ( -  1000  meters)  - 

1  kilometer  (Km)         - 

3280.83^3 

1093. on 

.621370 

10  kilometers  ( - 10000  meters)  - 

1  myriameter  (Mm)     — 

32808. 3''3 

10936. m 

6.21370 

9. — Lbngths,  Equivalents.     I-IO. 


HUli- 
Incbes.   meters. 


CJcntl- 
Inches.  meters. 


Feet.      Meters. 


U.S. 
Yards. 


Meters. 


U.S. 
MUes. 


Kilo- 
meters. 


0.03937- 
0.07874- 
0.11811  — 
0.15748- 

0.19685- 
0.23622- 
0.27559- 
0.31496- 
0.25433- 


0.3937-  1 
0.7874-  2 

1  -  2.54001 
1.1811-  3 

1.5748-  4 
1.9685-  5 

2  -   5.08001 
2.3622-  6 
2.7559-  7 


=  0.304801 
=  0.609601 
»  0.914402 
-1 


1  -0.914402 
1.093611-1 

2  - 1.828804 
2.187222-2 


0.62137- 
1 

1.24274- 
1.86411» 


I  -  25.40013 

3  -  50. 

3  -  76. 

4  - 101.6002 


).80013 
5.2002  3 


—  7.62002 

.1496-  8 

.5433="  9 

4         -10.16002 


8  -2.438405 

9  -2.7432056 
9. 84250  =-3 

13.12333  =  4 


- 127.0003 S 
-152.4003  6 
-177.800417 
=  203.2004'8 
-228.6005|9 


=  12.70003 
» 15.24003 
= 17.78004 
-20.32004 


16.40417-5 
19.68500=6 
22. 96583 « 7 
26.24667-8 


-22.86005,29.52750-9 


4  -1.2192023  -2.743205 

5  —1.524003  3.280833-3 

6  -1.828804  4  -  3.657607 13 
6.56167^2             4.374444-4 

7  —2.133604  5  -4.572009 


5.468056-5 

-5.486411 
6.561667-6 
7  -6.400813 


2 

2.48548- 
3 

3.10685- 
3.72822- 

4  - 

4.34959- 
4.97096« 
5 


1.60935 

2 

3 

3.21869 

4 

4.82804 

5 

6 

6.43739 
7 
8 
8.04674 


7.655278-7 

8  -7.315215  6 
.748889-8 

9  -  8.229616  8 
842500-9 


5.59233-  9 

-   9.65606 

7  -11.26548 

-18.87478 
- 14.48412 


|k_ 


LENGTHS— FEET  AND  INCHES  TO  METERS. 


71 


1-350. 


10. — Lbnotbs — Fbbt  to  Mbtbrs. 
From  1  to  1.000  Units. 


F«et.  Meters. 

Feet 

.    Meters. 

Feet.    Meters. 

Feet 

.    Meters. 

Feet 

.    Meters. 

a 

1  .90480 

2  .60960 

3  .91440 

4  1.21920 

50 

15.24003 
15.54483 
15.84963 
16.15443 
16.45923 

100    30.48006 

1  30.78186 

2  31.08966 

3  31.39446 

4  31.69926 

150 

45.72009 
46.02489 
46.32969 
46.63449 
46.93929 

300 

60.96012 
61.26492 
61.66972 
61.87452 
62.17932 

5  1.52400 

6  i.mso 

7  2.13360 

8  2.43840 

9  2.74321 

16.76403 
17.06883 
17.37363 
17.67844 
17.98324 

6    32.00406 

6  32.30886 

7  32.61367 

8  32.91847 

9  33.22327 

47.24409 
47.54890 
47.85370 
48.15850 
48.46330 

62.48412 
62.78893 
63.09373 
63.39853 
63.70333 

10      3.04801 

1  3.35281 

2  3.65761 

3  3.96241 

4  4.26721 

60 

18.28804 
18.59284 
18.89764 
19.20244 
19.50724 

110    33.52807 

1  33.83287 

2  34.13767 

3  34.44247 

4  34.74727 

160 

48.76810 
49.07290 
49.37770 
49.68250 
49.98730 

310 

64.00813 
64.31293 
64.61773 
64.92253 
65.22733 

5  4.57201 

6  4.87681 

7  5.18161 

8  5.48641 

9  5.79121 

19.81204 
20.11684 
20.42164 
20.72644 
21.03124 

5  35.05207 

6  35.35687 

7  35.66167 

8  35.96647 

9  36.27127 

50.29210 
50.59690 
50.90170 
51.20650 
61.51130 

65.53213 
65.83693 
66.14173 
66.44653 
66.75133 

30      6.09601 

1  6.40081 

2  6.70561 

3  7.01041 

4  7.31521 

70 

21.33604 
21.64084 
21.94564 
22.25044 
22.55525 

120    36.57807 
1    36.88087 
3    37.18567 

3  37.49047 

4  37.79628 

170 

51.81610 
52.12090 
52.42570 
52.73051 
53.03531 

330 

67.05613 
67.36093 
67.66574 
67.97064 
68.27534 

f      7.62002 

6  7.92482 

7  8.22962 

8  8.53442 

9  8.S922 

22  88005 
23.16485 
23.46965 
23.77445 
24.07926 

5  38.10008 

6  38.40488 

7  38.70968 

8  39.01448 

9  39.31928 

53.34011 
63.64491 
53.94971 
54.25451 
54.55931 

68.68014 
68.88494 
69.18974 
69.49454 
69.79934 

30      9.14402 

1  9.44882 

2  9.75362 
2    10.05842 
4    10.36322 

80 

24.38405 
24.68885 
24.99365 
25.29815 
25.60325 

130    39.62408 

1  39.92888 

2  40.23368 

3  40.53848 

4  40.84328 

180 

64.86411 
55.16891 
65.47371 
55.77851 
66.08331 

330 

70.10414 
70.40894 
70.71374 
71.01854 
71.32334 

5  10.66802 

6  10.97282 

7  11.27762 

8  11.58242 

9  11.88722 

26.90805 
26.21285 
26.51765 
26.82245 
27.12725 

5  41.14808 

6  41.45288 

7  41.75768 

8  42.06248 

9  42.36728 

56.38811 
66.69291 
56.99771 
57.30251 
57.60732 

71.62814 
71.93294 
72.23774 
72.64255 
72.84736 

40    12.19202 

1  12.49682 

2  12.80163 

3  13.10643 

4  13.41123 

00 

27.43205 
27.73688 
28.04166 
28.34646 
28.65126 

140    42.67209 

1  42.97689 

2  43.28169 

3  43.58649 

4  43.89129 

190 

57.91212 
58.21692 
58.52172 
58.82652 
59.13132 

340 

73.15216 
73.45695 
73.76175 
74.06655 
74.37135 

5  13.71603 

6  14.02083 

7  14.32663 

8  14.63043 

9  14.93523 

28.95606 
29.26086 
29.56566 
29.87046 
30.17526 

5  44.19609 

6  44.50089 

7  44.80569 

8  45.11049 

9  45.41529 

59.43612 
59.74092 
60.04572 
60.35052 
60.65532 

8 
9 

350 

74.67615 
74.98095 
75.28575 
75.59055 
75.89535 

76.20015 

lineli  «-.  02540  meter. 
Itacbet  -.05080 meter. 
Jla^bea  -  .07620  meter. 
41aetan  -.10160 


6  Inches  «-  .  12700  meter. 
0  Inches  »  .  1 6240  meter. 

7  Inches  —  .17780  meter. 

8  Inches  —  .  20320  meter. 


9  Inches  «-  .22860  meter. 

10  Inches  <«. 2 5400  meter. 

11  lnche««—.  27  940  meter. 

12  Inches  —.30480  meter. 


72 


i.—MEASURES,  WEIGHTS  AND  MONEY. 


350-500. 


10. — Lengths — Feet  to  Meters  (Continued). 


Feet.    Meters. 


Feet.    Meters.    Feet.    Meters.    Feet.    Meters.     Feet.    Meters. 


350  76.20015 

1  76.50495 

2  76.80975 

3  77.11455 

4  77.41935 

5  77.71416 

6  78.02896 

7  78.33376 

8  78.63856 

9  78.94336 

360  79.24816 

1  79.55296 

2  79.85776 

3  80.16256 

4  80.46736 

5  80.77216 

6  81.07696 

7  81.38176 

8  81.68656 

9  81.99136 

370  82.29616 

1  82.60097 

2  82.90577 

3  83.21057 

4  83.61537 

5  83.82017 

6  84.12497 

7  84.42977 

8  84.73457 

9  85.03937 

380  85.34417 

1  85.64897 

2  85.95377 

3  86.25857 

4  86.56337 

5  86.86817 

6  87.17297 

7  87.47777 

8  87.78258 

9  88.08738 

390  88.39218 

1  88.69698 

2  89.00178 
8  89.30658 

4  89.61138 

5  89.91618 

6  90.22098 

7  90.52578 

8  90.83058 

9  91.13538 


300  91.44018 

1  91.74498 

2  92.04978 

3  92.35458 

4  92.65939 


5 
6 
7 
8 
9 

310 

1 
2 
3 
4 

5 

6 
7 


330 


2 
3 
4 

5 
6 
7 
8 
9 

340 

1 
2 


92.96419 
93.26899 
93.57379 
93.87859 
94.18339 

94.48819 
94.79299 
95.09779 
95.40259 
95.70739 

96.01219 
96.31699 
96.62179 
96.92659 
97.23139 

97.53620 
97.84100 
98.14580 
98.45060 
98.75540 


5  99.06020 

6  99.36500 

7  99.66980 

8  99.97460 

9  100.27940 


100.58420 
100.88900 
101.19380 
101.49860 
101.80340 

102. 10820 
102.41300 
102.71781 
103.02261 
103.32741 

103.63221 
103.93701 
I04.241SI 
104.54661 
104.85141 

105.15621 
105.46101 
105.76581 
106.07061 
106.37541 


350 

1 
2 

3 

4 

6 
6 

7 
8 
9 


2 

3 

4 

5 
6 

7 
8 
9 

390 

1 
2 
3 
4 

5 

6 
7 


106.68021 
106.98501 
107.28981 
107.59462 
107.89942 

108.20422 
108.5Q902 
108.81382 
109.11862 
109.42342 


0  109.72822 

1  110.03302 

2  110.33782 

3  110.64262 

4  110.94742 


5  111.25222 

6  111.55702 

7  111.86182 

8  112.16662 

9  112.47142 

370  112.77623 

1  113.08103 

2  113.38583 

3  113.69063 

4  113.99543 


114.30023 
114.60503 
114.90983 
115.21463 
115.51943 

115.82423 
116.12903 
116.43383 
116.73863 
117.04343 

117.34823 
117.65304 
117.95784 
118.26264 
118.56744 

118.87324 
119.17704 
119.481S4 
119.78664 
120.09144 

120.39624 
120.70104 
121.00584 
121.31064 
121.61544 


400 
1 
2 
3 

4 


121.92024 
122.22504 
122.52985 
122.83465 
123.13945 


5  123.44425 

6  123.74905 

7  124.053» 

8  124.35866 

9  124.66346 

410  124.96835 

1  125.27305 

2  125.57785 

3  125.88265 

4  126.18745 

5  126.49225 

6  126.79705 

7  127.10185 

8  127.40665 

9  127.71146 

430  128.01626 

1  128.32106 

2  128.62586 

3  128.93066 

4  129.23546 

5  129.54026 

6  129.84506 

7  130.14986 

8  130.45466 

9  130.75946 

430  131.06426 

1  131.36906 

2  131.67386 

3  131.97866 

4  132.28346 


132.58827 
132.89307 
133.19787 
133.50267 
133.80747 


440  134.11227 

1  134.41707 

2  134.72187 

3  135.02667 

4  135.33147 

5  135.63627 

6  135.94107 

7  136.24587 

8  136.55067 

9  136.85547 


450  137.16027 

1  137.46607 

2  137.76988 

3  138.07468 

4  138.37948 

5 
6 

7 
8 
9 


470    143.2563» 

1  143.56109 

2  143.86689 
144.17069 
144.47549 


480  146.30429 

1  146.60909 

2  146.91389 

3  147.21889 

4  147.52350 


5 
6 
7 
8 
9 

490  149.35230 

1  149.65710 

2  149.96190 

3  150.26670 

4  '150.57150 

5 
6 

7 
8 
9 

500    152.40030 


d  by  Google 


LENGTHS— FEET  TO  METERS. 


73 


soa-7so. 


10. — ^LBMGTBa — P«»T  TO  Mbtbrs  (Continued). 


Poet.    Ifetcn. 


Feet.    Meters. 


Feet.    Meters. 


Feet.    Meters. 


Feet.    Meters. 


9»  1S.40030 

1  1S2.70^11 

2  153.00e91 

3  113.31471 

4  iS3.«1951 

5  158.92431 
C  154.22fll 

7  1M.53391 

8  154.83871 

9  195.14351 

810  155.4461 

1  155.75311 

2  155.05791 

3  156.36271 

4  156.66751 

5  156.97231 

6  157.27711 

7  157.58192 

8  157.88672 

9  158.19152 

830  158.49633 

1  158.80112 

3  159.10593 

3  169.41072 

4  159.71552 

5  160.02092 

6  160.32513 

7  100.62992 

8  100.93472 

9  161.23952 

830  161.54433 

1  161.84912 

3  163.16393 

3  163.45872 

4  162.76353 

5  163.06833 

6  163.37313 

7  163.67793 

8  163.98273 

9  164.28753 

840  164.50233 

1  164.89713 

2  165.20193 

3  165.50673 

4  165.81153 

8  166.11633 

0  166.42113 

7  166.72593 

8  197.03073 

9  167.33593 


8 

3 

4 

5 

6 
7 
8 
9 


1 
2 

3 

4 

6 
6 
7 
8 
9 

570 

1 
2 
3 

4 


117.64034 
167.94514 
168.24994 
168.55474 
168.85954 

169.16434 
169.46914 
169.77394 
170.07874 
170.38354 

170.68834 
170.99314 
171.29794 
171.60274 
171.90754 

172.21234 
172.51714 
172.82195 
173.12675 
173.43155 

173.73635 
174.04115 
174.34596 
174.65075 
174.95665 


5  175.26035 

6  175.56515 

7  175.86995 

8  176.17475 

9  176.47955 


1 
2 
3 
4 

5 

6 
7 
8 
9 

SfO 

1 
2 
8 
4 

5 
6 
7 
8 
9 


176.78485 
177.08915 
in.39395 
177.69876 
178.00366 

178.30836 
178.61316 
178.91796 
179.22276 
179.62766 

179.83236 
180.13716 
180.44196 
180.74676 
181.06156 

181.85636 
181.66116 
181.96596 
183.27076 
183.57567 


1 
2 
3 

4 

6 
6 

7 
8 
9 

610 

1 
2 
3 
4 

6 
6 
7 
8 
9 

630 

3 

3 

4 

5 
6 

7 
8 
9 


182.88037 
183.18517 
183.48997 
183.79477 
184.09957 

184.40437 
184.70917 
185.01397 
185.31877 
185.62357 

185.92837 
186.23317 
186.53797 
186.84277 
187.14757 

187.45237 
187.75718 
188.06198 
188.36678 
188.67158 

188.97638 
189.28116 
189.58598 
189.89078 
190.19558 

190.50038 
190.80518 
191.10998 
191.41478 
191.71968 

192.02438 
192.32918 
192.63399 
192.93879 
193.24369 

193.54839 
193.85319 
194.15799 
194.46279 
194.76759 

0  195.07339 

1  195.87719 
195.68199 
195.98679 
196.29169 


196.69639 
196.90119 
197.20599 
197.61080 
197.81560 


680  198.12040 

1  198.42520 

2  198.73000 

3  199.03480 

4  199.33960 


6  199.64440 

6  199.94920 

7  200.25400 

8  200.55880 

9  200.86360 

660  201.16840 

1  201.47320 

2  201.77800 

3  202.08280 

4  202.38760 

5  202.69241 

6  202.99721 

7  203.30301 

8  203.60681 

9  203.91161 

670  204.21641 

1  204.52121 

2  204.82601 
8  205.13081 

4  205.43561 

5  205.74041 

6  206.04521 

7  206.35001 

8  206.65481 

9  206.95961 

680  207.26441 

1  207.56922 
207.87402 
208.17882 
208.48362 


208.78842 
209.09322 
209.39802 
209.70282 
210.00762 

210.31242 
210.61722 
210.92202 
211.22682 
211.63162 


6  211.83642 

6  212.14122 

7  212.44602 

8  212.75083 

9  213.05563 


213.36043 
213.66523 
213.97003 
214.27483 
214.57963 


6  214.88443 

6  215.18923 

7  215.49403 

8  216.79883 

9  216.10363 

710  216.40843 

1  216.71323 

2  217.01803 

3  217.32283 

4  217.62764 

6  217.93244 

6  218.23724 

7  218.54204 

8  218.84684 

9  219.15164 

730  219.45644 

1  219.76124 

2  220.06604 

3  220.37084 

4  220.67664 

6  220.98044 

6  221.28524 

7  221.59004 

8  221.89484 

9  222.19964 

730  222.50445 

1  222.80925 

2  223.11405 

3  223.41885 

4  223.72365 

6  224.02845 

6  224.33325 

7  224.63805 

8  224.94285 

9  225.24765 

740  225.55245 

1  225.85725 

2  226.16205 

3  226.46685 

4  226.77165 


227.07645 
227.38125 
227.68606 
227.99086 
228.29566 


750    228.60046 


d  by  Google 


74 


4— MEASURES,  WEIGHTS  AND  MONEY. 


750-1000. 


10. — ^Lbnoths — Pbbt  to  Mstbrs  (Concluded). 


Feet.    Meters.    Feet.    Meters. 


Feet.    Meters. 


Feet.    Meters. 


Feet.    Meters. 


7S0  228.60046 

1  228.90526 

2  229.21006 

3  229.51486 

4  229.81966 

6  230.12446 

6  230.42926 

1  230.73406 

8  231.03886 

9  231.34366 

760  231.64846 

1  231.95326 

2  232.25806 

8  232.56287 

4  232.86767 

6  233.17247 

6  233.47727 

7  233.78207 

8  234.08687 

9  234.39167 

770  234.69647 

1  235.00127 

2  235.30607 

3  235.61087 

4  235.91667 

5  236.22047 

6  236.52527 

7  236.83007 

8  237.13487 

9  237.43967 

780  237.74448 

1  238.04928 

2  238.35408 

3  238.65888 

4  238.96368 

5  239.26848 

6  239.67328 

7  239.87808 

8  240.18288 

9  240.48768 

790  240.79248 

1  241.09728 

2  241.40208 

3  241.70688 

4  242.01168 

6  242.31648 

6  242.62129 

7  242.92609 

8  243.23089 

9  243.53569 


2 

8 

4 

5 
6 
7 
8 
9 

830 

1 
2 
3 
4 

5 
6 
7 


243.84049 
244.14529 
244.45009 
244.75489 
245.05969 

245.36449 
245.66929 
245.97409 
246.27889 
246.58369 


810  246.88849 

1  247.19329 

2  247.49810 

3  247.80290 


248.41250 
248.71730 
249.02210 
249.32690 
249.63170 

240.93660 
250.24130 
250.54610 
250.85090 
251.15570 

251.46050 
251.76530 
252.07010 
252.37490 
252.67971 

252.98451 
253.28931 
253.59411 
253.89891 
254.20371 

254.50861 
254.81331 
255.11811 
225.42291 
255.72771 

256.03251 
256.33731 
256.64211 
256.94691 
257.25171 

257.55652 
257.86132 
258.16612 
258.47092 
258.77572 


259.08012 
259.38532 
259.69012 
259.99492 
260.29972 

260.60452 
260.90932 
261.21412 
261.51892 
261.82372 

263.128S2 
262.43332 
263.73813 
263.04293 
263.34773 

263.65263 
263.95733 
264.26213 
264.56693 
264.87173 


870  265.17658 

1  265.48133 

2  265.78613 

3  266.09093 

4  266.39573 


266.70053 
267.00533 
267.31013 
267.61494 
267.91974 

268.22454 
268.52934 
268.83414 
269.13894 
269.44374 

269.74854 
270.05334 
270.35814 
270.66294 
270.96774 


890  271.27254 

1  271.67734 

2  271.88214 

3  272.18694 

4  272.49174 

5  272.79655 

6  273.10135 

7  273.40615 

8  273.71095 

9  274.01575 


930 

1 
2 

3 

4 


930 

1 
2 
3 
4 

5 
6 
7 
8 
9 


274.32096 
274.62535 
274.93015 
275.23495 
276.53975 

275.84466 
276.14935 
276.45415 
276.75895 
277.06375 

277.86861 
277.67336 
277.97816 
278.28296 
278.58776 

278.89266 
279.19736 
279.50216 
279.80696 
280.11176 

280.41656 
280.72136 
281.02616 
281.33096 
281.63576 

281.94056 
282.24536 
282.55017 
282.85497 
283.15977 

283.46457 
283.76937 
284.07417 
284.37897 
284.68377 

284.98857 
285.29337 
285.59817 
285.90297 
286.20777 

286.51257 
286.81737 
287.12217 
287.42697 
287.73178 

288.03658 
288.34138 
288.64618 
288.95098 
289.25578 


950  289.560M 

1  289.86538 

2  290.17018 
8  290.47498 

4  390.77978 

5  291.08458 

6  291.38938 

7  291.69418 

8  291.99898 

9  291.30178 

960  292.60859 

1  292.91239 

2  298.21819 

3  293.53299 

4  293.82779 

5 
6 

7 
8 
9 


1 
2 
3 

4 

6  S00.228GO 

6  300.53340 

7  300.83810 

8  301.14300 

9  301.44780 


6 
6 
7 
8 
9 

1000   304.80081 


d  by  Google 


LENGTHS^METERS  TO  FEET. 


75 


1-350. 


11. 


-Lbnoths — ^Mbtbrs  to  Pbbt. 
From  1  to  1.000  Units. 


MMm».    Teet.    Meters.    Feet.     Meters.    Feet.     Meters.    Feet.    Meters.    Feet, 


9 

1  a. 28083 

2  f. 51167 

3  9.S4250 

4  U. 12333 

f  K. 40417 

«  19«8500 

7  23.M663 

8  28.24687 
8  29.52750 

10  33.80033 

1  38.08917 

2  39.37000 

3  43.65083 

4  45.93167 

6  49.21250 

6  53.4»33 

7  55.77417 

8  50.05600 

9  62.33583 

aO  65.61667 

1  68.89750 

2  72.17833 

3  75.45917 

4  78.74000 

5  82.02083 

6  85.30167 
T  88.58250 

8  91.86333 

9  95.14417 

JO  98.43500 

1  101 .70583 

2  104.98667 

3  108.26750 

4  111.54833 

5  114.82917 
8  118.11000 

7  131.39083 

8  134.67167 

9  127.9S3W 

40  131.23333 

1  134.51417 

2  137.79500 

3  141.07583 

4  144.35667 

5  147.63750 

6  150.91833 

7  154.19917 

8  1B7.48000 

9  160.76083 


1 
2 

3 

4 

5 
6 
7 
8 
9 

70 

1 
8 
3 
4 


1 
3 
3 
4 

5 
6 

7 
8 
9 

90 
1 
2 

3 
4 

6 
6 
7 
8 
9 


164.04167 
167.32250 
170.60333 
173.88417 
177.16600 

180.44583 
183.78667 
187.00750 
190.28833 
193.56917 

196.85000 
800.13083 
203.41167 
306.69250 
209.97333 

213.25417 
216.53500 
219.81583 
223.09667 
226.37750 

229.65833 
232.93917 
336.22000 
239.50083 
242.78167 

246.06250 
249.34333 
252.62417 
255.90500 
259.18583 

262.46667 
265.74750 
269.02833 
272.30917 
275.59000 

278.87083 
282.15167 
285.43250 
288.71333 
291.99417 

295.r500 
298.55583 
301.83667 
305.11750 
808.39833 

811.67917 
314.96000 
318.24083 
321.52167 
324.80250 


100  328.08333 

1  331.36417 

2  334.64500 

3  337.92583 

4  341.20667 


344.48750 
347.76833 
351.04917 
354.33000 
357.61083 


no  360.89167 

1  364.17250 

2  367.45333 

3  370.73417 

4  374.01500 

5  377.29583 

6  380.57667 

7  383.85750 

8  387.13833 

9  390.41917 

laO  393.70000 

1  396.98083 

2  400.26167 

3  403.54250 

4  406.82333 


410.10417 
413.38500 
416.66583 
419.94667 
423.22750 


130  426.50833 

1  429.78917 

2  433.07000 

3  436.35083 

4  439.63167 


442.91260 
446.19333 
449.47417 
452.75500 
456.03583 


140  459.31667 

1  462.59750 

2  465.87833 

3  469.15917 

4  472.44000 


475.72083 
479.00167 
482.28250 
485.56333 
488.84417 


150  492.12500 

1  495.40683 

2  498.68667 
8  501.96750 

4  505.24833 

5  508.53917 

6  611.81000 

7  515.09083 

8  518.37167 

9  521.65250 

IM  524.93333 

1  538.21417 

2  531.49600 

3  634.77583 

4  538.06667 

5  541.33750 

6  544.61833 

7  547.89917 

8  551.18000 

9  554.46083 

170  657.74167 

1  661.02250 

2  564.30333 

3  667.58417 

4  570.86500 

5  574.14583 

6  577.42667 

7  580.70750 

8  583.98833 

9  587.26917 

180  590.55000 

1  593.83083 

2  597.11167 

3  600.39260 

4  603.67333 

5  606.95417 

6  610.23500 

7  613.51583 

8  616.79667 

9  620.07760 

190  623.35833 

1  626.63917 

2  629.92000 
8  633.20083 

4  636.48167 

5  639.76250 

6  643.04333 

7  646.32417 

8  649.60600 

9  652.88583 


1 
2 
3 
4 

5 
6 
7 
8 
9 

310 

1 
2 
3 
4 

5 

6 
7 
8 
9 

330 

1 
2 
3 

4 

5 
6 
7 
8 
9 

330 

1 
3 
3 

4 

5 
6 
7 
8 
9 

340 

1 
2 


666.16667 
659.44750 
662.72833 
666.00917 
669.29000 

672.57083 
675.85167 
679.13250 
682.41333 
685.69417 

688.97500 
692.25583 
695.53667 
698.81750 
702.09833 

705.37917 
708.66000 
711.94083 
715.22167 
718.50250 

721.78333 
725.06417 
728.34500 
731.62h83 
734.90667 

738.18750 
741.46833 
744.74917 
748.03000 
751.31083 

754.59167 
767  87250 
761.15333 
764.43417 
767.71500 

770.99583 

774.27667 
777.55750 
780.83833 
784.11917 

787.40000 
790.68083 
793.%I67 
797.24250 
800.52333 

803.80417 
807.08500 
810.36583 
813.64667 
816.92750 


d  by  Google 


75 


i.—MEASURES,  WEIGHTS  AND  MONEY. 


2S0-500 


11. — Lbnoths — ^Mbtbrs  to  Pbit  (Continued). 


Meters.    Feet.   Meters.     Feet.     Meters.    Feet.     Meters.    Feet.     Meters.    FMt. 


350  820.20833 

1  823.48917 

2  826.77000 
8  830.08" 
4  833.83167 


836.61250 
839.89333 
843.17417 
846.46500 
849.73583 

853.01667 
856.29750 
859.57833 
862.85917 
866.14000 

869.42083 
872.70167 
875.98260 
879.26333 
882.54417 


360 
1 
2 


370  885.82500 

1  889.10583 

2  892.38667 

3  895.66750 

4  898.94833 


1 
2 
3 
4 

5 

6 
7 
8 
9 

390 

1 
2 
3 

4 

5 
6 
7 
8 
9 


902.22917 
905.61000 
908.79083 
912.07167 
915.35250 

918.66333 
921.91417 
925.19500 
928.47583 
931.75667 

935.03750 
938  31833 
941.59917 
944.88000 
948.16083 

951 .44167 
954.72250 
958.00333 
961.28417 
964.56500 

967.84583 
971.12667 
974.40750 
977.68833 
980.96917 


1 
2 

3 

4 

5 
6 
7 
8 
9 

310 
1 
2 
3 
4 

5 
6 
7 
8 
9 

330 
1 
2 

3 
4 

5 
6 

7 


330 

1 
2 
3 

4 

6 
6 
7 
8 
9 

340 
1 
2 
3 
4 

5 
6 
7 
8 
9 


984.25000 
987.53083 
990.81167 
994.09250 
997.37333 

1.000.65417 
1.003.93500 
1.007.21583 
1.010.49667 
1,013.77750 

1.017.05833 
1.020.33917 
1.023.62000 
1.026.90083 
1.030.18167 

1.033.46250 
1.036.74333 
1.040.02417 
1,043.80500 
1.046.58583 

1.049.86667 
1,053.14750 
1.056.42833 
1.059.70917 
1.062.99000 

1.066.27083 
1.069.55167 
1,072.83250 
1.076.11333 
1.079.39417 

1.082.67500 
1.085.95583 
1.089.23667 
1.092.51750 
1.095.79833 

1.099.07917 
1.102.36000 
1.105.64083 
1.108.92167 
1.112.20250 

1.115.48333 
1,118.76417 
1,122.04500 
1,125.32583 
1.128.60667 

1.131.88750 
1.135.16833 
1.138.44917 
1.141.73000 
1.145.01083 


3S0 
1 
2 
3 
4 

6 
6 

7 


340 

1 
2 
3 
4 

5 
6 
7 
8 
9 

370 

1 
2 
3 
4 

5 
6 

7 


380 

1 
2 
3 

4 

5 

6 

7 


390 
1 
2 
3 
4 

5 
6 

7 


1.148.29167 
1.151.67250 
1.154.85333 
1.158.13417 
1.161.41500 

1.164.69583 
1.167.97667 
1.171.25750 
1.174.53833 
1.177.81917 

1,181.10000 
1.184.28083 
1.187.66167 
1.190.94250 
1.194.22333 

1.197.60417 
1.200.78500 
1.204.06583 
1.207.34667 
1.210.62750 

1.213.90833 
1.217.18917 
1.220.47000 
1.223.75083 
1.227.03167 

1.230.31250 
1.233.59333 
1.236.87417 
1.240.15500 
1.243.43583 

1.246.71667 
1.249.99750 
1.253.27833 
1,256.55917 
1.259.84000 

1. 263.12083 
1,266.40167 
1.269.68250 
1.272.96333 
1.276.24417 

1.279.52500 
1.282.80583 
1.286.08667 
1,289.36750 
1.292.64833 

1.295.92917 
1.299.21000 
1.302.49083 
1,305.77167 
1.309.05250 


2 
3 
4 

5 
6 

7 
8 
9 

410 
1 
2 


430 

1 
2 
3 
4 

5 
6 

7 
8 
9 

430 

1 
2 
3 
4 

5 
6 
7 
8 
9 


1.312.33333 
1.315.61417 
1,318.89500 
1.322.17583 
1.325.45667 

1.328.73750 
1.332.01833 
1,335.29917 
1.338.58000 
1.341.86083 

1.345.14167 
1 .348.42250 
1.351.70333 
1.354.98417 
1.358.26500 

1.361.54583 
1.364.82667 
1.368.10750 
1 .371 .38833 
1.374.66917 

,377.95000 
1,381.23083 
1,384.61167 
1.387.79250 
1.391.07333 

1.394.35417 
1.397.63500 
1.400.91583 
1.404.19667 
1,407.47750 

1.410.76833 
1.414.03917 
1.417.32000 
1.420.60083 
1.423.88167 

1.427.16250 
1.430.44338 
1.433.72417 
1.437.00500 
1.440.28583 

1.443.56667 
1.446.84750 
1,450.12833 
1,453.40917 
1,456.69000 

1.459.97083 
1,463.26167 
1.466.53250 
1.469.81333 
1.473.09417 


450 
1 
2 

3 
4 

6 
6 
7 
8 
9 


470 

1 
2 
3 
4 

6 
6 
7 
8 

9 


1 
2 
3 

4 

6 
6 
7 
8 
9 

490 

1 
3 
3 

4 

6 
6 
7 
8 
9 


d  by  Google 


LENGTHS—METERS  TO  FEET. 


77 


SIMK7S0. 


11. — LBNGTBa — Mbtbrs  to  Pbbt  (ContinuMl). 


Meters.    Ftet. 


Feet. 


Meters.    Feet. 


Meten.    Feet. 


Meters.    Feet. 


SOO  1.M0.41667 

1  1, Ml. 69750 

I  l.tU. 97833 

S  l.«5e.  25917 

4  l.»5S.54O00 

5  1.656.81083 
«  1.660.10167 

7  1.663.38250 

8  1.666.66333 

9  1,669.94417 

sia  i.<n. 22500; 

1  1.676.50563 

2  1.679.78667 
S  1.688.06750 

4  1.686.34833 

5  1.689.63917 

6  1.692.91000 

7  1,696.19083 

8  1.699.47167 

9  1.702.75250 

fat  1.706  08333 

1  1.709.31417 

2  1.712.59500 

3  1.715.87583 

4  1.719.15667 

5  1.722.43750 

6  1.725.71833 

7  1,728.99917 

8  1.732.28000 

9  1.735.56183 

•30  1.738.84167 

1  1.742.12250 

2  1.745.40333 

3  1.748.68417 

4  1.751.96500 

5  1.755.24583 

6  1.766.51667 
T  1.761.80750 
i  1.765.08838 
9  1.768.36917 

S4t  l.ni.6SO00 

1  1.774.93083 

2  1.778.:il67 

3  1.781.49250 

4  1,784.77333 

5  1.788.06417 

6  1.791.33500 

7  1.794.61583 

8  1.797.89667 

9  1.801.17750 


650 

1 

2 


1.804.45833 
1.807.73917 
1.811.02000 
1.814.30083 
1.817.58167 


5  1.820.86250 

6  1.824.14333 

7  1.827.42417 

8  1.830.70500 

9  1.833.98583 


1.837.26667 
1.840.54750 
1.843.82833 
1.847.10917 
1.850.39000 


2 
3 

4 

5 

6 
7 
8 
9 

570 

1 
2 

3 

4 

5 
6 
7 
8 
9 

580 

1 
2 
3 
4 

5 
6 
7 
8 
9 


1.853.67083 
1.856.95167 
1.860.23250 
1.863.51333 
1.866.79417 

1.870.07500 
1.^3.35583 
1.876.63667 
1.879.91750 
1.883.19833 

1.886.47917 
1.889.76000 
1.893.04083 
1.896.32167 
1.899.60250 

1.902.88333 
1.906.16417 
1.909.44500 
1.912.72583 
1.916.00667 


1 
2 
3 
4 

5 
6 

7 
8 
9 

610 

1 
2 
3 

4 

5 
6 

7 
8 
9 

630 

2 
3 
4 

5 
6 
7 
8 
9 

630 
1 
2 
3 
4 


1.919.28750 
1,922.56833 
1.925.84917 
1.929.13000 
1.932.41083 

1 .935.69167 
1.938.97250 
1. 942.25333 
1.945.53417 
1.948.81500 

1.952.09583 
1 .955.87667 
1. 958.65750 
1.961.93833 
1.965.31917 


1.968.50000 
1.971.78083 
1.975.06167 
1.978.34250 
1.981.62333 

1.984.90417 
1.988.18500 
1.991.46583 
1.994.74667 
1.998.02750 

2.001.36 

2.004.58917 

2.007.87000 

2.011.15083 

2.014.43167 

2.017.71250 

2.020.99333 

2.024.2741 

2.027.55500 

2.030.83583 

2.034.11667 
2.037.39750 
2.040.67833 
2.043.95917 
2.047.24000 

2.050.62083 
2.053.80167 
2.057.08250 
2.060.36333 
2.063.64417 

2.066.92500 
2.070.20583 
2.073.48667 
2.076.76750 
2.080.04833 

2.083.32917 
2.086.61000 
2.089.89083 
2.093.17167 
2.096.45250 

2.099.73383 
2.103.01417 
2.016.29500 
2.109.57583 
2.112.85667 

2.116.13750 
2.119.41833 
2.123.69917 
JS. 125. 98000 
2.129.26083 


670 

1 
2 
3 
4 

5 
6 

7 
8 
9 

680 

1 
2 

3 

4 

5 

6 
7 
8 
9 


2.132.54167 
2.135.82250 
2.139.10333 
2.142.38417 
2.145.66500 

8.148.94583 
2.152.23667 
2.155.50750 
2.158.78833 
2.162.06917 

2.165.35100 
3.168  63083 
2.171.91167 
2.175.19250 
2.178.47333 

8.181.75417 
2.185.03500 
2.188.31583 
2.191.59667 
2.194.87750 

2.198.15833 
2.201.43917 
2.204.72000 
8.208.00083 
2.211.28167 

2.214.56250 
2.217.84333 
2,221.12417 
2.224.40500 
2.227.68583 

2,230.96667 
2.234  24750 
2.237.52833 
2.240.80917 
2.244.09000 

2,247.37083 
2.250.65167 
2.253.93250 
2.257.21333 
2.260.49417 

2.263.77500 
2.267.0558.} 
2.270.33667 
2,273.61750 
2.276.89833 

2.280.17917 
2.283.46000 
2.286.74083 
2.290.02167 
2.293.30250 


700 

1 
2 
3 
4 

5 

6 

7 
8 
9 

710 

1 

2 
3 

4 

5 

6 
7 


720 
1 
2 
3 
4 

5 
6 
7 
8 
9 

730 
1 
2 


5 
•  6 
7 
8 
9 

740 

1 
2 


2.296.58333 
2.299.86417 
2.308.14500 
2.306.42583 
2,309.70667 

2.312  98750 
2.816  26833 
2.319.54917 
2.322.83000 
2.826.11083 

3.829.39167 
2.832.67250 
2.335.95333 
2,339.23417 
3.342.51500 

2.345.79583 
2.349.07667 
2.352.35750 
2.356.63833 
2.358.91917 

2362.20000 
2.365.48093 
2,368.76167 
2.372.04250 
2.375.32333 

3.378.60417 
2.381.88500 
2.385.16583 
2.388.44667 
2.391.72750 

2.395.00833 
2.398.28917 
2.401.57000 
2.404.85083 
2.408.13167 

2.411.41250 
2.414.69333 
2.417.97417 
2.421.25500 
2.424.53583 

2.427  81667 
2.431.09750 
2.434.37833 
2.437.65917 
2.440.94000 

2.444.22083 
2.447.50167 
2,460.78250 
2.454.06333 
2.457.34417 


750    2.460.62500 


d  by  Google 


78 


A.^MEASURES,  WEIGHTS  AND  MONEY. 


750-1000. 


11, — ^Lbnoths — ^Meters  to  Fket  (Concluded). 


Meters.    Feet.    Meters.    Feet.     Meters.    Feet. 


Meters.    Feet. 


Meters.    Feet. 


1.4«0. 82500  800 

2.463.90583 

2.467.18667 

2.470.46750 

2.473.74833 


5  2.477.02917 

6  2.480.31000 

7  2.483.59083 

8  2.486.87167 

9  2.490.15250 

7«0  2.493.43333 

1  2.496.T1417 

2  2.499.99500 
8  2.503.27583 

4  2.506.55667 

5  2.509.83750 
«  2.513.11833 

7  2.616.39917 

8  2.519.68000 

9  2.522.96083 

770  2.526.24167 

1  2.529.52250 

2  2.532.80333 

3  2.536.08417 

4  2.539.36500 

5  2.542.64583 

6  2.545.92667 

7  2,549.20750 

8  2,552.48833 

9  2.555.76917 

780  2,559.05000 

1  2,562.33083 

2  2.565.61167 

3  2.568.89250 

4  2.572.17333 

5  2,675.45417 

6  2,578.73500 

7  2.582.01583 

8  2,585.29667 
0  2.588.67750 


6 

6 
7 
8 
9 

810 

1 
2 
3 
4 


7 
8 
9 

830 

1 
2 

3 

4 

5 
6 
7 


2.591.85833 
2,595.13917 
2,598.42000 
2,601.70083 
2.604.98167 

2.608.26250 
2.611.54333 
2.614.82417 
2.618.10500 
2.621.38583 


840 

1 
2 


2.624.66667 
2.627.94750 
2.631.22833 
2.634.50917 
2.637.79000 

2,641.07083 
2.644.35167 
2,647.63250 
2,650.91333 
2.654.19417 

2.657.47500 
2.660.75583 
2.664.03667 
2.667.31750 
2.670.59833 

2,673.87917 
2.677.16000 
2,680.44083 
2.683.72167 
2.687.00250 

2.690.28333 
2.693.56417 
2.696.84500 
2,700.12.583 
2.703.40667 

2.706.68750 
2,709.96833 
2.713.24917 
2,716.53000 
2.719.81083 

2.723.09167 
2.726.37250 
2.729.65333 
2.732.93417 
2.736.21500 

2.739.49583 
2.742.77667 
2.746.05750 
2.749.33833 
2.752.61917 

2,755.90000 
2,759.18083 
2,762.46167 
2,765.74250 
2,769.02333 

2.772.30417 
2.775.58500 
2,778.86583 
2,782.14667 
2.785.42750 


850 

1 
2 
3 
4 

6 
6 

7 


870 

1 
2 
3 

4 

5 
6 
7 
8 
9 


2.788.70883 
2.791.98917 
2.795.27000 
2.798.55083 
2.801.83167 

2.805.11250 
2.808.39333 
2.811.67417 
2.814.95500 
2.818.28583 

2.821.51667 
2.824.79750 
2.828.07833 
2. 831.35917 
2,834.64000 

2.837.92083 
2.841.20167 
2.844.48250 
2.847.76333 
2.861.04417 

2.854.32600 
2.857.60583 
2.860.88667 
2.864.16750 
2.867.44833 

2.870.72917 
2.874.01000 
2.877.29083 
2,880.57167 
2,883.85250 

2,887.13333 
2,890.41417 
2,893.69500 
2,896.97683 
2.900.26667 

2.903.53750 
2.906.81833 
2.910.09917 
2.913.38000 
2.916.66083 

2.919.94167 
2,923.22250 
2,926.50333 
2.929.78417 
2.933.06500 

2.936.34583 
2,939.62667 
2.942.90750 
2.946.18833 
2.949.46917 


910 
1 
2 

3 
4 

5 
6 
7 
8 
9 

920 

1 
2 


2.952.75000 
2,966.03083 
2.959.31167 
2,962.59250 
2.965.87383 

2.969.15417 
2.972.43500 
2. 975. 71 583 
2,978.99667 
2.983.27750 

2.985.55833 
2.988.83917 
2.992.12000 
2.995  40083 
2.998.68167 

3,001.96250 
3.005.24333 
3.008.52417 
3.011.80500 
8.015.08583 

3.018.36667 
3.021.64750 
3.024.92833 
3.028.20917 
3.031.49000 

3.034.77083 
3.038.05167 
3.041.33250 
3.044.61333 
3.047.89417 

3.051.17500 
3.054.45583 
3.057.73667 
3.061.01750 
3.064.29833 

3,067.67917 
3,070.86000 
3.074.14083 
3.077.42167 
3.080.70250 

3.083.98333 
3,087.26417 
3.090.54500 
3.093.82583 
3.097.10667 

3.100.38750 
3,103.66833 
3.106.94917 
3.110.23000 
3,113.51083 


1 
2 
3 

4 

5 
6 
7 
8 
9 

60  3.l49.6000t 

1  3. IS. 88083 

2  3.156.  IflC; 

3  3.159.44259 

4  3.162.72333 

5  3.166.00417 

6  3,I69.28SM 

7  3.172. S6«3 

8  3.175.84667 

9  3.179.11750 

70  3.182.411833 

1  3.18S.6891: 

t  3.188.97009 

3  3.192.2M83 

4  3.19S.531(7 

6 
6 
7 
8 
9 

60  8.215.21667 

1  3.218.4975C 

2  S. 221. 77833 

3  3.225.0S91T 

4  3.228.34600 

5 

6 
7 


I 
2 
3 
4 

5 
6 
7 
8 
9 

1000  3.280.83313 


d  by  Google 


AREAS^METRIC  AND  ENGLISH, 


70 


12.— Arbas. 


1  sq,  mUHm^ter  (sq.  mm)  - 
100  8Q.  millimeters  » 

1  sq.  c»nHmH€T  («q. cm)  — 
100  sq.  centimeters-" 

1  sq.  decimeter  (sq.  dm)  — 

100  sq.  decimeters  ( -» 1  centare)  — 

1  sq.  mtttr.  - 
100  sq-  meters  ( —  1  are)  — 

1  sq.  dtkatntUt  (sq.  Dm)  — 
100  sq.  ddcameters  ( —  1  hectare) 

—  1  *7.  k^ctom^Ur.  — 
100  sq.  hectometers— 

1  sq.  kilomeUr  (sq.  K  m)  — 
100  sq.  kilometers"' 

1  sq.  myriartuUr  (sq.  Mm)  — 


Sq.  Ins. 


Sq.  Feet. 


Sq.  Yds. 


Acres. 


00156000 


00001076 


15499969|. 00107639  .0001196 

10763867.0119699 

9969(10 .  76386711 .  1959853 

6911076.3867119.59853 

107638.6711959.86312 

10763867   1195985 


15.499969 
1549. 
154999. 
Sq.  Miles 
.3861 
38.61 


.0002471 

.0247104 

4710489 

31247.10489 

24710.489 


d  by  Google 


80 


i.—MEASURES,  WEIGHTS  AND  MONEY. 


13. — Areas,  Equivalbnts.    1-10. 


Square 

Square 

Square 

Square 

Square 

Square 

Inches. 

Millimeters. 

Inches. 

Centimeters. 

Feet. 

Meters. 

0.00165 

M 

1 

0.1550 

„ 

1 

« 

O.O9290 

0.00310 

a 

2 

0.3100 

a 

2 

■■ 

0.18581 

0.00465 

. 

3 

0.4650 

« 

3 

1. 

0.27871 

0.00620 

- 

4 

0.6200 

- 

4 

- 

0.87161 

0.00775 

» 

5 

0.7750 

a 

5 

„ 

0.46462 

0.00930 

ca 

6 

0.9300 

■■ 

6 

■> 

0.55742 

0.01085 

mt 

7 

1 

C31 

6  452 

7 

B> 

0.65033 

0.01240 

a 

8 

1.0850 

■■ 

8 

■■ 

0.74323 

0.01395 

- 

9 

1.2400 

= 

9 

- 

0.83618 

1 

_ 

645.16 

1.3950 

_s 

10.764 

„ 

1 

2 

M 

1.290.33 

_ 

12.903 

21.528 

mt 

2 

3 

. 

1.935.49 

n 

19.855 

32.292 

n 

3 

4 

- 

2.580.66 

- 

25.807 

43.055 

- 

4 

5 

M 

8.225.81 

« 

32.258 

68.819 

^ 

5 

6 

M 

8.870.98 

E> 

38.710 

64.588 

■• 

6 

7 

M 

4.516.14 

>1 

45.161 

75.847 

M 

7 

8 

B 

6.161.30 

OS 

51.613 

86.111 

M 

8 

9 

" 

5.806.46 

9 

■■ 

58.065 

96.875 

"• 

9 

Square 

Yards. 

Square 
Meters. 

Square 

Miles. 

Square 
Kilometers. 

Acres. 

Hectors. 

1.1960 

2 

2.8920 

- 

0.8361 

0.6723 
2 

0.3861 
0.7722 
1 
1.1583 

- 

2 

2.5900 

3 

1 
2 

2.471 
3 

E 

0.4047 
0.8094 

1.2141 

3 

3.6880 
4 

4.7839 
5 

2 

2.5084 

3 

3.3445 

4 

4.1807 

1.5444 

1.9306 

2 

2.3166 

2.7027 

- 

4 
5 

5.1800 
6 

7 

4 

4.942 

5 

6 

7 

2 

1.6187 

2 

2.0384 

2.4281 

2.8828 

5.9799 
6 

7 
7.1769 

2 

5 

5.0168 
5.8529 
6 

3 

3.0888 
3.4749 

4 

- 

7.7700 
8 
9 
10.3600 

7.418 

8 

9 

9.884 

"* 

3 

8.2376 
3.6422 

4 

8 

8.3719 
9 

9.6679 
10.7689 

2 

6.6890 

7 

7.5262 

8 

9 

5 
6 

7 
8 
9 

- 

12.9500 
15.5400 
18.1300 
20.7200 
23.3100 

12.856 
14.826 
17.297 
19.768 
22.239 

2 

5 

6 

7 
8 
9 

d  by  Google 


AREAS,  VOLUMES— METRIC  AND  ENGUSH, 


81 


14. — ^Lanb  Mbasurb  (Squarb) 

1  square  inch '^ 

144  SQuare  inches —  1  square  foot 

9  square  feet —  1  square  yard 

304  square  yards  (  —  272J  sq.  ft.) —  1  square  rod   — 

40  square  rods  (— 1210  sq.  yds.— 

10890  sq.ft.) -Irood  - 

4  roods  ( «  160  sq.  rods—  4840  sq. 

yds.  —  48660  sq.  ft.) "  I  acre  — 

640  acres  (-3.097,600  sq.  yds.- 

27.878.400  sq.  ft.) -  1  square  mile~ 

36  square  miles  (  —  23040  acres— 

1.003.622.400  sq.  ft.) - 1  township     - 


6.4516  sq.  centimeters 
0.09290341  sq.  meter. 
0.836131  sq.  meter. 
25.292954  sq.  meters. 

0.1011718  hectars. 

0.4046873  hectars. 

258.99985  hectars. 

9323.9945  hectars. 


15. — ^Tbxas  Land  Mbasurb. 
(Also  tised  in  Mexico,  New  Mexico,  Arizona  and  California.) 


24. MO, 000 


sq.  raras  (sq.  of  5 ,099 


1.000.000 

2$. too. 000 

12.500.000 

1,333,333 

6.250,000 

7. 225. COO 

1.612,800 

l.SO€.40O 

903.200 

451.600 

225,800 


sq.  vans  (sq.  of  1 .000 
sq.  Tsras  (sq.  of  5,000 
sq.  Taraa  (aq.  of  3 .535. 5 
sq.  varas  (sq.  of  2 .886. 7 
aq.  varas  (sq.  of  2.500 
sq.  varas  (sq.  of  2,688 
sq.  varas  (sq.  of  1 .900. 8 
sq.  varas  (sq.  of  1 ,344 


77 

-  4.428 

-  2,214 
»  1.476. 

-  1,107. 

-  1,280 

-  640 

-  320 
sq.  varas  (sq.  Of  950.44  varas)  —  i  section  —  160 
sq.  varas  (sq.  of  672  varas)  —  i  section  —  80 
sq.  varas  (sq.  Of      475         varas)— 1. 16  section—        40 

5.645.376  sq.  varas  (sq.  Of        75.137  varas)— 4.840sq. yd.-  1 

To  find  the  number  of  acres  in  any  number  of  square  varas, 

the  latter  by  177  (or  to  be  more  exact,  by  177i),  and  cut  off  six 

1  vara  —  33|  inches  1.900.8  varas  —  1  mile 


varas) «- 1  league  and 

1  labor  —  4.605 

varas)  —  1  labor  —      177. 136  acres, 

varas) »  1  league  —4.428.4     acres, 

varas) » i  league  —2,214.2     acres, 

varas)— i  league  —  1.476.13   acres, 

varas)  —  i  league  —1,107.1 
varas) 

varas)— 1  section 
varas)  —  i  section 


acres. 

acres. 

acres. 

acres. 

acres, 
acre, 
mtdtiply 
decimals. 


16. — Wbights  and  Mbasurbs  of  thb  Philippines. 


1  polgada  (11  lines)  - 

ipie 

1  Tara  — 

igantsb  — 


.927 
11.126   Inches. 
33.375   Inches. 

.8796  gallon. 
21.991    gaUons. 


1  Ubra  (16  onao)     -  1 .  0144  lb.  av. 

1  arroba                  —  25.360    lb.  av. 

1  catty  (16  tael)     -  1.394    lb.  av. 

1  pecul(  100 catty)  -  139.482    lb.  av. 


17. — ^VOLUMBS. 


Cu.  Ins. 

Cu.  Feet. 

Cu.  Yds. 

(1  cubic  cm)    - 1  milliliter  (m  1).. . .  - 

.06102338 

.61023378 

6.1023378 

61.023378 

610.23378 

6102.3378 

61023.378 
610233.78 

.00003531 

.00035314 

.00353145 

.03531445 

.35314455 

3.5314455 

35.314455 
858.14455 

10  milliliters  (  —  10  cubic  c  m)  — 

I  centilit^  (cV) - 

10  centiliters  ( —  A  cubic  d  m)  — 

I  deciliter d\) - 

10  deciUters  (-  1  cubic  dm)  - 

1  liter - 

.00130794 

10  Htert  ( « 10  cubic  d  m) 

l<fcfea/*W(Dl)....- 
10  dekaliters  (  —  A  cubic  meter)  — 

I  hectoliter  {H\)....'« 
10 hectoliters  (-1  cubic  meter)  - 

1  kiloliter  {K\) - 

lOkiloUters - 1  myrialiter  (M 1).. .  - 

.01307943 

.13079428 

1.3079428 
13.079428 

82 


i.— MEASURES,  WEIGHTS  AND  MONEY, 

18. — VOLUMBS.  EgUIVALBNTS.      1-10. 


Cubic 
Inches. 


Cubic 
Millimeters 


Cubic       Cubic 
Inches.  Centimet's 


Cubic 
Feet. 


Cubic 
Meters. 


Cubic     Cubic 
Yards.   Meters, 


0.000061- 
0.000122  > 
0.000183- 
0.000244- 

0.000305- 
0.000366- 
0.000427- 
0.000488- 
0.000549- 

1 
2 
3 
4 

6 

6 
7 
8 
9 


•  16.387.2 
.  32.774.3 

•  49.161.5 

•  65.548.6 

•  81.935.8 

•  98.323.0 
.114.710.1 
-131.097.3 
'  147.484.5 


0.0610- 
0.1220- 
0.1831- 
0.2441- 

0.3051- 
0.3661- 
0.4272- 
0.4882  = 
0.5492- 

1 
2 
3 
4 

5 

6 

7 


•  16.3872 

•  32.7743 

-  49.1615 

-  65.5486 

-  81.9358 

-  98.3230 
-114.7101 
-131.0973 
-147.4845 


2 
3 
4 

5 
6 
7 
8 
9 

35.314- 

70.629- 

105.943- 

141.258- 

176.572- 
211.887  = 
247.201- 
282.516- 
317.830- 


-0.02832 
>  0.05663 
-0.08495 
-0.11327 

-0.14159 
-0.16090 
-0.19822 
-0.22654 
-0.25485 

-1 
-2 
-3 
-4 

•5 

-6 
-7 
=  8 
-9 


1 

1.8079- 
2 
2.6159- 

3 

3.9238- 

4 

5 

6.2318- 

6 

6.5397- 
7 
7.8477- 


-  0.7645 
•1 

- 1.5291 
-2 

>  2.2937 
-3 

-3.0582 
'  3.8228 
>4 

.4.5874 
'5 

.5.3519 
•6 


8  -6.1165 

9  -6.8810 
9.1550-7 

10.4635-8 
11.7715-9 


19. — Cubic  Mbasurb. 

1  cubic  inch  —16. 887S  cubic  centimeters. 

1728  cubic  inches —  1  cubic  foot  —    .02832  cubic  meter. 

27  cubic  feet  ( -  46656  cu.  ins.)  —  1  cubic  yard  —   0 .  7646  cubic  meter. 
16  cubic  feet  ( -  27648  cu.  ins.)  —  1  cord  foot    —  0 .  45307  cubic  meter. 
8  cord  feet  ( -  4IS  cu.  yds.  - 
128  cu.  it.  -  221184  cu.  ins.)  - 1  cord  (wood) -8. 6246  cubic  meter. 


20. — CAPAcrriBS  (Liquid). 


U.S. 
Apoth. 
Scruples 


U.S. 
Apoth. 
Drams. 


U.S. 
Liquid 
Ounces. 


u.a 

Liquid 
Quarts. 


(1  cubic  cm)  —  1  milliliUr  (m  1).. .  ■ 
10  milliliters  ( =  10  cubic  c  m)  ■= 

IcentiliUr  (cl) - 

10  centiliters  ( —  A  cubic  d  m)  — 

I  deciliter  {dl)...." 
10  deciliters  t  —  1  cubic  d  m)  — 

I  liter ■ 

10  liters  ( —  10  cubic  d  m)  => 

I  dekaliter  (Dl)..,' 
10  dekaliters  (A  cubic  meter)  == 

I  hectoliter  (Hl)...- 
10  hectoliters  ( —  1  cubic  meter)  =. 

IkiloliteriKl)...." 
10  IdloUters - 1  myrialiiers  (M  1). ■ 


81153168 .27061066 


8.1153168^2 
U.S. 


.7051066 


0010S666 
338138201.01050682 


Liquid  {27.051056,3.3813820 .10566619 

26417047|270.51056{33.8138201  0566619 

2.641704712705. 1056|338. 1382010  566811 

126.417047127051 .05613381 .3820105  6GSi9 


1264.17047 
12641.7047 


vGqc 


33813.8201066  6819 
838138.20,10666.^9 


CAPACITIES— METRIC  AND  ENGLISH. 


8S 


21. — Capacitibs.  Bquivalbnts.    I-IO. 


(ec) 


U.S. 

Uquld 

Oi. 


MlUfll- 
tere. 
(oe.) 


Apothe-Apothe- 


Drama.  Scruples. 


u.a 

pothe- 
caries' 


MUUli- 

ters. 

(cc.) 


U.S. 
Liquid 
Quarto. 


Liters. 


U.a 
Liquid 
Gallons.   Liters. 


2  -0.06763 

3  -0.10144 

4  -0.13526 


•0.16I07 
-0.20Z88 
-0.23670 
-0.27061 
-0J4M32 


2S.S74-I 

».  147-2 
88.721.J 
llg.296.4 

1I7.0E9-5 
in.442-6 
207.0K-7 
m.S90-8 

2CC.163-9 


1  -0.2705 

2  -0.M10 

3  -0.8115 
3.6867-1 

4  -1.0820 

5  -  U525 

6  -lUt231 

7  -1.8936 
7.3934-2 

8  -2.1641 

9  -2.4346 
11.0901-3 
14.7869-4 

18.4836-5 
22.1803-6 
25.8770-7 
29.5737-8 
33.2704-9 


0.8115-  1 

1  -  1.2322 
1.6231-  2 

2  -  2.4645 

2.4346-  3 

3  -  3.6967 
3.2461-  4 

4  -  4.9290 
4.0577-  5 

4.8692-  6 

5  -  6.1612 
5.6807-  7 

6  —  7.3934 

6.4923-  8 

7  -   8.6257 
7.3038-  9 

8  —  9.8579 

9  -11.0901 


1 

1.05668- 

2 

2.11336« 

3 

3.17005- 

4 

4. 22673 > 

5 

5.28341- 
6 

6.34009- 
7 

7.39677= 

8 

8.45345- 

9 

9.51014- 


0.94636 
I 

1.89272 
2 

2.83908 

3 

3.78543 

4 

4.73179 

5 

5.67815 

6 

6.62451 

7 

7.57088 

8 

8.51723 

9 


0.26417-  I 

0.52834—  2 

0.79251-  3 

1  -  3.78543 

1.05668-  4 

1.32085-  8 

1.58502-  6 

1.84919-  7 

2  -  7.57087 

2.11336—  8 
2.37763—  9 

3  -11.35630 

4  -15.14174 


- 18.92717 
—  22.71261 

7  -  26.49804 

8  -30.28348 

9  *        -34.06891 


22. — Liquid  Mbasurb. 

1^*7/    -0.1183 

4  gills. -Iptni -0.47318 

2  pints  (-8  gills) —  1  quart -0.94636 

4  quarts  (-8  pinU- 32  gills)   "Xeallon -3.78543 

aijgallons  (-126  quarts-252  pints) -  1  5arrW       ...- 119. 2412 

2  barrels  ( -  63 gals.  =  252  qts.  -  504  pts.) .  .  -  1  hogshead. . . .  =  238 .  4824 
2  hoesheads(  -  4  bbls. »  126  gals  -  504qts.)  -  1  pipe,  or  buH  ^  470 .  9647 

2  pipes  (-8  bbls.-  252  gals.  -  1008  qts). .  .  -  Uwn       -  953.9295 

1  tiera— 42  gals.     1  puncheon  —  84  gals. 


liters 


23. — Apothbcaribs'  Mbasurb  (Fluid). 

1  mtntm  (drop)  =  0 .  00006161  liters 

60  minims. =  1  fluid  drachm  -0.0036967 

8  fluid  drachms  ( —  480  minims) —  1  fluid  ounce.  .  —  0 .  029574 

16  fluid  otmces  ( - 128  drachms  -  7680 

minims) '"Ipint -0.473179 

gpinte  (-128  Buid  ounces- 1024  ,^^^».i 

drachms-  61440  minims) -  1  gallon., .  Bigrti?e?!,^W)gle 


84 


i.—MEASURES.  WEIGHTS  AND  MONEY. 
24. — Capacitibs  (Dry). 


U.S. 
Dry 
Pints. 


U.S. 

Dry 

Quarts. 


U.S. 
Pecks. 


U.S. 
Bxishels. 


(i  cubic <: f»)  —  1  milliliUr  (ml).. 
10  milliliters  ( —  10  cubic  c  m)  — 

1  centiliter  (cl)... 
10  centiliters  ( —  ^ycubic  d  m)  = 

1  deciliter  (dl)... 
10  deciliters  ( —  1  cubic  d  m)  — 

llHtr 

10  liters  (  —  10  cubic  d  m)  — 

I  dekaliter  (D\).. 
10  dekaliters  ( -•  A  cubic  meter)  «- 

\  hectoliter  H\)... 
10  hectoliters  (  —  1  cubic  meter)  — 

lkihliter(K\)... 
10kik>liters - 1  myrialiter  (M  1). 


.00181616 
.01816155 
18161551 
1 .8161551 
18.16155l'9 
181.6155190 


00000606 

00906078 

00060775 

9060n54 

060n54 

807754 


00113510 
01135007  00283774 
11360069  02837742 
28377423 
11.35096012.8377423 


1816. 1551  >906 
118161. 55lk)080 


07754 

7754 


113. 
1135. 


5006028 


0060283 


.377428 
t.77423 


26. — Capacitibs.  Equivalbnts.    I-IO. 


U.S. 
Dry 
Quarts.  Liters. 


U.S. 
Pecks. 


Deka- 
Lltere.   liters. 


U.S. 
Pecks. 


U.  8.      Hecto- 
Bushels.    liters. 


U.  S.     Heoto- 
Busbels    Uters 
per  per 

Acre.    Hectar. 


0.9081-1 

1  —1.1012 
1.8162-12 

2  -2.2025 

2.7242=3 

3  -3.3037 
3.6323-4 

4  -4.4049 
4.5404-5 

5  -6.5061 
5.4485-6 

6  -  6.6074 
6.3565-7 


0. 11351 »« 
0.22702- 
0.34053- 
0.45404- 

0.56755- 
0.68106- 
0.79457  = 
0.90808- 
1 

1.02157- 

2 

3 

4 


7  -7.7086    5 
7.2646-8  6 

8  -8.8098  |7 
8.1727-9  8 

9  -9.9110   9 


I 
2 
3 
4 

5 

6 

7 
8 
8.80982 

-  9 

-17.61964 
-26.42946 
-35.23928 

-44.04910 
-52.85892 
-61.66874 
-70.47856 
=  79.28838 


0.8810= 

1 

1.7620- 

2 

2.6429- 

3 

3.5239- 

4 

4.4049- 

S 

5.2859- 

6 

6.1669- 

7 

7.0479- 

7.9288- 

8 

9 


I 

1.1351 

2 

2.2702 

3 

3.4053 
4 

4.5404 
5 

6.6755 
6 

6.8106 

7 

7.9457 

8 

9 

9.0808 
10.2159 


1  -  0.35239 

2  -0.70479 
2.83774-1 

3  -1.05718 

4  -1.40957 

5  -1.76196 
5.67548=-a 

6  -2.11436 

7  -2.46675 

8  -2.61914 
8.51323-3 

9  -3.17154 
11.35097-4 

14.18871-5 
17.02645-6 
19.86420-7 
22.70194—8 
25.53968-9 


1  -0.87078 
1.14840-1 

2  -1.74158 
2.29680-2 

3  -2.61333 
3.44519-3 

4  -8.48311 
4.59350—4 

5  -44538B 

5.74199-5 

6  -5.234«7 
6.89039-6 

7  -6.09545 

8  -6.96<» 
8.03879-7 

9  -7.83700 

9.18719-8 
10.33558-9 


26. — Dry  Mbasurb. 

1  pint . .  -  0 .  55061  liter. 

2  pints '•'I  quart -  1 .10128  liters. 

8  quarts  (-16  pints) -1  peck -8.80082  liters. 

4  pecks  ( =»  32  quarts  -  64  pints) -  1  Uruck  bushel"  0 .  35230  hectoliter. 

Note. — 1  heaped  bushel  — 1 J  struck  bushels     The/<eonc  ofithe  beaped 
bushel  must  not  be  less  than  6  mches  high.       Digitized b  *  -^^^iio 


"^^^CSb^t 


WEIGHTS^METRJC  AND  ENGUSH, 

% 

27. — Massbs  (Wbiohts). 


Grains. 


Avoir. 
Oiinces. 


Troy 
Ounces. 


Troy 
Pounds. 


(*1  atbic mm)  I  miUigram  (m g) .  - 
10  milligrams  (*10  cubic  m  m) 

->  1  cfHiiiram  (c  g) . .  - 
10  centigrams  (*A  cubic  c  m) 

—  1  decigram  (d  g). . .  ■ 
10 decigrams    {*l  cubic  cm) 

—  1  gram ■ 

10 grams  (*10 cubic  cm) 

—  1  dekagram  (Dg) . .  ■ 
10  dekagrams  (*1  deciliter) 

—  1  htctogram  (H  g)  .  ■ 
10  hectograms  (*1  liter) 

.     -  1  kilogram  (Kilo).  - 
10  kilograms    (*10Uters) 

—  1  myriagram  (Mg)  ■ 
10  myriagram  (♦I  hectoliter) 

—  1  QUtHtal ■ 

10  quintals       {*1  cubic  meter) 

—  1  milltr  or  tonneau  ■ 


01543236 
15432356 
1.5432856 


15.432366 
Avoir. 
Pounds. 
.02204622 


00036274 
00362740 
03527396 

36273057 


00082151 
00321507 
03215074 


.32150742 
.5273&57^.2150742 


00026702 
00267023 

02679220 
26792285 


220462233.1 
t2.2046223|35.278957|32.150742|2.6702285 
!22.046223|352. 739571321 .50742126.792285 
220.4622313527.8957  3215.0742|267.92285 
2204.6223I35273.057I32150.742I2679.2286 


'Equivalent  quantity  of  water  at  max.  density. 


38. — Wbiohts,  BQurvALBNTS.    I-IO. 


OTalD&    Orams. 


Arotrdu- 

pols 
Ounees. 


Troy 
Orams.  Ounces.    Orams. 


Avoirdu- 
pois      Kllo- 
Poonds.  grama. 


Troy       KUo- 
Pounds.  grams. 


1  .0.06480  0. 

2  —0.129600. 

3  -.0.194400. 

4  -0.25920  0. 


03S37-  I 

07055-  2 

10582-  3 

14110-  4 


0.03215-  I 

0.06430-  2 

0.09645-  3 

0.12860-  4 


1  —0.45.159 

2  -0.9071 
2.20462-1 

3  - 1.36078 


-0.32399  0 
-0.38879  0 
-0.45359  0 
-0.51839  0 
-  0.58319  0 


17637- 
.21164- 
34692- 
28219- 
31747- 


0.16075- 
0.19290- 
0.22506- 
0.25721- 
0.28936- 


15.4324-1 

30  8647-2 

46.2971-3 
61.7294-4 

77.1618- S 
93. 5941-6 
168  0265-7 
123.4589-8 
U8.S912-9 


-  28.34951 

-  56.69912 

-  85.0486  3 
-113.39814 

- 141.7476  B 
-170.0972  6 
-198.4467  7 
-226.79628 
-265.1467  9 


8 

6 
7 
8 
9 

-  31.10348 

-  62.20696 

-  93.31044 
-124.41392 


4 

4.40924- 
8 

6 

6.61387- 

7 

8 

8.81849- 
9 


-165.5174011.02811- 


[.02811- 

-Id6.62088jl3. 22773- 

7  15.43236- 

.63698= 

n9.84160«: 


-165.5 

-id6.fi 

-217.72437  1 
-248.82785 17. ( 
-279.931331 


1.81437 

2 

2.26796 

2.72155 

3 

3.17515 
3.62874 
4 
4.08233 

5 

6 

7 
8 
9 


1  -0.37324 

2  -  0.74648 
2.67923-1 

3  -1.11973 

4  -1.49297 

5  - 1.86621 
5.35846-2 

6  »=  2.23945 

7  -2.61269 

8  -2.98593 
8.03769=- 3 

9  =3.35918 
10.71691-4 

13.39614=^5 
16.07537=6 
18.75460-7 
21.43383-8 
24.11306-9 


d  by  Google 


8$  i.^MEASURES,  WEIGHTS  AND  MONEY. 


29. — ♦Apothrcaribs  Weight. 

—  1  grain -  0 .  06480  gran\. 

20  grains -  1  scrupk 1 .  29698  gram^ 

3  scruples  (  -  60  grains) -  1  dram -  3 .  88794  grams. 

8  drams  ( —  24  scruple  *  480  grains) —  1  ounce »  31 .  10348  grams. 

12o\mces  (  —  96  drams —  228  scruples  — 

5760  grains) —  1  p<mmd —  0 .  87824  kilogram. 


30. — *Troy  Wbioht. 

1  grain —  0 .  06480  gram. 

24  grains —  I  pennyweight  —  1 .  55517  grams. 

20  pennyweights  (  —  480  grains) —  1  ounce —  31 .10348  grams. 

12oimces  (-240  penn3rweights  -  5760 

grains) --l  pound -0.37324 kilogram. 


31. — Avoirdupois  Weight  (Short  Tons). 

1  grain —0.06480     gram. 

27U  grains  (-27.34376  grains).. . .  —  1  dram -1.771845   grams. 

16  drams  ( -  437|  grains) -  1  ounce —  28 .  3495     grams. 

16  ounces  ( -  256  drams  =  7000 

grains) -1  pound -0.4535924  kilogram. 

25  pounds  ( —  400  ounces) —  1  Quarter —11. 33981 1  kilograms. 

4  quarters —  1  hundred  weight  =  45 .  35924    kilograms. 

20  hundred  weight (2000  lbs.)  - 1  ton -  907. 18486 kilograms. 


32. — Avoirdupois  Weight  (Long  Ton). 

1  grain —  0 .  06480     gram. 

27H  grains  (-27.34375  grains).. -1  dram -  1  771846   grams. 

16  drams =.  1  ounce -  28 .  3495     grams. 

16  ounces =  1  ^ound -  0 .  4535924  kilogram, 

112  pounds —  1  hundred  weight  =  50.S02Z&     kilograms. 

20  hundred  weight .  . .  (2240  lbs.)  -^l  ton =  1016 .  047    kilograms. 

*  The  grain,  ounce  and  poxmd  Apothecary  and  Troy  weight  are  respect- 
ively equivalent. 


d  by  Google 


WEIGHTS— METRIC  AND  ENGUSH. 


87 


IS. COMPAUSOlf  OV  THB  VaRIQUS  ToNS  AND  P0XTND6  IN  V8B 

IN  TRB  Unitbd  States. 
Prom  1  to  10  Units. 


Long  Tons. 

Short  Tom. 

If  etrie  Tons. 

KUogrsms. 

Avoirdupois 

TT07  Pounds. 

.0003673$ 
90044643 

!90073469 

.00098421 

.00041143 
00060000 
!00082286 
.00100000 
.00110231 

.00037324 
.00045359 
.00074648 
.00090718 
.00100000 

.37324 
.46359 
.74648 
.90718 

1 

1.64571 
2 
2.20462 

1.21528 
2 

2.43056 
2.67923 

.09110204 
.90133929 
.001 46939 
.00178971 
.90183673 

.00123439 
.00158000 
.00164571 

!00205714 

.00111973 
.00136078 
.00149297 
.00181437 
.00186621 

1.11973 
1.36078 
1.49297 
1.81437 
1.86621 

2.46857 

3 

3.29143 

4 

4.11429 

3 

3.64583 
4 

4.86111 
5 

.00196841 

!00223214 
.00257143 

.00267857 

.00220462 
.00246857 
.00260000 
.00288000 
.00300000 

.00200000 
.00223945 
.00226796 
.00261269 
.00272155 

2 

2.23945 

3.26796 

2.61269 

2.72155 

4.40924 

4.93714 

8 

5.76000 

6 

5.35846 

6 

6.07639 

7 
7.29167 

.00293878 
.00295262 
.00312500 
.00330612 
.08357143 

illff 

.00298593 
.00300000 
.00317515 
.00335918 
.00362874 

2.98693 

3 

3.17515 

3.35918 

3.62874 

6.58286 

6.61387 

7 

7.40571 

8 

8 

8.03769 
8.50694 
9 
9.72222 

.0(893683 
.60401786 
.00492103 
.0O59OS24 
.00088944 

.00440924 
.00410000 
.00561156 
.00661387 
.00ni618 

.00400000 
.00408233 
.00500000 
!00600000 
.00780000 

4 

4.08233 
8 
6 

7 

8.81849 

9 

11.0231 
13.2277 
15.4324 

10.71691 
10.93760 
13.39614 
16.07537 
18.76460 

.00787365 
.00888786 
.89287 
.98421 

1 

.00881849 
.00992080 

1 

1.10231 

1.12000 

!90718 
1.01605 

8 

9 

907.18 
1,000.00 
1.016.05 

17.6370 
19.8416 
2.000.00 
2.204.62 
2.240.00 

21.43383 
24.11306 

2.430.56 

2.679.23 

2.722.22 

1.78S71 
1.96841 

2 

2.67857 

2.90263 

2 

2.20464 

2.24000 

J 

3.30693 

1.81437 
2 

3.03209 
2.72155 

J 

1.814.37 
2,000.00 
2.033.09 
2.721.65 
3.000.00 

4.000.00 
4.409.24 
4.480.00 
6.000.00 
6.613.87 

4,861.11 

6.358.46 
6.444.44 
7,291.67 
8.037.69 

a 

3  67143 
3.93683 
4 
4.46429 

4' 

4.40924. 
4.48000 

5 

3.04814 

3.62874 

4 

4  06419 

4.63592 

3.048.14 
3,628.74 
4.000.00 
4.064.19 
4.535.93 

6.720.00 
8.000.00 
8,818.49 
8,960.00 
10.000.00 

8.166.67 
9.722.22 
10.716.91 
10.888.89 
12.152.78 

4.92103 
S 

5.35714 
5.90524 

6.51156 
5.60000 

6 

6.61387 

6.72000 

5 

5.08024 
5.44311 
6 
6.09628 

5.000.00 
5.080.24 
5.443.11 
6.000.00 
6,096.28 

11.023.11 
11.200.00 
12.000.00 
13.227.73 
13.440.00 

13,396.14 
13.611.11 
14.583.33 
16.075.37 
16.333.33 

6.25000 

6.88044 

7 
7.14288 

7.87365 

7 

7.71618 
7.84000 
8 

8.81849 

6.35029 
7 

7.11232 
7.25748 

8 

6,350.29 
7.000.00 
7.112.32 
7.257.48 
8.000.00 

14.000.00 
15.432.36 
15,680.00 
16.000.00 
17.636.98 

17.013.89 
18.754.60 
19.055.56 
19,444.44 
21.433.83 

8 
8.03571 

8.85788 

• 

8.96000 

9 

9.92080 
10.08000 

8.12838 
8.16466 
9 
9.14442 

8.128.38 
8.164.66 
9.000.90 
9.144.42 

17.920.00 
18.000.00 
19,841.60 
20.160.00 

21.777.78 
21.875.00 
24.113.06 
24,500.00 

68 


i.—MEASURBS,  WEIGHTS  AND  MONEY. 


84. — SiMPLB  AND  Compound  Units  in  Common  Usb,  Bqtjivalbnts. 
Base:    1  Meter-  39.37  Inches,  as  per  U.  S.  Law. 


To  reduce  A  to  M. 


Mult,  by  I     Log. 


To  reduce  M  to  A. 


Log.        Mult,  by 


LENGTH. 


MlladOOOthflOfanln.). 

lOOthBof  an  Inch 

64UiB  of  an  Inch 

Inches 

Feet 

Yards 

Rods 

Chains  (66  ft.) 

Stations  (100  ft.) 

Miles 


.0254 

.264 

.3968758 

2.540005 

.3048006 


8.4048346  1. 
9.40483460. 
9.5986546  0. 
0.4048346  9. 
9.48401580. 


5.029210 
20.11684 
30.48006 
1.609347 


91440189.961137: 


0.70149983 
1.3035597  8 
1.48401588 
0.2066497  9, 


5951654 

5951654 

4013454 

5951654 

51598423, 

03886291, 

2985002    , 

6964403    , 

5159842    , 

7933503 


39.37 

3.937 

2.51968 

.3937 

28083''3 

09361^1 

1988384 

0497096 

0328083 

.62137 


Millimeters 

Mllllmeten 

MUUmeters 

Centimeters 

Meters 

Meters 

Meters 

Meters 

Meters 

Kilometers 


AREA  (Square  or  circular). 


Square  mils 

Square  Inches 

Square  feet 

Square  yards 

Square  rods 

Acres 

Quarter  sections  (160  a.) 
Sections  (eq.  miles) . . , 
Townsliips  (36  sec.). 


.0006452 

6.451626 

.0929034 

.8361307 

25.29295 

0.4046873 

64.75 

258.99985 

9323.9945 


6.8096692 
0.8096692 
8.9680316 
9.9222742 
1.4029996 
9.6071196 
1.8112402 
2.4132995 
3.9696020 


3.1903308 
9.1903308 
1.0319684 
0.0777258 
8.5970004 
0.3928804 
8.1887598 
7.5867005 
6.0303980 


1649.997 
.1549997 
10.76387 
1.195985 
.0395367 
1.4710439 
.015444 
.003861 
00010725 


Sq.  mllllmeten 
Sq.  centimeten 
Sq.  meters 
Sq.  meters 
Sq.  meters 
Hectars 
Hectars 
Hectars 
Hectars 


VOLUME  (Cubic  or  globular). 


Cubic  inches. 
Cubic  feet.... 
Cubic  irards. . 
Acre  feet 


16.38716 

02831702 

.7645594 

43560 


1.2145038 
8.4520475 
9.8834! 
4.6390879 


8.7854962 
1.6479525 
0.1165887 
5.3609121 


.0610234 
35.31445 
1.3079428 
00002296 


CTublc  oent'mtrs 
Oiblc  meters 
Oiblc  meters 
(^bic  feet 


CAPACITY  (Liquid). 


Quarts  (U.  S.) 

Gallons  (U.  8.) 

Barrels  (3 li  galls.). 


. 9463586  9. 976055K0. 0239442 
3.  78543410.  5781 15819.4218842 
119.2412  2.076426417.9235736 

I  I 


1.056682 

.264170 

.0083864 


Liters 
Liters 
Liters 


CAPACITY  (Dry). 


Quarts  (U.  8.) 

Bushels  (U.  8.  struck). . 


0.0418771  9.9581229    .9080775   Liters 


35.23928  1.54702708.4529730    .0283774 


Liters 


Examples  to  illustrate  the  use  of  above  table: 
i5  xnils-45X.0254  millimeters.  16  centimeters- 16 X. 3937 


UNIT  EQUIVALENTS— SIMPLE  AND  COMPOUND,  89 

ai.— SiMPLB  AWD  CoMPouiTD  Units  im  Com mon  Usb,  Bquivalbnts.  (Cont'd.) 


To  reduce  A  to  M. 


Molt,  by       Log. 


To  redace  M  to  A. 


Log.        Mult,  by 


WEIGHT. 


I  (Avob'.) . 
PoaoOB  (Jirotr.) 
Tone  (2000  lbs.) 
Ton  (2000  Ita.) 
ToDf  (2240  llM.) 
Ttsm  (2240  Iba.) 


28.3496 
.453593 
907.186 


.4525461 


8.5474539 


9.65666580.3433342 


2.9576964 
.907186  9.9576964 
1016.053.0069141 
1.016050.0069141 


7.0423036 
0.0423036 
6.9930859 
9.9930859 


.035274 

2.20462KUogTam8 
.00110231  Kilograms 

1.10231  Metric  tons 
.00098421 

.984206 


Kilograms 
Metric  tons 


MOMENTS. 


Inch-Poands... 
FootrPouoda. . 


1152.133. 
.138255  9. 


4068180.8593182 


.  00086  8k}entlmeter-grm8 
7 .  23800pieter-kllogTam8 . 


STRESS  PER  AREA. 


Pounds  per  sq.  In 

Pounds  per  sq.n 

Ttnt  (2000  n».)  p.  sq.  ft. 


.^03067 
4.88243 
9.76486 

8.8469968 
0.6886361 
0.9896661 

1  1530032 
9.3113639 
9.01C3339 

14.2234 
.204816 
.102408 

Kllog.p.sq.cent'r. 
Kllog.  p.sq.meter 
Met.ton8p.8q  .mtr 


WEIGHT  PER  VOLUME. 


PWBds  per  eu.  In 

Poonds  per  eu.  ft 

Tarn  (2900  lbs.)p.cn.yd . 


27.6797 
16.0184 


.4421621 
,2046184 


1.186550.0742851 


8.5578379  .0361275Grms.p.cu.cent'r. 
8.7953816  .  0624283  Kllog.  p.  cu.m'tr 
9.9257149^  .  8427813  Metton8p.cu.mtr 


VELOCITY. 


ftet  per  second.. 
Feet  per  seeond.. 
Feet  per  seeoDd. 
Feet  per  minute. 
MDcfl  per  minute 
MBes  per  minute 
Miles  per  hour. . . 


9. 4840158|0. 5159842 

1.9444827 

9.833668610.1663314 


1.609347 
1.609347 


.304801 
01136364 

.681^81 
01136364 
26.822451.4284984 


0.2066497 
0.2066497 


9444827 
8.5715016 
9.7933503 
9.7933503 


3. 28083^3 Meters  p.  second 
88.  Miles  p.  minute 

1.46'^6MUe8perbour 
88.  Miles  per  bour 

.0372822  Meters  p.  second 

.62137Kllomtr8.  p.  mln. 

.62l37jKllomtrs.  p.  bour 


ACCELERATION. 


Feet  per  see.  per  sec 
(g-32.2— .av.) 


.30480 


9.4840158 


0.5159842 


3.28083^3 


Meters  p.sc.p.sc. 
(g-9.81-    av.) 


Bxamples  to  illustrate  the  use  of  above  table: 
100  foot-pounds'- lOOX  .138255  kg.-meters. 
10X88  ft.  per  sec. 


10  miles  per  min, 

'igitized  by  VjOOQ IC 


90 


i.— MEASURES,  WEIGHTS  AND  MONEY. 


34~SufPLB  AND  Compound  Units  in  Common  Use.  Equivalents.  (Concl'd.) 


.To  reduce  A  to  IL 


Mult,  by  I     Log. 


To  reduce  M  to  A. 


Log.        Mult.  b7 


DISCHARGE  (Cu.  ft..  OaUodi  or  Liters.) 


Cu.  ttpereooond.. 
Cu.  ft.  peraeooDd.. 
Cu.  ft.  per  second.. 
Cu.  ft.  per  second . . 
Cu.  ft.  per  second . . 
Cu.  ft.  per  minute. 
Cu.  ft.  per  minute. 
Cu.  ft.  per  minute. 
Cu.  ft.  per  minute. 
Cu.  ft.  per  minute. 
Cu.  ft.  per  minute. 
Gallons  per  minute 
Cu.  ft.  per  second.. 


60 
8600 

86.4 

S.592 

31.536 

60. 

1440. 

43.2 

625.6 

7.480521 

28.31702 

3.785434 

1.98347 


7781513 

5563025 

9365137 

4136350 

4988066 

7781613 

1583625 

6354837 

7206554 

8739318 

4520475 

678116819 

29742589 


2218487 
4436975 
0634863 
5863650 
5011934 
2218487 
8416376 
3645163 
2793446 
1260682 
6479525 
4218842 
7025742 


.016^6lcu.  ft.  p.  minute 
.0002?^7;cu.  ft,  per  hour 
0  U  67  407Tli8'd.cu.ft.p.day 
.  3858025  MlU.cu.ft.p.  mtli. 
.03l7098Mlll.cu.ft.  p.  year 

.016''6Cu.  ft.  per  hcmr 
,  000694^4  Cu.  ft.  per  day 
023 1 481 5Thsnd.cu.ft.p.mo 
,  00 1 90259  Tlisnd.cu.ft.p.yr. 
1336805^5 Galla.(U.8.)p.  m. 
0353 1445  Liters  p.  mlnut« 
26417047  Uters  p.  minute 
.  6041667  Acre-tt.  per  day 


WORK  AND  POWER  (Power- Rate  of  Work.) 


Foot-pounds 

Foot-pounds 

Meter-Kilograms 

Foot-pounds 

Meter-kilograms 

Foot-pounds 

•Foot-pounds 

Mcter-kllograms 

Foot-pounds  per  sec 

Foot-pounds  per  sec 

Foot-pounds  per  sec 

Foot-poimds  per  mln.  . . 
Foot-pounds  per  mln.  . . 
Foot-pounds  per  mln.  . . 
Foot-pounds  per  hour.  . 
Foot-pounds  per  hour  . . 
Foot-pounds  per  hour  . . 
Meter-kllog.  per  mln. . . . 
Meter-kllog  per  mln.... 
Meter-kllog.  per  mln. . . . 
Meter-kllgg.  per  hour. . . 
Meter-kllog.  per  hour. . . 
Meto'-kllog.  per  hour. . . 

Mechanical  H.  P 

Mechanical  H.  P 

Electric  H.  P 


.138265  9. 


1.356284 

9.81 

.0012853 

.0092969 

.0012853 

.0003239 

.0023428 

.OOIS^'IS 

.0013563 

.0018434 

. 00003^03 

.0000226 

.00003072 

.0000008"^ 

.0637675* 

0661206* 

.Os21918* 

.Oj 16350* 

.0002^2 

.0« 36530* 

.0«27250* 

.0^7^037* 

7459666 

1.01387 

1.35916 


14068180. 
1323508i9. 


0, 

0. 

7, 

7. 

7, 

6 

7, 

7. 

7, 

7, 

5 

6 

5 

3 

3.5760482 

3.7093179 

6 

6 

6 


9916690 
1090204 
9683386 
1090204 
6104139 
3697321 
2596373 
1323608 
2656205 
4814861 
3541995 
4874692 


3408043  3 
21351783 
34678753 
5626530  5 
4353665  5 
6686362  5 
87271350 
0059832  9 
1332697  9 


8593182 

8676491 

0083310 

8909796 

0316614 

8909796 

4895861 

6302679 

7403627 

8676492 

7343796 

6186139 

6458005 

6125308 

2966652 

4239518 

290682 

6591957 

7864822 

6532125 

4373470 

5646335 

4313638 

1272865 

9940168 

8667303 


7 .  23300Meter-Kllogms. 
.737308  Joules 


.101 
778 
107.6626, 
778 
3087.35 
426.843 
650 
737.30! 
542.47 
33000 
44238.51 
32548.49 
1980000 
2654311 
1952909 
4562.424 
6116.20: 
4500 
273745. 
366972. 
270000 
1.34056 
.9863177 


937  Joules 


Pnd.-deg.  (Fahr.) 

Pnd.-deg.  (Fahr.) 

Brit,  thenn-unlte 

Knog*m-deg.  <C0 

Kllog'm-deg.  (C.) 

Mechanical  H.  P. 
H.  P. 
5^Metric  H.  P. 

Mechanical  H.  P. 

Electric  H.  P. 

Metric  H.  P. 

Mechanical  H.  P. 

Electric  H.  P. 

Metric  H.  P. 

Mechanical  H. 

Electric  H.  P. 

Metric  H.  P. 
5  Mechanical  H.  P. 
5  Electric  H.  P. 

Metric  H.  P. 

Electric  H.  P. 

Metric  H.  P. 
H.  P. 


.  P. 


73575  Metric] 


Note. — 1  electric  horse-power—  1  kilowatt  —  1000  watts— 1000  jotUes  per 
second. 
1  metric  horse-power— 75  meter-kilograms  per  second. 
Examples  to  illxistrate  the  use  of  above  table: 

8  meter-kilograms  — 8 X  9.81  joules.    10  British  thermal  units—  10 X 
778  £t.-lbs. 


*.M7076-.000  000  37675;  0a37''087- 0.000  003  703  7037 :  etc 


d  by  Google 


UNIT  EQUIVALENTS—SmPLE  AND  COMPOUND, 


91 


35. — Blbctrical.  Mbchamical  and  Hbat  Units — Equivalbnt 

Valubs. 

(See  also  preceding  table.) 


1  Foo&-pound 
<-  l.35«284  Joules. 

—  0.  i38255kllognuii-iiieten. 

-  0.00000037879  kUowatt  boun. 
»  0.00i28S3  heat  units. 

«  0. 0000005^05  bone-power  hour. 


1  Kil 
«  9'81  jotilea. 

-  7.23300  (t.-Ib8. 

*  0.0000036530  liorae-power  hour. 

-  0. 0000027250  Ulowatt  hour. 

-  f.  0092969  heat  units. 

1  JwU 
«  0. 737308  ft.-lbB. 

-  0. 101937  Idlogram-meters. 

-  0.000947697  heat  units. 
»  1  watt  seoond. 

-  0.00000027^7  kilowatt  hour. 

«  0.000000372378  horse-powo' hour. 

1  Heal  UnU  iB.T.U.) 
<-  1055. 18932  Joules. 

-  1055. 18932  watt-seoonds. 

-  778  n.-]bB. 

-  107.5626  kttosram-meterB. 
«  0. 0003931 1  kilowatt  hour. 

«  0. 00039293  horse-power  hour. 

-  9.0000688  lb;  carbon  oxidized.* 

«  0. 001036  lb.  water  evaporated  Crom 
and  at  212^  F.* 

1  Wau 

-  1  Joule  per  second. 

"  0. 00134056  hocse  power. 

-  3.411711  heat  units  per  hour. 

-  0.737308  ft-ib.  per  second. 

->  0.0035  lb.  water  evaporated  p^ 
hour.* 

-  44.23851  tk-Ibs.  per  minute. 

-  0.00135916  metric  horse  power. 

1  Kikmatt 

-  1000  watts. 

«  1 .  34056  horse  power. 

-  2654311  n.-lbe.  per  hour. 

«  44.23851  ft.-lb8.  per  minute. 

-  737 .  308  ft.-lbs.  per  seoond. 

-  3411.711  heat  units  per  hour. 

-  56. 86185  heat  units  per  minute. 

-  0.9476975  heat  units  per  second. 
»  0.2275  ib.   carbon   oxidized   per 

boor.* 
•■  3.53   lbs.   water  erapprated  per 
hour  firom  and  at  2120  p.* 

1  Watt  P€r  Square  Inch 
•-  8.l9beatunltsper8q.ft.permln.* 

-  6371  ft.-lbs.  per  sq.  ft.  per  mln.* 
«  0. 193  boTBe  power  p»  sq.  (t.* 


KiiovoattrliauT 

»  1000  watt-hours. 

»  1.34056  horse-power  hours. 

-o  2654311  ft.-lbs. 

-  3600000  Joules. 

-  3411.711  heat  units. 

—  366972. 5  kilogram  meters. 

—  0.2351b.  carbon  ozldlsed  with  per- 

fect effldmoy. 
-1  3 .  53  lbs.  water  evaporated  from  and 
at  2120  F.* 

—  23.75  lbs.  of  water  raised  from  620 

to  2120  F.* 

1  Hone  Power 

-  745. 9566  watts. 

-  0.7459566  kilowatts. 
»  550  tt-lbs.  per  second. 

">  33000  ft.-lbs.  per  minute. 
«  2544. 987  heat  units  per  hour. 
»  42. 41645  heat  units  per  minute. 

—  0. 706941  heat  units  per  second. 

»  0.175  lbs.  carbon  oxidized  per  hour.* 
»  2. 64  lbs.  water  evaporated  per  hour 
from  and  at  2120F.* 

1  Horte  PoweT'houT 
»  0.7459566  kilowatt-hours. 

-  1980000  ft.-lbs. 

-  2544. 987  heat  units. 

»  273745. 5  kilogram-meters. 

«  0. 175  lb.  carbon  oxidized  with  per- 
fect efllciency.* 

«  2. 64  lbs.  water  evaporated  Irom  and 
at  2120  F.* 

—  17.0  lbs.  water  raised  from  620  to 

2120  F.* 

1  Lb.  Carbon  Oxidized  with  Perfect  Effl' 
eiencv* 
-i  1 . 1 1  lb.  Anthracite  coal  oxidized. 
»  2 . 5  lbs.  dry  wood  oxidized. 
«  21  cubic  feet  lUxmiiDatlng  gas. 
-i  4.26  kilowatt-hours. 
■*  5 . 7 1  horse-power  hours. 

-  1131 5000  ft.-lbs. 

—  15  lbs.  water  evaporated  from  and  at 

2120  F.» 

-  14544  heat  units. 

1  Lb.  Water  Evaporated  from  and  at  2120  F.* 
«  0.283  kilowatt-hour. 
«  0.379  horse-power  hour. 
»  965.7  heat  units. 
-*  1 03  9  00  kilogram-meters. 
«  1019000  Joules. 
«  751300  ft.-lbe. 

—  0. 0664  lb.  of  carbon  oxidized. 

1  Heat  Unit  per  square  ft.  per  min.* 
<a  0. 122  watt  per  square  inch. 

—  0.0176  kilowatt  per  sq.  ft. 

»  0.0236  horse  power  per  sq.  ft. 


•  Values  by  H.  W.  Leonard.—- See  The  Electrical  Engineer.  Feb.  26. 1895. 

Digitized  by  VjOOQ IC 


93 


i.—MEASURES,  WEIGHTS  AND  MONEY. 


H       V 

2  Q 
n    « 


Si 


o^iisiiiiifi 

,li!l|-lis|il 

•«■    -    -    .00      ,*K9-.    .    -5    .    .    •    •♦* 

•«  CO  CO  ■«■  t»  <B  ^  C<9  ••  C4  •«  n  "  C«  •«  •-<  00         K<- 


Ph  (I4  ^  !S  PQ  tf  GO  O 


miUi 


ill 
ill 


&|fjlll9ass§l2«, 


CM  X  —  CO  CO  CO  CQ  « •*•  w  B  ■♦  ca      o-*- •*   .  oew  —  w  aB»»iS*»    .  »»_*  j 


^u    -is  ^  o  o  o  o  o  o  oja.a  «>?     F*ox^s 


<<<-S-<cQ    a    ffiSnnffiSS    o 


FOREIGN  WEIGHTS  AND  MEASURES. 


93 


^oooooo 


.    .    .cr^***®         ■    .c^o* —  coweow    .    ■ 


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gs 


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94 


i.— MEASURES,  WEIGHTS  AND  MONEY, 


s 


I 


A    .w  r  §•*»  «  — "cm  — oo«eo«  O  O  —  eoo  — «o» 

MOM  K^A«q£-<V>OC« ^-"O*     .t^     •»     • 


p 

■<cr 

u 


I 


I 

6 

11 


ilUiU  iN^^i,^  4l"h 

r~ia&5||.&|||| 

-««««»oioo  X  "^©oo  ft   -w 

^  Ol  •«  O  M  M  **!*•**  0»     .        -•      . 


CM*"^'gcQ«0 

•     .  — M**  — o 
t^w    •    -<ooc^ 

MM  — 00  09  —"^ 


iipii  tiitiiiii 


MONEY—DOMESTIC  AND  FOREIGN,  9S 


Nanbcrs. 

37. — Abstract  Numbers. 

10  txniU. -=  1  ten —  10 

10  tens *-l  hundred —        .  100 

10  hundreds —  1  thousand —         1  000 

10  thousands »  1  ten  thousand —       10  000 

10  ten  thousands —  1  hundred  thousand  .  *     100  000 

10  h\mdred  thousand  .  ->  1  million —  1  000  000 

A  pure  decimal,  where  the  first  significant  figtire  is  far  removed  from 
the  decimal  point,  may  be  abbreviated  by  a  subscript  to  the  first  cipher  to 
indicate  the  number  of  ciphers  at  the  right  of  the  decimal  point  and  to  the 
left  of  the  first  significant  figure.    Thus, 

2  millionths.  or  .000002,        may  be  written.  .O52. 

65  hundred  millionths.  or  .00000065.    may  be  written.  .0«65. 

4  billionths.  or  .000000004.  may  be  written.  .(^4. 


38. — Duodecimo  Nxtmbbrs. 
12  units  —  1  dozen. 

12  dozen «1  gross "■144.  (20  units'"  1  score.) 

12  gross  -  1  great  gross- 1728. 


39.— Papbr. 
24  sheets  — 1  quire.  2  reams    -  1  bundle—   960. 

20  quires- 1  ream  — 480.  5  bundles- 1  bale      —4800. 


Money. 

40. — United  States  Monet. 

10  mills  (m)  - 1  cent  (ct.)  (Unit  is  $1.) 

10  cents        -ldime(d.)       10  dollars «1  eagle  (E J 

10  dimes       - 1  dollar  (I.)         2  eagles  -  1  double  eagle  (BE.) 


41. — PoREioN  Money. 

English  Monty:    4  farthings  (far.)  —  1  penny  fd.) ;   12  pence  - 1  shilling  (s.) ; 

20  shillings— 1  pound  (jfi)"l  sovereign  (  —  $4.8666.  U.  S.  money). 

1  guinea  =-  21  shillings;    i  crown  —  5  shillings;    1  florin  =•  2  shillings. 
French  Money:     10  centimes— 1  decime;     10  decimes»l  franc  (Ir.) 

(  -  $0,193,  U.  S.  money). 
German  Money:    100  pfennig—  1  mark  (  —  $0,238.  U.  S.  money). 
Italian  Money:    100  centesimi—  1  lira  (  —  $0,193.  U.  S.  money). 
Russian  Money:    100  copecks- 1  ruble  (  —  $0,515.  U.  S.  money). 
Ausiro'Hungarian  Money:    100  kreutzers—  1  fiorin. 


d  by  Google 


»6 


*.— MEASURES.  WEIGHTS  AND  MONEY. 


i 
§ 


1  '"■ 

II: 

-  Hi 


llsisSssslilsllssilllllllll 


GO'S 


lOroco  — vo      -<«  — «oco      maot^roro  ao<o  ro  m  wmooaor4^aoor>      lOr 


222>22>2     >    222222222222222222222222222 

SSSiSSso  ffi  SSS00SSS88SSSSSSS8888SSSSSS 


«a 


VALUE  OF  FOREIGN  COINS, 


97 


12b. — Value  of  Foreign  Coins  and  Paper  Notes  in  American  Monet 
Based  Upon  the  Values  Expressed  in  Table  42. 


% 

Aao 

1 

k 

^^ 

i 

(SI 

< 

V  -.6* 

90.23.8 

80.19.3 

$0.73.6 

$0.40.2 

$0.49.8 

$0.51.5 

$0.20.3 

»s 

0.47.6 

0.38.6 

1.47.2 

0.80.4 

0.99.6 

l.Od 

0.40.6 

1        M 

0.71,4 

0.57.9 

2.20.8 

1.20.6 

1.49.4 

1.54.5 

0.60.9 

1        .6 

0.86.2 

0.77.2 

2.94.4 

1.60.8 

1.99.2 

2.06 

0.81.2 

a      .21 

1.19 

0.96.5 

3.68.0 

2.01 

2.49.0 

2.67.5 

1.01.5 

a      .9 

1.42.8 

1.15.8 

4.41.6 

2.41.2 

2.98.8 

3.09 

1.21.8 

I       .54 

1.66.6 

1.35.1 

5.15.2 

2.81.4 

3.48.6 

3.60.5 

1.42  1 

3         .2 

1.90.4 

1.54.4 

6.88.8 

3.21.6 

3.98.4 

4.12 

1.62.4 

i       1.84 

2.14.2 

1.73.7 

6.62.4 

3.61.8 

4.48.2 

4.63.5 

1.82.7 

10 

i         .5 

2.38 

1.93 

7.%6.0 

4.02 

4.98.0 

5.15 

2.03 

20 

4.76 

3.86 

14.72.0 

8.04 

9.96.0 

10.30 

4.06 

SO 

14        i.5 

7.14 

5.79 

22.08.0 

12.06 

14.94.0 

15.45 

6.09 

40 

H        i 

9.88 

7.72 

29.44.0 

16.08 

19.92.0 

20.60 

8.12 

90 

»         .5 

11.90 

9.65 

36.80.0 

20.10 

24.90.0 

25.75 

10.15 

100 

488.65 

23.80 

19.30 

73.60.0 

40.20 

49.80.0 

51.50 

20.30 

d  by  Google 


i.^MEASURES,  WEIGHTS  AND  MONEY. 


43. — Comparison  of  Prices 

French  and  German  prices  for  metric  units,  British  prices  for  Imperial 
units,  and  United  States  prices  for  United  States  standard  weights  and 
measures. 

[Based  upon  the  circular  of  the  Secretary  of  the  Treasury  dated  Octo- 
ber 1,  1002,  fixing  the  legal  equivalent  of  the  ^German)  mark  at  23.8  cents, 
of  the  (French)  franc  at  10.3  cenU.  and  the  British  pound  sterling  at  $4.8M&J 


|3 


II 


u 


a    2a£ 


ill 


m&5     H^tj 


1  -  .088 

3  -  .175 

3  «  .263 

4  -  .350 


5 

6 
7 
8 
9 

11.423  -  I 
22.846  -  2 
34.269  »  3 
45.691  »  4 

57.115  —  5 
68.537  «  6 
79.960  =■  7 
91.383  -  8 
102.806  -  9 


.438 

.525 
.613 
.700 
.788 


1 
3 
3 
4 

S 

6 
7 
8 
9 

5.667  . 
11.334  > 

17.000  . 

22.667  • 

28.334  « 

34.001  • 

39.668  > 
45.334  > 
51.001  ' 


.176 
.353 
.529 
.705 


1.058 
1.234 
1.411 
1.587 

I 

2 
3 
4 

5 

<  6 

7 
'  8 

9 


1 
3 
3 

4 

I 
5 
6 

7 
8 
9 

1.369  • 

2.738  . 

4.106  ' 

5.476  = 

6.844  ' 
8.213  < 
9.581  - 

10.950  . 

12.319  > 


.731 
.  .461 
2.192 
2.922 

3.653 
4.384 
5.114 
5.844 
6.575 

1 

2 
3 

4 

5 

6 
7 
8 
9 


1 
3 
3 

4 

S 

6 

7 
8 
9 

14.703  • 
29.407  • 
44.110  • 
58.813  . 

73.517  . 

88.220  < 
102.923  • 

17.627  . 
132.330  • 


.068 
.136 
.204 

.r2 

.340 
.408 
.476 
.544 
.612 


.606 
.819 

l.fU 
1.216 
1.41B 
1.621 

1.824 


4.935  -  I 

9.871  -  2 

14.806  -  3 

19.742  «  4 

24. en  -  5 

29.612  -  6 

34.548  -  7 

39.488  -  8 

44.419  -  9 


11 


S3 


If 


1^ 


1-1 


y 


ss 


-I 


5I 

ISl 


IJ 

o  .3 


1 
3 
3 
4 

5 

6 
7 
8 
9 

9.263  . 
18.526  . 
27.789  . 
37.052  < 

46.316  < 
56.579  < 
64.842  • 
74.105  . 
83.368  < 


.108 
.216 
.324 
.432 

.540 
.648 
.756 
.864 
.972 


I 

2 
3 
4 

5 

6 

7 
8 
9 

4.595  > 
9.190  < 

13.785  . 

18.380  < 

22.975  ' 
27.570  ' 
32.165  > 
36.760  • 
41.355  - 


.  .218 

:  .435 

.  .653 

.  .871 

r  1.088 

.  1.306 

.  1.523 

.  1.711 

.  1.959 

<  I 
2 
3 
4 

5 

6 

7 
8 
9 


1 

3 
3 

4 

5 

6 
7 
8 
9 

I. 110  - 

2.220  . 

3.330  . 

4.440  ' 

5.550  . 

6.660  • 

7.770  ■ 

8.880  ■ 

9.990  . 


'  .901 
.  1. 
.  2.703 
.  3.604 

.  4.505 
.  5.406 
.  6.307 
.   7.20: 

>  8.108 

•   I 

2 
3 

>  4 

5 

6 
7 
8 
9 


1 

3 
3 

4 

5 

6 
7 
8 
9 

11.923  > 
23.847  . 
35.770  . 
47.693  > 

59.616  > 
71.640  > 
83.463  ' 
95.386  . 
107.310  < 


.084 
.168 
.252 
.335 

.419 
.503 
.587 
.671 
.755 


3 
3 

4 

5 

« 
7 
8 
9 

4.241  I 

8.483  < 
12.724  . 
16.965  > 

21.207  • 
25.448  < 
29.689  < 
33.931  . 

38.172  • 


.2K 
.472 
.797 
.943 

1.179 
1.415 
1.6i« 
1.896 
2.122 

I 

a 
3 

4 

8 

6 
7 
S 

9 


d  by  Google 


TIME  AND  CIRCULAR  MEASURES.  99 

Miscall —eom. 

44.~TiMB  Mbasurb. 

I  second  (s)        —    15  seconds  (O^—OC— 15*)  of  longitude. 

60 seconds 1  mimUf  (m)     -^    15  minutes  (0^— 150  of  longitude. 

60  minutes  (  —  3600  seconds)  — 

1  hour  (h)  ->   15  degrees  (15<*)  of  longitude. 
24  booxB  (  - 1440  m  -  85400  8) - 

1  solar  day  (d)  ^  360  degrees  (360^)  of  longitude. 
7  days  (- 168  h  - 10080  m -  604800  s) » 

134  wmks  (- 865  d  -  8760  h  -  525600  m)  - 

1  comntott  ytar, 
62f  weeks  (- 366  d  -  8784  h  -  527040  m) - 

1  Uap  ytar. 
160  years  («  75  common +25  leap)  — 

1  cttOiwry, 

45. — CiRCtXLAR  Mbasuuk. 

- 1  s9Cond  Q   -A  (.06''6)  second  of  time. 

^  -1,^^- —  1  minut4  (0    ■■  4  seconds  of  time. 

60  minutes  (  —  8600  seconds)  —  1  dggr§€  i°)   —  4  minutes  of  time. 


60  seconds —  1  minuU  (0    ""  4  seconds  of  time. 

60  minutes  (  —  3600  seconds)  -      " 

30  degrees  ( -  ISOO'- 108000^ 


*lsitH 


the  angle  at  the  base  of  a 
right  triangle  whose  alti- 
tude is  1,  hypothenuse  2. 
.  and  base  n/3. 


90  degrees  (-6400'-3240000 

—  1  tigh^  angU  (L)  *  6  hours  of  time. 
180  degrees  (- 10800'- 6480000 

—  1  stmi-circumferenc^^x"  3.14159265. . . . 
160  degxves  (-21600^-1296000') 

—  1  drcwmftnncf  2n  .radius— « .diameter. 


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5.— ALGEBRA. 

An  algebraic  equation  is  a  shorthand  mathematical  expression,  and 
every  such  exprension  may  be  transformed  by  observing  certain  algebraic 

rules.    The  first  Utters  of  the  alphabet,  a,  b,  c ,  represent  the  loiowo 

quantities  of  the  equation,  and  the  last  letters, .  ..x,y,  b,  the  unknown. 
M9mb«rs  of  an  equation  are  separated  by  the  sign  of  equality  (  »  ) :  Urwa 
of  a  member  are  separated  by  plus  (  +  )  and  minus  (— )  signs;  and  faOoti 
of  a  term  are  separated  by  the  signs  of  multiplication  (X)  or  (.).  either 
expressed  or  understood. 

Any  factor  or  set  of  factors  of_a  term  may  be  considered  the  denomittation 
of  that  term.  Thus,  in  ax  y/y,  either  a,  x,  y/y,  ax,  a^/y,  x\/y  or  ax\/y 
may  be  chosen  as  the  denommation,  as  may  be  expedient. 

Addition  and  Subtraction. — Place  like  terms  (terms  having  the  same 
denomination)  in  the  same  coltmin.  and  reduce  fractions  to  a  commoo 
denominator,  before  adding  or  subtracting: 


ix  +  5x*y  +  vT+  — — 


x*  y«       _     X*  -i-  y* 

V^       a+6a  +  6"      a  +  b 


-2x+Zx^y-2^^^^        (a±6)»_(a+6)»-(y-^)(a^fr)' 


Sum-     2x+  Sx*y  -  Vd  +—.- 


3  V37±  \^Wx  -  (3  ±  2)  \/lx 


Diflf.  -     6«+2*«y-3Vd 

}i^ote. — In  subtraction,  reverse  the  +  and   —  signs  of  the  subtrahend 
and  proceed  as  in  addition. 

Exponents. — The  following  hints  are  given  without  discussion: 
ny.fiY.n-'  nnu  -  nn*  -  n*n  -  n»+«  -  n«+»  -  «»  -^  -  «^  -  v^^ 

M  Vlry  -  nVxV'y'-  n  x^  y*-  ^—^  "^ -J  "4  "'^»*^"  (»«xy)* 


V: 

-8^ 
27  y* 

l/27>* 

(-8)*  (x*)^ 
(27)*  (y«)* 

-  2* 
"    3y« 

2x 
3y» 

xi 

4 

7'.      a«- 

X 

Va*7    a      - 

^a-     «■• 

1 

_x 

n  ' 

1 

.(l 

x" 

-a  „ 

x'^-l^l. 

a°  "  1. 

n"  - 

1* 

X» 

«"    - 

-    ^n-t-n     „ 

x«».      a»  a« 

-    an+x.     an 

• 

jno""   „ 

a" 

*Any  number  whose  exponent  is  0,  is  equal  to  1. 
100 

Digitized  by  VjOOQ  IC 


BINOMIAL  FORMULA.  '  lOJ 

MnhipUcatioa  AodTo^cr^ 

:    »«  X  H*  -  n«ff*  -  »«i  -  nt  -V^  -  ^• 

fli»  X  a  »«  -  a%«.    2VI X  8vT-  6VI6.    SV^x  X  ^^a.  x  -  3a«^. 
Like  signs  give  plus:     a  X  b  '^  ab.  —a  X  (  —  b  )  ^  ab. 

Unlike  signs  give  mti(M5:  —a  X  6  —  —ab.         a  X  (— M  —  —06. 

PdynoiaiaU:    Multiply  each  term  of  the  mutliplicand  by  each  term  of  the 
multiplier,  placing  Kke  terms  of  the  products  in  "  column."  and  add. 

ab»  -  a*b 
ab^  -  a*b* 

«  o  ««  +  4  >/6_  -  ^b*  +  a*l^ 

Product  -  3  a  x«  V6~+  20  Product  -         a«  6*  -  2a»  6*  +  a«6« 

-  o«(6»  -  2o6*  +  a«6»). 

-  aa6»(6  -  a)». 

(x-i-  *^»-  ««4-  2  « i/+'u«  ?  These  two  formulas  are  the  foun- 
)tA«\  ^^^^1.^  ;5^  Vdation  of  many  short  methods  in 
U+y)(ic-y)-.x«-y'.  j  arithmetic.    (See  page  11). 


U-»-y+«)«- jt»+y»-f  *«  +  2  jcv+2*i+2y». 

(*+y+«)»-jr»  +  y»-f  £»+ 3 *»  (y+s)  +  3 3^  («+»)  +  8  ««  (a:+y)  +  6  « y  ». 

BfawmJal  formula  for  expanding  the  sum  or  difference  of  two  numbers,  to 
any  power: 

.       •  »-»        .  n(»— 1)    ii-«    ^      ,    «(n-l)(w-2)    n-«     .    . 

(a±«)-a     ±    »a        *+TxT''       *^     =*=       1X2X3      ^       «'+•.. 

Tu    /^N.  ^j^«^_t.5X4^**-L5X4X3,.  ^5X4X3X2  ^^ 
Thus:  (a+^)..ai  4  5a^+  nr2  ^^  ^  fxlxl^'^  "^  1  X  2  X  3  X  4^^ -*• 

5X4X3X2X1  5 
1X2X3X4X6* 
-a»  +  6a4«  +  10o»«» -f  10a«*«  +  6a  «*  +  ««. 

|(-i)(-U)(--2i)    -a   . 

1X2X3X4        "      '^ 

^  ^j  _^_£ *!_+ JL_if! 3X5^ 

2Va'    2X2«n/^    2X3X2«N/a»    2X3X4X2*\/^ 
+  3X6X7jc» 

2X3X4X6X  2^V^ 

(a  +  ,)l-ai  +  Ja-l*  +  ^a-U    ^a  +  itJ^  a-2l  ^ 

|(-|)(-H)(--2i)         31 

1X2X8X4        "*        *^ 

^  ^j  ^__x 2ac«  _  2  XJ^      _       2X.6X83g« 

3  <^«    2X3«*^^    2X3X3»<^^    2X3X4X3**^ 
^         2  X  6  X  8  X  11  x» 

2X8X4X6X3»    ^^O" Digitized  by  Google 


102  b.— ALGEBRA, 

•    'DhriBiaii  ad  Roots. 

X* 

atbJ  +  oA  -  (a>-»)  (6»-»)  -  ab^.        -  +  -  -  ^X-  -  — . 

jr      n       jT      f       ex 

Division:  vT  .T         /I*      v/l5      \/l5      ^  ,   /r^ 

Squart  Root  by  Binomial  formula: 
Example:    Find  the  square  rcx»t  of  5? 

Solution :  In  (a  +  a;)  ^  let  a  —  4  and  x^\\  thence  by  expansion  (see  page  101) 

.11,*  x^      ,       x*  Sx*       ,        7x'i 


(a4-*)'-a'+   -^ =-z=+  -■■■      ■ ^^-F=  + 


2Va       8Va»      16>/a»       128^07       266V tf»  ' 


2X2      8X8      16X32      128X128 

>-  2  +  .25  -  .015625  +  .001058  -  .000306  <-  3.236±. 

Cubt  Root  by  Binomial  formula: 

Example:    Find  the  cube  root  of  9? 

Solution:  8  is  the  cube  of  2  and  1  less  than  0;  hence  from  expanskxi 
formula,  page  101,  there  is  obtained. 

(a+*)*-  (8+  D*  -  8*(1+*)*  -  2  (1+J)*.    But 

I       I  X  «*  6**  lOaf* 

(a+xy^a'  +     ,  __  -  — j^^T  +  — nr » ■**  •  •  ••   Therefore 

3Va«       3»Va»        8*\/a»        yVo" 

VT.2(l+i)»-2[l+3-L-^-+^-^. ] 

-  2[1  +  .0416^6  -  .001736n  +  .00012064  -  .00001006 1 

-  2  X  1.04004>  2.08008.    Ans. 

Completinf  the  &|uare. — Ihis  is  performed  by  adding  a  certain  amount 
(*  (a  third  term),  to^the  first  member  of  the  (affected  quadratic)  equation 
to  msdke  it  a  p«rfect'  square,  anojthe  same  amount  to  the  second  member 
so  as  to  preserve  the  equality. 

Example  1:    Find  the  value  of  x  in  the  equation  a:*  +  4jr— 21? 

Solution:    By  adding  c*  to  both  members  we  have  je*  +  4x  +  c*— c*+21. 
in  which  the  first  member  is  a  perfect  square,  the  middle  term,  4x,  being 
equal*  to  ly/x*  v/<^i  whence  c'—  2»—  4. 
and  ic«  +  4  «  +  2«   =.  4  -f  21  -  25. 

Extracting  the  sq.  rt.,  a;  +  2    —  ±  5 

and         x    «»±5—  2—  3or—  7.    Ans. 

Note. — Make  the  first  term  a  perfect  square  before  completing  the 
square  of  the  first  member  of  the  equation.    This  may  be  done  by  multi- 

£  lying  or  dividing  the  whole  equation  by  a  constant.    The  first  term  must 
e  positive, 

♦  The  square  of  a  member  of  two  terms  —  the  sqttar*  of  t)u  first  4-  iwici 
the  product  of  the  two  +  the  square  of  the  second,  ^^^ed  by  LjOOQVQ 


COMPLETING  SQUARE.    SIMULTANEOUS  EQUATIONS.  103 


Example  2:    Solve 


2ax>  +  56x-a0? 
10& 


Here. 
00 


Muh.  by  2.  dhr.  by  a  and  add  c«:     i«»  +  ^^x  +  c«  -  c«  + 

a 


Eztncttns  the  sq.  rt. 
106^ 


-2(2«Xc),orc- 


56 
2a' 


I         fiO 
2*  4-  c  —  -*  c*  H .in  which 

JV ^ 

9  .       ;256«  .60      5b 

^"^\l^"*"7"2a 

.  1      ,'256>  ^  60      56       . 
^  4a«        a       4a 

Remarks  on  apparent  fallacy  of  the  above.    To  prove  that  4  —  5? 
Let  16  -  36  -  25  -  45 
81 
and  to  complete  the  sqtxare,  let  c*  —  -j  ;    then 

16-36+  J-  25-45+  ^. 

Extracting  the  sq.  rt..    4  -  |   -  5  -  |,  I  But,  ±  (4-$)  -  =F  (5-|). 

.hence.apparently.4-  5    (or  1  *  -  +  i^.r^^^^^'^^-^'^'*-**  —  5+^*- 
In  a  somewhat  similar  way  it  may  also  be  "shown"  that  2  —  1, 1  -^  0.  etc. ; 
bat  the  discrepancies  are  always  apparent  upon  inspection. 

Si  am  I  tan  eons  Equations.— To  solve  any 
problem,  the  number  of  equations  must  be  equal  to 
tke  number  of  unknown  quantities.  This  can  be 
onderstood  quite  readily  by  considering  that  each 
equation  is  realW  the  equation  of  a  curve  of  some 
Idnd.  Thus,  in  Fig.  1,  let  curve  A  be  represented 
by  the  equation  y  —  m  x  +  c,  and  curve  B  by  the 
equation  >•  —  A  a  x.  The  equations  of  these 
curvea  are  nmultaneoxis  equations  when  the 
curves  intersect  at  any  point,  as  p,  with  common 
coordinates  Xo  and  yo',  and  the  problem  is  solved 
by  determining  the  values  of  these  coordinates. 
Inus.  by  substitution,  yo^—  (m«  +  c)*  —  4  a*; 
y  —  c        y* 

(w  jt  +  c)*  —  4  a  «,  or  the  equation  ^ —  -~.  each  one    containing  only 

one  unknown  quantity,  x  or  y. 

Simultaneous  equations  may  be  solved  by  three  methods  of  eliminat- 
ing all  but  one  unknown  quantity: 
'1)    Elimination  by  substitution,  as  above. 

BHmtnation  by  addition  or  subtraction,  and  by  substitution. 
3ar+4y-18.        Mult,  by  2:  6*+8y-36 

2*  +  ay-  13.        Mult,  by  3:  &c+9y  =  39 

Whence  by  subtraction ,  y  —  3 


>^ 


Fig.  1. 


from  which  we  have  only  to  solve  the  equation 


Example: 


y-3.«-2. 


And.  by  substituting  this  value  in  the  first  equation. 
ar+4X3-18;   *-2. 
(3)    BBmination  by  comparison. 

p,^^^,^.     a«  +  4y-18.       ^,  18-4y       13-3y.    . 
Example.     2*+3!y-13.      * 3 2 — •• 

If  more  than  two  equations  are  given,  eliminate  one  unknown  quantity 
by  combining  two  of  the  equations,  and  proceed  until  one  equation,  with 
one  unknown  quantity,  remains.  Then  solve  for  that  unknown  quantity 
and  substitute  its  value  in  one  of  the  equations  to  obtain  the  value  of  another 
unknown  quantity.  Proceed  in  this  manner,  substituting  the  values  thus 
obtained  in  another  equation;   and  so  on. 

For  Cubic  Equations,  see  Plane  Trigonometry.  r^^^^T^ 

Digitized  by  V^OOQlC 


6— LOGARITHMS  OF  NUMBERS. 


Logarithms  are  useful  in  finding  the  product,  quotient,  powers  and  roots 
of  numbers.  A  system  of  logarithms  may  be  foimded  on  any  base,  as  a. 
If  the  base  a  raised  to  the  mth  power  —  M,  then  m  is  the  logarithm  of 
M  to  the  base  a;  and  conversely,  M  is  the  antt'logarithm  (that  is,  the 
number  corresponding  to  the  logarithm)  of  m,  to  the  same  base.     Thus, 


LetM- 

Let  N  = 


>a  number;  m  its  log  to  base  a. 
'  a  ntmiber ;  h  its  log  to  base  a. 


Then  log.  M^m;  or  a™  —  Jtf . 
Then  log,  N^n;  or  op  -AT. 


The  following  formulas  and  methods  illustrate  the  use  of  logarithms  in 
the  process  above  mentioned: — 


To: 
Multiply  M  by  N, 
Divide  M  by  N. 

Raise  M  to  the  Nth 

power. 
Extract  theiV<*  root 

ofM. 


Formula: 

MN  -  cp^*  -  a"*" 
M       a™ 

N'   ^    -«"-" 
Af «  -  (cf^f  -  a"" 

W N m 

y/M  —  Va«-"  a^f 


Process:  find  anti- 

logarithm  of 

(Logof  Af)  +  (log  of  N) 

(Logof  M)-.(log  of  A-) 

(LogofM)xN. 

(Logof  Af)-i- AT. 


Two  systems  of  logarithms  are  in  use,  namely: 


Common  or  Briggs  System. 
(Founded  by  Briggs.) 
In  general  use  for  all  practical  pur- 
poses. 

Base  a  —  10. 

o»    =  A^   .-.   log     N  "  n, 

100  -       1  ...  log       1  -   0. 

101  -     10  .-.  log    10  -   1. 

10»    -  100  .'.  log  100  -   2. 
10»«-  302.-.  log  302  -   2.48+ 


Hyperbolic.  Natural  or  Naperian 
System. 
(Founded  by  Napier.) 
Used  in  pure  mathematical  discus- 
sion and  m  steam  engineering. 
Base  -*  -  2.7182818... 
Derivation  of  *: 

•  "(l+-j    &s  X  approaches  infinity. 
1 


-i+i+*+t+A+. 

-2.7182818 


1.2.8.4" 


The  naperian  log.  of  a  number  =  iu    common  log.  X  2 .  8025851 

The  common  log.  of  a  number  —  its  hyperbolic  log.  X  0 .  4342045 
Ck>mmonlog.  of  2.3025851  -  0.3622157;  of  0.4342045-  9.6377843-10. 

Note  from  the  above  that — 

The  naperian  log.  of  the  naperian  base  (*  —  2 .  7182818 . . .)  —  unity. 
The  common  log.  of  the  naperian  base,  2.7182818. . ..—  0.4842046. 
The  common  log.  of  the  common  base  (a  —  10)  —  unity. 
The  naperian  log.  of  the  common  base,  10,  —  2 .  3025851. 

Common  or  Briggs  System.— The  logarithm  of  a  number  is  composed 
of  the  characteristic,  or  mte^ral  portion  to  the  left  of  the  decimal  point 
and  the  tnantissa  or  decimal  fraction.  The  mantissa  is  all  that  appears  in 
any  table  of  logarithms  and  the  degree  of  accuracy  is  dependent  on  the  n\im- 
ber  of  decimal  places  used  in  the  mantissa.  Vega's  tables,  to  seven  docinud 
places,  are  recommended  for  general  office  use  m  city  surveying,  and  where 
the  results,  in  general,  are  required  accurately  to  the  sixth  or  seventh 
significant  figxire. 


104 


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COMMON  OR  BRIGGS  SYSTEM.  lOS 

Table  1.  following,  to  five  decimal  places,  will  be  found  compact  and 
convenient  where  the  result  to  five  sisnificant  figures  is  sufficiently  accu- 
rate. Tables  to  six  decimal  places,  unless  arranged  on  the  "  Vega  system" 
(in  which  case  they  would  comprise  180  pages — ^too  bulky  for  any  hand 
book)  are  not  recommended. 

In  the  logarithm  of  any  number  the  mantissa  is  independent  of  the 
position  of  the  decimal  pomt,  while  on  the  contrary  the  characteristic  is 
dependent  only  on  the  position  of  the  first  significant  figure  of  the  number 
with  relation  to  the  decimal  point.    Thus  in  the  following  examples: 

(a)  log.  4021 . 7  -  3 . 60441         "S  >'Z^M  S  J 

(b)  tog.     402.17  -  2.60441 

(r)  tog.       40.217         -  1.60441 

id)  log.         4.0217       -  0.60441 

(#)  log.  .40217     -  1.60441   -   9.60441   -    10 

(/)  tog.  .040217  -  2.60441   -   8.60441   -    10 

it  win  be  seen  that  the  characteristic  is  equal,  algebraically,  to  the  number 
of  places  minus  one,  which  the  first  significant  figure  of  the  nimiber  occupies 
to  the  left  oC  the  decimal  point.  In  {a)  the  characteristic  is  3;  in  (6).  2; 
in  (d).  0;  in  (*).  —  1;  and  in  (/),  —  2.  Some  mathematicians  prefer  the 
use  OC  the  n^itive  characteristic,  but  most  of  them  emptoy  the  "  positive," 
by  algebraicsJly  adding  10  to  the  integer  and  placing  — 10  to  the  right  of 
the  mantissa  or  omittmg  the  latter  ( — 10)  altogether.  For  example,  log 
.040317  —  8.60441,  the  — 10  being  understood  and  the  value  of  the  char- 
acteristic  being,  of  course.  ~  2.  In  the  ca«e  of  finding  the  root  of  (or  divid- 
ing) a  pure  decimal,  however,  the  — 10  must  be  employed. 

Example:  Find  the  fourth  root  of  .0081? 

Solution:  log  .0081  -   7.90849  -10 

Quotient  obtained  by  dividing  by  4  -    1.97712  —   2.5 

2.6 


.-.Antitog  or  fourth  root  -  0.8.     Ans.  9.47712-10 

To  find  the  logaritJim  of  a  number. 

Example:   Find  the  log  of  678.57? 

Solution:  The  characteristic  is  3  —  1  »  2.  The  mantissa  for  the  first 
four  figures.  67.85.  is  read  directly  from  Table  1.  and  »  .83155.  To  this, 
however,  must  be  added  Vio  (the  next  figure  of  the  number  is  7}  of  the 
difference  between  .83155  and  the  tog  of  67.86  »  .83161.  This  difference 
is  6  ami  in  the  proportional  parts  (P.  P.)  column  under  6  and  opposite  7 
win  be  found  the  value  4 . 2.  call  4,  which  added  to  .  83155  -  83159.  Hence 
the  tog  of  678.57-  2.83159.    Ans. 

To  find  the  antMogarifhm  (ntmiber  corresponding  to  a  logarithm). 

Example:     1 .92513  is  the  logarithm  of  what  number? 

Solution:  This  is  the  reverse  of  finding  the  logarithm  of  a  number. 
No^ecting,  for  the  present,  the  characteristic,  the  next  lower  mantissa  to 
.92513  is  .92511  and  the  ntmiber  corresponding  is  8416.  The  difference 
between  .92511  and  the  next  higher  mantissa  in  Table  1.   .92516  is  5,  and 

the  proportional  difference   qokia  Z  q2511    ^^ T  ^^^  ^^  .4  to  be  added 

to  the  fourth  figurcjj.  e..  4  to  the  fifth  place  of  the  number,  as  shown  in 
the  P.  P.  column.  Therefore-  the  nxmiber,  disregarding  the  decimal  point 
is  S4164.  The  characteristic,  1,  calls  for  two  places  to  the  left  of  the  decimal 
point,  hence  the  antilog  of  1 .  9251 3  is  84 .  164.    Ans. 


100  t.— LOGARITHMS  OF  NUMBERS. 

To  maltiply  one  nuniber  by  another.     (Add  the  logs.) 

Example. — Mtiltiply  23.142  by  85.7? 

Solution.—  log  23.142  -   1. 86480 

4  -  P.  P.  fori, 
log  86.7       -    1.98298 
.'.  AntOog  -  product  -        1983.3  8.29738 

Ans.  t2 

6  -  P.  P.   -   8  - 

To  divide  one  number  by  enother.    (Subtract  the  logs.) 
Example.—     Divide  846 .  94  by  36 .  42? 
Solution.—  log  846.94  -   2.92785 

log    36.42  -   1.56134 

.*.  Antilog  -  quotient  -   23.255  1.36651 

Ans.  ^2 

9  -  P.P.  -   5- 

To  raise  a  nnnber  to  any  power.    (Multiply  the  log  by  the  index  <A  the 

power.) 

Example. — 25. ff  -  ? 

Solution.—  log    25.3     -    1.40312 

Multiply  by  3  :  8 

.*.  Antilog  -  3rd  power  -  1619.4  4 . 20936 

Ans.  25 

n     P.  P.  -   4 

To  extract  the  root  off  a  number.     (Divide  the  log  by  the  index  of  the 

root.) 

Example  1.  ^^286. 12  -  ? 

Solution.—  log  286.12  -   2.45655 

Divide  by   5  : 

.'.  Antilog  -  5th  root  -  3.1096  0.49131- 

Ans.  122 

9     P.  P.  -f  6 
Example  2. — Find  the  square  root  o£  the  fifth  power  of  23.2? 

Solution. — ^The  square  root  of  the  fifth  power  of  N  —  ^.therefore 
multiply  the  log  of  23.2  by  2\  or,  better,  divide  by  .4. 
log    23.2     -    1.36549 
Divide  by  .4  :  


.-.  Antilog  -  v'23.2»  -  2592.5 

Ans. 


9    P.  P.  -   5  + 


Example  3 —V  09463  -  ? 

Solution—  log  .09463  -   8.97603  -    10. 

Dividing  by  2         -   4.48801.5  -5. 

—  5 

.-.  Antilog  -  square  root  -  .30762  9.48801.5  -   10 

Ans.  799 

2.5 

Naperian,  Natural  or  Hyperbolic  System. 

A  table  of  naperian  logarithms  of  numbers  from  1  to  10,  advandng  by 
hundredths,  is  griven  as  a  part  of  Table  1  of  the  common  logarithms  of 
numbers.  The  range  of  this  table  may  be  extended  greatly,  to  include  the 
logarithms  of  other  numbers,  as  follows: 

For  logarithms  of  numbers  from  1  to  10  advancing  by  hundredths  and  ' 
ten  thousandths:   use  the  "  difference"  colimuj  in  the  table.    Thus,  to  find  1 


NATURAL  OR  HYPERBOLIC  SYSTEM.  107 

For  logarithms  of  numbers  from  10  to  100:  Divide  the  number  by  10, 
find  the  log  of  the  quotient,  from  the  table,  and  add  2 .  302586  (the  log  of  10). 
Thw,  to  fiid  the  log  of  46.72.  Log  4.672  -  1 .64116  +  43,  which,  added 
to  2.302585  -  3.84418.    Ans. 

Rule. — ^Add  2 .  302585  to  the  log  of  Vio  ol  the  number. 

For  logarithms  of  ntmibers  from  100  to  1000:  Divided  the  number  by 
100,  find  Uie  log  of  the  quotient,  from  the  table,  and  add  2X2. 302585  - 
4.00517  (the  log  of  100). 

Rule. — ^Add  4.60517  to  the  log  of  Vioo  of  the  number. 

In  general,  to  find  the  naperian  logarithm  of  any  number,  add  n  X 
3.302585  to  the  naperian  log  of  —  X  the  ntmiber;  the  factor  m  to  be  selected 

aod  some  power  of  10.  ao  as  to  bring  the  new  nimiber  within  the  range  of 
the  table,  i.  e..  from  1  to  10. 

Log  of  10. 

2.3025851  X  2  - 
X  3  - 
X    4  - 

To  find  the  antilog,  proceed  in  a  manner  inverse  to  the  above  method 
of  finding  the  log. 

Example. — Of  what  number  is  4 .85208  the  log? 

Solution. — ^The  highest  multiple  of  2.3025851  below  the  given  log  is 
4.60517,  obtained  by  the  factor  2  cor-  Given  by  log  =  4 .85203 

responding  with  the  factor  100  of  the  Multiple  —  4.60517 

nombcar.    From  the  table  of  napfrian  piff.  „  0 .  24686 

logarithms.  Table  1.  we  find  that  the 
number  corresponding  to  the  \oa  of 

the  difference,  0 .  24686,  is  1 .  28.    But  the  given  log.  4 .  85203,  is  of  a  number 
100  times  afi  large,  therefore  its  antilog  is  1 .28  X  100  »  128.    Ans. 


Multiple: 

Log  of  10.                       Multiple: 

4.6051702 

2.8025851   X   5  -    11.5129255 

6.9077553 

X    6  -    13.8155106 

9.2103404 

X   7  -    16.1180967 

( '' 


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108 


^.—LOGARITHMS  OF  NUMBERS. 
I. — ^Logarithms. 


No. 

NftperUn. 

\ 

L.    O 

1 

2 

3 

4 

6 

6 

7 

8 

9 

P.  P. 

No. 

Log.  Dlf. 

100 

00  000 

043 

087 

130 

173 

217 

260 

303 

346 

389 

44  43  43 

1.00 

.00000  MK 
.00996  »S 

.01980 ;~ 

.02956  JiJ 

.03922^ 

957 

.04879  ft^ 

913 
.09531  aft- 
.10436  5J5 

.12222  ^ 
.13103  «8* 

873 
.13976  a^ 
.14842  «• 
.15700  Si? 
.16651  gj 
.17896*** 

837 
.18232  «j« 
.19062^ 
.19885  JtJ 
.20701  1  • 
.21511  **" 

803 
.22314,^ 
.23111  J»J 
.23902  JU 
.24686  J" 
.25464  "* 

772 
.26236  yg. 
.27008  JS 
.27763  \% 
.28518  J^ 
.29267  ^*» 

743 

.30010    yjg 

.30748^5 
.31481  Jg 
.32208  Jg 
.32930  ^" 
717 
.33647  -,j 

692 

.87166  ^ 
.37844  S 

.39204  g-^ 
.89878^ 

.40M7 

1 

432 

476 

618 

561 

604 

647 

669 

732 

775 

817 

1 

4    4    4 

1.01 

2 

860 

903 

945 

988 

030 

072 

115 

157 

199 

242 

2 

9    9    8 

1.02 

8 

01  284 

326 

368 

410 

452 

494 

636 

578 

620 

662 

13  13  13 

1.03 

4 

703 

745 

787 

828 

870 

912 

953 

996 

036 

078 

18  17  17 

1.04 

105 
6 
7 
8 
9 

02  119 

160 

202 

243 

284 

326 

366 

407 

449 

490 

22  22  21 

1.05 

631 

572 

612 

658 

694 

735 

776 

816 

857 

898 

26  26  25 

1.06 

938 

979 

019 

06O 

TOO 

141 

181 

222 

263 

302 

31  30  29 

1. 07 

03  842 

383 

423 

463 

503 

543 

683 

623 

663 

703 

36  34  34 

1.08 

743 

782 

822 

862 

902 

941 

981 

021 

060 

TOO 

40  39  38 

1.09 

110 

1 

04  139 

179 

218 

258 

297 

336 

376 

415 

454 

493 

4140  39 

1.10 

632 

571 

610 

650 

689 

727 

766 

805 

844 

883 

4    4    4 

l.ll 

2 

922 

961 

999 

038 

W7 

115 

154 

192 

231 

269 

8    8    8 

1.12 

3 

06  308 

346 

385 

423 

461 

500 

538 

676 

614 

652 

12  12  12 

1.13 

4 

690 

729 

767 

805 

843 

881 

918 

956 

994 

032 

16  16  16 

1.14 

115 
9 

06  070 

108 

145 

183 

221 

258 

296 

333 

371 

408 

21  20  20 

1.16 

446 

483 

521 

558 

595 

633 

670 

707 

744 

781 

25  24  23 

1.16 

7 

819 

866 

893 

930 

967 

004 

041 

078 

115 

161 

29  28  27 

1.17 

8 
9 

07  188 

225 

262 

298 

335 

372 

408 

445 

482 

518 

83  32  81 

1.18 

655 

591 

628 

664 

700 

737 

773 

809 

846 

882 

37  36  35 

1.19 

120 

918 

954 

990 

027 

063 

009 

T35 

171 

207 

343 

38  37  36 

1.20 

08  279 

314 

350 

386 

422 

458 

493 

629 

665 

600 

4    4    4 

1.21 

2 

636 

672 

707 

743 

778 

814 

849 

884 

920 

955 

8    7    7 

1.22 

3 

991 

036 

061 

096 

132 

167 

202 

237 

272 

307 

11  11  11 

1.23 

4 

09  342 

377 

412 

447 

482 

517 

552 

687 

621 

656 

15  15  14 

1.24 

125 

691 

726 

760 

795 

830 

864 

899 

934 

968 

003 

19  19  18 

1.25 

6 

10  037 

072 

106 

140 

175 

209 

243 

278 

312 

846 

23  22  22 

1.26 

7 

380 

415 

449 

483 

517 

551 

585 

619 

653 

687 

27  26  25 

1.27 

8 

721 

755 

789 

823 

857 

890 

924 

958 

992 

035 

30  30  29 

1.28 

9 

11  069 

093 

126 

160 

193 

227 

261 

294 

327 

361 

34  33  32 

1.29 

130 

894 

428 

461 

494 

528 

561 

694 

628 

661 

694 

35  34  33 

1.30 

1 

727 

760 

793 

826 

860 

893 

926 

959 

993 

024 

4    8    3 

1.31 

2 

12  057 

090 

123 

166 

189 

222 

254 

287 

320 

352 

7    7    7 

1.32 

3 

385 

418 

450 

483 

516 

548 

581 

613 

646 

678 

11  10  10 

1.33 

4 

710 

743 

775 

808 

840 

872 

905 

937 

969 

001 

14  14  13 

1.34 

135 

13  033 

06G 

098 

130 

162 

194 

226 

258 

290 

322 

18  17  17 

1.35 

6 

354 

386 

418 

450 

481 

613 

545 

577 

609 

640 

21  20  20 

1.36 

7 

672 

704 

735 

767 

799 

830 

862 

893 

925 

956 

25  24  23 

1.37 

8 

988 

019 

061 

083 

114 

145 

176 

208 

239 

270 

28  27  26 

1.38 

9 

14  301 

333 

364 

395 

426 

457 

489 

520 

551 

582 

32  31  80 

1.39 

140 

613 

644 

675 

706 

737 

768 

799 

829 

860 

891 

32  3130 

1.40 

1 

922 

953 

983 

014 

045 

076 

106 

137 

168 

198 

3    3    3 

1.41 

2 

15  229 

259 

290 

320 

351 

381 

412 

442 

473 

503 

6    6    6 

1.42 

3 

534 

564 

594 

625 

655 

685 

716 

746 

776 

806 

10    9    9 

1.43 

4 

836 

866 

897 

927 

957 

987 

017 

047 

077 

107 

13  12  12 

1.44 

145 

16  137 

167 

197 

227 

266 

286 

316 

346 

376 

406 

16  16  15 

1.45 

6 

435 

465 

495 

624 

554 

584 

613 

643 

673 

702 

19  19  18 

1.46 

7 

732 

761 

791 

820 

850 

879 

909 

938 

967 

997 

22  22  21 

1.47 

8 

17  026 

056 

085 

114 

143 

173 

202 

231 

260 

289 

8 

26  25  24 

1.48 

9 

319 

348 

377 

406 

435 

464 

493 

522 

551 

580 

9 

29  28  27 

1.49 

150 

609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

1.50 

i009 

f     ' 

LOGARITHMS  OF  NUMBERS. 
1. — Logarithms. — Continued. 


109 


No. 


Common  Logmrtthma  of  Nnxfiben. 


Nftperlan. 


L.    O 


No.  Log.  DU. 


ISO 

2 
3 
4 

155 
6 
7 
S 
f 

160 

1 

2 

3 

4 

1S5 
S 
7 
8 
f 

170 


185 

< 
7 


Its 

« 

7 
8 
f 


17  €09 
898 

18  1S4 


19  033 
812 
5B0 
8C6 

20  140 


952 

21  219 
484 

748 

23  Oil 

272 

631 

788 

23  045 
300 
853 
805 

24  055 

304 
551 
797 

25  042 
285 

527 
788 

26  007 
245 
482 

717 
991 

27  184 
416 


875 

28  103 
330 
656 

780 

29  003 
226 
447 
8«7 


30  108 


725 
013 

298 
583 
865 

145 
424 
700 
976 
249 

520 
790 
059 
325 
590 

854 
115 
376 
634 
891 

147 
401 
654 
905 
155 

403 
650 
895 
139 
382 

624 
864 
102 
340 
576 

811 
045 
277 
508 
738 

967 
194 
421 
646 
870 

092 
314 
535 
754 
973 


869 
156 
441 
724 
008 

285 
562 
838 
112 


656 
925 
192 
458 
722 

985 
246 
505 
763 
019 

274 
528 
779 


39  38 

3  3 

6  6 

9  8 

12  11 

15  14 
17  17 
20  20 

23  22 

26  25 

27  36 

3  3 

6  5 

8  8 

11  10 

14  13 

16  16 
19  18 
22  21 

24  23 

35  34 

3  2 

5  5 

8  7 

10  10 


34  33 

2  2 

5  5 

7  7 

10  9 


1.50 
11 
1.52 
1.53 
1.54 


1.56 

1.57 

58 

69 


33  31 

2  2 

4  4 

7  6 

9  8 

II  11 

13  13 

15  15 

18  17 

20  19 


I 

1.60 
1.61 
1.62 
1.63 
64 

1.65 
66 
1.67 
1.68 
1.69 

70 

71 

1.72 

1.73 

1.74 

75 
1.76 
1.77 
1.78 
1.79 

1.80 

1.81 

I. 

I. 

1.84 

1.85 
1.86 
1.87 
1.88 
1. 

1.90 
1.91 
1.92 
1.93 
1.94 

1.95 

1.96 

1.97 

1 

I 

2.00 


.40547  «. 
.41211  SJJ 
.41871  SS 
.42627  55J 
.43178  *" 

647 
.43825  »MA 
.44469  SJ 
.45108  g; 
.45742  %\ 
.46373  ^^ 

627 
.47000  s,^ 
.47623  JIJ 
.48243  Jf5 
.48868  J^ 
.49470  "" 


50078 
50682 
51282 
51879 
52473 


604 
600 
597 
694 


.53063  «,« 
.63649  SS 
.64232  JU 
.54812  ^ 
.66389  ^^^ 
573 
.55062  eito 
.56631  S, 

.57098  r:l 

.57661  Sj 

.58222  ^* 

557 

.58779  554 

.59884  Z)i 
.60432  ^° 
.60977  ^" 

542 
.61519  530 
.62058  ^: 
.62594  g* 
.63127  °xf 
.63658  ^^ 

527 
.64185  „5 

.66233  JfX 
.68752  5  : 
.66269  ^" 

614 
.66783  rii 
.67294  rij 
.67803  JX? 
.68310^ 
.68813  **^ 

603 
.69315 


no 


6— LOGARITHMS  OF  NUMBERS. 
1. — ^LoGAJiiTHiiS. — Continued. 


300 

30  103 

125 

146 

168 

190 

211 

233 

256 

276 

298 

23 

2.00 

.89315  4fla 
«813  J~ 
.70310  HI 

1 

320 

341 

363 

384 

406 

428 

449 

471 

492 

614 

2 

2.01 

2 

635 

657 

678 

600 

621 

643 

664 

685 

707 

728 

4 

2.02 

3 

750 

771 

792 

814 

836 

856 

878 

899 

920 

942 

7 

2.03 

.70804  IJJ 

4 

963 

984 

006 

027 

048 

069 

001 

112 

133 

164 

9 

2.04 

.71295  *»* 
489 
.71784  4^ 
.72271  12 
.72755  gj 

.76081  *" 
466 
.76547  -^ 
.77011  JS 
.77473  J~ 
.77932  Jg 
.78390  *^ 
456 

.79751  S 
,80200  J2 
'.80648  *^ 

445 
.81093   .„ 
.81536  J« 
.81978  ;*• 
.82418  IS 
.82856^^ 

435 
.83291   .^ 
.83725  J*J 
.84157  iS 
.84687  J2 
.85015  *" 

427 
.85442   .,, 

418 
.87547   ..^ 
.87963  J  ; 
.88377  J  J 
.88789  Ijj 
.89200  ^" 

409 
.89609  -n- 
.90016  J2 
.90422  2J 
.90826  JJJ 
.91228  -"» 

401 
.91629 

205 

81  176 

197 

218 

239 

260 

281 

302 

323 

345 

366 

11 

2.05 

6 

387 

406 

429 

450 

471 

492 

613 

634 

556 

676 

13 

2.06 

7 

697 

618 

639 

660 

681 

702 

728 

744 

765 

786 

16 

2.07 

8 

806 

827 

848 

869 

890 

911 

931 

962 

973 

994 

18 

2.08 

9 

32  016 

035 

056 

077 

098 

118 

139 

160 

181 

201 

20 

2.09 

310 

222 

243 

263 

284 

306 

325 

346 

366 

387 

408 

31 

2.10 

1 

428 

449 

469 

490 

610 

531 

552 

572 

593 

613 

2 

2.11 

2 

634 

654 

675 

696 

716 

736 

756 

777 

797 

818 

4 

2.12 

3 

838 

858 

879 

899 

919 

940 

960 

980 

001 

021 

6 

2.13 

4 

33  041 

062 

082 

102 

122 

143 

163 

183 

203 

224 

8 

2.14 

215 

244 

264 

284 

304 

325 

345 

366 

386 

406 

425 

11 

2.16 

6 

445 

465 

486 

606 

626 

546 

566 

586 

606 

626 

13 

2.16 

7 

646 

666 

686 

706 

726 

746 

766 

786 

806 

826 

16 

2.17 

8 

846 

866 

885 

906 

925 

945 

965 

985 

005 

025 

17 

2.18 

9 

34  044 

064 

084 

104 

124 

143 

163 

183 

203 

223 

19 

2.19 

330 

242 

262 

282 

301 

321 

341 

361 

380 

400 

420 

30 

2.20 

1 

439 

459 

479 

498 

518 

537 

657 

577 

596 

616 

2 

2.21 

2 

635 

655 

674 

694 

713 

733 

763 

772 

792 

811 

4 

2.22 

3 

830 

850 

869 

889 

908 

928 

947 

967 

986 

005 

6 

2.23 

4 

36  025 

044 

064 

083 

102 

122 

141 

160 

180 

199 

8 

2.24 

225 

218 

238 

257 

276 

295 

315 

334 

353 

372 

392 

10 

2.25 

6 

411 

430 

449 

468 

488 

507 

526 

545 

564 

583 

12 

2.26 

7 

603 

622 

641 

660 

679 

698 

717 

736 

755 

774 

14 

2.27 

8 

793 

813 

832 

851 

870 

889 

908 

927 

946 

965 

16 

2.28 

9 

984 

003 

021 

DiO 

059 

078 

097 

116 

135 

154 

18 

2.29 

330 

36  173 

192 

211 

229 

248 

267 

286 

306 

324 

342 

19 

2.30 

1 

361 

380 

399 

418 

436 

455 

474 

493 

511 

530 

2 

2.31 

2 

549 

568 

586 

605 

624 

642 

661 

680 

698 

717 

4 

2.32 

3 

736 

754 

773, 

791 

810 

829 

847 

866 

884 

903 

6 

2.33 

4 

922 

940 

959 

977 

996 

014 

033 

051 

070 

068 

6 

2.34 

235 

37  107 

126 

144 

162 

181 

199 

218 

236 

264 

273 

10 

2.36 

6 

291 

310 

328 

346 

365 

383 

401 

420 

438 

457 

11 

2.36 

7 

476 

493 

511 

630 

548 

666 

685 

603 

621 

639 

13 

2.37 

8 

658 

676 

694 

712 

731 

749 

767 

785 

803 

822 

15 

2.38 

9 

840 

858 

876 

894 

912 

931 

949 

967 

985 

003 

17 

2.39 

340 

38  021 

039 

057 

075 

093 

112 

130 

148 

166 

184 

18 

2.40 

202 

220 

238 

256 

274 

292 

310 

328 

346 

364 

2 

2.41 

2 

382 

399 

417 

435 

453 

471 

489 

507 

525 

543 

4 

2.42 

3 

561 

578 

596 

614 

632 

650 

668 

686 

703 

721 

5 

2.43 

4 

739 

757 

775 

792 

810 

828 

846 

863 

881 

899 

7 

2.44 

245 

917 

934 

952 

970 

987 

005 

023 

041 

058 

076 

9 

2.45 

6 

39  094 

111 

129 

146 

164 

182 

199 

217 

235 

252 

11 

2.46 

7 

270 

287 

305 

322 

340 

358 

375 

393 

410 

428 

IS 

2.47 

8 

445 

463 

480 

498 

515 

533 

550 

568 

585 

602 

14 

2.48 

9 

620 

637 

655 

672 

690 

707 

724 

742 

759 

777 

16 

2.49 

350 

794 

811 

829 

846 

863 

881 

898 

915 

933 

950 

2.50 

Die 

tized 

by_ 

Go 

bgk 

LOGARITHMS  OF  NUMBERS. 
1. — ^Logarithms. — Continued. 


in 


1 
a 

3 

4 

« 

7 
8 
9 

330 

1 
2 
3 

4 

S75 
6 
7 
8 
» 


CommoD  Logaritbms  of  Nombas. 


L.  O   1 


39  794 
9e7 

40  140 
312 
483 

094 

834 

993 

41  163 
330 

497 


42  160 

325 
488 

661 
813 
975 

48  136 
297 
457 
616 
775 

933 
44  091 

348 
404 
560 

716 
871 
46  035 
179 
332 


637 
788 
939 


240 


687 
835 


47  129 
276 
422 

867 

712 


169 
329 
489 
648 
807 

965 
122 
279 
436 
592 

747 
902 
056 
209 
362 

515 
667 
818 
969 
120 

270 
419 
568 

716 
864 

012 

159 
305 
451 

741 


756 


813  828 


010 

163 
317 
469 

621 
773 
924 
075 
225 

374 
523 
672 
820 
967 

114 
261 
407 
553 
698 


Naperlan. 


No.  Log.    DIL 


2.50 
2.51 
2.52 
2.53 
2.54 

2.55 
2.56 
2.57 
2.58 
2.56 

2.60 
2.61 
2.62 
2.63 
2.64 

2.65 
2.66 
2.67 
2.68 
2.69 

2.70 
2.71 
2.72 
2.73 
2.74 

2.75 
2.76 
2.77 
2.78 
2.79 

2.80 
2.81 
2.82 
2.83 
2.84 

2.85 
2.86 
2.87 
2.88 
2.89 

2.90 
2.91 
2.92 
2.93 
2.94 

2.95 
2.96 
2.97 
2.98 
2.99 


842|  3.00 

Uigitized 


wGrOOg 


.91629  -vft 

.92028  *;; 

.92426  ^l 
.92822  ill 
.93216  '**'* 
393 
.93609  3ft, 

.94001  55; 

.94391  ,JJ 

.94779  ,5? 

.95166  ^^^ 

385 

.95551  osi 

.95935  ill 

.96317  2? 

.96698  ill 

.97078  ^^" 

878 

.97466  *,, 

.97833  ?il 

.98208  ill 

.98582  %il 

.98954  ^^^ 

371 

.99325  370 

.99696  iU 

.00063  5!? 

.00430  JJi 

.00796  ^® 

364 

1.01160  «»« 

1.01523  5;? 

1.01885  ,JJ 

1.02245^60 

1 .02604  ^^ 
358 
1.02962  9K« 
1.03318  ^S 
1.03674  i^ 
1.04028  i^ 
1.04380  "^^^ 
352 
1.04732  350 
1.05082  ^5J 
1.05431  ill 
1.05779  i\^ 
1.06126  ■**' 
345 
1.06471  -.. 
1.06815  ill 

1.07158  izi 
1.07500  i\: 

1.07841  ''" 
340 


1.08181  qofl 

1.08519  5^; 

.08856  lil 


1.08856  Hi 

.09192  33; 

1.09527  ^^^ 

334 

1.09861 


112 


t,—LOGARITHMS  OF  NUMBERS. 
1 . — ^Loo  AMTHMS. — Continued . 


Common  LogarlUimfl  of  Numbers. 


L.  O 


47  712 
B57 

48  001 
144 
287 

430 
S72 

714 
855 
996 

49  136 
276 
415 
554 


969 

50  106 
243 
879 

615 
651 
786 
920 

51  055 

188 
322 
455 
587 
720 

851 

983 

62  114 

244 

375 

504 
634 
763 
892 

53  020 

148 
275 
403 
529 
656 

782 
908 

54  033 
158 
283 


407  419  432  444 


456  469  4S1 


574  7 


706 
838 

970 
101 
231 
362 
492 

621 
750  6 
879 
007  8 


263 
390  1 


P.  P. 


Xftperian. 


No.   Log.     DIf. 


3.00 
3.01 
3.02 
3.03 
3.04 

3.05 
3.06 
3.07 
3.08 
3.09 

3.10 
3.11 
3.12 
3.13 
3.14 

3.15 
3.16 
3,17 
3.18 
3.19 

3.20 
3.21 
3.22 
3.28 
3.24 

3.25 
3.26 
3.27 
3.28 
3.29 

3.30 
3.31 
3.32 

3.; 

3.34 

3.35 
3.36 
3.37 
3.38 
3.39 

3.40 
3.41 
3.42 
3.43 
3.44 

3.45 
3.46 
3.47 
3.48 
3.49 

3.50 


1.09861  ,^ 
1.10194  ?« 
1.10526  J^J 
1.10866^0 
1.11186  **" 
328 
1.11514  . 
1.11841  \ 
1.12168; 
1.12493  ; 
1.12817  * 


1.13140  . 

1.13462  : 
.13783  : 
.14103  : 
.14422  "^ 

a 

.14740  5 

.15057  \ 

1.15373  * 

1. 

1 

1. 
1. 


by  Google 


f  327 
i327 
?325 
*  324 


323 

322 
321 
320 
319 

318 

817 

.15688  ?}J 

.16002  ^" 

313 

.16315  3,2 

.16627  3  2 

.16938  IIJ 

1.17248  liJ 

1.17667  ^™ 

308 

1.17865  .ne 

1.18173  fS 

1.18479'^ 
1.18784  Is 
.19089  '"* 
803 
1.19392  3j- 
1.19696  Jj* 

1.20297  IXJ 
1.20597  ^"" 

299 
1.20896  Mfi 
1.21194  gj 
1.21491  SI 
1.21788  ^i 
1 .22083  *•• 

295 
1.22378  -Q. 
1.22671  Jg 
1.22964  |g 
1.23256  S? 
1.23547  ^* 

290 
1.23837  ,M 
1.24127  ^ 

1.24415^ 
.24703  ^ 
.24990  jg^ 


LOGARITHMS  OF  NUMBERS. 
1. — ^Logarithms. — Cootintied. 


113 


Oommoa  Logarltlima  of  Numbers. 


Nftperlaa. 


L.   O      1 


Log.      DIf. 


2M  M407 
531 
CM 

m 


355  91023 
145 


751 

871 

9fl 

5$  110 


365 

7 


371 

1 
I 
Z 

4 

rs 
< 

7 
8 

f 


385 


8 
7 
8 
f  4 


848 

487 


837 

97  084 
171 
387 


5lf 

834 
748 


548 
888 

771 
883 
889 

>  108 
218 
828 
438 
650 

878 


108 


373 
480 
608 
728 

844 

Ml 
078 
184 
310 

438 

542 

657 

n2 

887 

001 

115 
228 
343 
456 

569 

681 
794 
906 
017 

129 
240 
351 
461 
572 

682 

791 
901 
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118 


456 
588 

704 
827 
949 

073 
194 
315 
437 
558 

678 
799 
919 
038 
158 

277 
396 
514 
632 
750 

867 
984 
101 
217 
334 

449 
566 
680 
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910 

m^ 

138 
252 
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591 
704 
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151 
262 
373 
483 
594 

704 
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141 


518 
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765 
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011 

138 
255 
376 
497 
618 

739 
859 
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098 
217 

336 
455 
573 
691 
808 

926 
043 
159 
276 
392 

507 
623 
738  7 
852 
967 

061 
195 
309 
422 


217     228 


282     293     304 


3.50 
3.51 
3.52 
3.53 
3.54 


8.55  1.26695 

3.56  1.26976 

8.57  1.27257 

3.58  1.27536 

3.59  1.27815 

3.60 
3.61 
3.62 
3.63 
3.64 


3.65 
3.66 
3.67 
3.68 
3.69 

3.70 
3.71 
3.72 
3.73 
3.74 

3.75 
3.76 
3.77 
3.78 
3.79 

3.80 
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3183 
3.84 

3.85 
3.86 
3.87 
3.88 
3.89 

3.90 
3.91 
3.92 
3.93 
3.94 

3.95 
3.96 
3.97 
3.98 
3.99 


25r6 
25562 
25846 
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286 
284 
284 
283 


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r 

.29473  . 

9tktAC    ^ 


281 
281 
279 
279 
278 

278 
276 
276 
275 
275 

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1.30291  g; 

i .30563  ^^^ 

270 
.30833  270 
.31103  £J 
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267 
.32176  »-. 
.32442  III 
.32707  III 
.32972  ;55 
.33237  2*5 

263 
.33500  -R- 
.33763  ;g 
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.34286  il\ 
.34547  ^®^ 

260 
.34807  ,j5n 
.35067  ;52 
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.35584  ,^; 
.35841  ^^' 

257 
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.36354  ;?X 
.36609  III 
.36864  iZ 
.37118  ^^ 

254 
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1.37877  ^9f 
1.38128  il\ 
1.38379  ^^*^ 

250 


2 
1 .38629 


yCdogl 


114 


%.^LOGARITHMS  OF  NUMBERS. 
1 . — Logarithms. — Continued. 


CommoD  Logartthms  of  Namben. 


Napoteo. 


L.    O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

►.  p.      No. 

Jjog.      Dtf. 

400 

80  206 

217 

228 

239 

249 

260 

271 

282 

293 

304 

II      4.00 

1.3S818_ 
1.38879  12 
1.39128*2 
1.8»37T;J? 

24S 

1.38878.,^ 
1.40118  IS 
1.403*4  1^ 
1-40810  |« 
1.40854  ^ 
345 
1.41088  _ 
1.41842  |g 

1.41585*5 
1.41838  12 
1.42070^ 
241 
1.42311  ^, 
1.42552  fJl 

1 

314 

325 

336 

347 

358 

369 

379 

390 

401 

412 

1 

1 

4.01 

2 

423 

433 

444 

455 

466 

477 

487 

498 

509 

620 

2 

2 

4.08 

a 

531 

541 

552 

563 

574 

584 

595 

606 

617 

627 

3 

3 

4.03 

4 

638 

649 

680 

670 

681 

692 

703 

713 

724 

738 

4 

4 

4.04 

405 

748 

758 

767 

778 

788 

799 

810 

821 

831 

842 

6 

8 

4.05 

6 

853 

863 

874 

885 

895 

906 

917 

927 

938 

949 

6 

7 

4.06 

7 

959 

970 

981 

991 

002 

013 

023 

034 

045 

055 

7 

8 

4.07 

8 

61  066 

077 

087 

098 

109 

119 

130 

140 

151 

162 

8 

9 

4.06 

9 

172 

183 

194 

204 

215 

226 

236 

247 

257 

268 

9 

10 

4.09 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

4.10 

1 

384 

395 

405 

416 

426 

437 

448 

458 

469 

479 

1 

4.11 

2 

490 

500 

511 

621 

532 

542 

553 

663 

574 

684 

2 

4.12 

595 

606 

616 

627 

637 

648 

658 

669 

679 

690 

8 

4.18 

4 

700 

711 

721 

731 

743 

752 

763 

773 

784 

794 

4 

4.14 

415 

805 

815 

826 

836 

847 

857 

868 

878 

888 

899 

5 

4.15 

909 

920 

930 

941 

951 

962 

972 

982 

993 

003 

6 

4.18 

7 

62  014 

024 

034 

045 

055 

066 

076 

086 

097 

107 

7 

4.17 

1.42792  JS 

8 

118 

128 

138 

149 

159 

170 

180 

190 

201 

211 

8 

4.18 

1.43831  2 

9 

221 

232 

242 

252 

263 

273 

284 

294 

304 

316 

9 

4.19 

1.43270^ 

1.43508  _ 

1.43748  2 

420 

335 

335 

346 

356 

366 

377 

387 

397 

408 

418 

10 

4.10 

428 

439 

449 

459 

469 

480 

490 

600 

511 

521 

1 

4.21 

2 

531 

542 

552 

562 

572 

683 

593 

603 

613 

624 

2 

4.22 

1.43884  g 
1.44220  S 
1.44458°* 
286 
1.44882  •« 
1.44927  2! 

3 

634 

644 

655 

665 

675 

686 

696 

706 

716 

726 

3 

4.23 

4 

737 

747 

757 

767 

778 

788 

798 

808 

818 

829 

4 

4.24 

425 

839 

849 

859 

870 

880 

890 

900 

910 

921 

931 

6 

4.25 

6 

941 

951 

961 

972 

982 

992 

002 

012 

022 

033 

6 

4.26 

7 

63  043 

053 

063 

073 

083 

094 

104 

114 

124 

134 

7 

4.27 

1.45161  gj 
1.45396  gj 
1.45828*" 

233 
1.45681  M 
1.48QM^ 
1. 46328  gf 
1.48557  gi 
1.46787  ^ 

231 
1.47818  M 
1.47247  S 

8 

144 

155 

165 

175 

185 

195 

206 

216 

225 

236 

8 

4.28 

9 

246 

256 

266 

276 

286 

296 

306 

317 

327 

337 

^ 

4.29 

430 

847 

357 

367 

377 

387 

397 

407 

417 

428 

438 

4.30 

1 

448 

458 

468 

478 

488 

498 

508 

518 

528 

638 

^ 

4.81 

2 

548 

558 

568 

579 

589 

699 

609 

619 

629 

639 

8 

4.32 

3 

649 

659 

669 

679 

689 

699 

709 

719 

729 

739 

8 

4.33 

4 

749 

769 

769 

779 

789 

799 

809 

819 

829 

831 

4 

4.84 

435 

849 

859 

869 

879 

889 

899' 

909 

919 

929 

939 

5 

4.35 

6 

949 

959 

969 

979 

988 

998 

008 

018 

028 

038 

6 

4.36 

64  048 

058 

068 

078 

088 

098 

108 

118 

128 

137 

7 

4.37 

1.47478  S 
1.47706  g 
1.47833  ^ 
227 
1.48188  2- 
1-48387  gl 
1.48614  EI 

8 

147 

157 

167 

177 

187 

197 

207 

217 

227 

237 

8 

4.38 

9 

246 

256 

266 

276 

286 

296 

306 

316 

326 

336 

9 

4.39 

440 

345 

356 

365 

376 

385 

396 

404 

414 

424 

484 

4.40 

1 

444 

454 

464 

473 

483 

493 

603 

513 

623 

532 

1 

4.41 

2 

542 

552 

562 

572 

682 

691 

601 

611 

621 

631 

2 

4.42 

3 

640 

650 

660 

670 

680 

689 

699 

709 

719 

729 

3 

4.43 

1.48848  g 

1.49065"* 

225 

1.49280  _ 

1.49515  5* 

4 

738 

748 

768 

768 

777 

787 

797 

807 

816 

826 

4 

4.44 

445 

836 

846 

856 

865 

876 

885 

895 

904 

914 

924 

5 

4.5 

4.45 

6 

933 

943 

953 

963 

972 

982 

992 

002 

Oil 

021 

6 

5.4 

4.48 

7 

65  031 

040 

050 

060 

070 

079 

089 

099 

108 

118 

7 

4.47 

1.4973»S} 

8 

128 

137 

147 

157 

167 

176 

186 

196 

205 

215 

8 

4.48 

1.49963  ^ 

9 

225 

234 

244 

254 

263 

273 

283 

292 

302 

312 

9 

4.49 

1.60185  «* 

480 

321 

331 

341 

350 

360 

369  J  379 

389 

398 

408 

^ 

4.60 

T 

*     223 
1.50488 

Digiti2 

edby 

t: 

lOO^ 

^le  ■ 

LORARITHMS  OF  NUMBERS. 


1 . — ^Logarithms. — Continued. 


116 


r 

No. 

Common  Logartttunfl  of  Nomben. 

NftperlMi. 

L.    O 

1 

2 

3 

4 

5 

• 

7 

8 

9 

P 

.  P. 

No. 

Lo8.      Dlf. 

491 

•6  321 

331 

341 

350 

360 

369 

379 

389 

398 

408 

10 

4.60 

1.50408  ,„ 

1.50630  ;*J 

1 

418 

437 

437 

447 

456 

466 

475 

485 

495 

504 

1 

4.51 

1 

514 

523 

533 

543 

553 

563 

571 

581 

591 

600 

2 

4.52 

a 

•10 

619 

629 

639 

648 

658 

667. 

677 

686 

696 

3 

4.53 

1:51072  ;2| 

* 

7M 

715 

725 

734 

744 

753 

763 

772 

782 

792 

4 

4.54 

1.61293  221 

230 

1.51513  ,,« 

48 

801 

811 

820 

830 

839 

849 

858 

868 

877 

887 

5 

4.55 

< 

8M 

906 

916 

925 

935 

944 

954 

963 

978 

982 

6 

4.56 

1.61732  III 

7 

992 

•01 

on 

020 

9S0 

m 

049 

058 

068 

077 

7 

4.57 

1-61961  !  ! 

t 

•6  087 

096 

106 

115 

134 

134 

143 

158 

162 

172 

8 

4.58 

1.52170  III 

f 

181 

191 

200 

210 

319 

229 

338 

847 

257 

266 

9 

4.50 

1.52388  »»8 

4M 

27« 

385 

295 

304 

314 

333 

332 

342 

351 

361 

4.60 

218 
1.52606  ,,- 
1.62823  III 

1 

370 

380 

389 

398 

408 

41T 

427 

436 

445 

455 

1 

4.61 

2 

464 

474 

483 

492 

502 

511 

521 

530 

539 

549 

2 

4.62 

1.53039  l\i 

a 

558 

567 

577 

586 

596 

•05 

614 

624 

633 

642 

3 

4.63 

1.53256  III 

4 

•52 

661 

•71 

680 

689 

699 

708 

717 

727 

736 

4 

4.64 

1.63471  ^** 

as 

745 

756 

764 

773 

783 

792 

801 

811 

820 

829 

5 

4.65 

216 
1.63687  ,,. 

6 

839 

848 

857 

867 

876 

885 

894 

904 

913 

922 

6 

4.66 

1.53902  515 

T 

932 

941 

960 

960 

969 

978 

987 

997 

006 

015 

7 

4.67 

1.54116  VA 

8 

67  025 

034 

043 

052 

062 

071 

080 

089 

099 

108 

8 

4.68 

1.64330  51* 

» 

117 

127 

136 

145 

164 

164 

173 

182 

191 

201 

9 

4.69 

1.64543  213 

4M 

310 

319 

228 

237 

24r 

25^ 

366 

274 

284 

293 

4.70 

213 

1.54756  ,,« 

1 

303 

311 

321 

330 

339 

348 

357 

867 

376 

385 

1 

4.71 

1.54969  51! 

2 

394 

403 

413 

422 

431 

440 

449 

459 

468 

477 

2 

4.72 

1.55181  5Ii 

2 

486 

495 

504 

514 

623 

533 

541 

550 

560 

669 

3 

4.73 

1.66393!? 

4 

578 

587 

596 

605 

614 

634 

633 

642 

601 

660 

4 

4.74 

1.55604  211 

479 

669 

679 

688 

697 

706 

715 

724 

733 

742 

752 

5 

4.5 

4.76 

210 
1.65814  ,,, 
1.66025  5!1 

< 

7«t 

770 

779 

788 

797 

806 

815 

825 

834 

843 

6 

5.4 

4.76 

7 

853 

861 

870 

879 

888 

897 

906 

916 

925 

934 

7 

4.77 

1.66235  5U 

8 

943 

953 

961 

970 

979 

988 

997 

006 

015 

024 

8 

4.78 

1.66444  52 

9 

68  OM 

043 

053 

061 

070 

079 

068 

097 

106 

115 

9 

4.79 

1.66663  209 

209 

1.56862  «fto 

4M 

134 

133 

143 

151 

160 

169 

178 

187 

196 

206 

4.80 

1 

215 

324 

233 

242 

251 

260 

269 

278 

287 

296 

1 

4.81 

1.57070  ;JJ 

1 

305 

314 

323 

333 

341 

350 

359 

368 

377 

386 

2 

4.82 

1.57277  ,"0 

3 

395 

404 

413 

422 

431 

440 

449 

458 

467 

476 

3 

4.83 

1.67485  ;SJ 

4 

485 

494 

502 

511 

520 

539 

538 

547 

866 

565 

4 

4.84 

1.67691  20« 

207 

1.57898  ,nA 

1.68104  2j; 

48ft 

674 

663 

592 

601 

610 

619 

628 

637 

646 

655 

5 

4.85 

< 

664 

673 

681 

690 

699 

708 

717 

726 

786 

744 

6 

4.86 

7 

753 

763 

771 

780 

789 

797 

806 

815 

824 

833 

7 

4.87 

1.58309  205 

8 

842 

851 

860 

869 

878 

886 

895 

904 

913 

922 

8 

4.88 

1.58515  5X5 

» 

931 

940 

949 

958 

966 

976 

984 

993 

003 

on 

9 

4.89 

1.68719  204 

490 

69  020 

028 

037 

046 

055 

064 

073 

062 

090 

099 

4.90 

205 
1.58924  9m 

] 

108 

117 

126 

135 

144 

163 

161 

170 

179 

188 

1 

4.91 

1.59127  52 

2 

197 

205 

214 

223 

232 

241 

249 

268 

267 

276 

2 

1.6 

4.92 

1.69331  2M 

3 

385 

294 

202 

311 

320 

329 

338 

346 

365 

364 

3 

3.4 

4.93 

1.59534  203 

4 

J73 

381 

390 

399 

408 

417 

425 

434 

443 

452 

4 

4.94 

1.59737  203 
202 
1.59939  202 
I.60I4I  *J* 
1.60342  20 
1.60.543  201 
1.60744  201 
206 
1.60944 

4»5 

461 

469 

478 

487 

496 

504 

513 

522 

631 

539 

5 

4.96 

• 

648 

557 

566 

574 

583 

692 

601 

609 

618 

627 

6 

4.96 

7 

636 

644 

653 

662 

671 

679 

688 

697 

705 

714 

7 

5.6 

4.97 

8 

733 

732 

740 

749 

758 

767 

775 

784 

793 

801 

8 

6.4 

4.98 

9 

810 

819 

827 

836 

845 

864 

862 

871 

880 

888 

9 

4.99 

fOQ 

897 

906 

914 

« 

932 

940 

949 

958 

966 

975 

5.00 

byCoogle 


m 


6.— LOGARITHMS  OF  NUMBERS, 
1. — ^LooARiTHirs.— Continued. 


No. 

Oommoa  hogaxithma  of  Numben. 

N*pertui. 

L.    O 

I 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.  P. 

No. 

I-og.       Dit 

800 

69  897 

906 

914 

988 

932 

940 

949 

958 

966 

975 

5.00 

1.60944^ 
1.61144  f2 

1.61343  ;2 

1.61542  IS 

1.61741  *" 

196 

1.6213T  12 
1.62234}" 
1.62531  is 
1.62728  ^ 
196 
1.62824  .^ 
1.63120  12 
1.63315  JS 

1.63511  ;2 

1.63706  '** 
195 
1.63800  ,„ 
1.64094  Is 
1.64287  JS 
1.64481  Is 
1.64673  *" 
183 
1.64866  ,„ 
1.65M8  ^ 
1.65250    Jf 

1.65441 };; 

1.65632  *" 

191 

1.65823  .« 

1 

984 

992 

001 

010 

D18 

027 

036 

044 

053 

062 

5.01 

2 

70  070 

079 

088 

096 

105 

114 

122 

131 

UO 

148 

5.02 

3 

157 

165 

174 

183 

191 

200 

209 

217 

226 

234 

5.03 

4 

243 

252 

260 

269 

278 

286 

295 

303 

312 

321 

5.04 

605 

329 

338 

346 

355 

364 

372 

381 

389 

398 

406 

4.5 

5.05 

6 

415 

424 

432 

441 

449 

458 

467 

475 

484 

492 

6.4 

6.06 

7 

501 

509 

518 

526 

535 

544 

552 

561 

669 

678 

5.07 

8 

586 

595 

603 

612 

621 

629 

638 

646 

655 

663 

6.08 

9 

672 

680 

689 

697 

706 

714 

723 

731 

740 

749 

5.08 

810 

757 

766 

774 

783 

791 

800 

808 

817 

825 

834 

5.10 

1 

842 

851 

859 

868 

876 

885 

893 

902 

910 

919 

6.11 

2 

927 

935 

944 

952 

961 

969 

978 

986 

996 

003 

5.12 

3 

71  012 

020 

029 

037 

046 

054 

063 

071 

079 

088 

5.13 

4 

096 

105 

113 

122 

130 

139 

147 

155 

164 

172 

6.14 

615 

181 

189 

198 

206 

214 

223 

231 

240 

248 

257 

5.15 

6 

265 

273 

282 

290 

299 

307 

315 

324 

332 

341 

5.16 

7 

349 

357 

366 

374 

383 

391 

399 

408 

416 

425 

6.17 

8 

433 

441 

450 

458 

466 

475 

483 

492 

500 

508 

6.18 

9 

617 

525 

533 

642 

550 

559 

567 

576 

584 

592 

5.19 

830 

600 

609 

617 

625 

634 

642 

650 

659 

667» 

675 

5.20 

1 

684 

692 

700 

709 

717 

725 

734 

742 

750 

759 

5.21 

2 

767 

775 

784 

792 

800 

809 

817 

825 

834 

842 

1.6 

5.22 

3 

850 

858 

867 

875 

883 

892 

900 

908 

917 

925 

2.4 

6.23 

4 

933 

941 

950 

958 

966 

975 

983 

991 

999 

006 

5.24 

535 

72  016 

024 

032 

041 

049 

057 

066 

074 

062 

090 

5.25 

6 

099 

107 

115 

123 

132 

140 

148 

156 

165 

173 

5.26 

1.66013  JS 

7 

181 

189 

198 

206 

214 

222 

230 

239 

247 

255 

5.6 

6.27 

1.66203  }S 

8 

263 

272 

280 

288 

296 

304 

313 

321 

329 

337 

6.4 

5.28 

1.66393    g 

9 

346 

354 

362 

370 

378 

387 

395 

403 

411 

419 

5.29 

1.66582  *®» 

530 

428 

436 

444 

452 

460 

469 

477 

485 

493 

501 

6.30 

189 
1.66771  ,« 

1 

509 

518 

526 

534 

542 

650 

558 

567 

575 

583 

5.31 

1.66958  ;g 

2 

591 

699 

607 

616 

624 

632 

640 

648 

656 

665 

5.32 

1.67147  Jg 

3 

673 

681 

689 

697 

705 

713 

722 

730 

738 

746 

5.33 

1.67335  Is 

4 

754 

762 

770 

779 

787 

795 

803 

811 

819 

827 

5.34 

1.67523  ^^ 
187 

535 

835 

843 

852 

860 

868 

876 

884 

892 

900 

908 

5.35 

1.67710  ,5^ 

6 

916 

825 

933 

941 

949 

957 

965 

973 

981 

989 

5.36 

1.67896  Jf! 

7 

997 

006 

014 

022 

030 

038 

046 

054 

m 

070 

5.37 

1.68(W   Jg 

8 

73  078 

086 

094 

102 

111 

119 

127 

135 

143 

151 

5.38 

1.68269   JS 

9 

159 

167 

175 

183 

191 

199 

207 

215 

223 

231 

5.39 

1.68455  *** 

840 

239 

247 

255 

263 

272 

280 

288 

296 

304 

312 

5.40 

ie« 

1 

320 

328 

336 

344 

352 

360 

368 

376 

384 

392 

0.7 

5.41 

1.^  Jg 

2 

400 

408 

416 

424 

432 

440 

448 

456 

464 

472 

1.4 

5.42 

1-6901O  J£ 

3 

480 

488 

496 

504 

612 

520 

528 

536 

544 

152 

6.43 

1.69194   ;JJ 

4 

560 

568 

576 

584 

592 

600 

608 

616 

624 

632 

5.44 

1.69378  *" 

545 

640 

648 

656 

664 

672 

679 

687 

695 

703 

711 

3.5 

5.45 

18^ 

1.69S62  ,- 

6 

719 

727 

735 

743 

751 

759 

767 

775 

783- 

791 

4.2 

5.46 

1.69745  J~ 

7 

799 

807 

815 

823 

830 

838 

846 

854 

862 

870 

6.47 

1.69928  ;g 

8 

878 

886 

894 

902 

910 

918 

926 

933 

911 

949 

5.6 

5.48 

1.70111  ;g 

9 

957 

965 

973 

981 

989 

997 

005 

013 

020 

028 

9 

6.3 

5.49 

1.7029®  **^ 

850 

74  036 

044 

052 

060 

068 

076 

084 

092 

099 

107 

5.50 

1.70475 

LOGARITHMS  OF  NUMBERS. 
1. — ^LooAUTHMS. — Continued. 


117 


Ko. 

Oommoa  Logartttims  of  Nnmben. 

Napertan. 

L.   O 

1 

2 

3 

4 

6 

6 

7 

8 

9 

P.  P. 

No. 

Log.      DIL 

SM 

74  tM 

844 

053 

060 

068 

076 

084 

092 

099 

107 

5.60 

1.70475  ,„ 
1.70656    5; 
1.70838    15 
1.71019    5i 
1.71199  *^ 
181 
1.71380  ,on 
1.71560    °X 
1.71740    ?X 

1.71919  5; 

1.72098  '^* 
179 
1.72277  ,-« 
1.72455  JJJ 
1.72633    55 
1.78811    5? 
1.71988  *^^ 
178 
1.73166  ,-- 
1.73342    55 
1.73519    Ji 
1.73695  "J 
1.73871  *^* 
176 
1.74047  ,,_ 
1.74222    75 

1.74397  ;;J 
1.74572  JJ 
1.74746  "* 

174 
1.74920  ,-- 
1.75094  '* 
1.75267  \i,\ 
1.75440  ;* 
1.76613  *7' 

173 
1.75786  ,72 

1.75958  ;; 

1.76130  I'f 
1.76302  }J 
1.76473  "* 

171 
1.76644  ,7, 
1.76816  5J 
1.76985  \ip. 
1.77156  ?1 
1.77326  *7® 

169 
1.77496  ,7ft 
1.77665  IJ 
1.77834  JJ 
1.78002  JJS 
1.78171  *** 

168 
1.78339  ,-- 
1.78507  IS 
1.78675  Jf 
1 .78842  S5 
1.79009  **' 

167 
1.79176 

1 

lis 

123 

131 

139 

147 

156 

162 

170 

178 

186 

5.51 

2 

194 

303 

810 

218 

225 

233 

241 

249 

257 

266 

5.62 

3 

xn 

280 

288 

296 

304 

312 

830 

327 

836 

343 

5.53 

4 

Ul 

358 

867 

374 

883 

390 

898 

406 

414 

421 

6.54 

SS 

4M 

437 

445 

453 

461 

468 

476 

484 

492 

500 

5.55 

« 

m 

616 

523 

581 

639 

647 

564 

662 

570 

578 

5.56 

7 

m 

583 

601 

609 

617 

624 

638 

640 

648 

666 

5.57 

8 

•n 

871 

679 

987 

695 

702 

710 

718 

726 

733 

5.58 

9 

741 

749 

757 

764 

772 

780 

788 

798 

803 

811 

5.59 

540 

819 

827 

834 

842 

880 

886 

865 

873 

881 

889 

8 

5.60 

1 

89< 

904 

912 

920 

927 

935 

943 

950 

958 

966 

1 

6.61 

2 

974 

981 

989 

997 

005 

012 

02O 

028 

035 

043 

1.6 

5.62 

3 

rsisi 

8»» 

066 

074 

082 

089 

097 

105 

113 

120 

2.4 

5.63 

4 

138 

138 

143 

151 

150 

166 

174 

183 

189 

197 

3 

5.64 

565 

808 

813 

230 

238 

236 

243 

251 

250 

268 

274 

4 

5.65 

6 

883 

389 

297 

305 

312 

320 

388 

835 

343 

35^ 

5 

5.66 

7 

858 

388 

374 

381 

389 

897 

404 

412 

420 

427 

6.6 

5.67 

a 

438 

442 

450 

458 

465 

473 

481 

488 

496 

504 

6.4 

5.68 

9 

811 

619 

536 

584 

542 

649 

557 

666 

672 

68( 

7 

5.69 

ITt 

887 

895 

603 

610 

618 

626 

633 

641 

648 

666 

5.70 

1 

884 

871 

879 

886 

694 

702 

709 

717 

724 

732 

5.71 

2 

748 

747 

755 

762 

770 

778 

786 

793 

800 

808 

5.72 

3 

815 

833 

831 

838 

846 

853 

861 

868 

876 

884 

5.73 

4 

881 

899 

906 

914 

921 

929 

987 

944 

962 

969 

5.74 

579 

987 

974 

982 

989 

997 

008 

018 

020 

027 

035 

6.75 

C 

78  8U 

050 

067 

065 

072 

080 

087 

095 

103 

110 

5.76 

7 

118 

125 

133 

140 

148 

165 

163 

170 

178 

185 

5.77 

S 

193 

300 

208 

216 

223 

230 

238 

246 

263 

260 

5.78 

f 

898 

375 

283 

290 

298 

305 

313 

320 

328 

336 

5.79 

SM 

843 

390 

358 

365 

873 

380 

388 

395 

403 

410 

7 

5.80 

1 

418 

425 

433 

440 

448 

465 

462 

470 

477 

485 

0.7 

5.81 

Z 

483 

500 

507 

515 

583 

530 

637 

646 

558 

559 

1.4 

5.82 

3 

667 

674 

582 

689 

607 

604 

612 

619 

626 

634 

2 

5.83 

4 

811 

849 

856 

664 

671 

678 

686 

693 

701 

708 

3 

5.84 

5»5 

716 

723 

730 

738 

745 

763 

760 

768 

775 

782 

3.5 

5.85 

6 

T90 

797 

805 

812 

819 

887 

834 

842 

849 

866 

4.2 

5.86 

7 

884 

871 

879 

886 

893 

901 

908 

916 

923 

930 

5 

5.87 

i 

838 

945 

953 

960 

967 

976 

982 

^89 

997 

004 

5.6 

5.88 

9 

nou 

019 

028 

034 

041 

048 

056 

063 

070 

078 

6.3 

5.89 

9M 

686 

803 

100 

107 

116 

182 

129 

137 

144 

151 

5.90 

I 

168 

186 

178 

181 

188 

195 

203 

210 

217 

225 

5.91 

2 

383 

240 

247 

254 

863 

269 

276 

283 

291 

298 

5.92 

3 

886 

313 

380 

327 

836 

348 

349 

357 

364 

371 

5.93 

4 

879 

386 

393 

401 

408 

415 

422 

430 

437 

444 

5.94 

M5 

458 

459 

466 

474 

481 

488 

495 

603 

610 

517 

5.95 

6 

638 

582 

539 

546 

554 

661 

668 

576 

583 

690 

5.96 

7 

197 

806 

612 

619 

627 

634 

641 

648 

656 

663 

5.97 

8 

870 

877 

685 

608 

690 

706 

714 

721 

728 

735 

8 

5.98 

9 

743 

750 

757 

764 

772 

779 

786 

793 

801 

808 

9 

5.99 

MM 

816 

823 

830 

837 

844 

861 

859 

866 

873 

880 

6.00 

r^.n 

UyiL 

118 


6.— LOGARITHMS  OF  NUMBERS. 
1. — ^Logarithms. — Continued. 


No. 

Naperian. 

L.    O 

1 

2 

8 

4 

5 

6 

7 

8 

9 

P 

.P. 

No. 

Log.      Die. 

600 

77  815 

822 

830 

837 

844 

851 

869 

866 

873 

880 

8 

6.00 

1.79176  .^ 
1.79342    g 

1.79609    S 
1.79676    Jj 
1.79840  **^ 
166 
1.80006  ,^ 
1.80171    g 
1.80336  }g 
1.80500    g 
1.80665*^ 

1.80829  ... 
1.80993  }g 
1.81166  }g 
1.81319    g 
1.81482  1® 
163 
1.61645  .«. 
1.81808  ;g 
1.81970  }g 

l:gJS- 

161 
1.82455  ... 
1.82616    •} 
1.82777  \l] 
1.82938  I" 
1.83098  ^^ 

1.83258  ,M 
1.88418  ;J5 
1.83S78  12 
1.83737  iS 
1.83806  **■ 

156 
1.84055  .^ 
1.84214  }2 
1.84372  }2 
1.84530  IS 
1.84688  *" 

157 

1.85003  ;g 
1.65160  }E 
1.85317  }S 
1.86478  >» 

157 
1.86630  ,„ 
1.85786  }2 
1.85048  IS 
1.86097  iS 
1.86253  ** 

155 
1.86408  IB 
1.86563  }| 
1.86718  IS 
1.86872  H 
1.87026*** 

194 
1.87180 

887 

895 

902 

909 

916 

924 

931 

938 

945 

952 

1 

1 

6.01 

960 

967 

974 

981 

988 

996 

003 

010 

W 

025 

2 

1.6 

6.02 

78  038 

039 

046 

053 

061 

068 

075 

082 

089 

097 

3 

2.4 

6.03 

104 

111 

118 

126 

132 

140 

147 

154 

161 

168 

4 

8 

6.04 

606 

176 

188 

190 

197 

204 

211 

219 

226 

233 

240 

5 

4 

6.05 

847 

854 

262 

269 

876 

283 

290 

297 

805 

812 

6 

5 

6.06 

819 

826 

333 

340 

847 

856 

362 

369 

376 

883 

7 

5.6 

6.07 

890 

398 

405 

412 

419 

426 

433 

440 

447 

456 

8 

6.4 

6.06 

462 

469 

476 

483 

490 

497 

504 

612 

619 

626 

9 

7 

6.09 

610 

633 

540 

547 

564 

561 

669 

576 

583 

590 

597 

6.10 

604 

611 

618 

625 

633 

640 

647 

654 

661 

668 

1 

6.11 

675 

682 

689 

696 

704 

711 

718 

725 

732 

739 

2 

6.12 

746 

753 

760 

767 

774 

781 

789 

796 

802 

810 

8 

6.18 

817 

824 

831 

838 

845 

862 

859 

866 

873 

880 

4 

6.14 

615 

888 

895 

902 

909 

916 

923 

930 

937 

944 

951 

E 

6.15 

858 

965 

972 

979 

986 

993 

000 

007 

014 

021 

< 

6.16 

79  029 

036 

043 

050 

057 

064 

071 

078 

085 

092 

7 

6.17 

099 

106 

113 

120 

127 

134 

141 

148 

155 

162 

8 

6.18 

169 

176 

183 

190 

197 

204 

211 

218 

226 

232 

9 

6.19 

630 

839 

246 

253 

260 

267 

274 

281 

288 

295 

302 

7 

6.80 

809 

316 

323 

330 

337 

344 

351 

358 

865 

372 

1 

0.7 

6.21 

879 

386 

393 

400 

407 

414 

421 

428 

435 

442 

2 

1.4 

6.22 

449 

456 

463 

470 

477 

484 

491 

498 

605 

511 

3 

2 

6.23 

616 

525 

532 

539 

546 

653 

660 

667 

574 

681 

4 

8 

6.24 

625 

668 

595 

602 

609 

616 

623 

630 

637 

644 

650 

6 

3.5 

6.25 

657 

664 

671 

678 

685 

692 

699 

706 

713 

720 

6 

4.8 

6.26 

727 

734 

741 

748 

754 

761 

768 

775 

782 

789 

7 

5 

6.27 

796 

803 

810 

817 

824 

831 

837 

844 

851 

858 

8 

6.6 

6.28 

865 

872 

879 

886 

893 

90O 

906 

913 

920 

927 

9 

6.3 

6.29 

630 

934 

941 

948 

955 

962 

969 

976 

962 

989 

996 

6.30 

80  003 

010 

017 

024 

030 

037 

044 

051 

058 

065 

1 

6.31 

072 

079 

085 

092 

099 

106 

113 

120 

127 

134 

2 

6.32 

140 

147 

154 

161 

168 

175 

182 

188 

195 

202 

3 

6.33 

209 

216 

223 

229 

236 

243 

250 

257 

264 

271 

4 

6.34 

635 

277 

284 

291 

298 

305 

312 

318 

325 

332 

839 

5 

6.35 

846 

353 

359 

366 

373 

380 

387 

393 

400 

407 

6 

6.36 

414 

421 

428 

434 

441 

448 

455 

462 

468 

475 

7 

6.37 

482 

489 

496 

602 

609 

616 

g? 

530 

536 

543 

8 

6.38 

600 

557 

564 

670 

677 

684 

698 

604 

611 

9 

6.39 

640 

618 

625 

632 

638 

645 

652 

669 

665 

672 

679 

6 

6.40 

686 

693 

699 

706 

713 

720 

726 

733 

740 

747 

1 

0.6 

6.41 

754 

760 

767 

774 

781 

787 

794 

801 

808 

814 

2 

1.2 

6.42 

821 

828 

835 

841 

848 

855 

862 

868 

876 

882 

3 

1.8 

6.43 

889 

895 

902 

909 

916 

922 

929 

936 

943 

949 

4 

8.4 

6.44 

645 

956 

963 

969 

976 

983 

990 

996 

003 

010 

017 

6 

3 

6.45 

81  023 

030 

037 

043 

050 

057 

064 

070 

077 

084 

6 

3.6 

6.46 

090 

097 

104 

111 

117 

124 

131 

137 

144 

151 

7 

4.2 

6.47 

158 

164 

171 

178 

184 

191 

198 

024 

211 

818 

8 

4.8 

6.48 

224 

231 

238 

245 

251 

258 

265 

271 

278 

285 

9 

5.4 

6.49 

650 

291 

298 

305 

311 

318 

325 

331 

838 

346 

851 

6.60 

zjogarithms  of  numbers. 

1. — LooARiTHMS. — Continued. 


119 


No. 

OommoD  Losarltlimfl  of  Numbers. 

Naperian. 

L.    O 

1 

2 

8 

4 

5 

6 

7 

8 

9 

F 

.  P. 

No. 

W.      Dlf. 

«• 

81191 

298 

305 

311 

318 

326 

331 

838 

346 

861 

6.50 

1.87180  |« 
1.87334    g 
1.87487    S 
1.87641    S 
1.87794  *^ 
153 
1.87947  ,-, 
1.88099  \ll 
1.88251    g 
1.88403  jg 
1.88556^52 

152 
1.88707  ,,, 
1.88858  \l\ 
1.89010  S 
1.89160  15? 
1,89311  *5l 

151 
1.89462  _ 
1.89612  \Z 
1.89762  IS 
1.89912  JJ 
1.90061  *** 

150 
1.90211  ,.• 
1.90360  JJ! 
1.90509  j; 
1.90658  J» 
1.90806  *" 

148 

llSlS  J« 
1.91250  \*l 
1.91398  g 
1.91545  ^" 

147 
1.91692  ,4- 
1.91839  JJI 
1.91986  IJJ 
1.92132  }j; 
1.92279  ^" 

146 
1.92425,^ 
1.92571  JJ5 
1.92716  J J* 
1.92862  \il 
1.93007  "5 

146 
1.93152  ,4B 
1.93297  J; 
1.93442  JJ 
1.93586  JJ 
1.93730  "* 

144 
1.93874  ,., 
1.94018  IJJ 
1.94162  J* 
1.94305  IJJ 
1.94448  *" 

143 
1.94691 

1 

SS8 

285 

371 

878 

886 

391 

398 

406 

411 

418 

1 

6.51 

1 

429 

431 

438 

446 

461 

458 

465 

471 

478 

485 

2 

6.52 

1 

491 

496 

505 

611 

618 

625 

631 

638 

544 

661 

3 

6.53 

4 

968 

594 

571 

678 

684 

691 

696 

604 

611 

617 

4 

6.64 

CS6 

•24 

931 

937 

644 

661 

687 

664 

671 

677 

684 

6 

6.66 

« 

990 

997 

704 

710 

717 

723 

730 

737 

743 

760 

6 

6.56 

7 

7S7 

793 

770 

776 

783 

790 

796 

803 

809 

816 

7 

6.57 

8 

823 

929 

836 

842 

849 

856 

862 

869 

875 

882 

8 

6.58 

9 

888 

895 

902 

908 

916 

921 

928 

936 

941 

948 

9 

6.59 

6M 

966 

991 

968 

974 

981 

987 

994 

000 

007 

014 

7 

6.60 

1 

88  920 

027 

033 

040 

046 

053 

060 

066 

073 

079 

1 

0.7 

6.61 

2 

•69 

093 

099 

105 

112 

119 

126 

132 

138 

145 

2 

1.4 

6.62 

2 

151 

198 

164 

171 

178 

184 

191 

197 

204 

210 

3 

2 

6.63 

4 

217 

228 

230 

236 

243 

849 

266 

263 

269 

276 

4 

8 

6.64 

60 

282 

289 

296 

303 

308 

316 

321 

828 

834 

341 

6 

3.6 

6.65 

6 

247 

254 

360 

367 

373 

380 

387 

393 

400 

406 

6 

4.2 

6.66 

7 

413 

419 

426 

432 

439 

446 

453 

458 

465 

471 

7 

6 

6.67 

8 

478 

484 

491 

497 

504 

610 

617 

623 

630 

636 

8 

6.6 

6.68 

» 

»<3 

549 

566 

562 

660 

676 

682 

688 

696 

601 

9 

6.3 

6.69 

«?• 

907 

914 

920 

627 

633 

640 

646 

668 

659 

666 

6.70 

1 

972 

979 

686 

692 

698 

706 

711 

718 

724 

730 

1 

6.71 

3 

727 

743 

750 

766 

763 

769 

776 

782 

789 

795 

2 

6.72 

8 

802 

808 

814 

821 

827 

834 

840 

847 

853 

860 

3 

6.73 

4 

899 

872 

879 

886 

898 

898 

905 

911 

918 

924 

4 

6.74 

175 

920 

937 

943 

950 

956 

963 

969 

976 

982 

988 

6 

6.75 

1 

995 

«0I 

008 

014 

027 

033 

040 

046 

062 

6 

6.76 

7 

83  959 

065 

072 

078 

086 

091 

097 

104 

110 

117 

7 

6.77 

8 

123 

129 

136 

142 

149 

166 

161 

168 

174 

181 

8 

6.78 

9 

187 

193 

200 

206 

213 

219 

286 

232 

238 

246 

9 

6.79 

«M 

SI 

287 

264 

270 

276 

288 

289 

296 

802 

308 

6 

6.80 

1 

215 

321 

327 

334 

840 

347 

853 

359 

366 

372 

1 

0.6 

6.81 

3 

278 

285 

391 

398 

404 

410 

417 

423 

429 

436 

2 

1.2 

6.82 

8 

442 

448 

466 

461 

467 

474 

480 

487 

4» 

499 

8 

1.8 

6.83 

i 

509 

512 

618 

626 

631 

637 

644 

660 

656 

563 

4 

2.4 

6.84 

$a 

809 

975 

683 

888 

694 

601 

607 

613 

620 

626 

5 

3 

6.86 

i 

932 

989 

645 

661 

656 

664 

670 

677 

683 

689 

6 

3.6 

6.86 

7 

999 

702 

708 

716 

721 

727 

734 

740 

746 

753 

7 

4.2 

6.87 

8 

790 

795 

771 

778 

784 

790 

797 

803 

809 

816 

8 

4.8 

6.88 

• 

822 

838 

836 

841 

847 

868 

860 

866 

872 

879 

' 

6.4 

6.89 

«M 

885 

891 

897 

904 

910 

016 

923 

939 

936 

942 

6.90 

I 

948 

954 

960 

967 

973 

979 

986 

992 

998 

004 

1 

6.91 

2 

84  011 

017 

023 

029 

036 

042 

048 

055 

061 

067 

2 

6.92 

1 

973 

060 

086 

092 

096 

106 

111 

117 

123 

130 

8 

6.93 

4 

129 

142 

148 

166 

161 

167 

173 

180 

186 

192 

4 

6.94 

655 

198 

205 

211 

817 

228 

230 

236 

242 

248 

256 

5 

6.95 

6 

291 

297 

tii 

280 

286 

292 

296 

305 

311 

317 

6 

6.96 

7 

223 

330 

236 

342 

348 

854 

361 

367 

373 

379 

7 

6.97 

8 

389 

293 

898 

404 

410 

417 

423 

429 

436 

442 

8 

6.98 

9 

448 

454 

460 

466 

478 

479 

486 

491 

497 

504 

9 

6.99 

9W 

510 

519 

522 

628 

636 

641 

647 

663 

669 

566 

7.00 

~ 

itized  h) 

\jOi 

3^te- 

120 


^.—LOGARITHMS  OF  NUMBERS. 
1. — ^LoOARiTHUS. — Continued. 


No. 

Common  Losaritlunfl  of  Numben. 

Napertan. 

L.    O 

1 

2 

8 

4 

6 

6 

7 

8 

9 

I 

>.  P. 

No. 

Log.       DU. 

700 

84  510 

516 

522 

628 

535 

641 

547 

653 

559 

566 

7 

7.00 

1.94591  ... 
1.94734  ;S 
1.94876  Jl 
1.95019  IS 
1.95161  ^^ 

143 
1.96303  ... 
1.95444  liJ 
1.95586  }}? 
1.96727  }J» 
1.96869  *** 

140 
1.96009  ij. 
1.96150  IJJ 
1.96291  1*1 
1.96481  }JX 
1.96571  **0 

140 
1.96711  ,^ 
1.96851  ;*J 
1.96991  }*; 
1.97130  \il 
1.97269  *^' 

139 
1.97408  ,„ 
1.97547  !*J 
1.97686  IS 
1.97824  }2 
1.97962  *^ 

138 
1.98100  ,», 
1.98238  }g 
1.98376  15 
1.98513  }J5 
1.98660  »" 

137 

1:S?U  1 

1.09834  '^ 
136 
1.99470  ,^ 
1.99606  JS 
1.99743  }?J 
1.99877  IJJ 
2.00013  *^ 
135 
2.00148  ,» 
2.00283  IJS 
2.00418  J" 
2.00553  Jg 
2.00687  *34 

2.00811  !^ 
2.00956  !S 
2.01089  }g 
2.01323  iJj 
3.01387  ^ 
133 
3.014M 

672 

578 

684 

590 

597 

603 

609 

615 

621 

628 

0.7 

7.01 

634 

640 

646 

652 

658 

665 

671 

677 

683 

689 

i 

1.4 

7.02 

696 

702 

708 

714 

720 

726 

733 

739 

746 

761 

3 

3 

7.03 

767 

763 

770 

776 

782 

788 

794 

800 

807 

813 

4 

3 

7.04 

705 

819 

825 

831 

837 

844 

850 

856 

862 

868 

874 

5 

8.6 

7.05 

880 

887 

893 

899 

905 

911 

917 

924 

930 

936 

6 

4.2 

7.06 

942 

948 

954 

960 

967 

973 

979 

985 

991 

997 

7 

5 

7.07 

86  003 

009 

016 

022 

028 

034 

040 

046 

052 

058 

8 

5.6 

7.08 

066 

071 

077 

083 

089 

095 

101 

107 

114 

120 

1 

6.3 

7.09 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

7.10 

187 

193 

199 

205 

211 

217 

224 

230 

236 

242 

1 

7.11 

248 

254 

260 

266 

272 

278 

285 

291 

297 

303 

2 

7.12 

809 

815 

321 

327 

333 

339 

345 

352 

358 

364 

3 

7.13 

370 

876 

382 

388 

394 

400 

406 

412 

418 

426 

4 

7.14 

715 

431 

437 

443 

449 

455 

461 

467 

473 

479 

485 

8 

7.15 

491 

497 

503 

509 

616 

522 

528 

534 

640 

646 

6 

7.16 

562 

558 

564 

670 

576 

582 

588 

594 

600 

606 

7 

7.17 

612 

618 

625 

631 

637 

643 

649 

655 

661 

667 

8 

7.18 

673 

679 

685 

691 

697 

703 

709 

715 

721 

727 

9 

7,19 

720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 

6 

7.20 

794 

800 

806 

812 

818 

824 

830 

836 

842 

848 

1 

0.6 

7.21 

854 

860 

866 

872 

878 

884 

890 

896 

902 

908 

2 

1.2 

7.22 

914 

920 

926 

932 

938 

944 

910 

956 

962 

968 

3 

1.8 

7.23 

974 

980 

986 

992 

998 

004 

010 

m 

022 

028 

4 

8.4 

7.24 

725 

86  034 

040 

046 

052 

056 

064 

070 

076 

0^ 

088 

6 

3 

7.25 

094 

100 

106 

112 

118 

124 

130 

136 

141 

147 

6 

8.6 

7.26 

153 

159 

165 

171 

177 

183 

189 

196 

201 

207 

7 

4.2 

7.27 

213 

219 

225 

231 

237 

243 

249 

255 

261 

267 

8 

4.8 

7.28 

273 

279 

285 

291 

297 

303 

306 

814 

320 

326 

9 

6.4 

7.29 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 

7.30 

392 

398 

404 

410 

415 

421 

427 

433 

439 

446 

1 

7.31 

451 

457 

463 

469 

475 

481 

487 

493 

499 

504 

2 

7.82 

510 

516 

522 

528 

534 

540 

546 

552 

658 

664 

3 

7.83 

670 

676 

681 

587 

693 

599 

605 

611 

617 

623 

4 

7.84 

736 

629 

635 

641 

646 

652 

658 

664 

670 

676 

682 

8 

7.85 

688 

694 

700 

705 

711 

717 

723 

729 

735 

741 

« 

7.36 

747 

753 

759 

764 

770 

776 

782 

788 

794 

800 

7 

7.37 

806 

812 

817 

823 

829 

836 

841 

847 

853 

859 

fl 

7.38 

864 

870 

876 

882 

888 

894 

900 

906 

911 

917 

1 

7.89 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

5 

7.40 

962 

988 

994 

999 

005 

Oil 

017 

023 

029 

036 

1 

0.6 

7.41 

87  040 

046 

052 

058 

064 

070 

075 

081 

087 

093 

2 

1 

7.42 

099 

105 

HI 

116 

122 

128 

134 

140 

146 

151 

3 

1.5 

7.43 

157 

163 

169 

175 

181 

186 

192 

198 

204 

210 

4 

2 

7.44 

745 

216 

221 

227 

233 

239 

245 

251 

256 

262 

268 

5 

2.5 

7.45 

274 

280 

286 

291 

297 

303 

309 

315 

320 

326 

6 

3 

7.46 

332 

338 

344 

349 

355 

361 

367 

373 

379 

384 

7 

3.5 

7.47 

8 

390 

396 

402 

408 

413 

419 

426 

431 

437 

442 

8 

4 

7.48 

9 

448 

454 

460 

466 

471 

477 

483 

489 

496 

500 

9 

4.5 

7.49 

750 

506 

512 

518 

523 

529 

635 

541 

547 

553 

658 

/^~> 

7.50 

T 

Di 

gitized 

"by 

Go 

oyk 

LOGARITHMS  OF  NUMBERS. 
1. — ^LooAKiTBiis. — Continued. 


131 


Ho. 

Common  LogarlUmii  ot  Numben. 

Naperlan. 

L.    O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P.P. 

No. 

Log.      DIf. 

780 

87  508 

513 

518 

523 

529 

535 

541 

547 

652 

658 

7.80 

2.01490  ,-. 
2.01624  \t* 
2.01757  g 
2.01890  IJ 
2.02022  *" 

133 
2.02155  ,32 
2.02287  \ll 
2.02419  \ll 
2.02551  II 
2.02683  *'* 

182 
2.02815  ,., 
2.02946  111 
2.03078  \l\ 
2.03209  {!} 
2.03340  "' 

131 
2.03471  ,30 
2.03601  J!" 
2.03732  IJ 
2.03862  IJ 
2.03993  "° 

130 
2.04122  ,30 
2.04252  IJ 
2.04381  |f: 
2.04611  \ll 
2.04640  "* 

129 
2.04769  ,20 
2.04898  Jl; 
2.05027  }|; 
2.05156  IIJ 
2.05284  '*" 

128 
2.05412  ,2« 
2.05540  Is 
2.05668  IS 
2.05796  IS 
2.05924  ^^ 

127 
2.06051  ,.« 
2.06179  1; 
2.06306  g 
2.08433  g 
2.06660  '*^ 

126 
2.06686  ,27 
2.06813  \f. 
2.06939  \il 
2.07065  IS 
2.07191  *2« 

126 
2.07317  ,.- 

2.07443  ;!; 

2.07568    5J 
2.07694  JU 
2.07819  *" 
125 
2.07944 

q\£ 

584 

670 

576 

681 

587 

593 

699 

604 

610 

616 

7.51 

8» 

638 

633 

639 

645 

651 

656 

662 

668 

674 

7.52 

878 

685 

691 

697 

703 

708 

714 

720 

726 

731 

7.53 

717 

743 

749 

754 

760 

766 

773 

Z77 

783 

789 

7.54 

755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 

7.65 

858 

858 

864 

869 

875 

881 

887 

892 

898 

904 

7.56 

110 

915 

921 

627 

933 

938 

944 

950 

955 

961 

7.57 

987 

873 

978 

964 

990 

996 

001 

007 

013 

018 

7.58 

88  084 

030 

036 

041 

047 

053 

058 

064 

070 

076 

7.59 

M0 

881 

087 

093 

098 

104 

110 

116 

121 

127 

133 

6 

7.60 

138 

144 

150 

166 

161 

167 

173 

178 

184 

190 

0.6 

7.61 

198 

201 

207 

313 

218 

224 

230 

235 

241 

247 

1.2 

7.62 

352 

358 

264 

370 

275 

281 

287 

292 

298 

304 

1.8 

7.63 

809 

315 

831 

326 

332 

338 

343 

349 

355 

360 

2.4 

7.64 

765 

386 

372 

377 

383 

389 

395 

400 

406 

412 

417 

3 

7.65 

423 

429 

434 

440 

446 

451 

457 

463 

468 

474 

3.6 

7.66 

480 

485 

491 

497 

602 

508 

513 

519 

525 

530 

4.2 

7.67 

538 

642 

547 

553 

559 

564 

570 

576 

581 

587 

4.8 

7.68 

583 

508 

604 

610 

615 

621 

627 

632 

638 

643 

5.4 

7.69 

770 

848 

655 

660 

666 

672 

677 

683 

689 

694 

700 

7.70 

705 

711 

717 

722 

728 

734 

739 

745 

750 

756 

7.71 

763 

767 

773 

779 

784 

790 

795 

801 

807 

812 

7.72 

818 

824 

829 

835 

840 

846 

852 

867 

863 

868 

3 

7.73 

874 

880 

885 

891 

897 

902 

908 

913 

919 

925 

4 

7.74 

77! 

«»0 

836 

941 

947 

953 

958 

964 

969 

975 

981 

J 

7.75 

90S 

902 

997 

903 

0O9 

014 

020 

025 

031 

037 

7.76 

89  043 

048 

053 

059 

064 

070 

076 

081 

087 

092 

7.77 

098 

104 

109 

115 

120 

126 

131 

137 

143 

148 

7.78 

154 

159 

165 

170 

176 

182 

187 

193 

198 

204 

7.79 

780 

209 

315 

221 

226 

232 

237 

243 

248 

254 

260 

8 

7.80 

865 

371 

376 

382 

287 

293 

298 

304 

310 

315 

0.5 

7.81 

321 

336 

332 

337 

343 

348 

364 

360 

365 

371 

1 

7.82 

376 

382 

387 

393 

398 

404 

409 

416 

421 

426 

1.6 

7.83 

633 

437 

443 

448 

454 

459 

465 

470 

476 

481 

2 

7.84 

789 

487 

483 

498 

504 

509 

515 

520 

526 

531 

537 

2.5 

7.85 

543 

548 

563 

569 

564 

570 

575 

581 

586 

592 

3 

7.86 

597 

603 

609 

114 

620 

625 

631 

636 

642 

647 

3.5 

7.87 

653 

658 

664 

669 

675 

680 

686 

691 

697 

702 

4 

7.88 

708 

713 

719 

724 

730 

735 

741 

746 

752 

757 

4.6 

7.89 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 

7.90 

818 

833 

829 

834 

840 

845 

851 

856 

862 

867 

7.91 

873 

878 

883 

889 

894 

900 

905 

911 

916 

922 

7.92 

827 

883 

838 

944 

949 

955 

960 

966 

971 

977 

7.93 

882 

988 

993 

998 

004 

009 

015 

020 

026 

031 

7.94 

71S 

80  037 

043 

048 

053 

059 

064 

069 

075 

080 

086 

7.95 

091 

097 

102 

108 

113 

119 

124 

129 

135 

140 

7.96 

146 

151 

157 

163 

168 

173 

179 

184 

189 

195 

7.97 

200 

206 

211 

217 

222 

227 

233 

238 

244 

24^ 

7.98 

355 

360 

366 

371 

276 

282 

287 

293 

298 

304 

7.99 

308 

314 

330 

325 

331 

336 

342 

347 

352 

358 

E 

W 

^.00 

112 


^.—LOGARITHMS  OF  NUMBERS. 
1. — ^Logarithms. — Continued. 


No. 

CommoD  Logftrtthms  of  Numbers. 

Napertu. 

L.    O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P 

.  P. 

No. 

Log.      Dtt. 

800 

90  309 

314 

320 

325 

331 

336 

343 

347 

352 

358 

8.00 

2.07944  .^ 
2.08069    f* 
2.08194  }g 
2.08318  H 

1 

363 

369 

374 

380 

385 

390 

396 

401 

407 

412 

1 

8.01 

2 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 

8 

8.02 

3 

472 

477 

482 

488 

493 

499 

504 

509 

515 

520 

3 

8.03 

4 

526 

531 

536 

542 

547 

553 

.558 

563 

569 

574 

4 

8.04 

2.06443  *^ 
124 
2.08667  ,-^ 
2.08691  !« 
2.08815  U 
2.08939    Jl 
2.09063  *** 
123 
2.09186  ,g. 
2.09310  1^ 

806 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 

5 

8.05 

6 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 

6 

8.06 

7 

687 

693 

698 

703 

709 

714 

720 

725 

730 

786 

7 

8.07 

8 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 

8 

8.08 

9 

795 

800 

806 

811 

816 

822 

827 

833 

838 

843 

9 

8.09 

810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 

6 

8.10 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 

1 

0.6 

8.11 

2 

956 

961 

966 

972 

977 

982 

988 

993 

998 

0O4 

2 

1.2 

8.13 

2.09433    g 
2.09556  ^ 
2.09679  *23 

122 
2.09802  ,., 
2.09924  |g 
2.10047    g 
2.10169  jg 
2.10291  *** 

122 
2.10413  ,M 
2.10535  \Z 

3 

91  009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

3 

1.8 

8.13 

4 

062 

068 

073 

078 

084 

089 

094 

100 

105 

no 

4 

2.4 

8.14 

815 

116 

121 

126 

132 

137 

142 

148 

163 

158 

164 

5 

3     1  8.15 

6 

169 

174 

180 

185 

190 

196 

201 

306 

212 

217 

6 

3.6 

8.16 

7 

222 

228 

233 

238 

243 

249 

254 

259 

265 

ro 

7 

4.2 

8.17 

8 

r5 

281 

386 

291 

297 

302 

307 

312 

318 

323 

8 

4.8 

8.18 

9 

828 

334 

339 

344 

360 

355 

360 

865 

371 

376 

9 

6.4 

8.19 

830 

881 

887 

392 

397 

403 

408 

413 

418 

424 

429 

8.80 

434 

440 

445 

450 

455 

461 

466 

471 

477 

482 

1 

8.11 

2 

487 

492 

498 

503 

508 

514 

519 

524 

529 

535 

2 

8.22 

2.10657    2 

3 

540 

545 

551 

556 

561 

566 

573 

577 

582 

58? 

3 

8.23 

2.10779  }Jf 

4 

593 

598 

603 

609 

614 

619 

624 

630 

635 

640 

4 

8.24 

2.10900  *** 

121 

2.11021  .-„ 

2.11142  iii 

2.11263  ill 

825 

645 

651 

656 

661 

666 

672 

677 

682 

687 

693 

6 

8.25 

6 

698 

703 

709 

714 

719 

724 

730 

735 

740 

745 

6 

8.K 

7 

751 

756 

761 

766 

772 

777 

782 

787 

793 

798 

7 

8.r 

8 

803 

808 

814 

819 

834 

829 

834 

840 

845 

850 

8 

8.88 

2.11384    1 
2.11505  "* 

121 
2.11626  ... 
2.11746  12 
2.11866  IS 
2.11986  |S 
2.12106  ■"' 

120 
2.12226  ,M 
2.12346  ;*! 

9 

855 

861 

866 

871 

876 

882 

887 

892 

897 

903 

9 

6.10 

830 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 

S 

8.80 

960 

965 

971 

976 

981 

986 

991 

997 

003 

807 

1 

0.5 
1 

8.81 

2 

92  012 

018 

023 

028 

033 

038 

044 

049 

054 

059 

2 

8.32 

8 

065 

070 

075 

080 

085 

091 

096 

101 

106 

111 

3 

1.5 

8.83 

4 

117 

122 

127 

132 

137 

143 

148 

153 

158 

163 

4 

2 

6.34 

835 

169 

174 

179 

184 

189 

195 

200 

205 

210 

215 

5 

2.5 

8.85 

6 

221 

226 

231 

236 

241 

247 

252 

257 

262 

267 

6 

3     18.36 

7 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

7 

3.5 

8.37 

2.12465  111 

8 

324 

330 

335 

340 

345 

350 

355 

361 

366 

871 

8 

4 

8.38 

2.13585  }» 

9 

376 

381 

387 

392 

397 

402 

407 

412 

418 

423 

9 

4.5 

8.89 

2.12704  *" 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 

8.40 

119 
2.12833  ... 

1 

480 

485 

490 

495 

500 

505 

511 

516 

521 

526 

1 

8.41 

2.I2M2  \\l 

2 

531 

536 

542 

547 

552 

557 

562 

567 

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578 

2 

8.42 

2.18061  1  ; 

2.13180  J}J 
2.13298  "' 

119 
2.12417  ,,. 
2.13SS5  ill 
2.136S3  in 
2.18771  IIS 
2.13889"' 

118 
2.14007 

8 

583 

588 

593 

598 

603 

609 

614 

619 

624 

629 

3 

8.43 

4 

634 

639 

645 

650 

655 

660 

665 

670 

675 

681 

4 

8.44 

845 

686 

691 

696 

701 

706 

711 

716 

722 

727 

732 

5 

8.45 

6 

737 

742 

747 

752 

758 

763 

768 

773 

778 

783 

6 

8.46 

7 

788 

793 

799 

804 

809 

814 

819 

824 

829 

834 

7 

8.47 

8 

840 

845 

850 

855 

860 

865 

870 

875 

881 

886 

8 

8.48 

9 

891 

896 

901 

906 

911 

916 

921 

927 

832 

937 

9 

8.49 

880 

943 

947 

952 

957 

962 

967 

973 

978 

983 

988 

8.50 

1 

1 

1 

C.n 

-^nlry 

-irmr 

rw 

OglC 

LOGARITHMS  OF  NUMBERS. 
1. — ^LfOOARiTHMS. — Continued. 


13t 


Ko 

Ck»minoa  LocArtthnu  ot  Numbers. 

Naperlan. 

L.    O 

1 

2 

2 

4 

5 

6 

7 

8 

9 

li 

.  P. 

No. 

Log.      Dlf. 

m 

e  §42 

947 

952 

957 

9a 

967 

973 

978 

983 

988 

6 

8.50 

2.14007  ,,- 
2.14124  {I 
2.14242  J 
2.14359  }}: 
2.14476  "^ 

117 
2.14593  ,.- 
2.14710  }jj 
2.14827  " 
2.14943  {j; 
2.15060  *" 

116 
2.15176  ,,- 

2.15292  ;;; 

2.15409  " 
2.15524  1  J 
2.16640  "' 

116 
2.15756  ... 
2.15871  5 
2.15987  J 
2.16102  5 
2.16217  *" 

115 
2.16332  ... 
2.16447  JJ 
2.16562  ;JJ 
2.16677  i; 
2.16791  "* 

114 
2.16905  ... 
2.17020  ; 
2.17134  {  1 
2.17248  J 
2.17361  "^ 

114 
2.17475  „. 
2.17589  \\\ 
2.17702  J!J 
2.17816  JIJ 
2.17929  "' 

113 
2.18042  ,,3 
2.18155  f 
2.18267  J  S 
2.18380  \\i 
2.18493  *" 

112 
2.18605  ,,, 
2.18717  5 
2.18830  5 
2.18942  1  f 
2.19054  "^ 

Ul 
2.19165  ,12 
2.19277  {J; 

MS 

998 

ooa 

008 

013 

D18 

024 

029 

034 

039 

1 

0.6 

8.61 

98  044 

949 

054 

059 

064 

069 

075 

080 

085 

090 

2 

1.2 

8.52 

09S 

100 

105 

110 

115 

120 

125 

131 

136 

141 

3 

1.8 

8.53 

la 

151 

159 

1 

161 

199 

171 

176 

181 

189 

192 

4 

2.4 

8.54 

m 

\ti 

202 

207 

212 

217 

222 

227 

232 

237 

242 

5 

8 

8.55 

247 

252 

258 

263 

268 

273 

278 

283 

288 

293 

6 

3.6 

8.56 

298 

303 

398 

313 

318 

823 

328 

334 

339 

344 

7 

4.2 

8.57 

249 

354 

359 

364 

369 

374 

379 

384 

389 

394 

8 

4.8 

8.58 

299 

404 

409 

414 

420 

425 

430 

435 

440 

445 

9 

5.4 

8.59 

8M 

4S0 

459 

460 

465 

470 

475 

480 

485 

490 

495 

8.60 

900 

605 

510 

515 

530 

526 

631 

636 

541 

646 

1 

8.61 

Ul 

559 

591 

596 

571 

576 

681 

686 

591 

696 

2 

8.62 

901 

909 

611 

916 

621 

626 

631 

636 

641 

646 

3 

8.63 

991 

999 

961 

999 

671 

676 

683 

687 

692 

697 

4 

8.64 

K5 

792 

797 

712 

717 

722 

727 

732 

737 

742 

747 

5 

8.65 

752 

757 

762 

767 

772 

777 

782 

787 

792 

797 

6 

8.66 

802 

807 

812 

817 

822 

827 

832 

837 

842 

847 

7 

8.67 

8sa 

857 

862 

897 

872 

877 

882 

887 

892 

897 

8 

8.68 

902 

107 

112 

917 

932 

027 

932 

937 

942 

947 

9 

8.69 

87» 

992 

967 

992 

997 

972 

977 

982 

987 

992 

997 

8 

8.70 

94  903 

997 

012 

017 

022 

027 

032 

037 

042 

047 

1 

0.5 

8.71 

992 

957 

062 

067 

072 

077 

082 

086 

091 

096 

2 

1 

8.72 

101 

109 

HI 

116 

121 

126 

131 

136 

141 

146 

3 

1.5 

8.73 

151 

159 

161 

199 

171 

176 

181 

186 

191 

196 

4 

2 

8.74 

m 

201 

309 

211 

216 

221 

229 

231 

236 

240 

245 

6 

2.5 

8.75 

280 

355 

290 

295 

270 

276 

280 

285 

290 

295 

6 

3 

8.76 

200 

305 

810 

315 

320 

825 

330 

335 

340 

345 

7 

3.5 

8.77 

249 

354 

359 

394 

369 

374 

379 

384 

389 

394 

8 

4 

8.78 

299 

404 

409 

414 

419 

424 

429 

433 

438 

443 

9 

4.5 

8.79 

m 

448 

453 

458 

493 

468 

473 

478 

483 

488 

493 

8.80 

498 

903 

507 

512 

517 

522 

627 

532 

637 

542 

1 

8.81 

947 

562 

557 

663 

567 

671 

576 

581 

586 

591 

2 

8.82 

599 

901 

609 

911 

616 

621 

626 

630 

635 

640 

3 

8.83 

149 

650 

955 

990 

665 

670 

676 

680 

686 

689 

4 

8.84 

994 

999 

704 

709 

714 

719 

724 

729 

734 

738 

5 

8.85 

743 

748 

753 

758 

763 

768 

773 

778 

783 

787 

6 

8.86 

792 

797 

802 

807 

812 

817 

822 

827 

832 

836 

7 

8.87 

841 

849 

851 

856 

861 

866 

871 

876 

880 

88^ 

8 

8.88 

899 

895 

900 

905 

910 

915 

019 

924 

929 

934 

9 

8.89 

m 

931 

944 

949 

954 

959 

963 

968 

973 

978 

983 

8.90 

988 

993 

998 

603 

907 

D12 

017 

022 

027 

032 

1 

0.4 

8.91 

99  939 

941 

049 

051 

056 

061 

066 

071 

075 

080 

2 

0.81    8.92 

985 

990 

095 

100 

105 

109 

114 

119 

124 

129 

3 

1.2 

8.93 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

4 

1.6 

8.94 

IB2 

187 

192 

197 

202 

207 

211 

216 

221 

226 

5 

8.95 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 

6 

2.4 

8.96 

ro 

284 

289 

294 

299 

303 

308 

313 

318 

323 

7 

2.8 

8.97 

2.19389  J  ; 

228 

333 

837 

842 

347 

353 

357 

361 

366 

371 

8 

3.2 

8.98 

2.19500  Ul 

279 

381 

386 

390 

395 

400 

405 

410 

415 

419 

9 

3.6 

8.99 

2.19611 

111 

m 

434 

429 

434 

439 

444 

448 

453 

458 

463 

468 

^.00 

2.19722 

iok 

1S4 


^.--LOGARITHMS  OF  NUMBERS, 
1. — ^LooAUTHMS.— Continued. 


No. 

Oonunoo  Locwlthmfl  ot  Numban. 

Nftperton. 

L.    O 

1 

2 

8 

4 

5 

6 

7 

8 

9 

I 

'.  P. 

No. 

Loc      ML 

fOO 

00  424 

429 

434 

439 

444 

448 

453 

468 

403 

468 

9.00 

2.19722.,, 
2.19834    " 

2.«i66;;; 

2.20276  til 

2.80607  i|A 
2.20717  "" 

IM 

2.21 1S7  III 
2.21266  '" 

166 
2.21375  „A 
2.21485  ^ 
2.21S04  IS 
2.21703  IS 
2.21812  *" 

166 
2.2U20  ,M 
2.22029  S 
2.22188  IS 
2.22246  iS 
2.22264  *" 

168 
2.t24<2  ,M 
2.22676}" 
2.22678  Is 
2.22786  " 
2.22894*" 

107 
2.23001  ,M 
2.23109  JS5 
2.23216  |£ 
2.23324  ;« 
2.23431  '" 

107 
2.23SM,« 
2.23645  S 
2.23751  J? 
2.23858  J 
2.23965  *■' 

106 
2.24071  iM 
2.24in  S 
2.24284    S 

2.24390  S 
2.24496  ** 

166 
2.24601  ,H 
2.24707  IS 
2.24813  IS 
2.24918  IS 
2.28024  ** 

166 
2.35129 

472 

477 

482 

487 

492 

497 

501 

606 

511 

516 

1 

9.01 

2 

521 

525 

530 

535 

540 

645 

650 

654 

559 

664 

2 

9.02 

3 

669 

674 

578 

583 

588 

593 

598 

602 

607 

612 

3 

9.03 

4 

617 

622 

626 

631 

636 

041 

646 

660 

655 

660 

4 

1.04 

905 

665 

670 

674 

679 

684 

689 

694 

698 

703 

708 

B 

1.05 

6 

713 

718 

722 

727 

732 

737 

742 

746 

761 

766 

1 

9.00 

7 

761 

766 

770 

775 

780 

785 

789 

794 

799 

804 

7 

9.07 

8 

809 

813 

818 

823 

828 

832 

837 

842 

847 

862 

^ 

9.08 

9 

856 

861 

866 

871 

875 

880 

885 

890 

896 

899 

» 

9.00 

910 

904 

909 

914 

918 

923 

928 

933 

038 

942 

947 

5 

9.10 

1 

952 

957 

961 

966 

971 

976 

980 

985 

990 

995 

^ 

0.6 

9.11 

2 

999 

004 

009 

014 

019 

023 

028 

033 

038 

042 

2 

1 

9.12 

3 

96  047 

052 

057 

061 

066 

071 

076 

080 

085 

090 

3 

1.5 

9.12 

4 

095 

099 

104 

109 

114 

118 

123 

128 

133 

137 

4 

2 

9.14 

915 

142 

147 

152 

156 

161 

166 

171 

175 

180 

186 

6 

2.8 

0.15 

6 

190 

194 

199 

204 

209 

213 

218 

223 

227 

232 

6 

3 

9.10 

7 

237 

242 

246 

251 

256 

261 

265 

270 

275 

280 

7 

3.6 

9.17 

8 

284 

289 

294 

298 

303 

308 

313 

317 

322 

827 

8 

4 

9.18 

9 

832 

336 

841 

346 

350 

355 

360 

865 

369 

874 

9 

4.6 

9.19 

920 

879 

384 

388 

393 

398 

402 

407 

412 

417 

421 

9.20 

i 

426 

431 

435 

440 

445 

450 

454 

459 

464 

468 

1 

9.21 

2 

473 

478 

483 

487 

492 

497 

501 

506 

511 

615 

2 

9.22 

3 

520 

525 

530 

534 

539 

544 

548 

553 

558 

6a 

3 

9.23 

4 

567 

572 

577 

581 

586 

591 

695 

600 

605 

609 

4 

0.24 

925 

614 

619 

624 

628 

633 

638 

642 

647 

652 

666 

6 

9.26 

6 

661 

666 

670 

675 

680 

685 

689 

694 

699 

703 

6 

9.26 

7 

708 

713 

717 

722 

727 

731 

736 

741 

745 

760 

7 

9.27 

8 

765 

759 

764 

769 

774 

778 

783 

788 

792 

797 

8 

9.28 

9 

802 

806 

811 

816 

820 

825 

830 

834 

839 

844 

9 

9.29 

930 

848 

853 

858 

862 

867 

872 

876 

881 

886 

890 

4 

9.80 

1 

895 

900 

904 

909 

914 

918 

933 

928 

932 

937 

1 

0.4 

9.31 

2 

942 

946 

961 

956 

960 

965 

970 

974 

979 

984 

2 

0.8 

9.32 

3 

988 

993 

997 

003 

007 

on 

016 

021 

025 

030 

3 

1.2 

9.33 

4 

97  035 

039 

044 

049 

053 

058 

063 

067 

072 

077 

4 

1.6 

9.34 

935 

081 

086 

090 

095 

100 

104 

109 

114 

118 

123 

6 

2 

9.35 

6 

128 

132 

137 

142 

146 

151 

155 

160 

165 

169 

6 

2.4 

9.80 

7 

174 

179 

183 

188 

192 

197 

202 

206 

211 

216 

7 

2.8 

9.37 

8 

220 

225 

230 

234 

239 

243 

248 

253 

257 

262 

8 

3.2 

9.S8 

9 

267 

271 

276 

280 

285 

290 

294 

299 

304 

808 

9 

8.6 

9.29 

940 

313 

317 

322 

327 

831 

336 

340 

345 

350 

354 

9.40 

1 

359 

364 

368 

373 

377 

382 

387 

391 

396 

400 

1 

9.41 

2 

405 

410 

414 

419 

424 

428 

433 

437 

442 

447 

2 

9.42 

3 

451 

456 

460 

465 

470 

474 

479 

483 

488 

493 

3 

9.43 

4 

497 

502 

506 

511 

516 

520 

525 

529 

634 

639 

4 

9.44 

945 

643 

648 

552 

557 

562 

566 

571 

575 

580 

586 

S 

9.45 

6 

589 

594 

598 

603 

607 

612 

617 

621 

626 

630 

6 

9.40 

7 

635 

640 

644 

649 

653 

658 

663 

667 

672 

676 

7 

9.47 

8 

681 

685 

690 

695 

699 

704 

708 

713 

717 

722 

8 

9.48 

9 

727 

731 

736 

740 

745 

749 

754 

759 

763 

768 

9 

9.49 

9S0 

772 

777 

782 

786 

791 

795 

800 

804 

809 

813 

9.60 

• 

c 

» 

^T^ 

ea  Dy 

■^ 

jOO 

g+e- 

LOGARITHMS  OF  NUMBERS. 
1. — LooARiTBUs. — Continued. 


126 


Common  Logartthms  of  Numbers. 


Naperlan. 


fit 

97  T72 

777 

782 

786 

791 

795 

800 

804 

809 

813 

9.60 

2.25129  ... 
2.25234  Sk 
2.25339  j; 

2.26072  *" 

104 

2.26176  .ft. 

2.26280  jJJ 

2:26488  }JJ 
2.26692  '*^ 

104 
2.26696  ,M 
2.26799  S 
2.26903  g 
2.27006  IS 
2.27109  ^^ 

104 
2.27213  ,oa 
2.27316  S 
2.27419  S 
2-27521  ^ 
2.27624  ^^ 

103 
2.27727  ,02 
2.27829  \g 
2.27932  J3 
2.28034  Jl 
2.28136  ^^^ 

102 

2.28340  Jl 
2.28442  J; 
2.28544  Xl 
2.28646  *°2 
101 
2.28747  ,02 

S18 

823 

827 

832 

836 

841 

845 

850 

856 

859 

9.61 

M4 

888 

873 

877 

882 

886 

891 

896 

900 

905 

9.52 

N§ 

914 

918 

923 

928 

932 

937 

941 

946 

950 

9.53 

«55 

858 

964 

968 

973 

978 

982 

987 

991 

996 

9.54 

iss 

MOM 

MS 

009 

014 

019 

023 

028 

032 

037 

041 

9.55 

046 

050 

059 

069 

064 

068 

073 

078 

082 

087 

9.66 

091 

086 

100 

105 

109 

114 

118 

123 

127 

132 

9.67 

va 

141 

146 

150 

155 

159 

164 

168 

173 

177 

9.68 

182 

186 

191 

196 

200 

204 

209 

214 

218 

223 

9.69 

Mt 

127 

232 

238 

241 

245 

250 

254 

259 

263 

268 

8 

9.60 

272 

277 

281 

286 

290 

296 

299 

304 

308 

313 

0.6 

9.61 

318 

322 

327 

331 

336 

340 

346 

349 

354 

858 

1 

9.62 

SS3 

367 

373 

376 

381 

385 

390 

394 

399 

403 

1.5 

9.63 

4N 

412 

417 

421 

438 

430 

435 

439 

444 

448 

2 

9.64 

Itt 

4S8 

457 

463 

468 

471 

475 

480 

484 

489 

493 

3.6 

9.65 

4M 

508 

507 

511 

516 

620 

625 

529 

534 

538 

3 

9.66 

543 

547 

552 

558 

661 

566 

670 

574 

579 

583 

3.5 

9.67 

H8 

592 

697 

601 

605 

610 

614 

619 

623 

628 

4 

9.68 

632 

637 

641 

646 

860 

665 

669 

664 

668 

673 

4.5 

9.69 

f70 

«n 

682 

686 

691 

695 

700 

704 

709 

713 

717 

9.70 

722 

728 

731 

736 

740 

744 

749 

753 

768 

762 

9.71 

767 

TtX 

776 

780 

784 

789 

793 

798 

802 

807 

9.72 

til 

818 

820 

825 

829 

834 

838 

843 

Ml 

861 

9.73 

856 

880 

885 

869 

874 

878 

883 

887 

892 

896 

9.74 

976 

100 

905 

909 

914 

918 

923 

937 

932 

936 

941 

9.76 

949 

949 

954 

958 

963 

967 

972 

976 

981 

986 

9.76 

989 

984 

998 

003 

0O7 

013 

016 

021 

025 

029 

9.77 

89  034 

038 

043 

047 

052 

066 

061 

065 

069 

074 

9.78 

078 

083 

087 

093 

096 

100 

105 

109 

114 

118 

9.79 

98t 

123 

ir 

131 

136 

140 

145 

149 

154 

158 

162 

4 

9.80 

167 

171 

178 

180 

185 

189 

193 

198 

202 

207 

0.4 

9.81 

III 

216 

220 

224 

229 

233 

238 

242 

247 

261 

0.8 

9.82 

196 

260 

264 

269 

373 

277 

282 

286 

291 

295 

1.2 

9.83 

800 

304 

306 

313 

317 

322 

826 

330 

335 

339 

1.6 

9.84 

MS 

344 

348 

353 

387 

861 

366 

870 

874 

379 

383 

3 

9.85 

388 

392 

396 

401 

406 

410 

414 

419 

423 

427 

3.4 

9.86 

2.28849  Jf 
2.28950  J 
2.29051  J 
2.29152  *°* 
101 
2.29253  ,0, 
2.29354  J 
2.29455  J} 
2.29556  J 
2.29657  '"' 

IfIA 

432 

436 

441 

449 

449 

454 

468 

463 

467 

471 

2.8 

9.87 

476 

480 

484 

489 

493 

496 

502 

506 

611 

615 

8.2 

9.88 

520 

524 

528 

533 

537 

543 

546 

550 

556 

559 

3.6 

9.89 

9W 

584 

588 

972 

577 

681 

585 

580 

594 

599 

603 

9.90 

107 

613 

616 

621 

626 

629 

634 

638 

642 

647 

9  91 

891 

698 

860 

664 

669 

673 

677 

682 

686 

691 

9.92 

899 

698 

704 

708 

712 

717 

721 

726 

730 

734 

9.93 

739 

743 

747 

762 

768 

760 

766 

769 

774 

778 

9.94 

Mf 

788 

787 

791 

796 

800 

804 

806 

813 

817 

822 

9.95 

lUU 

2.29767  ,0, 
2.29858  ^ 
2.29958  IJX 
2.30068  J" 
2.30158  *"" 

828 

830 

835 

839 

843 

848 

862 

856 

861 

865 

9.96 

870 

874 

878 

883 

887 

891 

896 

900 

904 

909 

9.97 

818 

917 

922 

928 

980 

935 

939 

944 

948 

952 

9.98 

997 

961 

965 

970 

974 

978 

983 

987 

991 

996 

9.99 

■M 

mooo 

043 

087 

130 

174 

217 

260 

304 

347 

891 

10.00 

2.302585 

120  e.— LOGARITHMS  OF  NUMBERS. 

Slide  Rules  — Logarithmic  slide  rules  are  instruments  graduated  on  a 
logarithmic  basis  for  performing  calculations  involving  multiplication  (in- 
clnding  powers)  and  division  (including  roots  and  reciprocals)  of  numbers. 

LogarHhrrrtc  Ba^e  of  Upper  Ftxed  Sca\e. 

Upp«r  fixed  &cal«,A. 
I  e       s   4  ft  •  7e9w  20     30  40  Bo«o  00  too 

• 1 *    I   ■  I  'Ml  ■  I  Ml ■     I    '  I  'Ml  1  i».v 

I  «         3     4    5  «  70910  20       30  40  0060  80  100 

Upper  Sliding  Scale, a. 


LITZIZX    I.    I     I     I     I     I      I     I     I      I     I     I  -L- 


zrrrjD 


laistsssaja 

logari-Himic  Boee  of  Upper  Sliding  Scale. 
Pig.  1. 

The  principle  of  the  slide  rule  is  very  simple,  although  some  of  the  instru- 
ments themselves  are  complex  and  expensive. 

The  plain  slide  rule,  Fig.  1,  is  usually  from  ten  to  eighteen  inches  kmg. 
(The  longer  the  scale,  the  more  accurate.)  It  consists  of  the  upper  and  lower 
••fixed"  scales  A  and  B,  graduated  on  one  piece  and  grooved  to  receive  the 
sliding  piece,  on  which  are  graduated  the  scales  a  and  b.  Note  that  scales 
A  and  a  are  similar,  as  are  also  B  and  6:  but  that  the  former  are  in  double 
series  (from  1  to  10)  while  the  latter  are  in  single  series  only.  The  advantage 
of  this  system  will  be  explained  below. 

Pig.  1  shows  the  upper  fixed  and  sliding  scales,  A  and  a,  together  with 
their  logarithmic  bases.  These  two  scales  (or  the  two  lower  ones,  either) 
may  be  used  in  performing  any  simple  operation  in  multiplication  or  divi- 
sion. Por  instance,  as  the  scales  A  and  a  are  now  set  we  can  find  the  product 
of  any  number  multiplied  by  2;  or,  inversely,  the  quotient  of  any  number 
divided  by  2.  Thus.  2X1-2;  2X2  =  4;  2X3-6.  etc.  Likewise. 
lO-i-2—5;  20-(-2—10;  etc.  Note  that  the  logarithm  of  the  product 
—  the  sum  of  the  logarithms  of  the  factors;  thus,  log  of  40  (—  1 . 6)  is  equal 
to  log  of  20  +  log  of  2  —  1.3+0.3.  Similarly,  the  log  of  the  quotient  is 
the  log  dividend  minus  the  log  divisior.  Of  course  the  logarithms  them- 
selves do  not  appear  on  the  sRde  rule,  but  the  numbers  are  arranged  so 
their  logarithms  torm  series  equally  spaced,  and  the  principle  remains.  To 
multiply  any  number  q  by  n:  Set  1  of  scale  a  opposite  9  of  scale  A,  and 
opposite  n  of  scale  a  read  the  product  p  on  scale  A.  To  divide  any  number 
phy  n:  Set  n  of  scale  a  opposite  p  of  scale  A ,  and  opposite  1  of  scale  a  read 
the  quotient  q  on  scale  A .  To  find  the  reciprocal  of  a  number:  Divide  1  by 
that  number;  or,  invert  the  sliding  scale,  end  for  end.  with  ends  of  both 
scales,  A  and  a,  opposite,  and  the  reciprocal  of  any  number  on  one  scale, 
as  A ,  will  be  found  directly  opposite  on  the  other  scale,  as  a. 

To  facilitate  operations,  and  for  accuracy,  each  slide  rule  is  provided 
with  a  movable  index  with  a  vertical  hair  line. 

Fig.  2  shows  the  ordinary  slide  rule  with  double  scale.  With  the 
movable  index,  the  square  root  of  any  number  on  scale  A  will  be  found 


M- 


B 


4.  ft  eTft^w  w    30   40  00  40  Ao  no 

1'   M  ^"1    II  iTii  ' — W    'MM 

\A    Z        »     4.    ftftTSdlO  to     80    40 , 


h 


•     7    8    e  10 


P»«-2.  Digitized  by  Google 


SLIDE  RULES,  127 

dfaectiy  below  on  scale  B.  In  like  manner,  the  square  of  anv  number  on 
fcate  B  is  found  opposite,  on  scale  A .  Furthermore,  the  cube  ot  any  number 
(m  scale  B  may  be  found  by  multiplying  its  corresponding  sqttare  on  scale 
A  by  the  number  itself  on  scale  a,  reading  the  cube  on  scale  A.  Thus. 
Fig.  2.  the  cube  of  1.59  (scale  B)  is  found  on  scale  A  opposite  1.59  ot 
saiie  a,  and  is  equal  to  4.  Clearly,  then,  the  cube  root  ot  any  number  n 
(scale  A)  is  found  by  making  the  reading  on  scale  a,  opposite  n.  equal  to 
the  reading  on  scale  B  opposite  1  of  scale  b,  and  these  eqtial  "readings  are 
the  cube  root  of  the  number.    Thus,  the  cube  root  of  4  —  1 .  59. 

Thatdur's  calculating  instrument  is  a  cylinder  four  inches  in  diameter 
tod  about  eighteen  inches  k>nc.  which  acts  as  a  sliding  scale  inside  a  frafne- 
VDik  of  twenty  parallel  bars  forming  the  fixed  scales.  This  instrument  is 
by  far  the  best  on  the  market.  It  was  sold  formerly  at  $25. 00,  a  price  barely 
exceeding  the  cost  of  manufacttire,  and  is  now  listed  at  $35.00;  and  with 
leading  glass,  $45.00.  Results  may.be  obtained  to  four  or  five  decimal 
phoes.    It  is  nearly  as  accurate  as  a  five-place  logarithmic  table. 

S&de  rules  are  used  in  all  logarithmic  and  trigonometric  operations,  and 
00  engineer  should  be  without  one.  Books  giving  full  directions  in  the  use 
oC  the  dide  rule  can  be  obtained  for  from  25  to  75  cents.  They  explain  the 
method  of  solving  such  equations  as: 

ax  ax  aafl  «»  fax  fx 


d  by  Google 


7.— PLANE  GEOMETRY 

(See  also  Meiituntion.) 

Aoglet  and  Lines. — 

Straight  tins:  a  b.    Oblique  lines:      ob,  cd. 
Broken  lifts:    aod.  Oblique  angles:    A,  B, 
A<9tU  angle:    A.      Adjacent  angles:  A,  B\  A,  C 
Obtuse  angle:  B,      Reflex  angle:        Greater  than 

180^  and  less  than  360^. 
Complementary  angles:  A  and  C  (il+C— 9(r);  each  is  the  complement  ol 

the  other. 
Supplementary  angles:  A  and  B  (il-HB  — 180°);  each  is  the  supplement  of 

the  other. 
Right  angle:  aoe  (" 90°) ;  e o  is  perpendicular  to  a b. 
Straight  angle:  a  o  6  ( =»  180°) ;   sides  form  two  right  angles. 
Conjugate  angles:  Two  angles,  about  a  point,  whose  sum  equals  360°. 
Vertical  angles:  A  and  A ;  B  and  B. 

Triangles. — 
Triangle:   Plane  bounded  by  three  straight  sides,  Pig.  2. 
Perimeter:  Sum  of  the  sides. 
Angles:  The  interior  angles  (sum— 180°). 


Fig.  2. 


Base 
Pig.  3. 


Fig.  4. 


Successive  partial  exterior  angles:  A*  B*  and  C*  (sum  —  360^. 
Right  triangle:    One  of  its  angles  a  right  angle.  Pig.  3. 
Scalene    "  No  two  of  its  sides  equal.  Fig.  4. 

Obtuse      "  One  of  its  angles  obtuse.  Pig.  4. 


Pig.  6. 


Pig.  6. 


Figs.  7. 


Isosceles  triangle:  Two  of  its  sides  equal,  Pig.  6L 
Acute  All  of  its  angles  acute.  Pig.  3L 


Equilateral    **      All  of  its  sides  equal.  Fig.  6. 
'^  uianguJar  **      All  of  its  angles  equal^  Fig.  f 
Area  of  any  triangle  «  i  base  X  altitude. 


Quadrilaterals. — 

Quadrilateral:   Plane  bounded  by  four  straight  sides.  Pig.  8. 

Sum  of  interior  angles  (A,  B,  C,  D)  —  360°; 

Sum  of  partial  successive  exterior  angles  (A\  B',  C,  IX)  —  860"; 

Sum  of  exterior  angles  (complete)  —  1080°. 
Square:  All  sides  equal,  and  each  angle  90°,  Fig.  9. 
Rectangle:  Opposite  sides  parallel,  and  each  angle  90°,  Pig.  10. 
Parallelogram:   Opposite  sides  parallel.  Pig.  11. 


128 


d  by  Google 


POLYGONS.    CIRCLE. 


in 


a 


Pig.  8. 


D 

Fig.  9. 


Fig.  10. 


/Z7 


Fig.  11. 


r\  EX 


p«is. 


Fig.  IZ. 


Fig.  14. 


Fig.  15. 


Rhomboid:  Opposite  sides  parallel,  and  all  angles  oblique,  Fig.  12. 
Rhombus:  All  sides  equal,  all  angles  oblique,  Pig.  13. 
Trapexotd:  Two  sides,  only,  parallel.  Fig.  14. 
Trapegium:   No  two  sides  parallel.  Pig.  15. 

Polysons  (Qcnenl). — 

Polygon:   Plane  bounded  by  straight  sides.  Fig.  16. 
3"- triangle.  4 1- quadrilateral, 5'- pentagon,  6 —hexagon. 
7  =- heptagon,  8 —octagon.  0  — nonagon,  10— decagon, 
11— txndecagon.  1 2  —  dodecagon. 

Sum  of  interior  angles  (A,  B,  C,  etc.)  —  180*X  (number 
A  fides—  2). 

Suxn  of  partial  successive  exterior  angles  (il',  B', 
r'.  etc.)-85a»- 

Sum   of  exterior  angles   (complete)  — 860** + num- 
ber of  sides  X  180**. 

Rccvlar  Potycons. — 

ReguJar  polygon:   All  sides  equal  and  all  angles  equal, 

Pig.  17. 
Tirck:   A  regular  polygon  with  an  infinite  number  of 

sides. 
Radius  of  polygon:   Radius  (r)  of  circumscribed  circle. 
\pcih€n%  oj  polygon:   Radius  (a)  of  inscribed  circle. 
f'rr«M#l#r.-   Sum  of  the  sides. 
\r€a:    i  apothem  X  perimetei. 

Circle.— 

Vaug/nU:    Touches   circumference 

at  ooe  point. 
Secani:     Intersects  circumference 

at  two  points. 
l^tameUr:    Intersects  center  and 

is  limited  by  circumference. 
Radius:    Distance  from  center  to 

circtunference. 
7hord:     A  secant  limited  by   the 

circtunference. 
ire:    A  portion  of  the  circumfer- 
ence. 
Sfgmeni:    Area  bounded   by  arc 

and  chord. 
Sector :    Area  bounded  by  two  radii 

and  the  intercepted  arc. 
}uadrani:   Sector  eqiial  to  quarter 

of  a  circle. 
ifmicirck:   Sector  eqiial  to  half  a  circle. 
ircumfer€HC9  -  diameter  X    r.  »r  -  3.1415927. 


Fig.  17. 


-  0.3183099. 


"HamtUr  —  circumference  X  - .  - 

lr»a  of  circk  -  diameter*  X  ^  .  |  -  0.7853982. 


d  by  Google 


130 


l.^PLANE  GEOMETRY. 


Problems  in  Constrnctioo  of  Fiffures. — 


InUrceptinf  circks:  Common  chord  is  at  right  angle  to  line  joining  centers 
of  circles.  Fig.  19.     Used  in  laying  off  «0**. 


To  lay  off  flO*,  -^.  60^  and  SCPl 


^—-^^•"^  If-  48*  eS»         «>^3o* 


Pig  20. 
Intersection  of  perpendiculars  bisecting  any  two  chords. 


Fig.  19. 

Center  of  circle: 
Fig.  21. 

An  inscribed  angle  in  a  semicircle  —  90**,  Fig.  22. 

An  angle  from  a  point  on  the  circumference  is  measured  by  half  the  inter- 
cepted arc  (angle—  i  arc),    Fig.  23. 

An  angle  included  by  a  tangent  and  adjacent  chord  is  measured  by  half  the 
intercepted  arc;  (angle  —  i  arc),  Fig.  24. 


Fig.  21. 


Fig.  22. 


Fig.  23. 


Fig.  24. 


Equal  angles  from  a  point,  o,  on  the  circumference  subtend  equal  arcs  and 

equal  chords.  Fig.  25. 
Railway  curve:    The  two  preceding    propositions  are  fundamental  in  the 

laymg  out  of  railway  curves.    The   chord    is  usually    100   ft.   with    a 


Fig.  25. 


Fig.  26. 


Fig.  27. 


central  angle  D**  which  equals  the 
degree  of  curvature.  The  deflection 
angle  d^  is  always  one-half  the  central 
angle  £>**;  hence  for  one  chord,  or 
station,  the  deflection  angle  is  one- 
half  the  degree  of  curvature. 

Circle  inscribed  in  a  triangle:  Center  of 
circle  is  intersection  of  lines  bisecting 
the  angles,  Fig.  27.  Radius  is  shortest 
distance  to  either  side. 

Circle  circumscribing  a  triangle:  Center 
of  circle  is  intersection  of  perpendicu- 
lars bisecting  the  sides,    Fig.  28. 


CONSTRUCTION  OF  FIGURES, 


131 


Proportion  by  stgnunts  of  chords:    ab^cd;  -  —  rl    ?•  —  r.  «rf#and  ebf 

e       o      a       o 
are  gtmilar  triangles.  Pig.  29. 

MtOH   proportional:     By   similar  triangles,  -  —  r.  whence  c  is  a  mean 

c       o 
proportional  between  a  and  6  (a  6  «  c*)»  Pig.  30. 
Inscribgd  sqttare  and  octagon;    Circumscribed  circle.  Pig.  31. 
Circufnscribgd  squar0  and  octagon;    Inscribed  circle.  Pig.  drL 


P«.2«. 


Pig.  30. 


Pig.  31. 


Pentagon  inscribed  in  a  circk:     bd  is  one  side  of  the  pentagon  (6  sides). 

Process:  Bisect  radius  at  a;    ac  '^ab;bd  "be.  Step  off  <i#,  #/.  etc..  «  6d. 

and  connect.  Pig.  38. 
Dtcagon  inscribed  in  a  circk:  Bisect  the  circular   arcs  of  an  inscribed 

pentagon,  making  twice  the  number  of  sides.  Fig.  84. 
Pnoagon  of  given  side  ab:    Erect  the  perpendicular  be  —  Iside  ab;  produce 

ae  to  0  so  that  cd  —  cb:  then    bd   —   m  —  <w  —  radius  of  pentagon  — 

radius  of  circumscribea  circle,  with  center  at  #.     Step  on  a  f,  f  g, 

etc.,  «  ab,  and  connect.  Pig.  86. 


P«.  38. 


Pig.  34. 


Pig.  86. 


Hexagon  inscribed  in  a  circle:   Each  side  is  equal  to  the  radius.  Pig.  36. 
EqiBilateral   Triangk:  Connect   alternate    points  of  hexagon,  making  half 

the  number  of  sides.    Pig.  87. 
Dodecagon:    Bisect  the  circular  arcs  of  an  inscribed  hexagon,   making 

twice   the  number  of  sides.  Pig.  38. 


P«.  86. 


Pig.  37. 


Pig.  88. 


8.— SOLID  GEOMETRY. 


Planet,  Aoglct  and  Unei. — 

Plant:    Determined  by  (1)  two  parallel  lines:    (2)  two  intersecting  lines; 

(8)  three  points  not  in  the  same  straight  line;   (4)  a  straight  line  and  a 

point  outside  of  it. 
Straiiht  lute:  Intersection  of  two  planes  not  parallel,  as  a  fr.  Pig.  1. 
Dihedral  angle:  The  angle  between  two  planes,  measured  at  right  ainle  to 

each  plane  and  to  the  line  of  their  intersection,  or  edge,  as  A,  Fig.  L 
Right  dihedral  angle:  A  dihedral  angle  that  ia  »©•,  Pig.  2. 


Fig.  1.  Fig.  2. 

Other  angles:  Acute,  obtuse,  complementary,  supplementary,  adjacent,  etc,  . 

as  in  Plane  Geometry. 
Coordinate  planes:  V  and  H,  Pig.  3,  are  planes  perpendicular  to  each  other 

hence,  any  line  v  in  one  plane,  if  perpendicular  to  afr,  is  perpendicular 

also  to  theother  plane. 


Pig.  8. 
Polyhedrons. — 

Polyhedron:  Solid  boimded  by  planes. 
Tetrahedron:   4  triangular  faces;   6  edges.  Pig.  4. 
Hexahedron:   6  square  faces;   12  edges.  Pig.  6. 


Fig.  4 


Octahedron:    8  triangular  faces;    12  edges.  Pig.  6. 
Dodecahedron:    12  pentagonal  faces;    30  edges.  Fig.  7. 
Icosahedron:   20  triangular  faces;   30  edges,  Fig.  8. 


Pig.  8. 


132 


d  by  Google 


PRISMS.     PYRAMIDS. 


133 


Pnsm:  A  polyhedrDti  with  two  opposite  faces  parallel  and  equal  polygons 

the  other  faces  parallelograms.  Fig.  9. 
Kigkt  prism:    Lateral  edges  perpendicular  to  bases,  Fig.  10. 
Kmtar  prisfm:   A  right  prism  whose  bases  are  regular  polygons. 
ObHqm  prism:   Lateral  edges  are  oblique  to  bases.  Fig.  11. 
TnanguJar  prism:   Bases  are  triangles.  Fig.  1 1. 


/fi 

\ 

Fig.  10. 


Fig.  11. 


Qmadramgular  prism:   Bases  are  quadrilaterals.  Fig.  12. 
PamlUiopiptd:   Prism  whose  bases  are  parallelo^ams. 

Rigkt  paralUlopiPtd:   Lateral  edges  are  perpendicular  to  the  bases.  Fig.  1 2. 
Rfdattgular  paralUh^ped:   Six  faces  are  rectangles,  Fig.  12. 
Cmbr:    Parallelopiped  whose  six  faces  are  squares.  Pig.  13. 
Voiumte  of  any  prism  —  area  of  base  X  altitude. 

TrmuaUd  prtsm:   Portion  included  between  base  and  plane  section  oblique 
to  base.  Fig.  14. 


-+- 


U 


Pis.  12. 


Fig.  13. 


Fig.  14. 


Pyratmd:  Polyhedron  whose  base  is  a  TOlygon  and  whose  sides  are  tri- 
angles Joinmg  a  common  apex  or  top.  Pig.  15. 

Attii9tdr:  Perpendicular  distance  from  apex  to  plane  of  base. 

Triantuiar  fyramid:  Base  is  a  triangle  (.*.  solid  is  a  tetrahedron). 

QmadranttUttr  pyramid:   Base  is  a  quadrilateral. 

Rtt^fUar  pyramid:  Base  is  a  polygon,  and  apex  is  directly  over  its  center, 
Fig.  Itt. 


F« 


Fig.  16. 


Fig.  17. 


trrmtnlar  i 

VahMmcfanypyramt-.    . ,, 

Siant  fmght:   Dtftance  along  any  lateral  face  from  its  apex  ^  the  middle 

Otf  its  base.  Digitized  by  VjOOQIC 


sr  fyramid:  One  that  is  aot  regular. 

r  of  any  pyramid:   |  area  of  base  X  altitude. 


m 


B.^SOUD  GEOMETRY. 


TruncaUd  pyramid:  That  portion  between  the  base  and  a  plane  sectioo 
cutting  all  the  sides,  Fig.  17.  ,     ,  ^        ,  _^ 

Frustum  of  a  pyramid:  That  portion  between  the  base  and  a  plane  section 
parallel  with  the  base.  Fig.  18. 

CyllDden. — 

Cylindtr  -  circular  cylinder:    Two  bases  are  circidar  and  parallel;  all  sec- 

tions  parallel  with  the  bases  are  circular,  Fig.  19. 
Ellip^  cylinder:  Two  bases  are  eUiptical  and  parallel;  all  sections  parallel 

with  the  bases  are  elliptical. 


Pig.  19. 

Right  cylinder:   Elements  arc  perpendictdar  to  the  bases. 
Clique  cylinder:   Elements  are  oblique  to  the  bases. 
Volume  of  any  cylinder  —  area  of  base  X  altitude. 

Cones. — 

Cone  —  circular  cone:   Base  and  all  sections  parallel  with  it  are  drcular; 
elements  composing  the  sides  meet  at  a  common  apex  or  top^  Fig.  20l 
Elliptic  cone:    Baise  and  all    sections    parallel  with  it  are  elliptical. 
Altitude:  Perpendicular  distance  from  apex  to  plane  of  base. 
Rieht  cone:  Cone  with  axis  perpendicular  to  base. 
Oblique  cone:  Cone  with  axis  oblique  to  base. 


Fig.  20. 


Fig.  21. 


Pig.  as. 


Volume  of  any  cone:    i  area  of  base  X  altitude. 

Truncated  cone:  That  portion  between  the  base  and  a  plane  cutting  all  the 

elements.  Fig.  21.  .       ^  ^  .».     ^  ^         , 

Frustum  of  a  cone:    That  portion  between  the   base  and  a  plane  sectioa 

parallel  with  the  base,  Fig.  22. 

Spheres. — 

Sphere:   Solid  whose  every  section  is  circular,  Fig.  23. 
Radius:  Distance  from  center  to  surface. 
Diameter:  Two  radii  forming  one  straight  Ime. 
Grtat  circle:  The  largest  plane  section  (cuts  center  of  sphere). 
Pole  of  a  circle:  End  of  diameter  or  axis  perpendicular  to  the  plane  o£  the 
circle. 


Fig.  24.  Fig.  25.       Digtizei^j^^pgle    pjg.  27. 


SPHERES.  136 

Arc  of  a  gnat  drck:  Shortest  soi&ce  distance  between  two  points  on  siif- 

nce  of  sphere. 
Polar  distance  of  a  circle:  Distance  from  nearest  pole  to  drcumf efence  of 

code. 
QuadroHt:  Polar  distance  of  a  great  drde. 
Surface  of  spkert  —  4  x  radiuS*. 

Volutm  of  sphere  *  -s- «  radiusP. 

Zone:  Portion  of  surface  between  two  parallel  i>lanes.  Pig.  24. 

Ltme:   Portion  of  suifaoe  between  two  semi-circumferences  of  great  circles, 

Pi^.  26. 
Spkertcal  segment:   Portion  of  sphere  between  two  parallel  i)lane8.  Pig.  26. 
Spherical  pyramid:  Apex  oo/responds  to  center  of  sphere,  sides  are  radial 

planes,  and  base  is  a  spherical  polygon   Pig.  27. 
SpkericxU  €one:  Cone  with  spherical  base.  Pig.  27. 


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9.— PLANE  TRIGONOMETRY. 


Plane  Trigonometry  deals  with  the  functions  of  plane  triangles,  and 
shows  how  to  compute  the  imknown  elements  when  certain  of  the  known 
elements  are  given.  The  six  elements  of  a  triangle  are  its  three  sides  and 
three  angles:  and  three  of  these,  one  of  which  must  be  a  side,  must  bo 
known  in  order  to  solve  the  triangle. 

TricoDometric  functions  are  the  ratios  of  the  sidesof  a  right  angle  triangle. 
There  are  six  primary  ratios,  namely,  siiu,  cosine,  taug0nt,  cotangent,  secant 
and  cosecant.  In  addition  to  these,  however,  there  are  two  secondary 
ftmctions  sometimes  employed,  namely,  vwrstd  sine  and  cowrsed  sine;  and 
two  tertiary  functions  seldom  used,  namely,  txstcant  and  coexstcani. 

The  following  trigonometric  ftmctions  or  ratios  refer  to  Fig.  1.  in 
which - 


k  —  hypothenuse, 
^  =-  perpendicular, 
0  —  base, 
A  —  angle  at  base, 
B  —  angle  opposite  base, 
sine  A  »  cosine  o,  etc. 

Priuary  Functions: 
in  A  (— cosB)  —  f 


Fig.  L 


Sbcondart  Fuhctions: 


cos  A  ( =-  sin  B)  —  r 
tan-A  (-cot  B)  -^ 


cot  A  (-tanB)  -- 
P 


sec  A  (—CSC  B)  — 
cscA  (-secB)  - 


vrs  <4  (  — CVS  B)  — 1  — cos  A  — 1  — T  —     ,     . 
cvsA  (-vrsB)-l-sin  A-l-|-^~^. 


Tertiary  Functions: 
h 


xsc  A  (— cxcB)  —sec  A  — 1  — 
cxcA  (  —  xscB)  —CSC  A  — 1  — 


-1. 


-!■ 


b 

■  *-/> 

P 


1. — ^Equivalent  Values  of  Primary  Functions  of  Any  Angle  x  In  Puita 
Terms  of  Each  of  the  Other  Functions. 


\/l— sin**  — 


cos  X      — - 


ian 
tan  x' 

N/l+tan^i 
1 


cot 
1 


sin  X       —  Vl— cos««  —  — ; =  — =1=^ — r  " 

N/l  +  COt'x 

cot  X 


\/l— sin'x 


SUkX 

1 

Vl-  8in«« 

1 


Vl  — cos^y 
cos* 

COS  X 

y/l—Qos?x 

1_ 

cosx 

1 

Vl— cos'* 


-s/l-htan'x      Vl+cot»jc 
1 


v^scc**-! 
sec* 

1 
sec  * 


CSC 

1 


cot  X 


-  — Vsec«jt-1  — ■ 


VcscH— 1 

C3CX 
J 

\/«c'»»— 1 


tan  X 


'  v/l+tan*«- 
Vl+tan** 


Vsec**— 1 


-  V'cac%~l 


—  -     sec  X     — - 


V'csc'ar— I 


tan  X 


\/l+cot»ae-  - 


Vsec*x— 1 


136 


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TRIGONOMETRIC  FUNCTIONS. 


187 


Otbu  Equttalbmt  Values  of  Primart  Functions  of 
AND  (Anglb  *)*. 


cos  X 
cot  X 
sin  X 
tan  X 


cos  X  tan  x, 

—  sin  X  cot  X. 


sm  X 

tjiQ  X  a, «  sin  >ic  gee  ar. 

cos  X 
cos  X 

cot  jr  —  -: —cos  X  CSC  «. 

sm  j; 

tan  j; 
•ec  s  —  -: —  tan  xcacx. 

sm  if 

cot  X        _^ 

esc  X  — —  cot  X  sec  X. 

cosx 

Values  of  Trie ooomsCric 
faoctiofis  in  the  four  quad- 


L — In  Pier.  2  the  angle 
xi  lies  wholly  within  the  first 
qnadrant;  (r  to  90^;  x%  ex- 
tends mto  the  second 
qaadrant.  comprising  angles 
from  90^  to  180°;  xs  extends 
into  the  third  quadrant,  com- 
prising angles  from  180°  to 
*7(P;  and  X4  extends  into 
the  fourth  quadrant,  com- 
"'-'  ^  angles  from  270°  to 


It  will  be  noticed  that  in 
all  cases  the  sine  falls  perpen- 
dicularly  upon  the  axis  A  —  X 
tnd  that  the  cosine  falls  per- 
pendicularly  upon  the 
coordinate  axis  Y—Y. 
Assuming  arbitrarily  that, 
vhen  the  sine  is  above  the 
axis  oiX  —  X,  it  is  plus  and 
when  below,  it  is  minus',  also, 
that  when  the  cosine  is  to 
the  r«£A/  of  the  axis  Y-  Y 
it  is  plus,  and  when  to  the 
j«f(  it  is  minus',  we  obtain 
the  following  sign  yalues  of 
the  fundamental  sign  func- 
tions: 


sin*  X  —  1  —  cos*  X. 
coS*  X  —  1  —  sin*  X. 
tan*x  —  sec*  x  —  1. 

cot*  X  —  CSC*  X  —   1. 

sec*  X  —  1  +  tan*  x. 
CSC*  X  —  1  -h  cot*  X. 


B  OF  Ant  Anglb  x 

1 

1  + 

COS*  X 

sin*  X 

sin*  X 

1 
cos*  X 

1  + 

sin*  X 
cos*  X 

1 

COS^  X 

tan*x 

sin*  X 

1 

sin*  X 

cot*x 

COS*  X 

1 

sec*  X 

sin*  X 
tan*x 

1 

CSC*  X 

cos*  X 
cot*  X 

Quadrarrr 


5"'Qoadrant 
l80*-t70* 


4^Quadrant 


Fig.  2. 


Cosine. 


1st  qxiad.    2nd  quad.    8rd  quad.    4th  quad. 
-K  +  -  - 

+  -  -  -I- 


The  sign  values  may  further  be  extended  to  the  other  trigonometric 
nmctions  by  remembering  that 

sin  X       ^         cos  X  1  1 

tan  X  — ,  cot  X  —  -: ,  sec  x  —  ■         ,  esc  x  —  — : , 

cos  X  sm  X  oos  x  sm  x 

▼rsx— 1  — cos  X,  CVS  x— 1  — sin  x,  xscx— sec  x— 1,  exc  x  =  csc  x— 1; 
and  that  in  either  mtiltiplication  or  division,  like  signs  give  plus  and  unlike, 
nunus.    Hence  the  following  table: 

Ist  quad.     2nd  quad.     3rd  quad.      4th  quad. 


Sine,  cosecant,  coexsecant. . 

Cosine,  secant,  exsecant 

Tangent,  cotangent 

Versed  sine,  co  versed  sine  . 


+ 
+ 
+ 


di+Go(bgIe+ 


138 


9.— PLANE  TRIGONOMETRY. 


2. — Natural  Functions  of  Anolbs  prom  0*  to  360®. 


Angle 

Sin 

Cos 

Tan 

Cot 

Sec 

Csc 

Vni 

Cvs 

Xsc 

Cxc 

Qo 

0 

1 

0 

00 

1 

00 

0 

1 

0 

00 

*» 

16® 
30® 

1 

2 

3 

\F 

2\F 
3 

2 

2-V3 

i 

2VF-3 
3 

2 

1 

*§ 

45® 

vr 

2 

2 

1 

1 

vr 

VF 

2-\2 

2-V2 

\F-1 

VF-1 

Q 

2 

2 

M 

60® 

vr 

2 

* 

vr 

VF 

3 

2 

2V3 
3" 

i 

2-\l 

1 

2\3-3 

2 

8 

75® 
90® 
106® 

120® 

1 

vr 

2 

0 

00 

0 

VF 

3 

00 

-2 

1 

2\'3 
3 

1 
i 

0 

2-V3 

00 
-8 

0 
2vl-8 

2 

3 

1 

135® 

vr 

2 

sT 

2 

-1 

-1 

-vF 

\F 

2+V'2 

2-V2 

-(vF+i) 

V^-1 

o 

2 

2 

1 

160® 

i 

V8 

V3 

-Va 

-2Vl 

2 

2+V3 

1 

2V8+3 

3 

1 

2 

3 

8 

2 

4* 

1 

166® 
180® 
IW® 

210® 

0 

-1 

V3 
2 

0 

V3 
3 

00 

-VF 

-1 

2V3 
3 

00 
-2 

2 

2-HVl 

1 
i 

-2 

2VFf-3 
8 

00 

2 

—8 

■y 

226® 

2 

2 

1 

1 

-VF 

-vF 

2+V'^ 

2+V2 

^(\F+l) 

-KVFt-i) 

o 

2 

2 

1 

240® 

vr 

2 

-* 

vF 

vF 
"F 

-2 

-2V3 

! 

2+\^ 

-8 

2NFi-3 

3 

2 

3 

266® 
270® 
286® 

300® 

-1 

vF 

2 

0 
* 

00 

-vF 

0 

VF 

3 

oo 
2 

-1 

2V3 
3 

1 

2 
2+V'3 

00 

1 

-2 

2VF4-3 

•n 

3 

8 

315® 

\2" 
2 

2 

-1 

-1 

vF 

-vF 

2-V2 

2+V2 

\^1 

-(vFi-i> 

ta  ■ 

2 

2 

330® 

-i 

2 

vF 

v'^ 

2^F 
3 

-2 

2-V3 

1 

2VF-8 
3 

-s 

3 

2 

345® 
360« 

0 

1 

0 

oo 

1 

00 

0 

1 

0 

oo 

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FUNCTIONS  OF  ANGLES. 


139 


pHoctlons  off  complement,  supplement,  etc,  off  any  ancle  x. 

The  complement  of  any  angle  x  is  00°  — x.  Thus,  in  Pig.  1.  page  136, 
Ba  the  complement  of  A. 

The  supplement  of  any  angle  x  is  180°— x,  etc. 

In  the  following  Table,  the  first  four  primary  functions  of  angles  extend- 
ing into  either  of  the  four  quadrants  (see  Fig.  2,  page  137)  are  reduced  to  the 
fnnctions  of  angles  not  greater  than  00**. 


1st  Quadrant. 


2nd  Quadrant. 


cos  X 
tans 
oot  X 


sm  X 

COST 

Uknx 
cots 


sin  ^1— cos  (00° -xi) 
cos  Xi— sin  (00°— Xi) 
tan  xi- cot  (00°-*,) 
cot  xi=»tan(0O°-*i) 


sin  *3=»— sin  (  xj— 180°) 
sin  ira-  —  cos  (270^— xg) 
COSX3—— cos(  3gi— 180°) 
cos  xa— —  sin  (270°  — xs  ) 
tanxa-  tan  (  ^^-180°) 
tan*3-  cot  (270°— «3  ) 
cotxj-  cot  (  iri|-180°) 
cot  xa-     tan  (270*^ -^3     ) 


sin  X2*-sin  (180°— xj) 
sin  flfa'-cos  (     xj  — 00°) 

Jcosx2=»— cos  (ISV^  —  x^  ) 

jcos  xa— — sin  ( 

I  tan  xa  —  —  tan  ( 

I  tanxa—  —cot  ( 

jcot  X2=-  —cot  ( 

(cot  xa—  —tan  ( 

4th  Quadrant, 
(sin  X4«-sin  (360° 

(sin   X4—  —cos  (        Xa 

)cosx4*     cos  (360° 
(cosx4-»     sin 
( tan  X4 «»  —  tan 
\  tan  X4  —  —  cot  (     x^ 
I  cot  X4  =»  —  cot 
( cot  X4  -»  —  tan 


FunctkMis  of  the  sum  of  two  angles  (x+y). 

sin  (x+y)  -■  sin  x  cos  y+cos  x  sin  y. 

cos  (x+y)  —  cos  X  cos  y  — sin  x  sin  y. 

>    .    .  tanx+tany 

tan  (x+y)  —  -, — ^         . 

1— tanxtany 

^  ,    ,    .        cot  X  cot  y—1 

cot  (x+y)  — 7 — 7—^ • 

coty+cotx 

sin  x  +  sin  y  —  2  sin  J  (x+y)  cos  J  (x— y). 

cos  x  +  cos  y  —  2  cos  J  (x+y)  cos  J  (x— y). 


V^onctions  of  the  difference  of  two  angles  ix—y), 
sin  (x— y)  —  sin  x  cos  y  — cos  x  sin  y. 
COB  (x— y)  —  cos  X  cos  y+sin  x  sin  y. 
tan  X— tan  y 


tan(x— y)  — 
cot  (x-y)  - 


1+tanx  tany  * 

cot  xcot  y+1 

cot  y— cot  X 
sin  x-sin  y  -  2  cos  J  (x+y)  sin  J  (x-y). 
cosx-cosy  --2  sin  i  (x+y)  sin  i  (x-y).    izedbyGoOglc 


140  9.— PLANE  TRIGONOMETRY. 

Panctions  of  lulf  an  anflcd  x). 


sin  1 1;  — 

Sin  X    _ 
2cos  i^P 

cos  J  «- 

sin  X 

2sin  i  X 

tani«- 

1-cos* 
sin  X 

cot  4  «  — 

1  +  cosx 

versa: 


/±zi 


I  1-f  cosa: 


1  +  cos  ac 

sin  X 


—  oosec  «— cot  X 


-    /Ins 


sin  X  1  —cos  «        vers  x       coaec  jr— cot  s 

PonctJoiu  off  twice  an  angle  (2  jt). 

o  «    •  2  tan « 

sm  2  af  —  2  sin  ac  cos  ar  —  .  .  - — r— • 
1  +  tan«  « 

cos  2  %  -  cos«jc-8in*ac-l-2  sin*«-2  co8««—  1  —  ,  -"  tatf^^ 

1  +  taa>jr 

^      „  2  tan  X  sin  3  «— sin  x 

tan  2  %  -  - 


cot  2ac« 


1  —  tan«  X       cos  3  «  +  cos  x  ' 
cot'a:-! 


2cot  %    * 
Functions  of  three  times  an  angle  (3jk). 

sin  3  a:  =»  3  sin  a;  —  4  sin'  x. 
cos  3  af  =•  4  cos*  x—  3  cos  x. 

„  3  tan  X  —  tan'  a: 

tan  3  X  -=  ",      _  ^ — , -. 

1-3  tan'  X 

Functions  off  ffour  times  an  angle  {Ax) . 

sin  4  a;  —  4  sin  x  cos  x—%  sin'  x  cos  «. 
cos  4  x  =  1  —  8  cos'  a:  +  8  cos<  :r. 

4  tan  y  —  4  tan'  % 
1-6  tan'  a:  +  tan<  a;* 

Inverse  Trigonometric  Functions. — In  logarithms  we  have  seen  that  fte 
anti-logarithm  N  is  a  number  whose  logarithm  is  n-  that  is,  it  is  the  numbef 
corresponding  to  the  logarithm  n.    Similarly,  in  Trigonometry,  we  have— 

The  anti-sine  of  5  =»  angle  whose  sine  is  s— angle  corresponding  to  sine  u 
Thus,  sin  A  —s,  or  A  =  sin-»i  (Reads  il  =  anti-sine  or  inverse  sine  of  i.) 

The  anti-cosine  of  c  «  angle  whose  cosine  is  c  =>  angle  corresponding  to  cosine  c. 
Thus,  cos  A  T,  or  i4  —cos-*  c  (Reads  A  =- anti-cosine  or  inverse  cosine 
of  c). 

And  so  on  with  the  remaining  functions. 

This  must  not  be  confused  with  the  negative  exponent,—  l.as  •'^■"jr*' 

ar*  =■  — ;  (sin  x)-^  =  -: ;  (cos  y)->  — ; etc.    But  sin  A  —sin  (sin"*i) -^J 

X  sin  «  cos  y  ^ 

cos  A  ^cos  (cos-'c)  —  c;   etc. 

Examples:        i-sin  30°  .'.  the  anti-sine  of  \  is  30°. 

\/2— cos  46°  .'.  the  anti-cosine  of  \/2  is  41!*. 

"-  '^  -    I 

V  3-  tan  60" .-.  the  anti-tangent  of  VS  i»  ^Ps 


SOLUTION  OF  TRIANGLES, 


141 


Natural  and  locarithmic  trlfooonetiic  f  onctioiu. — On  pages  144  to  175 
win  be  fcmnd  tables  (8  and  4)  of  natural  functions,  and  on  pages  176  to  196 
a  table  (5)  of  logarithmic  functions,  of  angles  up  to  90^  or  in  the  first 
quadrant.  For  angles  greater  than  90^  see  Table  1  of  functions  of  any 
angle  reduced  to  function  of  an  angle  not  greater  than  90**.  In  general,  the 
(oDowing  rules  are  convenient  to  memorize: 

Sine  of  an  angle  —  the  cosine  of  its  complement. 

*•  *'        '*     —  '*     sine  '*    supiSlement. 

Tangent"        "     —  "     cotangent  **    complement. 

'•  *•        '•     —  •*  —tangent      **   supplement. 

In  using  the  natural  f tmctions  the  processes  of  multiplication  and  divi« 
mm  have  to  be  performed,  while  the  logarithmic  functions  are  designed  to 
reduce  these  to  the  simple  processes  of  addition  and  subtraction.  Log- 
arithmic ftmctions  are  simply  logarithms  of  the  natural  functions. 

The  tables  are  as  follows: 

Table  3,  page  144.  Nattiral  Sines,  Tangents.  Cotangents,  Cosines, 
(Versed  Sines.  Coversed  Sines). 

Table  4.  page  167,  Natiiral  Secants,  Cosecants,  (Exsecants.  Coexse- 
cants). 

Table  5.  page  176..  Logarithmic  Sines,  Tangents,  Cotangents.  Cosines 
(Secants.  (Cosecants). 

Solntioa  of  right  angle  triangles. — The  six  primary  functions  are  all 
that  need  be  employed  in  the  solution  of  any  triangle: 

(1)   sin  A  (— cos^— ^,  Whence,  p  —  fc  sin  i4"Acos  B. 

b 


(2)    cosi4  (— sin  B)-*j; 
(?)   tanA(=cotB)-|-. 
(4)   eoti4  (-tanB)-^ 

b 
P  ' 


{JSi   9tcA  (-csci>)- 

(«)    CSC  A  (-secB) 

[Al8o*»-6»  +  p«.    Whence  A -\/^+]? 
Example  1. 
Given:   A -Sr,  A-20.3. 
KeQtdiicd:  p. 

Solution:   {\)  p^htxaA. 

By  natural  functions, 

finA-stna^**-     .52992 

P-.62992X 20.3- 10.757.   Ans. 
By  logarithmic  functions. 
log  20.8  -   1.30750 
logsin32«     -   9.72421 
Aos.  10.757.  1.03171 


5  —ft  cos  A  —  ft  sin  B. 
p^b  tan  A -6  cot  B. 

6  — pcot  A-p  tanB. 
ft— 6  seci4— 6  cscB;  or  ft— 
ft- 


Fig.  3. 


cos  A      sin  B 

p  CSC  A -p  sec  B ;  or  ft- -T~- -  — ^ 
sm  A      cosB 

ifr-v/ft*^;  p-N/ft«^.J 
Example  2. 
Given:   p— 25.  6-20. 
Required:   Angle  B. 
Solution:   (4)  tan  B  -  -  . 


By  natural  functions, 
8. 


*      D     fr      20 
tanB---25 


Angle B-tan-t.8-38<'-40'.   Ans. 
By  logarithmic  functions. 
log  20  -    1.30103 
log  25  -    1.39794 
Ans.  38*»-40'     9.90309   glc 


141  ^.—PLANE  TRIGONOMETRY. 

Exampk  3. 
Given:  il-ld'-lC.  p-40. 
Required:  h. 

Solution:   (6)  fc-p+sinii. 
By  natural  functions. 
8ini4-8in  16*»- KK- 0.27843. 
A-40-1-0. 27848- 143.66.   Ans. 
By  logarithmic  functions. 
log  40  '='   1.60206 
log  sin  160-  10'-  9.44472 
Ans.  143.66  2.15734 


..-^ 


Solation  of  any  triangle. — ^The  following  princi- 
ples, easily  memorized,  lead  to  the  solution  of  any 
A       triangle,  nght  or  oblique. 

Sides  are  proportional  to  sines  of  opposite  angles 

Fig.  4.  "^ (1) 

Th       ^^  ^  —  sin  B  ^  sin  C 
a  b  c     ' 

Sin  ang  opp  given  side  :  sin  ang  opp  req  side  ::  given  side  :  req  side. . . . (S) 

_,         sin  B        given  side  h        .       .  .  .    ^    »      j  t 

Thus,  - — -T  —  — — : — 3-  .~5 .  m  which  A,  B  and  b  are  given. 

sin  A     required  side  a 

Sum  of  sides  :  diff ::  tang  half  siun  of  other  two  angles  :  tang  half  diff . ...  (3) 

Thus,  z —  I TTB — 7^.  »n  which  A,  b  and  c  are  given. 

b  —  c     tan  J  (B  — C) 

The  square  of  any  side  as  a— a*— 6*+c«— 2  6<:coe  A (i) 

b*+c*  —  a* 
Thus,  cos    i4  —  — St — -.  in  which  a,  b  and  c  are  given. 

i  oc  ^ 

.      .  .  .         a+b-he     . 
,  m  which  s  —  — s ,  giv«n. 

,  in  which  s  — 5 — ,  given. 

Rul4s  in  conjunction  with  the  above: 

Given:    One  side  and  two  angles.  Solve  for  "Req  side"  in  (2). 
Given:    Two  sides  and  angle  opposite  one  of  them.     Solve  for  **Req 
side"  and  for  one  of  the  angles,  in  (2). 

Given:    Two  sides  and  included  angle.    Solve  for  'Tang  half  diff '*  in  (3J)- 
Given:    Three  sides. 

(a).    Solve  for  cos  A,  in  (4),  tmless  A  is  very  small. 

lb).    Solve  for  sin  h  A,  in  (4),  unless  A  is  very  large. 

(c).    Solve  for  tan  § i4,  in  (4),  in  general  preferred.  * 

If  all  the  angles  are  required  we  may  use  the  formulas: 


■in  \A- 

'(5 

-b) 

(s- 

■c) 

■\ 

b 

c 

tenM- 

-b) 
sis 

is- 
-a) 

_£) 

1  -  r       .       ...  lis-a)  (s-b)  (5— c). 

tanii4  —  .inwhichr  — -/ ; 

s—a  ^  s 

Circular  Measure. — It  is  sometimes  convenient  in  mathematical  calcu- 
lations to  express  ancles  in  circular  measure.  The  unit  of  circular  measure 
is  an  angle  subtended  by  an  arc  whose  length  is  equal  to  the  radius  of  the 
circle.  The  value  of  such  an  angle  in  common  measure  —  67*— 17'— 46*— 
67 .2958*.  called  a  radian.  The  number  of  radians  in  180*  is  8. 141502.  and 
as  this  value  is  equal  to  ;r  we  call  180*^=-  r  in  circular  measure.  Hence* 
2r  -  360* 
n   -    180* 

^  -     00* 


2"        *^"  .  Digitized  by  Google 


CIRCULAR  MEASURE.    CUBIC  EQUATIONS.  14S 

Cubic  E^oatioiu. — ^The  general  form  of  a  cubic  eqtiation  is 

a««+6««+c«+d-0 (1) 

DiTiding  by  a,  we  have 

«»+-«»  +  -»  +  -  -0 (3) 

a  a  a  ^  ' 

By  substitution,  this  can  be  reduced  to  the  second  general  form 

^+Bx^+Cx'¥D''0 (8) 

p 
To  eliminate  «•.  let  *— y—  ^ ,  then  equation  (3)  reduces  to 


^-^(--f)-(f-f-)-o 


(4) 

By  substitution,  this  can  be  reduced  to  the  third  general  form 

y^+px+q-^O (6) 

Now  if  we  let  y^u  +  v,  equation  (6)  reduces  to 

u^+v»  +  (u+v)  (Znv  +  p)  +«-0 (6) 

Whence.  8  fco  +  p-0:  i^+i^+q^O;  nM--^;  and«i^+«»--« 

And  we  have  for  the  final  equations 

"^  2  +\4  ^27 ^^ 

"^  2      \T^27 ^^^ 


(9) 


Therefore  y-M-l-v-l  Li +\|?!  +  £L  +  !/_?  _\|^  +  £?... 
\     2^^4^27      \     2        ^4^  27 
p 
And  « —y—  r      (see  above) (10) 

Note  that  the  above  is  a  purely  algebraic  solution,  which  can  obtain 

only  when  4+27**  *^"*^  ^  ^  greater  than  0.    When  j-  +  ^  <0  we  have 

to  resort  to  the  trigometric  solution,  following. 
TrigOHOtmiric  Solution. — In  the  equation,  (9). 

\      2^>4^27       \      2       \4^27 
if  ~  +  ^  <  0.  then  the  roots  are  imaginary  and  y  is  the  sum  of  two  imaginary 
quantities.    To  solve  the  equation  for  y,  tuider  these  conditions,  proceed  as 

follows:    Let  —  «  ""  **  ^^'  *'  *"*^   4  "*"  27""  ""*  **°*  ^'  ^^^^^^  **  *"  A,'"  2?' 

and  ooa  9—^3-.    From  this,  the  values  of  the  three  roots,  y,  are 

2V;rcos|-.    -2l/7cos(6a<'-|-).    2V;rcos(l20<'-|-). 

And  «  —  y  -  g-. 

Theae  calculations  can  be  made  readily  by  the  use  of  logarithms.  It  is 
well  to  insert  the  value  of  x,  thus  foimd.  m  the  original  eauatioiLTU).  ao" 
srive  as  a  check.  D'S'feed  by  V^OOg LC 


144  9.— PLANE  TRIGONOMETRY. 


8. — Natural  Sines,  Tanobnts,  Cotanobnts.  Cosinbs. 
(Versed  sine  —1— cosine;  covcrsed  sine— 1  — sine.) 


Note. — Secant  —  1  +  cosine ;  cosecant  —  1  +simeuzed  by  CjOOQ  Ic 


NATURAL  SINES,  ETC. 


146 


1— Natural  SiaM,  Tangbmts.  Cotangbnts.  Cosikib. — (Continued). 

(Versed  sine  —  1  — cosine;  coversed  sine^l— sine.) 
3° 


' 

1    Sloe. 

Tang.  ICotanR.I  Coelne. 

1 

1  ' 

Sine. 

1  Tang.  ICotang.l  Cosine. 

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4 

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4 

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1  Coalne. 

Ootang   Tang.  |    Sine.    1   '  11      1  Cosine. 

Colanel  Tanf?. 

Sine. 

3 

Note. — Secant  —  l-i- cosine. 


8r  80» 

Cosecant-  l-i-sineed  by  GoOglc 


146  ^— PLANE  TRIGONOMETRY. 

S.— Natural  Sines,  Tangents.  Cotangents.  Cosines. — (Continued). 

(Versed  sine  ■- 1  — cosine;  coversed  sine™  1— sine.) 
4«  5« 


Note. — Secant  —  1-i-cosine.         Cosecant  pi  J^Ttt^iGoOglc 


NATURAL  SINES,  ETC. 


147 


1. — Natnral  Sines,  Tanobnts.  Cotangbnts,  Cosinbs. — (Continued). 
(Vened  sine  —  1— cosine;  cov^ned  sine— 1— Bine.) 


J_ 

fltee.    1  TsDC  IOotaii«.|  Cosine.  I      II  ' 

Sine. 

Tan«.  1  CotanK.j  Cosine. 

• 

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.1128252 

.U8344 

8.82918 

.9936375 

32 

28 

.1299494 

.131060 

7.630053 

.9915206 

52 

2f 

.11»142 

.113641 

8.799644 

.9936047 

31 

29 

.1302378 

.131356 

7.612865 

.9914828 

31 

m 

.1122082 

.113935 

8.776887 

.9935719 

30 

30 

.1305262 

.131652 

7.595754 

.9914449 

30 

31 

.1124922 

.114286 

8.754246 

.9935389 

29 

31 

.1308146 

.131948 

7.578717 

.9914069 

29 

22 

.1127812 

.114525 

8.731719 

.9935058 

28 

32 

.1311030 

.132244 

7.561766 

.9913688 

28 

23 

.1140782 

.114819 

8.709307 

.9934727 

27 

33 

.1313913 

.132540 

7.644869 

.9913306 

27 

24 

.1143502 

.115114 

8.687008 

.9934395 

26 

34 

.1316797 

.132836 

7.528057 

.9912923 

26 

JS 

.1148482 

.115409 

8.664822 

.9934062 

35 

35 

.1319681 

.133132 

7.511317 

.9912540 

35 

3« 

.1140372 

.115703 

8.642747 

.9933728 

24 

36 

.1322564 

.133428 

7.494651 

.9912155 

24 

27 

.1152281 

.115998 

8.620783 

.9933393 

23 

37 

.1325447 

.133724 

7.478057 

.9911770 

23 

3t 

.1155151 

.116393 

8.598929 

.9933057 

22 

38 

.1328330 

.134020 

7.461535 

.9911384 

22 

3f 

.1158040 

.116588 

8.577183 

.9932721 

21 

39 

.1331213 

.134316 

7.445085 

.9910997 

21 

4* 

.1180929 

.116883 

8.555546 

.9932384 

20 

40 

.1334096 

.134612 

7.428706 

.9910610 

30 

41 

.1183818 

.117178 

8.834017 

.9932045 

41 

.1336979 

.134909 

7.412397 

.9910221 

19 

43 

.1188707 

.117473 

8.512594 

.9931706 

42 

.1339862 

.135205 

7.396159 

.9909832 

18 

43 

.1189598 

117767 

8.491277 

.9931367 

43 

.1342744 

.135501 

7.379990 

.9909442 

17 

44 

.1172485 

.118062 

8.470065 

.9931026 

44 

.1345627 

.135797 

7.363891 

.9909051 

16 

4S 

.1175374 

.118357 

8.448957 

.9930685 

43 

.1348509 

.136094 

7.347861 

.9908659 

18 

4« 

.1178283 

.118652 

8.4r953 

.9930342 

46 

.1351392 

.136390 

7.331898 

.9908266 

14 

47 

.1181151 

.118947 

8.407051 

.9929999 

47 

.1354274 

.136686 

7.316004 

.9907873 

13 

48 

.1184040 

.119242 

8.386251 

.9929655 

48 

.1357156 

.136983 

7.300178 

.9907478 

12 

4t 

.1108928 

.119537 

8.365553 

.9929310 

49 

.1360038 

.137279 

7.284418 

.9907083 

11 

9» 

.1109816 

.119832 

8.344955 

.9928965 

50 

.1362919 

.137575 

7.268725 

.9906687 

10 

SI 

.1192704 

.120127 

8.334457 

.9928618 

51 

.1365801 

.137872 

7.253098 

.9906290 

9 

52 

.1105503 

.120423 

8.304058 

.9928271 

52 

.1368683 

.138168 

7.237537 

.9905893 

8 

53 

.1190481 

.120718 

8.283757 

.9927922 

53 

.1371564 

.138465 

7.222042 

.9905494 

7 

M 

.1201388 

.131013 

8.263554 

.9927573 

54 

.1374445 

.138761 

7.206611 

.9905095 

6 

85 

.1204358 

.121308 

8.243448 

.9927224 

55 

.1377327 

.139058 

7.191245 

.9904694 

5 

58 

.1207144 

.131603 

8.223438 

.9926873 

56 

.1380208 

.139354 

7.175943 

.9904293 

4 

57 

.1210031 

.131898 

8.203523 

.9926521 

57 

.1383089 

.139651 

7.160705 

.9903891 

3 

M 

.1212919 

.122194 

8.183704 

.9926169 

58 

.138.W0 

.139947 

7.145530 

.9903489 

2 

5f 

1215898 

.122489 

8.163978 

.9925816 

59 

.138«850 

.140244 

7.130419 

.9903085 

80 

.1218893 

.122784 

8.144346 

.9925462 

60 

.1391731 

.140540 

7.115369 

.9902681 

0 

-    1  6oritoe. 

Oouuiff 

Tsng. 

Stne. 

'    1      1  Cosine. 

CotanRl  Tang. 

Bine. 

"~»" 

NoU.— Secant  -  l-*-cosine. 


Cosecant  - 1  +^^d  by  GoOglc 


148 


9.— PLANE  TRIGONOMETRY. 


8.— Natural  SIom,  Tanobnts,  Cotanobnts.  Cosinbs. — (Continued.) 
(Versed  sine  o  1  — cosine;  coversed  sine >■  1— sine.) 


' 

Bine. 

Tang. 

1  Cotang.l  Cosine. 

1 

1   ' 

BlDe. 

Tang.  1  Cotang.l  Cosine.  | 

0 

.1391731 

.140540  7. 115369 1.9M268I 

60 

0 

.1564345 

: 158884 

6.313761 

.9676883 

4 

1 

.1394618 

.140837  7.100382 

.9902276 

59 

1 

.1567218 

.158682 

6.301886 

.9876488 

1 

2 

.1397492 

.141134  7.085457 

.9901869 

68 

2 

.1570091 

.168980 

6.290065 

.9876978 

1 

3 

.1400372 

.141430  7.070593 

.9901463 

67 

3 

.1572963 

.159879 

6.278286 

.9878B14 

1 

4 

.1403252 

.  141727 17. 0557901. 9901056 

66 

4 

.1676836 

.169677 

6.266561 

.9875057 

] 

5 

.1406132 

.142024  7.041048!  .9900646 

55 

S 

.1578708 

.169875 

6.854868 

.9674518 

i 

6 

.1409012 

.142321  7.0263661.9900237 

64 

6 

.1681581 

.160174 

6.848808 

.9874138 

7 

.1411892 

.14261717.0117441.9899826 

63 

7 

.1584453 

.160472 

6.831600 

.9878678 

8 

.1414772 

.142914  6.997180  .9699415 

62 

8 

.1687325 

.160770 

6.880034 

.•873816 

9  .1417651 

.143211  6.9826781.9899003 

51 

9 

.1590197 

.161069 

6.808510 

.987r54 

10 

.1420531 

.143608  6.9682331.9898690 

SO 

10 

.1593069 

.161367 

6.197027 

.9878891 

i 

11 

.1423410 

.143805  6.953847  .9898177 

49 

11 

.1596940 

.161666 

6.185586 

.9871887 

12 

.1426289 

.14410216.939519  .9897762 

48 

12 

.1598812 

.161964 

6.174186 

.9871863 

13 

.1429168 

.144399,6.925248  .9897347 

47 

13 

.1601683 

.162263 

6.162827 

.9870817 

14 

.1432047 

.144696  6.9110351.9896931 

46 

14 

.1604555 

.162561 

6.151508 

.9870431 

15 

.1434926 

.144993  6.8968791.9896614 

45 

IS 

.1607426 

.162860 

6.140230 

^ 

16 

.1437806 

.145290] 6. 882780  .9896096 

44 

16 

.1610297 

.163159 

6.128992 

! 9869496 

17 

.1440684 

.14558716.868737  .9895677 

43 

17 

.1613167 

.163457 

6.117794 

.9868027 

18 

.1443562 

.145884  6.854750  .9895258 

42 

18 

.1616038 

.163766 

6.106636 

.9868557 

19 

.1446440 

.14618116.8408191.9894838 

41 

19 

.1618909 

.164055 

6.096517 

30 

.1449319 

.146478  6.826943 

.9894416 

40 

30 

.1621779 

.164353 

6.084438 

!9e67615 

i 

21 

.1452197 

.146775  6.813122 

.9893994 

39 

21 

.1624660 

.164652 

6.073397 

.9867143 

22 

.1455075 

.14707216.799356 

.9893572 

38 

22 

.1627520 

.164951 

6.062396 

.9866670 

23 

.1457953 

.1473696.785644 

.9893148 

37 

23 

.1630390 

.165260 

6.051434 

.9866196   . 

24 

.1460830 

.147667  6.771986 

.9892723 

36 

24 

.1633260 

.165548 

6.040510 

.9868722 

35 

.1463708 

.147964  6.758382 

.9892298 

35 

35 

.1636129 

.165847 

6.029624 

.9865246 

26 

. 1466585 

.148261  6.744831 

.9891872 

34 

26 

.1638999 

.166146 

6.018777 

.9864770 

27 

.1469463 

.149559  6.731334 

.9891445 

33 

27 

.1641868 

.166445 

6.007967 

.9864893 

28 

.1472340 

.148856  6.717889 

.9891017 

32 

28 

.1644738 

.M6744 

5.997195 

.9868815 

29 

.1475217 

.149153  6. 7a4496 

.9890588 

31 

29 

.1647607 

.167043 

6.986461 

.9888836 

-30 

.1478094 

.149451 '6.691156 

.9890159 

30 

30 

.1650476 

.167342 

5.976764 

.9868858 

31 

.1480971 

.14974816.677867 

.9889728 

29 

31 

.1653345 

.167641  6.966104 

.9863875 

32 

.1483848 

.150045  6.664630 

.9889297 

28 

32 

.1656214 

.167940  5.954481 

.9861894 

33 

.1486724 

.150343  6.651444 

.9888866 

27 

33 

.1659082 

.168239 

6.943895 

.9881412 

34 

.1489601 

.150640  6.638310 

.9888432 

26 

34 

.1661951 

.168539 

6.933345 

.9860989 

35 

.1492477 

.150938,6.625225 

.9887998 

35 

35,. 1664819 

.168838 

5.922832 

.986044S 

36 

.1495353 

.151235  6.61219! 

.9887564 

24 

36 

.1667687 

.169137 

5.912355 

.9859080 

37 

.1498230 

.151533  6.599208 

.9887128 

23 

37 

.1670556 

.169436  6.901913 

.98BM75 

38 

.1501106 

.151830  6.686273 

.9886692 

22 

38 

.1673423 

.169735  5.891608 

.9868968 

39 

.1503981 

.152128  6.573389 

.9886255 

21 

39 

.1676291 

.170035  5.881138 

.9888901 

40 

.1506857 

.152426.8.560553 

.9885817 

30 

40 

.1679159 

.170334' 5.870804 

.98S8013 

i 

41 

.1509733 

.152723  6.647767 

.9885378 

19 

41 

.1682026 

.170633; 5. 860505 

.9697584 

42 

.1612608 

.153021,6.635029 

.9884939 

18 

42 

.1684894 

.170933  6.860241 

.9857036 

43 

.1515484 

.153319  6.623339 

.9884498 

17 

43 

.1687761 

. 1712326.840011 

.9858544 

44 

.1518359 

.153617  6.509698 

.9884057 

16 

44 

.0690628 

.171532  5.829817 

.9856053 

45 

.1521234 

.153914  6.497104 

.9883615 

15 

45 

.1693496 

.171831  5.819657 

.9866881 

1 

46 

.1524109 

.1542I2'6. 484558 

.9883172 

14 

46 

.1696362 

.172130  6.809531 

.9866068 

47 

.1526984 

.154510!6.472059 

.9882728 

13 

47 

. 1699228 

.172430  5.799440 

.9654674 

48 

.1529858 

.15480816.459607 

.9882284 

12 

48 

.1702095 

.172730  5.789382 

.9864079 

49 

.1532733 

.155106  6.447201 

.9881838 

11 

49 

.1704961 

.173029  5.779358 

.9853583 

SO 

.1535607 

.155404 '6. 434842 

.S881392 

10 

50 

.1707828 

.173329  6.769368 

.9663887 

1 

51 

.1538482 

.155701  6.422530 

.9880945 

91 

51 

.1710694 

.173628  5.759412 

.9853890 

52 

.1541356 

.155999 

6.410263 

.9880497 

8 

53 

.1713560 

.173928  5.749488 

.9^a 

53 

.1544230 

.166297 

6.398042 

.9880048 

7 

63 

.1716425 

.174228  5.739598 

.9e61993 

54 

.1547104 

.156595 

6.385866 

.9879599 

6 

54 

.1719291 

.174527  6.729741 

.9861093 

55 

.1549978 

.156893 

6.373735 

.9879148 

5 

55 

.1722156 

.174827  6.719917 

.9680693 

56 

.1552851 

.157191 

6.361650 

.9878697 

4 

56 

.1726022 

.176127  5.710125 

.SSni 

57 

.1555725 

.157490 

6.349609 

.9878245 

3 

57 

.1727887 

.175427  5.700366 

.9869589 

58 

.1558598 

.1577H8  6.337612 

.9877792 

2 

68 

.1730752 

.176727  5.690639 

59 

.1561472 

.158086  6.325660 

.9877338 

1 

59 

.1733617 

.176027  5.680944 

!9e48883 

60 

.1564345 

.158384  6.313751 

.9876883 

^i 

60 

.1736482 

.176327  6.671281 

.9848078 

.^ 

Coelne. 

CotanKl  TaiiR. 

Sine.     1   '  11 

Cosine. 

Ootang  TMng. 

^ne. 

"^ 

81°  a 

Note.— Secant  - 1 + cosine.         Cosecant  welK^OOglc 


NATURAL  SINES,  ETC, 


S.— Natural  Sacs,  Tanobnts,  Cotangents.  Cosinbs. — (Continued.] 

(Versed  sine  =  1— cosine;  coversed  sine—  1  — sine). 
Mf  11° 


—  '^'otang.l  Coalne. 


144554 

.9816272 

136576 

.9815716 

128622 

.9815160 

120692 

.9814603 

112785 

.9814045 

104902 

.9813486 

097042 

.9812927 

089206 

.9812366 

081392 

.9811805 

073602 

.9811243 

065835 

.9810680 

058090 

.9810116 

050369 

.9809552 

042670 

.9008986 

034993 

.9808420 

027339 

.98078.53 

019707 

.9807285 

012098 

.9806716 

004511 

.9806147 

996945 

.9805.'^76 

989402 

.9805005 

981881 

.9804433 

974381 

.9803860 

966903 

.9803286 

959447 

.9802712 

952012 

.9802136 

944599 

.9801  SCO 

937206 

.98009S;{ 

929835 

.9800405 

922485 

.9799827 

915157 

.9799247 

907849 

.9798*167 

900562 

.9798086 

893295 

.9797504 

886049 

.9796931 

878824 

.9796,117 

871620 

.9795752 

864435 

.9795167 

857271 

.9794581 

850128 

.9793994 

843004 

.9793406 

835901 

.9792818 

828817 

.9792228 

821753 

.9791638 

814709 

.9791047 

807685 

.97904:'fi 

8n0680 

.97h'9S»;2 

793695 

.97H926H 

786730 

.97886:4 

779783 

.9788079 

772856 

.9787483 

765949 

.97K6SSh 

759060 

.9786288 

752190 

.978r,.is<. 

745340 

.978.W,H) 

73850H 

.97H441UI 

731695 

.97S3SS!! 

724901 

.97832^7 

718125 

.9782r.si 

7I136« 

.9782(is(i 

704630 

.9781476 

rang.  I     Slue. 


79*' 


Note. — Secant  =•  1-4- cosine. 


Cosecant 


^m'i^^^^gl^ 


180 


^,— PLANE  TRIGONOMETRY. 


8.— Natural  Stnct,  Tanobnts.  Cotanobnts,  Cosinbs. — (Contmued.) 
(Versed  sum  ■- 1  — cosine;  coversed  sine—  1  —sine.) 


'      Sine. 

Tang.  1  Ootang.l  Cosine.  1     II  ' 

Sine. 

Tang.  1  Ootang.l  Cosine.  1 

.2079117 

.212556'4.704630 

.9781476 

^! 

0 

.2249511 

.230868 

4.331475 

.9743701 

.2081962 

.212860 

4.697910 

.9780*71 

69 

.2252345 

.231174 

4.325734 

.9743046 

.2084807 

.213164 

4.691208 

.9780265 

58 

.2255179 

.231481 

4.320007 

.9742390 

.2087652 

.213468 

4.684624 

.9779658 

67 

.2258013 

.231787 

4.314295 

.9741734 

.2090497 

.213773 

4.677859 

.9779050 

56 

.2260846 

.232094 

4.308597 

.9741077 

.2093341 

.214077 

4.671213 

.9778441 

55 

.2263680 

.232400 

4.302913 

.9740419 

.2096186 

.214381 

4.664583 

.9777832 

54 

.2266513 

.232707 

4.297244 

.9739760 

.2090030 

.214685 

4.657972 

.9777222 

53 

.2269345 

.233014 

4.291588 

.9739100 

.2101874 

.214990 

4.651378 

.9776611 

62 

.2272179 

.233320 

4.285947 

.9738439 

.2104718 

.215294 

4.644803  .9775999 

61 

.2275012 

.233627 

4.280319 

.9737778 

.2107661 

.215598 

4.638245 

.9775386 

50 

.2277844 

.233934 

4.274706 

.9737116 

.2110405 

.215903 

4.631705 

.9774773 

49 

.2280877 

.234241 

4.269107 

.9736453 

.2113248 

.216207  4.625183 

.9774159 

48 

.2283509 

.234547 

4.263521 

.9735789 

.2116091 

.216512 

4.618678 

.9773544 

47 

.2286341 

.234854 

4.257950 

.9735124 

.2118934 

.216816 

4.612190 

.9772928 

46 

.2289172 

.235161 

4.252392 

.9734458 

.2121777 

.217121 

4.605720 

.9772311 

45 

.2292004 

.235468 

4.246848 

.9733792 

.2124619 

.317425 

4.599268 

.9771693 

44 

.2294835 

.235775 

4.241317 

.9733135 

.2127462 

.217730 

4.692832 

.9771075 

43 

.2297666 

.236082 

4.235800 

.9732457 

.2130304 

.2180J5 

4.586414 

.9770456 

42 

.2300497 

.236390 

4.230297 

.9731789 

.2133146 

.218340 

4.580012 

.9769835 

41 

.2303328 

.236697 

4.224808 

.9731119 

ao 

.2135988 

.218644 

4.573628 

.9769215 

40 

20 

.2306159 

.237004 

4.219331 

.9730449 

.2138829 

.218949  4.567261 

.9768593 

39 

21 

.2308989 

.237311 

4.213869 

.9729777 

22 

.2141671 

.219254 

4.560911 

.9767970 

38 

22 

.2311819 

.337618 

4.208419 

.9729105 

23  .2144512 

.219559 

4.654577 

.9767347 

37 

23 

.2314649 

.237926 

4.202983 

.9728432 

24 

.2147353 

.219864  4.548260 

.9766728 

36 

24 

.2317479 

.238233 

4.197560 

.9727759 

35 

.2150194 

.220169  4.541960 

.9766098 

35 

25 

.2320309 

.238541 

4.192151 

.9737084 

26 

.2153035 

.220474  4.535677 

.9765472 

34 

26 

.2323138 

.238848 

4.186754 

.9726409 

27 

.2155876 

.220779  4.529410 

.9764845 

83 

27 

.2325967 

.239156 

4.181371 

.97257SS 

28 

.2158716 

.221084  4.523160 

.9764217 

32 

28 

.2328796 

.239463 

4.176001 

.9725056 

29 

.2161556 

.221389  4.516926 

.9763589 

31 

29 

.2331626 

.239771 

4.170644 

.9724378 

30 

.2164396 

.221694  4.510708 

.9763960 

30 

30 

.2334454 

.240078 

4.165299 

.9723699 

31 

.2167236 

.221999 

4.604507  .9762330 

29 

31 

.2337282 

.24038^ 
.2406M 

4.159968 

.9723020 

32 

.2170076 

.222305 

4. 498322  .9761699 

28 

32  .2340110 

4.164660 

.9722339 

33 

.2172915 

.222610 

4.492153 

.9761067 

27 

33  .2342938 

.241001 

4.149344 

.9781658 

34 

.2175754 

.222915 

4.486000 

.9760435 

26 

34  .2345766 

.241309 

4.144051 

.9720976 

35 

.2178593 

.223221 

4.479863 

.9769802 

25 

35  .2348594 

.241617 

4.U8771 

.9720394 

j 

36 

.2181432 

.223626 

4.473742 

.9759168 

24 

36  .3351421 

.241925 

4.133504 

.9719610 

37 

.2184271 

.223831 

4.467637 

.9758533 

23 

37  .2354248 

.242233 

4.128249 

.9718938 

38 

.2187110 

.224137 

4.461548 

.9757897 

22 

38  .2367075 

.242541 

4.123007 

.9718840 

39 

.2189948 

.224442 

4.455475 

.9757260 

21 

38  .2359902 

.242849 

4.117778 

.9717664 

40 

.2192786 

.224748 

4.449418 

.9756623 

20 

40 

.2362729 

.243157 

4.112561 

.9716867 

41 

.2195624 

.225054 

4.443376 

.9755985 

19 

41 

.2365555 

.243465 

4.107356 

.9716180 

42 

.2198462 

.225359  4.437350 

.9755345 

18 

42 

.2368381 

.243773  4.102164 

.9715491 

43 

.2201300 

.225665 

4.431339 

.9754706 

17 

43 

.2371207 

.244081 

4.096985 

.9714802 

44 

.2204137 

.225971 

4.425343 

.9754065 

16 

44 

.2374033 

.244390 

4.091817 

.9714112 

45 

.2206974 

.226276 

4.419364 

.9753423 

15 

45 

.2376859 

.244698 

4.086662 

.9718421 

46 

.2209811 

.226582 

4.413399 

.9752781 

14 

46 

.2279684 

.245006 

4.081519 

.9713729 

47 

.2212648 

.226888 

4.407450 

.9752138 

13 

47 

.2382510 

.245315 

4.076389 

.9718036 

48 

.2215485 

.227194;4.40I5I6 

.9751494 

12 

48 

.2385335 

.245623 

4.071270 

.9711343 

49 

.2218321 

.227600 

4.395597 

.9750849 

11 

49 

.2388159 

.245932  4.066164 

.9710649 

50 

.2221158 

.227806 

4.389694 

.9750203 

10 

50 

.2390984 

.246240  4.061070 

.9709^3 

51 

.2223994 

.228112 

4.383805  .9749556 

9 

51 

.2393808 

.246549 

4.055987 

.9709858 

52 

.2226830 

.228418 

4.377931 

.9748909 

8 

52 

.2396633 

.246857 

4.050917 

.9708561 

53 

.2229666 

.228724 

4.372073 

.9748261 

7 

53 

.2399457 

.247166 

4.046859 

.9707863 

54 

.2232501 

.229030 

4.366229 

.9747612 

6 

54 

.2402280 

.247475 

4.040812 

.9707165 

55  .2235337 

.229336 

4.360400 

.9746962 

5 

55 

.2405104 

.247783  4.035777 

■9706466 

56 

.2238172 

.229642 

4.354586 

.9746311 

4 

56 

.2407927 

.248092  4.030755 

.970^66 

67 

.2241007 

.229949 

4. 348786. 9745660 

3 

57 

.2410751 

.248401 

4.025744 

.9706065 

58 

.2243842 

.230255 

4.343001 

.9745008 

2 

58 

.2413574 

.248710 

4.020744 

.9704363 

59 

.2246676 

.230561 

4.337231 

.9744355 

1 

59 

.2416396 

.249019 

4.015757 

.9703660 

60 

.2249511 

.230868 

4.331475 

.9743701 

0 

60 

.2419219 

.249328 

4.010780 

.9702867 

Cosine. 

Ootang 

Tang.  1    Sine. 

1  '   1      1  Cosine.  ICoteDffi  Tang.  I    dtna. 

" 

TT 


Note. — Secant  —!•«- cosine. 


Coseamtfffe|(t£i©Ogle 


NATURAL  SINES,  ETC.  161 

ti— Naitaral  SIom,  Tam gbnts,  Cotanobnts.  Cosinbs. — (Continued.) 
(Vened  tine  «1  ^cosine;  covened  sine^l— sine.) 


76"  74- 

Note. — Secant  » 1  •«- cosine.         Cosecant  -  l-«-sinc^ed  by  UoOg  Ic 


C52  9.— PLANE  TRIGONOMETRY. 

a.— Natanil  Sines,  Tangents.  Cotangbnts.  Cosines. — (Contmued.) 

(Versed  sine  —1— cosine;  coversed  sine^l— sine.) 
16°  ir 


73°  7r 

Note. — Secant -!•«- cosine.  Cosecanta^tt^sixt^OOglc 


NATURAL  SINES,  ETC.  163 

a— Natanl  Sinct,  Tanobnts.  Cotangbnts.  Cosinbs. — (Continued.) 
(Versed  sine  ■- 1— cosine;  coversed  sine-*!— sine.) 


710  7(r» 

Note.— SecMt  -1-i-cosine.         Cosecant- l-^-sindied  by Go Ogle 


164 


9.— PLANE  TRIGONOMETRY. 


Sr-Natnral  Sines,  Tanobntb.  Cotangents.  Cosinbs. — (Contintied.) 

(Versed  sine  -•  1  — cosine;  coversed  sine—  1  — sine.) 
7tf  21'» 


'  1    sine.    ITang.  ICotang.l  Cosine.  |      ||  '  |    Sine. 

Tang.  1  Cotang.|  Cosine,  i 

0 

.3420201 

.863970 

2.747477 

.93M926 

60 

.3583679 

.388864 

2.605089 

.8335804 

1 

.3422935 

.364299 

2.744992 

.9396931 

69 

.3686395 

.384197 

2.602825 

.9334761 

2 

.3425668 

.364629 

2.742512 

.9394935 

58 

.3689110 

.384531 

2.600565 

3 

.3428400 

.364958 

2.740035 

.9393938 

67 

.3691825 

.384865 

2.598309 

.9332673 

4 

.3431133 

.365288 

2.737562 

.9392940 

66 

.3594640 

.385199 

2.596066 

.9331628 

5 

.3433865 

.365618 

2.735093 

.9391942 

55 

.3597264 

.385633 

2.593806 

8380582 

6 

.3436597 

.866948 

2.732628 

.9390943 

64 

.3699968 

.386867 

2.591660 

! 9328535 

7 

.3439329 

.366277 

2.730167 

.9388943 

53 

.3602682 

.386202 

2.589317 

.9328488 

8 

.3442060 

.366607 

2.727710 

.8888942 

52 

.3605396 

.386536 

2.687078 

.8327438 

9 

.3444791 

.366937 

2.725256 

.9387940 

61 

.3608108 

.386870 

2.684842 

.8326380 

10 

.3447521 

.867268 

2.722807 

.9386938 

50 

.3610821 

.387205 

2.682609 

.8325340 

11 

.3450252 

.367598 

2.720362 

.9386934 

49 

.3613534 

.387639 

2.580380 

.9334280 

12 

.3452982 

.867928 

2.717920 

.9384930 

48 

.3616246 

.387874 

2.678163 

13 

.3455712 

.368258 

2.715482 

.9383925 

47 

.3618958 

.388209 

2.676931 

.9322186 

U 

.3458441 

.368589 

2.713048 

.9382920 

46 

.3621669 

.388643 

2.573711 

.8321133 

15 

.3461171 

.368919 

2.710618 

.9381913 

45 

.3624380 

.388878 

2.571495 

.8320078 

16 

.3463900 

.369250 

2.708192 

.9380906 

44 

.3627091 

.389213 

2.669283 

.8218024 

17 

.3466628 

.369580 

2.705769 

.9379898 

43 

.3629802 

.389548 

2.667073 

.8317868 

18 

.3469357 

.369911 

2.703351 

.9878889 

42 

.3632512 

.389883 

2.664867 

.9316812 

19 

.3472085 

.370242 

2.700936 

.9377880 

41 

.3635222 

.390218 

2.662664 

.8315656 

» 

.3474812 

.870572 

2.698525 

.9376869 

40 

30 

.3637932 

.390554 

2.560464 

.8314787 

21 

.3477540 

.370903 

2.696118 

.9375858 

39 

.3640641 

.890889 

2.668368 

.8913739 

22 

.3480267 

.871234 

2.693714 

.9374846 

38 

.3643351 

.S91224 

2.666075 

.8312678 

23 

.3482994 

.371565 

2.691314 

.9373833 

37 

.3646059 

.391660 

2.563885 

.8311818 

24 

.3485720 

.371896 

2.688919 

.9372820 

36 

.3648768 

.391895 

2.661699 

.8310558 

35 

.3488447 

.372227 

2.686626 

.9371806 

35 

35 

.3651476 

.392231 

2.649516 

.880M86 

26 

.3491173 

.372559 

2.684138 

.9370790 

34 

.3654184 

.392667 

2.647335 

.9308434 

27 

.3493898 

.372890 

2.681753 

.9369774 

33 

27 

.3656891 

.392902 

2.545159 

8307370 

28 

.3496624 

.373221 

2.679372 

.9368758 

32 

28 

.3659599 

.393238 

2.542985 

.8306300 

29 

.3499349 

.373553 

2.676995 

.9367740 

31 

29 

.3662306 

.393574 

2.540815 

.8305241 

30 

.3502074 

.373884 

2.674621 

.9366722 

30 

30 

.3665012 

.393910  2.538647 

.8304176 

31 

.3504798 

.374216 

2.672251 

.9366703 

29 

31 

.3667719 

.394246 

2.636483 

.8303109 

' 

82 

.3507523 

.374547 

2.669885 

28 

32 

.3670425 

.394682 

2.634323 

.8302042 

83 

.3510246 

.374879 

2.667522 

.9363662 

27 

33 

.3673130 

.394918 

2.632165 

.8300874 

84 

.3512970 

.375211 

2.665163 

.9362641 

26 

34 

.3675836 

.395255 

2.630011 

.8109005 

35 

.3515693 

.375543 

2.662808 

.9361618 

35 

35 

.3678941 

.395561 

2.527859 

.83M8S5 

36 

.3518416 

.375875 

2.660456 

.9360595 

24 

36 

.3681246 

.395928 

2.625711 

.8207765 

37 

.3521139 

.376207 

2.658108 

.9369571 

23 

37 

.3683950 

.396264 

2.623566 

.8806694 

38 

.3523862 

.376539 

2.655764 

.9358547 

22 

38 

.3686654 

.396601 

2.621424 

.8896622 

89 

.3526584 

.376871 

2.653423 

.9357521 

21 

39 

.3689358 

.396937 

2.619286 

.8304M9 

40 

.3529306 

.377203 

2.651086 

.9356496 

30 

40 

.3692061 

.397274 

2.617150 

.8293475 

41 

.3532027 

.377536 

2.648753 

.9355468 

19 

41 

.3694765 

.397611 

2.515018 

.9292401 

42 

.3534748 

.377868 

2.646423 

.9354440 

18 

42 

.3697468 

.397948 

2.512889 

.9291336 

43 

.3537469 

.378201 

2.644096 

.9353412 

17 

43 

.3700170 

.398285 

2. U 0762 

.9390260 

44 

.3540190 

.378533 

2.641774 

16 

44 

.3702872 

.398622 

2.608639 

.1»89173 

45 

.3542910 

.378866 

2.639454 

.9351352 

15 

45 

.3705574 

.398959 

2.506619 

.92S8096 

46 

.3545630 

.379198 

2.637139 

.9350321 

14 

46 

.3708276 

.399296 

2.604403 

.9387017 

47 

.3548350 

.379631 

2.634827 

.9349289 

13 

47 

.3710977 

.399634 

2.502289 

.8286038 

48 

.3551070 

.379864 

2.632518 

.9348267 

12 

48 

.3713678 

.399971 

2.500178 

.8884858 

49 

.3553789 

.380197 

2.630213 

.9347223 

11 

49 

.3716379 

.400308 

2.498070 

.9283778 

50 

.3556508 

.380530 

2.627912 

.9346189 

10 

50 

.3719079 

.400646 

2.495966 

.8282696 

fil 

.3559226 

.380863 

2.625614 

.9345154 

9 

51 

.3721780 

.400984 

2.493864 

:^iat 

52 

.3561944 

.3811% 

2.623319 

.9344119 

8 

52 

.3724479 

.401321 

2.491766 

63 

.3564662 

.381529 

2.621028 

.9343082 

7 

53 

.3727179 

.401659 

2.489670 

.tt7M47 

54 

.3567380 

.381862 

2.618741 

.9342045 

6 

54 

.3729878 

.401997 

2.487578 

55 

.3570097 

.382196 

2.616457 

.9341007 

5 

55 

.3732577 

.402335 

2.485488 

66 

.3572814 

.382529 

2.614176 

.9339968 

4 

56 

.3736275 

.402673 

2.483402 

67 

.3576531 

.382863 

2.611899 

.9338928 

3 

57 

.3737973 

.403011 

2.481319 

•9275104 

58 

.3578248 

.383196 

2.609625 

.9337888 
.9336846 

2 

58 

.3740671 

.403349 

2.479238 

.9176016 

69 

.3580964 

.383530 

2.607355 

ll 

59 

.3743363 

.403687 

2.477161 

•9272928 
.tt7l839 

60 

.3583679 

.383864 

2.606089 

.9335804 

0 

60 

.3746066 

.404026 

2.476086 

cosine. 

CoUng 

Tang. 

Bine. 

ZI 

I  Cosine. 

Cotang 

TBBg. 

dine. 

"■ 

Note. — Secant —l-^*  cosine.  Cosecant 


TzlA^Soogle 


NA  TURA  L  SINES,  ETC.  150 

a^— Natoral  SiiiM,  Tangbnts.  Cotangbnts.  Cosines. — (Continued.) 

CVersed  sine  « 1— cosine;  coversed  sine—  1~ sine.) 
fP  230 


070  Qfjf> 

Note— SccMit   -1+cosine.        Cosecant -l+fiSig^d  by  GoOglc 


156 


9— PLANE  TRIGONOMETRY. 


a.— Natural  Sines,  TANOBirrs,  Cotanobnts,  Cosines. — (Cootinued.) 
(Versed  sine  «1— cosine;  coversed  sine^l— sine.) 


'  1    sine.    1  Tang.  |  Cotang.l  Cosine.  | 

1  '      Sine.    1  Tang.  |  Cotang.l  Cosine.  | 

0 

.4067366 

.445228 

3.246036 

.9136455 

64 

0 

.4228183 

.466307 

2.144506 

.9063078 

60 

1 

.407UO24 

.445577 

2.244279 

.9134271 

5 

1 

.4228819 

.466661 

2.142879 

.9061848 

59 

2 

.4072681 

.445926 

2.242524 

.9183087 

5 

2 

.4231455 

.467016 

2.141258 

.9060618 

58 

3 

.4075337 

.446274 

2.240772 

.9131902 

5 

3 

.4234090 

.467370 

2.139630 

.9059386 

67 

4 

.4077993 

.446623 

2.239021 

.9130716 

5 

4 

.4236725 

.46n25  2.1380081 

.9068154 

66 

5 

.4080649 

.446972 

2.237273 

.9129529 

Si 

5 

.4239360 

.468079 

2.136389 

.9056922 

55 

6 

.4083305 

.447321 

2.235528 

.9128342 

5 

6 

.4241994 

.468434 

2.134771 

.9055688 

54 

7 

.4085960 

.447670 

2.233784 

.9127154 

5 

7 

.4244628 

.468789 

2.133155 

.9054454 

63 

8 

.4088615 

.448020 

2.232043 

.9125965 

6 

8 

.4247262 

.469143 

2.131542 

.9058819 

52 

9 

.4091269 

.448369 

2.230304 

.9124775 

5 

9 

.4249895 

.469498 

2.129930 

.9051983 

51 

10 

.4093923 

.448718 

2.228567 

.9123584 

5* 

0 

.4252528 

.469853 

2.128321 

.9050746 

5Q 

11 

.4096577 

.449068 

2.226833 

.9122393 

4 

tl 

.4255161 

.470269 

2.126713 

.9049509 

41 

12 

.4099230 

.449417 

2.225100 

.9121201 

4 

12 

.4257793 

.470564 

2.125108 

.9048871 

4f 

13 

.4101883 

.449767 

2.223370 

.9120008 

4 

13 

.4260425 

.470919 

2.123604 

.9047088 

41 

U  .4104536 

.450117 

2.221643 

.9118818 

4 

14 

.4263056 

.471275 

2.121903 

.9045792 

4< 

151.4107189 

.450467 

2.219917 

.9117620 

4J 

5 

.4265687 

.471630 

2.120S03 

.9044651 

4j 

16 

.4109841 

.450817 

2.218194 

.9116425 

4 

[6 

.4268318 

.471986 

2.118705 

.9043310 

4^ 

17 

.4112492 

.451167 

2.216473 

.9115229 

4 

17 

.4270949 

.472342 

2.117110 

.9042068 

A'a 

18 

.4115144 

.451517 

2.214754 

.9114033 

4 

18 

.4273579 

.472697 

2.115516 

.9040825 

4! 

19 

.4117795 

.451867 

2.213037 

.9112835 

4 

19 

.4276208 

.473053 

2.113924 

.9039582 

4 

20 

.4120445 

.452217 

2.211323  .9111637  | 

4( 

!0 

.4278838 

.473409 

2.112334 

.9038338 

44 

21 

.4123096 

.452568 

2.209611 

.9110438 

3 

!1 

.4281467 

.473765 

2.110747 

.9037093 

3! 

22 

.4125745 

.452918 

2.207901 

.9109238 

3 

!2 

.4284095 

.474122 

2.109161 

.9036847 

3 

23 

.4128395 

.453269 

2.206193 

.9108038 

3 

!3 

.4286723 

.474478 

2.107577 

.9034600 

S 

24 

.4131044 

.453620 

2.204487 

.9106837 

3 

84 

.4289351 

.474834 

2.105995 

9033359 

3 

35 

.4133693 

.453970 

2.202784 

.9105635 

31 

15 

.4291979 

.475191 

2.104415 

.9038105 

3J 

26 

.4136342 

.454321 

2.201083 

.9104432 

3 

!6 

.4294606 

.475548 

2.102836 

.9030856 

3 

27 

.4138990 

.454672 

2.199384 

.9103228 

3 

J7 

.4297233 

.475904 

2.101260 

.9029606 

3 

28 

.4141638 

.455023 

2.197687 

.9102024 

3 

:8 

.4299859 

.476261 

2.099686 

.9028356 

3 

29 

.4144285 

.455375 

2.195992 

.9100819 

3 

29 

.4302485 

.476618 

2.098114 

.9027106 

2 

30 

.4146932 

.455726 

2.194299 

.9099613 

3< 

10 

.4305111 

.476975 

2.096543 

.9025853 

3 

31 

.4149579 

.456077,3.1926091.9098406  | 

2 

n 

.4307736 

.477332 

2.094975 

2 

32 

.4152226 

.456429 

2.190921 

.9097199 

2 

12 

.4310361 

.477689 

2.098408 

! 9023947 

: 

33 

.4154872 

.456780 

2.189234 

.9095990 

2 

)3 

.4312986 

.478047 

2.091843 

.9028092 

: 

34 

.4157617 

.457132 

2.187551 

.9094781 

2 

)4 

.4315610 

.478404 

2.090280 

.9020838 

a 

35 

.4160163 

.457483 

2.185869 

.9093572 

2 

15 

.4318234 

.478762 

2.088720 

.9019588 

2 

36 

.4162808 

.457835 

2.184189 

.9092361 

2 

)6 

.4320857 

.479119 

2.087161 

.9018325 

37 

.4165453 

.458187 

2.182511 

.9091150 

J7 

.4323481 

.479477 

2.085603 

.9017068 

J 

38 

.4168097 

.458539 

2.180836 

.9089938 

)8 

.4326103 

.479835 

2.084048 

.9015810 

• 

39 

.4170741 

.458891 

2.179163 

.9088725 

J9 

.4328726 

.480193 

2.082495 

.9014661 

40 

.4173385 

.459243 

2.177492 

.9087511 

10 

.42»31348 

.480551 

2.080943 

.9018292 

2 

41 

.4176028 

.459596 

2.175822 

.9086297 

II 

.4333970 

.480909 

2.079394 

.9013631 

421.4178671 

.459948 

2.174155 

.9085082 

12 

.4336591 

.481267 

2.077846 

.9016770 

43  .4181313 

.460301 

2.172491 

.9083866 

13 

.4339212 

.481625 

2.076300 

.9009668 

44  .4183956 

.460653 

2.170828 

.9082649 

a 

.4341832 

.481984 

2.074766 

.9008246 

451.4186597 

.461006 

2.169167 

.9081432 

15 

.4344453 

.482342 

2.073214 

.9006982 

461.4189239 

.461359,2.167509 

.9080214 

46 

.4347072 

.482701 

2.071674 

.9008718 

47. 4191880 

.461711  2.165852 

.9078995 

47 

.4349692 

.483060 

2.070135 

.9004483 

48  .4194521 

.462064  2.164198 

.9077775 

48 

.4352311 

.483418 

2.068599 

.9008188 

49  .4197161 

.462417  2.162546 

.9076554 

49 

.4354930 

.483777 

2.067064 

.9001921 

50]. 4 199801 

.462771  2.160895 

.9075333 

SO 

.4357548 

.484136 

2.065531 

.9000654 

511.4202441 

.46312412.159247 

.9074111 

61 

.4360166 

.484495 

2.064000 

.8999386 

62  ,.4205080 

.463477,2.157601 

.9072888 

62 

.4362784 

.484855 

2.062471 

.8998117 

63,. 42077 19 

.46o831  2.155957 

.9071665 

53 

.4366401 

.485214 

2.060944 

.8996848 

64 '.42 103.58 

.464184'2. 154315 

.9070440 

54 

.4368018 

.485573 

2.059418 

.8995578 

551.4212996 

.46453812.152675 

.9069215 

$5 

.4370634 

.485933 

2.057895 

.8964307 

66 {.42 15684 

.46489112.151037 

.9067989 

56 

.4373251 

.486293 

2.056373 

.8963626 

57  .4218272 

.46.5245,2.149402 

.9066762 

57 

.4375866 

.486652 

2.054853 

.8991763 

68'. 4220909 

.465599  2. 147768,. 9065535 

' 

11  58 

.4378482 

.487012 

2.053334 

.8990489 

591.4223546 

..465953'2.146136|. 9064307 

1    59  .4381097 

.487372  2.051818 

.8969815 

60  .4226183 

1. 4663071 2. 144506  .9063078 

c 

1   60  .4383711 

.487732  2.050303 

.898798Q 

J 

CoBlne. 

iCotanRl  Tang.       Sine.    |  ' 

1        1  Cosine. 

Cotang  Tang. 

mn^ 

65° 


Note. — Secant  —  1  -«•  cosine. 


Cosecan«fliif4^POgle 


NATURAL  SINES,  ETC.  167 

&r-Natanl  SisM,  Tanobnts,  Cotanobnts.  Cosinbs. — (Contintied.) 

(Versed  sixie  —1  — coeine;  coversed  eine^l— sine.) 
2?» 


63° 
Note. — Secant  —  1  •«- cosine.  Cosecant  =  1  +sirie^ 


tizedbyGoOQie 

le.  o 


U8 


9.— PLANE  TRIGONOMETRY. 


8.— Natural  Sinct,  Tanobnts.  Cotanobnts.  CosiNBa. — (Continued.) 
(Versed  sine  » 1  — cosine;  ooversod  sane*  l—sine.) 


»» 


JJ 

Sine.     Tang.  |  Ootang.l  GoslDe. 

II  ' 

Sine. 

Tanir.  1  Ootang.|  Cosine. 

0 

.46M716 

.631709 

1.880726 

.8829476 

60 

0 

.4848096 

.554809 

1.804047 

.8746197 



1 

.4697284 

.632082 

1.8794(r7 

.8828110 

69 

1 

. 4850640 

.554689 

1.802810 

.8744786 

59 

2 

.4699862 

.632465 

1.878089 

.8826743 

68 

2 

.4863184 

.656069 

1.801575 

.8743276 

58 

8 

.4702419 

.632829 

1.876773 

.8826376 

67 

3 

.4865727 

.556460 

1.800340 

.8741962 

57 

4 

.4704986 

.533202 

1.876468 

.8824007 

66 

4 

.4868270 

.666881 

1.799107 

.8740650 

66 

5 

.4707663 

.633576 

1.874145 

.8822638 

55 

5 

.4860812 

.656211 

1.797875 

.8739127 

SS 

6 

.4710119 

.633950 

1.872833 

.8821269 

64 

6 

.4863364 

.666692 

1.796645 

.^37722 

M 

7 

.4712685 

.634324 

1.871523 

.8819898 

63 

7 

.4866896 

.656973 

1.796416 

.8736207 

53 

8 

.4715250 

.634698 

1.870214 

.8818527 

62 

8 

.4868436 

.667366 

1.794188 

.8784891 

52 

9 

.4717816 

.636072 

1.868906 

.8817166 

61 

9 

.4870977 

.667736 

1.792961 

.8788475 

51 

10 

.4720380 

.636446 

1.867600 

.8816782 

50 

10 

.4873617 

.668117 

1.791786 

.8732068 

SO 

il 

.4722944 

.636820 

1.866295 

.8814409 

49 

11 

.4876067 

.668499 

1.790512 

.8780640 

40 

12 

.4725508 

.636195 

1.864992 

.8813035 

48 

12 

.4878697 

.668881 

1.789289 

.8729221 

48 

13 

.4728071 

.636669 

1.863690 

.8811660 

47 

13 

.4881136 

.669262 

1.788067 

.8727801 

47 

14 

.4730634 

.636944 

1.862389 

.8810284 

46 

14 

.4883674 

.669644 

1 .788847 

.8725281 

40 

15 

.4733197 

.637319 

1.861090 

.8808907 

45 

15 

.4886212 

.660026 

1.785628 

.8724960 

45 

16 

.4735769 

.637694 

1.869792 

.8807530 

44 

16 

.4888750 

.660409 

1.784410 

.8723528 

44 

17 

.4738321 

.638069 

1.858496 

.8806162 

43 

17 

.4891288 

.660791 

1.783194 

.8722115 

43 

18 

.4740882 

.538444 

1.857201 

.8804774 

42 

18 

.4893826 

.661173 

1.781979 

.872M92 

42 

19 

.4743443 

.638819 

1.855908 

.8803394 

41 

19 

.4896361 

.661656 

1.780765 

.8719269 

41 

30 

.4746004 

.539195 

1.854615 

.8802014 

40 

30 

.4898887 

.661939 

1.779662 

.8717814 

40 

21 

.4748564 

.539570 

1.853325 

.8800633 

39 

21 

.4901433 

.662321 

1.778340 

.8716419 

39 

22 

.4761124 

.539946 

l! 852035 

.8799251 

38 

22 

.4903968 

.562704 

1.777130 

.8714M8 

38 

23 

.4753683 

.640322 

1.850747 

.8797869 

37 

23 

.4906503 

.563087 

I .776921 

.8712556 

37 

24 

.4756242 

.640698 

1.849461 

.8796486 

36 

24 

.4909038 

.663471 

1.774714 

.8712188 

86 

35 

.4768801 

.541074 

1.848176 

.8795102 

35 

35 

.4911672 

.563854 

1.773607 

.8710710 

35 

26 

.4761359 

.541450 

1.846892 

.8793717 

34 

26 

.4914106 

.664237 

1.772302 

.8709281 

34 

27 

.4763917 

.641826 

1.845609 

.8792332 

33 

27 

.4916638 

.664621 

1.771098 

.8707851 

33 

28 

.4766474 

.542202 

1.844328 

.8790946 

32 

28 

.4919171 

.665005 

1 .769895 

.8705420 

33 

29 

.4769031 

.642579 

1.843049 

.8789569 

31 

29 

.4921704 

.665388 

1.768694 

.8704989 

31 

30 

.4771588 

.642955 

1.841770 

.8788171 

30 

30 

.4924236 

.565772 

1 .767494 

.8708561 

30 

31 

.4774144 

.643332 

1.840494 

.8786783 

29 

31 

.4926767 

.566166 

1.766295 

.8702124 

29 

32 

.4776700 

.643709 

1.839218 

.8785394 

28 

32 

.4929298 

.566641 

1.766097 

.8700591 

28 

33 

.4779266 

.644086 

1.837944 

.8784004 

27 

33 

.4931829 

.666925 

1.763900 

.8698255 

27 

34 

.4781810 

.544463 

1.836671 

.8782613 

26 

34 

.4934359 

.667309 

1.762705 

.8697881 

26 

35 

.4784364 

.644840 

1.835399 

.8781222 

35 

35 

.4936889 

.567694 

1.761611 

.8698266 

35 

86 

.4786919 

.545217 

1.834129 

.8779830 

24 

36 

.4939419 

.668079 

1.760318 

.86949^ 

24 

37 

.4789472 

.545595 

1.832861 

.8778437 

23 

37 

.4941948 

.668463 

1.769126 

.8692512 

23 

38 

.4792026 

.545972 

1.831593 

.8777043 

22 

38 

.4944476 

.668848 

1.757936 

.8698074 

22 

39 

.4794579 

.546350 

1.830327 

.8775649 

21 

39 

.4947005 

.669233 

1.756747 

.8690835 

21 

40 

.4797131 

.546728 

1.829062 

.8774264 

30 

40 

.4949532 

.669619 

1.766669 

.8689106 

30 

41 

.4799683 

.547106 

1.827799 

.8772868 

19 

41 

.4952060 

.670004 

1.754372 

.86«n56 

19 

42 

.4802235 

.647484 

1.826537 

.8771462 

18 

42 

.4954587 

.670389 

1.763186 

.8688215 

18 

43 

.4804786 

.547862 

1.825276 

.8770064 

17 

43 

.4957113 

.570775 

1.752002 

.8684874 

17 

44 

.4807337 

.648240 

1.824017 

.8768666 

16 

44 

.4959639 

.671161 

1.760819 

.8683431 

16 

45 

.4809888 

.54861 8! 1.822759 

.8767268 

15 

45 

.4962165 

.671647 

1.749637 

.8681888 

15 

46 

.4812438 

.548997 

1.821502 

.8765868 

14 

46 

.4964690 

.671933 

1.748466 

.8680644 

14 

47 

.4814987 

.549375 

1.820247 

.8764468 

13 

47 

.4967215 

.572319 

1 .747276 

.8679100 

13 

48 

.4817537 

.549754 

1.818993 

.8763067 

12 

48 

.4969740 

.672705 

1.746098 

.86n555 

12 

49 

4820086 

.550133 

1.817740 

.8761665 

11 

49 

.4972264 

.673091 

1 .744921 

.8675209 

11 

50 

.4822634 

.650512 

1.816489 

.8760263 

10 

50 

.4974787 

.573478 

1.743745 

.8574782 

to 

51 

.4825182 

.550891  1.815239 

.8758859 

9 

51 

.4977310 

.573864 

1.742670 

.8678314 

9 

52 

.4827730 

.551270 

1.813990 

.8757455 

8 

52 

.4979833 

.574251 

1.741396 

.8671866 

8 

63 

.4830277 

.651650 

1.812743 

.8756051 

53 

.4982365 

.674638 

1 .740324 

.8670417 

7 

54 

.4832824 

.552029 

1.811496 

.8754645 

6 

54 

.4984877 

.675025 

1 .739053 

.8658187 

6 

55 

.4835370 

.652409 

1.810252 

.8753239 

5 

55 

.4987399 

.576412 

1.737883 

.8687517 

5 

66 

.4837916 

.552789 

1.809008 

.8751832 

4 

56 

.4989920 

.676799 

1.736714 

.858«885 

4 

67 

.4840462 

.653168  1.807766 

.8750425 

3 

57 

.4992441 

.676187 

1.736546 

.8604514 

2 

68 

.4843007 

.553548 

1.806525 

.8749016 

2, 

58 

.4994961 

.576574 

1.734380 

.8653151 

2 

69 

.4845552 

.553928 

1.805286 

.8747607 

1      59 

.4997481 

.576962 

1.733214 

.8881708 

1 

«0 

.4848096 

.654309 

1.804047 

.8746197 

•r 

.6000000 

.577350 

1.732050 

.8580854 

• 

Ooalne. 

Coumg 

Tanif. 

Sine. 

'  1 

Cosine. 

Ootang 

Tsnt. 

(ilne. 

3 

61' 


Note. — Secant  =«l-i- cosine. 


^  Digitized  by. VjOOQIC 

Cosecant  ^  l-i-sine.      o 


d  by  Google 


160  9.-'PLANE  TRIGONOMETRY. 

3.— Natnrml  Sines,  Tanobnts,  Cotangbnts.  Cosinbs. — (Contintted.) 

(Vened  sine  —  1  —cosine;  coversed  sine « 1— sine.) 
32»  33» 


Note. — Secant   —  1-4- cosine.         Cosecant 


izeH  by  Google 


NATURAL  SINES,  ETC.  161 

&--NstBnl  Sinac,  Tanobnts,  Cotanobkts,  Cosines. — (Contintied.) 

(Versed  sine  —  1— cosine;  coversed  sine—  1— sine.) 
9f>  36° 


Kote.— Secant  - 1 + cosine.         Cosecant  - 1  +siftifeed  by  GoOg  Ic 


103 


%^PLANE  TRIGONOMETRY. 


S.— Nataral  Siaet,  Tanobkts,  CoTANCBKTt,  Cosinbs. — (Continiaed.) 

(Versed  sine  «1— coone;  coversed  8ine-"l— nne.) 
88*  ST 


'  1    Slae.    |Taii«.  ICotang.l  CosIdc.  |      ||  '  |    Sine.    |  Tang.  I  Cotang.l  Ootfae.  | 

0 

.5877853  '.72«542 11.876381  .8090170 

«o|    . 

.6018150 

.758564 

1.827044 

.79S6SK 

40 

1 

.5880206     .726987,1.375540  .8088460 

69       I 

.6010478 

.754010 

1.826242 

.79MM4 

59 

2 

.5882558 

.727431 

1.874699  .8086749 

58  1    2 

.6022795 

.754466 

1.835489 

S8 

8 

.5884910 

.727876 

1.373859  .8085037 

57!      3 

.6025117 

.754923 

1.824686 

!7t»ioe 

87 

4 

.5887262 

.728321 

1.3730191.8083325 

56  ,     4 

.6027439 

.756879 

1.828887 

.797tS«Y 

s« 

5 

.5889613 

.728767 

1.872180,. 8081612 

551 

.6029760 

.756836 

1 .328086>  .7977M« 

5S 

6 

.5891964 

.729212 

1.8713421.8079899 

54' 

.6038080 

.756294 

1. 882287 1.7STS839 

54 

7 

.5894314 

.729658 

1 .370604 

.8078185 

53 

.766761 

1. 821487 '.7974«M 

53 

8  .5896668 

.730104  1.369667 

.8076470 

S2 

!6086719 

.757209 

1.820a9  .79723M 

S3 

9  .5899012 

.730550  1.368831 

.8074754 

51 

.6039038 

.757666 

1.819841   .79705n 

51 

10 

.6901361 

.730996  1.367995 

.8073038 

50 

16 

.6041366 

.758124 

1.819044 

.7900SIS 

11 

.5903709 

.731442  1.367161 

.8071321 

49 

.6043674 

.758582 

1.818847 

.79<7«58 

49 

12 

.5906057 

.731889  1 .366326 

.8069603 

48, 

.6045991 

.759041 

1.817461 

.7MU00 

48 

13 

.5908404 

.732336  1.365493. 8067885 

47 1 

.6048308 

.769499 

1.816655 

.79SSMO 

47 

14 

.5910750 

.732783  1 .364660 

.8066166 

46 

.6060624 

.759958 

1.815861 

.7t<iygo 

4H 

15 

.5913096 

.733230  1.363827 

.8064446 

45     15 

.6052940 

.760417 

1.315066 

48 

16 

.5915442 

.783677  1 .362996 

.8062726 

4^1 

16 

.6055266 

.760876 

1.814278 

!796ea50 

44 

17 

.6917787 

.7341251.362165 

.8061005 

43 

17 

.6057570 

.761336 

1.318460 

.7f6M7 

43 

18 

.5920132 

.734573  1.361335 

.8059283 

42 

18 

.6069884 

.761795 

1.312687 

.7954T3S 

42 

19 

.5922476 

.735021  1.3605051.8057560 

41' 

19 

.6062198 

.763255  1.311896 

.7W2m 

4t 

30 

.5924819 

.735469  1.359676 '8055837 

40  |30 

.6064511 

.762715,1.811104 

.7961288 

48 

21 

.5927163 

.735917  1.358848  .8054113 

39  1  21 

.6066824 

.763175 

1.810814 

.7049444 

29 

22 

.5929505 

.736366  1.358020  .8052389 

38  :  22 

.6069136 

.763636 

1.809523 

.7947678 

38 

23 

.5931847 

.736814  1.3571931.8050664 

37 

23 

.6071447 

.764096 

1.808734 

.7945813 

IT 

24 

.5934189 

.737263, 1.35636718048938 

36 

24 

.6073788 

.764557 

1.807945 

.7944148 

86 

35 

.5936530 

.737712 

1.355541  .8047211 

35 

35 

.6076069 

.765018 

1.807157 

.7942379 

38 

26 

.5938871 

.738162 

1.3547161.8045484 

34 

26 

.6078379 

.765480 

1.806869 

.7940611 

34 

27 

.6941211 

.738611 

1.353891  .8043766 

33 

27 

.6080689 

.765941 

1.305582 

.7938843 

23 

28 

.5943550 

.739061 

1.353068  .8042028 

32 

28 

.6082998 

.766403 

1.804796 

.7937074 

23 

291.6945889 

.739511 

1.352244    8040299 

311,  29 

.6085306 

.766864 

1.804010 

.79SS304 

u 

30 

.5948228 

.739961,1. 351422]. 8038569 

30, 

30 

.6087614 

.767327 

1.808225 

.79^^ 

38 

81 

.5950566 

.740411  1.350600  .8036838 

29 

31'  6089922 

.767789  1.801440 

.7911762 

29 

32 

.5952904 

.740861  1.349779  .8035107 

28' 

32 

6092229 

.768251  1.301656 

.7929890 

22 

33 

.5955241 

.741312  1.34 8958,. 803337 5 

27  '  33 

.6094535 

.768714  1.300873 

.7988218 

37 

34 

.6957577 

.741763  1.348139    8031642 

26,    34 

.6096841 

.769177!  1. 3000W 

.7918445 

26 

35 

.5959913 

.74221411.347319  .8029909 

35'   35 

.6099147 

.769640 

1.299808 

.7924671 

38 

36 

.5962249 

.742665,1.346501  .8028175 

24 

36 

.6101452 

.770103 

1 .298526 

24 

37 

.5964584 

.743117  1.345683  .8026440 

23 

37 

.6108766 

.770567 

1 .297745 

^7921121 

n 

38 

.5966918 

.743568 '1.344865  .8024705 

22 

38 

.6106060 

.771030 

1.296964 

.7918845 

n 

89 

.5969252 

.74402011  344049 

.8022969 

21 

39 

.6108363 

.771494*1.296185 

•7917580 

11 

40 

.5971586 

.74447211.343233 

.8021232 

30    40 

.6110666 

.771958  1.295405 

.79157« 

9 

41 

.5973919 

.744924  1.342417 

.8019495 

19     41 

.6112969 

.772423  1.294627  .7914014 

19 

42 

.5976251 

.74537711.341602 

.8017756 

18|    42  .6115270 

.772887  1 .293848,  .791323S 

18 

43 

.5978583 

.745829ll. 340788  .8016018 

17  ;  43  .6117672 

.773352  1 .293071 

.7910456 

17 
14 

44 

.5980915 

.746282; 1.339975 

.8014278 

16     44  .6119873 

.773817 

1.292294 

.7908676 

45 

.5983246 

.7467351 1.339162 

.8012538 

15    45 

.6122178 

.n4282 

1.291517 

.79068i6 

18 

46 

.5985577 

.747188  1.338350 

.8010797 

14  1  46 

.6124478 

.774748 

1.290742 

■  7905115 

14 

47 

.5987906 

.747642  1.337538 

.8009056 

13  !  47 

.6126772 

.n5213 

1.289966 

.7908333 

)§ 

48 

.5990236 

.748095  1.336727 

.8007314 

12  1  48 
11  1  49 

.6129071 

.775679 

1.289192 

.7901550 

49 

.5992565 

.748549  1.335917 

.8005571 

.6131369 

.776145 

1.288418 

.7899767 

11 

50 

.5994893 

.749003  1.335107 

.800;<827 

10    50 

.6133666 

.776611 

1  287644 

.7897883 

M 

51 

.6997221 

.749457,1.334298  .8002083 

9i|  51 
S'l  52 

.6135964 

.777078 

1.286871 

.7896198 

9 

52 

.5999549 

.749911  1.333490  .8000338 

.6138260 

.777544 

1.286099 

.7894412 

% 

63 

.6001876 

.750366 1 1.332682 

.7998593 

71    53,. 6140556 

.778011 

1.285327 

.7892837 

T 

54 

.6004202 

.75082r  1.331875 

.7996847 

6     541.6142852 

.778478 

1.284566 

.7890841 

e 

55 

.6006528 

.751276  1.33106H 

.7995100 

5     55  .6145147 

.778946 

1 .283786 

.7889054 

f 

56 

.6008854 

.751731 il. 330262 

.7993352 

41  56  .6147442 

.779413 

1.283016 

.7887268 

4 

57 

.6011179 

.752186  1.329457 

.7991604 

3i    57  .6149736 

.779881 

1.282246 

.7885477 

% 

58 

.6013503 

.75264211.328652 

.7989855 

2M  58 

.6152029 

.780349 

1 .281477 

.78S36lfeR 

2 

1 
0 

59 

.6016827 

.753098,1.327848 

.7988105 

11     59 

.6154322 

.780817 

1.280709;.  7881 8S« 

•0 

.6018150 

.763554  1.327044 

.7986355 

0  '60  .6166615 

.781285 

1.279941  .7880106 

Coalne.  ICoUngl  I^dk.  |     Sine.    I'll      1  CoBlne.  |Cotan« 

TMMf.  1   einsr-' 



LI 

63° 


Note. — Secant  —l-»- cosine. 


sr 


Cosecant  - 1  -i-sme.^  , 

Digitized  by  VjOOQ  IC 


NATURAL  SINES,  ETC. 


168 


Su— NatnnI  Sines,  Tanobnts,  Cotangbnts.  Cosinbs, — (Continued.) 
(Veraed  sine  —  1— coaine;  coveraed  sine— 1— sine.) 


V 


'  1    Sbie.    1  Tame.  1  Ootam^.l  Ooelne.  1      II  '  1    Sine.    |  Tang.  1  Cotang.j  Cosine.  | 

oj.ilfMU 

.781385 

1.279941 

.7880108 

60 

0 

.6293204 

.809784 

1.234897 

.7771460 

60 

1  .€I5»07 

.781754 

1.279174 

.7878316 

59 

1 

.6295164 

.810265 

1.234162 

.7769629 

59 

2  .S161I98 

.783332 

1.278407 

.7876524 

58 

2 

.6297724 

.810747 

1.233429 

.7767797 

58 

3   SlCUSt 

.782691 

1.277641 

.7874732 

57 

3 

.6299983 

.811230 

1.232696 

.7765965 

57 

4  .nf57» 

.783161 

1.276876 

.7872939 

56 

4 

.6302242 

.811712 

1.231963 

.7764132 

56 

5  .61MMI 

.783630 

l.r6lll 

.7871145 

55 

5 

.6304500 

.812195 

1.231231 

.7762298 

55 

€l.€170U9 

.784100 

1 .275347 

.7889350 

54 

6 

.6306758 

.812678 

V. 230499 

.7760464 

54 

7  .6172i48 

.784570 

1.274583 

.7867556 

53 

7 

.6309015 

.813161 

1.229768 

.7758629 

53 

8).  6174986 

.785040 

1 .273820 

.7865759 

52 

8 

.6311272 

.813644 

1.229038 

.7756794 

52 

»  .«I77224 

.785510 

1 .273057 

.7863963 

51 

9 

.6313628 

.814128 

1.228308 

.7754957 

51 

W  .SI7W11 

.785980 

1.372295 

.7862165 

50 

10 

.6315784 

.814611 

1 .227678 

.7753121 

50 

U  .6181798 

.786451 

1.271534 

.7860367 

49 

11 

.6318039 

.818095 

1.226849 

.7751283 

49 

12  .6184M4 

.786922 

1 .270773 

.7858569 

48 

12 

.6320293 

.815580 

1.226121 

.7749445 

48 

13  .6186370 

.787393 

1.270013 

.7856770 

47 

13 

.6022547 

.816064 

1.225393 

.7747606 

47 

14  .6I886H 

.787864 

1.26925S 

.7854970 

46 

14 

.6324800 

.816549 

1.224665 

.7745767 

46 

If  .619M39 

.788336 

1.368494 

.7853169 

48 

15 

.6327063 

.817034 

1.223938 

.7743926 

45 

16 

.6193224 

.788808 

1.367735 

.7851368 

44 

16 

.6329306 

.817519 

1.223212 

.7742086 

44 

17 

.6195307 

.789280 

1.266977 

.7849566 

43 

17 

.6331557 

.818004 

1.222486 

.7740244 

42 

If 

.619n90 

.789752 

1.266219 

.7847764 

42 1 

18 

.6333809 

.818490 

1.221761 

.7738402 

43 

19 

.6300073 

.790224 

1.265462 

.7r"161 

«!; 

19 

.6336059 

.818976 

1.221036 

.7736559 

41 

a»L63Q83S5 

.790097 

1.264706 

.71       57 

40 

30 

.6338310 

.819462 

1.220312 

.7734716 

40 

21  i. 6204636 

.791170 

1.263950 

.7i      152 

39| 

21 

.6340559 

.819948 

1.219588 

.7732872 

39 

22  .6206917 

.791643 

1.263195 

.71      47 

38 

22 

.6342808 

.820435 

1.218865 

.7731027 

38 

23>  .6209198 

.792116 

1.262440 

.71      '41 

37 

23 

.6345057 

.820922 

1.218142 

.7729182 

37 

241.6211478 

.792590 

1.261688 

.71      135 

36 

24 

.6347305 

.821409 

1.217419 

.7727336 

36 

28  .6213757 

.7K064 

1.260932 

.71       27 

35 

35 

.6349553 

.821896 

1.216698 

.7725489 

35 

211.016036 

.793537 

1.260179 

.71      120 

34 

26 

.6351800 

.822384 

1.215976 

.7723642 

34 

ri. 6218314 

.794012 

1.259426 

.71      111 

33 

27 

.6354046 

.822871 

1.215256 

.7721794 

33 

28,  .6220093 

.794486 

1 .258674 

.71       02 

32 

28 

.6356292 

.823359 

1.214535 

.7719945 

32 

2f 

.8222870 

.794961 

1.257923 

.71      192 

31 

29 

.6358537 

.823847 

1.213816 

.7718096 

31 

30 

.6225146 

.795435 

1.257172 

.7Uv082 

30 

30 

.6360782 

.824336 

1.213097 

.7716246 

30 

11 

.8227423 

.795911 

1.256421 

.7824270 

29 

31 

.6363026 

.824825 

1.212378 

.7714395 

29 

33 

.8229608 

.796386 

1.255672 

.7822459 

28 

32 

.6365270 

.825314 

1.211660 

.7712544 

28 

33 

.6331974 

.796861 

1.254922 

.7820646 

27 

33 

.6367513 

.825803 

1.210942 

.7710692 

27 

34 

.8834248 

.797337 

1.254174 

.7818833 

26 

34 

.6369756 

.826292 

1 .210225 

.7708840 

26 

.6230522 

.797813 

1.253426 

.7817019 

35 

35 

.6371998 

.826782 

1.209508 

.7706986 

35 

36 

.8238798 

.798289 

1.252678 

.7815205 

24 

36 

.6374240 

.827271 

1 .208792 

.7705132 

24 

37 

.6341009 

.798765 

1.251931 

.7813390 

23 

37 

.6376481 

.827762 

1.208076 

.7703278 

23 

38 

.8243343 

.799342 

1.251184 

.7811574 

22 

38 

.6378721 

.828252 

1.207361 

.7701423 

22 

39 

.6345614 

.799719 

1 .250438 

.7809757 

21 

39 

.6380961 

.828742 

1.206646 

.7699567 

21 

.6247885 

.800196 

1.249693 

.7807940 

30 

40 

.6383201 

.829233 

1.205932 

.7697710 

30 

41 

.82S0150 

.800673 

1.348948 

.7806123 

19 

41 

.6385440 

.829724 

1.205219 

7695853 

19 

e 

.6252427 

.801151 

1.248204 

.7804304 

18 

42 

.6387678 

.830216 

1.204505 

.7693996 

18 

43 

.8254096 

.801628 

1.247460 

.7802485 

17 

43 

.6389916 

.830707 

1.203793 

.7692137 

17 

44 

.6250968 

.802106 

1 .246716 

.7800665 

16 

44 

.6392153 

.831199 

1.203081 

.7690278 

16 

48 

6^036 

.802584 

1.245974 

.7798845 

15 

48 

.6394390 

.831691 

1.202369 

.7688418 

IS 

46 

!63615<B 

.803063 

1.245232 

.7797024 

14 

46 

.6396626 

.832183 

1.201668 

.7686558 

14 

47 

.6283771 

.803541 

1.244490 

.7795202 

13 

47 

.6398862 

.832675 

1 .200947 

.7684697 

13 

48 

.6360088 

.804020 

1 .243749 

.7793380 

12 

48 

.6401097 

.833168 

1.200237 

.7682835 

12 

49 

.804499 

1 .243008 

.7791557 

11 

49 

.6403332 

.833661 

1.199527 

.7680973 

11 

98 

16278071 

.804979 

1.242268 

.7789733 

10 

50 

.6405566 

.834154 

1.198818 

.7679110 

10 

SI 

.805458 

1.241529 

.7787909 

9 

51 

.6407799 

.834648 

1.198109 

.7677246 

9 

93 

.6275102 
.6277306 

.80593811.240790 

.7786084 

8 

52 

.6410032 

.835141 

1.197401 

.7675382 

8 

52 

.806418  1.240051 

.7784258 

7 

63 

.6412264 

.835635 

1.196693 

.7673517 

7 

M 

.8379031 

.800898  1.239313 

.7782431 

6 

54 

.6414496 

.836129 

1.195986 

.7671652 

6 

S$ 

.6281884 

.80737811.238576 

.7780604 

5 

55 

.6416728 

.836624 

1.195279 

.7669785 

5 

St 

.6284157 

.807859 

1.237839 

.7778777 

4 

56 

.6418958 

.837118,1.194573 

.7667918 

4 

m 

.0886420 

.808340 

1.237103 

.7776949 

3 

67 

.6421189 

.82761311.193867 

.7666051 

3 

Si 

.6288682 

.808821 

1.236367 

.7775120 

2 

58 

.6423418 

.838108 

1.193162 

.7664183 

2 

89 

.6390943 

.80930211.235631 

.7773290 

1 

59 

.6425647 

. 838604 

1.192457 

.7662314 

1 

00^.6293204 

.809784  1.234897 

.7771460 

0 

601.6427876 

1       1 

.839099 

1.191753 

.7660444 

0 

lOoaloe.  1 

Cotoog   Tang,  j    Sine,    j  '  jl      1  Cosine.  jCotanR 

Tang.  1     Sine.    I  ' 

Note. — Secant  -l-i- cosine. 


510  60O 

Cosecant  —  1 +si»ie^zed  by  doOg  Ic 


IM 


9.— PLiliVJB  TRIGONOMETRY, 


3.— Nataral  Sines,  Tanobnts.  Cotangbnts.  Co8iNxs.'*(Continaed.) 

(Versed  sine  —1  — cosine;  coversed  sine  — 1— sine.) 
41" 


'  1    Bine.    1  Tang.  1  Cotan^.l  Cosine. 

1      II  '  1    Sine. 

Tang.  I  Ootang.l  Cosliie.  i 

.6427876 

.839099 

1.191753 

.7660444 

i         0 

.6560590 

.869286 

1.150368 

.7547096 

M 

.6430104 

.839595 

1.191049 

.7658574 

I 

.6562785 

.889797 

1.149692 

.7646187 

51 

.840091 

1.190346 

.7656704 

2 

.6564980 

.870308 

1.149017 

.7543278 

5t 

.6434559 

.840587 

1.189643 

.7654832 

3 

.6567174 

.870820; 1.148342 

.7541168 

K 

.6436785 

.841084 

1.188941 

.7652960 

4 

.6569367 

.871331 

1.147668 

.763M67 

51 

.6439011 

.841581 

1.188239 

.7651087 

1         5 

.6571560 

.871843 

1.146994 

.7837546 

51 

.6441236 

.842078 

1.187538 

.7649214 

6 

.6573752 

.872355 

1.146321 

.7635634 

5 

.6443461 

.842575 

1.186837 

.7647340 

7 

.6575944 

.872868 

1.145648 

.7533731 

5! 

.6445685 

.843073 

1.188136 

.7645465 

8 

.6578135 

.873380 

1.144976 

.7531808 

5 

.6447909 

.843570 

1.185437 

.7643590 

9 

.6580326 

.873893 

1.144304 

.7529894 

5 

.6450132 

.844068 

1.184737 

.7641714 

J         0 

.6582516 

.874406 

1.143632 

.7517980 

•1 

.6452355 

.844567 

1.184038 

.7639838 

11 

.6584706 

.874920 

1.142961 

.75M065 

4 

.6454577 

.845065 

1.183340 

.7637960 

12 

.6586895 

.875433 

1.142290 

.7524149 

4 

.6456798 

.845564 

1.182642 

.7636082 

13 

.6589083 

.875947 

1.141620 

.7511133 

4 

.6459019 

.846063 

1.181944 

.7634204 

14 

.6591271 

.876462 

1.140950 

.75M116 

4 

.6461240 

.846562 

1.181247 

.7632325 

5 

.6593458 

.876976 

1.140281 

.7518398 

4 

.6463460 

.847062 

1.180551 

.7630445 

16 

.6595645 

.877491 

1.139612 

.7516480 

4 

.6465679 

.847561 

1.179866 

.7628561 

17 

.6597831 

.878006 

1.138944 

.7514661 

4 

.6467898 

.848061 

1.179159 

.7626683 

18 

.6600017 

.878521 

1.138276 

.7612641 

4 

.6470116 

.848561 

1.178464 

.7624802 

19.6602202 

.879037 

1.137608 

.7510711 

4 

ao 

.6472334 

.849062 

1.177769 

.7622919 

i         « 

.6604386 

.879552 

1.136941 

.7608800 

4 

21 

.6474551 

.849563 

1.177075 

.7621036 

11 

.6606570 

.880068 

1.136274 

.7606879 

1 

22 

.6476767 

.850064 

1.176382 

.7619152 

\2 

.6608754 

.880585 

1.135608 

.7504957 

1 

23 

.6478984 

.850565 

1.175688 

.7617268 

13 

.6610936 

.881101 

1.134942 

.7501014 

X 

24. 6481199 

.851066 

1.174996 

.7615383 

!4 

.6613119 

.881618 

1.134277 

.7501111 

1 

35 

.6483414 

.851568 

1.174303 

.7613497 

i          » 

.6615300 

.882135 

1.133612 

.7499187 

3 

26 

.6485628 

.852070 

1.173612 

.7611611 

16 

.6617482 

.882653 

1.132947 

.7497262      : 

27 

.6487842 

.852572 

1.172920 

.7609724 

;       !7 

.6619662 

.883170 

1.132283 

.7495337 

\ 

28 

.6490056 

.853075 

1.172229 

.7607837 

!8 

.6621842 

.883688 

1.131620 

.7491411 

3 

29 

.6492268 

.853577 

1.171S39 

.7605949 

!9 

.6624022 

.884206 

1.130957 

.7491484 

1 

30 

.6494480 

.854080 

1.170849 

.7604060 

^        o 

.6626200 

.884725 

1.130294 

.7489557 

i 

31 

.6496692 

.854583 

1.170160 

.7602170 

11 

.6628379 

.885244 

1.129632 

.7487619 

32 

.6498903 

.855087 

1.169471 

.7600280 

12 

.6630557 

.885763 

1.128970 

.7485701 

33 

.6501114 

.855591 

1.168782 

.7598389 

13 

.6632734 

.886282 

1.128308 

.7483771 

34 

.6503324 

.856095 

1.168094 

.7596498 

14 

.6634910 

.886801 

1.127647 

.7481 8U 

35 

6505533 

1.167407 

.7594606 

:       5 

.6637087 

.887321 

1.126987 

.7479911  ; : 

86  .6507742 

! 857 103 

1.166720 

.7592713 

16 

.6639262 

.887841 

1.126327 

.7477981 

37 

.6509951 

.857608 

1.166033 

.7590820 

17 

.6641437 

.888361 

1.125667 

.7478049 

38 

.6512158 

.858113 

1.165347 

.7588926 

18 

.6643612 

.888882 

1.125008 

.7474117 

39 

.6514366 

.858618 

1.164661 

.7587031 

19 

.8645785 

.889403 

1.124349 

.7472184 

40 

.6516572 

.85912411.163976 

.7585136 

:      0 

.6647959 

.889924  1.1236901. 7470251 

41 

.6518778 

.85962911.163291 

.7583240 

Ll 

6650131 

.890445 

1. 123032  ;.74«8S17 

42 

.6520984 

.860135 

1.162607 

.7681343 

12 

.6652304 

.890967 

1.122375 

.7466382 

43 

.6523189 

.860641 

1.161923 

.7579446 

L3 

.6654475 

.891489 

1.121718 

.74€444« 

44 

.6525394 

.861148  1.161240 

.7577548 

14 

.6656646 

.892011 

1.121061 

.7462510 

45 

.6527598 

.861655 

1.160557 

.7575650 

1         15 

.6658817 

.892534 

1.120405 

.7460S74 

46 

.6529801 

.862162 

1.159874 

.7573751 

L6 

.6660987 

.893056  1.119749 

.7458636 

47 

.6532004 

.862669 

1.159192 

.7571851 

17 

.6663156 

.893579,1.119094 

.7466699  ' 

48 

.6534206 

.863176 

1.158511 

.7569961 

18 

.6665325 

.894103 

1.118439 

.7454760 

49 

.6536408     .863684 

1.157830 

.7568050 

19 

.6667493 

.894626 

1.117784 

.7452821   1 

50 

.6538609 

.864192  1.157149 

.7566148 

1         O 

.6669661 

.895160 

1.117130 

. 7450681 

51 

.6540810 

.8647001 1.1 56469  .7564246 

>1 

.6671828 

.895674 

1.116476 

.7448M1 

52  .6543010 

.865209  1.1 55789,. 7 562343 

>2 

.6673994 

.896199!l. 115823 

.7446999 

53 

.6545209 

.865718  1.155110 

.7560439 

)3 

.6676160 

.896723:1.115170 

.7448058 

54 

.6547408 

.866227  1.154431 

.75!i8&35 

>4 

.6678326 

.897248 

1.114518 

.7448115 

55 

.6549607 

.86673611.153753 

.7556630 

5 

.6680490 

.897773 

1.113866 

.7441173 

56 

.6551804 

.867246  1.153075 

.7554724 

>6 

.6682655 

.898299 

1.113214 

.7430229 

57  .6554002 

.8677 55  1.1 52397  .7552818 

)7 

.6684818 

.898825 

1.112563 

.7437385 

58 

.6556198 

.868265  1.151 721  .755091 1 

>8 

.6686981 

.899351 

1.111912 

.7436340 

59 

.6558395 

.868776,1.151044  .7549004 

i9 

.6889144 

.899877  1.111262 

.7433304 

60  .6560590  1.869286 

1.160368  .7547096 

0|.  6691306 

.900404  1.110612 

.7431448  . 

I  Cosine.  ICotangI  Tang:.  I     Sine. 

'1      1  Cosine. 

Coung  Tang. 

sane.    1 

49*» 


Note. — Secant  —  1 + cosine.  Cosecant  we\  Tl^fi©Ogle 


NATURAL  SINES,  ETC. 


IM 


a.— Natural  Sines,  Tanobnts.  Cotanobnts.  Cosinbs. — (Continued.) 

(Versed  sine  >»l~cosine;  covened  sine— 1— sine.) 
48» 


'1   Stoe.    1 

Tuig.    Gotsoc.l  Cosine.  |      ||  '  |    Sine.    |  Tang.  I  Cotang.l  Cosine.  | 

0 

.1881286 

900404 

1.110612 

.7431448 

60 

0 

.6819984 

.932515 

1.072368 

.7313537 

60 

1 

.6668468 

.908930 

1.109963 

.7429602 

59 

1 

.6822111 

.933059 

1.071743 

.7311563 

59 

2 

IgJ^IQ 

.901458 

1.109314 

.7427554 

58 

2 

.6824237 

.933603 

1.071118 

.7309568 

58 

S 

.668n88 

.901989 

1.108665 

.7426606 

57 

3 

.6826363 

.934147 

1.070494 

.7307583 

57 

4 

.6698948 

.902513 

1.108017 

.7423658 

56 

4 

.6828489 

.934692 

1 .069870 

.7305597 

56 

f 

.6768108 

.«»041 

1.107369 

.7421708 

W 

S 

.6830613 

.935238 

1.069246 

.7303610 

W 

t 

.6704268 

.903569 

1.106721 

.7419758 

54 

6 

.6832738 
.6834861 

.935783 

1.068623 

.7301623 

54 

T 

.6766434 

.904097 

1.106075 

.7417808 

53 

7 

.936329 

1.068000 

.7299635 

53 

tucmss 

»<.S710739 

.904626 

1.106428 

.7415857 

52 

8 

.6836984 

.936875 

1.067377 

.7297646 

52 

.906156 

1.104782 

.7413905 

51 

9 

.6839107 

.937421 

1.066755 

.7295657 

51 

M.67U8S5 

.905685 

1.104136 

.7411958 

SO 

10 

.6841229 

.937968 

1.066134 

.7293668 

SO 

U  .S7IS051 

.906214 

1.103491 

.7410000 

49 

11 

.938515 

1 .065512 

.7291677 

49 

U. 6717208 

.906744 

1.103846 

.7408046 

48 

12 

.6845471 

.939062 

1.064891 

.7289686 

48 

la  nitMi 

.907274 

1.102201 

.7406092 

47 

13 

.6847691 

.939610 

1.064271 

.7287695 

47 

M  .6721515 

.907805 

1.101557 

.7404137 

46 

14 

.6849711 

.940167 

I .063651 

.7285703 

46 

IS  .6723648 

90^36 

1.100914 

.7402181 

48 

IS 

.6851830 

.940706 

1.063031 

.7283710 

45 

161.6725821 

]908867 

1.100270 

7400225 

44 

16 

.6853948 

.941254 

1.062411 

.7281716 

44 

17 

.909398 

1.099628 

.7398268 

43 

17 

.6856066 

.941803 

1.061792 

.7279722 

43 

U 

.6730125 

.909930 

1.098985 

.7396311 

42 

18 

.6858184 

.942352 

1.061174 

.7277728 

42 

If 

.6722276 

.910461 

1.098343 

.7394353 

41 

19 

.6860300 

.942901 

1.060556 

.7275732 

41 

at 

.6734427 

.910994 

1.097702 

.7392394 

40 

20 

.6862416 

.943451 

1.059938 

.7273736 

40 

21 

.673«5n 

.911526 

1.097060 

.7390435 

39 

21 

.6864532 

.944001 

1 .059320 

.7271740 

39 

S,  .6738727 

.912059  1 .096420 

.7388475 

38 

22 

.6866647 

.944551 

1 .058703 

.7269743 

38 

0. 6746876 

.912992|l. 095779 

.7386515 

37 

23 

.6868761 

.945102 

1.058086 

.7267745 

37 

24 

.6743024 

.913125,1.095139 

.7384563 

36 

24 

.6870875 

.945653 

1 .057470 

.7265747 

36 

28 

.6749172 

.913659 

1.094000 

.7382592 

35 

28 

.6872988 

.946204 

1.056854 

.7263748 

35 

26 

.8747318 

.814192 

1.093881 

.7380629 

34 

26 

.6875101 

.946755 

1.056238 

.7261748 

34 

V 

.6748468 

.914727 

1 .093222 

.7378666 

33 

27 

.6877213 

.947307 

1.055623 

.7259748 

33 

28 

.6751812 

.915261 

1.092584 

.7376703 

32 

28 

.6879325 

.947859 

1.055008 

.7257747 

32 

29 

.6783757 

.915796 

1.001946 

.7374738 

31 

29 

.6881435 

.948411 

1 .054394 

.7255746 

31 

J8 

.8756808 

.916331 

1.091308 

.7372772 

30 

30 

.6883546 

.948964 

1.053780 

.7253744 

30 

21 

.6758046 

.916886 

1.090671 

.7370808 

29 

31 

.6885655 

.949517 

1.053166 

.7251741 

29 

22 

.6760190 

.917402 

1.090034 

.7868842 

28 

32 

.6887765 

.960070 

1.052553 

.7249738 

28 

22 

.6782333 

.917937 

1.089398 

.7366875 

27 

33 

.6889873 

.950624 

1.051940 

.7247734 

27 

24 

.8764476 

.918474 

1.088762 

.7364908 

26 

34 

.6891981 

.951178 

1.051327 

.7245729 

26 

J8 

.876U18 

.919010 

1.088126 

.7362940 

28 

35 

.6894089 

.951732 

1.050715 

.7243724 

28 

86 

.6768760 

.919547 

1.087491 

.7360971 

24 

36 

.6896195 

.952287 

1.050103 

.7241719 

24 

27 

.6770901 

.920084 

1.086857 

.7359002 

23 

37 

.6898302 

.952842 

1.049492 

.7239712 

23 

18 

.6773041 

.920621 

1.086222 

.7357033 

22 

38 

.6900407 

.953397 

1.048880 

.7237705 

22 

26 

.onsisi 

.921159 

1.085588 

.7355061 

39 

.6902512 

.953952 

1.048270 

.7235698 

21 

m 

.6777330 

.921696 

1 .084955 

.7353090 

20 

40 

.6904617 

.954508 

1.047659 

.7233690 

20 

41 

.6778459 

.922235 

1.084322 

.7351118 

41 

.6906721 

.956064 

1.047049 

.7231681 

19 

42 

.8781587 

.922773 

1.083689 

.7349146 

42 

.6908824 

.955620 

1.046440 

.7229671 

18 

O 

.r88734 

.923312 

1.083057 

.7347173 

43 

.6910927 

.956177 

1.045831 

.7227661 

17 

44 

.r85871 

.923851 

1.082425 

.7345199 

44 

.6913029 

.956734 

1 .045222 

.7225651 

16 

48 

.6788007 

.924391 

1.081793 

.7343226 

45 

.6915131 

.957291 

1 .044613 

.7223640 

IS 

46 

.6790143 

.924930 

1.081162 

.7341260 

46 

.6917232 

.957849 

1 .044005 

.7221628 

14 

47.  .878078 
48i  8794413 

.925470 

1.080532 

.7339275 

47 

.6919332 

.958407 

1.043397 

.7219615 

13 

.926010 

1.079901 

.7337299 

48 

.6921432 

.958965 

1.042790 

.7217602 

12 

!»..  6798547 

m.6798881 
U  .6880813 

.926550 

1.079271 

.7335322 

49 

.6923531 

.959524 

1.042183 

.7215589 

11 

.927091 

1.078642 

.7333345 

SO 

.6925630 

.960082 

1.041576 

.7213574 

10 

.927632 

1.078012 

.7331367 

51 

.6927728 

.960642 

1.040970 

.7211559 

9 

sl. 6882846 

.928173 

1.0n384 

.7329388 

52 

.6929825 

.961201 

1.040364 

.7209544 

8 

S3,  6889078 

.928715 

1.076756 

.7327409 

53 

.6931922 

.961761 

1.039758 

.7207528 

7 

S4t  6807209 

.929257 

1.076128 

.7325429 

54 

.6934018 

.962321 

1.039153 

.7205511 

6 

is;  .6889339 

.929799 

1.075500 

.7323449 

55 

.6936114 

.962881 

1.038548 

.7203494 

5 

»l  6811488 

.930342 1 1.074873 

.7321467 

56 

.6938209 

.963442 

1.037944 

.7201476 

4 

S7,.68ia5»8 
98i.681f728 

.93088411.074246 

.7319486 

57 

.6940304 

.964003 

1.037340 

.7199457 

3 

.931428 

1.073620 

.7317503 

58 

.6942398 

.964565 '1.036736 

.7197438 

2 

».  .6817866 

.931971 

1.072994 

.7315521 

59 

.6944491 

.965126|l. 036133 

.7195418 

1 

88|  .6819884 

.932515 

1.072368 

.7313537 

60 

.6946584 

.965688,1.035530 

.7193398 

0 

lOoiloe. 

Coung 

1^. 

Sine. 

Cosine. 

Cotangl  Tang. 

Sine.     1  ' 

Note. — Secant  —1-i-ooeine. 


470 
(Cosecant - 


1-i-sine. 


tized  by  Google 


46» 


166  9— PLANE  TRIGONOMETRY. 

3. — NatuTAl  Sia«,  Tangbnts,  Cotanobnts,  Cosinbs. — (Concluded.) 

(Vened  sine  ••  1  —  cosine;  co versed  sine  —  1 — sine.) 
44**  44*> 


I  Coatne.  ICotangI  Tang.  |    Sine.    |  '  ||      |  Cosine.  ICotangl  Tang,  j    Btne.     |  ' 
Note. — Secant  —  1  -i-  cosine.         Cosecant  —  1  +sine. 


d  by  Google 


d  by  Google 


168 


9.— PLANE  TRIGONOMETRY. 


4.— Natural  Secants*  Cosbcants  (Exsbcants,  (^bzsbcants). 
Secants. 


-(Cont'd.) 


' 

10«    1 

110     1 

ia«    1 

13<»    1     14<»    1     15»    1     16<»     1     17-    1     18«    1    ir>     1 

0 

1.01543 

1.01872 

1.02234 

1.02630 

1.03061 

1.03528 

1.04030 

1.04669 

1.06146 

1.05762 

1 

.01548 

.01877 

.02240 

.02637 

.03069 

.03536 

.04039 

.04678 

.05166 

.05773 

2 

.01553 

.01883 

.02247 

.02644 

.03076 

.03544 

.04047 

.04688 

.05166 

.05783 

3 

.01558 

.01889 

.02253 

.02661 

.03084 

.03662 

.04066 

.04697 

.05176 

.05794 

4 

.01564 

.01896 

.02259 

.02668 

.03091 

.03660 

.04066 

.04606 

.06186 

.06805 

5 

1.01569 

1.01901 

1.02266 

1.02665 

1.03099 

1.03568 

1.04073 

1.04616 

1.05106 

1.05815 

6 

.01574 

,01906 

.02272 

.02672 

.03106 

.03576 

.04082 

.04625 

.05206 

.05826 

7 

.01579 

.01912 

.02279 

.02679 

.03114 

.03684 

.04091 

.04636 

.05216 

.06886 

8 

.01585 

.01918 

.02686 

.03121 

.03692 

.04100 

.04644 

.06226 

.06847 

9 

.01590 

.01924 

.02291 

.02693 

.03129 

.03601 

.04108 

.04663 

.06236 

.06868 

10 

1.01595 

1.01930 

1.02298 

1.02700 

1.03137 

1.03609 

1.04117 

1.04663 

1.06246 

1.05869 

11 

.01601 

.01936 

.02304 

.02707 

.03144 

.03617 

.04126 

.04672 

.05256 

.05879 

12 

.01606 

.01941 

.02311 

.02714 

.01352 

.03625 

.04136 

.04682 

.06266 

.00890 

13 

.01611 

.01947 

.02317 

.02721 

.03169 

.03633 

.04144 

.04691 

.05276 

.06901 

U 

.01616 

.01953 

.02323 

.02728 

.03167 

.03642 

.04152 

.04700 

05286 

.05911 

15 

1.01622 

1.01959 

1.02330 

1.02735 

1.03176 

1.03650 

1.04161 

1.04710 

l!05297 

1.05922 

16 

.01627 

.01965 

.02336 

.02742 

.03182 

.03658 

.04170 

.04719 

.05307 

.06933 

17 

.01633 

.01971 

.02343 

.02749 

.03190 

.03666 

.04179 

.04729 

.05317 

.05944 

18 

.01638 

.01977 

.02349 

.02756 

.03198 

.03674 

.04188 

.04738 

.05327 

.05965 

19 

.01643 

.01983 

.02356 

.02763 

.03205 

.03683 

.04197 

.04748 

.05337 

.05965 

30 

1.01649 

1.01989 

1.02362 

1.02770 

1.03213 

1.03691 

1.04206 

1 .04757 

1.05347 

1.05976 

21 

.01654 

.01995 

.02369 

.02777 

.03221 

.03699 

.04214 

.04767 

.05357 

.05987 

22 

.01659 

.02001 

.02375 

.02784 

.03228 

.03708 

.04223 

.04776 

.05367 

.05998 

23 

.01665 

.02007 

.02382 

.02791 

.03236 

.03716 

.04232 

.04786 

.05378 

.06009 

24 

.01670 

.02013 

.02388 

.02799 

.03244 

.03724 

.04241 

.04795 

.05388 

.06020 

3S 

1.01676 

1.02019 

1.02395 

1.02806 

1.03251 

1.03732 

1.04250 

1.04805 

1.05398 

1.0603O 

26 

.01681 

.02025 

.02402 

.02813 

.03259 

.03741 

.04259 

.04815 

.05408 

.06041 

27 

.01687 

.02031 

.02408 

.02820 

.03267 

.03749 

.04268 

.04824 

.05418 

28 

.01692 

.02037 

.02415 

.02827 

.03275 

.03758 

.04277 

.04834 

.05429 

!o$063 

29 

.01698 

.02043 

.02421 

.02834 

.03282 

.03766 

.04286 

.04843 

.05439 

.06074 

'z 

30 

1.01703 

1.02049 

1.02428 

1.02842 

1.03290 

1.03774 

1.04296 

1.04853 

1.06449 

1.06<fl5 

31 

.01709 

.02055 

.02435 

.02849 

.03298 

.03783 

.04304 

.04863 

.05460 

.06096 

32 

.01714 

.02061 

.02441 

.02856 

.03306 

.03791 

.04313 

.04872 

.05470 

.06107 

33 

.01720 

.02067 

.02448 

.02863 

.03313 

.03799 

.04322 

.04882 

.05480 

.06118 

34 

.01725 

.02073 

.02454 

.02870 

.03321 

.03808 

.04331 

.04891 

.05490 

.06129 

35 

1.01731 

1.02079 

1.02461 

1.02878 

1.08329 

1.03816 

1.04340 

1.04901 

1.05601 

1 .06140 

36 

.01736 

.02085 

.02468 

.02885 

.03337 

.03825 

.04349 

.04911 

.05511 

.06161 

37 

.01742 

.02091 

.02474 

.02892 

.03345 

.03833 

.04358 

.04920 

.05521 

.06162 

88 

.01747 

.02097 

.02481 

.02899 

.03353 

.03842 

.04367 

.04930 

.05532 

.06173 

89 

.01753 

.02103 

.02488 

.02907 

.03360 

.03850 

.04376 

.04940 

.05542 

.06184 

40 

1.01758 

1.02110 

1.02494 

1.02914 

1.03368 

1.03858 

1.04385 

1.04950 

1.05562 

1.06195 

41 

.01764 

.02116 

.02501 

.02921 

.03376 

.03867 

.04394 

.04959 

.05563 

.06206 

42 

.01769 

.02122 

.02508 

.02928 

.03384 

.02876 

.04403 

.04969 

.05573 

.06217 

43 

.01776 

.02128 

.02516 

.02936 

.03392 

.03884 

.04413 

.04979 

.05584 

44 

.01781 

.02134 

.02521 

.02943 

.03400 

.03892 

.04422 

.04989 

.05694 

.06239 

45 

1.01786 

1.02140 

1.02528 

1 .02950 

1.03408 

1.03901 

1.04431 

1 .04998 

1.05604 

1.06250 

46 

.01792 

.02146 

.02536 

.02958 

.03416 

.03909 

.04440 

.05008 

.05615 

-.06261 

47 

.01798 

.02153 

.02542 

.02965 

.03424 

.03918 

.04449 

.05018 

.05625 

.06272 

48 

.01803 

.02159 

.02548 

.02972 

.03432 

.03927 

.04458 

.05028 

.05636 

.06283 

49 

.01809 

.02165 

.02555 

.02980 

.03439 

.03936 

.04468 

.05038 

.05646 

.06295 

50 

1.01815 

1.02171 

1.02562 

1.02987 

1.03447 

1.03944 

1.04477 

1.05047 

1.05657 

1.06306 

51 

.01820 

.02178 

.02569 

.02994 

.03455 

.03952 

.04486 

.05057 

.05667 

.06317 

52 

.01826 

.02184 

.02576 

.03002 

.03463 

.03961 

.04495 

.05067 

.05678 

53 

.01832 

.02190 

.02582 

.03009 

.03471 

.03969 

.04504 

.05077 

.05688 

.06339 

M 

.01837 

.02196 

.02.'i89 

.03017 

.03479 

.03978 

.04514 

.05087 

.05699 

.06350 

55 

1.01843 

.02203 

1.02596 

1.03024 

1.03487 

1.03987 

1.04523 

1 .05097 

1.05709 

1.06362 

56 

.01849 

.02209 

.02603 

.03032 

.03495 

.03995 

.04532 

.05107 

.05720 

.06373 

57 

.01854 

.02215 

.02610 

.03039 

.03503 

.04004 

.04541 

.05116 

.05730 

.06384 

58 

.01860 

.02221 

.02617 

.03046 

.03512 

.04013 

.04551 

.05126 

.05741 

69 

.01866 

.02228 

.02624 

.03054 

.a3520 

.04021 

.04560 

.05136 

.05751 

.06407 

60 

1.01872 

1.02234 

1 .02630 

1.03061 

1.03528 

1.04030 

1.04569  1.05146 

1.05762 

1.06418 

' 

790 

780 

77P 

76«    1      75«  1      74«  1      73"  |      72- 

71»  1       70»  1    ' 

Cosecants. 


^Bxsecant— secant— 1;  coexsecant— cosecant^^^OOglc 


NATURAL  SECANTS,  ETC.  IM 

4. — Natnrml  Secants,  Cosbcants  (Exsbcants.  Cobxsbcants).* — (Cont'd.) 
SwcofUs, 


CostcatUs. 
•  Bnecant  -  tecant  -  1 ;  coexaecant  -  cosecant  - 1.^^^  by  GoOg  Ic 


170 


Q.—PLANE  TRIGONOMETRY. 


4. — Natural  Secants,  Cosbcants  (Bxsbcants.Cobxsbcants).*— ^(Cont'd.) 
S9canis. 


* 

30O 

31» 

32" 

I     33* 

1    34* 

35» 

1    36«» 

37» 

1      38» 

390  1 

1.15470 

1.16663 

1.17918 

1.19236 

1.20622  1.22077 

1.23607 

1.25214 

1.26902 

1.28676 

U 

.16489 

.16684 

.17939 

.19259 

.20645 

.22102 

.23633 

.25241 

.2691 1 

.28706 

51 

.16609 

.16704 

.17961 

.19281 

.20669 

.22127 

.23669 

.25269 

.26960 

.28737 

5t 

.15528 

.16725 

.17982 

.19304 

.20693 

.22152 

.23685 

.25296 

.26988 

.28767 

5 

.15648 

.16745 

.18004 

.19327 

.20717 

.22177 

.23711 

.25324 

.27017 

.38797   5* 

1.15567 

1.16766 

1.18025 

1.19349 

1.20740 

1.22202 

1.23738 

1.25351 

1.27046 

1.28828  5J 

.16587 

.16786 

.18047 

.19372 

.20764 

.22227 

.23764 

.25379 

.27075 

.28858 

5 

.15606 

.16806 

.18068 

.19394 

.20788 

.22252 

.23790 

.25406 

.27104 

.28889 

5 

.16626 

.16827 

.18090 

.19417 

.20812 

.22277 

.23816 

.25434 

.27183 

.28919 

5 

.15645 

.16848 

.18111 

.19440 

.20836 

.22302 

.23843 

.25462 

.37162 

.28950 

5 

1.15665 

1.16868 

1.18133 

1.19463 

1 .20859 

1.22327 

1.23869 

1.26489 

1.37191 

1.28980 

» 

.15684 

.16889 

.18155 

.19485 

.20883 

.22352 

.23895 

.25511 

.27221 

.29011 

.16704 

.16909 

.18176 

.19508 

.20907 

.22377 

.23922 

.25545 

.27350 

.21042 

.15724 

.16930 

.18198 

.19531 

.22931 

.23402 

.25948 

.25572 

.27279 

.29072 

.15743 

.16950 

.18220 

.19554 

.20955 

.22428 

.^3975 

.25600 

.27308 

.29103 

1.15763 

1.16971 

1.18241 

1.19576 

1.20979 

1.22453 

1.24001 

1.25628 

1.27337 

1.29183 

.16782 

.16992 

.18263 

.19599 

.21003 

.22478 

.24028 

.25656 

.27366 

.29164 

.15802 

.17012 

.18285 

.19622 

.21027 

.22503 

.24054 

.25683 

.27396 

.29195 

.15822 

.17033 

.18307 

.19645 

.21061 

.22528 

.24081 

.25711 

.27425 

.29326 

.16841 

.17054 

.18328 

.19668 

.21075 

.22554 

.24107 

.25739 

.27454 

.19256 

20 

1.15861 

1.17075 

1.18350 

1.19691 

1.21099 

1.25579 

1.24134 

1.25767 

1.27483 

1.29287 

21 

.16881 

.17095 

.18372 

.19713 

.21123 

.22604 

.24160 

.25795 

.27513 

.29318 

22 

.15901 

.17116 

.18394 

.19736 

.21147 

.22629 

.24187 

.25823 

.27542 

.29349 

23 

.15920 

.17137 

.18416 

.19759 

.21171 

.22655 

.24213 

.25851 

.27572 

.29380 

24 

.15940 

.17158 

.18437 

.19782 

.21195 

.22680 

.24240 

.25879 

.27601 

.29411 

25 

1.15960 

1.17178 

1.18459 

1.19805 

1.21220 

1.22706 

1.24267 

1.25907 

1.27630 

1.29442 

26 

.15980 

.17199 

.18481 

.19828 

.21244 

.22731 

.24293 

.25935 

.27660 

.29473 

27 

.16000 

.17220 

.18503 

.19851 

.21268 

.22756 

.24320 

.25963 

.27689 

.29504 

28 

.16019 

.17241 

.18525 

.19874 

.21293 

.22782 

.24347 

.25991 

.27719 

.29535 

29 

.16039 

.17262 

.18547 

.19897 

.21316 

.22807 

.24373 

.26019 

.27748 

.39566 

30 

1.16059 

1.17283 

1.18569 

1.19920 

1.21341 

1.22833 

1.24400 

1.26047 

1.27778 

1.29597 

31 

.16079 

.17304 

.18591 

.19944 

.21365 

.22858 

.24427 

.26075 

.27807 

.29628 

82 

.16099 

.17325 

.18613 

.19967 

.21389 

.22884 

.24454 

.26104 

.27837 

.29659 

33 

.16119 

.17346 

.18635 

.19990 

.21414 

.22909 

.24481 

.26132 

.27867 

.29690 

34 

.16139 

.17367 

.18657 

.20013 

.21438 

.22935 

.24508 

.26160 

.27896 

.29721 

35 

1.16159 

1.17388 

1.18679 

1.20036 

1.21462 

1.22960 

1.24534 

1.26188 

1.27926 

1.29752 

36 

.16179 

.17409 

.18701 

.20059 

.21487 

.22986 

.24561 

.26216 

.27956 

.29784!  : 

37 

.16199 

.17430 

.18723 

.20083 

.21511 

.23012 

.24588 

.26245 

.27985 

.29615  : 

38 

.16219 

.17451 

.18745 

.20106 

.21535 

.23037 

.24615 

.26273 

.28015 

.29846!  ; 

39 

.16239 

.17472 

.18767 

.20129 

.21660 

.23063 

.24642 

.26301 

.28045 

.29877 

40 

1.16259 

1.17493 

1.18790 

1.20152 

1.21584 

1.23089 

1.24669 

1.26330 

1.28075 

1.29909 

2 

41 

.16279 

.17514 

.18812 

.20176 

.21609 

.23114 

.24696 

.26358 

.28105 

.29940 

42 

.06299 

.17535 

.18834 

.20199 

.21633 

.23140 

.24723 

.26387 

.28184 

.29971 

43 

.16319 

.17556 

.18856 

.20222 

.21658 

.23166 

.24750 

.26415 

.28164 

.30003 

44 

.16339 

.17577 

.18878 

.20246 

.21682 

.23192 

.24777 

.26443 

.28194 

.30034 

45 

1.16359 

1.17598 

1.18901 

1.20269 

1.21707 

1.23217 

1.24804 

1.26472 

1.28224 

1.80066 

1 

46 

.16380 

.17620 

.18923 

.20292 

.21731 

.23243 

.24832 

.26500 

.28254 

.300»7 

47 

.16400 

.17641 

.18945 

.20316 

.21756 

.23269 

.24859 

.26529 

.28284 

.30129 

48 

.16420 

.17662 

.18967 

.20339 

.21781 

.23295 

.24886 

.26557 

.28314 

.3016C 

49 

.16440 

.17683 

.18990 

.20363 

.21805 

.23321 

.24913 

.26586 

.28344 

.30192 

50 

1.16460 

1.17704 

1.19012 

1.20386 

1.21830 

1.23347 

1.24940 

1.26615 

1.28374 

1.30222 

61 

.16481 

.17726 

.19034 

.20410 

.21855 

.23373 

.24967 

.26643 

.28404 

.30251 

62 

.16501 

.17747 

.19057 

.20433 

.21879 

.23399 

.24995 

.26672 

.28434 

.30287 

53 

.16521 

.17768 

.19079 

.20457 

.21904 

.23424 

.25022 

.26701 

.28464 

.3031i 

64 

.16541 

.17790 

.19102 

.20480 

.21929 

.23450 

.25049 

.26729 

.28495 

.30350^ 

55 

1.16562 

1.17811 

1.19124 

1.20504.1.21953 

1.23476 

1.25077 

1.26758 

1.28525 

1.303» 

\ 

56 

.16582 

.17832 

.19146 

.20527 

.21978 

.23502 

.2'5104 

.26787 

.28555 

.3041: 

\ 

67 

.16602 

.17854 

.19169 

.20551 

.22003 

.23529 

.25131 

.26815 

.28585 

.3044 

5 

68 

.16623 

.17875 

.19191 

.20575 

.22028 

.23555 

.25159 

.26844 

.28615 

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1 

69 

.16643 

.17896 

.19214 

.20598 

.22053 

.23581 

.25186 

.26873 

.28646 

.3050 

» 

«0 

1.16663 

1.17918 

1.19236 

1.20622.1.22077 

1 .23607 

1.25214 

1.26902 

1.28676 

1.3054 

I 

590 

68^ 

57<^ 

560     ,     550 

54«»         53* 

52« 

eio 

50<» 

Cosecants. 
^  Bxsecant  -  secant  - 1 ;  cocxsecant  -  coSfefiatitt>¥-vtjOOg  Ic 


d  by  Google 


172 


PLANE  TRIGONOMETRY. 


4. — Natural  Secants,   Cosbcants  (Bzsbcants.  CoBZ8BCANT8).*--^Ccmt'4 
Stcatits. 


' 

50* 

61» 

62<» 

1     53-" 

1    64"> 

1    650 

560 

1     570 

1     580 

1    59»    1 

0 

1.65572 

1.58902 

1.62427 

1.66164 

1.70130 

1.74345 

1.78829 

1.83608 

1.88708 

I.94I60I 

1 

.66626 

.68959 

.62487 

.66228 

.70198 

.74417 

.78904 

.83690 

.88794 

.94254 

2 

.65680 

.69016 

.62548 

.66292 

.70267 

.74490 

.78984 

.83773 

.88884 

.94349 

3 

.66734 

.69073 

.62609 

.66357 

.70335 

.74562 

.79061 

.83855 

.88972 

.94443 

4 

.65789 

.69130 

.62669 

.66421 

.70403 

.74635 

.79138 

.83938 

.89040 

.94537 

5 

1.56843 

1.69188 

1.62730 

1.66486 

1.70472 

1.74708 

1.79216 

1.84020 

1.89148 

1.94432 

6 

.55897 

.69246 

.62791 

.66550 

.70540 

.74781 

.79293 

.84103 

.89237 

.94726 

7 

.56951 

.59302 

.62852 

.66615 

.70609 

.74854 

.79371 

.84186 

.89325 

.94821 

8 

.69360 

.62913 

.66679 

.70677 

.74927 

.79449 

.84269 

.89414 

.94916 

• 

.'66060 

.69418 

.62974 

.66744 

.70746 

.75000 

.79527 

.84352 

.89503 

.95011 

10 

1.56114 

1.59475 

1.63035 

1.66809 

1.70816 

1.75073 

1.79604 

1.84435 

1.89891 

1.95106 

11 

.56169 

.59533 

.63096 

.66873 

.70884 

.75146 

.79682 

.84518 

.89480 

.95201 

12 

.66223 

.59590 

.63157 

.66938 

.70953 

.75219 

.79761 

.84601 

.89769 

.95296 

13 

.56278 

.59648 

.63218 

.67003 

.71022 

.75293 

.79839 

.84685 

.89858 

.95392 

14 

.56332 

.59706 

.63279 

.67068 

.71091 

.75366 

.79917 

.84768 

.89948 

.95487 

15 

1.56387 

1.59764 

1.63341 

1.67133 

1.71160 

1 .75440 

1.79995 

1.84852 

1.90037 

1.9S583 

16 

.66442 

.69^2 

.63402 

.67199 

.71229 

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17 

.56497 

.59880 

.63464 

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.71298 

.75587 

.80162 

.85019 

.90216 

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18 

.56661 

.69938 

.63525 

.67329 

.71368 

.75661 

.80231 

.85103 

.90305 

.96870 

19 

.56606 

.69996 

.63587 

.67394 

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.80309 

.85187 

.90395 

30 

1.56661 

1.60054 

1.63648 

1.67460 

1.71506 

1.76808 

1.80388 

1.85271 

1.90485 

l!94062 

21 

.56716 

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.63710 

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.80467 

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22 

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.67691 

.71646 

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.90665 

.94265 

23 

.56826 

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.80625 

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.90755 

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24 

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.60287 

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.76105 

.80704 

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.90845 

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35 

1.56937 

1.60346 

1.63957 

1.67788 

1.71855 

1.76179 

1.80783 

1.85692 

1.90935 

1.96544 

24 

.56992 

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.64019 

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.80862 

.85777 

.91026 

.94441 

27 

.57047 

.60463 

.64081 

.67919 

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.76328 

.80942 

.85861 

.91116 

.94738 

28 

.67103 

.60521 

.64144 

.67985 

.72065 

.76402 

.81021 

.85944 

.91207 

.94835 

29 

.57168 

.60580 

.64206 

.68051 

.72135 

.76477 

.81101 

.86031 

.91297 

.94932 

30 

1.57213 

1.60639 

1 .64268 

1.68117 

1.72205 

1.76652 

1.81180 

1.84116 

1.91388 

1.97029 

31 

.67269 

.60698 

.64330 

.68183 

.72275 

.76626 

.81260 

.86201 

.91479 

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82 

.67324 

.60756 

.64393 

.68250 

.72346 

.76701 

.81340 

.86286 

.91670 

.97224 

33 

.67380 

.60815 

.64455 

.68316 

.72416 

.76776 

.81419 

.86371 

.91661 

.97322 

34 

.57436 

.60874 

.64518 

.68382 

.72487 

.76851 

.81499 

.86457 

.91752 

.97420 

35 

1.57491 

1.60933 

1.64580 

1.68449 

1.72557 

1 .76926 

1.81579 

1.86542 

1.91844 

1.97517 

S« 

.57547 

.60992 

.64643 

.68515 

.72628 

.77001 

.81659 

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.97415 

87 

.57603 

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.68582 

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.86713 

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.97713 

88 

.67659 

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.64768 

.68648 

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.77152 

.81820 

.86799 

.92118 

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39 

.67715 

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.64831 

.68716 

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.97910 

40 

1.67771 

1.61229 

1.64894 

1.68782 

1.72911 

1 .77303 

1.81981 

1.84970 

1.92302 

1.08008 

41 

.67827 

.61288 

.64957 

.68848 

.72982 

.77378 

.82061 

.87056 

.92394 

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42 

.57883 

.61348 

.65020 

.68915 

.73053 

.77454 

.82142 

.87142 

.92486 

.982<»& 

43 

.57939 

.61407 

.65083 

.68982 

.73124 

.77530 

.82222 

.87289 

.92578 

.98804 

44 

.57995 

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.65146 

.69049 

.73195 

.77606 

.82303 

.87316 

.92670 

.08403 

45 

1.68051 

1.61526 

1.65209 

1.69116 

1.73267 

1.77681 

1.82384 

1.87401 

1.92762 

1.08902 

46 

.68108 

.61586 

.65272 

.69183 

.73338 

.77757 

.82465 

.87488 

.92855 

.98601 

47 

.68164 

.61646 

.65336 

.69250 

.73409 

.77833 

.82546 

.87674 

.92947 

.98700 

48 

.58221 

.61705 

.65399 

.69318 

.73481 

.77910 

.82627 

.87661 

.93040 

.08799 

49 

.58277 

.61765 

.65462 

.69385 

.73652 

.77986 

.82709 

.87748 

.93133 

.08899 

60 

1.58333 

1.61825 

1.65526 

1.69452 

1.73624 

1.78062 

1.82790 

1.87834 

1 .93226 

1.08998 

51 

.68390 

.61885 

.66589 

.69520 

.73696 

.78138 

.82871 

.87921 

.93319 

.00098 

62 

.58447 

.61945 

.65653 

.69587 

.73768 

.78215 

.82953 

.88008 

.93412 

.00198 

63 

.68503 

.62005 

.65717 

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.73840 

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.93505 

.0029S 

54 

.58560 

.62065 

.65780 

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.73911 

.78368 

.83116 

.88183 

.93598 

.00898 

55 

1.58617 

1.62125 

1.65844 

1.69790 

1.73983 

1.78445 

1.83198 

1.88270 

1.93692 

1.00498 

66 

.58674 

.62186 

.66908 

.69858 

.74056 

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.83280 

.88357 

.93785 

.00598 

67 

.58731 

.62246 

.65972 

.69926 

.74128 

.78598 

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.93879 

.09498 

58 

.68788 

.62306 

.66036 

.69994 

.74200 

.78675 

.83444 

.88632 

.93973 

.00799 

69 

.68845 

.62366 

.66100 

.70062 

.74272 

.78752 

.83526 

.88620 

.94066 

.00899 

60 

1.58902 

1.62427 

1.66164 

1.70130 

1.74345 

1.78829 

1.83608 

1.88708 

1.94160 

2.00000 

89* 

38» 

1     37'* 

36«» 

360 

840 

53«~ 

3i* 

tx-   1  ao-  1 

^  Exsecant*  secant 


Cos9aints. 
-1;  ooexsecant -cosecant —iPOg'^ 


d  by  Google 


174 


9.--PLANE  TRIGONOMETRY. 


4. — NatHTAl  SDcaats,  Cosbcants  (Exsbcants.  CoBzsscANTt).*-— <CDnt'd 
Secants. 


7(f>    1     71«     1     72» 

73<»    1    74«»    1    75<»    1     76*    1     n»    1    78»    1    7f»    1 

2.92380 

1.07155 

1.23607 

8.42030 

3.68796 

8.86870 

4.18387 

1.44541 

1.80978 

5.M0M 

i 

.92614 

.07415 

.23897 

.42356 

.63164 

.86790 

;i3889 

.45102 

.81633 

.24871 

.92849 

.07675 

.14187 

.42682 

.63533 

.87211 

.14323 

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.88294 

.93083 

.07936 

.24478 

.43010 

.63903 

.87833 

.14809 

.46228 

.88956 

.'lC448 

.93318 

.08197 

.24770 

.43337 

.64274 

.88056 

.15295 

.46798 

.83481 

.27241 

2.93554 

S. 08459 

}. 25062 

3.43666 

3.64645 

3.88479 

4.15782 

4.47860 

4.84288 

5.28038 

J 

.93790 

.08721 

.25355 

.43995 

.65018 

.88904 

.16271 

.47988 

.84966 

.28833 

.94026 

.08983 

.25648 

.44324 

.65391 

.89330 

.16761 

.48498 

.85627 

.29834 

.94263 

.09246 

.25942 

.44655 

.65765 

.89756 

.17262 

.49069 

.86299 

.20436 

.94500 

.09510 

.26237 

.44986 

.66140 

.90184 

.17744 

.49642 

.86978 

.21241 

2.94737 

3.09774 

3.26531 

3.45317 

3.66515 

3.90613 

4.18238 

4.60216 

4.87649 

6.22049 

1 

.94975 

.10038 

.26827 

.45650 

.66892 

.91042 

.18733 

.50791 

.883r 

.22859 

.95213 

.10303 

.27123 

.45983 

.67269 

.91473 

.19228 

.51868 

.89007 

.22871 

.95452 

.10568 

-.27420 

.46316 

.67647 

.91904 

.19725 

.51947 

.89689 

24486 

.96691 

.10834 

.27717 

.46651 

.68025 

.92337 

.20224 

.52527 

.90373 

!3S804 

2.95931 

3.11101 

3.28015 

3.46986 

3.68405 

3.92770 

4.20723 

4.53109 

4.91068 

5.88124 

4 

.96171 

.11367 

.28313 

.47321 

.68785 

.93204 

.21224 

.53692 

.91746 

.38947 

.96411 

.11635 

.28612 

.47658 

.69167 

.93640 

.21726 

.54277 

.92486 

.27772 

.96652 

.11903 

.28912 

.47995 

.69549 

.94076 

.22229 

.54868 

.98128 

.28600 

.96893 

.12171 

.29212 

.48333 

.69931 

.94514 

.22734 

.55451 

.98821 

.28430 

2.97135 

3.12440 

3.29512 

3.48671 

3.70315 

3.94952 

4.23239 

4.66041 

4.94517 

5.40263 

4 

.97377 

.12709 

.29814 

.49010 

.70700 

.95392 

.23746 

.56632 

.95215 

.41099 

22 

.97619 

.12979 

.30115 

.49850 

.71085 

.95832 

.24255 

.57224 

.95914 

.41927 

23 

.97862 

.13249 

.30418 

.49691 

.71471 

.96274 

.24764 

.57819 

.96616 

.42778 

24 

.98106 

.13520 

.30721 

.50032 

.71858 

.96716 

.25275 

.58414 

.97320 

.42622 

\ 

35 

2.98349 

3.13791 

3.31024 

3.60374 

3.72246 

3.97160 

4.26787 

4.59012 

4.98025 

5.44488 

i 

26 

.98594 

.14063 

.31328 

.50716 

.72635 

.97604 

.26300 

.59611 

.98738 

.45817 

j 

27 

.98838 

.14335 

.31633 

.51060 

.73024 

.98050 

.26814 

.60211 

.99443 

.48169 

28 

.99083 

.14608 

.31939 

.51404 

.73414 

.98497 

.27330 

.60813 

5.00155 

.47083 

29 

.99329 

.14881 

.32244 

.51748 

.73806 

.98944 

.27847 

.61417 

.00869 

.47881 

JO 

2.99574 

3.15155 

3.32551 

3.52094 

3.74198 

3.99893 

4.28366 

4.62023 

6.01585 

5.48740 

31 

.99821 

.15429 

.32858 

.52440 

.74591 

.99848 

.28886 

.62630 

.02308 

.49603 

22 

3.00067 

.15704 

.33166 

.52787 

.74984 

4.00298 

.29406 

.63238 

.03024 

33 

.00316 

.15979 

.33474 

.53134 

.75379 

.00745 

.29929 

.63849 

.03746 

181337 

84 

.00562 

.16255 

.33783 

.53482 

.75775 

.01198 

.30452 

.64461 

.04471 

.52208 

as 

3.00810 

3.16531 

3.34092 

3.53831 

3.76171 

4.01652 

4.809n 

4.65074 

5.05197 

5.62081 

36 

.01059 

.16808 

.34403 

.54181 

.76568 

.02107 

.31503 

.65690 

.05926 

.68W8 

87 

.01308 

.17086 

.34713 

.54531 

.76966 

.02568 

.32031 

.66307 

.06657 

.64887 

38 

.01557 

.17363 

.35025 

.54883 

.77865 

.03020 

.32560 

.66925 

.07390 

.58720 

29 

.01807 

.17641 

.35336 

.55235 

.77765 

.03479 

.33090 

.67545 

.08125 

.56605 

40 

3.02057 

3.17920 

3.35649 

3.55587 

3.78166 

4.03938 

4.33622 

4.68167 

5.08863 

5.87483 

41 

.02308 

.18199 

.35962 

.55940 

.78668 

.04898 

.34154 

.68791 

.09602 

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42 

.02559 

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.36276 

.56294 

.78970 

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.34689 

.69417 

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.89277 

43 

.02810 

.18759 

.36590 

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.79374 

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.35224 

.70044 

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.88174 

44 

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.36905 

.57005 

.79778 

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.70678 

.11835 

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45 

3.03315 

3.19322 

3.37221 

3.57361 

8.80183 

4.06251 

4.36299 

4.71303 

5.12583 

5.81976 

1 

46 

.03568 

.19604 

.37537 

.57718 

.80589 

.06717 

.36839 

.71936 

.13334 

.82881 

47 

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.19886 

.37854 

.68076 

.80996 

.07184 

.37380 

.72569 

.14087 

.68790 

48 

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.64701 

49 

.04329 

.20453 

.38489 

.58794 

.81813 

.08121 

.38466 

.73843 

.15599 

.85616 

50 

3.04584 

3.20737 

3.38808 

3.59154 

3.82223 

4.08591 

4.39012 

4.74482 

5.16359 

5.86583 

1 

51 

.04839 

.21021 

.39128 

.59514 

.82633 

.09063 

.39558 

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.87454 

52 

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.39448 

.59876 

.83045 

.09535 

.40106 

.75766 

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.68877 

53 

.05350 

.21592 

.39768 

.60238 

.83457 

.10009 

.40656 

.76411 

.18652 

.69804 

M 

.05607 

.21878 

.40089 

.60601 

.83871 

.10484 

.41206 

.77057 

.19421 

.78884 

55 

3.05864 

3.22165 

3.40411 

3.60965 

3.84285 

4.10960 

4.41759 

4.77705 

5.20193 

5.71166 

56 

.06121 

.22452 

.40734 

.61330 

.84700 

.11437 

.42312 

.78365 

.20966 

.721081 

67 

.06379 

.22740 

.41057 

.61695 

.85116 

.11915 

.42867 

.79007 

.21742 

.72041 

58 

.06637 

.23028 

.41381 

.62061 

.85533 

.12394 

.43424 

.79661 

.22521 

.78983 

59 

.06896 

.23317 

.41705 

.62428 

.85951 

.12875 

.43982 

.80316 

.23301 

.74929 

«0 

3.07155 

3.23607  |3. 42030 

.3.62796 

3.86370 

4.13357 

4.44541 

4.80973 

6.24064 

5.76877 

1      19» 

18-     (      170 

1      16* 

15* 

140    1     13» 

12<»    1     11*    1    10» 

L 

Cosecants. 
^  Exiecant  —  secant  -  1 ;  coexsecant  —  cosecant -^P^8  ^^ 


) 


NATURAL  SECANTS,  ETC,  17« 

^^ — Natwal  Secaiitf.  Cosbcants  (Exsbcants,  Cobxsbcamts).*— (Cond'd.) 

Secants. 


I 
I 
7 
8 
f 
10 

u 
u 

13 
14 
If 

IC 
17 
18 
If 

38 

n 

23 
31 
34 
38 
21 
37 
28 
81 
38 
ft 
83 
33 
34 
3S 
34 
V 
88 
SI 
48 
41 
43 
43 
44 
48 
4« 
49 
48 
49 
M 
U 

s 
s 
» 


Cosecants. 
•EartecMt- secant- 1:  coexsecant  -  cosecant -I^^^qqJ^ 


176 


9.-'PLANE  TRIGONOMETRY. 


6. — Loffarithmic  Sinct,  Tangbnts,  Cotangbnts,  Cosmss. 
(Sbcants,  Cosecants.)* 


-r 

Blue.     Tang.  |  Cotang. 

Coelne.  I      II  '  |    Bine.  I  Tang.  |  Cotang.  I  Ooatoe.  | 

Inf.       Inf.   1 

0 

Neg. 

Nflg. 

Infinite. 

10.00000 

60 

0 

8.24186 

8.24198 

11.75808 

9.99993 

6 

6.46373 

6.46373 

13.53627 

.00000 

59 

1 

.24903 

.24910 

.75090 

.99991 

6 

a 

.76476 

.76476 

.23524 

.00000 

59 

2 

.25609 

.25616 

.74384 

.99991 

I 

3 

6.94085 

6.94085 

18.05915 

.00000 

57 

a 

.26304 

.26312 

.78688 

.99998 

e 

4 

7.06579 

7.06679 

12.93421 

.00000 

56 

4 

.26988 

.26996 

.73004 

.99998 

11 

5 

7.16270 

7.16270 

12.83730 

10.00000 

55 

5 

8.27661 

8.27669 

11.72331 

9.99992 

5 

6 

.24188 

.24188 

.75812 

.00000 

54 

6 

.28324 

.28332 

.71668 

.99998 

8 

7 

.30882 

.30882 

.69118 

.00000 

53 

7 

.28977 

.28986 

.71014 

.99998 

8 

.36682 

.36682 

.63318 

.00000 

62 

8 

.29621 

.29629 

.70371 

.99998 

I 

9 

.41797 

.41797 

.58203 

.00000 

51 

9 

.30255 

.30263 

.69787 

.99991 

I 

10 

7.46373 

7.46373 

12.53627 

10.00000 

50 

10 

8.30879 

8.30868 

11.69112 

9.99991 

8 

11 

.50512 

.50512 

.49488 

.00000 

49 

11 

.31495 

.31505 

.68495 

.99991 

4 

12 

.54291 

.54291 

.45709 

.00000 

48 

12 

.32103 

.32112 

.67888 

.99990 

i 

13 

.57767 

.57767 

.42233 

.00000 

47 

13 

.32702 

.32711 

.67289 

i 

14 

.60985 

.60986 

.39014 

.00000 

46 

14 

.33292 

.33302 

.66698 

!99990 

4 

15 

7.63982 

7.63982 

12.36018 

10.00000 

45 

15 

8.33875 

8.33886 

11.66114 

9.99990 

4 

16 

.66784 

.66785 

.33215 

10.00000 

44 

16 

.34450 

.34461 

.65539 

.99989 

i 

17 

.69417 

.69418 

.30582 

9.99999 

43 

17 

.35018 

.35029 

.64971 

.99989 

i 

18 

.71900 

.71900 

.28100 

42 

18 

.35578 

.35590 

.64410 

.99989 

i 

19 

.74248 

.74248 

.25752 

.99990 

41 

19 

.36131 

.36143 

.63857 

.99989 

i 

ao 

7.76475 

7.76476 

12.23524 

9.99990 

40 

30 

8.36678 

8.36689 

11.63311 

9.99988 

4 

21 

.78594 

.78595 

.21405 

.99999 

39 

ai 

.37217 

.37229 

.62771 

.99988 

; 

22 

.80615 

.80615 

.19385 

.99999 

88 

22 

.37760 

.37762 

.62238 

.99988 

J 

23 

.82545 

.82546 

.17454 

.99999 

37 

23 

.38276 

.38289 

.61711 

.99987 

J 

24 

.84393 

.84394 

.15606 

.99999 

36 

24 

.38796 

.38809 

.61191 

.99987 

J 

35 

7.86166 

7.86167 

12.13833 

9.99999 

35 

35 

8.39310 

8.39323 

11.60677 

9.99987 

I 

26 

.87870 

.87871 

.12129 

.99999 

34 

26 

.39818 

.39832 

.60168 

99986 

27 

.89509 

.89510 

.10490 

.99999 

33 

27 

.40320 

.40334 

.69666 

! 99986 

J 

28 

.91088 

.91089 

.08911 

.99999 

32 

28 

.40816 

.40830 

.59170 

.99986 

29 

.92612 

.92613 

.07387 

.99998 

31 

29 

.41307 

.41321 

.68679 

.99986 

3 

30 

7.94084 

7.94086 

12.05914 

0.99998 

30 

30 

8.41792 

8.41807 

11.58193 

9.99986 

J 

31 

.95508 

.95510 

.04490 

.99998 

29 

31 

.42272 

.42287 

.57713 

.99966 

32 

.96887 

.96889 

.03111 

.99998 

28 

32 

.42746 

.42762 

.57238 

.99984 

83 

.98223 

.98225 

.01775 

.99998 

27 

33 

.43216 

.43232 

.56768 

.99984 

84 

7.99520 

7.99522 

12.00478 

.99998 

26 

34 

.43680 

.43696 

.66304 

.99984 

35 

8.00779 

8.00781 

11.99219 

9.99998 

35 

35 

8.44139 

8.44156 

11.55844 

9.99983 

; 

86 

.02002 

.02004 

.97996 

.99998 

24 

36 

.44594 

.44611 

.55389 

.9H83 

87 

.03192 

.03194 

.96806 

.99997 

23 

37 

.45044 

.45061 

.64939 

.99983 

88 

.04360 

.04353 

.95647 

.99997 

22 

38    .45489 

.45507 

.64493 

.99983 

39 

.05478 

.05481 

.94519 

.99997 

21 

39 1   .45930 

.45948 

.64052 

.99988 

40 

8.06578 

8.06581 

11.93419 

9.99997 

30 

408.46366 

8.46385 

11.63616 

9.99988 

41 

.07650 

.07653 

.92347 

.99997 

19 

41 

.46799 

.46817 

.53183 

.99981 

42 

.08696 

.08700 

.91300 

.99997 

18 

42 

.47226 

.47245 

.52755 

.99981 

43 

.09718 

.09722 

.90278 

.99997 

17 

43 

.47650 

.47669 

.52331 

.99981 

44 

.10717 

.10720 

.89280 

.99996 

16 

44 

.48069 

.48089 

.51911 

.99980 

45 

8.11693 

8.11696 

11.88304 

9.99996 

15 

458.48485 

8.48505 

11.61496 

9.99980 

46 

.12647 

.12651 

.87349 

.99996 

14 

46 

.48896 

.48917 

.61083 

.99979 

47 

.13581 

.13585 

.86415 

.99996 

13 

46 

.49304 

.49325 

.60676 

.99979 

48 

.14495 

.14500 

.85500 

.99996 

12 

48 

.49708 

.49729 

.50271 

.99979 

49 

.15391 

.15395 

.84605 

.99996 

11 

49 

.50108 

.50130 

.49870 

.99978 

50 

8.16268 

8.16273 

11.83727 

9.99995 

10 

50 

8.50504 

8.50527 

11.49473 

9.99978 

51 

.17128 

.17133 

.82867 

.99995 

9 

51 

.50897 

.50920 

.49080 

.99977 

62 

.17971 

.17976 

.82024 

.99995 

8 

52 

.51287 

.51310 

.48690 

.99977 

53 

.18798 

.18804 

.81196 

.99995 

7 

53 

.51673 

.51696 

.48304 

.99977 

54 

.19610 

.19616 

.80384 

.99995 

6 

54 

.52055 

.52079 

.47921 

.99976 

55 

8.20407 

8.20413 

11.79587 

9.99994 

5 

55 

8.52434 

8.52459 

11.47641 

9.99976 

56 

.21189 

.21196 

.78805 

.99994 

4 

56 

.52810 

.52835 

.47166 

.99975 

57 

.21958 

.21964 

.78036 

.99994 

3 

57 

.53183 

.53208 

.46792 

.99975 

58 

.23713 

.22720 

.77280 

.99994 

2 

68 

.53552 

.53578 

.46422      .99074 

59 

.23456 

.23462'     .76538 

.99994 

59 

.53919 

.53945 

.46055      .99974 

60 

8.24186 

8.24192  11.75808 

1 

9.99993 

0 

60 

8.54282 

8.54308 

11.45692    0.99074 

Cosine. 

CotanKi   Tang. 

Sine.    1  '  II      1  Cosine.  1  Cotang 

1  Tang.   1   Sine.   I 

♦Log  secant  — colog  cosine— 1  — log  cosine;  log  cosecant— coloff  sine 
1  — log  sine. 

Ex.— Log  sec  0»-  SO'  - 10.00002.       £«.— Log  coscc  0*»-  Zff  -  12.05911 


LOGARITHMIC  SINES,  ETC. 


177 


5. — Loffarlthmic  Sines,  Tanobhts.  Cotanobnts,  Cosikbs. 
(Sbcants,  Cosbcants-)* — (Cont'd.) 


'  1  one.    1  Ikng.  1  Ootang.  |  Cotfne-I     ||  '  I  Sine.    I  Tang.  I  Ootong.  lOoilne.  | 

• 

8.M383 

8.54308 

11.45592 

9.99974 

to 

0 

8.71880 

8.71940 

11.28060 

9.99940 

to 

.i46tf 

.45331 

.99973 

59 

I 

.72120 

.72181 

.27819 

.99940 

59 

t 

.uaH 

:66027 

.44973 

.99973 

58 

2 

.72359 

.72420 

.27580 

.99939 

58 

S 

.iSSM 

.56382 

.44518 

.99972 

57 

3 

.72597 

.72659 

.27341 

.99938 

57 

4 

.warn 

.55734 

.44266 

.99972 

56 

4 

.72834 

.72896 

.27104 

.99938 

56 

A 

8.88094 

8.55083 

11.43917 

9.99971 

55 

B 

8.73069 

8.73132 

11.26868 

9.99937 

55 

€ 

.9t4tO 

.55429 

.43571 

.99971 

54 

6 

.73303 

.73366 

.26634 

.99936 

54 

7 

.6tr43 

.55773 

.43227 

.99970 

53 

7 

.73535 

.73767 

.73600 

.26400 

.99936 

53 

8 

.97t84 

.67114 

.42886 

.99970 

52 

8 

.73832 

.26168 

.99935 

52 

» 

.87411 

.57452 

.42548 

.99969 

51 

9 

.73997 

.74063 

.26937 

.99934 

51 

It 

s.snvr 

8.57788 

11.42212 

9.99969 

50 

10 

8.74226 

8.74292 

11.25708 

9.99934 

50 

tl 

.58089 

.58121 

.41879 

.99968 

49 

11 

.74454 

.74521 

.25479 

.99933 

49 

13 

.86419 

.58451 

.41549 

.99968 

48 

12 

.74680 

.74748 

.25252 

.99932 

48 

U 

.58747 

.5«n9 

.41221 

.99967 

47 

13 

.74906 

.74974 

.25026 

.99932 

47 

14 

.59072 

.59105 

.40895 

.99967 

46 

14 

.75130 

.75199 

.24801 

.99931 

46 

IS 

8.58295 

8.59428 

11.40572 

9.99967 

45 

15 

8.76353 

8.75423 

11.24677 

9.99930 

45 

IC 

.59715 

.59749 

.40251 

.99966 

44 

16 

.75575 

.75645 

.24365 

.99929 

44 

17 

.10023 

50058 

.39932 

.99966 

43 

17 

.75795 

.76867 

.24133 

.99929 

43 

18 

.50049 

.'50384 

.39616 

.99965 

42 

18 

.76015 

.76087 

.23913 

.99928 

42 

If 

t08tK! 

.50598 

.39302 

.99964 

41 

19 

.76234 

.76306 

.23694 

.99927 

41 

ai 

i'.mgn 

8.51009 

11.38991 

9.99964 

40 

30 

8.76451 

8.76525 

11.23475 

9.99926 

40 

21 

.41282 

.51219 

.38681 

.99963 

39 

21 

.76667 

.76742 

.23258 

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39 

IS 

.51588 

.51525 

.38374 

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38 

22 

.76883 

.76958 

.23042 

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38 

n 

.41804 

.61931 

.38069 

.99962 

37 

23 

.77097 

.77173 

.22827 

.99924 

37 

u 

.52198 

.62234 

.37766 

.99962 

36 

24 

.77310 

.77387 

.22613 

.99923 

36 

M 

8.63497 

8.52535 

11.37465 

9.99961 

35 

35 

8.77522 

8.77600 

11.22400 

9.99923 

35 

U 

.52795 

.52834 

.37166 

.99961 

34 

26 

.77733 

.77811 

.22189 

.99922 

34 

27 

.53091 

.53131 

.36869 

99960 

33 

27 

.77943 

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.21978 

.99921 

33 

3t 

.52385 

.53426 

.365)4 

! 99960 

32 

28 

.78152 

.78232 

.21768 

.99920 

32 

It 

.52578 

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.35283 

.99959 

31 

29 

.78360 

.78441 

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31 

J» 

8.58958 

8.54009 

11.85991 

9.99959 

30 

30 

8.78668 

8.78649 

11.21351 

9.99919 

30 

11 

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.54298 

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29 

31 

.78774 

.78855 

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29 

n 

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28 

32 

.78979 

.79061 

.20939 

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28 

13 

.54827 

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.35130 

.99957 

27 

33 

.79183 

.79266 

.20734 

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27 

U 

.55110 

.55154 

.34846 

26 

34 

.79386 

.79470 

.20530 

.99916 

26 

u 

8.55891 

8.56435 

11.34565 

9!99956 

35 

35 

6.79588 

8.79673 

11.20327 

9.99915 

35 

n 

.55570 

.65715 

.34285 

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24 

36 

.79789 

.79875 

.20125 

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24 

17 

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23 

37 

.79990 

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23 

38 

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22 

38 

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22 

n 

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21 

39 

.80388 

.80476 

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21 

m 

8.5C759 

8.56816 

11.33184 

9.99953 

20 

40 

8.80585 

8.80674 

11.19326 

9.99911 

30 

41 

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19 

41 

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19 

43 

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18 

42 

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18 

43 

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17 

43 

.81173 

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17 

44 

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16 

44 

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16 

45 

8.58104 

8.581fr4 

11.31846 

9.99960 

15 

45 

8.81560 

8.81653 

11.18347 

9.99907 

15 

44 

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14 

46 

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.81846 

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14 

47 

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13 

47 

.81944 

.82038 

.17962 

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13 

48 

.58885 

.68938 

.31062 

.99948 

12 

48 

.82134 

.82230 

.17770 

.99904 

12 

49 

.59144 

.59196 

.30804 

.99948 

11 

49 

.82324 

.82420 

.17580 

.99904 

11 

It 

8.59400 

8.59453 

11.30547 

9.99947 

10 

50 

8.82513 

8.82610 

11.17390 

9.99903 

10 

•1 

59454 

.59708 

.30292 

.99946 

9 

51 

.82701 

.82799 

.17201 

.99902 

9 

K 

'59907 

.69952 

.30088 

.99946 

8 

52 

.82888 

.82987 

.17013 

.99901 

8 

s 

.70159 

.70214 

.29786 

.99945 

7 

53 

.83075 

.83176 

.16825 

.99900 

7 

M 

.70409 

.70466 

.29535 

.99944 

6 

54 

.83261 

.83361 

.16639 

.99899 

6 

ii 

8.70558 

8.70714 

11.29286 

9.99944 

5 

55 

8.83446 

8.83547 

11.16453 

9.99898 

5 

M 

.70905 

.70962 

.29038 

.99943 

4 

56 

.83630 

.83732 

.16268 

.99898 

4 

S7 

.71151 

.71208 

.28792 

.99942 

3 

57 

.83813 

.83916 

.16084 

.99897 

3 

H 

.71395 

.71453 

.28547 

.99942 

2 

58 

.83996 

.84100 

.15900 

.99896 

2 

91 

.71538 

.71597 

.28303 

.99941 

1 

59 

.84177 

.84282 

.15718 

.99895 

1 

it 

1.71880 

8.71940 

11.28060 

9.99940 

0 

60 

8.84358 

8.84464 

11.16536 

9.99894 

0 

OiMlae. 

CotMDg. 

Tnn^ 

Sine. 

'    I      1  Cosine.  ICotanjf. 

Tang. 

Sine.   1  ' 

sr 


*Log  secant 'oolog  cosine— 1— log  cosine;  log  cosecant ^colog  sine  — 
^"'E.^^  sec  20-  SV  -  10.0004 1.       £;r.-Log  cos^e^b°y<S6ogI^032. 


178 


9.^PLANE  TRIGONOMETRY. 


5. — Lofarithmic  Sines,  Tanobnts,  Cotanobnts,  Cosinbs. — (Cont'd.) 
(Sbcants.  Cosbcants.)* 
4* 6° 


'     sine.    1  Tang.  I  Ootang.  |  Coeine.  |      |)  '  |    Sine.  1  Tang.  |  Ootang.  |  OoalQe.  | 

0 

8.84358 

8.84464 

11.16536 

9.99894 

60 

0 

8.94030 

8.94196 

11.05805 

9.99834 

1 

.84539 

.84646 

.15354 

.99893 

59 

.94174 
.94817 

.94340 

.056M 

.99833 

2 

.84718 

.84826 

.15174 

.99892 

58 

2 

.94485 

.05515 

.99832 

3 

.84897 

.85006 

.14994 

.99891 

67 

3 

.94461 

.94630 

.05370 

.99831 

4 

.85076 

.85185 

.14815 

.99891 

56 

4 

94603 

.94773 

.05227 

.99830 

5 

8.85252 

8.85363 

11.14637 

9.99890 

55 

5 

8! 94746 

8.94917 

11.06083 

9.99829 

6 

.85429 

.85540 

.14460 

.99889 

54 

6 

.94887 

95060 

.04940 

.99828 

7 

.85605 

.85717 

.14283 

.99888 

53 

7 

.95029 

! 95202 

.04798 

.99827 

8 

.85780 

.85893 

.14107 

.99887 

62 

8 

.95170 

.96344 

.04668 

.99825 

9 

.85955 

.86069 

.13931 

.99886 

51 

9 

.95310 

.96486 

.04614 

.99824 

10 

8.86128 

8.86243 

11.13717 

9.99885 

50 

10 

8.95450 

8.95627 

11.04373 

9.99823 

n 

.86301 

.86417 

.13583 

.99884 

49 

11 

.95689 

.95767 

.04233 

.99822 

12 

.86474 

.86591 

. 13409 

.99883 

48 

12 

.95728 

.95908 

.04092 

.99821 

13 

.86645 

.86763 

.13237 

.99882 

47 

13 

.95887 

.96047 

.03953 

.99820 

14 

.86816 

.86935 

.13065 

.99881 

46 

14 

.96005 

.96187 

.03813 

.99819 

15 

8.86987. 

8.87106 

11.12894 

9.99880 

45 

15 

8.96148 

8.96325 

11.03675 

9.99817 

16 

.87156 

.87277 

.12723 

.99879 

44 

16 

.96280 

.96464 

.03636 

.99816 

17 

.87325 

.87447 

.12553 

.99879 

43 

17 

.96417 

.96602 

.03398 

.99816 

18 

.87494 

.87616 

.12384 

.99878 

42 

18 

.96553 

.96739 

.03261 

.99814 

19 

.87661 

.87785 

.12215 

.99877 

41 

19 

.96689 

.96877 

.03123 

.99813 

20 

8.87829 

8.87953 

11.12047 

9.99876 

40 

20 

8.96825 

8.97013 

11.02987 

9.99812 

21 

.87995 

.88120 

.11880 

.99876 

39 

21 

.96960 

.97160 

.02850 

.99810 

22 

.88161 

.88287 

.11713 

.99874 

38 

22 

.97095 

.97285 

.02716 

.99809 

23 

.88326 

.88463 

.11547 

.99873 

37 

23 

.97229 

.97421 

.02579 

.99808  , 

24 

.88490 

.88618 

.11382 

.99872 

36 

24 

.97363 

.97556 

.02444 

.99807   1 

35 

8.88654 

8.88783 

11.11217 

9.99871 

35 

25 

8.97496 

8.97691 

11.02309 

9.99806   !  , 

26 

.88817 

.88948 

.11052 

.99870 

34 

26 

.97629 

.97825 

.02176 

.99804   . 

27 

.88980 

.89111 

.10889 

.99869 

33 

27 

.97762 

.97959 

.02041 

28 

.89142 

.89274 

.10726 

.99868 

32 

28 

.97894 

.98092 

.01908 

.'99802 

29 

.89304 

.89437 

.10663 

.99867 

31 

29 

.98026 

.98225 

.01775 

.99801 

30 

8. 89464 

8.89598 

11.10402 

9.99866 

30 

30 

8.98157 

8.98358 

11.01642 

9.99800 

J 

31 

.89625 

.89760 

.10240 

.99865 

29 

31 

.98288 

.98490 

.01510 

.99798 

32 

.89784 

.89920 

.10080 

.99864 

28 

32 

.98419 

.98622 

.01378 

.99797 

33 

.89943 

.90080 

.09920 

.99863 

27 

33 

.98649 

.98753 

.01247 

.99796 

34 

.90102 

.90240 

.09760 

.99862 

26 

34 

.98679 

.98884 

.01116 

.99795 

35 

8.90260 

8.90399 

ll.0%01 

9.99861 

25 

35 

8.98808 

8.99015 

11.00985 

9.99793 

36 

.90417 

.90567 

.09443 

.99860 

24 

36 

.98937 

.99145 

.00866 

.99792 

37 

.90574 

.90716 

.09286 

.99859 

23 

37 

.99066 

.99275 

.00726 

.99791 

38 

.90730 

.90872 

.09128 

.9985S 

22 

38 

.99194 

.99405 

.00696 

.99790 

39 

.90885 

.91029 

.08971 

.99857 

21 

39 

.99322 

.99534 

.99788 

40 

8.91040 

8.91186 

11.08815 

9.99856 

20 

40 

8.99450 

8.99662 

11.00338 

9.99787 

J 

41 

.91195 

.91340 

.08660 

.99855 

19 

41 

.99577 

.99791 

.00209 

.99786 

42 

.91349 

.91495 

.08505 

.99854 

18 

42 

.99704 

8.99919 

11.00081 

.99785 

43 

.91502 

.91650 

.08350 

.99853 

17 

43 

.99830 

9.00046 

10.99954 

.99783 

44 

.91655 

.91803 

.08197 

.99852 

16 

44 

8.99956 

.00174 

.99826 

.99782 

45 

8.91807 

8.91957 

11.08043 

9.99851 

15 

45 

9.00082 

9.00301 

10.99699 

9.99781 

i 

46 

.91959 

.92110 

.07890 

.99850 

14 

46 

.00207 

.00427 

.99673 

.99780 

1 

47 

.92110 

.92262 

.07738 

.99848 

13 

47 

.00332 

.00553 

.99447 

,99778 

1 

48 

.92261 

.92414 

.07686 

.99847 

12 

48 

.00456 

.00679 

.99321 

.99777 

I 

49 

.92411 

.92565 

.07435 

.99846 

11 

49 

.00581 

.00805 

.99196 

.99776 

1 

50 

8.92561 

8.92716 

11.07284 

9.99845 

10 

50 

9.00704 

9.00930 

10.99070 

9.99775 

51 

.92710 

.92866. 

.07134 

.99844 

9 

51 

.00828 

.01056 

.98946 

.99773 

52 

.92859 

.93016 

.06984 

.99843 

8 

52 

.00951 

.01179 

.98821 

.99772 

53 

.93007 

.93165 

.06835 

.99842 

7 

53 

.01074 

.01303 

.98697 

.99771 

54 

.93154 

.93313 

.06687 

.99841 

6 

54 

.01196 

.01427 

.98673 

.99769 

55 

8.93301 

8.93462 

11.06538 

9.99840 

5 

55 

9.01318 

9.01550 

10.98450 

9.99768 

56 

.93448 

.93609 

.06391 

.99839 

4 

56 

.01440 

.01673 

.98327 

.99767 

57 

.93594 

.937B6 

.06244 

.99838 

3 

57 

.01661 

.01796 

.98204 

.99765 

58 

.93740 

.93903 

.06097 

.99837 

2 

58 

.01682 

.01918 

.98082 

.99764 

59 

.93885 

.94049 

.05951 

.99836 

1 

59 

.01803 

.02040 

.97960 

.99763 

60 

8.94030 

8.94195 

11.05805 

9.99834 

0 

60 

9.01923 

9.02162 

10.97838 

9.99761 

3 

Cosine.  ICotang.l   Tang. 

Sine. 

'  II      1  Cosine. 

Cotang. 

Twg. 

Sine. 

86°  ~~8i 

*L0g  secant— colog  oosine— 1— log  cosine;  log  cosecant -"colog  sine- 
1  — log  sine. 

£*.— Log  sec  4'*-  ZV  - 10.00134.       Eic.— Log  cosec  4*»-  Sy- 11.10536. 


d  by  Google 


180 


9.^PLANE  TRIGONOMETRY. 


5. — Log arithmic  Sinet,  Tanobnts.  Cotanobnts.  Cosinbs.— (Cont'd.) 
(Secants,  (^secants.)* 
y      ' fl" , 


_u 

Sine. 

Tang.  1  Ootang.  |  Ooatne.  | 

1   ' 

1^    Sine. 

Tang. 

Ooung.  lOoslne.l 

0 

9.14359 

9.14780 

10.86220 

9.99676 



60 

0 

9.19433 

9.19971 

10.80029 

9.99463 

.14445 

.14872 

.85128 

.99574 

59 

1 

.19513 

.20053 

.79947 

.99460 

2 

.14535 

.14963 

.85037 

.99572 

58 

2 

.19592 

.30134 

.79866 

.99458 

3 

.14624 

.15054 

.84946 

.99570 

57 

3 

.19672 

.20216 

.79784 

.99456 

4 

.14714 

.15145 

.84855 

.99668 

56 

4 

.19751 

.20297 

.79703 

.09454 

5 

9.14803 

9.15236 

10.84764 

9.99566 

55 

5 

9. 19830 

9.20378 

10.79622 

9.09452 

6 

.14891 

.15327 

.84673 

.99565 

54 

6 

.19909 

.30459 

.79641 

.99450 

7 

.14980 

.15417 

.84583 

.99663 

53 

7 

.19988 

.20540 

.79460 

.99448 

8 

.15069 

.15508 

.84492 

.99561 

52 

8 

.20067 

.20621 

.79379 

.99446 

9 

.15157 

. 15598 

.84402 

.99569 

51 

9 

.20145 

.20701 

.79299 

.99444 

10 

9.15245 

9.15688 

10.84312 

9.99657 

SO 

10 

9.20223 

9.20782 

10.79218 

9.99442 

11 

.15333 

.15777 

.84223 

.99556 

49 

11 

.20302 

.20862 

.79138 

.99440 

12 

.15421 

.15867 

.84133 

.99564 

48 

12 

.20380 

.20942 

.79058 

.99a8 

13 

.15508 

.15956 

.84044 

.99552 

47 

13 

.20458 

.21022 

.78978 

.99486 

14 

.15596 

.16046 

.83954 

.99550 

46 

14 

.20535 

.21102 

.78898 

.99434 

15 

9.15683 

9.16135 

10.83865 

9.99548 

45 

15 

9.20613 

9.21182 

10.78818 

9.99482 

16 

.15770 

.16224 

.83776 

.99546 

44 

16 

.20691 

.21261 

.78739 

.99429 

17 

.15857 

.16312 

.83688 

.99545 

43 

17 

.20768 

.21341 

.7885« 

.99427 

18 

.16944 

.16401 

.83599 

.99543 

42 

18 

.20845 

.21420 

.78580 

.99425 

19 

.16030 

.16489 

.83511 

.99541 

41 

19 

.20922 

.21499 

.78501 

.99423 

20 

9.16116 

9.16577 

10.83423 

9.99539 

40 

20 

9.20999 

9.21578 

10.78423 

9.99421 

21 

.16203 

.16665 

.83335 

.99537 

39 

21 

.21076 

.21657 

.78343 

.99419 

22 

.16289 

.16753 

.83247 

.99535 

38 

22 

.21153 

.21736 

.78264 

.99417 

23 

.16374 

.16841 

.83159 

.99533 

37 

23 

.21229 

.21814 

.78186 

.99415 

24 

.16460 

.16928 

.83072 

.99532 

36 

24 

.21306 

.21893 

.78107 

.99413 

35 

9.16545 

9.17016 

10.82984 

9.99530 

35 

25 

9.21382 

9.21971 

10.78029 

9.99411 

26 

.16631 

.17103 

.82897 

.99528 

3i 

26 

.21458 

.22049 

.77951 

.99409 

27 

.16716 

.17190 

.82810 

.99526 

33 

27 

.21534 

.22127 

.77873 

.90407 

28 

.16801 

.17277 

.82723 

.99524 

32 

28 

.21610 

.22205 

.77795 

.99404 

29 

.16886 

.17363 

.82637 

.99522 

31 

29 

.21685 

.22283 

.77717 

.9M02 

30 

9.16970 

9.17450 

10.82550 

9.99520 

30 

30 

9.21761 

9.22361 

10.77639 

9.99400 

31 

.17055 

.17636 

.82464 

.99518 

29 

31 

.21836 

.22438 

.77562 

.99398 

32 

.17139 

.17622 

.^78 

.99517 

28 

32 

.21912 

.22516 

.77484 

.99396 

33 

.17223 

.17708 

.82292 

.99515 

27 

33 

.21987 

22593 

.77407 

.98394 

84 

. 17307 

.17794 

.82206 

.99513 

26 

34 

.22062 

! 22670 

.77330 

.90392 

as 

9.17391 

9.17880 

10.82120 

9.99511 

25 

35 

9.22137 

9.22747 

10.77258 

9.99890 

36 

.17474 

.17965 

.82035 

.99509 

24 

36 

.22211 

.22824 

.77176 

.99388 

87 

.17658 

.18051 

.81949 

.99507 

23 

37 

.22286 

.22901 

.77099 

.99885 

38 

.17641 

.18136 

.81864 

.99505 

22 

38 

.22361 

.22977 

.77023 

.99883 

39 

.17724 

.18221 

.81779 

.99503 

21 

39 

.22435 

.23054 

.76946 

.99881 

40 

9.17807 

9.18306 

10.81694 

9.99501 

20 

40 

9.22509 

9.23130 

10.76870 

9.99379 

41 

.17890 

.18391 

.81609 

.99499 

19 

41 

.22683 

.23206 

.76794 

.99S77 

42 

.17973 

.18475 

.81525 

.99497 

18 

42 

.22657 

.23283 

.76717 

.9W75 

43 

.18055 

.18560 

.81440 

.99495 

17 

43 

.22731 

.23359 

.76641 

.99872 

44 

.18137 

,18844 

.81356 

.99494 

16 

44 

.22805 

.23435 

.76566 

.99370 

45  9.18220 

9.18728 

10.81272 

9.99492 

15 

45 

9.22878 

9.23510 

10.76490 

9.98368 

46 

.18302 

.18812 

.81188 

.98490 

14 

46 

.22952 

.23586 

.76414 

.99866 

47 

.18383 

.18896 

.81104 

.99488 

13 

47 

.23025 

.23661 

.76339 

.99864 

48 

.18465 

.18979 

.81021 

.99486 

12 

48 

.23098 

.23737 

.76263 

.99362 

49 

.18547 

.19063 

.80937 

.99484 

11 

49 

.23171 

.23812 

.76188 

.99859 

50 

9.18628 

9.19146 

10.80854 

9.99482 

10 

50 

9.23244 

9.23887 

10.76113 

9.99357 

51 

.18709 

.19229 

.80771 

.99480 

9 

51 

.23317 

.23962 

.76038 

.99855 

52 

.18790 

.19312 

.80688 

.99478 

8 

52 

.23390 

.24037 

.76968 

.98353 

53 

.18871 

.19395 

.80605 

.99476 

7 

53 

.23462 

.24112 

.76888 

.99351 

54 

.18952 

.19478 

.80522 

.99474 

6 

54 

.23535 

.24186 

.76814 

.99848 

55 

9.19033 

9.19561 

10.80439 

9.99472 

5 

55 

9.23607 

9.24261 

10.75739 

9.98846 

56 

.19113 

.19643 

.80357 

.99470 

4 

66 

.23679 

.24335 

.76665 

.99844 

57 

.19193 

.19725 

.80275 

.99468 

3 

67 

.23752 

.24410 

.76690 

.98842 

58 

.19273 

.19807 

.80193 

.99466 

2 

58 

.23823 

.24484 

.75516 

.98840 

59 

.19353 

.19889 

.80111 

.99464 

1 

59 

.23895 

.24558 

.75442 

.98837 

60 

9.19433 

9.19971 

10.80029 

9.99462 

0 

60 

9.23967 

9.24632 

10.75368 

9.98835 

CoBlne. 

Ck>tang. 

Tang. 

1    Sine. 

1   '  ll~ 

Ooelne. 

a>tang. 

Tan?. 

Sine.    1 

81°  ^8 

♦Log  secant  — colog  cosine- 1  — log  cosine;  log  cosecant— colog  sine 
1  —  log  sine. 

£*.-Log  sec  80-  SC  -  10.00480.       Ex.-^l^  ,^^)^gW  "  10.8303C 


LOGARITHMIC  SINES,  ETC. 


181 


t,  Tanosnts.  Cotanobnts,  C08INB8. — (Cont'd.) 

(SBCANTS.  COSBCANT8.)* 


OoUDg.  1  Coalne.  1      ||  '  |    Sine.  |  Tan«. 

1  Ootang.  1  Cooine.  | 

10.753M    9.9«835 

60 

0 

9.28060 

9.28865 

10.71135 

9.99195 

60 

.7UM     .99333 

59 

1 

.28126 

.28933 

.71067 

.99192 

69 

.7S221 

.99331 

58 

2 

.28190 

.29000 

.71000 

.99190 

58 

.75147 

.99328 

67 

3 

.28264 

.29067 

.70933 

.99187 

57 

.75074 

.99326 

66 

4 

.28319 

.29134 

.70866 

.99186 

56 

10.75000 

9.99324 

55 

5 

9.28384 

9.29201 

10.70799 

9.99182 

55 

.74927 

.99322 

64 

6 

.28448 

.29268 

.70732 

.99180 

64 

.74854 

.99319 

63 

7 

.28512 

.29336 

.70665 

.99177 

53 

.74781 

.99317 

52 

8 

.28577 

.29402 

.70698 

.99175 

52 

.74708 

.99315 

61 

9 

.28641 

.29468 

.70632 

.99172 

61 

10.74835 

9.99313 

80 

10 

9.28705 

9.29535 

10.70465 

9.99170 

50 

.74583 

.99310 

49 

11 

.28769 

.29601 

.70399 

.99167 

49 

.74490 

.99308 

48 

12 

.28833 

.29668 

.70332 

.99165 

48 

.74418 

.99306 

47 

13 

.28896 

.29734 

.70266 

.99162 

47 

.74345 

.99304 

46 

14 

.28960 

.29800 

.70200 

.99160 

46 

10.74273 

9.99301 

45 

15 

9.29024 

9.29866 

10.70134 

9.99167 

45 

.74201 

.99299 

44 

16 

.29087 

.29932 

.70068 

.99165 

44 

.74139 

.99297 

43 

17 

.29150 

.29998 

.70002 

.99152 

43 

.74057 

.99294 

42 

18 

.29214 

30064 

.69936 

.99150 

42 

.73985 

.99292 

41 

19 

.29277 

.30130 

.69870 

.99147 

41 

10.73914 

9.99290 

40 

30 

9.29340 

9.30195 

10.69805 

9.99145 

40 

.73842 

.99288 

39 

21 

.29403 

.30261 

.69739 

.99142 

39 

.73771 

.99885 

38 

22 

.29466 

.30326 

.69674 

.99140 

38 

.73899 

.99283 

37 

23 

.29529 

.30391 

.69609 

.99137 

37 

.73828 

.99281 

36 

24 

.29591 

.30457 

.69543 

.99135 

36 

10.73557 

9.99278 

35 

35 

9.29664 

9.30622 

10.69478 

9.99132 

35 

.78488 

.99276 

34 

26 

.29716 

.30687 

.69413 

.99130 

34 

.73415 

.99274 

33 

27 

.29779 

.80662 

.69348 

.99127 

33 

.73345 

.99271 

32 

28 

.29841 

.30717 

.69283 

.99124 

32 

.73274 

.99269 

31 

29 

.29903 

.30782 

.69218 

.99122 

31 

10.73203 

9.99267 

30 

30 

9.29966 

9.30846 

10.69164 

9.99119 

30 

.73133 

.99264 

29 

31 

.30028 

.30911 

.69089 

.99117 

29 

.73063 

.99262 

28 

32 

.30090 

.30975 

.69026 

.99114 

28 

.73992 

.99260 

27 

33 

.30161 

.31040 

.68960 

.99112 

27 

.72922 

.99257 

26 

84 

.30213 

.31104 

.68896 

.99109 

26 

10.72852 

9.99255 

35 

35 

9.30275 

9.31168 

10.68832 

9.99106 

35 

.72782 

.99262 

24 

36 

.30336 

.31233 

.68767 

.99104 

24 

.72712 

.99250 

23 

37 

.30398 

.31297 

.68703 

.99101 

23 

.72843 

.99248 

22 

38 

.30459 

.31361 

.68639 

99099 

22 

.72573 

.99245 

21 

39 

.30621 

.31426 

.68576 

99096 

21 

10.72504 

9.99243 

30 

40 

9.30682 

9.31489 

10.68511 

9.99093 

30 

.72434 

.99241 

19 

41 

.30643 

.31562 

.68448 

.99091 

19 

.72365 

.99238 

18 

42 

.30704 

.31616 

.68384 

.99088 

18 

.72298 

.99236 

17 

43 

.30765 

.31679 

.68321 

.99086 

17 

.72227 

.99283 

16 

44 

.30826 

.31743 

.68257 

.99083 

16 

":?liS 

9.99231 

15 

45 

9.30887 

9.31806 

10.68194 

9.99080 

15 

.99229 

14 

46 

.80947 

.31870 

.68130 

99078 

14 

.72820 

.99226 

13 

47 

.81008 

.31933 

.68067 

.99075 

13 

.71961 

.99224 

12 

48 

.31068 

.31996 

.68004 

.99072 

12 

.71883 

.99221 

11 

49 

.31129 

.32059 

.67941 

.99070 

11 

10.71814 

9.99219 

10 

50 

9.31189 

9.32122 

10.67878 

9.99067 

10 

.71746 

.99217 

9 

51 

.31260 

.32185 

.67815 

.99064 

9 

.71877 

.99214 

8 

52 

.31310 

.32248 

.67752 

.99062 

8 

.71609 

.99212 

7 

68 

.31370 

.32311 

.67689 

.99059 

7 

.71841 

.99209 

6 

64 

.31430 

.32373 

.67627 

.99056 

6 

10.71473 

9.99207 

5 

55 

9.31490 

9.32436 

10.67564 

9.99054 

5 

.71406 

.99204 

4 

66 

.81649 

.32498 

.67502 

.99051 

4 

.71888 

.99202 

3 

67 

.31609 

.32561 

.67439 

.99048 

3 

.71270 

.99200 

2 

58 

.31669 

.32623 

.67377 

.99046 

3 

.71202 

.99197 

69 

.31728 

.32685 

.67315 

.99043 

1 

10.71185 

9.99196 

0 

60 

9.31788 

9.32747 

10.67253 

9.99040 

0 

'nuiC.       sine.   1 

'  1       1  0(Mlne.  1 

Coun«. 

Tang. 

Sine. 

~^ 

w 

78* 

oolog  cosine— 1  — log  cocnne;  log  cosecant  — colog  sine  — 

0«-  8(K  - 10.00733.      E*.— Log  cosec  10°-  30'  - 10.78937.  ^^^  ^  GoOqIc 


182 


9— PLANE  TRIGONOMETRY. 


6. — Logarithailc  Sines,  Tamobnts.  CoTi^GBNTs.  CotiVBS. — (Cont'd.) 
(Secants.  Cosecants.)* 
12°  *  13*» 


'  1   sine. 

Tang. 

Cotan«.  1  Coelne.  I      ||  '  |    Sine 

Tang. 

Couuig.  1  OoslncI 

9.31788 

9.32747 

10.67253 

9.99040 

60 

9.S6209 

9.36336 

10.63664 

9.98872 

40 

.31847 

.32810 

.67190 

.99038 

59 

.S5363 

.86394 

.63606 

.98869 

50 

.31907 

.32872 

.67128 

.99035 

58 

.35318 

.36452 

.63548 

.96867 

58 

.31966 

.32933 

.67067 

.99032 

57 

.86373 

.36509 

.63491 

.98864 

57 

.32025 

.32995 

.67005 

.99030 

56 

.35427 

.36566 

.65434 

.98861 

56 

9.32084 

9.33057 

10.66943 

9.99027 

55 

9.35481 

9.36624 

10.63376 

9.98868 

n 

.32143 

.33119 

.66881 

.99024 

54 

.35636 

.36681 

.63319 

.98865 

M 

.32202 

.83180 

.66820 

.99022 

53 

.35590 

.36738 

.63162 

.988S2 

53 

.32261 

.33242 

.66758 

.99019 

52 

.35644 

.36769 

.63305 

.98849 

62 

.32319 

.33303 

.66697 

.99016 

51 

.35698 

.36852 

.63148 

98846 

61 

9.32378 

9.33365 

10.66635 

9.99013 

SO 

9.35752 

9.36909 

10.63091 

9.98843 

SO 

.32437 

.33426 

.66574 

.99011 

49 

.35806 

.36966 

.63034 

.98840 

49 

.32496 

.33487 

.66513 

.99008 

48 

.35860 

.37023 

.62977 

.98837 

48 

.32553 

.33548 

.66452 

.99005 

47 

.35914 

.37080 

.62920 

.98834 

47 

.32612 

.33609 

.66391 

.99002 

46 

.85968 

.37137 

.62863 

.98831 

46 

9.32670 

9.33670 

10.66330 

9.99000 

45 

9.36022 

9.37193 

10.62807 

9.98828 

49 

.32728 

.33731 

.66269 

.98997 

44 

.36075 

.87250 

.62760 

.98825 

44 

.32786 

.83792 

.66208 

.98994 

43 

.36129 

.87306 

.62694 

.98822 

43 

.32844 

.33863 

.66147 

.98991 

42 

.36182 

.87363 

.62637 

.98819 

42 

.32902 

.33913 

.66087 

.98989 

41 

.36236 

.37419 

.62581 

.98816 

41 

30 

9.32960 

9.33974 

10.66026 

9.98986 

40 

20 

9.86289 

9.37476 

10.62624 

9.98813 

40 

21 

.33018 

.34034 

.65966 

.98983 

39 

21 

.36342 

.97532 

.62468 

.88810 

39 

22 

.33076 

.34095 

.65905 

.98980 

38 

22 

.36395 

.37588 

.62412 

.98807 

38 

23 

.33133 

.34155 

.65845 

.98978 

37 

23 

.36449 

.37644 

.62356 

.98804 

37 

24 

.33190 

.34215 

.65785 

.98975 

36 

24 

.36502 

.37700 

62300 

.98801 

36 

25 

9.33248 

9.34276 

10.65724 

9.98972 

35 

25 

9.36555 

9.37756 

lO! 62244 

9.98798 

as 

26 

.33305 

.34336 

.65664 

.98969 

34 

26 

.36608 

.37812 

.62188 

.98795 

34 

27 

.33362 

.34396 

.65604 

.98967 

33 

27 

.36660 

.37868 

.62132 

.98792 

33 

28 

.33420 

.84456 

.65544 

.98964 

32 

28 

.36713 

.37924 

.62076 

.98788 

32 

29 

.33477 

.34516 

.65484 

.98961 

31 

29 

.36766 

.37980 

.62020 

98786 

31 

30 

9.33534 

9.34576 

10.65424 

9.98958 

30 

30 

9.36819 

9.38035 

10.61965 

9.98783 

M 

31 

.33591 

.34635 

.65365 

.98955 

29 

31 

.86871 

.38091 

.61909 

.98780 

29 

32 

.33647 

.34695 

.65305 

.98953 

28 

32 

.36924 

.38147 

.61853 

.98777 

28 

33 

.33704 

.34755 

.65245 

.98950 

27 

33 

.36976 

.38202 

.61798 

.98774 

27 

34 

.33761 

.34814 

.65186 

.98947 

26 

34 

.37028 

.38257 

.61743 

.98771 

26 

35 

9.33818 

9.34874 

10.65126 

9.98944 

25 

35 

9.37081 

9.88313 

10.61687 

9.98768 

29 

36 

.33874 

.34933 

.65067 

.98941 

24 

36 

.37133 

.38368 

.61632 

.98765 

24 

37 

.33931 

.34992 

.65008 

.98938 

23 

37 

.37185 

.38423 

.61577 

.98762 

28 

38 

,33987 

.35051 

.64949 

.98936 

22 

38 

.37237 

.38479 

.61521 

.98709 

22 

39 

.34043 

.35111 

.64889 

.98933 

21 

39 

.37289 

.38534 

.61466 

.98766 

21 

40 

9.34100 

9.35170 

10.64830 

9.98930 

20 

40 

9.37341 

9.38589 

10.61411 

9.98753 

ao 

41 

.34156 

.35229 

.64771 

.98927 

19 

41 

.37393 

.38644 

.61356 

.98750 

19 

42 

.34212 

.35288 

.64712 

.98924 

18 

42 

.37445 

.38699 

.61301 

.98746 

13 

43 

.34268 

.35347 

.64653 

.98921 

17 

43 

.87497 

.38754 

.61246 

.98743 

IT 

44 

.34324 

.36405 

.64595 

.98919 

16 

44 

.37549 

.38808 

.61192 

.98740 

16 

45 

9.34380 

9.35464 

10.64536 

9.98916 

15 

45 

9.37600 

9.38863 

10.61137 

9.98737 

t» 

46 

.34436 

.35523 

.64477 

.98913 

14 

46 

.37652 

.38916 

.61082 

.96734 

14 

47 

.34491 

.35581 

.64419 

.98910 

13 

47 

.37703 

.38972 

.61028 

.98731 

13 

48 

.34547 

.35640 

.64360 

.98907 

12 

48 

.37755 

.39027 

.60973 

.98728 

12 

49 

.34602 

.35698 

.64302 

.98904 

11 

49 

.37806 

.39082 

.60918 

.98725 

11 

50 

9.34658 

9.35767 

10.64243 

9. 98901 

10 

50 

9.37858 

9.39136 

10.60864 

9.98782 

l« 

51 

.34713 

.35815 

.64185 

.98898 

9 

51 

.37909 

.39190 

.60810 

.98719 

9 

62 

.34769 

.35873 

.64127 

.98896 

8 

52 

.37960 

.39245 

.60755 

.98517 

8 

53 

.34824 

.35931 

.64069 

.98893 

7 

53 

.38011 

.39299 

.60701 

.98712 

7 

54 

.34879 

.35989 

.64011 

.98890 

6 

54 

.38062 

.39353 

.60647 

.98709 

6 

55 

9.34934 

9.36047 

10.63953 

9.98887 

5 

55 

9.38113 

9.39407 

10.60593 

9.98706 

S 

56 

.34989 

.36105 

.63895 

.98884 

4 

56 

.38164 

.39461 

.60539 

.98703 

4 

57 

.35044 

.36163 

.63837 

.98881 

3 

67 

.38215 

.39515 

.60485 

.98700 

3 

58 

.35099 

.36221 

.63779 

.98878 

2 

58 

.38266 

.39569 

.60431 

.98697 

2 

59 

.35154 

.36279 

.63721 

.98876 

I 

59 

.38317 

.39623 

.60377 

.98694 

60 

9.35209 

9.36336 

10.63664 

9.98872 

0 

60 

1 

9.38368 

9.39677 

10.60333 

9.98690 

O 

Cosine. 

Cotang. 

Tan^. 

Sine. 

~^ 

o 

Conine. 

Ootanir. 

Tang. 

Sine,   p 

77* 

*Log  secant  — colog  cosine— 1  — log  cosine;  log  cosecant -"colog  nne» 
1— log  sine. 

£«.— Log  sec  12<'-  80'-10.01042.      Ex.—Log  cosec  12°-  30'-10.e646e. 


LOGARITHMIC  SINES,  ETC. 


183 


5. — Locaritknic  Sines,  Tanosnts,  Cotangents.  Cosinbs. — (Coat'd.) 
(Secants.  Cosecants.)* 
I    14! 15! 


• 

Btne. 

1  Tang.  1  Ootang.  |  Costne.  | 

ILL 

1    81iie. 

1  Tang. 

1  Ootang.  1  Cosine. 

t'9.38W8 

9.29677 

10.60323 

9.98690 

60 

0 

9.41300 

9.42805 

10.67195 

9.98494 

60 

1 

.3841S 

.89731 

.60369 

.98687 

69 

1 

.41347 

.42856 

.67144 

.98491 

69 

2 

.39785 

.60215 

.98684 

68 

2 

.41394 

.42906 

.67094 

.98488 

68 

3 

!3S619 

.39838 

.60162 

.98681 

57 

3 

.41441 

.42957 

.67043 

.98484 

67 

4 

.3«70 

.39892 

.60108 

.98678 

56 

4 

.41488 

.43007 

.66993 

.98181 

66 

59.»O0 

9.39945 

10.50055 

9.98676 

55 

5 

9.41536 

9.43057 

10.56943 

9.98177 

55 

<    .3»70 

.39999 

.60001 

.98671 

54 

6 

.41582 

.43108 

.56892 

.98474 

64 

T 

.3«721 

.40052 

.59948 

.98668 

63 

7 

.41628 

.43158 

.66842 

.98471 

63 

S 

.28771 

.40106 

.59894 

.96665 

62 

8 

.41675 

.43208 

.66792 

.98467 

52 

» 

.38821 

.40159 

.59841 

.98662 

61 

9 

.41722 

.43258 

.56742 

98464 

51 

It 

9.38871 

9.40212 

10.59788 

9.98659 

50 

10 

9.41768 

9.43308 

10.56692 

9! 98460 

90 

11 

.38921 

.40266 

.69734 

.98656 

49 

11 

.41815 

.43358 

.56642 

.98457 

49 

11 

.3^71 

,40319 

.59581 

.98652 

48 

12 

.41861 

.43408 

.56692 

.98453 

48 

13 

.39021 

.40372 

.59628 

.98649 

47 

13 

.41908 

.43458 

.66542 

.98450 

47 

14 

.39071 

.40425 

.59575 

46 

14 

.41954 

.43508 

.56492 

.08447 

46 

15  9.3912!   1 

9.40478 

10.59522 

9! 98643 

45 

15 

9.42001 

9.43658 

10.56442 

9.98443 

45 

U 

.39170 

.40531 

.59469 

.98640 

44 

16 

.42047 

.43607 

.56393 

.98440 

44 

IT 

.39220 

.40584 

.59416 

.98636 

43 

17 

.42093 

.43657 

.56343 

.98436 

43 

IS 

.39270 

.40636 

.59364 

.98633 

42 

18 

.42140 

.43707 

.66293 

.98433 

42 

19 

.29319 

.40689 

.59311 

.98630 

41 

19 

.42186 

.43756 

.56244 

.98429 

41 

a9  9.3»3<9  1 

9.40742 

10. 59258 

9.98627 

40 

30 

9.42232 

9.43806 

10.66194 

9.98426 

40 

t\ 

.39418 

.40795 

.59205 

.98623 

39 

21 

.42278 

.43855 

.86145 

.98422 

39 

22 

.29407 

.40847 

.59153 

.98620 

38 

22 

.42324 

.43905 

.66095 

.98419 

38 

23 

.39517 

.40900 

.59100 

.98617 

37 

23 

.42370 

.43954 

.56046 

.98415 

37 

24 

.39566 

.40962 

.59048 

.98614 

36 

24 

.42416 

.44004 

.66996 

.98412 

36 

3f 

9.39615 

9.41005 

10.58995 

9.98810 

35 

25 

9.42461 

9.44053 

10.66947 

9.98409 

38 

2i 

.39664 

.41057 

.58943 

.98607 

34 

26 

.42607 

.44102 

.55898 

.98406 

34 

27 

.29713 

.41109 

.58891 

.98604 

33 

27 

.42663 

.44151 

.55849 

.98402 

33 

U 

.39762 

.41161 

.58839 

.98601 

32 

28 

.42699 

.44201 

.55799 

.98398 

33 

29 

.39811 

.41214 

.58786 

.98697 

31 

29 

.42644 

.44250 

.55750 

.98395 

31 

30 

9.29860 

9.41266 

10.58734 

9.98594 

30 

30 

9.42690 

9.44299 

10.65701 

9.98391 

30 

31 

.39909 

.41318 

.68682 

.98591 

29 

31 

.42736 

.44348 

..56652 

.98388 

29 

32 

.39958 

.41370 

.58630 

.98588 

28 

32 

.42781 

.44397 

.55603 

.98384 

28 

23 

.40006 

.41422 

.58578 

.98584 

27 

33 

.42826 

.44446 

.55554 

.98381 

27 

34    .40065 

.41474 

.68526 

.98581 

26 

34 

.42872 

.44496 

.56506 

.98377 

26 

35  9.40103 

9.41526 

10.68474 

9.98678 

25 

35 

9.42917 

9.44544 

10.55456 

9.98373 

35 

39 

.40152 

.41578 

.68422 

.98574 

24 

36 

.42962 

.44592 

.55408 

.98370 

24 

37 

.40200 

.41629 

.68371 

.98571 

23 

37 

.43008 

.44641 

.55359 

.98366 

23 

K 

.40249 

.41681 

.68319 

.98568 

22 

38 

.43053 

.44690 

.55310 

.98363 

23 

39 

.40297 

.41733 

.58267 

.98565 

21 

39 

.43098 

.44738 

.55262 

.98359 

21 

40 

9.40346 

9.41784 

10.58216 

9.98661 

20 

40 

9.43143 

9.44787 

10.55213 

9.98356 

20 

41 

.40394 

.41836 

.58164 

.98558 

19 

41 

.43188 

.44836 

.55164 

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19 

43 

.40443 

.41887 

.58113 

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18 

42 

.43233 

.44884 

.55116 

.98349 

18 

43 

.40490 

.41939 

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.98561 

17 

43 

.43278 

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.98345 

17 

44 

.40538 

.41990 

.58010 

.98548 

16 

44 

.43323 

.44981 

.55019 

.98342 

16 

45 

9.40596 

9.42041 

10.57959 

9.98545 

15 

45 

9.43367 

9.45029 

10.54971 

9.98338 

18 

46 

.40634 

.42093 

.67907 

.98541 

14 

46 

.43412 

.45078 

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.98334 

14 

47 

.40683 

.42144 

.57856 

.98538 

13 

47 

.43467 

.45126 

.54874 

.98331 

13 

4a 

.40730 

.42195 

.57805 

.98536 

12 

48 

.43602 

.45174 

.54826 

.98327 

12 

49 

.40778 

.42246 

.67754 

.98631 

11 

49 

.43546 

.45222 

.54778 

.98324 

11 

50 

9.40825 

9.42297 

10.57703 

9.98528 

10 

80 

9.43591 

9.45271 

10.54729 

9.9S320 

10 

SI 

.40873 

.42348 

.57652 

.98525 

9 

51 

.43635 

.45319 

.54681 

.98317 

9 

S2 

.40921 

.42399 

.57601 

.98521 

8 

62 

.43680 

.45367 

.54633 

.98313 

8 

53 

.40968 

.42450 

.57560 

.98518 

7 

63 

.43724 

.45415 

.54585 

.98309 

7 

54 

.41016 

.42501 

.67499 

.98515 

6 

54 

.43769 

.45463 

.54537 

.98306 

6 

55 

9.41063 

9.42553 

10.57448 

9. 98511 

5 

55 

9.43813 

9.45511 

10.54489 

9.98;}03 

8 

» 

.41111 

..42603 

.57397 

.98508 

4 

66 

.43857 

.45559 

.54441 

.98299 

4 

57 

.41158 

.42653 

.67347 

.98505 

3 

67 

.43901 

.45606 

.54394 

.98295 

3 

» 

.41205 

.42704 

.57296 

.98501 

2 

58 

.43946 

.45654 

.54346 

.98291 

2 

» 

.41252 

.42755 

.57245 

.98498 

1 

59 

.43990 

.46702 

.54298 

. 98288 

1 

«0,9.41300 

9.42805 

10.67196 

9.98494 

0 

60 

9.44034 

9.45750 

10.54250 

9.98284 

0 

icosme. 

Cotaag. 

-nuMP. 

Sine.    1  '  II      1  CoHlne. 

ICotam?. 

1    Tang. 

Sine.    1  ' 

76°  74° 

*Los  seamt— cok>g  oosine^l  — log  oosine;  log  cosecant » colog  sine*- 
1  —  loff  sine. 

Ei.— Log  Bee  14*-  3V  -  10.014W.      Ex.— Log  cosec  14<»-  ZV  - 10.60140. 


184 


^.— PLANE  TRIGONOMETRY. 


5. — Locarithmic  Sines,  Tanobnts.  Cotanobnts.  Cosimbs. — (Cont'd.) 

(SbCANTS.  CO8BCANTS.)* 

le^ ir 


JJ    sine. 

Tang.  lOotang.  |  Oodne.  |     ||  '  I    Sine.  |  Tang.  |  CJotang.  |  Ootfne. 

9.44034 

9.45750 

10.54260 

9.99284 

60 

0 

9.46594 

9.48534 

10.61466 

9.9806O 

« 

.44078 

.45797 

.64203 

.98281 

59 

1 

.46635 

.48579 

.51421 

.98056 

& 

.44122 

.45845 

.54155 

.98277 

68 

2 

.46670 

.48824 

.51376 

.98058 

5 

.44166 

.45893 

.54108 

.98273 

57 

3 

.46717 

.48669 

.51331 

.98048 

5 

.44210 

.45940 

54060 

.98270 

56 

4 

.46768 

.48714 

.51286 

.98044 

5 

9.44258 

9.45987 

10.54013 

9.98266 

55 

5 

9.46800 

9.48769 

10.61241 

9.9804O 

SJ 

.44297 

.46035 

V 53965 

.98262 

64 

6 

.46841 

.48804 

.61196 

.»te36 

5 

.44341 

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.63918 

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63 

7 

.46882 

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& 

.44385 

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.98256 

52 

8 

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.61106 

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6 

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.98251 

61 

9 

.46964 

.48939 

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.98025 

6 

9.44472 

9.46224 

10.53776 

9.98248 

50 

10 

9.47005 

9.48984 

10.51016 

9.98021 

54 

.44516 

.46271 

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.98244 

49 

11 

.47046 

.49029 

.60971 

.98017 

4 

.44559 

.46319 

.63681 

.98240 

48 

12 

.47086 

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.98013 

4 

44602 

.46366 

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.98237 

47 

13 

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4 

! 44646 

.46413 

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.98233 

46 

14 

.47168 

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4 

9.44689 

9.46460 

10.63540 

9.98229 

45 

15 

9.47209 

9.49207 

10.60793 

9.98001 

4J 

.44733 

.46507 

.63493 

.98226 

44 

16 

.47249 

.49252 

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4 

.44776 

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43 

17 

.47290 

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4 

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.98218 

42 

18 

.47330 

.49341 

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.97989 

4 

.44862 

.46648 

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.98216 

41 

19 

.47371 

.49385 

.60615 

.97980 

4 

30 

9.44905 

9.46694 

10.63306 

9.98211 

40 

30 

9.47411 

9.49430 

10.60570 

9.979S2 

<« 

21 

.44948 

.46741 

.63259 

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39 

21 

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3 

22 

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.63212 

.98204 

38 

22 

.47492 

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.50481 

.97974 

3 

23 

.45036 

.46835 

.63165 

.98200 

37 

23 

.47533 

.49663 

.50437 

.97970 

3 

24 

.45077 

.46881 

.63119 

.98196 

36 

24 

.47573 

.49607 

.50393 

.97966 

3 

35 

9.45120 

9.46928 

10.63072 

9.98192 

35 

35 

9.47613 

9.49652 

10.50348 

9.97962 

3J 

26 

.46163 

.46975 

.53025 

.98189 

34 

26 

.47654 

.49696 

.50304 

.97968 

3 

27 

.45206 

.47021 

.52979 

.98185 

33 

27 

.47694 

.49740 

.50260 

.97964 

a 

28 

.45249 

.47068 

.62932 

.98181 

32 

28 

.47734 

.49784 

.50216 

.97960 

3 

29 

.45292 

.47114 

.62886 

.98177 

31 

29 

.47774 

.49828 

.50172 

.97046 

3 

30 

9.45334 

9.47160 

10.52840 

9.98174 

30 

30 

9.47814 

9.49872 

10.60128 

9.97942 

34 

31 

.45377 

.47207 

.52793 

.98170 

29 

31 

.47854 

.49916 

.60084 

.97938 

2 

32 

.45419 

.47253 

.62747 

.98166 

28 

32 

.47894 

.49960 

.50040 

.97934 

2 

33 

.45462 

.47299 

.52701 

.98162 

27 

33 

.47934 

.50004 

.49996 

.97930 

2 

34 

.45504 

.47346 

.52654 

.98159 

26 

34 

.47974 

.50048 

.49952 

.97926 

2i 

35  9.45547 

9.47392 

10.52608 

9.98155 

35 

359.48014 

9.50092 

10.49908 

9.97922 

3] 

36 1   .45589 

.47438 

.52562 

.98151 

24 

36    .48054 

.50136 

.49864 

.97918 

2 

37 

.45632 

.47484 

.52516 

.98147 

23 

37'   .48094 

.50180 

.49820 

.97914 

2 

38 

.45674 

.47530 

.52470 

.98144 

22 

38'   .48133 

.50223 

.49777 

.97910 

Z 

39 

.45716 

.47576 

.52424 

.98140 

21 

39    .48173 

.50267 

.49783 

.97906 

2 

40 

9.45758 

9.47622 

10.52378 

9.98136 

30 

409.48213 

9.50311 

10.49689 

9.97902 

3< 

41 

.45801 

.47668 

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.98132 

19 

41;  .48252 

.50355 

.49645 

.97898 

42 

.45843 

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.52286 

.98129 

18 

42    .48292 

.50398 

.49602 

.97894 

li 

43 

.45885 

.47760 

.52240 

.98125 

17 

43 

.48332 

.50442 

.49558 

.97890 

1 

44 

.45927 

.47806 

.52194 

.98121 

16 

44 

.48371 

.50485 

.49515 

.97886 

11 

45 

9.45969 

9.47862 

10.52148 

9.98117 

15 

45 

9.48411 

9.50529 

10.49471 

9.97882 

l\ 

46 

.46011 

.47897 

.52103 

.98113 

14 

46 

.48450 

.50572 

.49428 

.97878 

1 

47 

.46053 

.47943 

.62057 

.98110 

13 

47 

.48490 

.50616 

.49384 

.97874 

II 

48 

.46095 

.47989 

.62011 

.98106 

12 

48 

.48529 

.60659 

.49341 

.07870 

1; 

49 

.46136 

.48036 

.51965 

.98102 

11 

49 

.48568 

.60703 

.49297 

.97866 

1 

50 

9.46178 

9.48080 

10.51920 

9.98098 

10 

50 

9.48607 

9.50746 

10.49254 

9.97861 

l< 

51 

.46220 

.48126 

.61874 

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9 

51 

.48647 

.50789 

.49211 

.97857 

52 

.46262 

.48171 

.61829 

.98090 

8 

52 

.48686 

.50833 

.49167 

.97853 

53 

.46303 

.48217 

.61783 

.98087 

7 

53 

.48725 

.50876 

.49124 

.97849 

54 

.46345 

.48262 

.61738 

.98083 

6 

54 

.48764 

.50919 

.49081 

.97845 

\ 

55 

9.46386 

9.48307 

10.51693 

9.98079 

5 

55  9.48803 

9.50962 

10.49038 

9.97841 

\ 

66 

.46428 

.48353 

.51647 

.98075 

4 

56 

.48842 

.61005 

.48995 

.97837 

67 

.46469 

.48398 

.61602 

.98071 

3 

57 

.48881 

.51048 

.48952 

.97833 

68 

.46511 

.48443 

.61557 

.98067 

2 

58 

.48920 

.61092 

.48908 

.97829 

59 

.46552 

.48489 

.51511 

.98063 

1 

59 

.48959 

.51135 

.48865 

.97826 

«0 

9.46594 

9.48534 

10.61466 

9.98060 

0 

«0 

9.48998 

9.61178 

10.48822 

9.97821 

{ 

n 

Coalne. 

Cotmng. 

Tang.   1    Sine. 

-Wv. 

Cosine. 

Cotang. 

Tanfe. 

Sine. 

—1 

*Log  secantocolog  cosine«>l— log  cosine;  log  co8e<»mt-"OoloK  sme- 


l~log  sine. 

Ex.— Log  sec  le^'-aC- 10.01826 


Ex.— Log  cosec  16*-  SC-lO.MOeC 


LOGARITHMIC  SINES,  ETC. 


185 


6. — Locaritkmic  Sliiet,  Tanobnts,  Cotanobnts.  Cosinbs.— (Cont'd.) 

(SbCANTS.  CO8BCANT8.)* 


*\   able.  1 

Twag.  1  Ootoag.  I  Cootne.  |      ||  '  |    Sine.  | 

Tang. 

Cotang.  1  Cosine.  1 

. 

9.48896 

9.51178 

10.48822 

9.97821 

00 

0 

9.51264 

9.53697 

10.46303 

9.97567 

60 

1 

.49037 

.51221 

.48779 

.97817 

59 

1 

.51301 

.53738 

.46262 

.97563 

59 

1 

.48078 

.51364 

.48736 

.97812 

58 

2 

.51338 

.53779 

.46221 

.97558 

58 

3 

.49115 

.51306 

.48694 

.97808 

57 

3 

.51374 

.53820 

.46180 

.97554 

67 

4 

.49158 

.51349 

.48651 

.97804 

56 

4 

.51411 

.53861 

.46139 

.97550 

66 

s 

9.49183 

9.51392 

10.48608 

9.97800 

8S 

5 

9.51447 

9.53902 

10.46098 

9.97545 

88 

« 

.49231 

.51435 

.48565 

.97796 

54 

6 

.51484 

.53943 

.97541 

54 

7 

.49289 

.51478 

.48522 

.97792 

53 

7 

.61520 

.53984 

! 46016 

.97636 

53 

t 

.48308 

.61530 

.48480 

.97788 

62 

8 

.51557 

.54025 

.45975 

.97532 

52 

» 

.49347 

.51563 

.48437 

.97784 

51 

9 

.61593 

.54066 

.45935 

.97528 

51 

!• 

9.49885 

9.51606 

10.48394 

9.97779 

80 

10 

9.51629 

9.54106 

10.45894 

9.97523 

50 

11 

.49434 

.51648 

.48352 

.97775 

49 

11 

.51666 

.54147 

.45853 

.97519 

49 

12 

.49482 

.51691 

.48309 

.97771 

48 

12 

.51702 

.54187 

.45813 

.97615 

48 

13 

.49680 

.51734 

.48266 

.97767 

47 

13 

.51738 

.54228 

.45772 

.97510 

47 

14 

.4909 

.51776 

.48224 

.97763 

46 

14 

.61774 

.54269 

.45731 

.97506 

46 

IS 

9.495n 

9.51819 

10.48181 

9.97759 

45 

15 

9.61811 

9.54309 

10.45691 

9.97501 

45 

IC 

.49815 

.51861 

.48139 

.97754 

44 

16 

.61847 

.54350 

.45650 

.97497 

44 

17 

.49854 

.61903 

.48097 

.97750 

43 

17 

.51883 

.54390 

!45610 

.97492 

43 

1& 

.49802 

.51946 

.48054 

.97746 

42 

18 

.51919 

.54431 

.45669 

.97488 

42 

1» 

.49730 

.51988 

.48012 

.97742 

41 

19 

.61955 

.54471 

.45529 

.97484 

41 

30 

9.49788 

9.62031 

10.47969 

9.97738 

40 

30 

9.61991 

9.54512 

10.45488 

9.97479 

40 

31 

.49808 

.62073 

.47927 

.97734 

39 

21 

.62027 

.54552 

.45448 

.97475 

39 

a 

.40844 

.52115 

.47885 

.97729 

38 

22 

.52063 

.54593 

.45407 

.97470 

38 

33 

.40882 

.52157 

.47813 

.97725 

37 

23 

.62099 

54633 

.45367 

.97466 

37 

34 

.49920 

.52200 

.47800 

.97721 

36 

24 

.52135 

! 54673 

.45327 

.97461 

36 

as 

9.49958 

9.52242 

10.47758 

9.97717 

35 

35 

9.52171 

9.54714 

10.45286 

9.97457 

35 

3S 

.49096 

.52284 

.47716 

.97713 

34 

26 

.52207 

.54754 

.45246 

.97453 

34 

37 

.50034 

.52326 

.47674 

.97708 

33 

27 

.52242 

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.45206 

.97448 

33 

28 

.50072 

.52368 

.47632 

.97704 

32 

28 

.52278 

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.45165 

.97444 

32 

39 

.90110 

.52410 

.47590 

.97700 

31 

29 

.52314 

.54875 

.45125 

.97439 

31 

Jt 

9.90148 

9.52452 

10.47548 

9.97696 

30 

30 

9.52350 

9.64915 

10.45085 

9.97435 

30 

31 

.90185 

.52494 

.47506 

.97691 

29 

31 

.52385 

.54955 

.45045 

.97430 

29 

32 

.90223 

.62536 

.47464 

.97687 

28 

32 

.52421 

,54995 

.45005 

.97426 

28 

32 

.90261 

.52578 

.47422 

.97683 

27 

33 

.52456 

.55036 

.44965 

.97421 

27 

34 

.50208 

.62620 

.47380 

.97679 

26 

34 

.52492 

.55075 

.44925 

.97417 

26 

33 

9.50336 

9.52661 

10.47339 

9.97674 

35 

38 

9.62527 

9.55115 

10.44885 

9.97412 

35 

33 

.60374 

.52703 

.47297 

97670 

24 

36 

52563 

.55155 

.44845 

.97408 

24 

37 

.60411 

.52745 

.47255 

.97666 

23 

37 

! 52698 

.55195 

.44805 

.97403 

23 

38 

.50449 

.52787 

.47213 

.97662 

22 

38 

.52634 

.55235 

.44765 

.97399 

22 

99 

.50486 

.52829 

.47171 

.97657 

21 

39 

.52669 

.65275 

.44725 

.97394 

21 

40 

9.50523 

9.52870 

10.47130 

9.97653 

30 

40 

9.52705 

9.55315 

10.44685 

9.97390 

30 

41 

.50661 

.52912 

.47088 

.97649 

19 

41 

.52740 

.55355 

.44645 

.97385 

19 

43 

.50608 

.52953 

.47047 

.97645 

18 

42 

.52775 

.55395 

.44605 

.97381 

18 

a 

.50635 

.52995 

.47005 

.97640 

17 

43 

.52811 

.55434 

.44566 

.97376 

17 

44 

.50673 

.63037 

.46963 

.97686 

16 

44 

.52846 

.65474 

.44526 

.97372 

16 

43 

9.50710 

9.63078 

10.46922 

9.97632 

15 

45 

9.52881 

9.55514 

10.44486 

9.97367 

15 

a 

.60747 

.63120 

.46880 

.97688 

14 

46 

.52916 

.65554 

.44446 

,97363 

14 

47 

.50784 

.63161 

.46839 

.97623 

13 

47 

.62951 

.55593 

.44407 

.97358 

13 

48 

.50821 

.53202 

.46798 

.97619 

12 

48 

.52986 

.55633 

.44367 

.97353 

12 

4* 

.9Ot08 

.53244 

.46756 

.97615 

11 

49 

.53021 

.55673 

.44327 

.97349 

11 

30 

9.50896 

9.63285 

10.46715 

9.97610 

10 

50 

9.53056 

9.55712 

10.44288 

9.97344 

10 

31 

.90933 

.53327 

.46673 

.97606 

9 

51 

.63092 

.55752 

.44248 

.97340 

9 

U 

.60970 

.58368 

.46632 

.97602 

8 

52 

.68126 

.55791 

.44209 

.97335 

8 

s 

.51007 

.53409 

.46591 

.97597 

7 

53 

.63161 

.55831 

.44169 

.97331 

7 

54 

.51043 

.53460 

.46560 

.97593 

6 

54 

.53196 

.55870 

.44130 

.97326 

6 

83 

9.51M0 

9.63498 

10.46508 

9.97589 

5 

55 

9.53231 

9.55910 

10.44090 

9.97322 

5 

58 

.51117 

.63533 

.46467 

.97584 

4 

56 

.53266 

.55949 

.44051 

,97317 

4 

97 

.61154 

.53574 

.46426 

.97580 

3 

67 

.53301 

.55989 

.44011 

,97312 

3 

58 

.51191 

.63615 

.46385 

.97576 

2 

58 

.53336 

.56028 

.43972 

.97308 

2 

98 

.51227 

.53656 

.46344 

.97571 

1 

59 

.53370 

.56067 

.43933 

.97303 

1 

« 

9.51264 

9.53697 

10.46303 

9  97567 

0 

60 

9.53405 

9.56107 

10.43893 

9,97299 

0 



Ooalne. 

Cotang. 

Taag. 

Bine.    1  '  1 

Coelne. 

Colang. 

Tang. 

Sine, 

~ 

•Log  secant *colog  cosine— 1- log  cosine;  log  cosecant— colog  sine  — 
£x.^^og  sec  18<>-  80^-10.03304.     Ex.— Log  cosec  18^-  30'-10.40852. 


186 


9.— PLANE  TRIGONOMETRY. 


5.— LiOgaritinnic  Sinet,  Tangents.  Cotanobnts.  Cosinbs. — (Cont'd.) 
(SscANTS.  Cosecants.)* 
20*^  21* 


'  1    sine.  1  Tang.  I  Ootang.  I  Coelne.  |      ||  '  1    Sine.  |  Taog.  I  OoUng.  I  Cosine.  | 

0 

9.63405 

9.56107 

10.43893 

9.97299 

60 

0 

9.65433 

9.68418 

10.41182 

9.97015 

60 

.53440 

.56146 

.43854 

.97294 

59 

1 

.55466 

.68466 

.41646 

.97010 

5f 

2 

.53476 

.56185 

.43815 

.97289 

58 

2 

.55499 

.68493 

.41607 

.97006 

58 

3 

.53509 

.S6224 

.43776 

.97285 

67 

3 

.55632 

.68631 

.41469 

.97001 

67 

4 

.63544 

.66264 

.43736 

.97280 

66 

4 

.55664 

.68569 

.41431 

.N9M 

66 

5 

9.53578 

9.56303 

10.43697 

9.97276 

55 

5 

9.55697 

9.68606 

10.41394 

9.N091 

15 

6 

.53613 

.56342 

.43658 

.97271 

64 

6 

.55630 

.68644 

.41356 

.96986 

54 

7 

.63647 

.56381 

.43619 

.97266 

63 

7 

.65663 

.68681 

.41319 

.96981 

53 

8 

.53682 

.56420 

.43580 

.97262 

52 

8 

.55695 

.68719 

.41281 

.96976 

62 

9 

.53716 

.56459 

.43541 

.97257 

51 

9 

.65728 

.68757 

.41243 

.96971 

61 

10 

9.53751 

9.56498 

10.43502 

9.97252 

50 

10 

9.65761 

9.68794 

10.41206 

9.96966 

50 

11 

.53785 

.66537 

.43463 

.97248 

49 

11 

.55793 

.58832 

.41168 

.96963 

49 

12 

.53819 

.56576 

.43424 

.97243 

48 

12 

.55826 

.58869 

.41131 

.96967 

46 

13 

.53854 

.66615 

.43385 

.97238 

47 

13 

.55858 

.68907 

.41093 

.96962 

47 

14 

.53888 

.66654 

.43346 

.97234 

46 

14 

.55891 

.58944 

.41056 

.96947 

48 

15 

9.53922 

9.S6693 

10.43307 

9.97229 

45 

15 

9.55923 

9.58981 

10.41019 

9.96942 

45 

16 

.53957 

.56732 

.43268 

.97224 

44 

16 

.55956 

.59019 

.40981 

.96937 

44 

17 

.53991 

.56771 

.43229 

.97220 

43 

17 

.55988 

.69056 

.40944 

.96932 

43 

18 

.54025 

.66810 

.43190 

.97215 

42 

18 

.56021 

.59094 

.40906 

.96937 

43 

19 

.54059 

.56849 

.43151 

.97210 

41 

19 

.56053 

.59131 

.40869 

.96022 

41 

30 

9.54093 

9.56887 

10.43113 

9.97206 

40 

30 

9.56085 

9.59168 

10.40832 

9.96917 

40 

21 

.64127 

.56926 

.43074 

.97201 

39 

21 

.56118 

.59205 

.40795 

.96912 

S9 

22 

.54161 

.56965 

.43035 

.97196 

38 

22 

.56150 

.59243 

.40767 

.96907 

Id 

23 

.54195 

.57004 

.42996 

.97192 

37 

23 

.56182 

.59280 

.40720 

.96903 

87 

24 

.54229 

.57042 

.42958 

.97187 

36 

24 

.56215 

.69317 

.40683 

.96898 

38 

25 

9.54263 

9.57081 

10.42919 

9.97182 

35 

35 

9.56247 

9.59354 

10.40646 

9.96893 

38 

26 

.54297 

.57120 

.42880 

.97178 

34 

26 

.56279 

.69391 

.40609 

.96888 

84 

27 

.54331 

.57158 

.42842 

.97173 

33 

27 

.56311 

.59429 

40571 

.96883 

S3 

28 

.54365 

.57197 

.42803 

.97168 

32 

28 

.56343 

.59466 

.40534 

.96878 

32 

29 

.54399 

.67235 

.42765 

.97163 

31 

29 

.56375 

.59503 

.40497 

.96873 

31 

30 

9.54433 

9.57274 

10.42726 

9.97159 

30 

30 

9.56408 

9.59540 

10.40460 

9.96868 

30 

31 

.54466 

.57312 

.42688 

.97154 

29 

31 

.56440 

.59577 

.40423 

.96863 

29 

32 

.54500 

.57351 

.42649 

.97149 

28 

32 

.56472 

.59614 

.40386 

.96868 

28 

83 

.54534 

.57389 

.42611 

.97145 

27 

33 

.56504 

.59661 

.40349 

.96853 

27 

34 

.54567 

.57428 

.42572 

.97140 

26 

34 

.56536 

.59688 

.40312 

.96848 

28 

35 

9.54601 

9.57466 

10.42534 

9.97135 

35 

35 

9.56568 

9.59725 

10.40275 

9.96843 

as 

36 

.54635 

.57504 

.42496 

.97130 

24 

36 

.56599 

.59762 

.40238 

.96838 

24 

37 

.54668 

.57543 

.42457 

.97126 

23 

37 

.56631 

.59799 

.40201 

.96833 

88 

38 

.54702 

.57581 

.42419 

.97121 

22 

38 

.56663 

.69835 

.40165 

.96828 

23 

39 

.54735 

.57619 

.42381 

.97116 

21 

39 

.56695 

.59872 

.40128 

.96823 

21 

40 

9.54769 

9.57658 

10.42342 

9.97111 

30 

40 

9.56727 

9.59909 

10.40091 

9.96818 

ao 

41 

.54802 

.57696 

.42304 

.97107 

19 

41 

.56759 

.59946 

.40054 

.96813 

It 

42 

.54836 

.57734 

.42266 

.97102 

18 

42 

.56790 

.59983 

.40017 

.96808 

18 

43 

.54869 

.57772 

.42228 

.97097 

17 

43 

.56822 

.60019 

.39981 

.96808 

17 

44 

.54903 

.57810 

.42190 

.97092 

16 

44 

.56854 

.60056 

.39944 

.96798 

18 

45 

9.54936 

9.57849 

10.42151 

9.97087 

15 

45 

9.56886 

9.60093 

10.39907 

9.96793 

II 

46 

.54969 

.57887 

.42113 

.97083 

14 

46 

.56917 

.60130 

.39870 

.96788 

14 

47 

.55003 

.57925 

.42075 

.97078 

13 

47 

.56949 

.60166 

.39834 

.96783 

12 

48 

.55036 

.57963 

.42037 

.97073 

12 

48 

.56980 

.60203 

.39797 

.96778 

12 

49 

.55069 

.58001 

.41999 

.97068 

11 

49 

.57012 

.60240 

.39760 

.96772 

11 

50 

9.55102 

9.58039 

10.41961 

9.97063 

10 

50 

9.57044 

9.60276 

10.39724 

9.96767 

10 

61 

.55136 

.58077 

.41923 

.97059 

9 

51 

.57075 

.60313 

.39687 

.96762 

9 

52 

.55169 

.58115 

.41885 

.97054 

8 

52 

.57107 

.60349 

.39651 

.98757 

8 

53 

.55202 

.58153 

.41847 

.97049 

7 

53!  .57138 

.60386 

.39614 

.96752 

7 

54 

.55235 

.58191 

.41809 

.97044 

6 

54!  .57169 

.60422 

.39578 

.96747 

8 

55 

9.55268 

9.58229 

10.41771 

9.97039 

5 

55  9.57201 

9.60459 

10.39541 

9.96742 

I 

56 

.55301 

.58267 

.41733 

.97035 

4 

56    .57232 

.60495 

.39505 

.96737 

4 

57 

.55334 

.58304 

.41696 

.97030 

3 

57    .57264 

.60532 

.39468 

.N732 

S 

58 

.55367 

.58342 

.41658 

.97025 

2 

58    .57295 

.60568 

.39432 

.96727 

2 

59 

.55400 

.58380 

.41620 

.97020 

1 

59    .57326 

.60605 

.39395 

.96722 

1 

60 

9.55433 

9.58418 

10.41582 

9.97015 

0 

60  9.57358 

9.60641 

10.39359 

9.96717 

0 

Oofllne.lCotang. 

Tang.    1    Sine.    1   '  | 

1  Cosine.  ICotang. 

Tang.  1  Sine. 

"^ 

9SP 

*Log  secant  — colog  cxjsine  » 1  -  log  cosine;  log  cosecant  ^oolog  sine «> 
1  — log  sine. 

£*.— Log  sec  2QP-  SC- 10.02841.      Ex.— Log  cosec  20*-  30^-10.45567. 


LOGARITHMIC  SINES,  ETC, 


187 


5. — Locarithmic  Sines,  Tanobnts,  Cotanobnts.  Cosinbs. — (Cont'd.) 

(SbCANTS.  CO8BCANT8.)* 


' 

Sine; 

Tang.  lOotang. 

Coalne. 

1  ' 

Sine 

Tang,  i  Cotaog.  j  Cosine. 

9.57358 

9.60641 

10.39859 

9.96717 

60 

0 

9.59188 

9  62785 

10.37215 

9.96401 

60 

.87389 

.60677 

.39323 

.96711 

59 

1 

.69318 

.37180 

.96397 

69 

.57430 

.60714 

.39288 

.96706 

58 

2 

.59247 

.62866 

.37145 

.96393 

58 

.87451 

.80750 

.89250 

.96701 

57 

8 

.59r7 

.63890 

.37110 

.96387 

67 

.57482 

.60786 

.39214 

96696 

66 

4 

.59307 

.62926 

.87074 

.96381 

66 

9.57514 

9.60823 

10.89177 

9.96691 

55 

8 

9.59336 

9.62961 

10.37039 

9.96376 

SS 

.57546 

.60859 

.39141 

.96686 

64 

6 

.59366 

.62996 

.37004 

.96370 

54 

.57576 

.60896 

.89106 

.96681 

63 

7 

.69396 

.63031 

.36969 

.96365 

53 

.57607 

.60931 

.39069 

.96676 

62 

8 

.59436 

.63066 

.36934 

.96360 

62 

.87838 

.60967 

.39033 

.96670 

51 

9 

.59466 

.63101 

.86899 

.96354 

61 

9.57689 

9.61004 

10.38996 

9.96666 

SO 

10 

9.59484 

9.63136 

10.36865 

9.96349 

SO 

11 

.^00 

.61040 

.38960 

49 

11 

.59614 

.63170 

.36830 

.96343 

49 

12 

.W731 

.61076 

.38924 

!  96656 

48 

12 

.69643 

.63206 

.36795 

.96338 

48 

U 

.57782 

.61113 

.38888 

47 

13 

.69573 

.63240 

.36760 

.96333 

47 

14 

.57793 

.61148 

.38853 

! 96646 

46 

14 

.59602 

.63276 

.36725 

.96327 

46 

IS 

9.^834 

0.61184 

10.38816 

9.96640 

48 

15 

9.59632 

9.63310 

10.36690 

9.96322 

4S 

u 

.57856 

.61220 

.38780 

.96634 

44 

16 

.59661 

.63345 

.36656 

.96316 

44 

17 

.57885 

.61256 

.38744 

.96629 

43 

17 

.69690 

.63379 

.36621 

.96311 

43 

11 

.57916 

.61292 

.88708 

96624 

42 

18 

.69720 

.63414 

.36586 

.96305 

42 

ir  .57»47 
M9.S7978 
21    .B8006 

.61328 

.38672 

.96619 

41 

19 

.69749 

.63449 

.36551 

.96300 

41 

9.61364 

10.88636 

9.96614 

40 

30 

9.69778 

9.63484 

10.36516 

9.96294 

40 

.61400 

.38600 

.96608 

39 

21 

.59808 

,63519 

.36481 

.96289 

39 

23    .58039 

.61436 

.38664 

.96603 

38 

22 

.59837 

63663 

.36447 

.96284 

38 

ZS    .58070 

.61472 

.88528 

.96598 

37 

23 

.59866 

.63588 

.36412 

.96278 

37 

24    .58101 

.61508 

.88492 

.96593 

36 

24 

.69895 

.63623 

.36377 

.96273 

36 

319.58131 

9.61544 

10.38456 

9.96688 

35 

25 

9.69924 

9.63667 

10.36343 

9.96267 

3S 

26,  .58162 

.61579 

.38421 

.96582 

34 

26 

.69964 

63692 

.36308 

.96262 

34 

ri  .58192 

.61615 

.38385 

.96sn 

33 

27 

.69983 

.63726 

.36274 

.96256 

33 

281  .58223 

.61651 

.88349 

.96672 

32 

28 

.60012 

.63761 

.36239 

.96251 

32 

29    .58153 

.61687 

.38313 

.96667 

31 

29 

.60041 

.63796 

.36204 

.96245 

31 

J0l9. 58284 

9.61722 

10.38278 

0.96562 

SO 

SO 

9.60070 

9.63830 

10.36170 

9.96240 

30 

31  i  .SOU 

.61756 

.38242 

.96556 

29 

31 

.60099 

.63865 

.36135 

.96234 

29 

32    .58345 

.61794 

.38206 

.96661 

28 

82 

.60128 

.63899 

.36101 

.96229 

28 

23    .58375 

.61830 

.38170 

.96646 

27 

33 

.60167 

.63934 

.36066 

.96223 

27 

34    .58406 

.61865 

.38135 

.96641 

26 

34 

.60186 

.63968 

.36032 

.96218 

26 

ii 

9.58436 

9.61901 

10.38096 

9.96636 

25 

35 

9.60216 

9.64003 

10.35997 

9.96212 

35 

18 

.58467 

.61936 

.88064 

.96530 

24 

36 

.60244 

.64037 

.35963 

.96207 

24 

r 

.50497 

.61972 

.38028 

.96625 

23 

37 

.60273 

.64072 

.35928 

.96201 

23 

38 

.58SX7 

.62008 

.37993 

.96530 

22 

38 

.60302 

.64106 

.35894 

.96196 

22 

39 

.58S57 

.62043 

.37967 

.96514 

21 

39 

.60331 

.64140 

.35860 

.96190 

21 

W 

9.58588 

9.62079 

10.37921 

9.96509 

30 

40 

9.60359 

9  64175 

10.35825 

9.96185 

30 

41 

.58618 

.62114 

.37888 

.96504 

41 

.60388 

.64209 

.35791 

.96179 

42 

.56648 

.62150 

.37860 

.96498 

18 

42 

.60417 

.64243 

.35767 

.96174 

43 

.58678 

.62185 

.r8l6 

.96493 

43 

.60446 

.64278 

.35722 

.96168 

44 

.58709 

.62221 

.37779 

.96488 

44 

.60474 

.64312 

.35688 

.96162 

45 

9.58739 

9.62256 

10.37744 

9.964S3 

48 

9.60503 

9.64346 

10.35654 

9.96157 

46    .58789 

.62292 

.87708 

.96477 

46 

.60632 

.64381 

.35619 

.96151 

47 

.58799 

.62327 

.37673 

.96472 

47 

.60561 

.64415 

.35585 

.96146 

48 

.5^29 

.62363 

.37638 

.96467 

48 

.60589 

.64449 

.35551 

.96140 

49 

.50869 

.633M 

.37602 

.96461 

49 

.60618 

.64483 

.35517 

.96135 

f» 

9.58889 

9.62433 

10.37567 

9.96466 

50 

9.60646 

9.64517 

10.35483 

9.96129 

51 

.58019 

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.96451 

61 

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53 

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52 

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a 

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63 

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M 

fljjQOO 

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54 

.60761 

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»% 

9!  99039 

9.62609 

10.37391 

•:Sai! 

55 

9.60789 

9.64688 

10.35312 

9.96101 

96 

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56 

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59 

.60903 

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9.62785 

10.37216 

9.96403 
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"^i 

^ 

9.60931 

9.64856 

10.35142 

9.96073 

J 

iooftne. 

Ootaog. 

Tang,   i 

'  II      1  Coalne. 

Cotang.j 

Tang. 

Sine. 

^ 

*Log  tecant^oolog  cosine-"  1— log  cosine:   log  cosecant— colog  sine  — 
^"^"^H  sine. 

£«.— Log  sec  ir-  80'-10.03438.     Ex.— hog  oosec  22«-  ZV^lCilUt, 


188 


-fLANt,   1  KlOUNUMt,!  KY , 


5.— LoKarithmk  Sinet,  Tanobnts.  Cotanobnts,  Cosinbs. — (Cont'd.) 

(SbCANTS.  CO8BCANT8.)* 


J_ 

Sine.      Tang.  |  Ootang.  i  Cosliie. 

II  ' 

Sine. 

Tang.  1  Ootang.  |  Oootne.! 

9.00031 

9.64858 

10.86142 

9.96073 

60 

0 

9.62595 

9.66867 

10.33133 

9.08728 

46 

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2 

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57 

3 

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57 

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56 

4 

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16 

9.61073 

9.65028 

10.34972 

9! 96046 

55 

5 

9.62730 

9.67032 

10.82968 

9.96698 

55 

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84 

6 

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64 

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53 

7 

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8 

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61 

9 

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61 

9.61214 

9.65197 

10.34803 

9.96017 

50 

10 

9.62865 

9.67196 

10.32804 

8.85668 

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49 

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48 

12 

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48 

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14 

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9.61354 

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10.34634 

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44 

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17 

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ao 

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9.66635 

10.84465 

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10.32476 

9.80608 

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24 

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9.61634 

9.66703 

10.34297 

9.95931 

35 

25 

9.63266 

9.67687 

10.32313 

9.86678 

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26 

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34 

26 

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84 

27 

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63319 

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32 

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29 

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31 

29 

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31 

30 

9.61773 

9.65870 

10.34130 

9.95902 

30 

30 

9.63398 

9.67860 

10.32160 

9.86M8 

36 

31 

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29 

31 

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32 

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33 

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as 

9.61911 

9.66038 

10.33962 

9.95873 

35 

35 

9.63531 

9.68012 

10.31988 

8.86618 

36 

36 

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24 

36 

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37 

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23 

37 

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21 

38 

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22 

38 

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21 

39 

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21 

39 

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n 

40 

9.62049 

9.66204 

10.33796 

9.95844 

20 

40 

9.63662 

9.68174 

10.81826 

9.86«n 

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41 

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42 

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43 

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43 

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44 

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H 

45 

9.62186 

9.66371 

10.33629 

9.95816 

45 

9.63794 

9.68336 

10.31664 

8.85668 

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46 

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46 

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SS 

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47 

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47 

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11 

48 

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48 

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a 

49 

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49 

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u 

50 

9.62323 

9.66637 

10.33463 

9.95786 

50 

9.63924 

9.68497 

10.31503 

8.88617 

16 

61     .62350 

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51 

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9 

52 

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62 

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iSMS 

4 

S3 

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53 

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f 

54 

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64 

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6 

55 

9.62459 

9.66702 

10.33298 

9.95757 

55 

9.64054 

9.68668 

10.31342 

8.08n7 

5 

66 

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56 

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4 

67 

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57 

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1 

68 

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68 

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oooro 

1 

69 

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59 

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SS5 

1 

60 

9.62596 

9.66867 

10.33133 

9.95728 

60 

9.64184 

9.68818 

10.31181 

« 

Cofltne. 

CJotanR. 

Tang. 

Sine. 

' 

~ 

Cosine. 

Ootang. 

Tang. 

StocL- 

"S 

"66^ 

♦Log  secant 
I— lop  sine. 

Ex. — ^Log  sec 


— colog  cosine— 1-log  cosine;  log  cooecant-^colos  aias* 
24*-  ZV  - 10.04098.      £«.— Log  coaec  34*-  W  -  ia883S7. 

Digitized  by  VjOOQ  IC 


LOGARITHMIC  SINES,  ETC. 


189 


Tanobnts,  Cotangbhts.  Cosinbs. — (Cont'd.) 
(Sbcants.iCosbcants.)  * 


Jl* 

27» 

31 

flbie. 

Tu«.    Ootang.  1 

Cootne.!      ||  '  I    Sine. 

Tang.  1  Cotang. 

OcMlne.1 

• 

3.34184 

9.68818 

10.31182 

9.95333 

60 

0 

9.35705 

9.70717 

10.29283 

9.94988 

60 

1 

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59 

I 

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59 

t 

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58 

2 

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58 

3 

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57 

3 

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57 

4 

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56 

4 

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.29159 

.94962 

66 

S 

3.343U 

9.38978 

10.31022 

9.95835 

39 

8 

9.65828 

9.70873 

10.29127 

9.94956 

85 

6 

.34333 

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.30990 

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54 

6 

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54 

T 

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53 

7 

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53 

g 

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52 

8 

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52 

f 

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61 

9 

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61 

'M 

9.34442 

9.39138 

10.30832 

9.95304 

90 

10 

9.36962 

9.71028 

10.28972 

9.94923 

SO 

11 

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49 

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49 

U 

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48 

12 

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48 

IS 

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47 

13 

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47 

14 

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46 

14 

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46 

U 

3.34971 

9.69298 

10.30702 

9.95273 

43 

18 

9.66076 

9.71184 

10.28816 

9.94891 

48 

1< 

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44 

16 

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44 

17 

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43 

17 

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i^ 

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42 

18 

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42 

If 

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41 

19 

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41 

» 

3.34338 

9.69457 

10.30543 

9.95242 

40 

30 

9.66197 

9.71339 

10.28661 

9.94858 

40 

n 

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39 

21 

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39 

n 

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88 

22 

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38 

n 

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37 

23 

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37 

14 

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36 

24 

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36 

as 

3.34823 

9.69315 

10.30386 

9.95211 

35 

35 

9.66319 

9.71493 

10.28507 

9.94826 

3$ 

as  .Mssi 

.69347 

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34 

26 

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84 

27 

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33 

27 

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33 

t8 

.34902 

.39710 

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32 

28 

.66392 

.71686 

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32 

S 

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31 

29 

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81 

3» 

9.34953 

9.39774 

10.30226 

9.95179 

30 

30 

9.66441 

9.71648 

10.28352 

9.94793 

30 

11 

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29 

31 

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29 

32 

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28 

32 

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28 

S3 

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27 

33 

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27 

34 

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.80100 

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26 

34 

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.28229 

.94767 

26 

3S 

3.39373 

9.39932 

10.30068 

9.95148 

35 

35 

9.66562 

9.71802 

10.28198 

9.94760 

35 

U 

.35154 

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24 

36 

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24 

37 

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23 

37 

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.94747 

23 

3S 

.35195 

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.95129 

22 

38 

.66634 

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.94740 

22 

H 

.35180 

.70058 

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.96122 

21 

39 

.66668 

.71925 

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21 

4t 

3.35206 

9.70089 

10.29911 

9.95116 

30 

40 

9.66682 

9.71955 

10.28045 

9.94727 

30 

41 

.39230 

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.29879 

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19 

41 

.66706 

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.28014 

.94720 

43 

fggffj^ 

.70152 

.29848 

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18 

42 

.66731 

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.94714 

«s 

!  39281 

.70184 

.29816 

.99097 

17 

43 

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44 

.88303 

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.29785 

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16 

44 

.68779 

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.27922 

.94700 

43 

9.39331 

9.70247 

10.29763 

9.95084 

15 

45 

9.66803 

9.72109 

10.27891 

9.94694 

43 

.33393 

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14 

46 

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47 

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13 

47 

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.27830 

.94680 

^ 

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.70341 

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96065 

12 

48 

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4» 

.35431 

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.29628 

! 95059 

11 

49 

.66899 

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.27769 

.94667 

m 

9.70404 

10.29596 

9.95052 

10 

50 

9.66922 

9.72262 

10.27738 

9. 94660 

u 

.35481 

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9 

61 

.66946 

.72293 

.27707 

.94654 

93 

.35906 

.70466 

.29534 

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8 

52 

.66970 

.72323 

.27677 

.94647 

93 

.35931 

.70498 

.29502 

.95033 

7 

63 

.66994 

.72354 

.27646 

.94640 

54 

.35666 

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.29471 

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6 

54 

.67018 

.72384 

.27616 

.94634 

SS 

9.39580 

9.70560 

10.29440 

9.95020 

5 

55 

9.67042 

9.72415 

10.27586 

9. 94627 

53 

.35605 

.70692 

.29408 

.95014 

4 

56 

.67066 

.72445 

.27555 

.94620 

57 

.35630 

.70623 

.29377 

.95007 

3 

67 

.67090 

.72476 

.27524 

.94614 

56 

.39666 

.70654 

.29346 

.95001 

2 

68 

.67113 

.72506 

.27494 

.94607 

53 

.35680 

.70386 

.29815 

.94995 

1 

69 

.67137 

.72537 

.27463 

.94600 

tfO 

9.69709 

9.70717 

10.23283 

9.94988 

0 

60 

9.67161 

9.72567 

10.27433 

9.94593 

~ 

Cosine. 

Oouuifd 

TMlg. 

Sine. 

n 

Cofllne. 

Cotang. 

Tang. 

Sine. 

""^ 

^ 

62« 

l-l 


*Log  secant—oolog  cosine— l~k>g  cosine;  log  cosecant— colog  sine— 
S.^^^ogsec  26«-»0'- 10.04821.     E«.— Log  cosec  26^- aV-lO.SWMT. 


190 


9.— PLANE  TRIGONOMETRY. 


6. — Locarithniic  Sines,  Tanobnts,  Cotanobnts,  Cobinss. — (Cont'd.) 
(Sbcants,  Cosbcants.)* 


28« 


JJ    sine. 

1  Tang.  1  Cotang.  1  Coelne.  |      11  '  |    Sine.  I  Tang.  |  Cotang.  |  Ocalne.  | 

0 

9.67161 

9.72667 

10.r433 

9.94693 

60 

0 

9.68857 

9.74876 

10.26626 

9.9418S 

« 

1 

.67185 

.72698 

.27402 

.94687 

69 

1 

.68680 

.74406 

.25696 

.94175 

s 

2 

.67208 

.72628 

.27872 

.94680 

58 

2 

.68603 

.74436 

.26M5 

.94168 

*c 

3 

.67232 

.72669 

.27341 

.94573 

57 

3 

.68625 

.74465 

.26636 

.94161 

s 

4 

.67256 

.72689 

.27311 

.94567 

56 

4 

.68848 

.74494 

.26506 

.94154 

5 

5 

9.67280 

9.72720 

10.27280 

9.94660 

55 

5 

9.68671 

9.74524 

10.26476 

9.94147 

5 

6 

.67303 

.72760 

.27260 

.94563 

64 

6 

.68694 

.74654 

.26446 

.94140 

9 

7 

.67327 

.72780 

.27220 

.94546 

53 

7 

.68716 

.74183 

.26417 

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3 

8 

.67350 

.72811 

.27189 

.94540 

62 

8 

.68739 

.74613 

.25387 

.94125 

1 

9 

.67374 

.72841 

.27169 

.94633 

61 

9 

.68762 

.74643 

.26357 

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i 

10 

9.67398 

9.72872 

10.27128 

9.94526 

50 

10 

9.68784 

9.74673 

10.25327 

9.94112 

S 

11 

.67421 

.72902 

.27058 

.94519 

49 

11 

.68807 

.74702 

.26298 

.94105 

A 

12 

.67445 

.72932 

.27068 

.94113 

48 

12 

.68829 

.74732 

.26268 

.M098 

4 

13 

.67468 

.72963 

.27037 

.94506 

47 

13 

.68852 

.74762 

.26238 

.94090 

4 

14 

.67492 

.72993 

.27007 

.94499 

46 

14 

.68875 

.74791 

.25209 

.94083 

H 

15 

9.67515 

9.73023 

10.26977 

9.94492 

45 

15 

9.68897 

9.74821 

10.26179 

9.94076 

4 

16 

.67539 

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.94485 

44 

16 

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.74851 

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4 

17 

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43 

17 

.68942 

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^ 

18 

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42 

18 

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^ 

19 

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41 

19 

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.74939 

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30 

9.67633 

9.73175 

10.26825 

9.94458 

40 

30 

9.69010 

9.74969 

10.26031 

9.94041 

4 

21 

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39 

21 

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..74998 

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i 

22 

.67680 

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38 

22 

.69055 

.75028 

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3 

23 

.67703 

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.94438 

37 

23 

.69077 

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: 

24 

.67726 

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.94431 

36 

24 

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] 

35 

9.67750 

9.73326 

10.26674 

9.94424 

35 

35 

9.69122 

9.75117 

10.24883 

9.94005 

J 

26 

.67773 

.73356 

.26644 

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34 

26 

.69144 

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i 

27 

.67796 

.73386 

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33 

27 

.69167 

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28 

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32 

28 

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29 

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31 

29 

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30 

9.67866 

9.73476 

10.26524 

9.94390 

30 

30 

9.69234 

9.76264 

10.24736 

9.93970 

i 

31 

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29 

31 

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32 

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28 

32 

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33 

.67936 

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27 

83 

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34 

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26 

34 

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35 

9.67982 

9.73627 

10.26373 

9.94365 

35 

35 

9.69345 

9.76411 

10.24589 

9.9S»4 

; 

36 

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24 

36 

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24569 

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37 

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23 

37 

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38 

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22 

38 

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39 

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21 

39 

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40 

9.68098 

9.73777 

10.26223 

9.94321 

30 

40 

9.69456 

9.76568 

10.24442 

9.98896 

41 

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19 

41 

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42 

.68144 

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18 

42 

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.93884 

43 

.68167 

.73867 

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.94300 

17 

43 

.69628 

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44 

.68190 

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16 

44 

.69545 

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45 

9.68213 

9.73927 

10.26073 

9.94286 

15 

45 

9.69567 

9.75706 

10.24295 

9.93862 

46 

.68237 

.73957 

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.94279 

14 

46 

.69589 

.75736 

.24265 

.93865 

47 

.68260 

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13 

47 

.69611 

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.24236 

.93847 

48 

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12 

48 

.69633 

.75793 

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49 

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11 

49 

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50 

9.68328 

9.74077 

10.26923 

9.94252 

10 

50 

9.69677 

9.75852 

10.24148 

9.93828 

61 

.68351 

.74107 

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9 

61 

.69699 

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52 

.68374 

.74137 

.25863 

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8 

52 

.69721 

.75910 

.24090 

.93811 

53 

.68397 

.74166 

.25834 

.94231 

7 

53 

.69743 

.75939 

.24061 

.93804 

64 

.68420 

.74196 

.25804 

.94224 

6 

54 

.69765 

.75969 

.24031 

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55 

9.68443 

9.74226 

10.25774 

9.94217 

5 

55 

9.69787 

9.75998 

10.24002 

9.93789 

56 

.68466 

.74256 

.25744 

.94210 

4 

56 

.69809 

.76027 

.23973 

67 

.68489 

.74286 

.26714 

.94203 

3 

57 

.69831 

.76056 

.23944 

.937T6 

58 

.68512 

.74316 

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2 

58 

.69853 

.76086 

.23914 

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69 

.68534 

.74345 

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1 

59 

.69875 

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60 

9.68657 

9.74375 

10.25626 

9.94182 

0    60 

9.69897 

9.76144 

10.23856 

9.96753 

Oodne.  Gotane. 

Tang. 

Sine. 

1  Cwdne. 

Cotang. 

Tsng. 

SIlMS.      f 

*Log 

secant "-colog  cosine— 1 

61"                                                                     < 
—log  cosine;  log  cosecant— colos  sine 

l~loRsinc 

Ex.—l 

x>gsec 

28«»-80'- 

-10.056 

10. 

E 

*.-Loi 

ccosec  i 

IS^'ZOr- 

-10.32 

i: 

GARITHMIC  SINES, 

ETC. 

»■ 

;,  Tanobkts,  C0TANOBNT8.  C08INB8. — (Cont'd.)                     yiv.    ^ 

(Sbcants.  Cosecants.)* 

V'-'\  '*  • 

'  '  '■'     ';\u 

*31o 

.    .-  •    .:.; 

.  1  CXMloc.  1      II  '  1    Bine.  I  Tan«r.  (  Ootan«:.  |  Cosine.  | 

^;,-.  .' 

9.W763 

60 

0 

9.71184 

9.77877 

10.22123 

9.93307 

«0 

.93746 

59 

I 

.71206 

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59 

t-    .   .-  .  ■    /• 

'"   '<- 

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58 

2 

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68 

y  ■'  ■■''".■ " 

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57 

3 

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57 

i   •     *  *.  .'.• 

■      .  '     ~" 

.98724 

56 

4 

.71268 

.77992 

.22008 

.93276 

66 

.      A 

9.93717 

55 

5 

9.71289 

9.78020 

10.21980 

9.93269 

55 

'; ';  -  :  • 

*         ■    .       -."**• 

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54 

6 

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54 

53 

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53 

7 

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.*:  -  *        •      ' 

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62 

8 

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52 

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51 

9 

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61             u-  ■    ■ : 

.    .w  - 

9.93680 

SO 

10 

9.71393 

9.78163 

10.21837 

9.93230 

80 

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11 

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48 

12 

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47 

13 

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47 

-  •:  "  -  ' 

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46 

14 

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46 

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45 

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45 

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■  V. 

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44 

16 

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44 

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43 

17 

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43             f.-  ■  .;  . 

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42 

18 

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42 

t     - 

•  •  jt"^ 

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41 

19 

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41 

r,-  ..     -. 

9.93606 

40 

30 

9.71602 

9.78448 

10.21552 

9.93154 

40 

^"4 

. .  *  ■ '  • 

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89 

21 

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39 

,-    • .   ^ 

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22 

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38                       %                ■ 

. '  Kf 

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37 

23 

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37 

?-•  •  ■  ■  .- 

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36 

24 

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36 

l-y  < 

'  *.'    '  ' 

9.93569 

35 

35 

9.71705 

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35 

V   ,   • 

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26 

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IJ 

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93554 

33 

27 

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r 

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32 

28 

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30 

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31 

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29 

}  • 

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28 

32 

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28 

s  . 

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33 

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34 

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}«> 

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28 

35 

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B.  78874 

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24 

36 

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37 

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22 

38 

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22 

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21 

39 

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30 

40 

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30 

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19 

41 

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19 

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42 

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18 

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17 

43 

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17 

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16 

44 

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16 

t-  '  '  ' 

9.93420 

15 

45 

9.72116 

d.79166 

10.20844 

9.92960 

18 

^  "^  ' .'- . 

■s"" 

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14 

46 

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14 

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13 

47 

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13 

k.        *  •" 

•■    *  ■  . 

.93397 

12 

48 

.72177 

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.92936 

12 

iv:  •..  • 

.93390 

11 

49 

.72198 

.79269 

.20731 

.92929 

11 

!*  ^  ^  •  ' 

y 

9.93382 

10 

50 

9.72218 

9.79297 

10.20703 

9.92921 

10 

.93375 

9 

61. 

.72238 

.79326 

.20674 

.92913 

9 

''  "^  ^  \"  * 

.93367 

8 

62 

.72259 

.79354 

.20646 

.92905 

8 

P 

.93360 

7 

53 

.72279 

.79382 

.20618 

.92897 

7 

>•_  • 

93362 

6 

54 

.72299 

.79410 

.20590 

.92889 

6 

9!  93344 

5 

55 

9.72320 

9.79438 

10.20562 

9.92881 

8 

.93337 

4 

66 

.72340 

.79466 

.20534 

.92874 

4 

.93329 

3 

67 

.72360 

.79495 

.20505 

.92866 

3 

■> 

.93322 

2 

68 

.72381 

.79623 

.20477 

.92858 

2 

.n314 

59 

.72401 

.79651 

.20449 

.92850 

1 

-.i    * 

9.93307 

0 

«0 

9.72421 

9.79679 

10.20421 

9.92842 

0 

t  » 

Sloe. 

— 

Cosine.   CotAHK. 

Tanif. 

Sine. 

~T 

osine— l—log  cosine;  log  cosecant— colog  sine— 
- 10.06468.      £«.— Log  cosec  80*>-  dV  - 10.20463. 


193 


Q.'-PLANE  TRIGONOMETRY. 


5. — Logaritlmlc  Sinet,  Tanobnts,  Cotangbnts,  CosiKBS.-^Cont'd.) 
(Sbcants.  Cosbcants.)* 
W* 33! 


♦ 

1    Sine. 

1   Tang. 

1  Ootang.  1  Cosine.  | 

1  ' 

Sine. 

1  Tang.  1  Ootang.  |  Cosine.  | 

0 

9.72421 

9.79S79 

10.10421 

9.92842 

60 

0 

9.73611 

9.81252 

10.18748 

9.92869 

1 

.72441 

.79607 

.20393 

.92834 

59 

] 

.78630 

.81279 

.18721 

.92351 

2 

.72461 

.79635 

.20365 

.92826 

68 

2 

.78660 

.81307 

.18693 

.92343 

3 

.72482 

.79663 

.20337 

.92818 

67 

3 

.78669 

.81335 

.18665 

.98835 

4 

.72502 

.79691 

.20309 

.92810 

56 

4 

.78689 

.81362 

.18638 

.02826 

5 

9.72622 

9.79719 

10.20281 

9.92803 

55 

5 

9.73708 

9.81390 

10.18610 

9.92318 

6 

.72542 

.79747 

.20263 

.92795 

64 

6 

.73727 

.81418 

.18582 

.92310 

7 

.72562 

.71776 

.20224 

.92787 

63 

7 

.73747 

.81446 

.18665 

.92302 

8 

.72582 

.79804 

.20196 

.92779 

62 

8 

.73766 

.81473 

.18627 

.92293 

9 

.72602 

.79832 

.20168 

.9r71 

51 

9 

.73786 

.81600 

.18500 

.92286 

10 

9.72622 

9.79860 

lO.SOUO 

9.92763 

80 

10 

9.72805 

9.81628 

10.18472 

9.92277 

11 

.72643 

.79888 

.20112 

.92756 

49 

11 

.73824 

.81556 

.18444 

.92269 

12 

.72663 

.79916 

.20084 

.92747 

48 

12 

.73843 

.81683 

.18417 

.92260 

13 

.72683 

.79944 

.20056 

.92739 

47 

13 

.73863 

.81611 

.18389 

.92252 

14 

.72703 

.79972 

.20028 

.92781 

46 

14 

.73882 

.81638 

.18362 

.92244 

15 

9.72723 

9.80000 

10.20000 

9.92723 

45 

15 

9.73901 

9.81666 

10.18334 

9.92236 

16 

.72743 

.80028 

.19972 

.92715 

44 

16 

.73921 

.81693 

.18307 

.92227 

17 

.72763 

.80056 

.19944 

.92707 

43 

17 

.73940 

.81721 

.18279 

.92219 

18 

.72783 

.80084 

.19916 

.92699 

42 

18 

.73969 

.81748 

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.92211 

19 

.72803 

.80112 

.19888 

.92691 

41 

19 

.73978 

.81776 

.18224 

.92202 

ao 

9.72823 

9.80140 

10.19860 

9.92683 

40 

ao 

9.739OT 

9.81803 

10.18197 

9.92194 

21 

.72843 

.80168 

.19832 

.92675 

39 

SI 

.74017 

.81831 

.18169 

.92186 

22 

.72863 

.80195 

.19805 

.92667 

38 

22 

.74036 

.81868 

.18142 

.92177 

23 

.72883 

.80223 

.19777 

.92669 

87 

23 

.74056 

.81886 

.18114 

.92169 

24 

.72902 

.80251 

.19749 

.92651 

36 

24 

.74074 

.81913 

.18087 

.92161 

35 

9.72922 

9.80279 

10.19721 

9.92643 

35 

35  9.74093 

9.81941 

10. 18059 

9.921S2     3 

26 

.72942 

.80307 

.19693 

.92636 

34 

26 

.74113 

.81968 

.18032 

.92144 

27 

.72962 

.80335 

.19665 

.92627 

33 

27 

.74132 

.81996 

.18004 

.92136 

28 

.72982 

.80363 

.19637 

.92619 

32 

28 

.74161 

.82023 

.17977 

.92127 

29 

.73002 

.80391 

.19609 

.92611 

31 

29 

.74170 

.82051 

.17949 

.92119 

30 

9.73022 

9.80419 

10.19581 

9.92603 

30 

30 

9.74189 

9.82078 

10.17922 

9.92111 

31 

.73041 

.80447 

.19653 

.92595 

29 

31 

.74208 

.82106 

.17894 

.92102 

32 

.73061 

.80474 

.19526 

.92587 

28 

32 

.74227 

.82133 

.17867 

.92094 

33 

.73081 

.80502 

.19498 

.92579 

27 

33 

.74246 

.82161 

.17839 

.92086 

34 

.73101 

.80530 

.19470 

.92571 

26 

34 

.74266 

.82188 

.17812 

.92077 

35 

9.73121 

9.80558 

10.19442 

9.92563 

35 

35 

9.74284 

9.82215 

10.17785 

9.92069 

36 

.73140 

.80586 

.19414 

.92555 

24 

36 

.74303 

.82243 

.17757 

.92060 

37 

.73160 

.80614 

.19386 

.92546 

23 

37 

.74322 

.82270 

. 17730 

.920S2 

38*  .73180 

.80642 

.19358 

.92538 

22 

38 

.74341 

.82298 

.17702 

.92044      2 

39    .73200 

.80669 

.19331 

.92530 

21 

39 

.74360 

.92325 

. 17675 

.92036     2 

40  9.73219 

9.80697 

10.19303 

9.92522 

30 

40 

9.74379 

9.82352 

10.17648 

9.98027     a 

41 

.73239 

.80725 

.19275 

.92514 

19 

41 

.74398 

.82380 

.17620 

.92018     1 

42 

.73269 

.80753 

.19247 

.92506 

18, 

42 

.74417 

.82407 

.17593 

.92010     1 

43 

.73278 

.80781 

.19219 

.92498 

171 

43 

.74436 

.82435 

.17666 

.98002      I 

44 

.73298 

.80808 

.19192 

.92490 

16l 

44 

.74455 

.82462 

.17538 

.91908     1 

45 

9.73318 

9.80836 

10.19164 

9.92482 

15 

45 

9.74474 

9.82489 

10.17511 

9.91085 

46 

.73337 

80864 

.19136 

.92473 

14 

46 

.74497 

.82517 

.17488 

.91076 

47 

.73357 

! 80892 

.19108 

.92465 

13  ,  47 

.74512 

.82544 

.17456 

.91968 

48 

.73377 

.80919 

.19081 

.92457 

12     48 

.74531 

.82571 

..17429 

.91959  , 

49 

.73396 

.80947 

.19053 

.92449 

11  .  49 

.74649 

.82599 

.17401 

.91951 

50 

9.73416 

9.80975 

10.19025 

9.92441 

10    50 

9.74568 

9.82626 

10.17374 

9.91942  ; 

51 

.73435 

.81003 

. 18997 

.92433 

9     51 

.74587 

.82653 

.17347 

.91994 

52 

.73455 

.81030 

.18970 

.92425 

8     52 

.74606 

.82681 

.17319 

.91925 

53 

.73474 

.81068 

.18942 

.92416 

7     53 

.74626 

.82708 

.17292 

.91917 

64    .73494 

.81086 

.18914 

.92408 

6     54 

.74644 

.82735 

.17266 

.91908 

55  9.73513 

9.81113 

10.18887 

9.92400 

5!   55 

9.74662 

9.82762 

10.17238 

9.91900 

56    .73533 

.81141 

.18859 

.92392 

4| 

56 

.74681 

.82790 

.17210 

.91891 

57 

.73552 

.81169 

.18831 

.92384 

3 

57'  .74700 

.82817 

.17188 

.91883 

58 

.73572 

.81196 

.18804 

.92376 

2, 

58    .74719 

.82844 

.17166 

.91874 

59 

.73591 

.81224 

.18776 

.92367 

1 

59    .74737 

.82871 

.17129 

.91896 

60  9.73611 

9.81262 

10.18748 

9.92359 

01 

60  9.74766 

9.82899 

10.17101 

9.91867 

Cosine. 

Cotang.    Tang. 

Sine. 

'  1 

ICoBlne. 

CoUBf. 

Tang. 

6liie. 

-1 

67^ 

a 

*Log  secant— colog  cosineal— log  cosine;  log  cosecant ■■coiQg  sine^ 

1— log  sine.  , 

Ex.— Log  sec  32<'-  8(r  - 10.07307.      Ex.— hog  cosec  820-  80"  - 10.2691^ 


LOGARITHMIC  SINES,  ETC. 


198 


8I» 


ft.^4<ocarlthHdc  Sines,  Tangbnts,  Cotanobnts.  Cosinbi . — (Cont'd.) 

(SbcAMTS.  C08BCANTS.)* 


' 

flIlM. 

1  rang. 

1  Cotang.  1  Oootne.  | 

1  ' 

Sine.  1  Tang. 

Cotang.  1  Cosine.  | 

t.T«TM 

9.82890 

lo.nioi 

9.91887 

50 

0 

9.75869 

9.84523 

10.15477 

9.91336 

60 

.T4n5 

.82926 

.17074 

.91849 

59 

1 

.76877 

.84660 

.15450 

.91328 

59 

.74m 

:82963 

.17047 

.91840 

58 

2 

.75895 

.84576 

.  .15424 

.91319 

58 

.74512 

.82980 

.17020 

.91832 

67 

8 

.75913 

84603 

.15397 

.91310 

57 

.74531 

.83008 

.16992 

.91823 

66 

4 

.75931 

! 84630 

.15370 

.91301 

56 

9.74150 

9.83035 

10. 16965 

9.91815 

BB 

B 

9.75949 

9.84657 

10.15343 

9.91292 

66 

.74855 

.83062 

.16938 

.91806 

54 

6 

.75967 

84684 

.15316 

.91283 

54 

.74887 

.83089 

.16911 

.91798 

53 

7 

.76986 

.84711 

.15389 

.91274 

53 

.74906 

.83117 

.16883 

.91789 

52 

8 

.76003 

.84738 

.15262 

.91266 

52 

.74524 

.83144 

.16856 

.91781 

51 

9 

.76021 

.84764 

.15236 

.91257 

51 

9.74948 

9.83171 

10.16829 

9.91772 

90 

10 

9.76039 

9.84791 

10.15209 

9.91248 

50 

.74961 

.83198 

.16802 

.91763 

49 

11 

.76067 

.84818 

.15182 

.91239 

49 

u 

.74980 

.83225 

.16775 

.91755 

48 

12 

.76075 

.84845 

.15155 

.91230 

48 

13 

.74909 

.83252 

.16748 

.91746 

47 

13 

.76093 

.84872 

.16128 

.91221 

47 

14 

.75017 

.8280 

.16720 

.91738 

46 

14 

.76111 

.84899 

.16101 

.91212 

46 

15 

9.75036 

9.88307 

10.16693 

9.91729 

45 

15 

9.76129 

9.84925 

10.15075 

9.91203 

45 

16 

.79054 

.83334 

.16666 

.91720 

44 

16 

.76146 

.84952 

.15048 

.91194 

44 

17 

.75073 

.S3361 

.16639 

.91712 

43 

17 

.76164 

.84979 

.15021 

.91185 

43 

U 

.75091 

.83388 

.16613 

.91703 

42 

18 

.76162 

.85006 

.14994 

.91176 

42 

19 

.75110 

.83415 

.16585 

.91695 

41 

19 

.76200 

.86033 

.14967 

.91167 

41 

^ 

9.75128 

9.83442 

10.16558 

9.91686 

40 

20 

9.76218 

9.85069 

10.14941 

9.91158 

40 

21 

.75147 

.83470 

.16530 

.91677 

39 

21 

.76236 

.85086 

.14914 

.91149 

39 

22 

.75165 

.83497 

.16603 

.91669 

38 

22 

.76263 

.85113 

.14887 

.91141 

38 

23 

.75184 

.83524 

.16476 

.91660 

37 

23 

.76271 

.85140 

.14860 

.91132 

37 

24 

.76302 

.83551 

.16449 

.91651 

36 

24 

.76289 

.85166 

.14834 

.91123 

36 

3S 

9.75221 

9.83578 

10.16423 

9.91643 

35 

25 

9.76307 

9.85193 

10.14807 

9.91114 

35 

H 

.75239 

.83605 

.16395 

.91634 

34 

26 

.76324 

.85220 

.14780 

.91105 

34 

27 

.75258 

.83632 

.16368 

.91635 

33 

27 

.76342 

.85247 

.14763 

.91096 

33 

2S 

.76276 

.83659 

.16341 

.91617 

32 

28 

.76360 

.85273 

.14727 

.91087 

32 

21 

.75294 

.83686 

.16314 

.91608 

31 

29 

.76378 

.85300 

.14700 

.91078 

31 

JO 

9.75313 

9.83713 

10.16287 

9.91599 

30 

30 

9.76395 

9.85327 

10. 14673 

9.91069 

30 

31 

.75831 

.83740 

. 16260 

.91591 

29 

31 

.76413 

.85354 

. 14646 

.91060 

29 

32 

.75860 

.83768 

.16232 

.91582 

28 

32 

.76431 

.85380 

. 14620 

.91051 

28 

33 

.79368 

.83795 

.16205 

.91573 

27 

33 

.76448 

.85407 

.14593 

.91042 

27 

34 

.75386 

.83822 

.16178 

.91565 

26 

34 

.76466 

.85434 

.14566 

.91033 

26 

» 

9.75405 

9.83649 

10.16151 

9.91556 

25 

35 

9.76484 

9.85460 

10.14540 

9.91023 

35 

U 

.75423 

.83876 

.16124 

.91547 

24 

36 

.76501 

.85487 

.14513 

.91014 

24 

37 

.75441 

.83903 

.16097 

.91538 

23 

37 

.76519 

.85514 

.14486 

.91005 

23 

3S 

.75459 

.83930 

.16070 

.91530 

22 

38 

.76537 

.85540 

.14460 

22 

3t 

.75478 

.83967 

.16043 

.91621 

21 

39 

.76564 

.85567 

.14433 

! 90987 

21 

40 

9.75496 

9.83984 

10.16016 

9.91512 

20 

40 

9.76572 

9.85594 

10.14406 

9.90978 

20 

41 

.75514 

.84011 

.15989 

.91504 

19 

41 

.76590 

.85620 

.14380 

.90969 

19 

42 

.75633 

.84038 

.15962 

.91495 

18 

42 

.76607 

.85647 

.14353 

.90960 

18 

43 

.75561 

.84065 

.15935 

.91486 

17 

43 

.76625 

.85674 

. 14326 

.90951 

17 

44 

.75569 

.84092 

.15908 

.91477 

16 

44 

.76642 

.85700 

.14300 

.90942 

16 

45 

9.75687 

9.84119 

10.15881 

9.91469 

15 

45 

9.76660 

9.85727 

10.14273 

9.90933 

15 

4C 

.79605 

.84146 

.15854 

.91460 

U 

46 

.76677 

.85754 

.14246 

.90924 

14 

47 

.75624 

.84173 

.15827 

.91451 

13 

47 

.76695 

.85780 

.14220 

.90915 

13 

4S 

.75642 

.84200 

.15800 

.91442 

12 

48 

.76712 

.85807 

.14193 

.90906 

12 

4» 

.75660 

.84227 

.15773 

.91433 

11 

49 

.76730 

.85834 

.14166 

.90896 

11 

50 

9.75678 

9.84254 

10.15746 

9.91425 

10 

50 

9.76747 

9.85860 

10.14140 

9.90887 

10 

SI 

.75696 

.84280 

.15720 

.91416 

9 

61 

.76765 

.85887 

.14113 

.90878 

9 

tt 

.75714 

.84307 

.15693 

.91407 

8 

52 

.76782 

.85913 

.14087 

.90869 

8 

53 

.75733 

.84334 

.15666 

.91398 

7 

53 

.76800 

.85940 

.14060 

.90860 

7 

M 

.75751 

.84361 

.15639 

.91389 

6 

54 

.76817 

.85967 

.14033 

.90851 

6 

55 

9.75769 

9.84888 

10.15613 

9.91381 

5 

65 

9.76835 

9.85993 

10. 14007 

9.90842 

5 

5i 

.75787 

.84415 

.15585 

.91372 

4 

66 

.76852 

.86020 

.13980 

.90832 

4 

57 

.75005 

.84442 

.15568 

.91363 

3 

67 

.76870 

.86046 

.13954 

.90823 

8 

58 

;;is? 

.84469 

.15531 

.91354 

2 

58 

.76887 

.86073 

.13927 

.90814 

2 

5« 

.84496 

.15504 

.91345 

1 

59 

.76904 

.86100 

.13900 

.90805 

1 

M 

9.75859 

9.84523 

10.15477 

9.91336 

0 

60 

9.76922 

9.86126 

10.13874 

9.90796 

0 

31 

CoHDe. 

Cotang. 

Iteig.   1    Bine. 

'II      1  Cosine.  ICotang. 

1    TaoK. 

Sine. 

3 

*Lqg  secant ""oolog  cosine— 1  — log  cosine:  log  cosecant -> colog  sine  — 
1— log  sine. 

&— Log  sec  34«»-  W - 10.08401.      £«.— Log  cosec  34'*-  30'  - 10.24687. 


194 


9.— PLANE  TRIGONOMETRY. 


6. — Lofaritiiiiilc  Slii«t,  Tangbnts,  Cotangents,  Cosinbs — (Cont'd.) 
(Sbcants,  Cosecants.)* 
dff*  3r 


'  1    Bine. 

1  Tang.  1  Ootang.  I  Ooaliie.|      II  '  I    Sine.  |  Tang.  |  Ootang. 

Oorine. 

~~ 

9.76922 

9.86126 

10.18874 

9.90796 

60 

0 

9.77946 

9.87711 

10.12289 

9.90286 

60 

.76989 

.86168 

.13847 

.90787 

59 

1 

.77963 

.87738 

.12262 

.90225 

59 

.76967 

.86179 

.13821 

.90777 

68 

2 

.77980 

.8n64 

.12239 

.90216 

68 

.76974 

.86206 

.13794 

.90768 

67 

3 

.77997 

.87790 

.12210 

.90206 

57 

.76991 

.86232 

.13768 

.90769 

66 

4 

.78013 

.87817 

.12183 

.90197 

56 

9.77009 

9.86259 

10.13741 

9.90750 

65 

5 

9.78030 

9.87843 

10.12157 

9.90187 

55 

.77026 

.86285 

.13715 

.90741 

64 

6 

.78047 

.87869 

.12131 

.90178 

54 

.77043 

.86312 

.13688 

.90731 

C3 

7 

.78063 

.87895 

.12105 

.90168 

53 

.77061 

.86338 

.18662 

.90722 

52 

8 

.78080 

.87922 

.12078 

.90159 

52 

.77078 

.86365 

.13635 

.90713 

61 

9 

.78097 

.87948 

.12062 

.90149 

61 

9.77095 

9.86392 

10.13608 

9.90704 

50 

10 

9.78113 

9.87974 

10.12026 

9.90139 

50 

.77112 

.86418 

.13682 

.90694 

49 

11 

.78180 

.88000 

.13000 

.90130 

49 

.77130 

.86445 

.13556 

.90685 

48 

12 

.781*7 

.88027 

.11973 

.90120 

48 

.77147 

.86471 

.13629 

.90676 

47 

13 

.78163 

.88053 

.11947 

.90111 

47 

.77164 

.86498 

.13502 

.90667 

46 

14 

.78180 

.88079 

.11921 

.90101 

46 

9.77181 

9.86524 

10.13476 

9".  90657 

45 

15 

9.78197 

9.88105 

10.11895 

9.90091 

48 

.77199 

.86651 

.13449 

.90648 

44 

16 

.78213 

.88131 

.11869 

.90082 

44 

.77216 

.86577 

.13423 

.90639 

43 

17 

.78230 

.88168 

.11842 

.90072 

43 

18 

.77233 

.86603 

.13397 

.90630 

42 

18 

.78246 

.88184 

.11816 

.90063 

42 

19 

.77260 

.86630 

.13370 

.90620 

41 

19 

.78263 

.88210 

.11790 

.90053 

41 

ao 

9.77268 

9.86656 

10. 13344 

9.90611 

40 

20 

9.78280 

9.88236 

10.11764 

9.90043 

40 

21 

.77285 

.86683 

. 13317 

.90602 

39 

21 

.78296 

.88262 

.11738 

.90034 

39 

22 

.77302 

.86709 

.13291 

.90592 

38 

22 

.78313 

.88289 

.11711 

.90024 

38 

23 

.77319 

.86736 

.13264 

.90583 

37 

23 

.78329 

.88316 

.11685 

.90014 

37 

24 

.77336 

.86762 

.13238 

.90574 

36 

24 

.78346 

.88341 

.11669 

.90005 

36 

25 

9.77353 

9.86789 

10.13211 

9.90566 

35 

25 

9.78362 

9.88367 

10.11633 

9.89995 

35 

2« 

.77370 

.86815 

.13185 

.90656 

34 

26 

.78379 

.88393 

.11607 

.89985 

34 

27 

.77387 

.86842 

.13158 

.90646 

83 

27 

.78395 

.88420 

.11580 

.89976 

33 

28 

.77406 

.86868 

.13132 

.90637 

32 

28 

.78412 

.88446 

.11564 

.89966 

33 

29 

.77422 

.86894 

.13106 

.90627 

31 

29 

.78428 

.88472 

.11628 

.89956 

31 

30 

9.77439 

9.86921 

10.13079 

9.90518 

30 

30 

9.78445 

9.88498 

10.11502 

9.89947 

30 

31 

.77466 

.86947 

.13053 

.90509 

39 

31 

.78461 

.88524 

.11476 

.89937 

29 

32 

.77473 

.86974 

.19026 

.90499 

28 

32 

.78478 

.88550 

.11450 

.89927 

38 

33 

.77490 

.87000 

.13000 

.90490 

27 

33 

.78494 

.88577 

.11423 

.89918 

27 

34 

.77507 

.87027 

.12973 

.90480 

26 

34 

.78510 

.88603 

.11397 

.89908 

26 

35 

9.77524 

9.87053 

10.12947 

9.90471 

25 

35 

9.78527 

9.88629 

10.11371 

9.89898 

38 

36 

.77541 

.87079 

. 12921 

.90462 

24 

36 

.78543 

.88665 

.11345 

.89888 

24 

87 

.77558 

.87106 

.12894 

.90462 

23 

37 

.78560 

.88681 

.11319 

.89879 

23 

38 

.77576 

.87132 

.12868 

.90443 

22 

38 

.78576 

.88707 

.11293 

.89869 

22 

39 

.77592 

.87168 

.12842 

.90434 

21 

39 

.78592 

.88733 

.11267 

.89859 

21 

40 

9.77609 

9.87186 

10.12815 

9.90424 

20 

40 

9.78609 

9.88759 

10.11241 

9.89849 

ao 

41 

.77626 

.87211 

.12789 

.90416 

19 

41 

.78625 

.88786 

.11214 

.89840 

19 

42 

.77643 

. 87238  • 

. 12762 

.90406 

18 

42 

.78642 

.88812 

.11188 

.89830 

18 

43 

.77660 

.87264 

.12736 

.90396 

17 

43 

.78658 

.88838 

.11162 

.89820 

17 

44 

.77677 

.87290 

.12710 

.90386 

16 

44 

.78674 

.88864 

.11136 

.89810 

16 

45 

9.77694 

9.87317 

10.12683 

9.90377 

15 

45 

9.78691 

9.88890 

fO. 11110 

9.89801 

15 

46 

.77711 

.87343 

.12657 

.90368 

14 

46 

.78707 

.88916 

.11084 

.89791 

14 

47 

.77728 

.87369 

.12631 

.90358 

13 

47 

.78723 

.88942 

.11068 

.89781 

13 

48 

.77744 

.87396 

.12604 

.90349 

12 

48 

.78739 

.88968 

.11032 

.89771 

12 

49 

.77761 

.87422 

.12578 

.90339 

11 

49 

.78766 

.88994 

.11006 

.89761 

11 

50 

9.77778 

9.87448 

10.12552 

9.90330 

10 

50 

9.78772 

9.89020 

10.10980 

9.897S2 

lO 

61 

.77795 

.87475 

. 12526 

.90320 

9 

51 

.78788 

.89046 

.10954 

.89742 

9 

52 

.77812 

.87501 

. 12499 

.90311 

8 

52 

.78805 

,89073 

.10927 

.89732 

8 

63 

.77829 

.87627 

.12473 

.90301 

7 

53 

.78821 

.89099 

.10901 

.89722 

7 

64 

.77846 

.87554 

.12446 

.90292 

6 

54 

.78837 

.89125 

.10875 

.89712 

6 

55 

9.77862 

9.87580 

10.12420 

9.90282 

5 

55 

9.78853 

9.89151 

10.10849 

9.89702 

5 

66 

.77879 

.87606 

.12394 

.90273 

4 

56 

.78869 

.89177 

.10823 

.89093 

4 

67 

.77896 

.87633 

.12367 

.90263 

3 

67 

.78886 

.89203 

.10797 

.89683 

3 

58 

.77913 

.87659 

.12341 

.90254 

2 

58 

.78902 

.89229 

.10771 

.89673         3 

69 

.n930 

.87685 

.12315 

.90244 

1 

59 

.78918 

.89255 

.10745 

.89663         1 

to 

9.77946 

9.87711  .10.12289 

9.90235 

0 

60 

9.78934 

9.89281 

10.10719 

9.80653        O 

'_ 

Coelne. 

Cotan«.i   Tang. 

Sine. 

'II 

Cosine. 

Cotang. 

Tang. 

Sine.        ' 

63° 

W 

*Log 
1  — lysine 

sccant-colog  cosine- 1 -log  cosine;  log  row 

icant— c( 

>log  sise— 

Ex.— I 

x)gsec 

8««»-  ac 

-10.094 

82. 

E 

X. — Log 

'  cosec  i 

je'-ac- 

-10.22 

Wl. 

LOGARITHMIC  SINES,  ETC. 


196 


5.— LogartthiBic  Siacs,  Tanobnts.  Cotanobnts,  Cosinm . — (Cont'd.) 

(Secants,  Cosbcants.)* 

^ 3?» 


'.    sine. 

Tanc  1  Ootanf.  ( Cooine.  | 

1  ' 

I    Sine. 

1  Tuig.  1  Ootang.  |  Ooelne.  | 

•'*.789}4 

9.89281 

10.10719 

9.89653 

00 

9.79887 

9.90837 

10.09163 

9.89050 

00 

ll  .78950 

.89307 

.10693 

.89643 

59 

.79903 

.90863 

.09137 

.89040 

59 

2    .T8BC7 

.89333 

.10667 

.89633 

68 

.79918 

.90889 

.09111 

.89030 

58 

3    .7890 

.89350 

.10641 

.89684 

57 

.79934 

.90914 

.09086 

.89020 

57 

4    .789f9 

.89385 

.10615 

.89614 

56 

.79950 

.90940 

.09060 

.89009 

56 

S  9.7»1S 

9.89411 

10.10589 

9.89604 

S$ 

9.79965 

9.90966 

10.09034 

9.88999 

55 

«;  .79831 

.89437 

.10563 

.89594 

54 

.79981 

.90992 

.09008 

.88989 

54 

;l  .79M7 

.89483 

.10537 

.89584 

53 

.79996 

.91018 

.08982 

.88978 

53 

61  .79M9 
9>  .TM7f 

.89489 

.10511 

.89674 

52 

.80012 

.91043 

.08957 

.88968 

52 

.89515 

.10486 

.89564 

61 

.80027 

.91069 

.08931 

.88958 

51 

IO,9.7M»5 

9.89541 

10.10459 

9.89554 

80 

10 

9.80043 

9.91095 

10.08905 

9.88948 

50 

11    .7flll 

.89587 

.10433 

.89544 

49 

u 

.80058 

.91121 

.08879 

.88937 

49 

12)  .71128 

.89508 

.10407 

.89534 

48 

12 

.80074 

.91147 

.08853 

.88927 

48 

131  .7fl44 

.89619 

.10381 

.89524 

47 

13 

.80089 

.91172 

.08828 

.88917 

47 

14I  .791M 

.89845 

.10355 

.89514 

46 

14 

.80105 

.91198 

.08802 

.88906 

46 

I5i9.7917< 

9.89871 

10.10329 

9.89504 

45 

15 

9.80120 

9.91224 

10.08776 

9.88896 

45 

H  .mn 

.89897 

.10303 

.89495 

44 

16 

.80136 

.91250 

.08750 

.88886 

44 

17    .79208 

.89723 

.10277 

.89485 

43 

17 

.80151 

.91276 

.08724 

.88875 

43 

IS|  .79224 

.89749 

.10251 

.89475 

42 

18 

.80166 

.91301 

.08699 

.88865 

42 

111  .79MO 

.89775 

.10225 

.89465 

41 

19 

.80182 

.91327 

.08673 

.88855 

41 

»l9.7ttS« 

9.89801 

10.10199 

9.89456 

40 

20 

9.80197 

9.91353 

10.08647 

9.88844 

40 

21    ,79372 

.89827 

.10173 

.89445 

39 

21 

.80213 

.91379 

.08621 

.88834 

39 

23    .79^8 

.89853 

.10147 

.89436 

38 

22 

.80228 

.91404 

.08596 

.88824 

38 

23   .79804 

.89879 

.10121 

.89425 

87 

23 

.80244 

.91430 

.08570 

.88813 

.37 

24   .79319 

.89905 

.10095 

.89415 

36 

24 

.80259 

.91456 

.08544 

.88803 

36 

^9.79925 

9.89931 

10.10069 

9.89405 

36 

25 

9.80274 

9.91482 

10.08518 

9.88793 

35 

3*\  .793S1 

.89957 

.10043 

.89395 

34 

26 

.80290 

.91507 

.08493 

.88782 

34 

27'  ,79897 

.89983 

.10017 

.89386 

33 

27 

.80305 

.91533 

.08467 

.88772 

33 

^  .793« 
2»J  .793M 

.90009 

.09991 

.89375 

32 

28 

.80320 

.91559 

.08441 

.88761 

32 

.90035 

.09965 

.89364 

31 

29 

.80336 

.91585 

.08415 

.88751 

31 

.^•19.79415 

9.90061 

10.09939 

9.89354 

30 

30 

9.80351 

9.91610 

10.08390 

9.88741 

30 

31    .79431 

.90886 

.09914 

.89344 

29 

31 

.80366 

.91636 

.08364 

.88730 

29 

33>  .79447 

.90112 

.09888 

.89334 

28 

32 

.80382 

.91662 

.88720 

28 

33;  .79403 

.90138 

.09862 

.89324 

27 

33 

.80397 

.91688 

.08312 

.88709 

27 

34i  .79478 

.90164 

.09836 

.89314 

26 

34 

.80412 

.91713 

.08287 

.88699 

26 

2SS.79494 

9.90190 

10.09810 

9.89304 

25 

35 

9.80428 

9.91739 

10.08261 

9.88688 

25 

3^1  .79810 

.90216 

.09784 

.89294 

24 

36 

.80443 

.91765 

.  08235 

.88678 

24 

Jg!  .79620 

.90242 

.09758 

.89284 

23 

37 

.80458 

91791 

.08209 

88668 

23 

^S  Imss 

.9(tt68 

.09732 

.89274 

22 

38 

.80473 

.91816 

.08184 

! 88657 

22 

.90294 

.09706 

.89264 

21 

39 

.80489 

.91842 

.08158 

.88647 

21 

««.799?3 
«j!.79n9 

9.90820 

10.09680 

9.89254 

ao 

40 

9.80504 

9.91868 

10.08132 

9.88636 

20 

.90348 

.09654 

.89244 

19 

41 

.80519 

.91893 

.08107 

.88626 

«3    .79108 
^i  .79821 

.90371 

.09629 

.89233 

18 

42 

.80534 

.91919 

.08081 

.88615 

.90397 

.09603 

.89223 

17 

43 

.80650 

.91945 

.08055 

.88605 

0^1  .7968 
^H.788S2 

.90423 

.09577 

.89213 

16 

44 

.80565 

.91971 

.08029 

.88594 

9.90449 

10.09551 

9.89203 

15 

45 

9.80580 

9.91996 

10.08004 

9.88584 

■el   .79888 
^2     79884 

.90475 

.09525 

.89193 

14 

46 

.80596 

.92022 

.07978 

.88573 

.90601 

.09499 

.89183 

13 

47 

.80610 

.92048 

.07952 

.88563 

M    .79889 

51  .Tins 

.90527 

.09473 

.89173 

12 

48 

.80625 

.92073 

.07927 

.88552 

.90663 

.09447 

.89162 

11 

49 

.80641 

.92099 

.07901 

.88542 

»<«.T9731 

a^    .79748 

9.90978 

10.09422 

9.89152 

10 

50 

9.80656 

9.92125 

10.07875 

9.88531 

.90604 

.09396 

.89142 

9 

61 

.80671 

.92150 

.07850 

.88521 

i»,     .79782 

.90830 

.09370 

.89132 

8 

52 

.80686 

.92176 

.07824 

.88510 

»1     .79ns 

.90688 

.09344 

.89122 

7 

53 

.80701 

.92202 

.07798 

.88499 

itff     '79781 

.90682 

.09318 

.89112 

6 

64 

.80716 

.92227 

.07773 

.88489 

»*«.79a89 

9.90708 

10.09293. 

9.89101 

5 

55 

9.80731 

9.92253 

10.07747 

9.88478 

m      -7968 

.90734 

.09266 

.89091 

4 

66 

.80746 

.92279 

.07721 

.88468 

ri    -79840 

.90759 

.09241 

.89081 

3 

67 

.80762 

.92304 

.076% 

.88457 

m      -798BC 

.90785 

.09215 

.89071 

2 

58 

.80777 

.92330 

.07670 

.88447 

0       '79871 

.90811 

.09189 

.89060 

1 

59 

.80792 

.92356 

.07644 

.88436 

pT'^-WB? 

9.90837 

10.09163 

9.89080 

0 

00 

9.80807 

9.92381 

10.07619 

9.88425 

OHtat.  Ootanc- 

Tftog. 

Sllie. 

Cosine. 

Cotang. 

Tang. 

Sine. 

z 

61** 
'•Log  tecant—colog  cooine— 1  — log  cosine;  log  cosecant  — colog  sine  — 

^loK  sec  3r-  ZV  - 10  10M6.     E*.— Log  coseft^ Md%  @(^^0.20586. 


IM 


9.^PLANE  TRIGONOMETRY. 


6.— Locarithmic  Sines,  Tanobnts,  Cotanobhts,  Cobinbs. — (Cont'd.) 
(Sbcants,  Cosbcants.)* 
40*      41^ 


'      Sine.  1  Tang.  I  Cotang.  |  Oortne.  |      ||  '  |    Sine. 

Tang.    Ootang.  i  Coelne.  I 

9.80807 

9.92381 

10.07619 

9.88425 

«0 

0 

9.81694 

9.93916 

10.06084 

9.87778    m 

.80822 

.92407 

.07693 

.88415 

69 

1 

.81709 

.93942 

.06058 

.Wm     51 

.80837 

.92433 

.07567 

.88404 

58 

2 

.81723 

.93967 

.06033 

.87766     51 

.80852 

.92458 

.07542 

.88394 

57 

3 

.81738 

.93993 

.87745     51 

.80867 

.92484 

.07516 

.88383 

56 

4 

.81762 

.94018 

!06988 

.87784     » 

9.80882 

9.92510 

10.07490 

9.88372 

S5 

6 

9.81767 

9.94044 

10.05956 

9.87721    5! 

.80897 

.92636 

.07466 

.88362 

54 

6 

.81781 

.94069 

.05931 

.877U     5 

.80912 

.92561 

.07439 

.88351 

53 

7 

.81796 

.94096 

.05905 

.87701     5 

.80927 

.92587 

.07413 

.88340 

52 

8 

.81810 

.94120 

.05880 

.87890     5 

.80942 

.92612 

.07388 

.88330 

51 

9 

.81826 

.94146 

.05854 

.87879     5 

9.80957 

9.92638 

10.07362 

9.88319 

50 

10 

9.81839 

9.94171 

10.05829 

9.87668    « 

.80972 

.92663 

.07337 

.88308 

49 

11 

.81854 

.94197 

.05803 

.87697     4 

.80987 

.92689 

.07311 

.88298 

48 

12 

.81868 

.94222 

.05778 

.87646     4 

.81002 

.9ri5 

.07285 

.88287 

47 

13 

.81882 

.94248 

.06762 

.87635     4 

.81017 

.92740 

.07260 

.88276 

46 

14 

.81897 

.94273 

.05727 

.87624     4 

9.81032 

9.92766 

10.07234 

9.88266 

45 

15 

9.81911 

9.94299 

10.05701 

9.87618    4 

.81047 

.92792 

.07208 

.88255 

44 

16 

.81926 

.94324 

.05676 

.87601     4 

.81061 

.92817 

.07183 

.88244 

43 

17 

.81940 

.94350 

.05660 

.87560     4 

.81076 

.92843 

.07157 

.88234 

42 

18 

.81955 

.94376 

.05625 

.87579     4 

.81091 

.92868 

.07132 

.88223 

41 

19 

.81969 

.94401 

.05599 

.87568  i 
9.87657     4 

20 

9.81106 

9.92894 

10.07106 

9.88212 

40 

20 

9.81983 

9.94426 

10.05574 

21 

.81121 

.92920 

.07080 

.88201 

39 

21 

.81998 

.94452 

.05548 

.87646      1 

22 

.81136 

.92945 

.07055 

.88191 

88 

22 

.82012 

.94477 

05623 

.87626     1 

23 

.81151 

.92971 

.07029 

.88180 

87 

23 

.82026 

.94603 

!05497 

.87524     : 

24 

.81166 

.92996 

.07004 

.88169 

36 

24 

.82041 

.94528 

.05472 

.87518     i 

25 

9.81180 

9.93022 

10.06978 

9.88158 

35 

25 

9.82055 

9.94654 

10.05446 

9.87501     J 

26 

.81195 

.93048 

.06952 

.88148 

34 

26 

.82069 

.94579 

.05421 

.87480     \ 

27 

.81210 

.93073 

.06927 

.88137 

33 

27 

.82084 

.94604 

.05396 

.87479     \ 

28 

.81225 

.93099 

.06901 

.88126 

32 

28 

.82098 

.94630 

.05370 

.87468     : 

29 

.81240 

.93124 

.06876 

.88115 

31 

29 

.82112 

.94655 

.05345 

.87457      ; 

30 

9.81254 

9.93150 

10.06850 

9.88105 

30 

30 

9.82126 

9.94681 

10.05319 

9.87446  J 
.87424      : 

31 

.81269 

.93176 

.06825 

.88094 

29 

31 

.82141 

.94706 

.05294 

32 

.81284 

.93201 

.06799 

.88083 

28 

32 

.82155 

.94732 

.05268 

.87422      : 

S3 

.81299 

.93227 

.06773 

.88072 

27 

33 

.82169 

.94757 

.05243 

.87412 

34 

.81314 

.93252 

.06748 

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26 

34 

.82184 

.94783 

.05217 

.87461 

359.81328 

9.93278 

10.06722 

9.88051 

25 

35 

9.82198 

9.94808 

10.05192 

9.87290     7 

36 

.81343 

.93303 

.06697 

.88040 

24 

36 

.82212 

.94834 

.05166 

.87278     1 

37 

.81358 

.93329 

.06671 

.88029 

23 

37 

.82226 

.94859 

.05141 

.87267 

38 

.81372 

.93354 

.06646 

.88018 

22 

38 

.82240 

.94884 

.05116 

.87256 

39 

.81387 

.93380 

.06620 

.88007 

21 

39 

.82255 

.94910 

.05090 

.87246 

40 

9.81402 

9.93406 

10.06594 

9.87996 

20 

40 

9.82269 

9.94935 

10.05065 

9.87224     : 

41 

.81417 

.93431 

.06669 

.87985 

19 

41 

.82283 

.94961 

.05039 

.87222 

42 

.81431 

.93457 

.06543 

.87975 

18 

42 

.82297 

.94986 

.05014 

.87211 

43 

.81446 

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.87964 

17 

43 

.82311 

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.04988 

.87260 

44 

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.93508 

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16 

44 

.82326 

.95037 

.04963 

.8726t 

45 

9.81475 

9.93533 

10.06467 

9.87942 

15 

45 

9.82340 

9.95062 

10.04938 

9.87277 

46 

.81490 

.93559 

.06441 

.87931 

14 

46 

.82354 

.95088 

.04912 

.87266 

47 

.81505 

.93584 

.06416 

.87920 

13 

47 

.82368 

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.04887 

.87265 

48 

.81519 

.93610 

.06390 

.87909 

12 

48 

.82382 

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.87262 

49 

.81534 

.93686 

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.87898 

11 

49 

.82396 

.95164 

.04836 

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50 

9.81549 

9.93661 

10.06339 

9.87887 

10 

50 

9.82410 

9.95190 

10.04810 

9.87211 

51 

.81563 

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9 

51 

.82424 

.96215 

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52 

.81578 

.93712 

.06288 

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8 

52 

.82439 

.95240 

.04760 

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53 

.81592 

.93738 

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7 

53 

.82453 

.95266 

.04734 

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54 

.81607 

.93763 

.06237 

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6 

54 

.82467 

.95291 

.04709 

.87in 

65 

9.81622 

9.93789 

10.06211 

9.87833 

6 

55 

9.82481 

9.95317 

10.04683 

9.271M 

56 

.81636 

.93814 

.06186 

.87822 

4 

66 

.82495 

•.95342 

.04658 

.mvm 

67 

.81651 

.93840 

.06160 

.87811 

3 

57 

.82509 

.95368 

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58 

.81666 

.93865 

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.87800 

2 

58 

.82523 

.95393 

.04607 

.wnm 

59 

.81680 

.93891 

.06109 

.87789 

1 

59 

.82537 

.95418 

.04582 

.87119 

60 

9.81694 

9.93916 

10.06084 

9.87778 

0 

60 

9.82651 

9.95444 

10.04666 

9.87..7   1 

Coaine. 

Cotang. 

Tang. 

Sine. 

~^ 

Coelne.  |  Ckitaog. 

Tang. 

Sine,    I 

49° 

\ 

*Log  secant— colog  cosine  — 1  — log  cosine;  log  cosecant— oolog  sin« 
1  — log  sine. 

Ex.—ljog  sec  40°-  SC-  10.11896.     £a:.— Log  cosec  40*»-  SO'- 10.187^ 


LOGARITHMIC  SINES,  ETC,  1« 

I.— Locvitlmilc  Sines,  Tamosnts.  Cotanobnts,  Cosinbs.— <Cont*d.) 

(Secants.  Cosecants.)* 

r 43» 


'1  8bMu 

Tang.  1  Ootan^  |  CcMliie. 

1 

1  ' 

Sine. 

1  Tune. 

1  Ootang.  1  Cofllne. 

! 

•'iSESU 

8.05444 

10.04566 

9.87107 

60 

9.83378 

9.96966 

10.03084 

9.86413 

00 

li  .82S6S 

.OMif 

.04531 

.87096 

59 

.83392 

.96991 

.03009 

.86401 

59 

V  .8tf7f 

.05495 

.04505 

.87085 

58 

.83405 

.97016 

.03984 

.86389 

58 

i{  .asm 

.06620 

.04480 

.87073 

57 

.83419 

.97042 

.03958 

.86377 

67 

.05545 

.04455 

.87062 

66 

.83433 

.97067 

.02933 

86366 

56 

ILSill 

9.06671 

10.04439 

9.87050 

55 

9.83446 

9.97092 

10.02908 

9!  86354 

68 

(  ,8MS9 

.96698 

04404 

.87039 

54 

.83459 

.97118 

.02882 

.86342 

54 

71  .et49 

.96823 

! 04378 

.87028 

53 

.83473 

.97143 

.02857 

.86330 

53 

s  ato 

.05047 

.04353 

.87016 

52 

.83486 

.97168 

.02832 

.86318 

53 

»  .82in 

.95073 

.04338 

.87006 

51 

.83500 

.97193 

.02807 

.86306 

51 

ll».8Mtl 

9.05098 

10.04303 

9.86993 

50 

9.83513 

9.97219 

10.02781 

9.86295 

50 

li   .«706 

.95723 

.04277 

.86983 

49 

.83527 

.97244 

.02766 

.86283 

49 

12,  .«nif 

.05748 

.04252 

.86970 

48 

.83540 

.97269 

.02731 

.86271 

48 

U'  .0733 

.95774 

.04226 

.86959 

47 

.83554 

.97295 

.or  05 

.86259 

47 

14  .«747 

.96799 

.64201 

.86947 

46 

.83567 

.97320 

.02680 

.86247 

46 

U<9.eK761 

9.95825 

10.04175 

9.86836 

45 

9.83581 

9.97345 

10.02656 

9.86235 

45 

11   .8S77S 

.95850 

.04150 

.86934 

44 

.83594 

.97371 

.02629 

.86223 

44 

171  .S7tt 

.95875 

.04125 

.86913 

43 

.83608 

.97396 

.02604 

.86211 

43 

u  .szsn 

.95901 

.04099 

.86903 

42 

.83621 

.97421 

.02579 

.86200 

43 

1»  .SUA 

.04074 

.86890 

41 

.83634 

.97447 

.02553 

.86188 

41 

M9.8S80 

9.' 95952 

10.04048 

9.86879 

40 

ao 

9.83648 

9.97472 

10.02528 

9.86176 

40 

21    .OS44 

.95077 

.04023 

.86867 

39 

21 

.83661 

.97497 

.02503 

.86164 

39 

n\  ,ma% 

.90002 

.03998 

.86855 

38 

22 

.83674 

.97523 

.02477 

.86152 

38 

n  .wot 

.90028 

.03973 

.86844 

37 

23 

.83688 

.97548 

.02452 

.86140 

87 

U  .BMB 

.90053 

03947 

.86833 

36 

24 

.83701 

.97573 

.02427 

.86128 

36 

2I,9.828M 

0.90078 

10.03922 

9.86831 

35 

28 

9.83715 

9.97598 

10.02402 

9.86U6 

35 

3|l    SStlS 

.90104 

.03886 

.86809 

34 

26 

.83728 

.97624 

.02376 

.86104 

34 

r    .8027 

.90129 

.03871 

.86798 

33 

27 

.83741 

.97649 

.02351 

.86092 

33 

tt   .SMI 

.90155 

.03045 

.86786 

32 

28 

.83756 

.97674 

.02326 

.86080 

33 

2ti  .»»» 

.90180 

.03820 

.86775 

31 

29 

.83768 

.97700 

.02300 

.86068 

31 

M».ttWS 

0.90205 

10.03795 

9.86763 

30 

30 

9.83781 

9.97725 

10.02276 

9.86056 

30 

3i;  .81983 

.96231 

.03769 

.86752 

29 

31 

.83795 

.97750 

.02250 

.86044 

29 

12'  .8Z9M 

.96256 

.03744 

.86740 

28 

32 

.83808 

.97776 

.02224 

.86032 

28 

n\  .81010 

.96201 

.03719 

.86728 

27 

33 

.83821 

.97801 

.02199 

.86020 

27 

h'  .8M23 

.96307 

.03693 

.86717 

26 

34 

.83834 

.97826 

.02174 

.86008 

26 

3S».83«37 

9.96333 

10.03668 

9.86705 

28 

36 

9.83848 

9.97851 

10.02149 

9.85996 

35 

U    .8M61 

.96357 

.03643 

.86694 

24 

36 

.83861 

.97877 

.02123 

.85984 

24 

ri  .83085 

.96383 

.03617 

.86682 

23 

37 

.83874 

.97902 

.02098 

.85972 

23 

tr  .S078 

.03593 

.86670 

22 

38 

.83887 

.97927 

.02073 

.85960 

22 

39;  .8IM2 

[96433 

.03567 

.86659 

21 

39 

.83901 

.97953 

.02047 

.86948 

4»9.Si06 

9.96459 

10.03541 

9.86647 

ao 

40 

9.83914 

9.97978 

10.02022 

9.85936 

ao 

41  .smo 

.96484 

.08516 

.86635 

19 

41 

.83927 

.98003 

.01997 

.85924 

421  .S3133 

.96510 

.03490 

.86624 

18 

42 

.83940 

.98029 

.01971 

.85912 

C'  .81147 

.96635 

.03465 

.86612 

17 

43 

.83954 

.98054 

.01946 

.85900 

44  .m<i 

.96560 

03440 

.86600 

16 

44 

.83967 

.98079 

.01921 

.85888 

48  9.881T4 

9.96586 

10!03414 

9.86589 

16 

45 

9.83980 

9.98104 

10.01896 

9. 85876 

4e,  .83186 

.96611 

.03389 

.86577 

14 

46 

.83993 

.98130 

.01870 

.8.^864 

«<  .88203 

.96636 

.03364 

.86665 

13 

47 

.84006 

.98155 

.01845 

.85851 

M  .83215 
'4^  .88221 

.96663 

.03338 

.86554 

12 

48 

.84020 

.98180 

.01820 

.85839 

.03313 

.86542 

11 

49 

.84033 

.98206 

.01794 

.85827 

■Of.  88348 

9!96713 

10.03288 

9.86530 

10 

50 

9.84046 

9.98231 

10.01769 

9.85815 

»,  .88318 

.96738 

.03262 

.86518 

9 

51 

.84059 

.98256 

.01744 

.85803 

B  .smo 

.96763 

.03237 

.86507 

8 

52 

.84072 

.98281 

.01719 

.85791 

13'  .83283 

.96788 

.03212 

.86495 

7 

53 

.84085 

.98307 

.01693 

.85779 

m  .83287 
■TO.  83310 

.96814 

.03186 

.86483 

6 

54 

.84098 

.98332 

.01668 

.85766 

9.96839 

10.03161 

9.86472 

8 

65 

9.84112 

9.98357 

10.01643 

9.85754 

m\  .81334 

.96864 

.03136 

.86460 

4 

56 

.84125 

.98383 

.01617 

.85742 

Jr    .8038 

.96890 

.03110 

.86448 

3 

67 

.84138 

.98408 

.01592 

.85730 

m  .8^51 

.96915 

.03085 

.86436 

2 

58 

.84151 

.98433 

.01567 

.85718 

SO^  .8M5 

.96940 

.03060 

.86425 

1 

59 

.84164 

.98458 

.01542 

.85706 

00^8078 

9.96966 

10.03034 

9.86413 

0 

60 

9.84177 

9.98484 

10.01516 

9.85693 

lOortne. 

Oouag. 

Tang. 

Sine. 

'  11      1  Coilne.  1  CoUng. 

1    Tang. 

Sine.   1  ' 

L~ 


Al^ ^ ~^  40« 

Log  secant— colog  cosine— 1— log  cosine;  log  cosecant ^colog  sine  — 

S.^iDg  sec  42»-  aC- 10.13237.      Ex.— Log  cosec  42*-  30^- 10.17032. 


198 


Q.—PLANE  TRIGONOMETRY. 


6. — Logarithniic  Sines,  Tangents.  Cotanobnts,  Cosinbs. — (Concl'd.) 
(Sbcants,  Cosbcants.) 
44! 44  *> 


' 

Sloe. 

Tans.    Ootang.  |  Codoe. 

[ 

_u 

Sine. 

TKog.  1  Ootang.  | 

OoBlDe.l 

0 

9.84177 

9.98484 

10.01516 

9.85693 

60 

30 

9.84566 

9.99242 

10.00758 

9.86324 

1 

.84190 

.98509 

.01491 

.85681 

59 

31 

.84579 

.99267 

.00733 

.85312 

2 

.84203 

.98534 

.01466 

.85669 

58 

32 

.84592 

.99293 

.00707 

.8S399 

3 

.84216 

.98560 

.01440 

.85657 

67 

33 

.84605 

.99318 

.00682 

.85287 

4 

.84229 

.98585 

.01415 

.85645 

56 

34 

.64618 

.99343 

.88274 

6 

9.84242 

9.98610 

10.01390 

9.85632 

65 

35 

9.84630 

9.99368 

10!00632 

9.86302 

6 

.84265 

.98635 

.01365 

.85620 

54 

36 

.84643 

.99394 

.00606 

.81950 

7 

.84269 

.98661 

.01339 

.85608 

53 

37 

.84656 

.99419 

.00581 

.85237 

8 

.84282 

.98686 

.01314 

.85596 

52 

38 

.84669 

.99444 

.00556 

.85225 

9 

.84295 

.98711 

.01289 

.85583 

51 

39 

.64682 

.99469 

.00531 

.85212 

10 

9.84308 

9.98737 

10.01263 

9.85571 

50 

40 

9.84694 

9.99496 

10.00505 

9.8S300 

11 

.84321 

.98762 

.01238 

.85559 

49 

41 

.84707 

.99520 

.00480 

.85187 

12 

.84334 

.98787 

.01213 

.85547 

48 

42 

.84720 

.99545 

.00455 

.85175 

13 

.84347 

.98812 

.01188 

.85534 

47 

43 

.84733 

.99570 

.00430 

.85102 

14 

.84360 

.98838 

.01162 

.85522 

46 

44 

.84745 

.99596 

.00404 

.85150 

15 

9.84373 

9.98883 

10.01137 

9.85510 

45 

45 

9.84758 

9.99621 

10.00379 

9.85137 

16 

.84385 

.98888 

.01112 

.85497 

44 

46 

.84771 

.99646 

.00354 

.85125 

17 

.84398 

.98913 

.01087 

.85485 

43 

47 

.84784 

.99672 

.00328 

.85112 

18 

.84411 

.98939 

.01061 

.85473 

42 

48 

.84796 

.99697 

.00303 

.85100 

19 

.84424 

.98964 

.01036 

.85460 

41 

49 

.84809 

.99722 

.00278 

.85087 

20 

9.84437 

9.98989 

10.01011 

9.85448 

40 

50 

9.84822 

9.99747 

10.00253 

9.85074 

21 

.84450 

.99015 

.00985 

.85436 

39 

51 

.84835 

.99773 

.00227 

22 

.84463 

.99040 

.00960 

.85423 

38 

52 

.84847 

.99798 

.00202 

.86049 

23 

.84476 

.99065 

.00935 

.85411 

37 

53 

.84860 

.99823 

.00177 

.86037 

24 

.84489 

.99090 

.00910 

.85399 

36 

54 

.84873 

.99848 

.00152 

.85024 

2S 

9.84503 

9.99116 

10.00884 

9.85386 

35 

55 

9.84885 

9.99874 

10.00126 

9.85012 

26 

.84515 

.99141 

.00859 

.85374 

34 

56 

.84898 

.99899 

.00101 

.84999 

27 

.84528 

.99166 

.00834 

.85361 

33 

57 

.84911 

.99924 

.00076 

.84986 

28 

.84540 

.99191 

.00809 

.85349 

32 

58 

.84923 

.99949 

.00051 

.84974 

29 

.84553 

.99217 

.00783 

.85337 

31 

69 

.84936 

.99976 

.00025 

.84961 

30 

9.84566 

9.99242 

10.00758 

9.85324 

30 

60 

9.84949 

10.00000 

10.00000 

9.84949 

' 

Ooslne.  ICotaog. 

TanK. 

Sine.    1  ' 

Ooelne. 

Ootang. 

Tang. 

Sine.    1  ' 

45° 

45 

5a. — ^Tablb  for  Finding  the  Logarithmic  Sines  and  Tangbnts  or 

Small  Angles. 

[Values  of  5  and  T  in  Formiilas  Below.*) 


*  Log  sin  i4— log  A  (seconds) +S. 


Lo^Wi'^^^k 


(seconds) +r. 


ERICAL  TRIGONOMETRY. 

I  —Spherical  Trigonometry,  in  its  broadest  sense, 
of  spherical  pyramids;  and,  more  directly,  of  the 
pherical  pyramids. 

ical  p3jamid  (Fig.  1)  is  a  triangular  pyramid  cut 
Dter  of  the  sphere  being  the  apex  of  the  pyramid, 
ice  forming  the  base.  T^e  base  is  therefore  bounded 
',ks. 

5  is  a  term  applied  to  the  outline  of  the  base  of  a 

amid;  thus.  Fig.  i,  A  B  C  A  iA  b,  spherical  triangle. 

rrigonometry  are  confined  usually  to  the  solution  of 

tie  practical  application  leads  us  into  the  fields  ot 

id  Astronomy. 

:tions  or  quantities  in  any 

allows  (Fig.  1):    Radius,  r;  ^/'  I^V  q 


A 

a 


B 

b 
bt 


C 
c 

Cl 


ius  as  unity,  and  remember- 
:les  are  proportional  to  the 
angles,  it  is  seen  that  the 
to  six  primary  functions. 
1  angles  A,  B.  C,  and  the 
Three  of  these 'must  be 
ve  the  other  three.  The 
c,  are  always  shown  on  the 
I  in  Figs.  2  and  3. 

1  Triangles. — ^The  spherical 
is  a  right  spherical  triangle, 
e  and  o  tne  center  of  the 
I  formulas  are  given  for 
triangles. 


o<---— 


FomuUas: 


8  B 
s  b' 

BnA  — 


sin  B  » 


sin  b 


Fig.  2. 


^  cos  A 
cos  a 


sin  b 


„       tan  a 
tan  c 


tanB  - 


tan  b 
sin  a 


cos  c  —    cot  A  cot  B. 


ormulas  are  all  that  are  necessary,  as  the  value  of 
may  be  determined  by  transposition.     Thus,  from 

tan  b         , 

«,  sm  a  *  r 3 ,  and  so  on. 

tanB 

the  side  6  if  the  angle  A  — 18**—  20'  and  the  hypoth- 

t  A  —  : ,  we  have,  tan  &»tan  c  cos  A ; 

tan  c 

log  tan  48<»-30'  -  0.05819 

log  cos  18*»-20'  -  9.97738 

gle6  -  4?»-01',as  0.03067-logUn6.       . 

B  (arc}  b  may  be  obtained  from  the  table  of  Circular 

100 


d  by  Google 


200 


l(i.^SPHERICAL  TRIGONOMETRY. 


ObUque  Spherical  Trianclcs.' 

Fortftulas. 
tan  A     sin  a         am  B 
sin  B     sin  6  '       sin  C 
cos  a  »  cos  6    cos  c 
cos  b   >"  cos  c    cos  a 
cos  c   —  cos  a    cos  6 
oosi4  —  —  cosB  cosC 
oosB  —  —  cos  C  COB  A 
oosC  "—  cos  A  cosB 


Pi«.8. 


sin  6 

sin  c  ' 
+  sin  6 


sin  c 

sin  a 


sin  ^„«n  a 
sin  C  sin  c 
sin  c    cos  A. 


sin  a  cos  B. 

sin  6  cos  C. 

sin  B  sin  C  cos  a. 

sin  C  sin  i4  cos  b. 

sin  A  sin  B  cos  c. 


tin  i  A 
sin  i  B 
sin  i  C 
cosiA 
cos  i  B 
cos  |C 


Vsin  (s—b)     sin  (s-c) 
sin  6  sin  c 

Vsin  (s—c) 
sin  I 


—  c)     sin  (s—a) 


sin  5  sin    (s  —  a) 
sin  6  sin  c 


/sin  (5  —  0) 
""   'Y  sin  £ 

si 

-V 
-V 


sin  (5— fe) 


a  sin  6 


sin  5  sin  (5  —  b) 
sin  c  sin  a 

sin  5   sin  (s  —  c) 
sin  a  sin  6 


/sin  (s—b)    sin  (s  —  c) 
Y      sin  5  sin  (s  —  a) 

/sin  (s—c)    sin  (5  — a) 
■^       sin  5  sin  (s—b) 

^  Jsin  (»-a)    rin  (.-t) 

\      Sin  £  sm  (5— c) 


taniB    - 


sin  ia 
sin  i  6 
sin  i  c 
cos  i  a 
cos  i  d 
cos  i  c 
tan  i  a  — 


-^|- 


COS  5     cos  (5  — A) 
sin  B  sin  C 


-V- 

-v 

-V- 


COS  5     cos  (5-g) 
sin  C  sin  A 

cos  5     cos(5-Q 
sin  A  sin  B 

cos  (5--B)  cos(5-0 
sin  B  sin  C 

cos (S—O  cos  (5— A) 
sin  C  sin  A 

cos  (5-A)  cos  (5-g) 
sin  A  sin  B 


I      cos  5     cos  (5— A) 

\  cos  (S-B)  cos(S-0 

,  .  /       cos  5  cos  (S—B) 

tan  to   --y/  cos(S-C  )  co8(S-A) 


tan  i  c 


j       cos  5  cos  (5  — O 
■\    cos(5-A)cos(5-B) 


Note.— In  the  above  fonnulas.  5-I  (a+b  +  c)\  S-HA+B  +  O- 

tanjc  cos  i  (A  +  B)     _  tan  j  c 


sin  i  (A  +  B) 

sin  i  (A-B) 

sin  t  (g  4-  6) 

sin  i  (a  —  6  ) 


tani  (a-b) 
cot  jC 


tan  i  (A-B) 

General  Rules. 


cos  i  (A  +  B) 
cosi  (A-B) 
cos  i  (o  +  fr) 
cos  J  (a  —  b) 


tan  i  (a  +  6) 

cot  jC 
tani  (A+B) 


1.  Sines  of  the  sides  are  proportional  to  the  sines  of  their  opposite  angles. 

Example. — In  Fig.  2.  sin  A  :  sin  a  :  :  sin  C  :  sin  c. 

2.  Cosine  of  any  side  equals  the  product  of  the  cosines  of  the  other  two 

sides,  plus  the  product  of  their  sines  and  the  cosine  of  their  included 
angle.    Example. — In  Fig.  2.  cos  a  — cos  &  cos  c+ sin  &  sin  c  cos  A. 

Special  Cases. 
Case  I.    Given  one  side  (c)  and  two  adjacent  angles  (A  and  B). 
1st.    Solve  for  b  and  c  in  the  following: 

tan  i  ib-a)  -  sin  i  (B-A)  coscc  J  (B  +  A)  tan  »  c. 
ii(b  +  a)  "CosiiB-A)      sec  }  (B+A)  tan  J  c. 


tan 
d.    S 
cot  J  C  —  sin  i 


2nd.    Solve  for  C  in  the  following:  (^r^nkn]o 

'i(b  +  a)cosec%(b-a)tai^^^B^9S^S^^ 


SPHERICAL  TRIANGLES.    CELESTIAL  SPHERE,  301 

Cmb  IL    Given  two  sides  (b  and  c)  and  their  included  angle  (A). 
1st.    Solve  for  B  and  C  in  the  following: 

tan  h  {B-C)  -  sin  *  ib-c)  coscc  f  ib+c)  cot  \  A\ 
tan  \  (B+O  -  cos  1  Ib-c)      sec  \  \b+c)  cot  \  A, 
2nd.    Solve  for  a  in  the  foUowing: 

tan  i  a  -  sin  i  {B+O  cosec  i  {B-O  tan  J  (i-c). 
Case  IIL    Given  the  three  sides  (a,  b  and  c).    Solve  for  i4,  B  and  C. 


:-^ 


m  which*-    ,>*>>w-Q)ain  (5-6)  sin  (5  ~c) 


sin  s 

and  *  -  i  (a+6+c). 

Case  IV.    Given  the  three  angles  (A,  B  and  Q.    Solve  for  a,  6  and  c. 

tan  i  a  -  /C  cos(S-i4);    tan  i  6  -  K  cos  (S-B);   tan  |  c  - 
iCoo«(S-0; 


. .  ,  «.        I  cos  5 

In  which/'        ' 


"cos  (S-i4)  cos  (5-B)  cos  (S-Q  * 
and  S-  i(i4+B+0. 
Case  V.    Given  two  sides  (a  and  b)  and  the  angle  (B)  opposite  one  of  them. 
1st.    Solve  f or  il  in  the  following: 

sin  A  —  sin  a  cosec  6  sin  B. 
2nd.    Solve  for  C  and  c  in  the  following: 

cot  4C  -  sin  i  (6  +  0)  coscc  i  (6 -a)    tan  J  (B-i4); 
tan  i  £   -  sin  }  \B'\-A)  cosec  \  {B-A)  tan  i  (&-a). 
Case  VI.    Given  two  angles  Mand  B)  and  the  side  (&)  opposite  one  of  them. 
1st.    Solve  for  a  in  the  following: 

sin  a  —  sin  A  cosec  B  sin  6.  ^^-^^S^ 

2nd.    Solve  for  c  and  C  in  the  following:  ^^^      \\"""^\ 

tanf  c  -sin  *(B+i4)  co8ec4(B-i4)  tan*(6-a);        X  \\      X 

cot  tC  —  sin  J  (6+ a)    co6ccJ(6-a)    tanJ(B->l).    /  JV     A 

Distance  between  two  points  on  the  Earth's  snr- /    \-\/     \ 

facc^ — Given    the   latitudes  and  lon^tudes  of  twop''  Ld^''"'N 

points  Band  C,  Fig.  4,  let  it  be  reqtured  to  find  thcK  ^tr  p      J\ 

shcMteat  distance,  a,  between  them.    Select  a  third  \  ^"^  UuA'^s^ I 

point,  A.  at  the  nearest  pole;  and  connect  the  points  \         ^^'^  / 

A  Be  with  arcsof  great  circle.    Produce  the  meridian    V-'"  / 

lines  A  B  and  -A  C  to  the  equator.    Then  will  /'  be      N.  y 

the  latitude  of  C;  T,  the  latitude  of  B;  and  L,  the         ^^>^      ^^ 
difference  of  longitude;  and.  in  the  spherical  triangle  „.      . 

ABC.b'-'W-r,  c-90*-r,  andtheangleA  -  L.  ^«- *• 

Solve  for  Case  11,  preceding. 

The  Celestial  Sphere. — In  solving  astronomical  problems,  the  center  of 
tlie  earth  is  assumed  to  be  the  ctniet  of  the  celestial  sphere;  and  its  axis 
pfodnced,  the  axis  of  said  sphere.  The  extremeties  of  the  axis  produced 
are  the  poltr^  and  the  great  circle  whose  plane  is  perpendicular  to  the  axis 
(at  the  center),  is  the  eituator.  A  plumb  line  at  any  given  point  is  called 
tlie  verUcal  line^  and  if  produced  it  intersects  the  celestial  sphere  in  the 
amcA  (above)  and  in  the  nadir  (below).  The  zenith  and  nadir  are  the  poles 
of  any  vertical  line;  and  a  gfeat  circle  whose  plane  is  perpendicular  to  said 
▼cnical  line,  forms  the  hortMon.  The  meridtan  is  the  great  circle  whose 
plane  passes  through  the  senith  and  the  poles,  and  the  points  where  it 
xzitersects  the  horizon  are  called  the  north  and  south  points.  The  prinu 
vertical  is  the  great  circle  whose  plane  passes  through  the  zenith  perpendicular 
to  the  meridian,  and  the  points  where  it  intersects  the  horizon  are  called 
the  §ast  and  wesi  points. 

A  vertical  circle  is  a  great  circle  whose  plane  passes  through  the  poles  of 
a  "Vertical  Une,  i.  e.,  through  the  senith  and  nadir.  It  is  therefore  per- 
pendicular to  the  horizon.  The  assimuih  of  a  star  is  the  arc  measured  on  the 
horiaan  between  the  north  point  (or  the  south  point)  and  the  vertical  circle 
pasnng  through  the  star;  hence  it  is  the  tangential  angle  at  the  zenith, 
l>etweea  the  meridian  and  said  vertical  circle.    The  altitude,  h  oIb,  star  ta 


202 


lO.—SPHERICAL  TRIGONOMETRY, 


its  distance  from  the  horizon  measured  on  a  vertical  circle.    The  rnnitk 
disUxHct  -«  «  —  90*-A. 

An  hour  circU  is  any  great  circle  whose  plane  passes  through  the  poles 
(and  perpendicular  to  the  equator).  The  hour  angle,  P,  of  any  star  is  the 
tangential  angle  which  its  hour  circle  measures  (westward  from  and)  with 
the  meridian,  at  the  pole;  the  arc  of  the  angle  is  measured  at  the  equator. 
The  right  ascension,  K.  A.,of  a.  star  is  the  distance  on  the  eqxiator  from  the 
vernal  equinox  (the  point  where  the  sun  crosses  the  equator  from  south  to 
north*},  eastward  to  the  hour  circle  of  the  star.  The  declination,  i^f  a  star 
is  its  distance  from  the  equator,  meastired  on  an  hour  circle.  The  polar 
distance,  p,  -  90*-*. 

Astronofnical  Time. — A  solar  day  is  our  common  day  of  twenty-four 
hours.  Any  particular  solar  day  is  an  apparent  solar  day,  and  is  the  interval 
between  two  successive  passages  of  the  sun  across  the  same  meridian.  A 
mean  solar  day  is  the  average  length  of  the  solar  davs  in  a  tropical  year. 
A  tropical  year  contains,  according  to  Hansen  and  Olufsen,  805 .  2422008 
mean  solar  days;  according  to  Bessel,  866.24222  mean  solar  days.  On 
account  of  the  earth's  revolution  around  the  sim,  there  is  one  more  sidereal 
day  in  a  year  than  solar  days.  Hence,  according  to  Bessel  there  are  300.- 
24222  sidereal  days  in  a  year,  and  we  have  the  ratios — 
1  solar  day  —  1.0027370  sidereal  day  -  1  sid.  day+  8m  56.655s  sid.  time. 
1  sid.    day  —  0.9972696  solar      day  «  1  solar  daV- 3m  65.9095  solar  time. 

The  equation  of  time  is  the  quantity  (time)  to  be  "added."  algebraic^ly, 
to  the  apparent  solar  time  to  give  the  mean  solar  time.  Its  value  for  any 
day  of  the  year  may  be  found  in  the  solar  ephemeris  tables  of  the  Nautical 
Almanac. 

The  following  are  conversion  tables  for  mean  solar  time  and  sidereal 
time: 

1. — Mean  Solar  Tiub  Rbducbd  to  Sidbrbal  Time. 


Mean 

I 

Sidereal 

Hours 

Ih  Om 

9.856s 

1 

Im 

0.164s 

Is 
1 

Time 

1 

1.003s 

2 

2     0 

19.713 

2 

2 

0.329 

2 

2  005 

3 

3     0 

29.569 

3 

0.493 

3 

3.008 

4 

4     0 

39.426 

4 

0.667 

4 

4.011 

6 

5     0 

49.282 

6 

0.821 

6 

6.014 

6 

6     0 

69.139 

6 

0.986 

6 

6.010 

7 

7     1 

8.996 

7 

1.150 

7 

7.019 

8 

8     1 

18.852 

8 

8 

1.314 

8 

8.022 

9 

9     1 

28.708 

9 

9 

1.478 

9 

0.025 

10 

10     1 

38.565 

10 

10 

1.643 

10 

10.027 

24 

24     8 

56.555 

30 

30 

4.928 

30 

80.082 

2. — Sidereal  Time  Reduced  to  Mean  Solar  Time. 

Sidereal 

Mean  Solar  Time. 

Sidereal 

Mean  Solar 

Sidereal 

Mean  Sol^r 

Hours 

Minutes 

Time 

Seconds 

Time 

1 

Oh  59m50.170s 

1 

Om      69.8368 

1 

0.997s 

2 

1     69     40.341 

2 

1         69.672 

2 

1.995 

3 

2     69     30.511 

3 

2         59.509 

2.992 

4 

3     69     20.682 

4 

3         69.345 

3.989 

6 

4     69     10.852 

6 

4         69.181 

4.986 

6 

5     69       1.023 

6 

6         69.017 

6  984 

7 

6     58     61.193 

7 

6         58.863 

6.981 

8 

7     68     41.364 

8 

7         68.689 

7.978 

9 

8     58     31.534 

9 

8         58.526 

8.975 

10 

9     58     21.704 

10 

9         58.362 

10 

9.973 

24 

23     66       4.091 

30 

29         66.086 

30 

29.918 

*  The  autumnal  equinox  is  the  point  where^the  ^ig(an>sses  the  eqaatoq 
from  north  to  sou^.  ^        ^  I 


11.— MENSURATION. 


A.— PLANE  SURFACES,  UNES.  ETC. 

2 


Trlansle. — Three  sides.    Area  — 


'  Vsis  —  a)  (5  —  6)  is—c),  in  which  s  — 


Center  of  gravity  is 


c-Va*+6»  +  2  ab  cos  C. 
Angles  i4+B  +  C- 180*. 
Rx^a-angled  triangle. — ^Angle  C' 

enuae   c  -  \/a«  +  6«;  hence  a-  Vc^-i^  „  V(<r  +  6)(c-6) ;  6  - \/'^~^^. 

Ua~b.  then  c«  1.4142  a  -  1.4142  6.  or  a-6- 0.7071  ^. 
Acute-angled  triangle. — Each  angle  less  than  90®. 
0&tesv-<mcZrd  triangle. — One  angle  greater  than  90*  (as  Fig.  1). 
Isosceles  triangle.-— Two  sides  (therefore  two  angles)  equal. 
Eqtnlateral  truingle. — ^Three  sides  (therefore  three  angles)  equal.    See  Table 

1,  Regular  Polygons. 


Pig.  2.  Pig.  3.  Fig.  4. 

Qvuulrilateral. — Four  Sides. 
Trapezium. — ^An  irregular  qtiadiilateral;   no  two  sides  parallel.    i4r«a  may 
be  obtained  by  cutting  it  into  two  triangles,  ana  solving. 

Trapezoid, — ^Two    sides    only,     parallel,     Fig.  2.    Area*^^  (6+6i).      See 

Section  29  for  center  of  gravity. 
Parallelogram. — Includes  the  rhomboid,   rhombus,   rectangle  and   square. 

A r»a->  length   of   one   side   multiplied   by    perpendicular   distance   to 

parallel  side  opposite. 
Rkomboid. — A    "skewed"    rectangle.  Fig.  3;    opposite  sides  (therefore  op- 
posite angles)  eqxial.    -Aftfa  — 6/i— 6a   sin  i4""o6  sin   <A=-aAi    (Fig.   3). 

Cen.  of  grav  is  at  intersection  of  two  diagonals. 
Rectangle. — Opposite  sid*s  equal  and  parallel,  as  with  the  rhomboid;  but 

xngicB  9(f,  Fig.  4.    Side  b>a.    Area^ab.    Diagonal  —  Vo^TP.     Cen. 

of  grav.  equi-distant  from  parallel  sides,  and  at  intersection  of  diagonals. 


B ^"5- 

Pig.  5.  Fig.  6. 

fOiombus. — Same    as    rhomboid    (Fig.  3)    but    with  all  sides  equal,  Fig.  5. 

Area— 6/1—6*  sin  A.  ^_^ 

Square. — All  sides  equal;  angles  90*.  Fig.  6.  Ar*a  -62.    Diagonal  ■=  VT~B^^ 

1.4142  6.     Side  6 -diagonal   X  0.7071. 

Digitized  by  VjOOQ  IC 


204 


ll.^MENSURA  TION. 


Reffnlar  Polygon. — ^Any  number  of  sides,  from  the 
triangle,  with  three  sides,  to  the  circle,  with  an  oo  number 
of  sides.    In  Table  1,  following. 

s    -  length  of  each  side  «■  2  i?  sin  i  a  -  2  r  tan  i  a; 
n   —  number  of  sides  in  polygon  (m  s  —  perimeter) ; 
R  —  radius  of  circumscribing  circle  =>  j  s  coscc   J  oc  -« 

r  sec  i  oc; 
r    —  apothem  =  radius  of  inscribed   circle  «  R  cos  i  oc  — 

i  J  cot  i  a; 
oc  —  angle  subtended  from  center  by  each  side— 360+ n; 
$    —  internal  angle— 180*- oc; 

.  srn       perimeter  X  apothem        .         _         .  ^         j*i^ 

Afta  -  —^  -  -^^ 2  — "  \nsR  cosjoc  —  hi*  tan  |  oc. 


Fig.  7. 


1. — ^Tablb  op  Regular  Polygons  (Fig.  7). 


I? 


Name 

o( 

Polygon 


CenUal 

Angle 

a 


Internal 
Angle 


SIdec 


ri 


9sS 


Outer 
radius  A 


Li 


Innor 
radtuar 


s«i 


Triangle 
Square 
Pentagon 
Hexagon 
Heptagon 
Octagon 
Nonagon 
Decagon 
Undecagon 
Dodecagon 
Circle 


I20°-00'-00' 
90-00-00 
72  -00-00 
60  -00-00 
51  -25-43 
45-00-00 
40  -00-00 
36  -00-00 
32  -43  -38 
30-00-00 
0 


60«-00'-00' 
90  -00-00 
108-00-00 
120  -00-00 
128  -34.-17 
135  -00-00 
140-00-00 
144  -00-00 
147  -16-22 
150  -00-00 
180* 


.732053. 
.41421 
.17557 
.000001. 
.86777 
,76537 
,68404 
61803 
56346 
61764 
0 


46410 
00000 
45308 
15470 
96315 
82843 
72794 
64984 
58725 
53590 
0 


5773502.00000 


.707107 
.850651 


41421 
1.23607 


1.0000001.15470 
I 


152382 
,306563 
461902 
618034 
774733 
931854 
00 


1.10992 
1.08239 
1.06418 
1.05146 
1.04222 
1.03528 
Pnlty 


2886S 
.60000 
,68819 
86603 
0382; 
20711 
37374 
638S4 
70287 
86603 
00 


5O000 

70711 


.90097 


93969 
951M 
95943 
96593 
Unity 


1! 

n 

Name 

o( 

Polygon 

Perimeter  p 

Area  A 

Equals 

8 

times 

Equals 

R 
times 

Equals 

r 
times 

Equals 
times 

timefl 

Equals 
times 

00 

Triangle 
Square 
Pentagon 
Hexagon 
Heptagon 
Octagon 
Nonagon 
Decagon 
Undecagon 
Dodecagon 
Circle 

3 

4 
5 
6 
7 
8 
9 
10 
11 
12 
00 

5.19615 
5.65685 
5.87785 
6.00000 
6.07437 
6.12293 
6.15636 
6.18034 
6  19813 
6.21166 
6.28319 

10.39230 
8.00000 
7.26542 
6.92820 
6.74204 
6.62741 
6.55146 
6.49838 
6.45977 
6.43078 
6.28319 

4330127 
1.0000000 
1.7204774 
2.5980762 
3.6339124 
4.8284271 
6.1818242 
7.6942088 
9.3656399 
11.1961524 

CO 

1.29904 
2.00000 
2.37764 
2.59808 
2.73641 
2.82843 
2.89354 
2.93893 
2.97352 
3.00000 
3.14169 

5.19616 
4.00000 
3.63271 
3.46410 
3.36502 
3.31370 
3.27578 
8.24920 
3.22989 
•3.21539 
3.14159 

rn 

;2 

Circle— Infi 

nite  number  of  sides. 

Circumference,  p 

-xd  -  8.1416  d.  -  2  «r  -  6.2832 

r; 

Area,  a  —           = 

»  0.7854  d*.  -  >rf»  -  3.1416f»; 

Ck) 

Diameter,  d  -  — 

-  0.318310  p.  -  2^'"'-  -   1.1283J 

\Val 

Radius,  r  —  ^ 

-  0.159155  p.  =J'^=  0.56419V 

^7. 

Fi«.S. 

n  — 

3.141592  6530 

Log=- 

0.497  149 

8727      - 

-0  318  a 

K)  886306 

igl^.502 

860 

H 

POLYGONS— CIRCLE. 


3M 


•Tabular  Values  of  Combinations  op  k,  with  Logs. 


Number.     Logarithm. 
&-  6.283186  0.7981799 


.1981199F' 

K 

6 

X 

7 


.  .2763012 -■ 


3c-  9.424778  0.9742712 

in-12.5603n  1. 

&-16.707903  1 

6r-18.849656  1 

7r-21.991l40  1 

8c»25. 132741  1. 

9r-28.Z74334  1 

Note. — In  circolar 

nmsure.  x»180^ 

-10800  min. 

*-648000sec. 
xi»  9.88960    0.9942997U*< 


0992099 --  1.273240 


.8422479-' 

X 

4003399^-  2.546479 


.4613024- 


-  2.864789 

180<* 

^      -67.296780 


Vtr-  1.77245    0.2486749  Vi-1. 46459 
^^2.60663    0.3990899^-1.84527 


-0.66419    9.7614251 


«/ —0.79788    9.9019401 


A  ^-1.25331    0.0080699^ 


Number.      Logarithm. 


-  0.636620 


0.964930 


-  1.501649 
1.909650 
2.228169 


9.8038801 
9.9799714 
0.1049101 
0.2018201 
0.2810014 
0.3479481 
0.4060401 
0.4670926 
1.7681226 


Number.    Logarithm. 
r»  1.670796         0.1961199 

g--  1.047198. 

^-  0.786398 

-|—  0.628319 

J"  0.623599 

r-  0.448799 


1180° 


-114.60156       2.0691526 
110800' 


3437.7468 
IB48000' 


-206264.81  6.3144261 
-31.00628  1.4914496*^ 

8.5065504 


0O57003[l-  0.03226 


■0.68278 


0. 
0 

9.8342834 


.86026 


j-1. 16246 


9.9346267 
0.0663783 


-  0.392699 


^-  0.349066 


0.0 

9.1 

9.7981799 

9.n89966 

9.6520519 

9.5940509 

9.6429074 


360° 


-.01746329  8.2418774 
-.00087266  7.9408474 


8.6362739 T7SSF"*>^^29089  6.4637261 


loeoo" 


NSOOO' 

-97.4091 
1 


0000048484.6865749 
1.9686996 


-  0.01027 


X* 

1657166^-1.33134 

A 

2660600  V2JC-1. 58323 
l/i-0.75118 


V?- 


*  '--0.89324 


v^ 


-1.11952 


8.0114005 
0.1242875 
0.1995450 
9.8757126 

9.9609700 

0.0490300 


*  For  multiples  1  to  9,  see  next  page. 


d  by  Google 


206 


U.— MENSURATION 


Tabular  Values  op  Combinations  op  x,  with  Logs. — Concluded. 
(Multiples  1  to  0.) 


«* 

Log. 

Log. 

Vi 

Log. 

3.1415927 
6.2831853 
9.4247780 
12.5663706 
15,7079633 
18.8495559 
21.9911486 
25.1327412 
28.2743339 

0.4971499 
0.7981799 
0.9742712 
1.0992099 
1.1961199 
1.2753012 
1.3422479 
1.4002399 
1  4513924 

0.3183099 
0.6366198 
0.9549297 
1.2732395 
1.5915494 
1.9098593 
2.2281692 
2.5464791 
2.8647890 

9.5028901 
9.8038801 
9.9799714 
0.1049101 
0.2018201 
0.2810014 
0.3479481 
0.4059401 
0.4570926 

0.5641896 
1.1283792 
1.6925688 
2.2567583 
2.8209479 
8.385137S 
3.9493271 
4.6135167 
5.0777063 

9.7514251 
0.0534561 
0.3285464 
0.3534851 
0.4503951 
0.5295764 
0.5965231 
0.6545151 
0  7056676 

1l» 

Log. 

1 

Log. 

V- 

Lo«. 

9.8696U44 
19.7392088 
29.6088132 
39.4784176 
49.3480220 
59.2176264 
69.0872308 
79.9568352 
88.8264396 

0.9942997 
1.2953297 
1.4714210 
1.5963597 
1.6932697 
1.7724510 
1.8393977 
1.8973897 
1.9485422 

0.1013210 
0.2026420 
0  3039631 
0.4052841 
0.5066051 
0.6079261 
0.7092471 
0.8105682 
0.9118892 

9.0057003 
9.3067303 
9.4828216 
9.6077608 
9.7046703 
9.7838616 
9.8507983 
9.9087903 
9  9599428 

1.7724539 
S. 5449077 
5.3173616 
7.0898154 
8.8822693 
10.6847281 
12.4071770 
14.1796308 
15.9520847 

0.2485749 
0.5496049 
0.7256963 
0.8506349 
0.9475449 
1.0367263 
1.0936729 
1.1516649 
1.2028174 

IC« 

Log. 

1 

1C* 

Log. 

;■ 

Log. 

81.0062767 
62.0125534 
93.0188300 
124.0251067 
155.0313834 
186.0376601 
217.0439368 
248.0502134 
279.0564901 

1.4914496 
1.7924796 
1.9685709 
2.0935096 
2.1904196 
2.2696009 
2.3365476 
2.3945396 
2.4456921 

8 
9 

9.0322515 
0.0645030 
0.0967545 
0.1290060 
0.1612575 
0.1935090 
0.2257605 
0.2^80120 
0.2902635 

8.5085604 
8.8095804 
8.9856717 
9.1106104 
9.2075204 
9.2867017 
9.3536484 
9.4116404 
9.4627929 

1.4645919 
2.9291838 
4.3937766 
5.8583675 
7.3229594 
8.7875513 
10.2521432 
11.7167351 
13.1813269 

0.1657166 
0.4667466 
0.6428379 
0.7677766 
0.8646866 
0.9438679 
1  0108146 
1.0688066 
1.1199991 

n* 

Log. 

1 

X* 

Log. 

v^ 

Log. 

1 
2 

8 
9 

97.4090909 
194.8181818 
292.2272727 
389.6363636 
487.0454545 
584.4545453 
681.8636362 
779.2727271 
876.6818180 

1.9885995 
2.2896295 
2.4657208 
2.5906595 
2.6875695 
2.7667508 
2.8336975 
2.8916895 
2.9428420 

0.0102660 
0.0205320 
0.0307979 
0.0410639 
0.0513299 
0  0615959 
0.0718619 
0.0821278 
0.0923938 

8.0114005 
8.3124305 
8.4885218 
8.6134605 
8.7103705 
8.7895518 
8.8564985 
8.9144905 
8.96.'>6430 

0.6827841 
1.3655681 
2.0483522 
2.7311363 
8.4139203 
4.0967044 
4.7794885 
5.4622725 
6.1450566 

0.8343884 
0.1353134 
0.3114047 
0.4363434 
0.5332S34 
0.6124347 
0  6793814 
0.7373734 
0.7885259 

Logarithms  of  Numbers  1  to  9,  for  Reference* 

Log  1-0.0000000  Lor  4  =  0.6020600  Log  7— 0.8450980 

••     2-0.3010300  "     ."4  =  0.6989700  "     8-0.9030900 

••    3-0.4771213  ••     6=0.7781513  "     9-0.9542425 

*See  Table  11,  pages  224  and  225.  for  values  of  k  when  multiplied  by  any 
whole  number  or  decimal.  (See  Foot-note  to  Table  11.)  Table  12  can  be 
used  in  a  similar  manner. 


Digitized 


by  Google 


CIRCULAR  ARC;  CHORD. 


207 


and  Chord. — 

inctiona  (a+  ;9-860O). 
ingle  in  degrees,  <  180**. 
tngle  in  degrees.  >  180®. 

>n8. 

;th  of  arc  a  to  radius  1. 

th  of  arc  h  to  radius  1. 

ance  to  cen.  of  grctv.  g  of  arc  a. 
rav.  G  oi 
'onnuias: 


S*      h 


ance  to  cen.  of  ^av.  G  of  arc  b. 
Fa 


-  ^.    Cosia- 


r-h 


cosi  )9  =- 


H-r  Fig.  9. 


Ty'^^^'Yuh^'    Vers  ic.^;  vers  i^-f 


745329  a: 


»r;9 


/?i-j^  -  0.01745329^ 


Arc6  -  f /?,  -  0.01746  rj9. 

.01745  c  i?        .01745//  ^ 


2sini^ 


versi  H 


01745  r  a; 
g^.01745  h  g 
c  "    vers  \  a   * 

a  -  2  r  sin   M  -  2>/A(2r-/»)-  2\///(2r-//) 
tan  i  a  -  2  (r-A)  tan  i^  -  2  (//-r)  tan  i  oc  -  2  (//-r) 

ni;? 

x-2*coti  ^-.2(2r-//)cotia-2(2r-//)coti^. 
ord  ( -r-j  isa  mean  proportional  between  A  and  //;  thus 

-2>/a77". 

sin_J_oc  ^  length  of  chord  c ^rc  \ 

0C|         "  length  of  arc  a       a  fyo^^_^i9^/?i 

sin  i  ;9  ^  length  of  chord  c  ^rc  [  Vq      o""cc""ai" 

^x          ""  length  of  arc  b       b  ) 

57.29578;  log  -  1.7581226  (see  under  Circle). 

slution  s  generated  by  arc  a  revolving  about  axis  X  —  X 
plied  by  length  of  path  traveled  by  point  g\ 

in  which  B  is  the  angle  of  revolution,  in  degrees) 

— ,  the  general  equation.   Thus,  to  get  the  surface   of   a  . 

180*".  «- 360";  then  5-4  IT  r»- 12.566371  f». 

itc  of  arc  a  /f  —   middle  ordinate  of  arc  A 

a)  -  f  vers  §  a  —  r  (1+cos  J  ^) 

f )  •-  ftan  i  OC.  -  r+^r.  -  (f)  '-|  tan  i  /I. 

tc  at  any  point  distant  x  from   center  =«/»  —  rf,  in  which 
ence,  ordinate  —  fc  —  r  +  Vr'  —  «'. 

Wa^57.29578a^ ^_  _  „  ___£ ^L_^   ; 

ra  "        a       ""  1  — cos  fa  "2  sin  i  cc     vers  i  a* 

806     57.295786  // ^ jW 

c;j  "  ti        "l+cosi  ^"2  sin  k   ^^  vers   i  >3  * 


d  by  Google 


208 


n.— MENSURATION. 


Values  of  ai  and  0i  (Fig.  9) 

2. — Lbnoths  op  Circular  Arcs  por  Radius  1. 

(Note  thftt  the  arc  is  directly  proportiooal  to  central  angle  and  to  radiaa.) 


Deg. 

Length. 

Deg. 

Length. 

MiD. 

Length. 

Sec. 

Length. 

15* 

0.M1799  3878 

!• 

.017453  2925 

1' 

.000290  8882 

r 

.000004  8481 

ZQP 

0.523598  7756 

2«» 

.034906  6850 

2' 

.000581  7764 

2' 

.000009  69<3 

46* 

0.785398  1634 

30 

.052359  8776 

3' 

.000872  6646 

3* 

.000014  5444 

60' 

1.047197  5512 

4» 

.069813  1701 

4' 

.001163  5528 

4* 

.000019  3925 

ly 

1.308996  9390 

5"» 

.087266  4626 

6' 

.001454  4410 

6* 

.000024  2407 

w 

1.670796  3268 

6«» 

.104719  7561 

6' 

.001745  3293 

6' 

.000039  0888 

135*» 

2.356194  4902 

70 

.122173  0476 

T 

.003036  2175 

7' 

.000033  9370 

180* 

3.141592  6536 

8« 

. 139626  3402 

8' 

.002327  1057 

8- 

.000038  7851 

J70O 

4.712388  9804 

90 

.157079  6327 

9' 

.002617  9939 

9' 

.000043  6332 

360« 

6.283185  3072 

10' 

.174532  9252 

10' 

.002908  8821 

10* 

.000048  4814 

Problem. — Find   the   length 
of  circular  arc  corresponding  to 
a  central  ancle  of  237*»  -  46'  -  58 . 8" 
and  to  a  radius  of  6387 .42. 


Solution. — From  Table  2. 


200*>    -    3.490659 
80°    -      .523599 

r    "      .122173 
40'    -      .011636 

6'    -      .001745 
50*    -      .000242 

8*    -      .000039 
.3*    -      .000001 

log           4.150094  « 
log               6387.42- 
Ans.  26508.4 

0.6180580 
3.8053255 
4.4233885 

Table  8,  following,  has  been  prepared  from  Table  2. 


d  by  Google 


CIRCULAR  ARC;  CHORD, 


209 


Values  of  ai  and  $i  (Pig.  9) 

3^ — ^Lengths  or  Cuicular  Arcs  por  Radius  1. 

(Deg.,  Min.,  Sec*  are  central  angles;   Length  is  length  of  subtended  arc.) 


DBf. 

Lencth. 

Deg 

Length. 

iDeg. 

Length. 

Mln. 

Length. 

Sec. 

Length. 

.0174533 

61 

1.0646508 

121 

2.1118484 

1 

.0002909 

1 

.0000048 

.0349000 

62 

1.0821041 

122 

2.1293017 

3 

.0005818 

3 

.0000097 

.0523590 

63 

1.0995574 

123 

3. 1467550 

3 

.0008727 

3 

.0000145 

.0698132 

64 

1.1170107 

124 

2.1642083 

4 

.0011636 

4 

.0000194 

.0872605 

65 

1.1344640 

126 

2.1816616 

5 

.0014544 

6 

.0000243 

.1047198 

66 

1.1519173 

126 

2.1991149 

6 

.0017453 

6 

.0000291 

.1221730 

67 

1.1693706 

127 

2.2165682 

7 

.0020362 

7 

.0000339 

.1396263 

68 

1.1868239 

128 

2.2340214 

8 

.0023271 

8 

.0000388 

.1570796 

69 

1.2042772 

129 

3.2514747 

9 

.0026180 

9 

.0000436 

.1745329 

70 

1.2217305 

130 

2.2689280 

10 

.0029089 

10 

.0000486 

.1919662 

71 

1.2391838 

131 

2.2863813 

11 

.0031998 

11 

.0000533 

.2094395 

72 

1.2566371 

132 

2.3038346 

13 

.0034907 

12 

.0000583 

.2268928 

73 

1.2740904 

133 

2.3212879 

13 

.0037815 

13 

.0000630 

.2443461 

74 

1.2915436 

134 

2.3387412 

14 

.0040724 

14 

.0000679 

.2617994 

75 

1.3089969 

135 

2.3561945 

15 

.0043633 

15 

.0000727 

.2792527 

76 

1.3264502 

136 

2.3736478 

16 

.0046542 

16 

.0000776 

.2967060 

77 

1.3439035 

137 

2.3911011 

17 

.0049451 

17 

.0000824 

.3141593 

78 

1.3613568 

138 

2.4085544 

18 

.0052360 

18 

.0000873 

.3316126 

79 

1.37881U1 

139 

2.4260077 

19 

.0055269 

19 

.0000921 

» 

.3490659 

80 

1.3962634 

140 

2.4434610 

30 

.0058178 

20 

.0000970 

21 

.3665191 

81 

1.4137167 

141 

2.4609142 

21 

.0061087 

21 

.0001018 

» 

.3839724 

83 

1.4311700 

142 

2.4783675 

22 

.0063995 

22 

.0001067 

23 

.4014267 

83 

1.4486233 

143 

2.4958208 

23 

.0066904 

23 

.0001115 

34 

.4188790 

84 

1.4660766 

144 

2.5132741 

24 

.0069813 

24 

.0001164 

2S 

.4363323 

85 

1.4835299 

145 

2.5307274 

25 

.0072722 

25 

.0001212 

21 

.4537856 

86 

1.5009832 

146 

2.5481807 

26 

.0075631 

26 

.0001261 

27 

.4712389 

87 

1.5184364 

147 

2.5656340 

27 

.0078540 

27 

0001309 

28 

.4886922 

88 

1.5358897 

148 

3.5830873 

28 

.0081449 

28 

.0001357 

29 

.5061455 

89 

1.5533430 

149 

2.6005406 

29 

.0084358 

29 

.0001406 

30 

.5235988 

90 

1.5707963 

150 

2.6179939 

30 

.0087266 

30 

.0001454 

31 

.5410521 

91 

1.5882496 

151 

2.6354472 

31 

.0090175 

31 

.0001503 

32 

.5585054 

92 

1.6057029 

152 

2.6529005 

32 

.0093084 

32 

0001551 

33 

.5759587 

93 

1.6231562 

153 

2.6703538 

33 

.0095993 

33 

0001600 

34 

.5934119 

94 

1.6406096 

154 

2.6878070 

34 

.0098902 

34 

.0001648 

25 

.6108652 

95 

1.6580628 

155 

2.7052603 

35 

.0101811 

35 

.0001697 

U 

.6283185 

96 

1.6755161 

156 

2.7227136 

36 

.0104720 

36 

.0001745 

37 

.6457718 

97 

1.6929694 

157 

2.7401669 

37 

0107629 

37 

.0001794 

28 

.6632251 

98 

1.7104227 

158 

2.7678202 

38 

.0110538 

88 

.0001842 

39 

.6806784 

99 

1.7278760 

159 

2.7750735 

39 

.0113446 

39 

.0001891 

40 

.6981317 

100 

1.7453293 

160 

2.7925268 

40 

.0116355 

40 

.0001939 

41 

.7155850 

101 

1.7627825 

161 

2.8099801 

41 

.0119264 

41 

.0001988 

42 

.7330383 

102 

1.7802358 

162 

2.8274334 

42 

.0122173 

42 

.0002036 

43 

.7504916 

103 

1.7976891 

163 

2.8448867 

43 

.0125082 

43 

.0002086 

44 

.7679449 

104 

1.8151424 

164 

2.8623400 

44 

.0127991 

44 

.0002133 

4$ 

.7853982 

105 

1.8325957 

165 

2.8797933 

45 

.0130900 

45 

.0002182 

H 

.8028515 

106 

1.8500490 

166 

2.8972466 

46 

0133809 

46 

.0002230 

47 

.8203047 

107 

1.8675023 

167 

2.9146999 

47 

.0136717 

47 

.0002279 

48 

.8377580 

108 

1.8849556 

168 

2.9321531 

48 

.0139626 

48 

.0002327 

49 

.8552113 

109 

1.9024089 

169 

2.9496064 

49 

.0142535 

49 

.0002376 

50 

.8726646 

110 

1.9198622 

170 

2.9670597 

50 

.0145444 

50 

.0002424 

61 

.8901179 

111 

1.9373155 

171 

2.9845130 

51 

.0148353 

51 

.0002473 

12 

.9075712 

112 

1.9547688 

172 

3.0019663 

52 

.0151262 

52 

.0002521 

S 

.9250245 

113 

1.9722221 

173 

3.0194196 

53 

.0154171 

53 

.0002570 

54 

.9424n8 

114 

1.9896753 

174 

3.0368729 

54 

.0157080 

54 

.0002618 

66 

.9599311 

115 

3.0071286 

175 

3.0543262 

65 

.0159989 

55 

.0002666 

SO 

.9773844 

116 

8.0245819 

176 

3.0717795 

56 

.0162897 

66 

.0002715 

57 

.9948377 

117 

2.0420352 

177 

3.0892328 

57 

.0165806 

57 

.0002763 

68 

1.0122910 

118 

3.0594885 

178 

3.1066861 

58 

.0168715 

58 

.0002812 

59 

1.0297443 

119 

2.0769418 

179 

3.1241394 

59 

.0171624 

59 

.0002860 

iO 

1.0471976 

120 

2.0943951 

180 

3.1415927 

60 

.0174533 

60 

.0002909 

Note. — ^Length  of  arc  is  directly 
zadius. 


proportional  to  central  angle  and  to 


d  by  Google 


210 


n.— MENSURATION, 


4. — Lengths  of  Circular  Arcs  for  Chord  1. 
(Note. — Multiply  the  tabular  number  by  the  length  of  chord.) 


ps6 


Ttaouaandths 


.001 


.002 


.003 


.004 


.005 


.006 


.007 


1.00000 
.00027 
00107 
.00240 
.00426 

1.00665 
.00957 
.01302 
.01698 
.02146 

1.02646 
.03196 
.03797 
.04447 
.05147 

1.05896 
.06693 
.07537 
.08428 


1.00002 
.00032 
.00117 
.00256 
.00447 

1.00692 
.00989 
.01338 
.01741 
.02192 


.10347 
.11374 
.22  .12444 
.23  .13557 
.24  .14714 


1.0 
.03254 
.03860 
.04515 
.05220 

1.05973 
.06775 
.07624 
.08519 
.09461 

1.10447 
.11479 
.12554 
.13671 


1.00002 
.00038 
.00128 
.00272 
.00469 

1.00720 
.01021 
.01376 
.01784 
.02240 

1.02752 
.03312 
.03923 
.04584 
.05293 

1.06051 
.06858 
.07711 
.08611 
.09557 

1.10548 
.11584 
.12664 
13785 


14832    .14951 


1.15912 
.17150 
.18429 
.19746 
.21102 

1.22495 
.23926 
.25391 
.26892 
.28428 

1.29997 
.31599 
.33234 
.34899 
.36596 

1.38322 
.40077 
.41861 
.43673 
.45512 

1.47377 
.49269 
.51185 
.53126 
.55091 


1.16034 
.17276 
.18559 
. 19880 
.21239 

1.22636 
.24070 
.25540 
.27044 
.28583 

1.30156 
.31761 
.33399 
.35068 
.36767 

1.38496 
.40254 
.42041 
.43856 
.45697 

1.47565 
.49460 
.51378 
.53322 
.65289 


50    1.67080 


1.16156 
.17403 
18689 
.20014 
.21377 

1.22778 
.24216 
.25689 
.27196 
.28739 

1.30315 
.31923 
.33564 
.35237 
.36939 

1.38671 
.40432 
.42221 
.44039 
.45883 

1.47753 
.49651 
.61571 
.53518 
.65487 


1.00004 
.00053 
.00153 
.00307 
.00515 

1.00776 
.01088 
.01453 
.01872 
.02339 

1.02860 
.03430 
.04051 
.04722 
.05441 

1.06209 

.07025 

.07799     .07888 


1.00003 
.00046 
.00140 
.00289 
.00492 

1.00748 
.01064 
.01414 
.01828 


1.02806 
.03371 
.03987 
.04652 
.05367 

1.06130 
.06941 


.08704 

.08797 

.09664 

.09762 

1.10650 

1.10762 

.11690 

.11796 

.12774 

.12885 

.13900 

.14015 

.15070 

.15188 

.16279 

1.16402 

.17530 

.17657 

.18820 

.18951 

.20149 

.20284 

.21515 

.21654 

1.22920 

1.23063 

.24361 

.24507 

.25838 

.25988 

.27349 

.27502 

.28895 

.29052 

1.30474 

1.30634 

.32086 

.32249 

.33730 

.33896 

.35406 

.35576 

.37111 

.37283 

1.38846 

1.39021 

.40610 

.40788 

.42402 

.42583 

.44222 

.44405 

.46069 

.46256 

1.47942 

1.48131 

.49842 

.50033 

.51764 

.51958 

.53714 

.53910 

.55685 

.55884 

1.00007 
.00061 
.00167 
.00327 
.00539 

1.00806 
.01123 
.01493 
.01916 


.02914 
.03490 
.04116 
.04792 
.06516 

.06288 
.07109 
.07977 


1.10855 
.11904 
.12997 
.14131 
.15308 

1.16526 

.17784 
.19082 
.20419 
.21794 

1.23206 
.24654 
.26138 
.27656 
.29209 

1.30794 
.92413 
.34063 
.35744 
.37456 

1.39196 
.40966 
.42764 
.44589 
.46441 

1.48320 
.50224 
.62152 
.64106 
.56083 


1.00010 
.00069 
.00182 
.00345 
.00563 

1.00834 
.01158 
.01633 
.01961 
.02440 

1.02970 
.03551 
.04181 
.04862 
.06691 

1.06368 
.07194 
.08066 
.08984 
.09949 

1.10958 
.12011 
.13108 
.14247 
.15428 

.16650 
.17912 
.19214 
.20565 
.21933 

1.23349 
.24801 
.26288 
.27810 
.29366 

.30954 
.32677 
.34229 
.35914 
.37628 

1.39372 
.41145 
.42945 
.44773 
.46628 

1.48509 
.60416 
.62346 
.64302 
.56282 


1.00013 
.00078 
.00196 
.00364 
.00587 

1.00864 
.01193 
.01573 
.02006 
.02491 


.03611 
.04247 
.04932 
.05667 

1.06449 
.07279 
.08156 
.09079 
.10048 

1.11062 
.12118 
.13219 
. 14363 
.15549 

1.16774 
.18040 
.19346 
.20691 
.22073 

1.23492 
.24948 
.26437 
.27964 
.29523 

1.31115 
.32741 
.34396 
.36084 
.37801 

1.39548 
.41324 
.43127 
.44957 
.46815 

1.48699 
.50608 
.52641 
.64499 
.66481 


ftAoS^;"^?"  ^  ^^<^  o^  215  ft.  and  rise  of  18  ft.:  The  rise  +  chord  • 
LOlM-ift^OO^     corresponding  arc  =-  215  X  (1.01828  +  .721  X  .00044)  -  215  J 


Digitized 


byGoogk 


FLAT  CIRCULAR  ARC,  211 


Fig.  10. 


Flat  afciilar  Arc.— 
Exact  formulas: 


a  -  chord  of  half  arc  --J/i«  +  Cj)  *  -y sec  }  a ; 
9    —  external  secant  —  r  (sec  J  oc  —  1)  —  r  (exsec  i  ex) 
t    —  tangent  distance  —  r  tan  i  CC  ■■  r  sec  i  OC . 


Approximate  formulas: 

gg-c. 

3     •  "*  "        2r  c« 


8^2— c  ,         «(<:—«)        4 /tap,        . 


c    —  chord  •»  8 c s—  8 a;  At  —  quarter  ordinate •=•  }  A  (  when  «  —7")  ; 


•   -  h\ 


-iV^^= 


A  —  rise  —  g-  ( /.  ^  —  sr)  J     yi  —   I  *.     («  -  cen.  of  grav.  of  arc.) 

The  coefficients  in  Table  5  (a  and  b),  following,  give  an  idea  of  the  ap- 
proximation of  the  aboye  formulas;  ana  they  will  also  be  found  convenient 
to  use  in  some  cases  where  fairly  correct  values,  simply,  are  sought. 


d  by  Google 


212 


ll.^MENSURA  TION, 


6. — CoBPPiciBNTS  TO  BB  usBD  WITH  Approximatb  FORMULAS   (Page,  pre- 
ceding) TO  oiVB  Exact  Valubs.     (Fig.  10.; 
•      (a) — Basbp  on  Cbntral  Anglb  a  -  10°.  20°,  30**,  etc. 
(Note. — Mixltiply  result  from  approximate  formiila.  by  (Coefficient.) 


Central        ^  _ 
Angle          ^  " 

idP 

20° 

30° 

40° 

50° 

60° 

Values  of   *    => 

.02183 

.04374 

.00588 

.06816 

.11065 

.13S97 

Values  of  J    - 

1.00127 

1.00610 

1.01152 

1.02000 

1.03245 

1.04720 

Values  of  -    - 
a 

.90873 

.9M98 

.96862 

.07962 

.96867 

.96493 

Values  of  -    =• 

r 

.17481 

.34730 

.51764 

.68404 

.84524 

1.00000 

Formulas. 


Coefficients.* 


"'%-- 

^        X 

1.00000 

1.00000 

90000 

.99997 

.99992 

.99964 

c  -  (8ca- 

-3a)  X 

1.00000 

.vww 

.99997 

QQQQ1 

.99977 

.99951 

U-h 

X 

1.00382 

1.01543 

1.03528 

1.06418 

1.10338 

1.15470 

^      8r 

X 

.99610 

.99240 

.98296 

.90986 

.96315 

.98301 

t*,-|A 

X 

1.00017 

1.00064 

1.00143 

1.00256 

1.00401 

1.00681 

t*2-iA 

X 

1.00060 

1.00191 

1.00429 

1.00765 

1.0U99 

1.01738 

tyi-|A 

X 

1.00014 

1.00062 

1.00116 

1.00204 

1.00321 

1.00464 

*t^    tc'     ^e  *     8sinJa-smioc    .  8  8m}a—  Uarc 

*  Coefficient  for  a  —  f  • = = —  ;  for  c  —  -. — i = ; 

arc  sin  t  oc 

for#-secia;  for  *-cos^  J  a;  for  h,-l l-co8  i  a  — 

cos  4  a— cos  4  ex 

.  ^.       4(l-co3ia)     .  ,    1-cosia 

for  *a«-  -p j-S-r^ ;  for  yi  —  | = — . 

1  — cos  i  oc  c  , 

'  cosja 

a 

t  Increase  in  coefficient  is  nearly  parabolic;  that  is,  nearly  proportional 
to  a«;  thus,  the  coefficient  of  hi  for  a  -  18°.  is  1+  .  00064  X  U^J  -  1.00052, 

using  the  coefficient  of  the  nearest  angle. 

I  Decrease  in  coefficient  is  nearly  parabolic 


d  by  Google 


FLAT  CIRCULAR  ARC. 


318 


5.— CoEFPiciBNTS  TO  BB  U8BD  WITH  AppROxiMATB  FORMULAS. — Concluded. 

(b)  Basbd  on  Rise  to  Chord.  -  .  or  Arc. 
c 


(Note. — ^Mtiltiply  result  from  approximate  formula,  by  Coefficient.) 

Values  of  — 

c 

- 

.02 

.M 

.06 

.06 

.10  ' 

.12 

Values  of  a 

- 

9*  00' 46' 

18»  17'  44'  27*  22'  16'  36o  21'  40*  45»  14'  23*  63*  68'  69' 

Values  of  ~ 

- 

6.3 

3.1 

2.1 

1.6 

1.3 

1.1 

Values  of  ~ 

- 

.16 

.32 

.47 

.62 

.77 

.91 

Formulas. 

Coefficients. 

t»- A 

X 

1.003 

1.013 

1.029 

1.062 

1.063 

1.122 

^< 

X 

.998 

.994 

.966 

.976 

.962 

.946 

t*i-i* 

X 

1.000 

1.001 

1.001 

1.002 

1.003 

1.006 

t*»-iA 

X 

1.0004 

1.0016 

1.0036 

1.0063 

1.0098 

1.0140 

t  Increase  in  coefficient  is  nearly  parabolic. 
t  Decrease  in  coefficient  is  nearly  parabolic. 


d  by  Google 


—jnniM^KJivni  iL/i\. 


Fig.  11. 

Circular  Segment;  and  Half  Sefment. — 

Diameter  <<  «  2  r . 


Point     g  - 

Formulas  for  CenUr  of  Gravity  (Fig.  11): 


position 
of  center 
of  grav- 
ity of 


segment  A 
\  (segment  ^4) 
segment  B 
.  i  (segment  B)  , 


with 
coordi- 
nates 


«-Ao:y-Ko. 


For  smaller  segment: 
ex  -  O'*  to  180*' 

For  larger  segment: 
)9  =  180**  to  360° 


(Geometrical) 
c.«-£!(r-*) 

area  A  of  segment 

c»_ 

area  i4  of  segment 

V     1  4sinn/?  +  pinHjg  cos  iff  Ct«+j-(H-r) 

""         l>?i  +  sinjff  cosjff     "  *  ''area  B  of  segment 


xo^\r 


4sin»ia— sin«§a  cosjoc 
iaj-sinjacosia 

sin^joc 

iai-sinjacosia 


-  \r 
"A 


Yo-\r~ 


sinHff 


Or.  yo  -jYA'  ^""^  12B 


i<?j  +  siniff  cosiff 


--A- 


area  B  of  segment 


Y"^  when  (X  +  ff  -  3W». 


Note  that  sin  \  a=»sin  J  ff;  cos  \  a— cos  i  ff;  but  sin  J  oc^cos  iff.etc. 
Table  6,  below,  gives  tabular  values. 


-Values  (Coeppicibnts)  op  xq,  yo.  -^o  and  Yq  por  Various  Values  of 

a  AND  ff.    (Fig.  11.) 

(Multiply  the  tabular  Coeflficient  by  the  radius.) 


xa^ 

^0  = 

Xo^ 

Yo- 

«o- 

yo- 

ATo-     K.- 

ex 

r 

r 

ff 

r 

r 

a 

r 

f 

ff 

r 

f 

times 

times 

times 

times 

times 

times 

times 

times 

0^ 

.00000 

Unity 

360° 

.42441 

.00000 

30" 

.09728 

.97957 

330° 

.42666 

.00369 

120° 

.33920 

.70S02 

240° 

.44102 

.17133 

00° 

.18930 

.91994 

300° 

.42211 

.03301 

160° 

.39058 

.66734 

210° 

.44162 

.28849 

90°  1.27124 

.82687 

270° 

.43972 

.08252 

1  180° 

.42441 

.42441 

180H 

.42441 

.42441 

d  by  Google 


'CIRCULAR  SEGMENTS.  215 


F  Circular  Segmtnt  (Fig  11;  Tables  7,  8).— 
;  greater  than  a  semi-circle,  i.  e.,  oc  not  >  180**. 
;  less  than  a  semi-circle,  i.  e.,  i?  not  <  180". 

■— *)— r  (^— rsin  i  a  cos  J  ex  J  —  YCo— r  sin  oc).  (1) 

t/_r)-r/|-+r  sin  J/Jcosi;?)  -y  (fc  +  r  sin  ;9).  (2) 
(2),  above,  are  General  Formulas.] 
and  b  arc  given  in  terms  of  r,  c  and  h ;  whence — 
■)— sin  ocl  —  area  of  sector  — area  of  triangle  be- 
J  tween  chord  and  radii.  (3) 

i+sinj?     1  —area  of  sector  +  area  of  triangle  be- 


i 


tween  chord  and  radii.  (4) 

c^ 
2r* 

-   in  which  vers  \  ex  -  —  -  2  sin*  \  oc.     (7) 

]2h 
in  which  tan  i  a .  (8) 

c 

and  central  angle  are  given  use  equation  (1),  (2), 
itral  angle,  use  (5)  or  (0);  rise  ancl  chord,  use  (5), 
id  rise,  use  (7).    Sec  also  foot-note  to  Table  8. 


I  — sin  oc   l .       u-  t.    •     1  ^       ^    *       1  ^     2A    ,.^ 
m  which  sm  i  oc  =-  2"  ;  tan  J  a  =-  — .  (5) 

-l-sin  ^      1.       ....,«        c     ,       ,  „        c     ,„. 
—    m  which  sm  i  ^  =  Tj;  ;  tan  I  /9  =  ^.  (6) 


I -sin  oc 


d  by  Google 


216 


11  .—MEN  SURA  TION, 


A^.- 


7. — ^Tablb  op  Circular  Sbombnts — ^Arbas,  Etc. 

To  fiAd  the  area:   Multiply  the  tabular  coefficient  in  coliimn  4  by  r*;  or  the 
coefficient  in  column  5  by  /i  X  c 


1 

2 

8 

4 

5 

1 

2 

3 

4 

5 

III 

Rise  A 
Radr 

Riaeh 

Area- 

IF 

Rise  h 

Rise  h 

Area 

- 

(Rad)* 
times 

he 
tlmee 

(Rad)t 
times 

Chord  c 

Radr 

Chorde 

times 

1" 

.00004 

.00218 

0000004 

.6667 

51« 

.0974 

.1131 

.0564860 

.67344 

2 

.00015 

.00436 

!0000035 

.6667 

53 

.1012 

.1154 

.0597802 

.67373 

3 

.00034 

.0000119 

.6667 

53 

.1051 

.1177 

.0631945 

.67400 

4 

.00061 

! 00873 

.0000284 

.6667 

54 

.1090 

.1200 

.0667304 

.67429 

6 

.00095 

.01091 

.0000554 

.6667 

55 

.1130 

.1223 

.0703896 

.67458 

6 

.00137 

.01309 

.0000956 

.6667 

66 

.1171 

.1247 

.0741734 

.67488 

7 

.00187 

.01528 

.0001518 

.6667 

67 

.1212 

.1270 

.0780885 

.67619 

8 

.00244 

.01746 

.0002266 

.6668 

58 

.1254 

.1293 

.0821214 

.67650 

9 

.00308 

.01965 

.0003226 

.6669 

69 

.1296 

.1316 

.0862885 

.67682 

10 

.00381 

.02183 

.0004424 

.66690 

60 

.1340 

.1340 

.0905861 

.67614 

11 

.00460 

.02402 

.0005886 

.66697 

61 

.1384 

.1363 

.0950156 

.67647 

12 

.00548 

.02620 

.0007639 

.66702 

62 

.1428 

.1387 

.0995783 

.67681 

13 

.00643 

.02839 

.0009709 

.66708 

63 

.1474 

.1410 

.1042755 

.67715 

H 

.00745 

.03058 

.0012121 

.66716 

64 

.1520 

.1434 

.1091084 

.67750 

15 

.00856 

.03277 

.0014902 

.66725 

65 

.1566 

.1457 

.1140781 

.67786 

16 

.00973 

.03496 

,0018076 

.66731 

66 

.1613 

.1481 

.1191859 

.67822 

17 

.01098 

.03716 

.0021671 

.66740 

67 

.1661 

.1505 

.1244328 

.67858 

18 

.01231 

.03935 

.0025711 

.66749 

68 

.1710 

.1529 

.1298200 

.67897 

19 

.01371 

.04155 

.0030222 

.66758 

69 

.1759 

.1563 

.1353484 

.67931 

20 

.01519 

.04374 

.0035229 

.66769 

70 

.1808 

.1576 

.1410189 

.67974 

21 

.01675 

.04594 

.0040756 

.66779 

71 

.1859 

.1601 

.1468326 

.68014 

32 

.01837 

.04814 

.0046829 

.66790 

72 

.1910 

.1625 

.1527903 

.68054 

23 

.02008 

.05035 

.0053473 

.66802 

73 

.1961 

.1649 

.1588928 

.68095 

24 

.02185 

.05255 

.0060712 

.66814 

74 

.2014 

.1673 

.1651410 

.68136 

25 

.02370 

.05476 

.0068570 

.66826 

75 

.2066 

.1697 

.1715366 

.68179 

26 

.02563 

.05697 

.0077073 

.66840 

76 

.2120 

.1722 

1780773 

.68222 

27 

.02763 

.05918 

.0086242 

.66853 

77 

.2174 

.1746 

.1847667 

.68365 

28 

.02970 

.06139 

.0096103 

.66868 

78 

.2229 

.1771 

.1916046 

.68310 

29 

.03185 

.06361 

.0106679 

.66882 

79 

.2284 

.1795 

.1985915 

.68355 

30 

.03407 

.06583 

.0117994 

.66897 

80 

.2340 

.1820 

.2057278 

.69401 

31 

.03637 

.06805 

.0130070 

.66913 

81 

.2396 

.1845 

.2130142 

.68448 

32 

.03874 

.07027 

.0142930 

.66929 

82 

.2453 

.1869 

.2204509 

.68495 

33 

.04118 

.07250 

.0156598 

.66946 

83 

.2510 

.1894 

.2280385 

.68543 

34 

.04370 

.07473 

.0171095 

.66964 

84 

.2569 

.1919 

.2357773 

.68592 

85 

.04628 

.07696 

.0186444 

.66983 

85 

.2627 

.1944 

.2436676 

.68641 

36 

.04894 

.07919 

.0202666 

.67000 

86 

.2686 

.1970 

.2517096 

.68692 

37 

.05168 

.08143 

.0219784 

.67019 

87 

.2746 

.1995 

.2599035 

.68743 

38 

.0S448 

.08367 

.0237818 

.67039 

88 

.2807 

.2020 

.2682495 

.68795 

39 

.05736 

.08592 

.0256790 

.67059 

89 

.2868 

.2046 

.2767477 

.68848 

40 

.06031 

.08816 

.0276721 

.67079 

90 

.2929 

.2071 

.2853982 

.68902 

41 

.06333 

.09041 

.0297630 

.67101 

91 

.2991 

.2097 

.2942010 

.68956 

42 

.06642 

.09267 

.0319538 

.67123 

92 

.3053 

.2122 

.3031561 

.69011 

43 

.06958 

.09493 

.0342466 

.67145 

93 

.3116 

.2148 

.3122634 

.69067 

44 

.07282 

.09719 

.0366432 

.67168 

94 

.3180 

.2174 

.3215227 

.69123 

45 

.07612 

.09946 

.0391457 

.67193 

95 

.3244 

.2200 

.3309340 

.69181 

46 

.07950 

.10173 

.0417558 

.67215 

96 

.3309 

.2226 

.8404971 

.69239 

47 

.08294 

.10400 

.0444755 

.67240 

97 

.3374 

.2252 

.3502116 

.69299 

48 

.08645 

.10628 

.0473066 

.67266 

98 

.3439 

.2279 

.3600773 

.69359 

49 

.09004 

.10856 

.0502504 

.67292 

99 

.3506 

.2305 

.3700938 

.69420 

50 

.09369 

.11085 

.0533101 

.67318 

100 

.3572 

.2332 

.3802607 

.69483 

d  by  Google 


218 


n.—MENSURA  TION. 


8. — *Arbas  of  Sbombnts  of  Circlbs  for  Diambtbr  1. 

To  find  the  area  of  any  circular  segment:  Mtiltiply  the  tabular  arc 
below,  corresponding  to  the  particular  value  of  rise  ••-  dtam.,  by  the  squar 
of  the  diam. 

Note  that  the  diam.^  rise  +(half  chord)* + rise;    hence,   (diam.)*   « 
ri-KhaJfchord)«1  \  ^^^  ^^  _^  duim.'  rise«+lrise«+  (half  chord)*]. 
L  nse J 


TbousaDdthfl. 


.001 


.002 


.003 


.004 


.005 


.007   .008 


.003 


.00 
.01 
.02 
03 
.04 
.05 
.06 
.07 
.08 
.09 
.10 
.11 
.12 
.13 
.14 
.16 
.16 
.17 
.18 
.19 
.20 
.21 
.22 
.23 
.24 
.25 
.26 
.27 
.28 
.29 
.30 
.31 
.32 
.33 
.84 
.35 
.36 
.37 
.38 
.39 
.40 
.41 
.42 
.43 
.44 
.45 
.46 
.47 
.48 
.49 
.50 


.001329 
.003749 
006866 
010538 
014681 
019239 
.024168 
.029435 
.035012 
040875 
047006 


059999 
066833 
073875 
.081112 


.096135 
.103900 
111824 
.119898 
128114 
.136466 
144945 
.153546 
.162263 
.171090 
.180020 
.189048 
.198168 
.207376 
216666 
.226034 
,235473 
244980 
254551 
264179 
.273861 
283593 
293370 
303187 
313042 
322928 
332843 
.342783 
352742 
.362717 
372704 
382700 
392699 


.000042 
001533 
.004033 
007209 
.010932 
.015119 
019716 
.024680 
.029979 
.035586 
.041477 
.047633 
.054037 
.060673 
067528 
074590 
081847 
.089288 
.096904 
104688 
.112625 
.120713 
128943 
137307 
145800 
.194413 
163141 
.171978 
18U918 
.189956 
.199086 
.208302 
217600 
.226974 
236421 
.245935 
.255511 
265145 
274832 
284569 
.294350 
304171 
.314029 
.323919 
.333836 
.843778 
353739 
363715 
.373704 
.383700 


.000119 

001746 
.004322 

007559 
.011331 
.015561 
.020197 

026196 
.030526 

036162 
.042081 
.048262 

064690 
.061340 

068225 
.075307 


.090042 
.097675 
.105472 
.113427 
.121530 
.129773 
.138151 
.146656 
.155281 
.164020 

172868 
.181818 

190866 


.209228 
.218534 
227916 
.237369 
246890 
.256472 
.266111 
275804 
.285545 
.295330 
305156 
315017 
.324909 
.334829 
.344773 
354736 
364714 
374703 
384699 


.000219 
.001989 
.004619 
.007913 
.011734 
.016008 

020681 
.025714 
.031077 
.036742 
.042687 

048894 
.055346 

062027 
.068924 

076026 
.083320 

090797 
.098447 

106261 

114231 
.122348 

130605 
.138996 

147513 
.156149 

164900 
.173758 

182718 
.191774 

200922 

210155 
.219469 
.228858 

238319 

247845 
.257433 

267078 
.276776 
.286521 

296311 
.306140 

316006 
.325900 
.335823 
.345768 
.355733 
.365712 
.375702 
.385699 


.000337 

002199 
.004922 

008273 
.012142 

016468 
.021168 

026236 
.031630 

037324 


000471 
.002438 

005231 
.008638 

012555 
.016912 

021660 
.026761 
.032186 
.037909 


.043296  -.043908 


049529 
.056004 

062707 

069626 
.076747 

084060 
.091555 

099221 
.107051 
.115036 
.123167 

131438 
.139842 
.148371 
.157019 
.165781 
.174650 
.183619 
.192685 
.201841 
.211U83 
.220404 
.229801 

239208 

248S01 
.258395 
.268046 

277748 
.287499 
.297292 
.307125 

316993 

326891 
.336816 

346764 
.356730 

366711 

376702 
.386699 


.050165 

056664 
.063389 

070329 
.077470 
.084801 
.092314 
.099997 

107843 
.115842 
.123988 
.132273 
.140689 
.149231 
.157891 
.166663 

175542 
.184522 

193597 
.202762 
.212011 

221341 
.230745 

240219 
.249758 
.259358 
.269014 

278721 
.288476 
.298274 

308110 
.317981 
.327883 
.337810 

347760 
.357728 
.367710 

377701 
.387699 


.00U61 9. 000779 
002685.002940 
005546.005867 
009008.009383 


.012971 

017369.017831 
.022155.022653 

027290.027821 


.032746 
038497 

.044523 
050805 

.067327 
064074 

.071034 


.033308 
.039087 
.045140 
.051446. 
057991 
064761 
.071741 


078194.078921 
085546.086290. 


.093074 
100774 


093837. 
.101553. 


.108636.109431 


.116651 
.124811 
.133109 
.14153fi 

150091 
.158763 
.167546 
.176436 

185425 
.194509 


212941 
.222278 

231689 
.241170 


117460. 

.125634 
133946, 

.142388. 
150953 

.159636, 
168431 

.177330, 
186329, 

.195423 
204605 
213871 
223216 
232634 
242122 


.250715.251673 


.260321 
.269982 


.261285 
870951 


.279695.280669 


.289454 


290432 


299256.300238 


.309096 
.318970 
.328874 
.338804 
348756 
.358725 
.368708 
.378701 


310082 
319958 
.329866 
.339799 
.349752 
.359723 
.369707 
S79701 


000952 
.003202 

006194 
.009763 

013818 
.018297 

023155 
.028356 
.033873 
.039681 

04S759 

0620M 

0586SS 

065449. 
.072460 . 

079650 
.087037 

094601 
.102334 

110227 
.118271 
.126459 

134784 

143239 
.151816 
.160511 

169316 
.178226 

187235 

196337 

205528 

214802 
.224154 

233580. 
.243074. 

252632. 
.262249 

271921 
.281643 
.291411 

301221 
.311068 


.0011«i 
00:4:; 

.OOCii. 

.010141 

.01424! 
018764 

.023664 

.028891 

.03444 
04027! 

.04638 
06273! 

.0593^ 

.066141 
07316: 

.08038 
08778 

.0953G 

.103111 
1110£ 
11908 

.12728 
U562 

.14409 
15268 

.16138 

.17020 
17912 
18814 
19725 
2064S 
21573 

.22501 
23453 
24401 
25359 
2C821 
2T289 
28261 
20289 
9Q22Q 

.31209 


.320949.32193 
330858.3318a 
340793.34178 


850749 
.360721 
.870706 

380700 


388699.389699.390699 


.36174 
36171 
.3717C 
.J817« 
.39161 


%:  AreaA-0.3928990817-[«(r«-«^*+f«sin-*-] 
and  *  =  radius— rise  =  0.5  — rise. 


♦Calculated  from  formula:  . 
in  which  f  "-radius  of  circle,  and  : 

Note  that  sin~*  —  =-  the  angle  (in  circular  tneasure)  whose  natural  sine 
— .  For  angles  reduced  to  circular  measure,  see  Tables  2  and  3. 


CIRCULAR  RING. 


319 


Circal«r  Ring ;  and  Half  Circolar  Ring.— 

Let     R  ->  radius  of  outer  circle"-  -r- ; 

r    —  radius  of  inner  drcle—  -r- ; 

R.—  radius  of  circle  with  area  equiyalent  to  that  Fig.  12. 

circular  ring; 
A  —  area  of  circular  ring;  x  — 8.1416. 

Then/2.-  V/?-f«-V(/?+r)  (/?-r)-i V(i?+<0(I>-<0--J^; 

A  -  »/2.«-»(i2»-f«)-«(ie+f)(i?-f)- j(D«-d«)--i(I?+d)(2?-<0; 
1?  -  Ji*+  J  -  Vf«+i?.«;  2?-Jd«+~; 

r    -  Jr^-^  "VR^-RJ;  d^Ju*-^. 

Formula  for  Center  of  Gravity  (Pig.  12): 
B     t.  «    •      1       .               0.42441  (jg*-f<)       0.21221  (i>«-d«)       _,.  ^ 
For  half  circular  nng.acto ^^5::^^^^ (D^^d^) d»tance 

to  cen.  of  grav.  g. 
The  above  valtie  of  ^may  be  obtained  from  Pappus's  Theorem,  page  243. 
by  usixig  it  inversely.  Thus,  we  know  that  the  volume  generated  by  the 
revolution  of  a  plane  area  Oiring  wholly  on  one  side  of  an  axis)  about  its 
axis  —  the  area  X  the  path  described  by  its  center  of  gravity.  Hence, 
vohune  V— 2»«oA;  or 

^    V  volume  of  spherical  shell      ^  1     -3  *  (^  ~  ^ 

*•  "  %kA  "   2>r .  Area  of  half  drctilar  ring  *"  %t 


y  iR^-f^ 


_4 


^-^ ;  in  which  ^  -  0 .  42441. 


Pappus's  Theorem  is  useful  in  finding  the  centers  of  gravity  of  any 
figures  (lines  or  areas)  of  revolution. 

ZoM,  and  Half  Zone,  of  Circle.— 

Area  of  sone  >»  Z  «■  area  of  circle  (3.1416  f^ 
—  (A+B);  in  which  t  —  radius  of  circle,  A  — 
area  of  upper  segment^  and  B  —  area  of  lower 
segment.  (See  preceding  tables  and  formulas 
for  areas  of  segments.) 

Formulas  for  Center  of  Gravity  (Fig.  13): 
Let  g  —  cen.  of  grav.  of  sone,  with  coordinates 
«— 0,  y^yo't 
tx  ->  cen.  of  grav.  of  half  zone,  with  coor- 
dinates x^xo,  y— yb; 
A  —  area  of  upper  segment,  with  cen.  of 

grav.  dist.  y»from  axis  Xi  — Xi; 
Z  —  area  of  xone.  with  cen.  of  grav.  dis- 
tant y,  from  Xx—Xi 


Y 

Fig.  18. 
B  —  area  of  lower  segment.'with  cen.  of  grav.  dist.  y^  from  Xx  —  Xi\ 
C  —   area  of  circle  (—3.141 6r*) ,  with  cen.  of  grav.  distant  r  from  Xx—Xi ; 


Then.s^  — 


0. 42441  fC-A3g>-gyw  . 
Z 

Cr  -  Ay.  ~  By^ 


Ordinates  x..  ar^,  y,  and  y% 
may  be  solved  by  use  of  formulas 
in  connection  with  Fig.  11. 


220 


11.— MENSURATION. 


Fig.  14. 
CircnUr  Lune  (Pig.  14)  «— 

Area  A  —  area  of  segment  with  riae  h  minus  area  of  segment  with  rise  h\ 
(Common  chord  c.) 
See  preceding  Tables.  7  smd  8,  of  Circular  Segments. 

Circular  Sector ;  and  Half  Sector  (Fig.  15). — 


Points   — 

g: 


position 
of  center 
of  grav- 
ity of 


sector  A     1  with 
i(sectori4)    Icoordi- 

sector  B     \  nates. 
.  i  (sector  B)  J 


af-0;y-yo 
x-0:y-Fo 

i*-A^o;y-Ko 


FormuJas  far  Center  of  Gravity  and  Arta  (Fig.  16): 
-    sin  i  a     .    sin  i  a     .   .sin  i  a     -   .sin  i  a 

yo  -t*'-y5E; — ^^—^^ — ^^—^ — *^-^r-- 

xo    -5^tanJa-ir^^-|r«X£riiE-,^I5!|i«. 
^0  -lr*-^-U-^-§r«i^ 


JVo  -    yotanJ^-|f 


vers  ^  fi 
Pi 


-Jf« 


vers  i  ff 


-If* 


vers  i  $ 


.        M        t  -M  ^        1                  •  _•  sin  i  oc     -  _,  vers  ioc 
Area  A  ^  ^r*  cCi  "  ^ar        -|f» — -|f»^ ^— 


A        n       t  ^  ^  11-  •  _•  sin  ^  0      -  _,  vers  i 

Ar«aB^^r*0t    -i6f         -|  f» — ~»^-|f« — -~ 

ro  Ao 

In  which  a  —  length  of  arc  of  sector  of  area  A  and  central  angle  oc, 
jth  of  arc  of  sector    '  -^       .  .        .     - 

(Xi  -   .0174583  a  rdcgrecs), 


b  —  length  of  arc  of  sector  of  area  B  and  central  angle 

-   .0174583  a  (■  _  ^     " 

fii   -   .0174533  fi  (degrees). 


(See  Tables  2  and  8  of  length  of 
circular  arcs  to  radius  1.) 


Relations  of  Circle  and  Square. — 

Let     D  —  diam.  of  circle;    C  —  circum.  of  cixx:le;  A  —  area  of  circle. 

d  —  diag.  of  square;    s  =»  side  of  square;       p  —  perimeter  of  square; 
a  —  area  of  square. 

n       C  D  4  4       4» 

rf  -  jVr-^Vr-V'25;  5--^-^-\/r:p-2d\/r-45-4VT; 
4  v''2     * 

d*        ,      ^ 
^-2--^'-i6- 
(For  convenience  of  calculation:    jr=  3.141592+ .  log- 0.4071499; 
1 


•^-0.785398  +  .  log- 9.8950899: 


0.318310-.  log- 9.6028601; 
log  4-0.6020600;  log  i-9.3979400;  log  2-0.3010800; 

vT-1.414214-,  log-0.1505160;  -4r -0.707107,  log -9.8494860.) 

v/2 


CIRCLE  AND  SQUARE,  RELATIONS. 


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11.— MENSURATION. 


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224 


1 1  .—MENS  URA  TION. 


11. CiRCUMPBRBNCBS  C  OF   CXRCLBS   FOR   GIVEN 

Circumferences  are  directly  proportional  to  the  diameters. 


.2 
.3 
.4 

0.5 
.6 
.7 
.8 
.9 

1.0 
.1 
.2 
.3 
A 

1.5 
.6 

.7 


2.0 
.1 
.2 
.3 
.4 

2.5 
.6 
.7 
.8 
.9 

3.0 
.1 
.2 


3.5 
.6 

.7 


4.0 
.1 
.2 
.3 
.4 

4.6 
.6 
.7 
.8 
.9 


.000000 
.314159 
.628319 
.942476 
1.25664 

1.57080 
1.88496 
2.19911 
2.51327 
2.82743 

3.14159 
3.45575 
3.76991 
4.08407 
4.39823 

4.71239 
5.02655 
5.34071 
5.65487 
5.96903 

6.28319 
6.69734 
6.91150 
7.22566 
7.53982 

7.85398 
8.16814 
8.48230 
8.79646 
9.11062 

9.42478 
9.73894 
10.0531 
10.3673 
10.6»14 

10.9956 
11.3097 
11.6239 
11.9381 
12.2522 

12.5664 
12.8805 
13.1947 
13.5088 
13.8230 

14.1372 
14.4513 
14.7655 
15.0796 
16.3938 


.031416 
.345575 
.659734 
.973894 
1.28805 

1.60221 
1.91637 
2.23053 
2.54469 
2.85885 

3.17301 
3.48717 
3.80133 
4.11549 
4.42965 

4.74381 
6.05796 
5.37212 
5.68628 
6.00044 

6.31460 
6.62876 
6.94292 
7.25708 
7.57124 

7.88540 
8.19956 
8.51372 
8.82788 
9.142U3 

9.45619 
9.77035 
10.0845 
10.3987 
10.7128 

11.0270 
11.3411 
11.6553 
11.9695 
12.2836 

12.5978 
12.9119 
13.2261 
13.5403 
13.8544 

14.1686 
14.4827 
14.7969 
15.1111 
15.4252 


.062832 
.376991 
.691150 
1.00531 
1.31947 

1.63363 
1.94779 
2.26195 
2.57611 
2.89027 

3.20442 
3.51858 
3.83274 
4.14690 
4.46106 

4.77522 
5.08938 
5.40354 
5.71770 
6.03186 

6.34602 
6.66018 
6.97434 
7.28849 
7.60265 

7.91681 
8.23097 
8.54513 
8.85929 
9. 17345 

9.48761 
9.80177 
10.1159 
10.4301 
10.7442 

11.0584 
11.3726 
11.6867 
12.0009 
12.3150 

13.6292 
12.9434 
13.2575 
13.5717 
13.8858 

14.2000 
14.5142 
14.8283 
16.1425 
15.4566 


.094248 
.408407 
.722566 
1.03673 
1.35088 

1.66504 
1.97920 
2.29336 
2.60752 
2.92168 

3.23584 
3.65000 
3.86416 
4.17832 
4.49248 

4.80664 
5. 12080 
5.43496 
5.74911 
6.06327 

6.37743 
6.69159 
7.00575 
7.31991 
7.63407 

7.94823 
8.26239 
8.57655 
8.89071 
9.20487 

9.61903 
9.83319 
10.1473 
10.4615 
10.7757 

11.0898 
11.4040 
11.7181 
12.0323 
12.3465 

12.6606 
12.9748 
13.2889 
13.6031 
13.9173 

14.2314 
14.5456 
14.8597 
15.1739 
15.4881 


15.7080  15.7394  15.7708  15.8022 


.125664 
.439823 
.753982 
1.06814 
1.38230 

1.69646 
2.01062 
2.32478 
2.63894 
2.95310 

3.26726 
3.58142 
3.89557 
4.20973 
4.52389 

4.83805 
5.15221 
6.46637 
5.78053 
6.09469 

6.40885 
6.72301 
7.03717 
7.35133 
7 


7.97965 
8.29380 
8.60796 
8.92212 
9.23628 

9.55044 
9. 86460 
10.1788 
10.4929 
10.8071 

11.1212 
11.4354 
11.7496 
12.0637 
12.3779 

12.6920 
13.0062 
13.3204 
13.6345 
13.9487 

14.2628 
14.5770 
14.8911 
15.2053 
15.5195 

15.8336 


.157080 
.471239 
.785398 
1.09956 
1.41372 

1.T2788 
2.04204 
2.35619 
2.67035 
2.98451 

3.29867 
3.61283 
3.92699 
4.24115 
4.55531 

4.86947 
5.18363 
5.49779 
5.81195 
6.12611 

6.44026 
6.75442 
7.06858 
7.38274 
7.69690 

8.01106 
8.32522 
8.63938 
8.95354 
9.26770 

9.58186 
9.89602 
10.2102 
10.6243 
10.8385 

11.1527 
11.4668 
11.7810 
12.0951 
12.4093 

12.7235 
13.0376 
13.3518 
13.6659 
13.9801 

14.2942 

14.6084 
14.9226 
15.2367 
15.5509 


.188496 
.502655. 
.816814 . 
1.130971 
1.445131.47656^1 


219911 
634071 
848230 
162391 


251327 
565487 

879M6 
.19381 
60796 


1.759291. 
2.07345  2. 
2.387612. 
2.70177  2. 


79071 
10487 
41903 
733192. 


1.82312 
2.13628 
2.45044 


015933.047343.07876 

3.33009  3.36150)3.39292 

3.644253.675663.70708  3 

3.958413 

4.27257 

4.58673 


98982  4. 
4.30398  4. 
4.618144.<496« 


03124  4 
33540  4.; 

i.i 


4.90088  4.1 
5.21504  5.: 


.93672 


2464«>5.27788  5.: 
56062  5.59203 
5.84336  5.874785  M6I 9 
6.167526.188M6.22035[6.: 


6.471686. 
6.785846. 
7.100007. 
7.414167. 
7.728327. 


9.61327 
9.92743 
10.2416 
10.5558 


50810 
817266. 
131427. 
44557  7. 
759737. 


5345116.  i 

84867 16.: 
1683h 
47699  7! 
7911517. 


8.042488.07389,8. 
35664 


!.10531S. 

41947  8.' 

8.7336318. 

9.04n»»i 

9.33053  9.3619519.: 


1.670808.70231 
K  01631 
9.29911 


9.644699.676119 
9.958859.9902611 


10.273010.3044 
10.587210.6186 
10. 8699 10. 9013110. 9327 


11.1841 11. 215511. 246K11 
11.498211.529611.5611  II 
11.8124  1 1. 843S1 1.8752  11 
I2.126512.1580tl2.1894l2 
12.4407  12.4721 12.50S5jl2 


12.754912.786312.1 

13.069013.: 

13.38321 

13.69731 

14.011514.0429(14.074314 


14.8257 

14.6398 

14. 

15.2681 

15.5823 


15.8650  16.8965 16.9279 


81TT  12 
13.131913 

7288;  13. 7602  13 


L1004 
13. 
13. 


14.3571 
14.6712 
9854 
16.2996 
15.6137 


14.388514 
14.7(07  14 
15.016S1S 


16.6451 II 


15.9593 


II 


Diameter  may  be  obtained  from  circumferences  b^r  inverse  Interpol 
Note.— ;Area  of  surface  of  Sphere  —  diameter  X  circumference  —  L 
Values  in  this  table  are  also  multiples  of  k. 


Digitized 


by  Google 


CIRCLES,  DIAM.  TO  CIRCUM.,  DEfflMALS. 


225 


— DiAlCBTBRS  D,  IN  DbCIM AL8. 

This  table  may  be  used  like  logarithmic  tables. 


15.7080 
1C.0331 
16.3 

if.esoij 

It.f 

17.2788 
17.6989 
17.9071 
18.2112 
18.53M 

18.8496 
If. 1637 
19.4779 
19.7920 
20.1062 

20.4204 
20.7345 
21.0487 
21.3628 
21.6770 

21.9911 
22.3053 
22.6195 
22.9336 
23.2478 

23.5619 
23.8761 
24.1903 
24.5044 
24.8186 

25.1327 
35.4469 

25.7611 
M.0752 
26.3894 

26.7036 
27.0177 
27.3319 
27.6460 
27.9602 

28.2743 
28.5685 

28.9027 
29.2168 
28.5310 

20.8451 
30.1593 
30.4724 
30.7876 
31.1018 


15.7394 
16.0539 
16.3677 
16.6819 
16.9960 

17.8102 
17.6243 
17.9385 
I8.25n 
18.5668 

18.8810 
19. 1951 
19.5093 
19.8235 
20.1376 

20.4518 
30.7659 
21.0801 
21.3943 
21.7084 

22.0226 
22.3367 
22.6509 
22.9650 
23.2792 

23.5934 
23.9075 
24.2217 
24.5358 
24.^00 

25.1642 
25.4783 
25.7925 
26.1066 
26.4208 

26.7350 
27.0491 
27.3633 
27.6774 
27.9916 

28.3058 
28.6199 
28.9341 
29.2482 
29.5624 

29.8765 
30.1907 
80.5049 
30.8190 
31.1332 


31.4159  31.4473 


16.7708 
16.0860 
16.3991 
16.7133 
17.0274 

17.3416 
17.6658 
17.9699 
18.3841 
18.5983 

18.9124 
19.2266 
19.5407 
19.8549 
20.1690 

20.4832 
20.7973 
21.1115 
21.4257 
21.7398 

22.0640 
22.3681 
22.6823 
22.9965 
23.3106 

23.6248 
23.9389 
24.2531 
24.5673 
24.8814 

25.1956 
25.5097 
25.8239 
26. 1381 
26.4522 

26.7664 
27.0806 
27.3947 
27.7088 
28.0230 

28.8372 
28.6613 
28.9655 
29.2796 
29.5938 

29.9080 
30.2221 
30.6363 
80.8504 
31.1646 

31.4788 


16.8022 
16.1164 
16.4305 
16.7447 
17.0588 

17.8730 
17.6872 
18.0013 
18.8156 
18.6296 

18.9438 
19.2580 
19.5721 
19.8863 
20.2004 

20.5146 
20.8288 
21.1429 
21.4571 
21.7712 

22.0854 
22.3996 
22.7137 
23.0279 
23.3420 

23.6562 
23.9704 
24.2845 
24.5987 
24.9128 

25.2270 
25.5411 
25.8553 
26.1695 
24.4836 

26.7978 
27.1119 
27.4261 
27.7403 
28.0644 

28.3686 
28.6827 
28.9969 
29.3111 
29.6252 

29.9394 
80.2535 
80.5677 
30.8819 
31.1960 

31.5102 


15.8836 
16.1478 
16.4619 
16.7761 
17.0903 

17.4044 
17.7186 
18.0327 
18.3469 
18.6611 

18.9762 

19.2894 

19.6 

19.9177 

20.2319 

20.5460 
20.8602 
21.1743 
21.4885 
21.8027 

22.1168 
22.4310 
22.7451 
23.0593 
23.3734 

23.6876 
24.0018 
24.3159 
24.6301 
24.9442 

25.2584 
25.5726 
25.8867 
26.2009 
26.5150 

26.8292 
27.1434 
27.4575 
27.7717 
28.0858 

28.4000 
28.7142 
29.0283 
29.3425 
29.6566 

29.9708 
80.2850 
30.5991 
30.9133 
31.2274 

31.5416 


15.8650 
16.1792 
16.4934 
16.8075 
17.1217 

17.4358 
17.7500 
18.0642 
18.3783 
18.6925 

19.0064 
19.3208 
19.6350 
19.9491 
20.2633 

20.6374 
20.8916 
21.2058 
21.5199 
21.8341 

22.1482 
22.4624 
22.7766 
23.0907 
23.4049 

23.7190 
24.0332 
24.8473 
24.6615 
24.9757 

25.2898 
25.6040 
25.9181 
26.2323 
26.5465 

26.8606 
27.1748 
27.4889 
27.8031 
28.1173 

28.4314 
28.7456 
29.0597 
29.3739 
29.6881 


16.8966 

16.2106 

16.5248 

16. 

17.1531 


16.927915.9593 
16.242016 

16.5562 
16.8704 
17.1845 


.2734 
16.5876 
16.9018 
17.2159 


17.4673 
17.7814 
18.0956 
18.4097 
18.723918. 


17.4987 
17. 

18.1270 

18.4411 

7553 


8128|17 

t97n  lO 


19.0381 

19.3622 

19.6664 

19.980520. 

20.2947 


19.0695 
19.3836 
19.6978 
1.0119 
20.3261 


17.6301 
.8442 
18.1584 
18.4726 
18.7867 

19.1009 
19.4150 
19.7292 
20.0434 
20.3575 


608820. 


1.6403  20.6717 

20.954420.9858 

21.2686  21.3000 

21.5827,21.6142 

865521.8969^1.9283 


20. 

20.9230 

21.2372 

21.5513 

21. 


22.179622 


22.4938 
22.8080 
23.1221 


23.4363  23 


23.7504 
24.0646  24 
24.378824 
24.6929  24 
25.007125. 


2111 

5262|22. 
8394,22. 
1535^3, 
4677p3, 

781  gb, 

0960,24. 
4102  24. 
7243  24. 
038525. 


2425 
5566 
8708 
1850 
,4991 

8133 
1274 
4416 
7558 
0699 


25.321225.3527  25.3841 
25.6354  25.666825.6982 
25. 9496125. 9810  26. 0124 
26.2637  26.295126.3265 
26.577926.6093  26.6407 


15.9907 
16.3049 
16.6190 
16.9332 
17.2473 

17.6615 
17.8757 
18.1898 
18.5040 
18.8181 

19.1323 
19.4466 
19.7606 
2U.0748 
20.3889 

20.7031 
21.0173 
21.3314 
21.6466 
21.9597 

23.2789 
22.5881 
22.9022 
23.2164 
23.5306 

23.8447 
24.1588 
24.4730 
24.7872 
^5.1013 

25.4155 
25.7296 
26.0438 
26.3580 
26.6721 


26. 8920^26. 9234  26. 9549  26. 9863 
27.2062  27.2376:27.2690  27.3004 
27.5204  27. 551827.5832127. 6146 
27. 8345 27. 8659127. 8973  27.9288 
28.1487  28.180128.2115  28.2429 

28.462828.4942128.5257  28.5571 
28.7770,28.8084  28.8398  28.8712 
29.0911,29.1226  29.1540  29.1854 
29. 4053'29. 4367  29.4681  29.4996 
29. 7195|29. 7509:29. 7823  29.8137 


30.033630.0650'30.0965  30.1279 
30.347830.3792  30.4106  30.4420 
30.661930.6934  30.7248  30.7562 


30.0022 

30.3164 

30.6305 

30.9447   30.9761131.007531.0389 

31.2588  31.2903  31.3217  31.3531 


31.5730 


31.6044 


31.0704 
31.3845 


LHff.  between  any  two  successive  circumferences  — .0314+-  hence,  if 
the  diameter  is  extended  to  the  third  decimal  place  (thousandths),  add 
'  00314+  multiplied  by  the  thousandth  figure).  £jf.—Dwtn.- 7.628;  then 
firci^m.  -  23.6248+.OO04- 23.6342. 


220 


•    11.— MENSURATION. 


12. — CiRCUMPBRBNCBS  OP  CiRCLBS  FOR  GlVBN — 

Circumferences  are  directly  proportional  to  the  diameters. 


Decimal 

.0000 

.083^ 

.1250 

.166^6 

.2500 

.333^3 

.8750 

.416^6 

FracUdDS-as  12tha  of  a  Foot  (Inches),  and  8tlis  of  an  Inch. 

Ft 

12tll8 

0 
"12 

1 
I2 

1.5 
12 

2 
"12 

3 
12 

4 
12- 

4.6 
IS 

5 

Ins. 

8ths 

0 

T 

1 

T 

2 
T 

3 

0 

.000000 

.261799 

.892699 

.623599 

.785398 

1.04720 

1.17810 

1.30900 

1 

3.14169 

3.40339 

3.53429 

3.66519 

3.92699 

4.18879 

4.31969 

4.45059 

2 

6.28319 

6.54498 

6.67588 

6.80678 

7.06858 

7.33038 

7.46128 

7.59218 

1 

00 

3 

9.42478 

9.68658 

9.81748 

9.94838 

10.2102 

10.4720 

10.6029 

10.7338 

4 

12.5664 

12.8282 

12.9591 

13.0900 

13.3518 

13.6136 

13.7445 

13.87M 

& 

6 

15.7080 

15.9698 

16.1007 

16.2316 

16.4934 

16.7552 

16.8861 

17.0r70 

6 

18.8496 

19.1114 

19.2423 

19.3732 

19.6350 

19.8968 

20.0277 

20.1586 

s 

7 

21.9911 

22.2529 

22.3838 

22.5147 

22.7766 

23.0383 

23.1692 

23.30U1 

.g 

8 

25. 1327 

25.3945 

25.5254 

25.6563 

25.9181 

26.1799 

26.3108 

26.4417 

c 

9 

28.2743 

28.5361 

28.6670 

28.7979 

29.0597 

29.3216 

29.4524 

29.5833 

•^ 

10 

31.4159 

31.6773 

31.8086 

31.9395 

32.2013 

32.4631 

32.5940 

32.7249 

i' 

11 

34.5575 

34.8193 

34.9502 

35.0811 

35.3420 

35.6047 

35.7356 

35.8665 

12 

37.6991 

37.9609 

38.0918 

38.2227 

38.4845 

38.7463 

38.8772 

39.0081 

ti 

13 

40.8407 

41.1026 

41.2334 

41.3643 

41.6261 

41.8879 

42.0188 

42.1497 

1 

14 

43.9823 

44.2441 

44.3750 

44.6059 

44.7677 

45.0295 

46.1604 

45.2913 

15 

47.1239 

47.3857 

47.5166 

47.6475 

47.9093 

48.1711 

48.3020 

48.4329 

1 

16 

50.2656 

60.6273 

50.6582 

60.7891 

61.0509 

61.8127 

61.4436 

51.5746 

17 

53.4071 

63.6689 

63.7998 

63.9307 

64.1925 

64.4543 

54.5852 

64.7161 

18 

56.5487 

66.8105 

66.9414 

67.0723 

67.3341 

57.6959 

67.7268 

67.8177 

io 

19 

59.6903 

69.9521 

60.0830 

60.2139 

60.4757 

60.7375 

60.8684 

60.9993 

< 

20 

62.8319 

63.0937 

63.2246 

63.3556 

63.6173 

63.8791 

64.0100 

64.1409 

21 

65.9734 

66.2352 

66.3661 

66.4970 

66.7588 

67.0206 

67.1515 

67.2824 

g 

22 

69.1150 

69.3768 

69.5077 

69.6386 

69.9004 

70.1622 

70.2931 

70.4240 

M 

23 

72.2566 

72.5184 

72.6493 

72.7802 

73.0420 

73.3038 

73.4347 

73.6666 

s 

24 

75.3982 

75.6600 

75.7909 

75.9218 

76.1836 

76.4464 

76.5763 

76.7072 

25 

78.5398 

78.8016 

78.9325 

79.0634 

79.3252 

79.5870 

79.7179 

79.8483 

1 

26 

81.6814 

81.9432 

82.0741 

82.2050 

82.4668 

82.728r 

«2.8595 

82.9904 

27 

84.8230 

85.0848 

85.2157 

85.3466 

85.6084 

85.8702 

86.0011 

86.1320 

a 

28 

87.9646 

88.2264 

88.3570 

88.4882 

88.7500 

89.0118 

89.1427 

89.2736 

'T 

29 

91.1062 

91.3680 

91.4989 

91.6298 

91.8916 

92.1534 

92.2843 

92.4162 

o 

30 

94.2478 

94.6096 

94.6405 

94.7714 

94.0332 

95.2950 

95.4259 

95.6668 

1 

31 

97.3894 

97.6512 

97.7821 

97.9130 

98.1748 

98.4366 

98.5675 

98.6984 

32 

100.531 

100.793 

100.924 

101.055 

101.316 

101.578 

101.709 

101.840 

33 

103.673 

103.934 

104.065 

104.196 

104.458 

104.720 

104.851 

104.962 

£ 

34 

106.814 

107.076 

107.207 

107.338 

107.600 

107.861 

107.992 

108. 123 

1 

35 

109.956 

110.218 

110.748 

110.479 

110.741 

111.003 

111.134 

111.265 

36 

113.097 

113.359 

113.490 

113.621 

113.883 

114.145 

114.145 

114.406 

g 

37 

116.239 

116.501 

116.632 

116.763 

117.024 

117.286 

117.417 

117.548 

S 

38 

119.381 

119.642 

119.773 

119.904 

120.166 

120.428 

120.569 

120.690 

Q 

39 

122.522 

122.784 

122.916 

123.046 

123.308 

123.669 

133.700 

123.831 

g 

40 

125.664 

125.926 

126.056 

126.187 

126.449 

126.711 

126.842 

126.973 

1 

41 

128.805 

129.067 

129.198 

129.329 

129.591 

129.852 

129.983 

130.114 

43 

131.947 

132.209 

132.340 

132.470 

132.732 

132.994 

133.126 

133.K6 

43 

135.088 

135.350 

135.481 

135.612 

136.874 

136.136 

136.267 

136.  S97 

44 

138.230 

138.492 

U8.623 

138.754 

139.015 

139.277 

139.408 

139.539 

1 

45 

141.372 

141.633 

141.764 

141.895 

142.157 

142.419 

142.550 

143.681 

46 

144.613 

144.775 

144.906 

145.037 

145.299 

145.660 

145.691 

145.822 

47 

147.655 

147.917 

148.048 

148.178 

148.440 

148.702 

148.833 

148.964 

48 

150.796 

151.058 

151.189 

151.320 

151.582 

151.844 

161.976 

153.105 

49 

153.938 

154.200 

154.331 

154.462 

154.723 

154.985 

166.116 

155.247 

60 

157  080 

157.341 

157.472 

157.603 

167.865 

168.127 

168.258 

158.389 

Diameters  may  be  obtained  from  circumferences  by  inverse  interpolation. 

jNote.— Area  of  surface  of  S^/wrff  =  diameter  X  circumference. 

The  Circumferences  are  in  the  same  Denomination  as  that  for  which  the 
First  Column  is  used.  Ex:— Dia.  -  14.126  ft.  -rH4t*^Ji>  ins.:  then. 
Circumference  -  44.375  ft.  d  g  tized  by  UxJCtgle  ^"*^' 


CIRCLES,  DIA,  TO  CIR.,  FRAC.  AND  DEC. 


227 


^DlAMBTBRS,  IK  PbBT  AND   InCHBS;  AKD  IN   InCHBS. 

This  table  may  be  used  like  logarithmic  tables. 


Dedmal 

.5000 

.583^       .6250 

.666^6 

.7500 

.833^3 

.8750 

.916^6 

FraetJoDs-as  I2ifa8  of  a  Foot  (Incbes).  and  8ths  ol  an  Inch. 

6 

7 

7.5 

8 

9 

10 

10.5 

11 

n. 

12tl0 

12 

IT 

TT 

12 

If 

12 

12 

12 

hm. 

ftlis 

4 

5 

T 

6 
T 

7 

T 

0 

1.57080 

1.83260 

1.96350 

2.09440 

2.35619 

2.61799 

2.74889 

2.87979 

] 

4.71239 

4.97419 

6.10509 

5.23599 

5.49779 

5.75959 

5.89049 

6.02139 

2 

7.  ©398 

8.11578 

8.24668 

8.37758 

8.63938 

8.90118 

9.03208 

9. 16298 

1 

3 

10.9966 

11.2574 

11.8883 

11.6193 

11.7810 

12.0428 

12.1737 

12.3046 

4 

14.1372 

14.8990 

14.5299 

14.6608 

14.9226 

15.1844 

15.3153 

15.4462 

CB 

5 

17.2788 

17.5406 

17.6715 

17.8024 

18.0642 

18.3260 

18.4569 

18.5878 

1 

6 

20.4204 

20.6822 

20.8131 

20.9440 

20.2058 

21.4675 

21.5984 

21.7293 

1 

e 

7 

23.6619 

23.8237 

23.9546 

24.0855 

24.3473 

24.6091 

24.7400 

24.8709 

8 

26.7035 

26.9653 

27.0962 

27.2271 

27.4889 

27.7507 

27.8816 

28.0125 

9 

29.8451 

30.1069 

30.2378 

30.3687 

30.6305 

30.8923 

31.0232 

31.1541 

10 

33.9867 

83.2485 

33.3794 

33.6103 

83.7721 

34.0339 

34. 1648 

34.2967 

i 

11 

86.1283 

36.3901 

36.5210 

86.6519 

36.9137 

37.1755 

37.3064 

37.4373 

12 

39.2699 

89.5317 

39.6626 

39.7935 

40.0553 

40.3171 

40.4480 

40.6789 

;: 

U 

42.4115 

42.6733 

42.8042 

42.9351 

43.1969 

43.4587 

43.6896 

43.7205 

"T 

14 

45.5531 

45.8149 

45.9458 

46.0767 

46.3385 

46.6003 

46.7312 

46.8621 

B 

15 

48.6947 

48.9565 

49.0874 

49.2183 

49.4801 

49.7419 

49.8728 

50.0037 

1ft 

51.8363 

52.0981 

52.2290 

62.3599 

62.6217 

72.8835 

63.0144 

63.1453 

1 

17 

54.9779 

65.2397 

56.8706 

65.6015 

65.7633 

56.0251 

66.1560 

66.2869 

fa 

18 

58.1195 

58.3813 

58.5122 

68.6431 

68.9049 

69.1667 

59.2976 

59.4285 

" 

19 

61.2611 

61.5229 

61.6538 

61.7847 

62.0466 

62.3083 

62.4392 

62.5701 

1 

20 

64.4026 

64.6644 

64.7953 

64.9262 

65.1880 

65.4498 

65.5807 

65.7116 

21 

67.5442 

67.8060 

67.9369 

68.0678 

68.3296 

68.5914 

68.7223 

68.8532 

1 

22 

70.6868 

70.9476 

71.0785 

71.2094 

71.4712 

71.7330 

71.8639 

71.9948 

5 

23 

73.8274 

74.0892 

74.2201 

74.3510 

74.6128 

74.8746 

75.0055 

75. 1364 

1 

24 

76.9690 

77.2308 

77.3617 

77.4926 

77.7644 

78.0162 

78.1471 

78.2780' 

25 

80.1106 

80.3724 

80.5033 

80.6342 

80.8960 

81.1578 

81.2887 

81.4196 

U 

83.2522 

83.5140 

83.6449 

83.7758 

83.0376 

84  2994 

84.4303 

84.5612 

27 

86.3938 

86.6556 

86.7865 

86.9174 

87.1792 

87^4410 

87.5719 

87.7028 

g 

28 

89.6354 

89.7973 

89.9281 

90.0590 

90.3208 

90.5826 

90.7135 

90.8444 

»« 

29 

92.6770 

92.9388 

93.0697 

93.2006 

93.4624 

93.7242 

93.8551 

93.9860 

3 

30 

95.8186 

96.0804. 

96.2113 

96.3422 

96.6040 

96.8658 

96.9967 

97.1276 

«• 

81 

98.9602 

99.2220 

99.3529 

99.4838 

09.7456 

100.007 

100.138 

100.269 

% 

32 

103.102 

102.364 

102.494 

102.625 

102.887 

103.149 

103.280 

103.411 

h. 

23 

105.243 

105.506 

105.636 

105.767 

106.029 

106.291 

106.421 

106.662 

B 

34 

108.385 

108.647 

108.778 

108.909 

109.170 

109.432 

109.563 

109.694 

35 

111.527 

111.788 

111.919 

112.050 

112.312 

112.674 

112.705 

112.836 

S 

30 

114.668 

114.030 

115.061 

115.192 

115.454 

115.715 

115.846 

115.977 

1 

9 

37 

117.810 

118.073 

118.202 

118.833 

118.596 

118.857 

118.988 

119.110 

38 

120.961 

121.213 

121.344 

121.475 

121.737 

121.999 

122.129 

122.260 

39 

124.093 

124.355 

124.486 

124.617 

124.878 

125.140 

125.271 

125.402 

40 

127.236 

127.496 

127.627 

127.758 

128.020 

128.282 

128.413 

128.543 

41 

130.376 

130.638 

130.769 

130.900 

131.161 

131.423 

131.554 

131.685 

1 

42 

133.618 

133.779 

133.910 

134.041 

134.303 

134.565 

134.696 

134.827 

2 

43 

136.659 

136.921 

137.053 

137.183 

137.445 

137.706 

137.837 

137.968 

a 

44 

139.801 

140.063 

140.194 

140.324 

140.586 

140.848 

140.979 

141.110 

45 

142.943 

143.204 

143.335 

143.466 

143.728 

143.990 

144.121 

144.251 

e 

48 

146.084 

146.346 

146.477 

146.608 

146.869 

147.131 

147.262 

147.393 

s^ 

47 

149.226 

149.487 

149.618 

149.749 

150.011 

150.273 

150.404 

150.535 

48 

152.367 

152.629 

152.760 

152.891 

153.153 

153.414 

153.545 

153.676 

49 

155.509 

155.771 

155.902 

156.033 

156.294 

156.556 

156.687 

156.818 

50 

158.650 

158.912 

159.043 

159.174'  169.436 

159.698 

169.829 

159.959 

Diff.  between  any  two  successive  circumferences  in  12ths  —  .2618;  hence 
if  the  diameter  is  extended  beyond  12ths,  this  diif.  must  be  used  proportion- 
ately. Diif.  between  any  two  successive  circumferences  in  8ths  =» .  3927;  hence, 
if  the  diameter  is  extended  beyond  8ths,  this  diif.  must  be  used  proportion- 

TTie  Circumferences  are  in  the  same  Denomination  as  that  for  which  the 
Flirt  Column  is  used.  °  9  '^^^  bT^UC 


228 


n.—MESSURATIOX, 


12. — CiRCUMPBRBNCBS  OF  CIRCLES  FOR  GlYBN 

Circumferences  are  directly  proportional  to  the  diameters. 


!>0 

51 

52 

JA 

53 

on 

54 

S 

55 
56 

1 

57 
58 

a 

59 

60 

1 

61 
62 

2 

63 

»- 

64 

^ 

65 

1 

66 

67 

KM 

68 

s 

69 
70 

71 

tl) 

72 

Q 

73 

»- 

74 

^ 

75 

^ 

76 

ja 

77 

a 

78 

79 

s 

80 

81 

^ 

82 

h 

83 

d 

84 

85 

1 

86 
87 

3 

88 

Q 

89 

90 

0 

91 

B 

92 

jJ 

93 

a 

94 

«A 

95 

c 

96 

pi: 

97 

98 

99 

100 

157.080 
160.221 
163.363 
166.504 
169.646 
172.788 
175.929 
179.071 
182.212 
185.354 
188.496 
191.637 
194.779 
197.920 
201.062 
204.204 
207.345 
210.487 
213.628 
216.770 
219.911 
223.053 
226.195 
229.336 
232.478 
236.619 
238.761 
241.903 
245.044 
248.186 
251.327 
254.469 
257.611 
260.753 
263.894 
267.035 
270.177 
273.319 
276.460 
279.602 
282.743 
285.885 
289.027 
292.168 
295.310 
298.451 
301.593 
304.734 
307.876 
311.018 
314.159 


157.341 
160.483 
163.625 
166.766 
169.908 
173.049 
176.191 
179.333 
182.474 
185.616 
188.757 
191.899 
195.041 
198.182 
201.324 
204.465 
207.607 
210.749 
213.890 
217.032 
220.173 
222.315 
226.456 
229.598 
232.740 
235.881 
239.023 
242.164 
245.306 
248.448 
251.589 
254.731 
257.872 
261.014 
264.156 
267.297 
270.439 
273.580 
276.722 
279.864 
283.005 
286.147 
289.288 
292.430 
295.572 
298.713 
301.851 
804.996 
308.138 
311.279 
314.421 


167.472 
160.614 
163.756 
166.897 
170.039 
173.180 
176.322 
179.463 
182.605 
185.747 
188.888 
192.030 
195.171 
198.313 
201.455 
204.596 
207.738 
210.879 
214.021 
217.163 
220.304 
223.446 
226.587 
229.729 
232.871 
236.012 
239.154 
242.295 
245.437 
248.579 
251.720 
254.862 
258.003 
261.145 
264.286 
267.428 
270.570 
273.711 
276.853 
279.994 
283.136 
286.278 
289.419 
292.561 
295.702 
298.844 
301.986 
305. 127 
308.269 
311.410 
314.552 


157.603 
160.745 
163.886 
167.028 
170.170 
173.311 
176.453 
179.594 
182.736 
185.878 
189.019 
192.161 
195.302 
198.444 
201.586 
204.727 
207.869 
211.010 
214.152 
217.293 
220.435 
223.677 
226.718 
229.860 
233.001 
236.143 
239.285 
242.426 
245.568 
248.709 
251.851 
254.993 
258. 134 
261.276 
264.417 
267.559 
270.701 
273.842 
276.984 
280.125 
283.267 
286.409 
289.550 
292.692 
295.833 
298.975 
302.116 
305.258 
308.400 
311.541 
314.683 


157.865 
161.007 
164.148 
167.290 
170.431 
173.573 
176.715 
179.856 
182.998 
186.139 
189.281 
192.423 
195.564 
198.706 
201.847 
204.989 
208.131 
211.272 
214.414 
217.555 
220.697 
223.838 
226.980 
230.122 
233.263 
236.405 
239.546 
242.688 
245.830 
248.971 
252.113 
255.254 
258.396 
261.538 
264.679 
267.821 
270.962 
274.104 
277.246 
280.387 
283.529 
286.670 
289.812 
292.954 
296.095 
299.237 
302.378 
805.520 
308.661 
311.803 
314.945 


IS 

of  an  Inch. 

4.5 

5 

12" 

12 

3 

8 

158.127 

158.258 

158.388 

161.268 

161.399 

161.530 

164.410 

164.541 

164.672 

167.552 

167.683 

167.813 

170.693 

170.824 

170.955 

173.835 

173.966 

174.097 

176.976 

177.107 

177.238 

180.118 

180.249 

180.880 

183.260 

183.390 

183.521 

186.401 

186.532 

186.663 

1B9.543 

189.674 

189.805 

192.684 

192.815 

192.946 

195.826 

195.957 

196.088 

198.968 

199.098 

199.229 

202.109 

202.240 

202.371 

205.251 

206. S8S 

205.613 

208.892 

208.523 

2U8.654 

211.534 

211.665 

211.796 

214.675 

214.806 

214.987 

217.817 

217.948 

218.079 

220.959 

221.090 

221.820 

224.100 

224.231 

224.368 

227.242 

227.373 

227.504 

230.383 

230.514 

230.645 

233.525 

233.656 

233.787 

236.667 

236.798 

236.928 

239.808 

239.939 

240.070 

242.950 

243.081 

243.218 

246.091 

246.222 

246.853 

249.233 

249.364 

249.485 

252.376 

252.506 

252.636 

255.516 

255.647 

255. T78 

258.658 

258.788 

258.880 

261.799 

261.930 

268.061 

264.941 

265.072 

265.103 

268.083 

268.213 

268.844 

?7 1.224 

271.355 

271.486 

274.366 

274.497 

274.688 

277.607 

277.638 

277.769 

280.649 

280.780 

280.911 

283.791 

283.921 

284.058 

286.832 

287.063 

287.194 

290.074 

290.205 

290.386 

293.215 

293.3^6 

293.477 

296.857 

296.488 

296.619 

299.498 

299.629 

299.760 

302.640 

302.771 

302.802 

305.782 

305.913 

306.843 

308.923 

309.054 

309. 18S 

312.065 

812.196 

312.827 

315.206 

315.337 

315.468 

Diameters  may  be  obtained  from  circumferences  by  inverse  interpolation. 

Note. — Area  of  surface  of  Sphere  =  diameter  X  circumference. 

The  Circumferences  are  in  the  same  Denomination  as  that  for  which  the 
First  Column  is  used.  Ex.— Dia.  «  02.25  ins.  ->  02|  ->  62i  ins.:  then. 
Circumference  —  196.664  ins. 


CIRCLES,  DIA.  TO  CIR.,  FRAC,  AND  DEC. 


229 


— DiAMBTBRS  IN  PbBT  AND   INCHES',   AND  IN   InCHBS. — CoHCluded. 

This  table  may  be  xised  like  logarithnuc  tables. 


Dedmal 

.5000 

.583^3 

.6250 

.666^6 

.7500 

.833^ 

.8750 

.916^6 

i 

Fi 

ractiona— as  I2tha  of  a  Foot  (Inches),  and  8ttas  of  an  Inch. 

L,  w- 

6 

7 

7.6 

8 

9 

10 

10.5 

11 

Pt 

'l2th8 

I2 

12 

IT 

12 

1^ 

U 

12 

12 

loa. 

9tha 

4 

8 

6 
8 

6 
8 

7 
8 

50 

158.650 

158.912 

159.043 

159.174 

159.436 

159.698 

159.829 

159.959 

51 

161.792 

162.054 

162.185 

162.316 

162.577 

162.839 

162.970 

163.101 

i 

52 

164.934 

165.195 

165.326 

165.457 

165.719 

165.981 

166.112 

166.243 

S3 

168.075 

168.837 

168.468 

168.599 

168.861 

169.122 

169.253 

169.384 

« 

54 

171.217 

171.479 

171.609 

171.740 

172.002 

172.264 

172.395 

172.526 

1 

S5 

174.358 

174.620 

174.751 

174.882 

175.144 

175.406 

175.536 

175.667 

» 

177.500 

177.762 

177.893 

178.024 

178.285 

178.547 

178.678 

178.809 

1 

57 

180.642 

180.903 

181.034 

181.165 

181.427 

181.689 

181.820 

181.951 

58 

183.783 

184.045 

184.176 

184.307 

184.569 

184.830 

184.961 

185.092 

B 

59 

186.925 

187.187 

187.317 

187.448 

187.710 

187.972 

188.103 

188.234 

« 

190.066 

190.828 

190.459 

190.590 

190.852 

191.114 

191.244 

191.375 

1 

61 

193.208 

193.470 

193.601 

191.732 

193.993 

194.255 

194.386 

194.517 

12 

196.350 

196.611 

196.742 

196.873 

197.135 

197.397 

197.528 

197.659 

!S 

63 

199.491 

199.753 

199.884 

200.015 

200.277 

200.538 

200.669 

200.800 

8 

64 

202.633 

202.895 

203.025 

203.156 

203.418 

203.680 

203.811 

203.942 

£ 

6S 

205.774 

206.036 

206.167 

206.298 

206.560 

206.822 

206.952 

207.083 

1 

66 

208.916 

209.178 

209.309 

209.440 

209.701 

209.963 

210.094 

210.225 

67 

212.058 

212.319 

212.450 

212.581 

212.843 

213.105 

213.236 

213.367 

66 

215.199 

215.461 

215.592 

215.723 

215.984 

216.246 

216.377 

216.508 

■ 

69 

218.341 

218.602 

218.733 

218.864 

219. 126 

219.388 

219.519 

219.650 

2 

70 

221.482 

221.744 

221.875 

222.006 

222.268 

222.529 

222.660 

222.791 

1 

71 

224.624 

224.886 

225.017 

225.147 

225.409 

225.671 

225.802 

225.933 

72 

227.765 

228.027 

228.158 

228.280 

228.551 

228.813 

228.944 

229.074 

73 

230.907 

231.169 

231.300 

231.431 

231.692 

231.954 

232.085 

232.216 

1 

74 

234.049 

234.310 

234.441 

234.572 

234.834 

235.096 

235.227 

235.358 

75 

237.190 

237.452 

237.583 

237.714 

237.976 

238.237 

238.368 

238.499 

1 

76 

240.832 

240.594 

240.725    240.856 

241.117 

241.379 

241.510 

241.641 

77 

243.473 

243.736 

243.866 

243.997 

244.259 

244.521 

244.652 

244.782 

s 

78 

246.615 

246.877 

247.008 

247.139 

247.400 

247.662 

247.793 

247.924 

k 

79 

249.757 

250.018 

260.149 

250.280 

250.542 

250.804 

250.935 

251.066 

O 

80 

252.898 

253.160 

253.291 

253.422 

253.684 

253.945 

254.076 

254.207 

1 

81 

256.040 

256.302 

256.433 

256.563 

256.825 

257.087 

257.218 

257.349 

82 

259.181 

259.443 

259.574 

259.705 

259.967 

260.229 

260.359 

260.490 

83 

262.323 

262.586 

262.716 

262.847 

263.108 

263.370 

263.501 

263.632 

£ 

84 

265.465 

265.726 

265.857 

265.988 

266.250 

266.512 

266.643 

266.774 

1 

85 

268.606 

268.868 

268  999 

269.130 

269.392 

269.653 

269.784 

269.915 

86 

271.748 

272.010 

272.140 

272.271 

272.533 

272.795 

272.926 

273.057 

s 

87 

274.889 

276.151 

275.282 

275.413 

275.675 

275.937 

■276.067 

276. 198 

i9 

88 

278.031 

278.293 

278.424 

278.556 

278.816 

279.078 

279.209 

279.340 

0 

89 

281.173 

281.434 

281.565 

281.696 

281.958 

282.220 

282.351 

282.482 

1 

90 

284.314 

284.576 

284.707 

284.838 

285. 100 

285.361 

285.492 

285.623 

1 

91 

287.456 

287.718 

287.848 

287.979 

288.241 

288.503 

288.634 

288.765 

92 

290.597 

290.859 

290.990 

291.121 

291.383 

291.645 

291.776 

291.906 

— 

93 

293.739 

294.001 

294.132 

294.263 

294.524 

294  786 

294.917 

295.048 

6 

94 

296.881 

297.142 

297.273 

297.404 

297.666 

297.928 

298.059 

298.190 

£ 

95 

300.022 

300.284 

300.415 

300.546 

300.807 

301.069 

301.200 

3U1.331 

96 

303.164 

303.425 

303.556 

303.687 

303.949 

304.211 

304.342 

304.473 

h 

97 

306.305 

306.567 

306.698 

306.829 

307.091 

307.352 

307.483 

?»07.614 

98 

309.447 

309.709 

309.840 

309.970 

310.232 

310.494 

310.625 

310.756 

99  • 

312.588 

312.850 

312.981 

813.112 

313.374 

313.636 

313.767 

313.897 

100 

315.730 

315.992 

316.123  >  316.254  '  316.515 

316.777 

316.908 

317.039 

Diff.  between  any  two  successive  circumferences  in  12th8  — .2618;  hence, 
d  the  diameter  is  extended  beyond  12ths,  this  diff.  must  be  used  proportion- 
ately. EHJf.  between  any  two  successive  circumferences  in  8ths  =* .  3927;  hence, 
if  the  diaxneter  is  extended  beyond  Sths,  this  diff.  must  be  used  proportion- 


ately, 
TheC 


_    •  Circumferences  are  in  the  same  Denomination  as  ,th^foi\wJich  the 
FiiHt  Column  is  used.  nzedBy^ucj^n. 


280 


IL— MENSURATION, 


13. — Arbas  of  Circles  in  Squarb  Inchbs  for  Given — 


hh^\ 


^Xo 


§-J 


5l,3i^a 


0 

.oooisl... 

.00077  1-16 

.00307  i 

.0069C  8-16 

.01227  4 

.01917  »-16 

.02761  f 

.03758  7-16 

.0490S  I 
.06213  »-l6 
.0767C 
.09281 
.11049  f 
.12962  13-16 
.15033 
.1726715-16 

.19638... 
.2216C    1-16 
.2485C        i 
.2768£   3-16 
.3068C 
.33824   5-l< 
.37122 
.40574 


.4417 J 

.47937 

.5184S 

.5591411-16 

.60132         I 

.64504  13-16 

.69021 

.7370{  16-16 
I     ^ 

.7854C 

.88664   1-16 

.99402 
1.1075 
1.2272 
1.3630 
1.4849 
1.6230 


1.7671 
1.9175 
2.0739 
2.2365 
2.4053 
2.5802 
2.7612 
2.9483 
2 
8.1416 
3.3410 
8.5466 
3.7583 
3.9761 
4  2000 
4.4301 
4.6664 

4.9087 
5.1572 
6.4119 
6.6727 
5.9396 
6.2126 
6.4918 
6.7771 


t 

11-16 


t 

7-16 


3-16 

6-16 
f 

7-16 

9-16 
f 

11-16 

113-16 
i 

16-16 


3 

7.0686 
7.3662 
7.669S 
7.979i 
8.295S 
8.6179 
8.9462 
9.2806 

9.6211 
9.967i 
10.321 
10.680 
11.045 
11.416 
11.793 
12.177 

12.566 
12.962 
13.364 
13.772 
14.186 
14.607 
15.033 
15.466 

15.904 
16.349 
16.800 
17.257 
17.721 
18.190 
18.665 
19.147 

5 
19.635 
20.129 
20.629 
21.136 
21.648 
22.166 
22.691 
23.221 

23.758 
24.301 
24.850 
25.406 
25.967 
26.536 
27.109 
27.688 
6 
28.274 
29.465 
30.680 
81.919 
33.183 
34.472 
35.785 
37.122 

7 
38.485 
39.871 
41.282 
42.718 
44.179 
45.664 
47.173 
48.707 


8 

60.265 
51.849 
63.456 
66.088 
66.745 
68.426 
60.132 
61.862 

9 

63.617 
65.397 
67.201 
69.029 
70.882 
72.76U 
74.662 
76.589 

10 
78.540 
80.516 
82.516 
84.541 
86.590 
88.664 
90.763 
92.886 

1 

95.033 
97.205 
99.402 
101.62 
103.87 
106.14 
108.43 
110.75 
13 
113.10 
115.47 
117.86 
120.28 
122.72 
125.19 
127.68 
130.19 

13 
132.73 
135.30 
137.89 
140.50 
143.14 
145.80 
148.49 
151.20 
14 
163.94 
156.70 
159.48 
162.30 
165.13 
167.99 
170.87 
173.78 

15 
176.71 
179.67 
182.65 
185.66 
188.69 
191.75 
194.83 
197.93 


16 

201.06 
204.22 
207.39 
210.60 
213.82 
217.08 
220.35 
223.66 

17 
226.98 
230.33 
233.71 
237.10 
240.63 
243.98 
247.46 
250.95 

18 
254.47 
258.02 
261.59 
265.18 
268.80 
272.46 
276.12 
279  81 

19 
283.63 
287.27 
291.04 
294.83 
298.66 
302.49 
306.35 
310.24 

20 
314.16 
318.10 
322.06 
326.05 
830.06 
334.10 
338.16 
342.26 

21 
346.36 
350.60 
354.66 
858.84 
363.05 
367.28 
371.54 
375.83 

22 
380.13 
384.46 
388.82 
393.20 
397.61 
402.04 
406.49 
410.97 

23 
415.48 
420.00 
424.56 
429.13 
433.74 
438.36 
443.01 
447.69 


24 

452.39 
457.11 
461.86 
466.64 
471.44 
476.26 
481.11 
485.98 

25 
490.87 
495.79 
600.74 
605.71 
510.71 
515.72 
620.77 
625.84 

26 
630.93 
636.06 
641.19 
646.36 
651.66 
656.76 
562.00 
667.27 

27 
672.56 
577.87 
583.21 
688.67 
693.96 
699.37 
604.81 
610.27 

38 
615.76 
621.26 
626.80 
632.36 
637.94 
643.65 
649.18 
654.84 

29 
660.52 
666.23 
671.96 
677.71 
683.49 
689.30 
695.13 
700.98 

30 
706.88 
712.76 
718.69 
724.64 
730.62 
736.62 
742.64 
748.69 

31 
754.77 
760.87 
766.99 
773.14 
779.31 
785.51 
791.73 
797.98 


32 

804.26 
810.64 
816.86 
823.21 
829.68 
836.97 
842.39 
848.83 

33 
866.30 
861.79 
868.31 
874.86 
881.41 
888.00 
894.62 
901.26 

34 
907.92 
914.61 
921.38 
928.06 
934.88 
941.61 
948.42 
966.26 

35 
962.11 
069.00 
976.91 
988.84 
989.80 
996.78 
1003.78 
1010.82 

36 
1017.87 
1024.95 
1032.06 
1039.19 
1046.36 
1063.62 
1060.73 
1067.96 

37 
1076.21 
1082.48 
1089.79 
1097.11 
1104.46 
1111.84 
1119.24 
1126.66 

38 
1134.11 
1141.59 
1149.08 
1156.61 
1164.15 
1171.73 
1179.32 
1186.94 

39 
1194.69 
1202.26 
1209.96 
1217  67 
1286  42 
1233  18 
1240  98 
1248.79 


E5.  DIAM.  TO  AREA,  IN  INCHES.  231 


iMBTBRS   IN   InCRBS  AKD  FRACTIONS. 


71 

80 

88 

96 

104 

4071.5 

5026.5 

6082.1 

7238.2 

8494.9 

3' 

4085.7 

6042.3 

6099.4 

7257.1 

8515.3 

Si  I 

4099.8 

. 

5058.0 

6116.7 

7276.0 

8535.8 

4114.0 

5073.8 

6134.1 

7294.9 

8556.2 

4128.2 

5089.6 

6151.4 

7313.8 

8576.7 

g  1  1 

4142.5 

5105.4 

6168.8 

7332.8 

8597.3 

^156.8 

5121.2 

6186.2 

7351.8 

8617.8 

4171.1 

5137.1 

6203.7 

7370.8 

8638.4 

wft.ft. 

73 

81 

89 

97 

105 

xss- 

4185.4 

5153.0 

6221.1 

7389.8 

8659.0 

g-2,2. 

4199.7 

5168.9 

6238.6 

7408.9 

8679.6 

^ 

4214.1 

5184.9 

6256.1 

7428.0 

8700.3 

^.^ 

4228.5 

5200.8 

6273.7 

7447.1 

8721.0 

4242.9 

5216.8 

6291.2 

7466.2 

8741.7 

°B-_. 

4257.4 

5232.8 

6308.8 

7485.8 

8762.4 

«^  a 

IS-" 

3'm.9 

4271.8 

5248.9 

6326.4 

75U4.5 

8783.2 

4286.3 

5264.9 

6344.1 

7523.7 

8803.9 

74 

83 

90 

98 

106 

4300.8 

5281.0 

6361.7 

7643.0 

8824.7 

s »» 

4315.4 

5297.1 

6379.4 

7562.2 

8845.6 

4329.9 

5313.3 

6397.1 

7581.6 

8866.4 

4344.5 

5329.4 

6414.9 

7600.8 

8887.3 

"i- 

4359.2 

5345.6 

6432.6 

7620.1 

8908.2 

?• 

4373.8 

5361.8 

6450.4 

7639.5 

8929.1 

Rk 

4388.5 

5378.1 

6468.2 

7658.9 

8950.1 

"^  to 

4403.1 

5394.3 

6486.0 

7678.3 

8971.0 

§*? 

75 

83 

91 

99 

107 

i^ 

4417.9 

5410.6 

6503.9 

7697.7 

8992.0 

4432.6 

5426.9 

6521.8 

7717.1 

9013.0 

•  ■ 

4447.4 

.  ■ 

5443.3 

6539.7 

7736.6 

9034.1 

; 

'i 

4462.2 

5459.6 

6557.6 

7766.1 

9055.2 

4477.0 

5476.0 

6575.5 

7775.6 

9076.3 

2" 

4491.8 

5492.4 

6593.5 

7795.2 

9097.4 

a.0 

4506.7 

5508.8 

6611.5 

7814.8 

9119.4 

• 

4521.5 

5525.3 

6629.6 

7834.4 

9139.7 

la 

S.8- 

76 

84 

93 

100 

108 

4536.5 

5641.8 

6647.6 

7854.0 

9160.9 

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4566.4 

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i 

4581.3 

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6720.1 

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4611.4 

5624.5 

6738.2 

7952.5 

9267.2 

4626.4 

5641.2 

6756.4 

7972.2 

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4641.5 

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77 

85 

93 

101 

109 

gg 

4656.6 

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4671.8 

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4686.9 

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4702.1 

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■ 

4732.5 

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4747.8 

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110 

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4839.8 

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; , 

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87 

95 

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wm. 

,'<;•-•■  ^V!f,-r  :;',>. 


y:.  .:-■ 


Digitized  by  V^jOC 


232 


n.—MENSURA  TION. 


14. — ^Arbas  of  Circlbs  in  Squarb  Pbbt*for  Givbn — 
Note. — DiAineters  in  feet  are  in  heavy  type,  with  decimals  of  a  foot 
"in  column"  opposite  the  areas. 


.4 


0 

.000000 
.007854 
.031416 
.070686 
.125664 
.196350 
.282743 
.384845 
.502655 
.636173 

I 

.785398 

.950332 

1.13097 

1.32732 

1.63938 

5|  1.76715 

6  2.01062 

2.26980 

8^  2.54469 

9^  2.83529 

2 

0|  3.14159 

3.46361 

3.80133 

4.15476 

4|  4.52389 

6  4.90874 

6  5.30929 

5.72555 

8(  6. 15752 

9  6.60520 

3 

Ol  7.06858 

7.54768 

2|  8.04248 

8. 55299 

4|  9.07920 

5   9.62113 

10.17876 

10.75210 

811.34115 

911.94591 

4  ■ 

0112.56637 

13.20254 

13.85442 

14.52201 

415.20531 

515.90431 

616.61903 

.34945 

8^18.09557 

918.85741 

5 

19.63495 

20.42821 

21.23717 

22.06183 

22.90221 


.1 

.22 

.32 

.4 

523.75829 
24.63009 
25.51759 
26.42079 
27.33971 


6 

27433 
.22467 
.19071 
.17245 
.16991 
.18307 
.21194 
.25652 
.31681 
.39281 

7 
.48451 

59192 

71504 
.85387 

00840' 


13 

113.0973 
14.9901 
116.8987 


254.4690452.3893 


18 


257.3043 
260.1553 
118.8229263.0220463.7698 
467.5947 


456.1671 
459. 


120.7628265.9044 
122.7185268.8025 
124.6898271.7163 


126.6769 
128.67% 


471.4352 

475.2916 

274.6459470.1636 


130.6981280.5521 


13 

132.7323 
134.7822 


19 

283.5287 
286.5211 


483.0513 

486.9547 

35 

490.8739 
494.8087 
498.7592 


39. 

40.71504  136. 84781289. 5292 

41.85387  138.9291  292.5630502.7255 

43, 

44.17865143.13881298.6477  510.7052 
45.36460{145.2672  301.7186  514.7185 
46.56626 147.4114p04.8052  518.7476 
47.78362149.6712 307. 9075(522.7924   ,^.— „«..«.. 
49.01670151.7468311.0255526.8529  799.22901128. 


8 
26548 
52997 
.81017 


14         2 
i.  93801314. 1593 


156. 1450{317. 8087 


158.3677  320. 4739  539. 1287 


.10608160.6061323.6547 


.41769 
.74502 
i.  08805 
44679 
1.82123 
.21139 
9 

.61725 
.03882 
.47610 
.92909 


162*.  8602'326'.  8513 


169.716; 
172.0336 
174.3662 
15 


176.7146346.8606 
179.0786'349.6671 


181.4584 
183.8539 


1.39778186.2650359.6809589.6456  876.1588  1219.2207 


.88218 
.38229 
.89811 

42964 
.97687 

10 


188.6919363.0503 
191.1345366.4354 
193.5928369.8361 
196.0668373.2526 


M1847 
11.71282 
1.32289 


24734 
92024 
60884 
31316 
II 


165.1300^30.0636551.5459 
167. 4155)333.2916 


336.6353 
339.7947 


352.9894 
356.3273 


78.53982  201.0619 

80, 

81 


593.9574 

598.2849 

602.6282 

606.9871 

198.55651376.6848611.3618 

33 

380. 1327 

383.5963 

387.0756 


16 


203.5831 
206.1199 
208.6724 
94867  211.2407 
59015213.8246 
216.4243 
219.0397 


03318226.9801 

76891  229.6583 

520351232.3522 

2875 

0703 

8689 

(832 

SI32 

3588 

2202 


34 


36 

630.9292 
535.0211 


37 

572.6553 
576.8043 
581.0690 
585.3494 


38 

616.7522 
620. 1582 
624.5800 


390.5707  629.0175 
394.0814  633.4707 
397.6078^637.9397 
401.1500^642.4243 
404.7078^646.9246 


221.6708408.2814  651.4407 


224.3176411.8707  656.9724 
17  33         39 

416.4756  660.6199 

419.0963  665.0830 

422.7327  669.6619 
235.0618426.3848674. 2566 
237.7871430.0526  678.8668 
240.5282  433.7361683.4928 
243.2849437.4354  688.1345  995.3822 
246. 0574  441 .  1503  692. 7919  lOOO.  9821 
248.8456 444. 88u9  697. 4650  1006. 5977 
251. 6494  448.6273|702. 153  8J1012. 2290 


36      I      43 

1017.876«1386.4424 

1023.6387  1392.04761817 

21721398.6685 

91131405.3061 

83361040.62121411.9574 


0662 1034. 


8449 

1063.6176 

9.4060 

37 

7676^1076.2101 


30 

706.8683 

711.6786 

716, 

721. 

726. 

730.6166 

735.4154 

740. 

745.0601 

749. 9( 

31 
754 
759. 
764, 

769.4467 
774.3712 
779.3113 
784.2672 
789. 
794 
799. 

33 
804.2477 
809.2821 
814.: 
819. 
824. 
829. 
834. 

839.8184 
844.96281 


20l21885.741ffi.O 

6450|1081. 0299^1468. 9635 1893.4457  . 1 

.8654  1465. 741  SI  901. 1662. 2 

1092.71661472.63521908.9024.8 

1098.68351479.34461916.8643.4 

1104.46621486.16971924.4218^.5 

110.3645 1493.0105 1932.2051^.8 

116.2786 1499.8670 1940.0041'.  7 

1506.73931947.8189^.8 

.  1538 1613.6272 1966.84931.  • 

38  44  50 

1 134. 1 149 1620. 6308 1 963 .  4954  . 0 

140.09181627.45021971.3672.1 


>.  23881 
22601122.2083 


33221146.0844 
543.2521   819.39801152.0927 
547.8911    824.47961158.1167 
57681164.1664 
555.7163   834.68981170.21181662. 
559.9025  839.81841176.28301569. 
564.1044  844.96281182.36981576. 
343.0698.568.3220  850.12281188.47241688. 
39  45 


29861194. 


33 

855.: 

860.4901 

865.6973 

870.9202 

876. 

881.4131 

886.6831 

891 

897.2703 

902.6874 

34 
907.9203 
913. 

918.6331 
924.0131 
929. 

934.8202 
940.2473 
945.6901 
951.1486 
966 

35 
962 
967. 

973.1397 
978. 
984 


1809.6674^.0 

105tf.l 

1824.6684.2 

1832.2475^.2 

1839.842^.4 

1046.8467  1418.6254 1847.4529.6 

1052.0880 1426.8092  1856. 079«. 8 

1482.00861862.72101.7 

1438.72381870.37861.8 

4546^1878.0519^.9 


1445. 

43 
1452. 


1534.3853|1979.: 

1541. 

1548. 

1555.2847 


1206.8742 


26881262 


1231.6300 
8582 
1244.1021 
1250.3617 

40 
1256.6371 
.9281 


1275.5573 


2348 

.1280 

0370 

2002.MI7 


33601987 


29622018 
32552026, 
87062034. 


.69061590. 
1200.72461697.5077 


1604.69992068. 


1213.03961611.7077 


1618.8313 


1225.41751625.97062083, 


.48262107 


1633.12652091 

1640, 

1647. 

1654.6847 


1661.9 
1669.1 


1269.23481676.3853 


1683.65022148. 


89551690.93082166, 
1288.24931698.2272 
1294.61891706.5392 
1301.00421712. 
1307.40521720.210512189, 
6228^1313.82191727.5697 


47 

112^1320.2543^1734.94^ 

6184 1326.7024  I742.336l|23l4, 


16352231 


1333.16631749.7 
67681339.64581767.1 

1410 1764.6012|2239.6100|.4 
989. 798rtl352. 6520 1772.0 
1359. 1786 1 


1779.5237 


.5 


0069.1 
2256.4176.6 
1365. 721^1787. 0086  2264. 8448 .7 
1372. 279U794. 6091  2273.2879 .8 
1378. 852911802.0254^281 .7466^.  9 


1.8681 
8289. 

8174^ 
61 
1.8206 

2050.8396 
8742 
2068.8246 
2074 

i.0723 

.1897 

2821 

4118 

2116.6563 

53 

).718< 

1.8926 

2140.0843 

.2917 

1.6149 

2164.7527 

2173.0082 

.2786 

.6844 

2197.8681 

53 

.1834 
6185 
8653 
2298 


*  Or  any  other  denomination.  Note  that  areas  of  circles  are  proportional 
to  the  squares  of  their  diameters,  and  that  the  range  of  the  table  may  there* 
fore  be  extended  greatly. 

Spheres:  Stirf ace  —  4  X  above  areas.    Volume "-id«am.X above  i 
(Assuming  diam.  of  sphere— diom.  of  circle.) 


d  by  Google 


284  n.— MENSURATION. 

15. — Areas  op  Circlbs  in  Square  Fbbt  for  Gitbn — 
Note. — Diameters  in  feet  are  in  heavy  type,  with  inches  "in  columc 
opposite  the  areas. 


10 

45 

i«.64 

1590. 

U.88 

1596. 

57.13 

1602. 

2.3» 

1608. 

7.e7 

1614. 

(2.95 

1620. 

18.25 

1625. 

«.56 

1631. 

«.87 

1637. 

»4.20 

1643. 

19.54 

1649. 

4.89 

1656. 

i 

46 

0.25 

1661. 

5.63 

1667. 

1.01 

1673. 

6.40 

1680. 

1.81 

1686. 

7.23 

1692. 

a.  65 

1698. 

«.09 

1704. 

3.54 

1710. 

9.00 

1716. 

4.47 

1722. 

9.95 

1728. 

2 

47 

5.44 

1734. 

0.96 

1741. 

6.46 

1747. 

1.98 

1763. 

7.62 

1759. 

3.07 

1765. 

8.63 

1772. 

4.19 

1778. 

9.77 

1784. 

5.36 

1790. 

0.97 

1797. 

6.58 

1803. 

1 

48 

2.20 

1809. 

7.84 

1815. 

3.4f 

1822. 

9.14 

1828. 

4.80 

1834. 

0.4( 

1841. 

6.17 

1847. 

1.87 

1853. 

7.M 

1860. 

z.ao 

1866. 

9.03 

1872. 

4.78 

1879. 

i 

49 

0.53 

1885. 

6.30 

1892. 

2.07 

1898. 

7.86 

1905. 

3.66 

1911. 

9.47 

1917. 

5.2S 

1924. 

1.12 

1930. 

6.96 

1937. 

2.8i 

1943. 

8.67 

1950. 

14.55 

1966. 

Areas  of  circles  are  proportional  to  the  squares  of  their  diameters. 
Spheres:  Surface  =  4  X  above  areas.    Volume  —  |  diam.  X  above  a 
(Assuming  diam.  of  sphere  —  diam.  of  circle.) 


Digitized 


by  Google 


d  by  Google 


236 


II.— MENSURATION, 


Fig.  16. 

Cycloid. — If  a  "  generating "  circle  C  of  diameter  d  is  rolled  alongr  a 
straight  base  or  chord  c,  any  point  as  p',  starting  from  a  point  A,  will  have 
tracal  a  cycloidal  arc  a.  from  A  to  B,  when  the  generating  circle  has 
performed  a  complete  revolution.  Moreover,  the  tvoltUe  of  the  cycloid  is 
composed  of  two  half -arcs  shown  below  the  base  and  meeting  at  the 
point  O.    Thus,  -A  O  =  i  arc  a. 

Properties  of  the  Cycloid  (Pig.  16): 

Length  of  arc  a  —  4  d  —  4  times  diam.  of  generating  circle  —  —  —  1.27324  c. 


Lengthof  chord  c-»rd- 3. 1416  d-Y  -0-7864  a. 

Area  of  cycloidal  segment  {bet.  a  and  c)  =  3  X  area  of  generating  circle  —  Imf*  — 
idc. 
from  base  to  ccn  of  grav  g  of  cycloidal  arc  (line)  —  |  d. 


\dc. 

yn  from  1 „        „         ,  , 

Distance  Vq  from  base  to  cen  of  grav  G  of  cycloidal  segment  (surface  above 


Distance  i 

Vof 

0    -    i»:Ci. 

Tangent  t^  at  point  p'  is  parallel  with  t;  ^  at  point  ^  ispar  with  ti. 
Normal  n'  at  point  p'  is  parallel  with  n;  c*  (f  at  pomt  p^is  par  with  «f 

Note  that  a'^^a*  ^  length  along  base  from  A  to  intersection  of  d  with  c. 
The  extremities  old  (f  touch  the  cycloidal  arc  above,  and  the  evolute  below. 
Area  contained  between  the  base  and  the  evolute  (below  c)  —  Jjcd'—JJc. 
If  the  half-arc  i4  O  is  inverted  it  forms  a  curve  along  which  a  body  will 
descend,  by  gravity,  from  O  to  A  in  the  least  space  of  time. 

For  Motion  of  Falling  Bodies  on  the  Cycloidel  Curve,  see  page  286. 

For  Equation  of  Cycloid,  see  p^e  260. 


d  by  Google 


LA,  SEGMENT  AND  SPANDRIL,  287 


Pig.  17. 

Segment ;  Parabolic  Half-Segment ;   and  Parabolic 

1  of  Parabola,  see  page  257.) 
\bola  (Fig.  17): 

ord;  -  may  have  any  value  desired. 


-# 


+  JA*.    (Approximate  t.) 
A-  }  base  X  altitude  -  }  c  A. 
ent  of  height  A'-  c^^. 


-..(, 


;,_!./        /A 


of  half  segment  of  height  *  "  I  X  |   —  ?«c. 

and  Gx  of  segment  and  half  segment  {h)  —  I  A. 

£  spandril  -  !  X  |   -  I  c 

f  spandril  —  ^  h. 

at  d\  Ti  is  tangent  at  i4 ;  7*2  at  ^2' 

Ti  "  r  "  c  • 

ural)  log  -  common  (Briggs)  log  muUhy  2.3026851, 

L  is  0.3622157. 

lues,  mult  result  from  approx  fonnula  by  0.99976 

0.9972  when  —  -0.2;   by  0.99  when  y-0.3;   by 
0.923  when  A— £. 


d  by  Google 


288 


n.--MENSURATION. 


Parabola  may  be  drawn  (1)  bv  drawing  T2  in  various  positions  between 
T  and  Ti,  varying  the  distance  A  Pi^  C  p  and  using  the  preceding  equa- 
tions for  position  of  p2.  although  the  latter  is  not  absolutely  necessary. 

Parabola  may  be  drawn  C2)  by  the  method  adopted  for  the  right-hand 
half  of  arc  a  (Fig.  17):  dividing  the  half-chord  and  the  height  into  equal 
spaces  (any  number)  and  joining  points  of  intersection  of  verticals  with 
corresponding  inclined  lines,  as  1  —  6  with  O  —  a,  2  — 6  with  0—b,  etc. 

Parabola  may  be  diawn  (3)  by  laying  off  ordinates  from  the  baae. 
Thus,  if  base  is  divided  into  8  parts  the  middle  ordinate  «-  (4)*  k  "  h,  in 
which  k  '-  SL.  constant— ^ A.  Then  the  ordinates  at  0  and  8  are  0X8^; 
at  1  and  7  are  1 X  7  )k;  at  2  and  6  are  12  k;  at  3  and  6  are  15  iir;  at  4  is  16  k. 
It  matters  not  how  many  divisions  of  the  base  are  used,  whether  odd  or 
even.  If  odd.  say  11.  the  middle  ordinate  —  (5.5)*  k.  Also,  the  ordinate 
midway  between  1  and  2  (Pig.  17)  -^  1.5X  6.5  Ar. 


16. — Lbnoths  op  Parabolic  Arcs  for  Chord  (Basb)  1. 
(The  final  figure  may  not  be  exact  in  some  cases.) 


Height 

Length  of  Arc 

Height 

Length  of  Arc 

Height 

Length  of  Arc 

div.  by 

—  Chord  mult. 

div.  by 

—  Chord  mult. 

div.  by 

—  Chord  mult. 

Chord. 

by 

Chord. 

by 

Chord. 

by 

.01 

1.000  267 

.11 

1.031  889 

.02 

1.001  066 

.12 

1.037  171 

.03 

1.002  396 

.13 

1.043  895 

.04 

1.004  261 

.14 

1.050  048 

.05 

1.006  627 

.15 

1.057  116 

.06 

1.009  519 

.16 

1.064  587 

.07 

1.012  918 

.17 

1.072  447 

.08 

1.016  814 

.18 

1.080  684 

.09 

1.021  199 

.19 

1.089  281 

.10 

1.026  061 

.20 

1.098  230 

Calr  ulatcd  from  the  exact  equation,  preceding. 


^^^     ^p 

w 6-2o- 

Fig.  18. 

Ellipse. — The  Ellipse  is  a  flattened  circle.     (See  Analjrtic   Geometry. 

Fig.  9.  page  258.) 

Notation  and  Methods  of  Drawing  the  Ellipse  (Fig.  18): 

d        /,.  .   ..     1        ,  /     .    V  X  bx 

a«=-semi-majoraxis=         -  /l*  .  j«     t  -     w.  .  ..v 


.N/6«+d«-ij-J(«+t>) 


6  — semi-minor  axis— d^ 


-l-v'a3-(f«->/(a+(i)(a-d)- 


tf— eccentricity  of  ellipse—  —  —  sin  0  — 


PARABOLIC  ARCS.    ELLIPSE,  280 


dm  I  (focal  distance)- Va»-6»->/(o+  b)  (0-6). 

A  J 

$  (-span)  —  major  axis  —  2a-i*+t;—  —  -  2^^^jj 


>  yariable  absciasa 


f  -  variable  ordinate 


,  Sometimes  used  in  platting    (p^ 
or  laying  out  the  ellipse. 


«  +  »  —  a  constant<"2  a  (see  point  p);    common  method  of  drawing  the 

ellipse, 
a  —  6  —  constant  distance  bet  axis  on  line  of  "elliptic  compass"  (see  pt.  p*). 

Other  Properties  af  the  Ellipse: 
Dist  xq  to  ccn  of  grav  ^,  of  quadrant  or  |^  of  half -ellipse  —  0.42441  a. 
Dist  yQ  to  cen  of  grav  gi  of  quadrant  or  u  of  half -ellipse  —  0.42441  b. 

Dist  fo  to  ccn  of  grav  ft  of  quadrant  —  Vj^+j^  —  0.42441  Vo^+fc*. 

Line  «  is  normal  to  the  ellipse  at  point  p.  and  bisects  angle  <x. 
Line  I  is  tangent  to  the  ellipse  at  point  p.  and  is  at  L  with  n. 

4f»aofcmpec-.iro6-^-"|-56  -^6(i«-l-v).  (ir-8.1416.) 
—  0.7864  X  major  axis  X  minor  axis. 

PORJfULAS  POR  ClRCUMPBRBNCB  OR  PbrIMBTBR  OF  ElLIPSB: 

MeAed  1. — Let /—perimeter;  «— miuor  axis— 2a;  #*— (eccentricity)'  —  — j— 
(a+b)(a-b). 

a« 
Terms  12  8  4  6 


P.5      .       8».5».7 


2».4«.6«         2«.4«.6».8« 

7  etc. 


Then/-,[,(l-l^-^.«. 

,     yy.T'.g     ^,    8'.5«.7».9».11  \1 

2«.4«.6«.8«.10«'^     2«.4«.6«.8«.10«.12«^         *•  7  J  ^*^ 
12  8  4  5 

men/     *['  ^^      i^      ^  ^        286     '^         16384     ^ 

6  7  etc. 

W538       ^  1048576  •••yjw 

Formulas  (1)  and  (2)  may  be  expressed:  l^n[s{k)] (3) 

in  which  the  continued  series  A;  is  a  coefficient  of  s,  xnaking  sk  the  diameter 
of  a  circle  whose  circumference  —  perimeter  of  the  ellipse. 

To  facilitate  the  use  of  equation  (2) :  Log  x  -  0. 4971490;  log  i  -  9.3979400; 
kiBA-8.6709413:  log  ,g«  -  8.2907300;  log  THf4  -  8.0286181;  log  «HM  « 
7.S279587;  log  Ti«ftV«  =•  7.6662314.  Note  that  logarithms  of  e*,  e^,  e»,  «">,  #" 
are  2.  8  6,  6  times  log  e^. 

Problem  1. — ^The  major  and  minor  axes  of  an  ellipse  are  86  and  24  ft., 
itspectivehr.    Find  the  perimeter? 

IRA 

So/Klum.— Majoraxis5-36;  0-I8;  6-12;  ««-4l?  :  log««- 9.7447275. 

Using  6-place  logarithms,  we  have  for  the  value  of  k,  by  terms: 
1  2  3  4  6  6  7 

Log  i-9.39704  A-8070M  8.29073  8.02862  7.82796  7.66623 
Log  tf^-9.74473  ^-9.48946  #<-9.23418  tf*-8.97891  tfio«»8.72364  #"-8.46837 
Sum    -9.14267    '     8.16040        7.62491         7.00753  6.65160         6.13360 

and  numbers  corresponding  to  above  logarithms  are  below: 
.Jk-14»000-  0.13889  -  0.01447    -  0.00335   -  0.00102   -  0.00036  -    0.00014 
minus  the  sum  of  the  value  of  terms  abovethe  7th,  which,  by  inspec- 
tion, we  will  assume  to  equal  0.00007.     Hence,  *  =-0.8417;  and  the 
perimeter /-«*- 3.1416  X  36  X  0.8417-96.194  ft.    Ans. 


240  n.— MENSURATION. 

Method  2. — Let /*  perimeter;  a  «  semi-major  axis;  6  »  semi-minor  axis; 
^    a+b- 


Terms:    12  3  4  5 

7 


Terms:     12  8 

[£*         E* 
1  +  ^  +  -^ 


^2«.4«.e».8«.10»       ^2«.4«.e».8«.10«.12«       ^J^^ 


Terms:     12  8  4  6 

~"  ~  £^        .        25E* 


256   "   16384 
6  7 

49  £W    .      441 E" 


05636    "     1048576     ^  J  ^*^ 

Formulas  (4)  and  (6)  may  be  expressed:   /—  K(a+b)K (6) 

in  which  (a+&)/i  is  the  diameter  of  a  circle  whose  circtLmference»  perimeter 
of  the  ellipse. 

ToTacilitate  the  use  of  equation  (5) :  Log  x— 0.4971499;  log  1-9.397400; 
log  A-8.1938200;  log  yh- 7.6917600;  log  1^^4-7.1835201;  log  «^^ 
6.8737162;  log  ToUiT«-  6.6238387.  Note  that  logarithms  of  M  M  £^.  £*. 
£»o.  £"  are  2,  4,  6.  8,  10.  12  times  log  E. 

Problem  2. — Solve  problem  1  by  formula  (5)  ? 

5o/M<iOft.-~a-18:  fr-12;  a+6-80;  a~&-6;  £-0.2;  log £-9.8010800. 
Using  5-place  logaritnms,  we  have  for  the  value  of  K,  by  terms: 
1  2  3  4  5  0  7 

Log  J-9.39794  A-8.19382         7.69176         7.18852  6.87872  0.62384 

Log  £«-8.60206  £^°7.20412  £»-5.80618  £»-4.40824  £>0-3.01030  £m- 1.61286 

Sum-2.00000         6.39794         7.39794         9.69176        11.88402        12.23820 
and  numbers  corresponding  to  above  logarithms  are  below: 

.-.K-l   +0.010000+0.000025  +  0.00000026+ + + 

-1.0100263;  and  the  perimeter /-;r(a+6)is:- 96.193.    Ans. 

Comparison  of  Methods  1  and  2. — A  mere  glance  at  the  solution  of 
Problems  1  and  2.  illustrating  the  two  preceding  methods  of  calctdating  the 
perimeter  of  the  ellipse,  clearly  shows  the  superiority  of  Method  2:  The  6th. 
6th.  7th,  etc.,  terms  giving  values  so  small  as  to  be  negligible  in  the  present 
instance.  Moreover,  ecjuation  (5),  with  the  accompanying  logarithmic 
values  given  just  below  it.  will  be  found  quite  as  rapid  to  use,  in  many  cases, 
as  many  of  our  so-called  approximate  formulas,  with,  in  addition,  the 
advant£^e  of  accuracy. 


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LENGTHS  OF  SEMI-ELUPTIC  ARCS. 


241 


17.— Lbnotbb  of  Sbmi-Blliptic  Arcs.  A  or  B 

For  a— Unity,  and  for  Successive  Values  of  — . 

a 


Note. — To  find  A  or  B:  Multiply  values  of  co- 
efficient C,  in  the  table,  by  length  of  semi-major 
axis,  or  a.   Thus,  A'-'B'^Ca, 

[Calculated  from  Formula  (4-fi).*] 


.M 

2.00000 

.01 

2.00061 

.tt 

2.00193 

.03 

2.00394 

.54 

2.00657 

.05 

2.00971 

.08 

2.01334 

.07 

2.01740 

.08 

2.02188 

.09 

2.02675 

.10 

2.03198 

.11 

2.03757 

.12 

2.04349 

.13 

2.04971 

.14 

2.05624 

.15 

2.06305 

le 

2.07014 

.17 

2.07749 

.18 

2.08509 

.19 

2.09293 

.20 

2.10100 

.21 

2.10931 

.23 

2.11782 

.23 

2.12655 

.24 

2. 13548 

.25 

2.14461 

.26 

2.15392 

.27 

2.16342 

.28 

2.17309 

.29 

2.18294 

.30 

2.19296 

.31 

2.20313 

.32 

2.21347 

.33 

2.22395 

•^  ArcA^ArcB 


.00061 
.00132 
.00201 
«00263 
.00314 
.00363 
.00406 
.00448 
.00487 
.00523 
.00559 
.00592 
.00622 
.00653 
.00681 
.00709 
.00735 
.00760 
.00784 
.00807 
.00831 
.00851 
.00873 
.00893 
.00913 
.00931 
.00950 
.00967 
.00985 
.01002 
.01017 
.01034 
.01048 


.33 

2.22395 

.34 

2.23469 

.35 

2.24537 

.36 

2.26629 

.37 

2.26735 

.38 

2.27854 

.39 

2.28986 

.40 

2.30131 

.41 

2.31288 

.42 

2.32467 

.43 

2.33638 

.44 

2.34831 

.45 

2.36035 

.46 

2.37249 

.47 

2.38475 

.48 

2.39710 

.49 

2.40956 

.60 

2.42211 

.51 

2.43477 

.52 

2.44752 

.53 

2.46036 

.54 

2.47329 

.56 

2.48632 

.56 

2.49943 

.67 

2.51262 

.58 

2.52590 

.59 

2.53926 

.60 

2.55270 

.61 

2.56622 

.62 

2.67982 

.63 

2.69349 

.64 

2.60723 

.65 

2.62105 

.66 

2.63494 

.01064 
.01078 
.01092 
.01106 
.01119 
.01132 
.01145 
.01157 
.01169 
.01181 
.01193 
.01204 
.01314 
.01226 
.01235 
.01246 
.01255 
.01266 
.01275 
.01284 
.01293 
.01303 
.01311 
.01319 
.01328 
.01336 
.01344 
.01352 
.01360 
.01367 
.01374 
.01383 
.01389 


.66 

2.63494 

.67 

2.64890 

.68 

2.66293 

.69 

2.67702 

.70 

2.69118 

.71 

2.70541 

.72 

2.71970 

.73 

2.73406 

.74 

2.74846 

.75 

2.76293 

.76 

2.77747 

.77 

2.79206 

.78 

2.80671 

.79 

2.82141 

.80 

2.83617 

.81 

2.85098 

.82 

2.86584 

.83 

2.88076 

.84 

2.89673 

.85 

2.91075 

.86 

2.92582 

.87 

2.94094 

.88 

2.95611 

.89 

2.97132 

.90 

2.98658 

.91 

3.00189 

.92 

3.01724 

.93 

3.03263 

.94 

3.04807 

.95 

3.06356 

.96 

3.07908 

.97 

3.09466 

.98 

3.11026 

.99 

3.12590 

1.00 

3.14159 

Difl. 


.01396 
.01403 
.01409 
.01416 
.01423 
.01429 
.01436 
.01441 
.01447 
.01454 
.01469 
.01465 
.01470 
.01476 
.01481 
.01486 
.01492 
.01497 
.01502 
.01507 
.01612 
.01517 
.01521 
.01526 
.01531 
.01535 
.01539 
.01644 
.01649 
.01562 
.01667 
.01561 
.01564 
.01569 


*  Number  of  terms  used  in  Formula  (4)  in  calculation  of  this  table: 

SOterms  for  — -0.01;  36.  for —  - 0.06;  20.  for  — -0.16;  13.  for —  - 0.26; 
a  a  a  a 

7. for—  -0.60;    6.  for-  -0.76;  4.  for  —  -0.90;  8,  for—  -  0.98;   and  2 
a  <x  a  a 

terms  for— —  0.99. 


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242 


lU—MENSURATION. 


Elliptic  Segmcat ;  and  Chord. —  - — -      -« 

Let  A  >-  areas  of  elliptic  segment  with  chord 
C: 
B  —  area  of  elliptic  segment  with  chord 

C; 
a   "  semi-major  axis  — rad  of  large  circle; 
b   —  semi-minor  axis  — rad  of  small  circle; 
6 — 6 '— rise  of  segment  A ; 
a— a*"  rise  of  segment  B. 

Then,  length  of  chord C. -2a*/ 1-  ijj   ; 

length  of  chord  Ck  -  26  Jl-  (-)  '.  --^-^-'' 

y        ^°^  Fig.  19. 

Area  segment  A  :  area  whole  ellipse  ::  area  Mg  small  circle  :  area  small  ciccle. 

.'.  A  —  (area  seg  small  circle  with  same  chord  CO   X  -r (I) 

o 

Area  segment  B  :  area  whole  ellipse  ::  area  seg  large  circle  :  area  large  circle. 

.'.  B  —  (area  S€g  large  circle  with  same  chord  Ck)   X    — (3) 

(See  Tables  7  and  8  of  Circular  Segments,  preceding.) 

Problem  1. — ^Pind  the  area  of  segment  A  of  the  ellipse  a— 10,  fr  — 8, 
whose  chord  is  distant  ^  —  6  from  and  parallel  with  the  major  axis? 

Solution. — Diam  of  small  circle—  16,  and  middle  rise  h  (— 6— 6')  of  arc 
from  chord  — 8— 5— 3.    Now  from  Table  8,  of  Circular  Segments,  the  area 

corresponding  to  ^^^.  or    .1875.-. 101943   diam> -.  101943  X46S:    and 

mtdtiplying  this  value  by -r- (see  Equation  1)  we  have. 

Area  A -.101943  X  4a6  -.101943  X  320  -  82.622.    Ans. 

It  is  to  be  noted  that  area  A  —  area  B  when  -r- "  ""• 

0      a 

Problem  2. — ^What  is  the  length  of  chord  C  of  the  ellipse  given  in 
Problem  1? 


SoluHon.— From  the  above  formula,  C. -2a^/l-  /-r-j  -20-Jl-^  — 


15.612.    Arts. 


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ELUPTIC  SEGMENT,    PRISMOIDAL  FORMULA. 


248 


B.— SOLIDS. 

.  _^,  _/«  TheoreiB.— If  a  plane  curve  /  or  area  a  lies  whollv  on  one  side 
of  a  strai^t  line  as  axis  in  its  own  plane,  the  surface  5  or  volume  V  gene- 
rated by  Its  whole  or  partial  revolution  about  that  axis  is: 
5  -  /  X  length  of  path^  p  traversed  by  cen  of  grav  g  of  line;   or  5  —  /^; 
K  —  a  X  length  of  path  JP  traversed  by  cen  of  grav  G  of  area;  or  V-^ar, 

"?.:  disss  w  ^  to  &}  ^«^  ^^  <»^«  ^'^pi*^  «^i"*ion. 

t  -♦2a&,;  .-.   S  -  2x1x9,   and  xh  -  S  +  2ir/ (1) 

P  -•2jt3'o;  .-.   V  -  2raXo,  and  Xo  -  V  +  2«i (2) 

Thos,  equations  (1)  and  (2)  are  used  for  finding  the  surfaces  and  vol- 
umes of  Uie  sphere,  cone,  cylinder,  torus  (cylindrical  ring),  paraboloid, 
dbpsoid.  etc. ;  also  of  their  sectors,  segments,  zones  and  frustums. 

It  is  to  be  noted  also  that  these  equations  enable  us  to  find  the  centers 
(tf  gravity  of  their  lines  and  areas  when  their  lines,  surfaces  and  volumes 
sie  known. 

PristoMal  Forniala^— The  volume  V  of  a  prismoid  is  equal  to  the 
length  /  nmltiplied  by  the  mean  area  A ;  and  A  is  equal  to  i  (sum  of  end 
anas,  Ot  and  03.  +4  times  the  middle  area  a«);  thus 


V-M--j-(ai  +  4a.+aa). 


(3) 

A  prismoid  is  a  solid  having  farallel  end  faces  or  areas,  joined  together 
by  nguJar  surfaces  or  sides,  as  tne  sides  of  prisms,  cylinders,  cones,  pyra- 
nuds.  wedges,  or  their  frustums,  or  any  lateral  combination  of  same.  The 
Iffismnidal  formula  will  apply  also  to  the  sphere,  hemisphere  and  spherical 
segment;  to  warped-surface  solids  where  the  warp  is  continuous  between 
ends  of  solid;  to  railroad  cuttings  that  can  be  aecomposed  into  prisms. 
wedges,  eto. :  to  two  equal  cones  arranged  like  an  hour  glass  with  bases  as 
end  areas;  to  the  conical  wedge  botmded  on  one  side  by  a  plane  radiating 
&om  the  apex  of  cone;  to  the  frustums  of  same;  and  to  many  other  solids. 


18. — Thb  Pivb  Rboular  Polthbdrons. 

(AH  dihedral  or  soUd  angles  are  equal,  and  all  faces  regtdar  polygons.    Five 

only.) 


Namb. 

Botmded 
by 

Tofal 
Surfaces 
-(ledge)' 

tunes 

Total 
Volume  V 
-(ledge)' 

times 

Apothem  a, 

or  radius  of 

inscribed 

sphere. 

-ledge 

times 

Radius  r, 
or  radius  of 

scribed 

sphere, 

-  ledge 

times 

leti  MifWi  r&n. ..... 

4-^'s 

1.7320608 

0.1178513 

0.2041 

0.6124 

Ciibe<hexahedron) 

CD's 

6.0000000 

1.0000000 

0.6000 

0.8660 

O^abedron 

8^'s 

8.4041016 

0.4714045 

0.4082 

0.7071 

Dodecahedron 

12  0*» 

20.6457788 

7.6631189 

1.1136 

1.4013 

koeahedron. 

20 -^'s 

8.6602540 

2.1816950 

0.7558 

0.9611 

The  volume  V  of  any  regular  polyhedron  is  equal  to  its  surface  5  times 
ooe-third  its  apothem  a;  or,  k  —  iSa;.'.  a  — 3K-*-5. 


*2«-0. 288186. 


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244 


n.—MENSURATlON 


Fig.  20. 

,  Prisms  and  Cylinders. — A  frism  is  a  solid  with  parcUkl  ends  and  paralUl 
stdg  edges.  Hence  the  ends  will  be  equal  and  similar  polygons  (r^iular  or 
irregular) ,  and  the  sides  will  be  parallelograms.  A  cylinder  is  a  prism  with  an 
infinite  number  of  sides.  The  ends  of  the  cylinder  may  be  circular,  elliptic, 
or  of  any  curvature. 

•  Area. — ^The  siuiace  of  any  prism  or  cylinder,  whether  right  or  oblique. 
IS  equal  to  the  two  end  areas  4-  the  perimeter  p  of  any  right  section  s  mul- 
tiplied by  the  length  /  of  any  lateral  element:   or  S-  2a+p/  (Fig.  20). 

Volume. — ^The  volume  of  any  prism  or  cylinder,  whether  right  or  oblique, 
is  equal  to  the  area  of  any  right  section  s  multiplied  by  the  length  I  of  any 
lateral  element;  or  V-5  /  (Fig.  20). 

Also,  volume  equals  area  of  either  end  multiplied  by  the  vertical  di«t.anoe 
between  the  end  faces;  or.  V— aA  (Fig.  20). 


>^ 


Fmstum  of  Prism  or  Cylinder. — Prism 
or  cylinder  with  end  faces  not  pansdlel 
(Fig.  21). 

Volume. — ^Let  gt^cen  of  grav  of  end 
area  Oi;  ^3  of  any  sectional  area  at;  g^  of 
end  area  a^.    Then 

V  =» axhx ;  (hx  —  vert  dist  from  gz  to  plane  Oj). 
V — 03^3 ;  (/13 — vert  dist  from  gx  to  plane  03) . 

V  — oafcg;  <M  is  vert  to  plane  o^,  bet  ft  and 

In  general,  V^area  a  of  any  plane 
section  multiplied  bv  the  perpendicular 
distance  h  between  planes  passing  through  -Jj 
centers  of  gravity  of  end  areas  and  par- 
allel with  the  said  plane  section,  if  a 
is  a  right  section  Oo.  V  — a©/.  These  for- 
mulas also  enable  us  to  find  the  relation 
between  certain  elements,  as  oo/— 01/4  — 

Note  that  Fig.  21  becomes  a  circular  cylindric  ungula  when  the  right 
section  oq  is  a  circle,  and  hence  /"-  i  (longest  side  +  shortest  side). 


Fig.  21. 


Circular  Cylindric  Pmstum. —  This  is  a 
special  case  of  the  preceding  in  which  Oq  is  a 
right    circular    section   whose   perimeter  is  p. 

Volume  V-ao/-iao(^  +  «; 

V="a|At;  Qix  is  perp  to  plane  Oj.) 
V- 03/13;  (/»3  is  perp  to  plane  03.) 
AreaA^ax-\-a%-\-pl^ax-\-az-\-p  (/i-H/a). 


Fig.  22. 


LINDERS;  CYLINDRICAL  WEDGES. 


245 


lalf-Wedgcs.  —  The  following  formulas  give  the 
If -wedges  cut  from  circular  cylinders ;  /i  being  the 
leasured  along  the  element  of  the  cylinder  at  Oi. 
»,  (W.  (c)  and  id) — as  follows: — 

iss  than  radius  r ;  lower  edge  Cf 

rea  of  base  at  bi)  (r—bi)  I  .  (Pig.  23a) 

-  r^  [C|f- (length  of  arcaO  (r-bi)  ].  (Fig.  23a) 

radius  of  cylinder;  lower  edge  —  d. 

(Fig.  23b) 
?-2ffc-(iA.  (Fig.  23b) 

>  r  and  <  diameter  d]  lower  edge  >-  Cj. 

ixcA  of  base  at  62)  (&a-o].  (Fig.  23c) 

h 

>  -  r-  [  C2r+  (2jcf  -arc  02)  (62-r)  1.         (Fig.  23c) 

02 

diameter  of  cylinder;  lower  edge  at  02. 

(area  of  circular  base).  (Pig.  23d) 

>->rrfc.  (Fig.  23d) 

rhether  figure  is  right  or  oblique.  (Fig.  23d) 


r  right  or  obliqM  figure,  h  being  perp  height, 
-face,  for  right  figure  only.    For  total  surface,  add 
kd  base  (circular). 


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240 


Ih—MENSU  RATION, 


19.— Propbrtibs  of  Hollow  Ctlindbrs  (Pipbs,  Tanks  or  Wbll8).Onb 
Foot  in  Lbngth. 

Note  that  Areas,  Volumes,  Capacities  and  Weights  are  proportional  to 
the  squares  of  the  diameters.  1728  cu.  ins. -7.4805  gallons- 1  cu.  ft.— 
62.6  lbs.  (nearly)  of  water;  231  cu.  ins.  -  1  gallon;    201. »74  gallons- 1  cu.  yd. 


Hjrdrau- 

Qrcum. 

Weight 

DIam. 

lie  Mean 

Clroum. 

Volume. 
Cu.  Ins. 

Area- 

Volume. 

Capacity 

of 

Radius 

Ins. 

Surface. 

Volume. 

Cu-Yds. 

Gallons. 

Water, 

d 

Ft. 

Ft. 

Pounds. 

ID.. 

Ft. 

"4* 

1  ■ 

.0104 

.0026 

.392699 

.032725 

. 147262 

.000085 

.000003 

.00064 

.00533 

3-  6 

.0156 

.0039 

.589049 

.049087 

.331340 

.000192 

.000007 

! 00143 

.01198 

.0208 

.0052 

.785398 

.065450 

.589049 

.000341 

000013 

.00265 

.02131 

.0312 

.0078 

1.17810 

.098175 

1.32536 

.000767 

.000028 

.00574 

.04794 

.0417 

.0104 

1.57080 

.130900 

2.35619 

.001364 

.000051 

.01020 

.08522 

.0521 

.0130 

1.96350 

.163625 

3.68155 

.002131 

.000079 

.01594 

.13316 

.0625 

.0156 

2.35619 

.196350 

5.30144 

.003068 

.000114 

.02295 

.19175 

.0729 

.0182 

2.74889 

.229074 

7.21585 

.004176 

.000155 

.03124 

.26099 

1 

.0833 

.0208 

3.14159 

.261799 

9.42478 

.005454 

.000202 

.04080 

.84088 

.1042 

.0261 

3.92699 

.327249 

14.7262 

.008523 

.000316 

.06375 

.63263 

.1250 

.0312 

4.71239 

.392699 

21.2058 

.012272 

.000465 

.09180 

.76699 

li 

.1458 

.0365 

5.49779 

.458149 

28.8634 

.016703 

.000619 

.12495 

1.04396 

2 

.1667 

.0417 

6.28319 

.523599 

37.6991 

.021817 

.000808 

.16320 

1.3635 

^ 

2 

.1875 

.0469 

7.06858 

.589049 

47.7129 

.027612 

.001023 

.20656 

1.7267 

.2083 

.0521 

7.85398 

.654498 

58.9049 

.034088 

.001263 

.25600 

2.1305 

2f 

.2292 

.0573 

8.63938 

.719948 

71.2749 

.041247 

.001528 

.30865 

2.5779 

8 

2500 

.0625 

9.42478 

.785398 

84.8230 

.049087 

.001818 

.36720 

3.0680 

3i 

.2917 

.0729 

10.9956 

.916298 

115.454 

.066813 

.002475 

.49980 

4.1769 

4 

.3333 

.0833 

12.5664 

1.04720 

150.796 

.087266 

.003232 

.66280 

6.4641 

4i 

.3750 

.0937 

14.1372 

1.17810 

190.852 

.110447 

.004091 

.82620 

6.9029 

6 

.4167 

.1042 

15.7080 

1.30900 

235.619 

.136354 

.005050 

1.02000 

8.6221 

H 

.4583 

.1146 

17.2788 

1.43990 

285. 100 

. 164988 

.006111 

1.2342 

10.31S 

6 

.5 

.1260 

18.8496 

1.67080 

339.292 

.196350 

.007272 

1.4688 

12.27S 

H 

.5417 

.1354 

20.4204 

1.70170 

398.197 

.230438 

.008535 

1.7238 

14.408 

7 

.5833 

.1458 

21.9911 

1.83260 

461.814 

.267254 

.009898 

1.9992 

16. 70S 

7i 

.6250 

.1662 

23.5619 

1.96350 

530.144 

.306796 

.011363 

2.2950 

19.175 

8 

.6667 

.1667 

25.1327 

2.09440 

603.186 

.349066 

.012928 

2.6112 

31.817 

H 

.7083 

.1771 

26.7035 

2.22529 

680.940 

.394063 

.014595 

2.9478 

24.629 

9 

.7500 

.1875 

28.2743 

2.35619 

763.407 

.441786 

.016362 

3.3048 

27.61S 

H 

.7917 

.1979 

29.8451 

2.48709 

850.586 

.492237 

.018231 

3.6822 

30.765 

10 

.8333 

.2083 

31.4159 

2.61799 

942.478 

.545415 

.020201 

4.0800 

84.088 

m 

.8750 

.2187 

32.9867 

2.74889 

1039.08 

601320 

.022271 

4.4982 

37.588 

11 

.9167 

.2292 

34.5575 

2.87979 

1140.40 

.659953 

.024443 

4.9368 

41.247 

l\i 

.9583 

.2396 

36.1283 

3.01069 

1246.43 

.721312 

.026715 

6.3958 

4S.068 

12 

1. 

.25 

37.6991 

3.14159 

1357.17 

.785398 

.029089 

5.8752 

49.087 

13 

1  0833 

.2708 

40.8407 

3.40339 

1592.79 

.921752 

.034139 

6.8952 

57.609 

U 

1.1667 

.2917 

43.9823 

3.66519 

1847.26 

1.06901 

.03959 

7.9968 

66.818 

15 

1.2500 

.3125 

47.1239 

3.92699 

2120.58 

1.22718 

.04545 

9.1800 

76.699 

16 

1.3333 

.3333 

50.2655 

4.18879 

2412.74 

1.29626 

.05171 

10.445 

87.368 

17 

1.4167 

.3542 

53.4071 

4.45059 

2723.76 

1.57625 

.05838 

11.791 

98.518 

18 

1.5 

.375 

66.5487 

4.71239 

3053.63 

1.76715 

.06545 

13.219 

110.45 

19 

1.5833 

3958 

59.6903  |4. 97419 

3402.34 

1.96895 

.07292 

14.729 

123.08 

20 

1.6667 

.4167 

62.8319  !5. 23599 

3769.91 

2.18166 
2.<Qt981 

.08080 

16.330 

136.35 

22 

1.8333 

.4583 

69.1150 

5.75959 

4561.59 

.09777 

19.747 

164.99 

24 

2. 

.6 

75.3982 

6.28319 

5428.67 

3.14159 

.11636 

23.601 

196.35 

The  Circumference  is  proportional  to  the  Diameter. 


d  by  Google 


ES  OF  HOLLOW  CYLINDERS. 


247 


s  OF  Hollow  Cylinders. — Concluded. 


Weight 

ty 

of 

18. 

Water. 
Pounds. 

1 

230.44 

7 

267.25 

306.80 

349.07 

394.06 

441.79 

492.24 

545.42 
601.32 

659.95 

721.31 

785.40 

852.21 

921.75 

994.02 

1069.0 

1227.2 

1484.9 

1767.1 

2073.9 

2405.3 

2761.2 
3141.6 

MV. 1199 

v«A4r .o 

iM.inia 

4.U6U1 

«uo.v0 

3408.8 

28.2743 

109931. 

63.6173 

2.3562 

475.89 

3976. 1 

31.4159 

135717. 

78.6398 

2.9089 

687.62 

4908.7 

84.5576 

164217. 

95.0332 

3.6197 

710.90 

5939.6 

37.6991 

195432. 

113.097 

4.1888 

846.03 

7068.6 

40.8407 

229361. 

132.732 

4.9160 

992.91 

8295.8 

43.9823 

266005. 

153.938 

6.7014 

1161.6 

9621.1 

47. 1239 

305363. 

176.716 

6.5450 

1028.2 

11045. 

50.2656 

357435. 

201.062 

7.4467 

1647.3 

12566. 

53.4071 

392222. 

226.980 

8.4067 

1697.9 

14186. 

56.5487 

439722. 

254.469 

9.4248 

1903.6 

15904. 

59.6903 

526938. 

283.529 

10.501 

2276.8 

17721. 

62.8319 

542867. 

314.159 

11.636 

2350.1 

19635. 

69.1150 

656869. 

380. 133 

14.079 

2843.6 

23758. 

75.8982 

781729. 

452.389 

16.755 

3384.1 

28274. 

78.5898 

848230. 

490.874 

18.181 

3672.0 

30680. 

81.6814 

917446. 

530.929 

19.664 

3971.6 

33183. 

87.9646 

615.752 
706.858 

22.806 
26.180 

4606.1 
6287.7 

38484. 

94.2478 

44179. 

100.531 

804.248 
907.920 
1017.88 
1134.11 
1256.64 
1386.44 
1520.53 

29.787 
33.627 
37.699 
42.004 
46.542 
51.313 
56.316 

6116.2 
6791.7 
7614.3 
8483.7 
9400.3 
10364. 
11374. 

50265. 

106.814 

56745. 

113.097 



63617. 

119.381 

70882. 

125.664 

78540. 

131.947 



865&0. 

138.280 

95033. 

144.513 

1661.90 
1809.56 
1963.50 

61.552 
67.021 
72.722 

12432. 
13536. 
14688. 

1038C9. 

150.796 

113097. 

157.080 

122719. 

d  by  Google 


248 


n.^MENSURATION. 


Pyramid  and  Pyramidic  Frustum.— A  "  regu- 
lar" pyramid  is  one  in  which  the  base  is  a  regu- 
lar polygon;  if  not,  it  is  "  irregular."  If  the  axis, 
from  the  aftx  to  the  cen  of  grav  g  of  the  base, 
is  perp  to  the  base  it  is  a  "  nght  pyramid ;  it 
not,  It  is  "oblique."  Fig.  24  shows  an  oblique 
pyramid  and  frustum  together  forming  a  right 
pyramid. 
Volu9H4  Vt  of  right  pyramid  —  J  (area  of  base  X 

perp  height)  —  i  Oihi. 
Volume  V*  of  oblique  pyramid  —  }  (area  of  base 

X  perp  height)  —  J  <h^. 

Volume  Vt  of  pyramidic  frustum  —  Vr  —  V«  — 

i(aiAi-aafca).  „.     ^. 

Fig.  24. 

If  Oa  is  parallel  with  Ot.  appljring  the  prismoidal  formula,  volume  Vt  of 
frustum  —  -~--2  (oi  +  as  +  Vo|Oa  j  ,  whether  pyramid  is  right  or  oblique. 

regular  or  irregular. 

The  area  of  the  sides  of  a  right  regular  pyramid  «  \  (perimeter  of  base  X 
least  slant  height)  *  of  a  right  regular  frustum  with  parallel  faces  —  \  (peri- 
meter of  top  +  perimeter  of  base)  X  least  slant  height. 

For  area  of  an  oblique  or  irregular  pyramid  or  frustum,  the  sides  must  be 
calculated — as  triangles,  or  as  trapezoids  or  trapesiums,  respectively.  No 
simple  general  formula  will  apply. 

Center  of  gravity  of  pyramid,  whether  right  of  oblique,  lies  in  the  axis, 
and  one-fourtn  its  length  from  the  base. 


Coae  and  Conic  Frustum. —  A  cone  may 
be  considered  as  a  pyramid  with  an  infinite 
number  of  sides.  If  the  axis  from  the  apex 
to  the  cen  of  grav  g  of  the  base,  is  peri>  to 
the  base  it  is  a  '  right"  cone;  if  not,  it  is 
'*  oblique."  Generally  speaking,  a  right  cone 
is  understood  to  have  a  circular  base;  and 
an  oblique  cone,  to  have  an  elliptic  base. 
Such  cones,  however,  are  sometimes  termed 
right-  and  oblique  circular  cones,  to  distin- 
gmsh  them  from  right-  and  oblique  elliptic 
cones  whose  base  of  right  cone  is  an  ellipse. 
Note  that  an  oblique  circular  cone  may  be 
cut  from  a  right  elliptic  cone;  or  that  an 
oblique  elliptic  cone  may  be  cut  from  either 
a  circular  or  an  elliptic  cone.  Fig.  25  shows 
an  oblique  cone  and  frustxmi  together  forming 
a  right  cone. 


Fig.  25. 


Volume  V,  of  right  cone—  J  (area  of  base  X  perp  height)  -  J  athi. 
Volume  Vo  of  oblique  cone—  J  (area  of  base  X  perp  height)  —  J  a^. 
Volume  Vt  of  conic  frustum  -  V,  —  V.  -  i  (ojfci — o^fea) . 

If  at  is  parallel  with  at.  applying  the  prismoidal  formula,  volume  Vrof 
hx-h2 


fnistum  —        .  '  fai+02+ Voiajj  .* 


The  area  of  the  curved  stirface  (side)  of  a  right  cone"  J  (perim  of  base  X 
slant  height) ;  of  a  right  frustum  with  parallel  faces—  Kperim  of  top  +  perim 
of  base)  X  slant  height. 


*  If  the  bottom  and  top  faces  of  the  frustum  are  circles  with  radii  r^ 
and  fa,  resp>cctively,  then  Ui  =-  irfi'  and  Oj  — ;rr2*.  If  they  are  elliptical,  use 
the  formula:  area  of  ellipse  — ttoo.  in  which  a  — seim^major  axis  and  6  — 
semi-minor  axis.    »r- 3.1416.  Digitized  by  GoOglc 


PYRAMID.    CONE.    WEDGE.    SPHERE. 


249 


The  arfa  o£  the  curved  suiiaqe  (side)  of  an  oblique  tllipUc  cone  of  height 
kf  (Pig.  24),  and  which  haf  been  cut  from  a  right  circular  com,  —  ^^^,  in 

which  Jbj  — pcrp  height.  02 -■area  of  elliptic  base,  and  r'— Aj ^perpdist 

cos  ex 

irom  side  of  right  circular  cone  to  point  where  axis  of  same  pierces  base  a^ 


of  obHque  cone.    Hence,  area»- 


oa^a  _  02  cos  <X 
sin;9 


Also,  area—  -7 (volume  of 


oblique  cone)— 


ZV. 


Center  of  gravity  of  cone,  whether  right  or  oblique,  lies  in  the  axis  and 
one-fourth  its  length  from  the  base. 


Coaic  Wedge  and  Fmstmn  from  right  cone. —  If 
the  wedge  is  cut  from  the  cone  by  a  plane  pass- 
ing through  the  apex  (Pig.  26),  with  Oa  parallel  to 
Of,  we  have. 

K-"t<^*i*.  At^\lHpt.  (Pi-penmofo,.) 
"i-ioj*?;  i*2-*A^.   G>2— pcnmof  a*.) 
Volume  of  frustum"  Vi  -  Ka  - 1  (oi*»  -  oM  - 
Area  of  frustum  —  Ai  —  i^a  ■-  t  (^Pi  —  ntp2)'» 
(ends  not  included). 

Volume  of  frustum  may  also  be  derived  from  the 
prismoidal  formula; 


thus,  Vr- 


ht-fh 


Fig.  26. 


(01  +  03+40.)  in  which  o»,  the  area  of  the  middle  section. 


-  JVai02+i(o,  +02);  or,  Vr-— ^^  (oj+oj+v/otaaj  . 

Note. — ^The  above  formulas  for  volume,  V,,  V2  and  Vr,  will  apply  also  if 
the  cone  is  oblioue.  For  an  oblique  circular  cone  the  above  formulas  for 
area  will  not  apply;  but  see  formulas  for  area  of  oblique  elliptic  cone  above. 


Wedge.— In  Pig.  27  let  w- width. and  /-length 
of  base,  which  must  be  a  parallelogram  but  not  neces- 
sarily a  rectangle;  let  h  be  the  perp height  of  cutting 
edge  above  the  base;  and  e  the  length  of  cutting 
et^.  which  must  be  parallel  with  /.    Then  volume 

V"  ^(2/+#).     The  two    ends  and  two  faces  of 

0 

height  h  may  slope  in  any  direction;   the  two  ends 
need  not  be  parallel. 


Sphere^— A  sphere  is  generated  by  the  complete  revolution  of  a  semi 
circle  (Pig.  28)  about  its  diameter.  The 
volume  of  the  sphere  is  equal  to  the  area  of 
the  semicircle  X  the  path  described  by  its 
center  of  gravity  G;  the  area  of  the  surface 
of  the  sphere  is  equal  to  the  length  of 
•emi-circular  arc  X  the  path  described  by 
its  center  of  gravity  g.  Any  section  of  a 
sphere  cut  by  a  plane  is  a  circle;  and  if 
toe  plane  cuts  the  center,  it  is  a  great  circle. 
The  axis  of  a  spthere  alwajrs  lies  in  the 
plane  of  a  great  circle.    The  ratio  of  vol- 


Pig.  28. 


nme  to  surface  of  a  sphere  is  greater  than  that  of  any  other  solid. 


gle 


260  n.— MENSURATION, 

Distanct  K.  to (7 of  semi-circle  {area)        "'%--  - 0.42441  31810 r. 

2f 
Distance  y,  to  got  semi-circular  arc  —       —  —  0.03661  97724  r. 

Area  of  semicircU  -       ^  - 1.57079  03268  f*. 

Length  of  semi-circular  arc  —      xr  —  8.14159  20530  r. 

The  following  are  some  of  th«  relations  of  Volume.  Surface,  Area  of 
Great  Cicrle.  Circtmiference,  Diameter  and  Radius,  of  the  sphere; 

Volums  of  Sphere  -  |ir  radius*  -  4. 1 8879  radius^  -  |  diam* 

-0.62360diam»-  ~-^  circum*- 0.010887  drcum* 

•- 1  radius  X  area  great  circle  —  }  diam  X  area  great  circle 

—  i  radius  X  surface  of  sphere—  i  diam  X  surface  of  sphere 

—  '^!^(- 2.101128)  volume  of  inscribed  cube* 
■-  g    ( —  0.62360)  voliune  of  circumscribing  cube 

—  >/3  ( — 1.732051)  volume  of  maximum  inscribed  cylinderf 
■•  I  volume  of  circumscribing  cylinder. 

Volumes  of  spheres  are  as  the  cubes  of  their  radii  or  their  diameters. 

Surface  of  Sphere  "Ax  radius*—  12.56637  radiu^-  n  diam< 

—  8. 14 159 diam*— -  circum*— 0.31831  circum*— diam  X  circum 

—  4  X  area  great  circle  — area  of  circle  whose  radius  is  equal  to  diam 

of  sphere—  3  X  volume-*- radius  of  sphere. 

""  K  (  —  1.57080)  area  of  surface  of  inscribed  cube 

""  r  ( —  0.52360)  area  of  surface  of  circtimscribing  cube 

—  4Xarea  of  convex  surface  of  inscribed  cylinder  of  ffiax  convex  sur- 

face t 
—convex  surface  of  circumscribing  cylinder 

—  3'\/3  (  —  5.19615)  convex  surface  of  inscribed  cone  of  max  convex 

surfacelT. 
Stirfaces  of  spheres  are  as  the  s<iuares  of  their  radii  or  their  diameterm. 

Area  of  Great  Circle  of  Sphere  —  x  radius^—  3. 141593    radiu^  —  j  diaxn^— 

0. 785398  diam*  —  ^  circuni  of  sphere  —  \  area  of  surface  of  sphere  —  \  volume 
of  sphere -H  diam. 


*  Edge  of  inscribed  cube—  — =(  —  0.57735)  diam  of  sphere. 

>/3 
t  Altitiide  of  inscribed  cylinder— J VT(— 1.15470)  rad  of  sphere; 

Diam  of  base  of  inscribed  cylinder  - 2>/i  (—1.03299)  rad  of  sphere. 
X  Altitude  of  inscribed  cylinder  —  diam  of  base  —  *\/2   radius  of  sphere. 
IT  Height  of  inscribed  cone  —  }  diam  of  sphere;  diam  of  base  of  inscribed 
cone-lV2  (-0.4714)  diam  of  sphere.  DgtizedbyGoOglc 


PROPERTIES  OF  SPHERES. 


251 


Ctrcun^tnce  of  Sphere''2x  radius—  6.283185radius  —  x  diam—  3.141693 
diam  —  (area  of  surface  of  sphere)  -«-  diam  —  Vx  surface  of  sphere  — 
L77246  Vsurface  of  sphere  -  Vei?  (-  8. 89778)  Vvolume  of  sphere  - 
^"59.21 703  volume  of  sphere. 

DiammUr  of  Sphen  —  2  radii  -  -  circum  -  0.318310  circum 
— ;=(  -    1.12838)  Varea  great  circle  —    >/l.273240   area  great    circle 

--J— (  —  0.56419)    y/ surface  of  sphere  —     v/0. 318310  surface  of  sphere 
-f/— (—  1.240701)   Vvolume  of  sphere  —    V  1.909859  volume  of  sphere. 

RadtMS  of  Sphert  —  J  diam  —  -x —  circum  —  0.159155  circum 
-J— (  -  0.56419)     Varea  great  circle  -     >/ 0.318310  area  great  circle 

-iJ— (—  0.282095)    Vsurface  of  sphere  —   V 0.079577  surface  of  sphere 

.» /L  (-  0.620350)      Vvolume  of  sphere  -    VO.238732  volume  of  sphere. 

20. — Arbas  op  thb  Surfaces  of  Spheres. 
(Surfaces  of  spheres  are  proportional  to  the  squares  of  their  diameters.) 


Diam. 

Area  Surface 

Logarithm 

Diam. 

Area  Surface 

^i 

O.OOO  766  99 

6.884  7899 

1^ 

0.000  005  326  322 

4.726  4274 

^ 

0.003  067  96 

7.486  8499 

A 

0.000  021  806  29 

5.328  4874 

A 

0.012  271  85 

8.0B8  9099 

A 

0.000  065  221  16 

5.930  5474 

f 

0.049  0674 

8.600  9699 

0.000  340  8846 

6.532  6074 

f 

0.196  350 

9.293  0299 

0.001  363  538 

7.134  6674 

I 

0.785  396 

9.806  0899 

0.005  454  154 

9.736  7274 

1 

3.141  593 

0.497  1499 

0.021  816  616 

8.338  7874 

0.031  415  93 

8.497  1499 

0.067  266  46 

8.940  8474 

0.125  6637 

9.099  2099 

0.196  349  56 

9.293  0299 

0.282  7483 

9.451  3924 

0.349  0660 

9.542  9074 

0.502  6648 

9.701  2609 

0.545  4154 

9.736  7274 

0.785  396       • 

9.896  0699 

0.785  396 

9.896  0699 

1.130  973 

0.063  4624 

1.069  014 

0.028  9835 

1.530  380 

0.187  3460 

0.396  264 

0.144  9674 

2.010  619 

0.303  3299 

1.767  146 

0.247  2724 

2.544  600 

0.406  6349 

2.181  662 

0.338  7874 

1.0 

3.141  603 

0.497  1499 

2.639  811 

0.421  6728 

Ex. — Surface  of  sphere  i^  in.  in 
diam  »  0.0l376699  sq.  in.;  therefore. 
Bxrface  of  sphere  A  in.  in  diam  — 
d.^76699  X  53- 0.019175  sq.  in. 

Ex. — Surface  of  sphere  7  units  in 
diameter-1.539380X  10>-153.9380. 


Ex. — Surface  of  sphere  f  in.  in 
diam- 0.033408846 sq.  ft.;  therefore, 
stirface  of  sphere  V  ins.  in  diam — 
O.O334O8846X  60«=  0.8522115  sq.  ft. 

Ex. — Surface  of  sphere  11  ins.  in 
diameter- 2.639811  sq.  ft. 


Rgmarks. — For  Surfaces  of  Spheres  of  various  diameters, 

(a)  Foot  note  to  Table  11,  of  Circles,  with  diameters  in  decimals. 

(b)  Foot-note  to  Table  12,  of  Circles,  with  diameters  in  8th8  and  12ths. 

(c)  Foot-note  to  Table  13,  of  Circles,  with  diameters  in  inches  and  fractions. 

(d)  Foot-note  to  Table  1 4,  of  Circles,  with  diameters  in  decimals. 

(e)  Foot-note  to  Table  15.  of  Circles,  with  diameters  in  feet  and  inches. 


252 


IL— MENSURATION. 


21. — VoLUkfBS  OP  Sphbrbs 
(Volumes  of  spheres  are  proportional  to  the  cubes  of  their  diameters.) 


Diam. 

Volume 

Logarithm, 

Diam. 

Volume 

Logarithm 

*\ 

0.000  001  997  37 

4.300  4586 

<^.i^ 

0.000  000  001  155  885 

1.062  9149 

i 

0.000  015  978  96 

5.203  5486 

0.000  000  009  247  065 

1.966  0049 

0.000  127  8817 

6.106  6386 

0.000  000  073  9767 

2.860  0049 

0.001  022  664 

7.009  7286 

0.000  000  501  8136 

3.772  1M9 

0.006  181  23 

7.912  8186 

.£ 

0.000  004  734  509 

4.675  2749 

0.065  449  84 

8.815  9086 

0.000  037  876  07 

5.578  3649 

0.523  5068 

9.718  9966 

Jw 

0.000  303  006  54 

6.4814549 

0.1 

0.000  523  5068 

6.718  9986 

^ 

0.002  424  069 

7.884  5449 

0.2 

0.004  188  790 

7.622  0886 

A 

0.008  181  232 

7.912  8187 

0.3 

0.014  137  17 

8.150  3624 

^ 

0.019  892  56 

8.287  6849 

0.4 

0.033  510  32 

8.525  1786 

0.087  876  07 

8.678  3549 

05 

0.065  449  84 

8.815  9086 

^ 

0.065  449  84 

8.815  90S6 

0.6 

0.113  0973 

9.053  4524 

0.103  931  94 

9.016  7490 

0.7 

0.179  5944 

9.254  2927 

\ 

0.155  1404 

0.190  7249 

0.8 

0.268  0826 

9.428  2686 

.  t 

0.220  8932 

9.844  1824 

0.9 

0.381  7017 

9.581  7241 

s 

0.303  0065 

9.481  4549 

1.0 

0.523  5088 

9.718  9086 

" 

0.403  3044 

9.606  6330 

Ex. — Volume  of  sphere  i\  in.  in 
diam -O.O&l 99737  cu.  in.;  therefore, 
volume  of  sphere  A  in.  in  diam» 
0.0fil99737X5>"  0.00024967  cu.  in. 


Ex. — Volume  of  sphere  7  imits  in 
diameter  =  0.1795044  X 10"  •=  179.5944. 


Ex. — Volume  of  sphere  i  in.  in 
diam  — 0.0e5918186cu.  ft. ;  therefore, 
voltmie  of  sphere  V  ins>  in  diam  — 
0.066918136X50»-0.0739767  cu.  ft. 


Ex. — Volume  of  sphere  11  ins.  in 
diameter- 0.4083044  cu.  ft. 
Remarks. — For  Volumes  of  spheres  of  various  diameters,  see — 

(a)  Foot  note  to  Table  13.  of  Circles,  with  diameters  in  inches  and  fractions 

(b)  Foot-note  to  Table  14,  of  Circles,  with  diameters  in  decimals. 

(c)  Foot-note  to  Table  15.  of  Circles,  with  diameters  in  feet  and  inches. 


Fig.  29. 
Spherical  Segment — 

Let     o  —  area  of  base  of  segment  —  icr*; 

A  —  area  of  great  circle  =  r.R}\ 

/»  =  height  of  segment. 
Then  r-Zesm  $;  h^^Rven  B'^rtan  J  B. 

Volunu  of  segment  —   ol^'^V)"  1 
»7rA»(/?-|-)  -3.14159 /»«(r-^)  . 


-  (3r«-»-A«)  -  0.52360  A  (3r«+^ 


Convex  Surface  of  segment  —  2 jc/?/i—  r^ volume  of  sphere  —  ^-^  surface 


of  sphere- 


2h  2hA 

■  jT  area  great  circle  "=  -^-  —  A  X  circumference  of  great  circle. 


It  is  thus  seen  that  area  of  convex  surface  is  directly  proportional  to  heieht  h 
of  segment.     Hence,  from  Table  of  Spheres  find  the  total  surface  of  the 

sphere  for  <iiam— 2/?,  and  multiply  this  result  by    ^B**  <>'•  better,   fTt>m 

Table  11  or  12,  of  Circles,  multiply  the  circumference  oHts^eat  circle  by  h. 
Area  of  Base  of  segment  —  sr'.  Digitized  by  VjOOglC  j 


SPHERE.    RING.    SPINDLE. 


2A3 


Spherical  Zone^ — Votutm  of  zone  *  volume  of 
^ihere  mimus  volume  of  aesments  (see  Spherical 

Segment,  page  288) -|-H(y  +f|«+ff«)  - 
1.57d79«  h(y  +  ri«  +  r^\  . 

Comotx  Surf  act  of  zone*  surface  of  sphere 
wtKiu  convex  surface  of  seffments  (see  Spherical 
ScKment,  pageSS)  "^kRH  ^  H  X  circum  of 
SKat  circle. 

Anas  of  Basts^  nr^  and  itr^. 


Pig.  30. 


Hollow  Sphere. — ^Let  K— radius  to  outside  surface,  and  r  — radius  to 
maide  surface.    Then, 

Ko/«wir-i«(l?»-f«)-4.18879(l?»-f*).  May  also  be  taken  from  Table 
of  Spheres,  by  deducting  volume  of  the  lesser  from  volume  of  greater  sphere. 

Surface  —  convex  surface  +  concave  surface  —  4jc(i?«+r*)  —  12. 66637  times 
{i?+f»).  May  also  be  taken  from  Table  of  Spheres,  by  adding  together  the 
surfaces  of  the  larger  and  the  smaller  spheres. 


Circalar  Segmental  Rfaig. — Let  ^  be  the  cen 
of  grav  of  area  A  of  segmental  section,  with  </ 
13  a  center,  forming  a  ring  about  the  axis  X^X. 
Also  let  >\)+(i— radial  distance  from  said  axis 
to  center  of  grav  g  of  segment.    Then. 

Volume  of  ring  —  2>tA  (yo+rf).  For  values  of 
y^  and  A  see  Fig.  11,  also  Tables  /and  8  of 
urcular  Segments. 

Note  that  when  d— 0.  Fig.  31  will  ivpresent 
a  sphere  with  a  hollow  cylindrical  core,  points 
a'  and  o^  being  identical  with  o.  The  above  for- 
mula holds  true  for  any  section  A,  provided  that 
jf^+d—dti^  tocenof  gravf.  Fig.  31. 

Convex  Surface  of  ring  — 2)ca  {Y^+d),  in  which  a— length  of  circular  arc. 
and  Yo-^d-'dist  to  cen  of  grav  of  arc.  (See  Fig.  9;  also  Tables  2.  3  and  4.  of 
Circular  Arcs.) 

Conaxoe  Surface  of  ring  — 2xrc,  in  which  c— chord  of  arc  — width  of  ring» 
(See  Pig.  9;  also  Tables  2  and  8  of  CLcular  Arcs.) 


Regular  Qrcolar  Riiig> — ^Por  any  circular  ring 
where  section  s—s  is  a  regular  polygon,  circle,  ellipse. 
etc,,  so  that  center  of  grav  of  area  A  and  of  perimeter 
P  oi  section  lies  midway  between  outer  and  inner 
circumferences  Pig.  32,  we  have. 

Volume  of  ring  — r  iD+d)  XareaAof  section;  — 5. 
Surface  of  ring  — r  (I? + J)  X  perimeter  P  of  section 


Circniar  Spindle  — Generated  by  revolving  circu- 
lar arc  a  or  segment  A  about  an  axis,  as  X  —  a  . 


Voiume 


-3.14159  [f -A  (f^-.)] 
-3.14159   (^-2A(i). 


Surface  -3.14169  [*(<»  +  <^)-^  ia-c)] 
- 6.283185 (CT'-od)  -  2»r(rr-mf). 


254 


IL--MENSURATION. 


Middk  Zom  (and  Fruslum)  of  circtilar  spindle. — ^Let  s  (Fig.  83)  behdght 
of  middle  zone;  then,  if  A^^area  of  zone  of  segment. 

Vo/miw- 3.14169   [-|(«*-f-)-2A.dl  . 

Cofwx  Surface  -  6.283185   X  length  of   "zone-arc"  a.  X  dist  from  axis 
X  —  X  to  cen  of  grav  of  o,. 

Segment  of  circxilar  spindle. — Let  s  (Pig.  83)  be  height  of  segment;  then. 
VolufM^^  (vol  of  spindle  minus  volume  of  middle  frustum). 
Com)9x  Surface"^  (surf  of  spindle  minus  convex  surface  of  middle  zone). 

Parabolic  Spindle. — Generated  b^  revolving  parabolic  arc  a  (asstmie  same 
Fig.  33)  or  segment  A,  about  axis  X  —  X, 

Volumg^^nch*^  1.^75516  ch^'^l^t  volume  of  circumscribing  cylinder. 

Convex  Surface  —  6.283185  X  length  of  arc  a  X  dist  from  axis  X—X  to 
cen  of  grav  of  arc. 

Middle  Zone  (and  Frustum)  of  parabolic  spindle. — Let  s  (Fig.  83)  be 
height  of  middle  zone,  assuming  arc  a  to  be  parabolic.  Then,  >»  77  "*  0.209440. 

Vo/f«m#-0.20«440«[8/i«+3^+4A#].   Note  that* -A  A  -  |V 

(The  above  formula  may  be  used  in  determining  the  contents  of  caalcs 
whose  staves  are  parabolic.) 

Convex  Suf/o<3r- 6.283185  X  length   of    "zone-arc"  a,   X  dist  from  axis 
X  —  X  to  cen  of  grav  of  o.. 

5rgm««a  of  parabolic  spindle. — Let;  (Fig.  33)  be  height  of  segment;  then. 
Volume '^^  (volume  of  spindle  minus  volume  ot  middle  frustimi). 
Convex  Surface  ^k  (surface  of  spindle  minus  convex  surface  of  middle  zone). 


Cycloidal  Spindle. — Generated  by  revolving  cycloidal  arc  a  (assume  same 
Pig.  33)  or  segment  A  about  axis  X  —  X. 


Volume^  |ir*^  -  6  1685QM- 


16k 


0.198944c«-|^a»-  0.09688aS- 


I  Rcli*'- 1.96350  c/i*  "- -^  voliune  of  circumscribing  cylinder.     Note  that 


fc-   -- 


4* 


Convex  Surface-  ^**-  16.75516fc«-  ~c«-  1.69765c«-  |-a«- 1.04720 a» 
1«  1. 


Paraboloid  or  Parabolic  Conoid.— Gen- 
erated by  revolving  one-half  parabola  of  arc  a, 
height  h,  base  c,  and  area  A  (Fig.  34),  about 
its  vertical  axis  Y  —  Y. 

Volume"^  c^li- 0.89270  c<;i-area  of  base 
X half  the  height. 

Volume  of  parabolic   segment   of   height 

Voltmie  of  parabolic  frustum  of  height 
hr  -  |-(c%-c^V).   Note  that  C-cJ^, 


yG®i&.gk 


d  by  Google 


12.— ANALYTIC  GEOMETRY. 

(See  alao  Mensuration.) 

Analytic  Geometry  treats  of  the  algebraic  analysis  of  geometries 
figures. 

Plane  Analytic  Geometry,  including  what  is  commonly  termed  Coni 
Sections  or  sections  cut  from  cones,  deals  with  the  analysis  of  plane  ctirvcs 
referred  to  two  coordinate  axes.  X  and  Y.  The  coordinate  distances  to  an 
point  p  i^jS'  1)  of  the  figure  are  x  andy;  x  being  measiired  from  1 
parallel  to  X,  and  y  being  measured  from  X  parallel  to  Y.  One.  usually  a 
IS  called  the  absctssa,  and  the  other,  usually  y,  is  called  the  ordinate,  to  th 
point  p.  They  are  dependent  variables  for  any  particular  figure.  Th 
coordinate  axes,  X  and  Y,  lie  in  the  plane  of  the  figure,  and  their  point  o 
intersection  is  called  the  origin.  If  the  axes  are  at  right  angle  with  eacJ 
other  they  are  called  "rectangular  coordinate  axes.*'  and  the  variables  . 
and  y  are  called    'rectangular  coordinates."   This  is  the  tisual  method. 

Solid  Analytic  Geometry  deals  with  the  analysis  of  solid  figures  and  i 
therefore  sometimes  termed  Analytic  Geometry  of  Space.  Three  coordinat 
axes  are  used,  namely.  X  Y  and  Z,  intersecting  at  the  origin;  and  an: 
point  in  space  may  be  located  by  the  three  coordinates  x.  y  and  s,  meas\ire< 
parallel  to  the  respective  axes. 

Straight  Line. — Equation:  ymx+b, 
X  and  Ir  are  coordinate  axes. 

X  -^  abscissa,  measured  from  axis  Y  to  any  point  p. 
y  "Ordinate,  measured  from  axis  X  to  any  point  p, 

y—b 
m^tangent  of  angle  of  inclination  — . 

b  »a  constant —distance  on  axis  Y  from  the  origin  O 
to  the  straight  line. 

Note. — For  any  point  i>  in  Ist  qudrant.  x  and  y  are  plus:   . 

X  iB  —,  y  is  + ;  ^d  quadrant,  x  and  y  are  minus;  4tn  quadrant.  ;c  is  -r- 
y  is  — .  For  angle  upward  to  the  right,  w  is  + :  downward  to  tne  right 
m  is  — .  Straight  line  cuts  K,  abov0  origin  O  when  6  is  + ;  bilcw,  Whei 
6  is  — . 

Problem.  1 — A  straight  line  cuts  the  axis  of  V  10  feet  above  the  origin 
and  makes  an  angle  of  ( 4- )  6*— 10'  with  the  axis  of  X.    Solve? 

Solution. — Natural  tang  of  6**—  10'-  .108;  6-10;  hence  the  equation 
y-. 108^+10 
from  which  the  value  of  y  may  be  obtained  for  any  value  of  x,  or  vice  vena 

Thus.if  «-0.y-10;  iP-1.  y- 10.108;  y-0,  iP-  — |^" -•^••'  «^ 

Problem  2. — Find  the  point  of  intersection  of  the  two  following  lineq 
and  plat  them:    y— —  Jaf+2,  and  y— «— 8. 

Equations:  Platting: 

Solution.— (1)  y- -  iac+  2  Whcny-0,«-4;  «-0,y-2. 

(2)  y-        x-  8 


Fifl.  1. 
2nd  quadrant 


y-0.jr-8;«-0,y-— 8, 
Y 


diff.    0--li*+10 
r.lx  -10 

Substituting  value  of  «— 6}  in  either  of  the  above  w. 
equations,  we  obtain  y—  —  ij.  * 

.*.  the  coordinates  of  the  point  p  at  intersection  of 
the  two  lines  are 

«-  +  6i.  andy--lj. 

This  is  also  a  graphical  .illustration  of  Simul-  ^^ 
taneous  Equations,  page  103.  Digitized  by  do^ 


*>  / 


STRAIGHT  UNE,    CIRCLE.    PARABOLA. 


257 


Gwdlm^-OrigiM  at  center  of  circk.    Eqtxatkm  of 

circle:    H-x'+y'.  

whence  r—±N/j?+P;  ac— ±Vf«— y>;  y^±Vr*—x*. 

Problem. — A  cu-cle  of  10  ft.  radius  is  cut  by  a 
vertical  Knc  8  ft.  to  the  right  of  its  center  at  the  points 
p  and  pi.    What  is  the  length  of  the  chord  ppi  ?         X 

Solution.— y -  ±  y/r*^^ -  ±  v^lOO -  64  -  ±  \/86 
—  ±6.  Hence,  for  ^,  y—  +  6,  and  for  Pi,  y—  —  6. 
.'.  the  length  of  chord- 12  ft. 

Intersection  of  circle  with  an  oblique  straight  line. 

Problem. — At  what  point   in  the    above  circle  „.     , 

win  the  straight  line  y- 2* -10  intersect?  *^«-  ^ 

Solution. — Equating  the  value  of  y*  for  the  circle  and  for  the  straight  line, 
>■—#•— «^-«  iZx—  10)*,  we  have,  eliminating  y  and  making  f«— 100, 
100-««-4««-40«+100 
whence        &c*— 40x 

.".  «-8,  orO; 
and  substituting  these  values  of  x  in  the  above  equation  of  the  straightline, 
we  have,  for  «—  8,  y—  6;  for  «— 0.  y  —  — 10.  Hence  the  line  intersects  the 
circle  at  a  point  jc— 8,  y  ■■  6;  which  is  the  same  point  as  p  in  the  above  figure. 
It  also  intercepU  the  axis  of  X  at  a  point  x^5;  and  the  axis  of  y  at  a 
point  y  — 10,  at  which  point  it  also  cuts  the  lowest  point  of  the  circle. 

Equation  of  Tangent  to  the  circle:  Xtx+Vx  yr*.  Y 

Problem.— The  equation  of  a  circle  (Fig.  4)  is 
j*+jf— 100.  Find  the  equation  of  the  tangent  to 
the  circle  at  point  p,  whose  abscissa  x  is  8? 

Solution. — Substituting  the  valueof  jr(  — 8)  in  the 
eqttttion  of  the  circle,  we  have 

y-«  + VlOO— 64— +0;p/««5,  since  p  ia  above 
the  axis  of  X;  y, 

and  substituting  these  values  of  x — 8  and  y  -»  6  in  the 
above  equation  of  the  tangent,  and  remembering  that 
they  correspond  with  Xt  and  yi  of  that  equation, 
we  have,  tor  equation  of  tangent,  8*+6y— 100. 
This  tangent  cuts  the  axis  ot  X  at  x  —  ^i^,  and  the 
axis  of  rat  y— 'S**  (by  making  y—0  in  the  first  case  y 

snd  :c  — 0  m  the  second).  Pig.  4. 

Equation  of  Normal  to  the  circle:  ytx—xi  y— 0.  Let  it  be  required  to 
find  the  normal  to  the  circle  (Pig.  4)  whose  equation  is  a:*+y*— 100. 
Proceeding  as  in  the  above  solution  for  the  tangent,  we  obtain  for  the 
normal,  ftt— $y— 0;  or,  y—  f*.  Clearly,  this  passes  through  the  origin,  at  O, 
lot  when  *— 0,  y— 0. 

Origin  not  at  center  of  circle.  Equation  :  r»  — 
Or~o)«-f  (y-6)«.  whence  r-  ±\/(a:-a)»4-(y-6)»; 
x-a±V'f«-(y-6)«;  y-6±N/r«-(jc-a)«. 

Equation  of  above  circle  may  be  reduced  to 
x«+>«-2a*-26y  +  a«+6»-f«-0;  or  letting -2a-//, 
-26-7,  and  <^+b^-r*''K,  we  have,  x*+y*+Hx  + 
Jy+IC~0. 

Equation  of  tangent  to  circle: 

x^+yty+j(x+Xt)  +  '^(y+yd  +  K''0. 

Parabola* — Next  to  the  circle  this  is  the   most 
useful  curve.     (See,  also.  Mensuration,  page  237.^ 
Equation:     y*— »«  (n    may   be   any   quantity), 

yt  y% 


whence  y—±\/fi*;  n 

The  laSus  rectum  (L  L) 
y— 2x.    To  find  this  point —        _ 
y  —  2*  —  Vnx 
.-.   4««->«* 


2y  at  a  point  where 


length  of  latUS  rectum. Digitized  by  LjE16)^Ic 


258 


n.—ANALYTIC  GEOMETRY, 


The  focHs  (P)  is  at  the  intersection  of  the  latus  rectum  with  the  uds  X, 


a  distance  of  ;r  —  7-  from  the  origin. 


O. 


The  directrix  is  a  line  parallel  with  the  axis  of  Kand  distant  7- (the  focal 

distance)  to  the  left  01  it,  so  that  the  axis  of  Y  lies  midway  between  the 
directrix  and  the  latus  rectum.  The  horizontal  distance  H  from  the  direc- 
trix to  any  point,  as  P,  on  the  parabola  is  eqtial  to  the  direct  distance  D 
from  the  focus  to  that  point  (Fig.  6).  Y 


Problem  1. — At  what  points  does  the  circle,  whose 
radius  is  3.  intersect  the  parabola  whose  value  of 
n-8? 


Solution. —  circle: 

parabola: 

(diflF.) 


X  —1;  y-3V2or  -2\/T 


Problem  2. — What  is  the  equation  of  a 
parabola  (that  is.  the  value  of  n)  whose  base 
is  10.  and  altitude  12? 

Solution.— When  ar-  the  altitude  -  12; 
y- half  the   base -8.     Then  n-^-Jl-^, 

X       1«        a 

and  the  equation  of  the  above  parabola  is 
y*—  -_-*,  so  y  can  be  determined  for  any 
value  of  X  (measured  from  the  top  down- 
ward). _Thu8,  for  af=3^y-\/l6-4:  *-(J. 
y-4\/2;  *-9,  ^-4^3;  *- 12,  y  =  4>/4-8. 


Equation  of  Tangent  to  the  parabola:  y\y 


ytx+^yxiyt-i-^yt. 
'nx  is, 


Equation  of  Normal  to  the  parabola; 
Radius  of  Curvature  r  of  the  parabola  y* 
At  any  point.    ♦*  ■=  -5  (y*+  7-)    • 

At  the  vertex.  O,   ♦'"■  o* 

Note. — ^The  equation  of  the  parabola  is  variously  given  as  y»  — 1 
-  2px,  y»  —  iax,  etc.    It  is  plain  that  in  these  equations  »  —  2p  —  4a.  etc 


Ellipse.-— The  ellipse  is  a  flattened  circle. 
Eq\iation :     ^  +  r?  -  1 .  whence  b^ + a V — a«6* ; 
b 


'±^\/b^-y;  y-±- 


■V^ 


bx 


b  =- 


dbvV-y* 
±  V'^-x* 


z  ■=  semi-major  axis; 


:  —  semi-mmor  axis. 


Fig.  9. 


Foct  (smgular.  focus).  F,  and  F3  are  foci,  so  situated  that  the  length  of 
any  broken  line  f,  P,  F2,  joming  any  point  P,  of  the  curve,  is  a  constant. 
Therefore,  the  distance  from  either  focus  to  either  cxtx^mity  p(  the  minor 
axis  is  equal  to  one-half  the  major  axis,  or  a.    Dg^.^d by GoOglc 


PARABOLA.    HYPERBOLA, 


259 


Problem. — ^The  major  axis  of  on  ellipse  is  20  (a— 10),  and  the  minor 
udb  10  (6  »  5).  For  a  point  P  whose  abscissa  x  —  6,  what  is  the  value  of  the 
ordinate  y?     (See  Fig.  0.) 

Solution.— y-~>/a*^^-^>/100-36-iV6i-4.    Ans. 

Tangent  to  the  ellipse*  Let  T  (Fig.  10}  be  the  tan- 
gent pomt  of  the  tangent  PT  to  the  auxiliary  circU; 
then  will  the  point  t,  lying,  verticallv  imder  i,  be  the 
tangent  point  of  the  tangent  Pt  to  the  ellipse,  drawn 
from  the  same  point  P, Tying  on  the  major  axis. 

Equation  bt  Tangent  to  the  ellipse:  bhcix+a*yiy 
-aV.  •*■ 

Equation  of  Normal  to  the  ellipse:     a^x—h^iy 


X*      yt 

Radius  of  Curvature  r  of  the  ellipse  — +^—  1  is. 


At  any  point,  r  — 


At  extremity  of  major  aX'S,  r  — 
At  extremity  of  minor  i 


Fig.  10. 


6* 

The  falM  ellipse  or  oval  is  simply  an  approximation  to  the  true  ellipse. 
For  instance,  the  true  ellipse  consists  of  an  infinite  ntmiber  of  infinitesimal 

arcs  with  radii  gradually  decreasing  in  length  from  r  —  -r-  at  extremity  of 

mixkor  axis,  to  r  —  —  at  extremity  of  major  axis;  whereas  the  false  ellipse  or 

oval  consists  of  a  definite  number  of  arcs  with  radii  decreasing  as  above. 
The  aemi-false  ellipse  is  sometimes  called  a  many-centered  arch:  the  most 
comtDon  forms  for  bridges  are  the  6-ccntered  and  8-centered.  These  terms 
may  also  be  applied  to  the  false  elliptic  arc  even  if  it  comprises  only  part  of 
the  senu-false  ellipse. 

Y 


HypcrtMkIa  (Pig. 


-1.  or6«««-ab^-aV. 


.(1) 


Problem. — In  a  hyperbola  the  coordinates  of  a  point  P  are,  «=»  6, 
>  4  V'a;  and  a  —  3.    Find  the  value  of  bjo  that  other  points  can  be  plotted  ? 
ay  ZX^VS  12VT 


Solution. —  b  — 


i>/^3^     ±V36^     ±3vT 


-±4. 


Then  for  any  point,  y-  ±  tVx*- 9;  and  flf-±lVl6+y«. 
Equation  of  Tangent  to  the  hyperbola 
Equation  of  Normal  to  the  hyperbola: 


Equation  of  Tangent  to  the  hyperbola:   b^xtx  —  a^yiy^a'b^.  j 

SM      ..         ,, ^_         ,.,  ,    a^ytX  +  bHty-ia^  +  b^xgle 


260 


\2.— ANALYTIC  GEOMETRY. 


EquUaUral  Hyperbola. — The  hyperbola  becomes  equilateral  when  the 
asymptotes  are  perpendicular  to  each  other:  hence  the  two  axes,  2a  and  ib 
(Fig.  11)  are  equal:  hence  a  —  6  in  Equation  (1),  page  250. 

The  equilateral  hyperbola  is  a  very  useful  curve.  It  enters  into  the 
solution  of  the  Howe-truss  brace  problem  (see  Section  33). 


Pig.  13. 
Cycloid  (Fig.  12). — Equation:  «— r  vere-»  -  — v2ry— y*,  in  which  ver«->- 

—the  angle,  in  circular  measure,  whose  vers—  ^. 

Hence.  «"rai-AfD-OD-iVD-ON (Fig.  12).    Also, 

ic-r(a,-sincx);  (oc,- 0.0174633  am  degrees.) 

y —r  (1 —  cos  oc) —r  vers  oc; 

r^x+  (a, —sin  a)  — y-n vers  oc. 
Radius  of  Curvature  r  —  2v^2ry — twice  the  length  of  the  normal.    (The 
normal  to  the  curve  at  p  is  a  straight  line  pD.) 

For  other  Properties  of  the  Cycloid,  see  page  28(J. 

Catenary  and  Modified  Catenary. — (See  Suspension  Bridges,  and  Arches.) 

Spiral  of  Archimedes. — Equation:    r-^aS. 

Logarithmic  Spiral.— Equation:    fa^  , 

Hyperbolic  Spiral. — Equation:    rS'^a. 

Lemnlscate  of  Bemouilli. — Equation:    t^-^a*  cos  2  B, 

Helix  or  Screw. — A  line  traced  from  a  fixed  point  bearing  on  a  cylinder 

which  is  made  to  revolve,  and  at  the  same  time  to  advance,  unitorrol^. 
The  pitch"' the  spacing  of  the  lines  or  threads  of  the  screw.  Note  that  if 
the  cylinder  is  developed,  i.  e.,  represented  on  a  flat  surface,  all  the  lines  or 
threads  will  be  straight. 

Common  Spiral. — ^A  line  traced  from  a  point  bearing  on  a  revolving 
plate  and  advancing  uniformly  outward  from  its  center. 


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13.— DESCRIPTIVE  GEOMETRY. 


»^»__lfA: 


^S,. 


H.L. 


V.P 


Descriptive  Geometry  deals  with  graphical  methods  of  representing  m«8< 
nxtndes  and  of  solving  problems  in  Geometry. 

Pwspectivo  pictures  an  -| 

object  as  if  seen  from  a  ^ 

fixute  distance.  Pig.  1  shows  VB  _"_ M^ts — i' 

the  perK>ectiTe  of  a  rect-  •■^-=- 

sngcuar  box.     Points  VP 

are    vt^tisking    points   on 

the  icriaon  Un€  HL,  which 

is  fopposed  tobeonalevel 

with  the  eye.    PS  is  the 

p^mi  cf  siifUt  directly 

opposite  the  eye  and   at 

the    intersection    of    HL 

vith  the  vertical  lins  VL,  _.      . 

AH  Unes  which    are  par-  ^^-  ^* 

sOd  in  the  object  must  meet  at  a  common  vanishing  point.     If  the  lines 

sre  boriaontal  in  the  object  the  VP  lies  on  HL.     If  the  lines  are  vertical 

in  the  object  the  VP  Ues  on  the  line  VL,  at  an  infinite  distance  from  PS\ 

thefdore,  vertical  lines  in  the  object  are  shown  vertical  in  the  perspective. 

Note    that    the   ground   line,  GL,  is  horizontal.     The  perspective  of  the 

object  may  occupy  any    position  with   reference   to    P5,   //L,    and  VL; 

Le.,  HL  may  lie  above  or  below  the  object,  or  cut  it,  and  VL  may  lie  to 

the  fight  or  left  of  the  object,  or  cut  it. 


Cabia«(  projsctioii  pictures  an  object  as  if  seen 
from  an  infinite  distance.  The  ground  line  GL  is  at 
an  aa^  of  45*  with  the  horlsontal,  and  lines  parallel 
with  Its  direction  are  drawn  to  i  scale.    (Pig.  2.) 


laooMtrlc  projectloo  pictures  an  object  as  if  seen 
fipocn  an  infinite  distance,  with  the  groimd  line  GL 
3<P  with  the  horizontal;  and  all  lines  drawn  to  full 
(Fig.  3,) 


ORTHOGRAPHIC  PROJECTION. 


Orthographic  projection,  or  Descrip- 
tive Geometrv  proper,  deals  graphically 
^nCtk.  the  pnsbiesns  of  position  and  dimen- 
sbn  of  the  (point.)  line,  stuiace  and 
•obd  in  space.  The  ground  line  GL 
n  the  intersection  of  two  coordinate 
piaaes,  V  (vertical)  and  H  (horizontal), 
unmng  four  dihedral  angles — 1st,  2nd, 
Mimd  4th  (Fig.  4). 


261 


igitizedby^j&Ogle 


262 


13.— DESCRIPTIVE  GEOMETRY, 


Revolved  planes. —  In  the  isometric  fi^re.  Piff.  4.  a  is  a  i>oint  in 
space,  a^  is  its  vertical  projection  on  the  honzontal  plane  H,  and  of  is  its 
horizontal  projection  on  the  vertical  plane  V;  further,  a©  is  the  horizontal 
projection  of  oh  and  the  vertical  projection  of  a',  on  the  ground  line.  If 
now  the  vertical  plane  V  is  revolved  on  the  ground  line  GL,  so  as  to  coincide 
with  the  horizontal  plane  H,  the  projection  a' 
of  o  will  fall  on  av  so  that  the  distance  a'v  oq^ 
a'  oo— a  oh,  and  oh  oo— o  o'. 

By  revolving  the  ground  line  to  a  horizontal  ^ 
position  as   in   rip.  o,  with    the  vertical   plane  ^ 
above  and  the  honzontal  plane  below,  it  will  be 
seen  that  the  point  a  in  space  may  be  repre- 
sented by  its  projections,  ov  and  oh. 

Projection  of  the  point. — A  point  mav 
be  situated  in  the  1st.  2nd,  3rd  or  4th 
dihedral  angle,  or  it  may  be  situated  in 
one  of  the  composite  planes.  Fig.  6  illus- 
trates the  system  of  lettering  adopted 
to  show  the  position  of  any  point.  A 
point  in  space  is  designated  by  a  small 
letter,  ana  its  projection  by  the  same  let- 
ter with  V  OT  h  written  above,  as  an 
index. 
Dihedral  angle  in  which  point  is  situated : 

Plane  **        "         **      **         **       : 


Fig.  6. 

(I)  (2)r3)(4)r5)(6)fr)(s)(9) 


H^ 


lo  y*  3° 


Fig.  «. 


?  f 


H  V   V  H 


fes 


c 


Note.— In  cases  (2)  and  (4),  /vhand  «vh 
represent  points  /  and  n  respectively  equi- 
distant from  the  coordinate  planes. 

Projection  of  the  right  line. — ^The  position  of  a  right  line  in  space  may 
be  determined  by  the  projection  of  two  of  its  points.  Fig.  7  illustrates 
the  system  of  lettering  adopted  to  show  the  position  of  any  Kne.  A  litte  in 
space  is  designated  bv  a  capital  letter,  and  its  projection  by  the  same  letter 
with  V  or  A  written  above,  as  an  index. 

(1)     (2)    (3)    (4)    (5)    (6)     (7)   (8)    (9)    (W)     (11) 


^ 


B^ 


H 

Dihed  ang:  1' 
Plane: 


-1 — U — I 


ritn 


!  >  i    I .-^ 


:        I  n\  I  I        i  I A  A      ^ 

•^    B"  ^.7. 

JO  2«>        y»       4«  3*»       1*        8«         1» 

H  V 

front  upper 

Remarks. — B  and  K  pierce  H\  C,  G  and  Hx  pierce  the  ground  line:  / 
pierces  V,  and  is  parallel  to  H;  B  and  G  are  perpendicular  to  H;  and  J  is 
parallel  to  H  and  V. 


Projection  of  two  lines. 

Remarks. — 

(1).  M  and  L  intersect 
at  o,  therefore  the  projec- 
tions of  their  intersec- 
tion are  ov  and  ah.        |-_ 


(2> 


5^ 


(3) 


>^^ 


ir^^ 


^ 


(2).  N  and  O  are  - 
not  in  the  same  plane,  as     -<...^./  l        i\ 

the  intersections  of  their  jP^^F-^-.^  --.^a*' '  ^-3^ 
projections  are  not  the  pro-  x^  ^"""^  Z^^^^-^**^^C[p* 
jectionsof  acommonp>oint.  ^ 

(3).  P  and  Q  are   par-  Fig.  8. 

allel.  as  their  common  projections  are  parallel. 

Note. — ^Two  lines  which  are  parallel  or  intersect,  represent  a  plane,  and 
the  horizontal  and  vertical  projections  of  their  point  of  intersection  must 
lie  in  the  same  perpendicular  line. 


PROBLEMS  OF  CONSTRUCTION. 


263 


Projectjon  of  the  plane. — A  plane  is  detennined  by  three  points,  or  a 
point  and  a  right  line,  or  two  right  lines  parallel  or  intersecting.  The  lines 
oi  intersection  of  a  plane  in  space  with  the  coordinate  planes  are  called 
traces.  Fig.  9  shows  the  vertical  and  horizontal  traces  of  various  planes 
m  the  1st  dihedral  angle. 


Fig.  9. 
Plane  A.        Plane  B,      Plane  C,      Traces  of  Traces  Traces  of       Plane  G, 
perpendic-     perpendic-  perpendic-  D  make     of  E.     F  make  parallel 

alar  to  ver-  ular  to         ular  to  acute 

tical  plane,    horizontal  both  co-       angles 
plane.         ordinate       with 

planes.        ground 
line. 


supplerocn-   to 
tary  angles  ground 
with  line, 

ground 
fine. 


ProMcms  of  Construction. —  In  problems  of  construction  the  following 
conventional  lines  are  employed: 

Principal  lines  (data  and  results).  fW/  when  visible  and  dots  when  invisible. 
Anxiltary  lints  (minor  lines),  small  dashes  and  dots. 
Cons^uction  lines,  (joining  projections  of  the  same  points  in  space),  fine 

dashes. 

Problem  1. — To  find  the 
projections  of  a  line  tn  space 
mdalso  its  length.  (Pig.  10.) 

A  right  line  A  in  the  1st 
dihedral  angle  pierces  the 
H  plane  at  a  p>oint  m.  3  ft. 
from  the  ground  line,  and 
the  V  plane  at  a  pointy  m, 
5  ft.  from  the  ground  Ime; 
the  distance  between  the 
projections  of  the  points, 
measured  paraillel   with  the  Fig.   10. 

ground  line,  being  15  ft.    What  is  the  length  of  the  line  A  in  space? 

Solution. — ^Let  the  points  n  and  m  be  represented  respectively  by  their 


.      .  ngtl  . 

A',  A'  Deing  the  hvpothenuse  of  a  right  triangle  whose  base  is  >4  vand  altitude 
Z  ft.;  and  A'  the  hypothenuse  of  a  right  triangle  with  base  Ah  and  altitude 
S  ft.  Hence,  by  scale,  A -16.1  ft.  (Analytically.  A- Vl5*+ 6»+ 3^- 
-s/iW-  16.09+ft.)     Ans. 

Problem  2. — To  find  where  a  given  right  line  A,  shown  in  the  1st  dihedral 
angle,  pierces  the  coordinate  planes  V  and  H  I     (Fig.  11.) 


Solution. — ^LetAv  and  Ah  be  the 
vertical  and  horizontal  projections 
of  the  Kne  A ;  then  will  mh,  the  point 
where  the  horizontal  projection  of  A 
intercepts  the  groxmd  line,  be  the 
horizontal  projection  of  the  point 
where  the  line  pierces  the  V  plane 
(at  myy ;  and  n^.  the  point  where  the  6 
vertical  projection  of  A  intercepts  the 
fpound  bne,  win  be  the  vertical  pro- 
jection of  the  point  where  the^Hne 
pierces  the  H  plane  (at  »h) 


1^ 


X 


^ 


^* 


Fig.  11. 
Therefore,  the  line   A  pierces  the  (upper) 


IZ.—DESCRIPTIVE  GEOMETRY. 


scale  9  ft.  from  the  ground  line;  and  it  pierces  the  (back) 
icale  12  ft.  from  the  Rround  line;  the  points  being  hori- 
mih  the  groimd  line)  17i  ft.  apart.     It  will  be  obeerved 

the  line  between  mvand  Hhis  in  the  2nd  dihedral  angle. 
o  ^s  a  plant  P  through  thfM  gnmi  points  notintht  samt 


— L 


m,  n  and  o  be  three  points  in  space,  in  the  1st  dihedral 
horizontal  distance  (parallel  with  ground  line)  between 
m  and  n  is  6  ft.,  and  between  those  of  n  and  o,  is  2|  ft. 
idicular  distances  from  the  points  in  space,  to  the  coordi* 
ollows:  m  to  H,  6ft.;  m  to  V,  2  ft.;  «  to  //.  4  ft.;  m  to  V, 
and  o  to  V.  3  ft.  That  is.  m  is  6  ft.  from  the  H  plane  ana 
lane,  etc. 

i  horizontal  projection  of  a  line  A  passing  through  tiie 
:en  Ah  will  pass  through  mh  and  nh;  also  where  i4hintcr- 
ine  GL  (Problem  2) .  ph  is  the  horizontal  projection  of  the 
le  A  pierces  the  V  plane,  at  ^v. 
pierces  the  H  plane  at  q».  By 
nd  B^  are  the  vertical  and  hon- 
of  the  line  B,  passing  throtigh 
in  space;  and  sVand  fh  are  the 
line  pierces  the  V  and 
tively.  It  is  evident  ^9^ 
points  on  the 
n  the  plane   P, 

and  that  rh  and  qh  lie  in  its  hori-  ©- 

zontal  trace,  HP. 

By  scale,  the  tangent  of  the 

angle  which  the  trace  of  each  plane  makes 

with  the  ground  line  is  .400,  and  the  point 

of  intersection,  at  G,  of  the  two  traces  at 

the  ground  line,  is  distant   20  ft.  from  m® 

of  i>oint  m. 

This  problem  is  very  useful  in  structtiral  shop 

details,  such  as  finding  the  end  bevel  of  hip   and 

valley  rafters,  in  framing,  etc. 

Problem  4. — To  find  ihe  point  b  where  a  per- 
pendicular line  L  from  a  given  point  a  pierces  a 
gwen  plane  P;  also  the  length  of  L      (Fig.  13.) 

Data.— Let  av  and  ah  be  the  vertical  and 
horizontal  projections  of  the  point  a.  and  let  VP 
ad  HP  be  the  traces  of  the  plane  P. 


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14.— THE  CALCULUS. 

The  Calculus  furnishes  us  with  direct  and  exact  methods  for  solving 
many  ploblems  which  could  be  solved  otherwise  only  bv  indirect  approxi> 
mations;  and  the  application  of  its  principles  provides  us  with  useful 
working  formulas  in  Mensuration,  Geometry,  Mechiifmics  and  other  subjects. 

The  two  processes  in  calculus  are  differtntiation  and  inUgrcUion,  each 
being  the  inverse  of  the  other.  The  former  comprises  the  subject  of  Dif- 
ferential Calculus,  and  is  analytic  in  its  nature;  the  latter  comprises  Integral 
Calculus,  and  is  synthetic. 

Problems  to  be  solved  by  the  Differetaial  Calcultis  may  be  reduced  to 
an  equation  which  will  be  the  equation  of  some  curve  referred  to  coordinate 
axes,  as  in  Analytic  Geometry.  If  there  are  two  variabUs  in  the  equation, 
as  X  and  y,  there  will  be  two  coordinate  axes.  X  and  Y.  The  proce^  ot 
differentiation  enables  us  to  find  the  slope  of  the  curve  at  any  point  p  whose 
coordinates  are  x  and  y;  and  from  this  angle  of  slope,  say  with  the  axis  of  X, 
we  may  detennine  (1)  the  actual  changt  in  y  for  a  corresponding  change  in  x^ 
and  (2)  the  rate  of  changt  in  y,  at  any  point  on  the  cxirve. 

Problems  to  be  solved  by  the  Integral  Calculus  may  be  reduced  to  an 
equation  which  will  be  the  equation  of  the  slopt  of  some  curve  referred  to 
coordinate  axes,  as  in  Analytic  Geometry.  If  there  are  two  variables  in  the 
equation,  as  x  and  y,  there  will  be  two  coordinate  axes.  X  and  Y.  The 
process  of  integration  enables  us  to  find  the  equation  of  the  curve,  i.  e..  the 
value  of  the  ordinate  y  for  any  value  of  the  abscissa  x, 

A.     DIFFERENTIAL  CALCULUS. 

DifferenHation  has  for  its  main  object  the  determination,  from  the  equa- 
tion ot  the  problem,  of — 

1st,  the  differential  <iy,  — the  actual  change  in  a  function,  due  to  a  corres- 
ponding change  dx  of  the  variable  x  upon  which  it  depends. 

2nd.  the  differential  coefficient  -j- ,  —  the  rate  of 
ax 
change  of  a  ftmction. 
To  illustrate:    In  the  equation  y— «*  let  y— 
the  area  of  a  square  of  which  x  is  the  side.    Now 
increase  x  by  the  distance  dx  (reads  "differential 
of  X,"   and  does   not  mean  dXx),  an  amoimt 
smaller  than  any  numerical  value-    then  will  the 
new%rea  yi  =JC|**»  {x  +  dx)*''x^-\-  2xdx+dx*\   and 
the    increment  or  actual  change   in   y   will   be 
dy''yt-yx^+2xdx+dx^-x*''2xdx+dx*.     But       w 
as  any  infinitesimal  quantity,  as  dx  or  dx*,  which     |p 
is  purely  additive  may  be  neglected,  we  have, 
differential  dy-=  2xdx, 


Fig.  1. 


dy 
and  the  differential  coefficient  j-  —  2a;' 


2x 
I' 


(1) 
(23 


Differential  Coefficient.— T/tedi^^en- 

tial  coefficient  is  simply  the  natural  tangent 
of  the  angle  which  a  tangent  to  a  curve 
makes  with  the  axis  of  X. 

The  preceding  equation,  y— a;*,  is  the 
equation  of  the  parabola.  y«=»wa:*  (see 
Analytic  Geometry),  in  which  i»=»  1.  Let 
Fig.  2  represent  such  a  cvu^e  and  let  x 
and  y  be  the  coordinates  of  any  point  ^ 
p.    Also  let  ^  be  another  point  so  that  ^' 

x+dx-^xf  andy+dy—y;  then  will    -r^ 

• ax 

*  Note  that  dy^increment  of  yy^^y, 
and    ox— increment  of  X— a/— a;. 

260 


Fig.  2. 


d  by  Google 


d  by  Google 


208 


li.—THE  CALCULUS. 


(f)  a  fraction,  is  the  differential  coefficient  of  the  numerator  multiplied  b 
the  denominator,  minus  the  differential  coefficient  of  the  denominate 
multiplied  by  the  niunerator,  this  difference  being  divided  by  the  aquai 
of  the  denominator. 

du  dv 


"dx 


'dx 


2"^Quad 


iSt^yQ^ 


dx 

ag«4-2     dy     2y(fty->-0)-(8a;«+2)>     &c«- 2 
^"      2x     •  dx"  4^  "     2x*    ' 

(g)  any  powtr  of  a  variable,  is  the  product  of  the  exponent,  the  power  wit 
exponent  diminished  by  1.  and  the  differential  coefficient  of  the  variabl 
^    dy         ^   .  du 
*  dx  dx 

y- 2(««+ 8)«;  ^ - (3X 2)(««+ a)«X2x- 12%(a;«+ 8)«. 
ax 

Maxima  and  Minima. — One 

of  the  principal  uses  of  the  differ- 
ential calculus  is  to  find  the 
maximum  or  minimum  value  of 
a  function.  In  any  ctirve,  as 
for  instance  the  ellipse,  a*y*  +  6*«* 
—  a*6*  (see  Analytic  Geometry), 
let  it  be  required  to  find  theV- 
maximum  value  of  the  ordinate 
y.  From  the  above  equation, 
placing  y  in  the  first  member. 
wehavea«y«-oV-6««».  Differ- 
entiating. 2a*  y  dy=>0  — 2fc*«fflc; 
whence  the  differential  coefficient 
dy        2b^       b^x      ^  ^     . 

J--"— s~;-«- — T-  —  tcmgent  of 
dx        2a*y        a^       ^^* 

angle  of  inclination  of  the  tangent  U,  with  the  axis  of  X. 


t^QLMOd 


4^Qucid. 


That  is,-—^  la  tl 
a*y 


value  of  m  in  the  equation  of  the  straight  line  U.  (See  Analjrtic  Geometry 
For  any  tangent  to  the  ellipse,  if  m  is  a  minus  quantity,  the  point  « 
contact  p  is  in  the  1st  or  3rd  quadrants,  and  if  it  is  a  plus  quantity  the  poii 
of  contact  is  in  the  2nd  or  4tn  quadrants.  This  is  made  evident  by  notsx 
whether  the  tanfi^ent  line  U  slopes  upward  to  the  right  or  downward  to  tl 
right.     If  the  pomt  of  contact  p  is  m  the  first  qtiadrant,  x  and  y  are  ph 

and  ^  —  — i\)  " — 5^;  if  in  the  second  quadrant,  aria  mwft«  and  y  is  pl« 

hence  ^-  --,  (=^)  -^;   if  in  the  ard  quadrant.  |^-  -^  (5^) 

— r- :  and  if  in  the  4th  quadrant,  7^  —  — r  ( — )  — -=r .   Jims,  vm  an  db 

a*y  ^  dx         a*\—y/     a*y 

i)  study  th4  slope  of  a  curve  at  any  point. 

By  inverse  analysis  we  may  find  the  values  of  x  and  y  (including  tb« 
maximum  and  minimum  values)  by  assigning  definite  values  to  the  sia\ 
dy 

J-.  Thus,  when  y  is  a  maximum  we  know  that  the  tangent  line  tt  mu 
ax 

move  so  as  to  be  parallel  with  the  axis  of  X:  hence,  it  will  coincide  with  tl 
tangent  line  TT,  touching  the  point  P  at  the  upper  extremity  of  the  mix> 
axis;  or  with  a  parallel  tangent  through  the  point  P  at  its  lower  extrexnit 
And,  when  y  is  a  minimum,  tt  will  be  perpendicular  to  the  axis  of  X,  touc 
ing  points  on  the  curve  at  either  extremity  of  the  major  axis.    In  the  £oxm 

case,  j~  (—  =t  -7-)  —  0;    whence  «  — 0.  which  value  substituted  in   t 

SenercU  equation  makes  y™  ±6,  a  maximum. 
y  i      i  ^x\  .  ^  .  . 

Jjc  \         cfly)  "°°'  ^ncnce  y  — 0,  a  mmimum. 

Maxima  and  Minima  obtain  at  points  where  j^  changes  from 
or  from  —  to  +,  r^  *        T 

Digitized  by  VjOOQ  IC 


And  in  the  latter  cw 


•#-    to 


MAXIMA  AND  MINIMA. 


360 


Problem  1. — It  is  desired  to  suspend  a 'a 
Wf^t  W  vertically  beneath  a  point  P  situated  Cl 
midway  between  two  level  supports  i4  andB. 
For  this  purpose  two  diagonal  rods.  AW  and 
BW.  of  eqtiaflength.  are  used.  At  what  angle 
a  shall  the  rods  be  inclined  so  that  a  mini- 
mam  amount  of  metal  will  be  required? 

W 

Sohition. — ^Thc  stress   in  each  rod  — -=- 

Kcant  At  and  the  length   of  each   rod— << 
cosecant  a  "  k  secant  a ;  hence,    the  amount  of 


Fig.  4. 

-^    metal  required  in  the 

rods  would  be.  making  n  a  constant,  and  h  variable. 


l^-n/j-  secaj  (h 
nhiV       ,         nh 


sec  a) 
2 


-|-  -^ J-  (1  +  tan^i) 

nhW    nkW    d« 
"     2    "*"    2     *A« 

fikW    nd^W 

"     2    "*■    2*    • 
.            dy     nW     29uPW     ^  , 
whence  j^^-y" iwr""  '        mtnimum.' 

.'.  A-d,ora-4«». 
This  proves  that  the  most  economical  angle  for  a  truss  diagonal  is  45^. 

Problem  2, — It  is  proposed  to  build  a  rail- 
road from  A,  a^int  opposite  B  and  distant  30 
mUes,  to  Z>  a  pomt  50  miles  below  B.  The  cost 
o£  grading  on  the  line  BC  is  $8,000  per  mile, 
while  the  cost  of  nading  ^m  A  oiagonally  J 

to  any   point  Cis  912^000  per  mile.    Find  the  Xr« 

pooi^on  of  the  point  C  so  that  the  entire  cost  #a«aa^..-^-.  /  <v>*i      i 
of  grading  will  be  a  minimum.  Ig000p<niig/x«?feg5m,  I 

Sohztion.— Lety-the  cost  of  grading  the  ^^'  * 

line,  and  from  the  data.  Pig.  5. 

•»-$12,000  ClB* +  16*)*  + $8.000 (BD-BQ. 
Let  BC— X.  ilB-  30.  and  BD-50;  then 


!3 


-X). 


ir-12000  (900+«^*  +  8000  (60- 
1^-  6000(900+««)-*(2«)-8000-0  for  minimum; 


12000SC 


-8000 


.*.    JK- 26. 83  miles.    Ans. 
Note.— The  tfUir»  cost  of  construction  and  the  cost  of  operation  would 
cl  course  enter  as  factors  to  reduce  the  distance  between  C  and  Z7,  for 
economy. 

Problem  3. — ^What  is  the  maximum  cylinder,  in 
volume,  that  can  be  inscribed  in  a  sphere  ? 

Solution. — Let  /?  — radius  of  sphere;  r  — radius, 
and  ik— altitude,  of  cylinder.  Let  V— volume  ot 
cylisder;  then, 


—  a  function  ot  h,  both 


in  whi^  V— a  function  of  k,  both  being  variable. 

with  R  constant.  Differentiating  and  making  77-  "  0, 

an 

we  have,  ^ -it/P-IkW-O; 

/.A— 4=/?-l  VT^.    Ans. 
V3 


dbyCpQ.qgle 


270  U.—THE  CALCULUS. 

Other  Forms  of  Differentiation. — ^There  are  two  forms  in  which  the 
result  of  difTerentiation  may  be  expressed,  namely,  difftrntiial  coefficient  or 
simply  differeniioL' 

y— ic»;    3^  —  2*      —differential  coefficient. 
ax 

y— a;*:    dy  —  2«d« —differential. 

dy 
Hence  the  differential  coefficient  -y-  may  be  considered  as  a  fraction. 

ax 

the  numerator  dy  being  the  perpendicular,  and  the  denominator  dx  the  base. 

of  an  infinitesimal  triangle  of  which  the  hypothenuse 

is  equal  to  y/dx^+dy*.    Multiplying  the  differential 

coefncient  by  dx  we  obtain  the  differential  dy  —  2x  dx. 

It  is  well  to  keep  this  graphical  analysis  in  mind  in 

dealing  with  problems  involving   both   Differential 

and  Integral  Calculus,  as  it  then  loses  much  of  its 

haze  and  mystery. 

Fig.  7. 

Besides  the  Algebraic  forms  (a)  to  (g) .  which  are  universal  in  their  applica- 
tion, the  following  formulas  for  differentiation  of  special  functions  will  be 
foimd  useful  for  reference.    (For  Algebraic  Functions,  see  pages  267. 2^.) 

Logarithmic  and  Exponbntial  Functions: 
logft  e  dx 


(h) 


(i) 


y-logaJt;     dy-- 
y-loge*:     dy--^. 

X 

du 

.  dy     .  dx       .       .  du 

y-logft«;    ^-loKa*  — '.    ^y-loga*"^- 

du 

.  dy    dx  J       du 


(j)         y  =  aU;  —•  =»  logg  oou  -t— ;     dy^log^  O'O^du. 

(k)       y-*«;  j|"'"j|'       dy^du. 

(1)         y=MV;       -r^'^vuy-^^+log^U'uy^;  dyvuy-^du+log^  U'K'ydo. 

Trigonombtric  Functions: 

dy  du  ,  . 

(m)       y  =  sm«;  ^— cosmj-;  dy^'coaudu. 

dy  .       du  J.J 

(n)        y^cosw;  ^j-  — — sin«T-;  dy=—sinudu. 

dx  .  ax 

(o)        y-tan«;  J^°'®®*^d"'  dywx?Hdu. 

(p)        y— cot  «;  -7^  —  —  cosec*«T-*.  dy— —  co8ec*i«di*. 

*'^'        '  dx  dx 

(q)        y»8ecM;  3— —  sec  k  tan  «  j— ;       dy— secM  tan  m^m. 

^^        "^  dx  dx 

(r)        y  — cosec  u\         -j-  —  — cosec  u  cot  u-j-\  dy  — cosec  u  cot  u  du. 
dx  dx 

rv  dy       .        du  J5_j. 

(s)        y— verstt;  j-  — sin«:j-;  dy^MftiLdu^]^ 

'  "^  dx  dx  Digitized  by  VjOngLc 


TIATION  FORA 


ix 

iy 

du 
dx 

Ix 

iy 

uVu^-l  ' 
du 

57 

ix 

du 
dx 

ix    V  2u-u* 
XPANSION  OF  F\ 

\-^l-X  +  X*-K^ 

¥x 

atloo  is  employed 

.    Let :)"»«  be  an^ 

fiferential   coefBcic 
J  is  the  difiE  coef 
if  of  the  2nd  diff  c 
W.  etc. 

n  enables  tis  to  e: 
y  the  use  of  succe 

expanded,  and  aa 
x"  +  jE«* ,  iisini 

valtie  of  u  suco 
iation,  we  have, 

I  y 

E^ .         ^ 

dx 

E:f .  ^ 

dx^ 


da* 
d^ 
dx< 

«^'  Digitized  by  Google 


272  U,—THE  CALCULUS. 

Substituting  the  above  values  of  the  indeterminate  coefficients  in  equa* 
tion  (1)  we  have  the  following  working  equation; 

**^^rf«  '^d*«     2^d*"     2Z^dx*     23-4^  ^^ 

remembering  that  y<-Mwhen,  in  all  the  successive  differential  coefficients. 
%-0. 

Examples  in  the  use  of  touaiion  (2). — It  is  to  be  noted  that  Madauren's 
Theorem  may  be  considerea  a  special  case  of  Taylor's  Theorem,  following. 
Also,  the  Binomial  Formula  (see  Algebra)  is  a  special  case  of  Madauren  s 
Theorem. 

Expansion  of  a  few  common  functions: 

loge  (l+*)-*-y+J-J+y .       Naperian  system. 

loga  (1+*)  "-^('-y+T-J+T ^)    Common  system. 

3^_  Common  log  (1-f-^)   _        J  ,.4342944819- the  mod- 

Naperian  log  (l  +  «)        2.30258509 
ulus  of  the  common  system  —  common  log  #  —  log^  e, 

'  -»+*  +  F-8+ 2^4+21^8+ ».7m818J8  +  . 

'^"^"*"l"*'l-2"^l-2-3"^l-2.3-4  * 

"""""'"rrs"*"  1.2.3-4.6"  l-2.3-4.5V7"*"  • 

«««-  1-172  "^  mi -Le  +  LS • 

thu..natcosof20o.l.j(f)%J-^(|)^A.(f)V . 

•J-  - 1-  §  +  4  -♦  +  ! .         /.  ir-  3.1415926536. 

Taylor's  Theorem  enables  us  to  expand  a  function  of  the  sum  of  two 
variables  arranged  according  to  the  ascending  powers  of  one  of  the  variables. 
Let «»,  —  a  function  of  («+/i),  be  the  function  to  be  developed.  Then,  for 
a  working  formula, 

remembering   that  y"=«  when,  in  all  the  successive  differential  coefficients 
of  u,  A— 0.    (See  Maclauren's  Theorem,  preceding,  for  illustration.) 
Expansion  of  a  few  common  functions: 

log  (x+A)-log  x+ A-^+g-^+  — -. 

u 

tan(ir+;»)-tan«+Asec*«+*«8ec«aftan«+-^sec»x(l  +  3tan««)  + 

o 

log  (l  +  8in*)-a;-f +|-i^+ . 

B.    INTEGRAL  CALCULUS. 

Integral  Calculus  is  the  process  of  summation  or  the  adding  up  of  an 
infinite  number  of  infinitesimal  quantities.  Its  operation  is  the  inverse  of 
differentiation.     In  the  equation  y  — x',  by  differentiation  we  have  dy 

2xdx,  hence  the  summation  or  integration  of  2acdaf-  I  2«iic— «'  (  "2^/  • 

Suppose,  for  example,  we  wish  to  find  the  area  of  a  triangle  whose  altitude 


INTEGRAL  CALCULUS,   METHOD  OF  LIMITS, 


273 


is  h  and  base  6.  Fig.  8. 

Beneral.  the  area  of  any  vertical  strip 


If  we  let  dA  represent,  m 

.    ot  len^h   y 

and  width  dx,  distant  x  from  the  axis  of  r,  then 


the  total  area  of  the  triangle  will  eqtial  the  summa- 
tion  of  all  these  strips  between  the  limits  x— 6  and 

x«0;  or.  area  < 


i.A-|di4      "  I  ydx. 


The  main  difficulty  in  Integral  Calculus  is  in 
fonning  the  equations  to  be  int^^rated  and  recog- 
nizing them  as  related  to  certain  fundamental  forms  ^^ 

whose  integrals  are  well  known,  many  of  which  are*  oj< 
given  in  tabluar  form  in  the  following  pages.  In  the  w 
above  case,  x  and  y  are  dependent  variables,  jt  in-  ■  Fig.  8. 

creasing  as  v  decreases,  and  vice  versa.  When  x^b^  y~0;  when  jt— 0. 
V"-4;  and  the  point  P.  whose  coordinates  are  x  and  y,  moves  along  the 
hypothenuae  in  a  straight  line  between  the  axetf  of  X  and  V,  as  x  and  y 
vary.  The  equation  of  this  straight  line,  of  which  y^mx+b  is  the  general 
eqitttkm,  is 

y.  ^jx+h 
bccauae  the  tangent  of  inclination  m  of  the  hypothenuae  with  the  axis  of  X 
is   —-^ (minus,  because  downward  to  the  right),  and  the  value  of  b  where 

the  hypothenuse  intercepts  the  axis  of  V  is  A.  But  dA  —  }>dx  — the  area  of 
an  innniteaimal  strip  of  length  y,  and  from   the   i^ve  equation,  ydx™ 

—g-xdx-^hdx;  hence. 


Area 


-'-f-i 


xdx-^Ux 


wfaicfa,  by  certain  fundamental  forms  given  in  the  table,  reduces  to 

I 


^      b 


Subatxtttting  the  value  of  x-^b  in  the  equation,  we  have 
Aieai4--j.  j+«>-i6A.    Ans. 


DaffnHe  Intcfration  a  Method  of  Units. — In  the  preceding  illustration 
ei  the  area  of  the  tria^igle  we  referred  to  the  upper  limit  x'^b.  and  the  lower 
Hmit  X  —0.  We  will  now  find  the  area  of  a  part  of  the  triangle  or  that  etched 
portion.  Pig.  8.  between  the  upper  limit  x—  {6.  and  the  lower  limit  x^^. 


Thus. 


After  integrating. 


Sobatituting  |6  and\ 
y>  lor  X,        / 


b  2 


X  dx+hdx 


upper 


lower 


^•-    l-26l6+***)-(-26l6-^T; 


.'.  partial  area  i4i— -j. 


Ans. 


Note. — Subtract  the  value  obtained  by  using  the  low4 
value  obtained  by  using  the  upper  limit. 


limit. /rom  the 


wer>limit.  *rc 
byVaOOgfe 


li.—THE  CALCULUS. 
Formulas  for  Integnitioa. — 


-a  log  X. 
I  a*  log  a  dx^a*. 


lo«*»d«- 


icoB  xdx'^sm  X.  icKM  2xdx'^ 

/sin  X  dx"  -cos  x.  I  -. — ^  —log  tan  x. 


1  +  loga  * 
sin  (x+a)  cos  («— a). 


I  sec  ^(fx— tan  x. 


Isecx  tan  ji^dx— sec  x. 
I cosec  xcotxdx^  — cosec  «. 
I  tan  xdx  — log  sec  x. 
I  cot  xdx'^  log  sin  x. 


|cosec*«d«— —  cot  X.      Icosec  xdx— log^/ 

J  J  ^l+< 

f 

/" 
I- 

I  sec  xdx-^log  (secx+tanx)— log  tan  (■t+'T')  • 

I  cosec  xdx— log  (cosec  x— cot  x)— log  tan  ~  —  log^  / 
J  *  \  l+( 

/*    (f X              1    .            ,X                  1  .  _,    X 

— - — i  — — tan-*— — cot-*  —  .  . 
x»  +  o»      a            a           a  a 

/dx  1    .      X  —  o       1    -      o— X 

x«-a«"  2o  ^"^  x+o"  2a  ^°^a  +  x' 

/*     dx  .      I  *  1  « 

»sin->— —  — cog~>  — . 
n/o«  -  x«  «  « 

r  /^     -log  (x+>/;?±^«) . 

«F  V  x»±  o* 

J'      dx  1  ,«  1  .  « 

y- -  — sec-1—  -  -  -.cosec-":^. 

C      dx  ,  X 

J  v2ax— x«  o  ^  T 

Digitized  by  VjOOQ  IC 


PLANE  CURVES— AREAS  AND  LENGTHS. 


%76 


(V) 
(V) 


Areas  of  Plane  Carves. — 
Pormtxla  (1).    A"  i  yiix     (Fig.  9.) 


Pormula  (2).    A 


-it 


x)dy     (Fig.  10.) 


Let  Figs.  9  and  10  each  represent  one- 
half  a  parabola  whose  base  is  2b  and  altitude  a. 
Required  the  area  of  the  figure?  From  the 
gmeral  equation  of  the  parabola,  o^^nx,  »— 

— .  When*— a,  y—6;  therefore »—^«- —.and 

the  equation  of  the  parabola  in  the  figure  is  j***  X* 

b*  x^  av* 

— *.     Prom  this  equation,  y— 6 —randx  —  -^. 


Method  (1).  tmrtical  strips, 
A^fydx^/lx^dx, 

"I    a*    '     f 

^0 


Fig.  10. 

Method  (2).  horiMontal  strips. 
rb  nb 

^-jifl-x^dy^j^a^^^dy, 

[ft 
0 


-|a&.    Ans. 


Equivalent 
values.      —  a6- 


\oib^\qb.    Ans. 


It  is  thus  seen  that  the  same  result.  ia6.  is  obtained  whether  we  assume 
the  strips  to  be  vertical  and  summate  horizontally  or  whether  we  assume 
the  stri^  to  be  horizontal  and  summate  vertically. 

Agam.  reqtiired  the  area  of  the  shaded  portion  of  the  parabola  in  Fig.  9, 
1).  between  the  limits  03—4  and  Oi  — 2: 


Formula  (1).  between  1 


-fr-f?"--  [>+  -  D^" 


-i? 

"  8 

b       4>/  2 
^a         3 

b 

rmula 

:    Length  L- 

;.. 

16-4\/^ 


b 


Vd««+dy«. 


2 

Ans. 


(See  Fig.  7.) 


Use       L«  I  I  1+  l-^\    I  ^*  when  x  is  the  independent  variable. 
U»e      L  -  I    [  1  +  /^)    I  * dy,  when  y  is  the  independent  variaW^^ 


270 


li.^THE  CALCULUS. 


Probtem.— The  catenary,   y—  yI#'+#     'j.  is  the  curve  which  a 

cable  assumes  when  suspended  at  both  ends,  as  at  i4  and  B,  Fig.  11.  Re- 
quired the  length  of  the  catenary  from  the  vertex  V,  on  the  axis  of  Y. 
to  any  point  p  whose  coordinates  are  x  and  yi 


X                  0 

vs 

Y 

Pig.  11. 


Solution.— 


hence.^- J  (*^ -*-"•) 

and  dL-  §  ^  #"^  +#"""'  ^  ds  (-^1  +  (gl)  'd») 

with  limits  «-«,  and  «-0,  L -i  I      (#~  +#*"")<** 

.-.    length   from    V  to  P-L  --I (#" -#~"  | .    Ans. 

Areas  of  Curved  Surfaces,  or  surfaces  of  revolution. — 

Formula  (1).    5-  2k  jydf -  2ir  fy    1+  (^)  *     dx,    (About  axis  of  X.) 

Formula  (2).    S''2xfxds'^2xfx    1+ flfV  |  dy      (About  axis o£  K.) 


Problem. — ^Let  it  be  required  to  find  the  area  of  the  shatUd 
sphere  of  radius  r.  Pig.  12. 


of  a 


Solution. — Use  Formula  (1): 


d  by  Google 


AREAS  OF  CURVED  SURFACES.    VOLUMES, 

Equation  of  circle  is  «^+3^«-f^ 

wbcnce,  3^— r*— **   or  y—Vr*— «■. 

ax         y  \dx/       y* 

SnbctHiztiiig  value  of  (^    in  Formula  (1)  then  it  obtained. 

-firl   (>*+««)*  d*-2«  I  f^   -2«r(6-a).   Ana. 

Yciwrnm,  or  planet  of  revolution. — 
Formula  (1).       V  -  « I  ^x     (Plane  revolved  about  axit  of  X.) 

JX'^h 

/•*■-« 

Formula  (2).       K-x  I  s^y      (Plane  revolved  about  azit  of  K.) 


277 


Pis.  13. 

ProUem. — Find  the  volume  generated  by  the  thaded  portion  of  the  para^ 
bok  )i*- 4ar.  Pig.  13,  about  the  axit  of  X. 

Sohrtion. — ^Piom  the  equation  of  the  parabola  and  Formula  (1)..  we  have, 

4acd» 


-«|*2««-2«(<^-M).   Ana. 


d  by  Google 


d  by  Google 


FUNDAMENTAL  EQUATIONS  OF  MOTION. 


270 


MOTION. 

I.  Uniform  notion :  vq  constant,  no  acceleration. — ^With  uniform  motion 
a  body  moves  at  a  constant  velocity  Vo.  imparted  to  it  by  a  force  which 
has  been  removed ;  hence  there  is  no  accelenition.  Note  that  Vq  becomes 
the  initial  velocity  in  tmiformly  varying  (accelerated  or  retarded)  motions, 
following. 

^-— — -— - — -;  A-t^;  <-— . 


t 


(iquaHonof 
Shaiaht  ^^ 
UneJ  ^ 


11.: 


Fig.  4. 

Ex.  2. — ^What  velocity  will  be  required  to  travel  16  miles  in  three- 
qoarters  of  an  hour? 

Ana.-t>b»7-    ^g^^    -31.29  ft.  per  sec. 

RglatiM  uniform  motion. — ^A  man  walking  forward  with  a  velocity  V, 
in  a  train  moving  with  a  velocity  vq',  acquires  an  actual  velocity  of  Vo  — 
i%'+«to'.  Similarly,  if  walking  backward  m  the  train  he  would  acquire  a 
Telocity  of  tih— tuo'— t^'.  in  the  direction  in  which  he  is  walking;  or,  vb— 
v^'—Vft,  in  the  direction  of  the  moving  train. 

II.  Uniformly  accelerated  motion;  no  Initial  velocity,  va. —  Problems 
that  coxne  under  ^is  head  are  those  in  which  the  body  starts  from  rest  and 
is  acted  upon  by  a  constant  force  in  the  direction  of  its  motion.  A  train 
startix^  from  a  station,  or  a  body  falling  from  a  height,  are  examples.  In 
the  foOowing,  friction  is  neglected: 


(a). ACCBLBRATION,  TiMB  AND  VbLOCITY. 

^   ^       V  V       Vi      V-Vi 


h      t-ti' 


(EquprHon  of  . 


Pig.  6. 


h 


(EcfuaHon  of  ^  „ 
SfraMht  '^X^ 
Une)  ^^  ^ 


tx 


Fig.  6. 


Ex.   3. — ^What  velocity  will  a  body  acquire  at  the  end  of  10  seconds, 
falfing  in  a  vacuum  ? 

Ana.—  v-^->  33.2X10- 322  ft.  per  sec. 


•  —-3-;  f^  — ;  V— -7— — ; — - — 
2  •  V  i  t-ix 


(fr). — ^TlMB.  VbLOCITY  and  DI8TANCB. 

vi  ^     Is  2s    2  (j-5i) 

$  —  -=-:<■■  —  :  t>— — — — ^ *^. 

2  •        t;  •  t         l-h 


(EquoHon  of^ 
Sfrvrighf'^ 


ifyg^dSy*  Google 


280 


li,^MECHAmCS. 


Ex.  4. — A  body  falling  in  a  Tacuum  attains  a  velocity  of  S23  ft.  V 
sec.  at  the  end  of  10  seconds.     Through  what  height  has  it  fallen? 

Ans.—  A-^-i  (322X10)  -  1610  ft. 


Note  that  y  is  the  averagfi  velocity  for  the  time  U 


(c). — Vblocity.  Distancb  and  Accblbration. 


«-li';A-^';«^-v^-8.02V^ 


(Uhjcrtion  of  . 


A<^. 


k±i. 


Pig.  9. 


(EquoHon  of  a 


Pig.  10. 


Ex.  6.— What  final  velocity  will  a  body  acquire  in  falling  1000  ft. 
the  earth? 

Ans.— Final  velocity -»- 8.02  \/A  -8.02 X  31.82-263.8  ft.  per  sec 


(d). — ^DisTANCB,  Accblbration  and  Timb. 


^-.249VA:«-^;;i-^-18.1(«. 


(Equafion  of 
nrrarboIa)y/^y 


Pig.  11. 


'25 


25 


a/» 


fiqucrHon  ^  ^ 
Ponvrbotcf)  yy     j^j 


Fig.  12. 


Ex.   6.— Starting  from  rest,  what  acceleration  per  sec  will   caua 
body  to  travel  2000  ft.  in  10  seconds? 


Ans. —  a  -  -J-  Vyy  -  40  ft.  every  second. 

Note  that  the  term  "acceleration  "  means 
second  "  — increase  in  velocity  per  second. 


rate  or  acceleration 


111.    Uniformly  accelerated  motion  with  ;K>8itive  Initial  velocity  i 

This  is  a  case  of  uniforml)r  varying  motion  m  which  the  constant  ii 
velocity  vd  is  in  the  iam»  dtrtction  as  the  accelerated  velocity  v  produce 
some  constant,  acting  force.  Let  V— v  +  cio  — the  resultant  velocity  at 
time  t  measured  from  the  instant  that  v  begins  to  act;  h  or  5  — the  dist 
traveled  in  that  time;  g  or  a=-the  rate  of  acceleration  per  second.  " 
the  followmg  relations  exist,  neglecting  friction: 


FUNDAMENTAL  EQUATIONS  OF  MOTION. 


281 


(i4). — ACCBLBRATION,  TlKB  AND  VbLOCITY. 


Ex.  7. — A  stone  is  thrown  from  a  balloon  vertically  downward  toward 
the  earth  with  a  velocity  of  100  ft.  per  sec.,  striking  the  earth  with  a  velocity 
d  1000  ft.  per  sec.    What  is  the  tune  of  its  descent? 


V-Po     1000-100 
C     "■       82.2 


—  28.0  seconds. 


(B), — TiMB,  Vblocitt  and  Distancb. 


2fc 
'V+vo' 


t' 


-o+^ 


r-j(V+*to)-<  {j+^)'' 


V+Vo 


■j+vo 


v-j-,^:v-2{j-,^):vo-j-j. 


Ex.  8. — At  what  height  above  the  ground  is  the  balloon  in  Ex.  7,  pre- 
ceding? 


Ans.- 


A-j(V^+«H>)-14X1100-16400ft. 


(O. — Vblocity,  Distancb  and  Accblbration. 


k- 


V*-vt^    p<P+2Pb)    v(2V-v) 

'     2k     "       2fc       "       2h       ' 

V»-oo'     p(t;+2oo)     v(2V-v) 


V-V    v(p4-2ob)     v(2V-v) 

**"      25      "       2j        "       2j       • 

.  V^- V^v(i>4-  2po)  ^v(2V''V) 

2a     "       20"       2a      * 


K-V2a5+ii^^;   vb  -VV^-2aj;   o- 
VV+2a5-tH). 


Ex.  0. — ^At  a  point  one  mile  above  the  earth's  surface  a  rifle  ball  is  fired 
downward  to  the  earth  with  an  initial  velocity  of  2200  ft.  per  sec.  With 
vhat  velocity  does  it  strike  the  earth? 


Ans.—  V-  V2«ili+t%«-V2X  32.2X6280+ (2200)«-  2276  ft.  per  sec. 


(D). — Distancb,  Accblbration  and  Timb. 


'-V(?)'-i-"- 


Ex.  10. — In  what  length  of  time  will  a  body  travel  2000  ft.,  if  the  initial 
'^'clocity  is  20  ft.  per  sec.,  and  the  acceleration  10  ft.  per  sec.? 


*"- '-VCi)'-i-'i-VQ'-^-«— ^-gk 


282 


15.— MECHANICS. 


IV.  Uniformly  accderated  motion  with  n«ffative  initial  velocity  c^:— 
This  is  a  case  of  uniformly  varying  motion  in  which  the  constant,  initial 
velocity  i;o  is  opposit4  in  dirtction  to  the  accelerated  velocity  v  pro- 
duced bjr  some  constant,  acting  force.  Let  v'—w  — tH)=»the  resultant 
velocity,  in  the  direction  of  v  at  any  time  t  meastired  from  the  instant  v 
begins  to  act;  h  or  s  — the  distance  (algebraic)  traveled  in  that  time;  gora^ 
the  rate  of  acceleration  per  second.  Then  the  following  relations  exist, 
neglecting  friction: 


(A'). — ACCBLBRATION,  TiMB   AND  VELOCITY. 


t;*— v-»to— «/  — 1^;  v^gi;  Vo^gi—v'. 


v'  +  vq     v_  v'-^vq      v_ 

g   ' g'   ^'    t     "r 


<-- 


v'-^vq      v_ 


a' 

Ex.  11. — Prom  a  point  distant  h  (unknown)  above  the  earth,  a  rock 
is  thrown  vertically  upward  with  a  velocity  of  200  ft.  per  sec.,  and  in  falling 
strikes  the  earth  with  a  velocity  of  400  ft.  per  sec.  What  length  of  time 
is  the  stone  in  the  air? 

.  ,     iZ+vo    400+200     ,„^. 

Ans.—  / ^-—^^-s—- 18.68  seconds. 

g  32.2 


(B'). — ^TiMB.  Velocity  and  Distance. 


'  /  #       .      ,        2j 


/    2i  ^  ,    2s         ^  /s  ,      \ 

V  -  j+wo;  t^o-t/'-y;  v-2  (y+t^j  • 


,     2h^  ,    2k        „/fc_L     \ 

v*-  j+vo;vo=v'-  y;t;-2  I  y+«o)  • 

Ex.  12. — In  example  11,  preceding,  find  the  distance  h  of  the  starting 
point  above  the  ground  ? 

Ans.—  A=i-(t,'-t;o)-^^  (400 -200) -1863  ft. 

Note.— From  formulas  (c)  we  find  that  the  rock  ascended  A-  5^  -  ^?5L 

-621  ft.;  and  then  descended  A- ^-'-^-^^-2484  ft.     Sec  Ex.  13.    illus- 

2g        2g 
iralmg  this. 


(C). — Velocity,  Distance  and  Acceleration. 


g  -- 


2h  "      2g     ' 


2gh. 


V'^-Vt? 


2a     * 

~y/v^-2as. 


Ex.  13. — In  Example  11,  find  the  distance  h  of  the  starting  point  above 
the  ground,  using  the  acceleration  instead  of  the  time  (Ex.  12)? 
(400)»-(200)« 
64.4 


Ans.-   fc-  ^-■^•- 
2g 


■  - 1863  ft. 


(V). — Distance.  Acceleration  and  Time. 


Ex.  14. — In  Example  11,  find  the  distance  h  of  the  starting  point  abov« 
the  ground,  using  the  time,  acceleration  and  initial  velocity? 


Ans.—  Jft  (y-vo)  -1863  ft. 


sf  the  starting 
tial  velocity? 

by  Google 


UNIFORMLY  ACCELERATED  MOTION. 


283 


1. — Falling  Boduis.* 
(Jk- height  of  fall;  /  —  time  in  seconds;  v« final  veloc.  in  ft.  per  sec.) 
<-     L     -.031096  1;, 


v    gt     -32.16/. 
-v^-   S.02Vkl 


-  Vt-^ 


2494  VA. 


A— ^  -  .015547  t;«, 
-^-l«.08/«. 


§ 

Time 
t 

Hebdit 

l» 

Time 
1 

Height 

h 

Time 
1 

Height 

1- 

Time 
1 

Height 

I"* 

l» 

> 

> 

> 

> 

I 

.00311 

.00016 

42. 

1.3060 

27.426 

490. 

15.237 

3732,8 

1040. 

32.389 

16816. 

!2 

.00(32 

.00062 

44. 

1.3682 

30.099 

600. 

16.647 

3886.7 

1060. 

33.961 

17469. 

.3 

.00933 

.00140 

46. 

1.4304 

32.897 

510. 

16.858 

4043.8 

1080. 

33.683 

18134. 

.4 

.01244 

.00249 

48. 

1.4926 

35.820 

520. 

16.169 

4203.9 

1100. 

34.204 

18812. 

.5 

.01556 

.00389 

50. 

1.5547 

38.867 

630. 

16.480 

4367.2 

1130. 

34.826 

19502. 

.< 

.01886 

00560 

55. 

1.7102 

47.030 

540. 

16.791 

4533.5 

1140. 

36.448 

20205. 

.7 

.02177 

.00762 

60. 

1.8657 

56.969 

660. 

17.102 

4703.0 

1160. 

36.070 

20920. 

.8 

.02488 

.00995 

65. 

2.0212 

66.686 

560. 

17.413 

4876.5 

1180. 

36.693 

21648. 

.9 

.02799 

.01259 

70. 

2.1766 

76.180 

670. 

17.724 

5051.2 

1200. 

37.314 

22388. 

1.1 

.03109 

.01655 

75. 

2.3321 

87.452 

680. 

18.035 

5230.1 

1260. 

38.869 

24292. 

1.2 

.03731 

.02239 

80. 

2.4876 

99.501 

690. 

18.346 

5411.9 

1300. 

40.423 

26274. 

1.4 

.M353 

.03047 

85. 

2.6431 

112.33 

600. 

18.657 

5596.9 

1350. 

41.978 

28334. 

I.< 

.(H975 

.03980 

90. 

2.7985 

125.93 

610. 

18.96d 

5785.0 

1400. 

43.633 

30472. 

1.8 

.(teSOT 

.05037 

95. 

2.9540 

140.31 

620. 

19.279 

5976.3 

1450. 

46.088 

32688. 

2.0 

.0«219 

.06219 

100. 

8.1095 

156.47 

630. 

19.690 

6170.6 

1500. 

46.642 

34981. 

2.U 

.06996 

.07871 

110. 

3.4204 

188.12 

640. 

19.901 

6368.0 

1550. 

48.197 

37352. 

2.59 

.07n4 

.09717 

120. 

3.7314 

223.88 

660. 

20.212 

6568.6 

1600. 

49.752 

39800. 

2.75, 

.08551 

.11757 

130. 

4.0423 

262.74 

660. 

20.523 

6772.3 

1650 

51.307 

42327. 

3.0 

.09328 

.13992 

140. 

4.3533 

304.72 

670. 

20.834 

6979.0 

1700. 

53.865 

44931. 

3.5 

.10883 

.19045 

150. 

4.6642 

349.81 

680. 

21.146 

7188.9 

1750. 

54.416 

47613. 

4.0 

.12438 

.24875 

160. 

4.9752 

398.00 

690. 

21.455 

7401.9 

1800. 

55.971 

50373. 

4.5 

.13993 

.31483 

170. 

6.2865 

449.31 

700. 

21.766 

7618.0 

1850. 

57.626 

63210. 

5.0 

.15547 

.88867 

180. 

5.5971 

503.72 

710. 

22.077 

7837.2 

1900. 

59.081 

66125. 

5.5 

.17102 

.47030 

190. 

5.9081 

561.25 

720. 

22.388 

8059.6 

1950. 

60.635 

69117. 

f.O 

.18657 

.55969 

200. 

6.2190 

621.88 

730. 

22.699 

8285.0 

2000. 

62.190 

62188. 

1.5 

.20212 

.65686 

210. 

6.6299 

685.62 

740. 

23.010 

8513.6 

2100. 

65.299 

68562. 

7.0 

.21766 

.76180 

220. 

6.8409 

752.47 

750. 

23.321 

8745.2 

2200. 

68.409 

75247. 

7.5 

.23321 

.87452 

230. 

7.1518 

822.44 

760. 

23.632 

8979.9 

2300. 

71.618 

82245. 

8.0 

.24876    .99501 

240. 

7.4828 

895.51 

770. 

23.943 

9217.8 

2400. 

74.628 

89551. 

8.5 

.26431  ,1.1233 

250. 

7.7737 

971.69 

780. 

24.254 

9458.8 

2500. 

77.737 

97169. 

1.0 

.27985 

1.2593 

260. 

8.0847 

1051.0 

790. 

24.565 

9702.9 

2600. 

80.847 

105100. 

f.5 

.29540 

1.4031 

270. 

8.3956 

11)3.4 

800. 

24.876 

9950.1 

2700. 

83.956 

113340. 

10.0 

.31095 

1.5547 

280. 

8.7066 

1218.9 

810. 

25.187 

10200. 

2800. 

87.066 

121890. 

11. 

.34204 

1.8812 

290. 

9.0175 

1307.5 

820. 

25.498 

10454. 

2900. 

90.175 

130750. 

12. 

.37314 

2.2388 

300. 

9.3285 

1399.2 

830 

25.809 

10710. 

3000. 

93.285 

139920. 

13. 

.40423 

2.6274 

310. 

9.6394 

1494.1 

840 

26. 120 

10970. 

3200. 

99.504 

159200. 

14. 

.43533 

3.0472 

320. 

9.9504 

1592.0 

850. 

26.431 

11233. 

3400. 

105.72 

179720. 

15, 

.46642 

3.4981 

330. 

10.2613 

1693.1 

860. 

26.742 

11499. 

3600. 

111.94 

201490. 

I«. 

.49753 

3.9800 

340. 

10.572 

1797.2 

870. 

27.053 

11768. 

3800. 

118.16 

224500. 

17. 

.52865 

4.4931 

350. 

10.883 

1904.5 

880. 

^7.364 

12040. 

4000. 

124.38 

248750. 

18. 

.55971 

5.0372 

360. 

11.194 

2014.9 

890. 

27.675 

12315. 

4200. 

130.60 

274250. 

10. 

.59081 

5.6125 

370. 

11.505 

2128.4 

900. 

27.985 

12593. 

4400. 

136.82 

300990. 

29. 

.62190 

6.2188 

380. 

11.816 

2245.0 

910. 

28.296 

12874. 

4600. 

143.04 

328970. 

22. 

.68409 

7.5247 

390. 

12.127 

2364.7 

920. 

28.607 

13159 

4800. 

149.26 

358200. 

24. 

.74628 

8.9561 

400. 

12.438 

2487.6 

930. 

28.918 

13447. 

5000. 

155.47 

388670. 

2$. 

.80847 

10.510 

410. 

12.749 

2613.5 

940. 

29.229 

13737. 

6500. 

171.02 

470300. 

n. 

.87066 

12.189 

420. 

13.060 

2742.5 

950. 

29.540 

14031. 

6000. 

186.67 

65%90. 

19. 

.93285 

13.992 

430. 

13.371 

2874.6 

960. 

29.851 

14328. 

6500. 

202.12 

656860. 

23. 

.99504 

15  920 

440. 

13.682 

3009.9 

970. 

30. 162 

14628. 

7000. 

217.66 

761800. 

24. 

1.0572 

17.972 

450. 

13.993 

3148.3 

980. 

30.473 

14931. 

7500. 

233.21 

874520. 

3C. 

1.1194 

20.149 

460. 

14.304 

3289.7 

990. 

30.784 

15238. 

8000. 

248.76 

995010. 

38. 

1.1816 

22.450 

470. 

14.615 

3434.3 

1000. 

31.095 

15547. 

9000. 

279.85 

1259300. 

49. 

1.2438 

24.875 

480. 

14.926 

3582.0 

1020. 

31.717 

16175. 

10000. 

310.95 

1554700. 

*  Ex. — ^A  body  falling  from  a  height  h  of  398  ft.  reaches  the  earth  in 
5  seconds,  attaining  a  final  velocity  t;  of  160  ft.  per  sec.  If  the  body  were 
shot  vertically  upward  with  an  initial  velocity  of  160  ft.  per  sec.  it  would 
reach  the  starting  point.  398  ft.  above  the  earth,  in  5  sec.  Each  motion 
wotild  be  just  the  inverse  of  the  other.  See,  also,  table  on  page  1155. 


284  U,-^MECHANICS. 

SUMMART  07  PrBCBDINO  MOTION  POUCULAS. 

Notation: 
a  —rate  of  acceleration  in  feet  per  second. 
g    —gravity  acceleration  in  feet  per  second. 

V  *  velocity  at  time  t,  in  ft.  per  sec.,  due  to  acceleration  only. 
vn  —constant  or  uniform  or  initial  velocity  in  ft.  per  sec. 

V  —v+ti^  — resultant  velocity  in  ft.  per  sec.  with  mitial  velocity  posituM. 
%/  —o—«^  — resultant  velocity  in  ft.  per  sec.  with  initial  velocity  n^fo/fiiif. 
5    —  direct  distance  in  ft.  from  point  of  starting.     (Used  with  a.) 

h   —direct  dutance  in  ft.  from  point  of  starting.     (Used  with  f .) 
I    —time  in  seconds  after  startmg. 

Formulas: 
L    Uniform  motion;  no  acceleration. 

t       X  Oo      Oo 

II.     Uniformly  accelerated  motion;  no  initial  velocity. 

III.     Uniformly  accelerated  motion;  initial  velocity  positive. 
t,0-V-f«-V-a/-y-|--j-y->/V»::2S-N/V«-2M. 


■7 — i 2* T  (t-W  =  "-7 — -t S 7  (.7-'V  ■ 

IV.     Uniformly  accelerated  motion;  initial  velocity  negative. 


2A  .  25  , 


t^-g/-v'-a<-v'-©'-^-v'-y-Vt/«-2«A-Vi^-2a5. 
v=g«-fl<-2  (y+Db)  -2(j+tio)  -V2gfc  +  Vto«+«to-'V^2a5+wo>+t)te. 

The  resttltaot  of  two  constant  velocities  in  different  directions  is  a 
motion  in  a  straight  line,  and  may  be  termed  the  parallelogram  of  motions 
or  the  triangle  of  motions.  Let  v^'  and  vo'  represent  two  velocities  of 
magnitude  and  direction  shown  m  Figs.  13  and  14.  and  making  any 
angle  B  with  each  other.  Then  will  Vq  oe  the  resultant  velocity  both  in 
magnitude  and  direction: 


Fig.   13.  Fig.  14. 

From  Trigonometry,   Vo* — uo'*  4-  t>o*»  +  to^v^  cos  6 ;  _ 
.'.    Vo  -  n/vo''  +  Ub**  +  2vo'wo'  cos  Q. 
Note. — ^The  polygon  of  motions  is  analogous  to  the  polygpn  of  forces 
(see  Figs.  31  to  35).  tizedbyv       '^     ^ 


RESULTANT  VELOCITIES.    PARABOUC  MOTION. 


286 


Pig.  15. 

Parabolic  Motion. — The  path  of  a  projectile,  or  of  a  jet  from  a  nozzle, 
illnstratea  the  resultant  of  a  constant  velocity  vo  in  one  direction,  and  a 
variable  velocity  v  in  another  direction.     Let  x  and  y  (Fig.  15)  be  the  co- 
ordinates of  any  point  p  in  the  path  of  the  resultant  ctirve;  then 
X  — t^  cos  0— horizontal  distance  traveled; 


y-/ 


(t^  sin  ^—  -o")  —vertical  distance  traveled 
8^        . 


—X  tan  0— 


^-tan   (?- 


2oto"  cos*  tf  • 


jx 


%H?  cos*  0 


— nat  tan  of  angle  which  the  tangent  to  the  curve 

dy 
makes  with  the  axis  of  X.    Making  ^^  —  0.  we  obtain  the  coordinates 

«'  and  y  of  the  point  ^  at  the  vertex  of  the  curve;  thus, 
.     «o*sin«costf        J  .     Vf?^xi*d 

x^j^^ .  andy-y'-:^^-^ — . 

When  p  falls  to  the  point  f^  on  the  axis  of  X,  y — y*— 0;  and  *  —  **  — 
3c^sin  tf  cos  $  .«,  ,^.  ,j.  ,  m  . 
.     . .  ar  —  *r,  or  the  horizontal  distance  from  o  to  ^  is 

doable  that  £rom  o  to  the  vertex  ff. 

The  general  equation  of  the  time  t  occupied  in  moving  from  o  to  any 
point  p  is 

/  /wpsin  d\  «     2y      ti^  sin  tf 

'"V  \~7~)  "  7"  ^  ~~1- 

In  moving  from  o  to  the  vertex  p',  (making  y      - — j  , 
i%sin  0 

e 

In  nu>ving  {rom  o  to  ^  on  the  axis  of  X,  (making  y— 0), 


«— 


ynoab 


sin  0 


I- 

The  above  discussion  is  a  general  case  of  which  the  following  are  special 
tes: 
Case  1.     IniiicU  velocity  horizontal  (9—0).  - 

Case  2.     Initial  velocity  vertical  (9»-  9(H. — 

(The  last  is  a  case  of  Uniformly  Retarded  Motion,  bein^  the  reverse  of 
"Uniformly  Accelerated  Motion  with  negative  initial  velcKaty,"  preceding. 
Note  that  y  corresponds  with  h  of  the  preceding  Motion  formulas;  and 
tliat  when  y  becomes  a  minus  quantity,  p  is  below  the  starting  point.) 

When  the  value  of  y  is  a  minus  quantity,  in  any  of  the^above  cases,  it 
•hows  that  the  projectue  p  has  fallen  below  the  axis  of  -^-^^OOqIc 


286 


n.—MECHANICS. 


Circular  Motion. — Let  p  be  a  point  on  the  rim 
of  a  fly-wheel  of  radius  r.  and  revolving  at  n  revo- 
lutions per  unit  of  time.  Then  the  velocity  v  of  the 
point  p  is 

v='2xr  n. 

(Note  that  t;  takes  the  compound  denomination 
of  r  and  n;  i.e.,  if  r-  rad  in  ft.,  and  n-rcv  per  sec, 
then  v-veloc  in  //.  per  stc.) 

Ex.  16. — A  driving  rope  traveling  at  the  rate  of 
300  ft.  per  min  runs  over  a  pullev  4  ft.  in  diam. 
How  many  revolutions  does  the  pulley.make  per  min? 

t;       300     «« «-  .         A 

Ans. —  »»-  o^"  IT  "  23.87  rev  per  mm.     Ans. 

Motion  on  Inclined  Plane.— Neglecting 
friction,  bodies  falling  from  A  would 
reach  o  (on  inclined  plane  Aa),  b  (on 
inclined  plane  Ab).  and  H  (distant  2r  ver- 
tically below)  in  the  same  length  of  time  t. 
Thus, 


Fig.  1 


from  general  formula, 


asA- 


as  It 


r__ 

sin  iJ' 


for  AH\ 


for  Aa; 


t^^j-^f-^   for  Ab. 

Fig.  17. 

Moreover,  the  velocities  ai  the  same  elevation  would  be  equal;  thus,  the 
velocity  of  the  body  at  a,  descending  on  the  inclined  plane  Aa,  would  be 
equal  to  the  velocity  of  the  body  at  a',  falling  freely  through  space.  Simi- 
larly, the  velocities  at  b  and  y  would  be  equal. 

The  following  formulas  relate  to  the  mclined  plane  Aa,  making  an 
angle  a  with  the  horizontal: 

gfisxna  %A 

2  2g  sin  a 


y^g^SAn  a  =y/2gl  sin  a.     /= 


a     yg  sin 


g  sm 

The  time  occupied  in  the  descent  of  bodies  down  inclined  planes  of  the 
same  height  varies  as  the  length  of  the  planes.  Thus,  let  i4ia-«2  X  Aa  — 
2/;  then  the  time  occupied  in  falling  from  Ai  to  a  would  be  double  that 
occupied  in  ffidUng  from  A  to  a. 


Motion  on  Cycloidal  Curve.— The 

cycloid  (Pig.  18)  is  often  called  the 
curve  of  quickest  descent.  Let  ACB 
be  the  cycloidal  curve  (of  length  4c/) 
generated  by  a  circle  of  diam  o  rolled 
along  the  plane  AB.  Then  will  a  body 
starting  at  A  fall  to  C  and  to  B  quicker 
than  by  any  other  curve.  (For  Proper- 
tics  of  the  Cycloid,  see  page  236.) 


Fig.   18. 


Time  occupied  in  reaching  C: 
Time  occupied  in  reaching  B: 


'-Wt-W^- 


By  cy- 
cloidal 


yCloogle 


MOTION.    CYCLOIDAL  CURVE.    PENDULUM.  287 

Time  occqpicd  in  descent  from  A  to  C  on   the   inclinsd  plant  AC,  is 

'"if^^n^"  1.8«2^— .  as  against  /  - 1.5708-/ —  for  the   cycloid.    (Sec 

ak>  Sonple  Cycloidal  Pendulum,  below.) 

Staple  Circular  Pendulam. — This  consists  of  a  mass  suspended  from 
«  fixed  point  O  bv  a  thread,  of  length  /,  considered  Q 

as  having  no  weight.    The  length  of  time  t  for  a  sin- 
gle vibration  from  A  to  £  is 


(Nearly  exact.) 


—    (Approximate  but  most  frequently  used; 


practically  exact  when  a  does  not  exceed  TZV).  Pig.  19. 

From  the  second  equation  we  get,  /  — ^  •.  ^— ^.     The  length  of  a 

pendulum  which  will  give  a  single  vibration  in  1  second  of  time  is  /—■ y  ft.  — 

0101 331  g  ft.  The  value  of  g  for  any  locality  may  be  obtained  from  the 
fnvmla* — 

C-32.1«964(l~0.00284cos2A)   (l -^)    ft.  per  sec. 

ifi  which  i<- latitude  of  the  place. 

Jk— its- elevation  in  feet  above  sea  level. 
JS— radius  in  feet  of  the  earth  at  the  latitude  A, 
-20  887  510  (1  + 0.00164  cos  2i). 
-  20  900  000  ft.,  approximately. 
The  value  of  c  in  England  is  32.2  ft.;  in  New  York  City.  82. 17.     The 
rabe  of  g  ustially  asstimed  in  the  U.  S.  is  32.16;  and  of  ^/2g,  is  8.02.  in 
aydnmlics.     The  length  of  a  pendulum  which  will  maJce  a  single  vibration 
i&  one  second  is  therefore  /-0. 101321  f»0. 101321X^32  16- 3.258  ft. - 
19  1  ins.,  or  a  little  less  than  I  meter  (-3.28  ft.-39.37  ins.). 

The  coapomd  circular  pendulum  consists  of  a  pendulum  in  which 
the  mass  is  more  or  less  distributed,  instead  of  being  concentrated  at  a  single 
point  as  above  (Fig.  19).  It  may  be  reduced  to  the  simple  circular  pen- 
iainua  by  finding  the  distance  /  from  O  to  the  center  of  oscilkuion,  otherwise 
tenncd  the  ctnStr  of  percussion.  Asstmiing  the  whole  pendulum  to  be 
ncid.  the  center  of  percussion  is  such  a  point  that  when  struck  sharplv  at 
Tight  angle  to  the  direction  of  the  pendulum  the  latter  will  begin  to  oscillate 
«r  vibrate  as  a  siniple  pendulum  without  producing  any  shock  at  its  upper 
<ml  or  axis  O.  If  the  pendulxim  is  a  rod  of  uniform  cross-section,  and 
homogeneous,  the  center  of  percussiont  will  be  a  point  distant  /—  }  of  the 
length  of  the  rod  from  O. 

Siuiple  Cycloidal  Pendulum.— Let  Op  (-2(f).  Pig.  18.  be  the  length 
of  the  pendulum  vibrating  between  the  cycloidal  arcs  OA  and  OB.  Then 
»iD  Op  be  the  evolute  of  the  cycloid  ACB,  and  the  mass  p  will  trace  the 
CTcIoidal  curve.  Hence  the  motion  of  the  mass  p  will  be  the  same  whether 
^i«  twinging  from  O  or  fimply  rolling  freely  on  ACB,  friction  neglected. 
M<aeover.  for  any  given  cycloid  the  time  of  descent  from  any  point  on  the 

*orve  will  be  '  ■■*'\/ «"•  "^^  *^®  ^xne  of  one  oscillation,  /  "■ir.^/ — .     In  order 

tfaat  the  time  of  one  oscillation  may  be  one  second,  make  2(i— ^  —  0.101 321 

r.  .*.  the  length  of  the  cycloidal  pendulum,  —  2d,  will  be  the  same  length 
••  the  Simple  Pendulum,  preceding.  The  cycloidal  pendultmi  is  exact  for 
tar  angle  of  vibration,  while  the  simple  pendulum  is  practically  correct 
ttHy  ^  small  arcs  if  tne  formula  is  adhered  to  strictly. 

^  *  See  alio  formula  for  g  under  Gravity  Acceleration.  Weights  and  Specific 
Gravities  of  Materials  (Section  27).  r^  T 

t  See  formula  for  Center  of  Percussion,  page  303.   Digitized  by  V^OOglC 


288  15.^MECHANJCS. 

DYNAMICS. 
Work,  Power,  Energy,  Etc 

Force. —  In  the  preceding  equations  of  motion,  the  mass  of  the  moviii 
body  is  not  considered — simply  abstract  motions.  When,  however,  tJi 
moving  body  is  considered  as  having  mass,  it  will  take  on  the  conceptio 
of  force  (- mass X acceleration),  work  («> force X distance),  power  (  — ra^ 
of  work  — work -+- time),  and  energy  (= capacity  for  work);  also  "  impulse 
(— force X time),  and  "  momentum  "  (  — mass X  velocity).  — remembering  thi 
the  momentum  imparted  to  a  body  is  equal  to  the  impulse  which  produd 
it.  ("Impact"  or  'collision"  is  a  blow,  or  pressure  of  such  short  duratic 
that  it  cannot  be  measured,  between  two  oodies.     See  page  308.) 

Considering  "  Force  "  F  to  be  a  constant,  unbalanced^  resultani  for\ 
acting  on  a  total  mass  M  of  weight  W  during  the  time  t,  the  above  relatioi 
may  be  summarized  as  follows: 

(a).    Fundameiital  Relatioiu;  Retttltant  Force  F  Constant 

(Distance  not  included.) 

Impulse  ~  force  X  time"- mass  X  velocity     •-momentum (| 

weight  X  velocity  ^ 


Therefore, 

Mass  Af- 


g 

F^  ^   ^  _  W 
V  a  g 


(Force-)     Accel  ^—"a?   "  T^  ""  "T  "*  ^^-  Persec. 


Weight      W-Af«  -  ^  -  ^  in  pounds. 


(Gravity-)  Accel  *" "If   -  -=-  -  -^  m  ft.  per  sec  . 


„  -     Mv       Wa     Wv  .  , 

Force         F  —  — 7-  —  —  —  —7-  m  potmds ( 

t  g        gt        ^  .    .  .  .  \ 

Time  <—  -^r  —  -=—  —   —  in  seconds i 

F         Fg         a  ' 

Ft        Fgt 
Velocity      """  ")i7   —  lir  ""  ^^  ^^  ^^  P^  sec i 

Remarks. — ^The  above  formulas  are  for  problems  in  which  the  for^ 
and  therefore  acceleration,  is  constant.  Equated  values  may:  be  subs 
tuted  from  one  formula  in  another. 

Problem  1. — A  railroad  train  weighing  000  tons,  6  minutes  after  starti 
attains  a  velocity  of  30  miles  per  hour.  Find  the  tractive  force  of  tj 
engine  drawing  the  train,  the  resistance  being  8  lbs.  per  ton.?  ' 

Solution. — Tractive    force    T—    unbalanced    force    F+ resistance 
1?  t         1      /^     17    ^t'     600X2000X30X6280     -.„,  ,^  ,     ^ 

From  formula   (7),   F-  — 32.iflx5x60X3eQ0 ^"^^  ^^-   ^^^    ^ 

600X8-4800  lbs.;  .*.  T-F+i?- 5473+ 4800- 10273  lbs.     Ans. 
Atwood's  Machine. 

Problem  2. — Atwood's  machine  consists  of  a  flexible 
cord  passing  over  a  (frictionless)  pulley  and  supporting 
equal  weights  at  each  end,  with  provision  for  an  "un- 
balanced" weight  at  either  end.  In  Fig.  20.  the  bal- 
anced weights  are  6  lbs.,  and  the  tmbalanced  weight 
is  2  lbs.  Find  the  acceleration  of  the  weights,  and  the 
tension  on  the  cord? 

Ft 
Solution. — Prom  formula  (4),  acceleration  a  —  -r^  — 

2X32.2     .  OT  f*  J    a      ^       2     .    ^ 

— Tg —o.S?  ft.  per  sec;  and   —'"r^-^-z'^t-lticon- 

sidering  the  tension  T  on  the  cord,  we  have  to  consider 

the    weight    W  whose  mass  is   At'    and    acceleration  a         F'^t.*     Ftg. 


d  by  Google 


2M 


16.— MECHANICS. 


Power 


(^- 


■ec.; 

f        t     t 

Za    Nv 
2  "2/ 

(21) 

Energy  (ft.-lb«.)  £ -^-^-^-samo  values a«for/C.above(- JO (22) 

(Remarks. — The  above  formulas  are  for  problems  in  which  the  force, 
and  therefore  acceleration,  is  constant.  Equated  values  may  be  substi- 
tuted  from  one  formula  in  another.) 

Problem  4. — ^How  much  energy  is  expended  in  raising  a  weight  of  800 
lbs..  10  ft.? 


Solution. — ^Prom    formula 
of  energy  or  work.    Ans. 


(20),    E-/C-F5-800X 10-8000    ft,-lb8. 


Problem  5. — A  weight  of  4000  lbs.  is  raised  100 
in  6  seconds.     Pind  the  tension  in    the   hoisting  rope, 
t^e   acceleration   being   tmiform?     (See   Pig.    22.) 

Solution. — ^Tension  7— unbalanced  force  F+the  re- 
sistance R  (-TV)  -  (formula 


ae.        t^      ^"^ 


i«s2H^*j.w     4000X200 


+  4000-904+4000-4004  lbs.     Ans. 


Pig.  22. 


13 


ss» 


Work. — ^Work  is  the  transformation  of  energy,  and  is  simply  force 
(F)X  distance  (5).  The  foot-potmd  (one  potmd  raised  one  foot  high,  or 
its  equivalent)  is  generally  considered  the  unit  of  work  unless  other  units 
are  specified.     The  element  of  tuH4  is  not  a  factor. 

The  Pundamental  Pormulas  for  Work  are — 
When  the  force  F  is  constant.  Woik  (K)  -Fi (23) 


When  the  force  F  is  tmiformly  variable.  Work  (K) 


-ff. 


Fhs. 


In  which  St  and  sq  &re  the  limiting  values  of  s,  in  feet. 

Problem  6. — ^A  rope  weighing  6  lbs.  per  lin.  ft.  and 
400-ft.  long,  is  suspended  at  one  end  from  a  drum. 
Find  the  least  number  of  ft.-lbs.  of  work  required  to 
wind  up  100-ft.  of  it? 

Solution. — Let  s  (Pig.  23)  be  the  variable  length  of 
the  hanging  rope;  then  6;  will  be  its  weight,  and  85  ds 
the  wonc  done  in  raising  it  through  the  distance  ds. 
Using  formula  (24).  the  total  work  done  in  raising 
the  rope  through  100-ft.  of  distance  is 


3(400«-800^ 


300 
-210  000ft.-lb8. 


Ans. 


This  is  represented  graphically  in  Pig.  24. 
the  vertical  ordinate  F  bein^  the  force  applied 
for  any  length  s  of  the  hanging  rope,  and  the 
shaded  area  representing  the  total  least  work 
performed.  Thus,  to  wind  up  the  whole  rope  the 
least  amount  of  work  reqtiired  would  be  (mak- 
ing ib»0)  |-*»«-3X400«-480  000ft.-lbs.-area 
whole  triangle.  Digitized 


.(24) 


I 
I 

I 


Pig.  23. 


byGoC  Pig.  24. 


d  by  Google 


292 


IS—MECHANICS, 


1*1  is  a  shxright  Lever 


Compound  LexMt. — ^Let  Fi  be  the 
force  required  to  raise  W.  Fx  and 
W  may  be  equated  with  F'  acting 
at  the  joint  of  the  two  levers.    Thus, 

F,5i-FV-F5:  buty-^-^: 


Pig.  26. 


Note  that  the  acting  force  multiplied  by  the   continued    product   of 
the    kft-kand    lever    arms  =  the  weight  raised  multiplied  by  the  continued 

Product    of    the    right-hand    lever   arms.     This    prmciple    holds    true  in 
elting  and  gearing  also. 


Fig.  27. 

Inclined  Plant. — Let  H^  be  a  weight  to  be  moved  up  an  inclined   plane 
of  length  Si  and  height  s,  by  the  force  Fi.     Then   FtSi^Ws,  or  Fi  — 

W^—,  in  which  —  —  sin  a. 

Wedge. — ^The  wedge  is  a  double  inclined  plane. 

Screw. — ^The  screw  is  an  inclined  plane  wound  around  a  cylinder.     The 

F  s       Fs 
formula  — |-^  —  -—  applies;  in  which  Fi  is  the  acting  force  at  the  end  of  a 

lever  attached  to  the  screw;  St  <- distance  traversed  by  the  lever  end  in  the 
time  t;  F^the  force  acted  against  by  the  screw;  and  s  the  progressive  dis- 
tance traversed  by  the  screw  in  the  time  i.     Or,  we  may  use  the  formulas 

FiJ(2r/)»+  ^?l.y^Fp    (Exact) (29) 

Fi(2n[)=Fp      (Approx.) (30) 

in  which  /--length  of  lever  from  cen  of  screw  to  applied  force  Fi» 
and  p  —  pitch  of  screw,  of  diant  d. 

Pulley. —From  formula  (26).F,5,-Wi.  in  which  W 
moves  the  distance  s  when  F|  moves  the  distance  5i. 
In  Fig.  28    it    is  evident    that    5i  — 2^;    hence, 

Another  method  of  determining  the  forces  in  pulley 
ropes  is  by  "  cutting  sections."  Thus,  imagine  all  the 
forces  to  be  in  equilibrium,  and  draw  a  cutting  plane 
ab.  Then  it  follows  that  each  of  the  two  ropes  cut.  sup- 
ports half  the  weight  W,  and  the  cutting  plane  d>  shows 

W 
that  Fi  has  the  same  stress  -^. 

Simple  and  compound  pulleys  are  thus  often    more 

easily  analyzed  by  the  *'  method  of  sections,"  although         ,       ' ' 

the  principle  of  '*  work  "  applies  universally.     tizedbyGoOQlJ'ig.  28. 


IMPULSE  AND  MOMENTUM.    ENERGY, 


MS 


Toggk, — If  the  weight  W  is  raised  by  the  force  Fi,  use 
fonnula  (26);  thxis.  FiSx^Ws,  or  F»-H^--W^?.     (It  is  to 

Sx  r^ 

be  noted  that  the  rcqxiircd  force  Ft  gradxmllv  decreases  as 
b  decreases,  and  that  an  almost  infinite  force  lymaybe 
raised  by  a  finite  force  Fi  when  b  approaches  zero.) 

Proof:  Let  Ft  force  the  toggle  joint  to  the  right  the 
mfinitfsimal  distance  Si;  then  Ir  will  be  raised  the  infini- 
tesimal distance  s,  that  is,  -j  ^^  each  lever  arm  /.  Now 
as  /  remains  constant,  we  have,  before  the  movement. 
P-6«+*«;  and  after  the  movement,  P  "  (b-si)*  +  (h+jj  .  Equa- 
ting. b^-i-h*^b^-2bsi  +  st*+k*+ks  +  ^.  Remembering  that  the  infini- 
tesimal quantities  5i*  and  -j"©.  this  reduces  to  hs^2bsi,  or— -»-r-.     The 

sasoe  result  may  be  obtained  by  the  parallelogram  of  forces  indicated  in 
P«.  29. 


Pig.  29. 


Inpolse  aod  Momentinii. —  If  a  constant  force  F  acts  for  a  length  of 
time  <  on  a  Mass  M,  the  latter  will  acquire  a  velocity  v  at  the  end  of  that 
time.  Furthermore,  the  product  F<.  called  impulst,  is  equal  to  the  product 
ifv.  called  monuntum',  or 

(Impulse,  Z—)    Ft^Mff-    (— Momentum,  N). 

The  acting  force  F  (lbs.)  may  be  any  amount  acting  through  any  length 
of  time  t  (sec.),  or  it  may  be  a  force  <-timcs  as  large  as  F  acting  for  one 
second  on  the  mass;  in  either  case  the  velocity  v  of  the  mass  at  the  end  of 
thai  time  (t  seconds  in  the  first  case  and  otu  second  in  the  last  case)  will 
be  the  same,  and  therefore  the  momentum  will  be  the  same.     Hence  the 

momentom  of  a  mass  M   I  — — j  moving  with  a  velocity  v  is  equal  to  that 

fofte  which  in  one  second  will  give  it   that   velocity;  or.   inversely,  the 
UDount  of  force  which  in  one  second  will  brin|;  it  to  rest. 

If  the  acting  force  is  tmiformly  variable  mstead  of  constant,  we  have 
the  equation 

pfdv-  iFdt   or    M  (»t-«o)-  r^rfi 

m  vhich  Vo  —the  velocity  when  t  equals  «b. 
aiid  Vi  —the  velocity  when  t  equals  /j. 


Energy. — Energy  is  capacity  for  work.  The  energy  of  a  body  is  meas- 
wed  ty  the  amotmt  of  work  which  it  is  capable  of  performing,  called  poten- 
tizl  energy;  or  by  the  amount  of  work  it  does  perform,  called 
kiaettc  energy. 


For   illustratkm,   a  cannon  ball    weighing    00  lbs.   is 
nised  from  il  to  B,  a  distance  of  20  feet.     The  work  per- 


iormtd  in  raising  it  is,  therefore, 


Jf^. 


F5- 60X20-  1200 


fMvttv 


ft.-lb«.  The  ball  at  B  may  now  be  considered  to  pos- 
sess, by  virtue  of  its  position  with  reference  to  i4,  a  potential 
for  statical)  energy  equivalent  to  1200  ft.-lbs.;  and  which. 
T^  the  ball  is  allowed  to  fall  back  to  A,  will  be  entirely 
expended  in  the  form  of  kinetic  (or  actual)  energy  when  it/^/-.^  ^ 
reaches  A  and  iu  vek)city  is  destroyed.  '^^^  byXjUpig.  30. 


fFds 


214  Ih.— MECHANICS. 

Prom  the  preceding  equation.   iFdl'^lMdv,    multiplying    both 

of  the  equation  by  v,  and  remembering  that  vdt^ds,  there  is  obtained. 
Work  in  as-      1  f  « Kinetic  en- 

cent  stored  /•  /•!».»*  it        ergy  in  des- 

up  at  B  as  I    Fds^  I   Mvdv        cent  expen- 

potential  en-      J  J   «  at  B         ded  at  A 

ergy-  J  I 

Or,  the  general  formula,  I  Fdj  —  J  M  W—v^ 


If  the  initial  velocity  v^  -"O,  then  Vi  <->v  and  we  have. 
Energy  £—  J  Afu*—  -=— 


Or.  M  A-^  (Ik).  £-H^A-F5-workX 

That  is.  the  energy  expended  —  the  work  performed. 

Problem  8. —  How  much  energy  is  expended  in  shooting  a  cannon 
weighing  50  lbs.  with  an  initial  velocity  of  2300  ft.  per  sec? 

Solution. — From  formula  (32)  energy  m  ft.-lbs.  — -r-- —    2x32  1 

4.112.250  ft.-lbs.     Ans. 

If  fired  vertically  it  would  ascend,  from  formula  (19). 

£^£^4  112  250^  ^ 

A--p-^- ^ 82  246  ft. 

RESULTANT  FORCES. 

Composition  and  Resdatioa  of  Forces. — On  page  284  are  explained 
parallelogram  and  triangle  of  uniform  motions  composed  of  two  cons 
mitial  velocities  vo'  and  vn",  producing  the  resultant  initial  velocity 
From  Mechanics  we  learn  that:  Forces  art  proportional  to  the  velociHfS  « 
they  xvill  impart  to  a  given  body  in  a  unit  of  time.  Hence,  if  Ft  imoai 
velocity  t\)'.  and  Ft  a  velocity  vo',  then  will  R,  the  resultant  of  Fi  am 
(Pigs.  31  and  32)  of  the  parallelogram  or  triangle  of  forces,  oorrcsi 
with  Vo.the  resultant  otvg  and  vo'  (Pigs.  18  and  14)  of  the  paraUekfl 
or  triangle  of  motions.  Thus.  Pig.  31, 
/2«-Fj»+Fa»+2F,Fj  cos   tf. 

or  1?-VF|»+F2»+ 2  F,F,  cos  .d. 
When  0  -QO".  cos  g-0.  and 

/?-VFi«+Fa«. 


i^ 


.^r 


Pig.  81.  Fig.  32.  Pig.  S8. 


Equilibrium.— If.  in  Pig  32,  the  resulUnt  R,  of  the  two  fonu 
and  Ff,  is  replaced  by  a  third  force  Fa  equal  in  magnitude  and  opposi 
direction  to  R,  then  will  the  triangle  represent  a  closed  tiiansi 
forces,  or  forces  which  if  allowed  to  act  at  any  common  point  P  (Pxg 
will  be  in  equilibrium.  Clearly,  any  one  of  the  forces  of  a  clewed 
angle  of  forces  is  equal  and  opposite  to  the  resultant  of  the  other  in 


FORCE  POLYGON,    MOMENTS  AND  REACTIONS. 


296 


Fig.  a*. 


Pig.  85. 


Polygoo  of  Forces. — It  is  evident,  from  the  preceding  demonstration, 
that  any  number  of  forces  as  Fi,  F3.  F3,  F4  and  F^  acting  in  equilib- 
rium at  a  common  point  P,  Fig.  34,  will,  if  drawn  consecutively  in  ro- 
tation in  the  direction  of  the  forces,  form  a  closed  polygon  of  forces,  Pig. 
35.  For  any  polygon  may  be  cut  into  triangles  by  the  diagonal  lines  Ru 
R3,  etc..  each  diagonal  being  the  resultant  of  two  other  forces,  and  consid- 
eied  as  replacing  them.  Thus  Ri  replaces  Fi  and  F2  so  that  we  may  con- 
sider only  four  forces  actinjs,  namely.  Ri,  F*,  F4  and  F^;  again.  R^  replaces 
R^  (»Fi  and  F4)  and  Fl  so  only  three  forces  remain,  namely,  aj.  F4 
and  Fs — a  triangle  of  forces.  Hence,  as  R2,  F4  and  Fs  are  in  equilib- 
rium, so  are  all  the  forces  composing  the  sides  of  the  polygon  in  equilib- 
ritan.  The  principle  of  the  force  polygon,  representing  static  eguilibrium 
of  forces,  is  fundamental  to  Graphical  Statics,  in  the  determination  of 
•tresses  in  structures. 

MoaMirts  and  RMctioos^Let  AB 

be  a  horizontal  lever  fiO-ft.  lon^,  fixed 
at,  and  free  to  rotate  around,  its  left 
hand  end  A  (Fig.  36).  If  now  a^o- 
vdfl^t  H^— 60#  is  applied  vertically 
downward  at  a  point  33i-ft.  distant 
(mm  A,  tending  to  cause  the  rod  to 
zotate  around  ^4  in  a  right  hand  mo- 
tion, it  is  evident  that  some  force  R^ 
appUed  at  the  other  end   B  of  thej 


35V 


IW-W 


Pig.  3d. 


mr^ 


Tftr^o* 


-^cr 


|W-60* 


■OB 


Pig.  37. 


|Rfc-40* 


hm  will  preserve  equilibrium  or  pre- 
^^eot  rotation.   The  viedue  of  Rt  is  ob- 
tained by  talcing  moments  M  about  A , 
as  origin;  thus, 
iJ^-0:     33|Pr-50i?a;     .'.i?,-!  W^-40f. 

In  a  similar  manner,  if  the  lever  is  considered  as  fixed  at,  and  free  to 
rotate  around,  B(Pig.  37). we  have  J3f-0:  16iH^-6(W2,;  .•J?»-ilV-20#. 

Fig.  38  is   the  combined  result  of  ^ 

the  two  operations  above,  considering  W«60 

the  lever  AB  asabeam  50-ft.  long  sup-  33  V  I     leV 

porting  the  weight  H''-  60#.   produc-  V;^ 5 so*      ^ 

^  a   reaction  of  2M  at  il  and  40#    Tr,-?0*         ^ 

at  B.    The  weight  of  the  beam  itself 

as  not  considered.  Pig.  38. 

CcBtOT  of  OravHy  and  Resultant  of  a  System  of  Parallel  Forces.— 1  he 

fine  of  the  resultant  of  a  system  of  parallel  forces  passes  through  the  C4nm 

of  tranUy  of  the  system.     In  Fig.  39, 

let  A    (-10#).  Pa  (-20#)    and    P^ 

( »  30j^  be  a  sjrstem  of  parallel  forces 

or  loads  acting  on  a  rigid  body  AB,  at 

poinU    26    ft.   apart.     Then    will    R 

(-60#)  acting  at  the  point  O.be  the 

remhant    of  the    above     forces  and 

capable  of  replacing  them  in  certain 

problems    where    the    reactions    are 

to  be  determin  ed.    In  Alligation ,  page 

57.  we  have  a  similar  problem,  that 

s,   finding   the  average    ooet    of  a 


^e^ 


I 
i 


Xo-»V-- 


^l-ii 


f^«30* 


R-fiO" 


Dp^dk^^oogk 


296  \S.^MECHANICS. 

mixture  where  oarreis  of  cement  replace  pounds,  and  cents  replace 
of  the  present  problem;  and  in  which  the  origin  of  momtnts  is  200  t* 
left  o(  A.     As  a  matter  of  fact,  the  origin  of  moments  may  be  at  any; 
but  for  convenience  it  will  be  assumed  at  A  in  the  present  case. 
taking  moments  about  A,  of  the  loads  Pi,  Pj  and  Pj,  we  have — 

2"  Px 
Distance  to  center  or  gravity  of  resultant  ^je^*       p  ; 

I  Px  "Sum  of  moments  of  all  the  forces  about  center  of  moments  A; 
I  P     —sum  of  all  the  forces  acting  —  /?;  whence. 

Taking  moments  about  A  as  origin: 
2  M 

Pi  10  X  0    -      0 

Pa  20   X    25  -      500 

Pa  30   X    60   -    1500 


Pi  +  Pa  +  Pa       -    60  2000 

R  IPXXQ      -    IM 

Therefore.   /?-601bs.;      and  :^,  -   7^-^-88|ft. 

Note  the  similarity  of  analysis  of  this  problem  of  concentrated  force 
the  following  problem  of  a  distributed  force. 

Resultant  of  a  Distributed  Force. — ^The  resultant 
force  is  equal  to  the  total  force,  acting  in 
a  line  passing  through  its  center  of  grav- 
ity. We  have  seen  (Fig.  39),  that  the 
horizontal  distance  xo  to  the  line  of  the 
resultant  of  any  system  of  forces,  from 
any  point  taken  as  the  origin  of  moments, 
is  equal  to  the  sum  of  the  moments  of 
the  forces  about  that  point,  divided 
the  sum  of  the  forces.     The  same 


noments  oi  a 

divided    by  rj* 

same  prin-  *'*^ 

buted  force  3^'".^ 

or   concen-  1^ 


ciple  holds  true  with  a  distributed  force         i'-^^  J***' 

as  with  a  system  of    forces    or    concen-         t^~~      ^^^       "** 
tratcd  loads.  Fig.  40. 

Problem  9.— Let  AB,  Fig.  40.  be  a  girder  of  60  ft.  span,  s, loaded  ^ 
distributed  force  whose  intensity,  at  any  p>oint  distant  x  from  the  left 
ment,  is  the  ordinate  y  from  the  line  AB  to  the  line  AC;  that  is,  the  int< 
of  the  force  increases  uniformly  from  0  lbs.  at  i4,  to  100  lbs.  per  lin. 

B,  so  that  y  — lbs.     1st,  find  the  general  equation  of  the  rcsuha 

and  its  distance  xo  from  the  left  abutment  A ;  2nd.  find  R  and  xo  fo 
span  completely  loaded  from  A  to  B;  Srd,  find  R  and  xo  for  the  span  k 
from  6  «  20'  to  a  =  60'. 

„  ,   ^.  ,  ^  I  Px     summationof  a:. Vfix  forces     IM 

Solution. — 1st.     Xo^-=r-.  — 


J  P        summation  of  ydx  forces         R 


/•«     100  X    ^^  lOOf^j^      100  py* 


a«-6« 


-xS^ 


In  which  — ^ —  X ■  —  sum  of  the  moments  of  all  the  infinitesimal 

xydx^SM', 
— - —  X —  sum  of  all  the  infinitesimal  forces  ydx^R', 

i  X  ~YZIy%  "distance  from  A  to  center  of  gravity  of   the 

tesimal  forces— Xo; 
a  — upper  limit  of  any  assigned  value  to  x\ 
b  —  lower  limit  of  any  assigned  value  to  «. 

Digitized  by 


DISTRIBUTED  AND  CENTRIFUGAL  FORCES.  297 

Jnd.  For  the  span  completely  loaded  from  A  Xx>  B,  the  upper  limit  of 
x^a^W,  and  the  lower  limit  of  ar-fc-O.  Substituting  these  values 
in  the  general  equation,  we  have, 

8rd.     For  a  span  loaded  between  «  — o  — 50',  and  «— 6  — 20',  we  have, 

/f.eiz^y  100^2100^  100      „^,.     .  ^      ,  ^-^^x   "7000^ 
/^--j—X-^—y-X-g^- 1750  lbs..  *b-|.^3j^-|.-2ioQ--37Mt. 

In  the  same  manner  we  may  find  the  resultant  and  center  of  gravity 
of  any  distributed  force,  as  parabolic,  circular,  elliptical,  etc.,  by  substi- 
ttiting  the  value  of  y  in  the  equation  of  the  curve  before  summing  up  all 
ihe  momtnts  of  the  ydx  forces  for  iPx^IM,  and  all  the  ydx  forces  for 
IP — R,  Note  that  the  resultant  R  » the  area  of  the  curve,  and  the  distance 
XB*the  distance  to  its  center  of  gravity. 


CMrtrifacal  Force. — Centrifugal  force  is  that  component  of  a  force 
acting  radially  outward  when  a  body  moves  along  a  curve  with  a  certain 
velocity.     In  the  general  equation  (16)  of  force,  F^Ma,  the  acceleration 


a  m  the  present  instance  is —  in  which  v-»  velocity  of  the  moving  body  in 

teet  per  second,  and  r— radius  of  curve  in  feet.     Hence, 

Centrifugal  foice-F.-M--—  •  — (84) 

I         Problem  10. — Find  the  tension  in  a  string  10  ft.  lon^,  fixed  at  one  end. 
vith  a  weight  of  40  lbs.  fastened  at  the  other  and  revolving  around  a  circle, 
vith  the  string  as  a  radius,  at  a  velocity  of  30  revolutions  per  minute  ? 
Soltction. — In  formula  (34)  F.  is  the  tension  in  lbs.  in  the  string:  and 

30 
t  «.  in  feet  per  second,  is  = . 2jtr,  or  »*—  **  r*. 

Therefore,  tension.  F.  — ^^  ..  . ««  r 

,40X9.87X10        3       . 
32.16        -122.8  lbs. 

Note  that  in  the  above  case,  F.  is  a  concentrated  resultant  force  acting 
aonnal  to  the  curve  at  oft§  point,  and  r  (  —radius  of  curve)  is  the  distance 
from  center  of  curve  to  cen  of  grav  of  moving  body.  Compare  above  prob- 
lem with  the  two  following. 

^Problem  11. — Find  the  radial  pressure  which  a  train  weighing  1000 
tons  and  moving  20  miles  per  hour,  will  produce  on  a  track  laid  on  a  7 
degree  curve. 

Solution. — ^The  radius  of  a  7^  cttrve  is  819  ft.     Use  formula  (34): 

loooxP^^^^^V 

J,      W    v^    ^"""^  V  60X60  /    , 
F,._    --^^-^3^  — tons 

— 32 .  63  tons  —  65300  lbs.     Ans. 
Note  that  in  the  above  case  the  force  F,  is 
s  distributed  force  acting  normal  to  the  curve, 
tfanmghout  the  length  ofthe  tndn. 

Problem  12.— Given  a  ring  (Fig.  41)  4  ft.  in 
diameter,  weighing  100  lbs.,  and  revolving 
about  its  axis  at  a  speed  of  1000  revolutions 
per  minute.  Find  the  tension  stress  in  the  ring? 

Solution. — (Note. — ^Distance  of  center  of 
gravity  of  the  semi-circular  ring  itom.  center  of 

circle— ro-  —  - —(see  page  207)1 


d  ^fiiQCgk 


208  15— MECHANICS. 

Consider  half  the  weight  of  the  rin^  acting  at  each  center  of  gravity 
of  the  semi-circle  on  the  axis  of  X,  causing  tension  at  points  a  and  b  on  the 
axis  of  K.    Then  the  total  stress  at  a  and  b,  from  formula  (34)    is 

Fc— -i  •  —      in  which  ]  vq   -2»croi»-*g«' 


i        ^0  [  \n  —revolutions  per  second  — ^gg^) 

/.  i  F<«  10845  lbs.  —  tension  at  a  or  6,  or  at  any  point.     Ans. 

Problem  13. — Prove  that  in  order  for  a  train  to  press  normally  upon 
the  track  in  going  arotmd  a  curve  of  radius  r  (feet),  tne  outer  rail  must  be 

elevated  an  amount  #  — —  .„   ^      (36) 

in  which  r— elevation  of  outer  rail  in  feet. 

V  —  velocity  of  train  in  feet  per  second, 

(7— gauge  of  track  in  feet, 

r— radius  of  curve  in  feet. 
Solution. — ^The  train  is  exerting  two  compo- 
nent forces,  one  horizontally  due  to  centrifiigal 
force  and  the  other  vertically  due  to  gravita- 
tion, which  can  be  reduced  to  one  resultant 
force  acting  normal  to  the  calculated  inclined 
surface  of  elevated  track.  In  Fig.  42  let  #i  rep- 
resent intensity  of  centrifugal  force,  and  d^ 
IV^  — weight  of  train;  then  Oi&i  is  the  resultant 
pressure  which,  in  order  to  be  normal  to  the 
track,  must  be  at  right  angle  to  ab,  G  being  the 
gauge  (practically)  and  «  the  required  elevation. 

€        G  W^  !;• 

Through  similar  triangles,——  7=-;  but  from  formula  (84),  #1— F«— and 

«i      C/i  g   r 

Gi^W. 

.  G^        ^TT 

•  *  Gx  W 

•'"      TT     ■"     ■^:^-  RtQHtr^d  proof. 

„„  1       ^-  *         1     gauge  of  track  X  (velocity  of  train)* 

Whence,  elevation  outer  rail—      To  o  s7     ^- i    -    g    .. • 

32 . 2  X  radius  of  curve  in  feet 

MOMENTS  OF  INERTIA,  ETC^  OF  PLANE  SURFACES. 

Bending  Moment— Resisting  Moment. —  We  will  now  consider  the 
relation  between  the  ntonunts  of  the  outer  forces  of  a  girder  and  the  moments 
of  the  inner  forces.  For  example,  let  Fig.  43  represent  a  wooden  beam 
4'   wide,   6*    deep  and    10'    k>n^ 

between  supports,  and  loaded  uni-  «p«cftft^  .o-itAA* 

formly  with    120  lbs  per  lin.  ft.  P  *°°  |V^~ 

Consider    the    bending     moment  !  ,  \ 

(of  outer    forces)     and    resisting  1 I  I  Li 

moment  (of  inner   forces)    about      ^.l__^Q«* 5^_     *^^'     L 

the  center  of  moments  o.  situated     ^^ "  y  i*~^ 

at  the  center  of  the  span  on   the         IR,>600  t  Tr»«600* 

neutral  axis  X  —  X  oi  the  beam. 

Then  from  the  natureof  the  loading,  Pig.  43. 

1 0  V   1 20 
/?j»Pj-p,-/?2-j  total  load-'"  ^^         -600  lbs.;  P,  and  P,  each  beins 

the  resultant  of  half  the  total  load;  R^  and  R2  the  reactions  at  the  points 
of  support.  Taking  moments  of  the  outer  forces  to  the  left  of  the  aection 
at  o,  we  have — 

Bending  moment  "Mt  -/?iX5-P,  X  21-150(K  ft^.-llg^J8000  inch-lba. 


d  by  Google 


800 


15.^MECHANICS 


If  now  another  similar  and  eaual  rectangle  is  added  b€law  the  axis  of 
X,  making  the  total  height  2k^d,  it  is  evident  that  the  above  moment  of 
inertia  will  be  doubled;  thus  (Pig.  45), 

for  a  beam  of  depth  d.    /4-2/fc-l  Wi*— ^ (38) 

the  general  formula  for  /  of  a  rectangular  beam,  of  depth  d,  about  its  neutral 
axis. 

Moment  of  Inertia  aboui  a  ParalUl  Axis. — Let  /  be  the  moment  of  inertia 

'    *e  plane  figure:  Z*", 
a  trom  X;  and  A, 


about  an  axis  X  passing  through  the  cen  oigrav  of  the  plane  figure:  I*", 
the  moment  of  inertia  about  a  parallel  axis  X*,  distant 


the  area  of  the  plane  figure;  then  will 

Moment  of  Inertia  about  an  Inclined  Axis. 
of  Plane  Surfaces.  Section  29. 


Properties  and  Tables 


Radius  of  Qyratfon 


-4 


Moment  of  inertia 


Area 


-a- 


■The  radius  of  gyra- 


tion r  of  a  plane  surface  as  bk,  where  moment 
of  inertia  is  lu,  and  area  Ah,  is  the   distance  r  — 
yn,  from  the  axis  of  X  to    a    point  (or  line)  at     f 
which  if  the  whole  area  were  concentrated   the    ^ 
moment  of  inertia  would  remain  the  same.  7 

From  the  above  and  equation  (37)  we  have,  x*- 

since  /».   —  -^  and  Ah  — 6A. 


>;«r«S77h 


■V^"VT'^''*"V8' 


hVi 


Fig.  46. 
.577* (39) 


And  for  a  beam  of  depth  d  —  2  /i,  with  axis  through  cen  of  grav,  equation  (38) . 


A4  "\"12 


2X3 


snd 


-  ^77* OBa) 


In  other  words,  the  radius  of  gyration  r  is  the  same  for  a  rectangle  bh  restins 
on  the  axis  of  X.  as  it  is  for  a  rectangle  bd  (in  which  d-^  2A)  about  its  neutriJ 
axis  passing  through  the  center  of  the  section. 

Caution. — ^The  radius  of  gyration  r  (=-yi),  Fig.  46,  must  not  be  con- 
fused with  the  distance  j/^.  Fig.  44,  for — 

f    -=  distance  from  axis  ol  A  to  cen  of  grav  of  moment-ortfos,  while 
j\)  —         "        "      "      *'     "     '*      "        '     "  moment-/<>rc*5. 
In  the  rectangle  bd  which,  for  simplicity,  has  been  referred  to  throughottt 
the  discussion, 

//  2W> 


yo  - 


M 

2F" 

y              21 
"bdT^     bTy- 
2 

JMy 
IfA 

.yo"' 

4         d*     4 
■  3'  "  9"9'' 

12 


bd* 
2 


-  J  -  «*= 


d 


3     ' 


■yo- 


2-s/J 
3 


r-1.165r(40) 


-- 2^o-.86«yto(4l) 


^-T>'«"-i2-^' 


whence,  yo'-  J''" -g"  q"^*'*      *°**     **  "  T  >'o'  "  f2"T ^**^ 

For  other  sections  than  rectangular,  these  ratios  will  not  hold,  neoessarfly. 

Problem  14. — Find    the    moment    of   inertia  /  and         y 
radius  of  gyration  r    of    a    circular    section    (complete 
circle)  of  diameter  D,    about    its    diameter. 

Solution. — ^Thc   moment    of   inertia  of  a   complete 
circle   is   4   times  that   of  the   quadrant,  Fig.  47;  and 


/  of  the  quadrant   equals    7, 
is  the  area  of  each    infinitesimal 


-X' 


xdy 


xdy,  because 

strip,  and    :^'!&^'=itfi^O^%ig.  47. 


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802 


15.-'MECHANICS. 


It  is  not  necessary,  however,  to  find  the  moments  of  infiniUsimal  areas; 
in  fact,  the  figure  may  be  divided  into  anv  number  of  areas  of  such  shape 
that  their  centers  of  gravity  are  easily  determined.  Then  the  distance 
from  the  fixed  axis  to  the  center  of  gravity  of  the  plane  figure,  is  equal  to 
the  sum  of  the  products  of  each  area  into  the  distance  of  its  center  of  gravity 
from  that  axis,  and  this  divided  by  the  total  area  of  the  figure.  Further- 
more, the  areas  whose  moments  are  thus  obtained  may  fomv  one  plane 
figiire  or  any  number  of  plane  figxires.  In  the  latter  case,  the  center  of 
gravity  obtained  would  be  the  center  of  gravity  of  all  the  figures.  The 
exact  point  of  the  center  of  gravity  is  determined  from  two  coordinate 
axes. 

The  center  of  gravity  of  a  plane  fi^tire  or  system  of  plane  figures  or 
areas,  connected  or  isolated,  is  the  position  of  the  resultant  of  a  uniformly 
distributed  force  over  the  figure  or  areas;  hence  a  thin  sheet,  of  any  outline, 
may  be  balanced  on  a  point  of  support  applied  at  its  center  of  gravity. 

MOMENTS  OF  INERTIA,  ETC^  OF  SOLIDS. 

Moment  of  IiMftia. — The  moment  of  inertia  of  a  solid  body,  about  a 
fixed  axis,  is  the  sum  of  the  products  of  the  weight  of  each  infinitesimal 
particle  ot  matter  (composing  the  body)  into  the  square  of  its  distance 
from  said  axis.  Hence,  the  moment  of  inertia  is  obtained  by  the  use  of 
the  Integral  Calculus.  An  approximation  to  exact  values  may  be  obtained 
by  assuming  a  definiU  number  of  vtry  small  particles,  multiplying  the 
weight  of  each  by  the  square  of  the  distance  from  its  center  of  gravity  to 
said  axis,  and  finding  the  sum  of  these  products. 

For  an  axis  X  passing  through  the  cen  of  frav  of  the  body,  the  moment 
of  inertia  /.  —  J  wt*',  where  w— the  weight  of  each  element,  and  r—iu  dist 
from  the  axis  X. 

For  an  axis  X'  parallel  with  and  distant  d  from  X,  the  moment  of  inertia 
/',  — /,  +Wd*;  where  H^  — the  total  weight  of  the  body.  Hence,  knowins 
the  value  of  /.  about  an  axis  passing  through  the  cen  of  gravity,  the  value 
of  /'•  about  any  axis  parallel  with  it  can  easily  be  obtained. 

2. — Moment  op  Inbrtia  op  Rbgular  Solids. 


Description. 


About  II  axis  X' 
dist  d  trom  X 


Sphere  of  total  weight  W^  and  radius  r 

Circular  plate  of  rad  f ;  axis  perp  to  plate  . . 


Circular  cylinder  of 
length  21,  and  ra- 
dius r 


Axis  longitudinal . . .  —^ 


Axis  perp  to  axis  of 
cylmd 


Circular  ring.outer  radr,  inner  rad  rj ;  axis  perp 


Rod  or  bar  of  imiform  cross-section  and 
length  21;  axis  perp  to  length  of  rod 


w 


Radius  of  Qyration. — ^The  radius  of  gyration  of  a  solid  about  a  fixed! 
axis,  is  the  square  root  of  the  quotient  obtained  by  dividing  the  momentt 
of  inertia  about  that  axis,  by  the  total  weight  of  the  body.     Thus.   Iron 
Table  2.  above,  the  radius  of  gyration  of  a  circular  plate  about  a  prrp  t 

through  its  center  •- ^ /— -I- IV  - -4=  - -^^^  . 
\    2  v/2  2 

The  radius  of  gyration  of  a  body  is  the  distance  from  the  axis  to 
ctnter  of  gyration  or  point  at  which  if  the  whole  mass  were  concent 
the  moment  of  inertia  would  remain  the  same. 


MOMENTS  OF  INERTIA,  ETC.,  OF  SOLIDS.  308 

Ccatcr  of  Onivlty.— The  distance  to  the  center  of  gravity  of  any  body 
from  a  fixed  plane,  is  eqtial  to  the  sum  of  the  moments  of  the  weight  of  each 
infinitesimal  particle  of  matter  of  the  body  into  its  perp  distance  from  that 
plane,  divided  by  the  weight  of  the  body. 

It  is  not  necessary,  however,  to  find  the  moments  of  infiniUsimal  par- 
tides;  in  fact,  the  body  may  be  divided  into  any  number  of  parts  of  such 
sl»pe  that  their  centers  of  gravity  are  easily  determined.  Then  the  distance 
from  the  fixed  plane  to  the  center  of  gravity  of  the  body,  is  equal  to  the 
siun  of  the  products  of  the  weight  of  each  mass  into  the  distance  of  its 
center  of  gravity  from  that  plane,  and  this  divided  by  the  total  weight  of 
the  body.  Furthermore,  the  masses  whose  moments  are  thus  obtained 
may  form  one  body  or  any  number  of  bodies.  In  the  latter  case,  the  center 
of  gravity  obtained  would  be  the  center  of  gravity  of  all  the  bodies.  The 
exact  pomt  of  the  center  of  gravity  is  determined  from  tkr0€  coordinate 
planes. 

If  the  center  of  gravity  of  a  solid  is  supported  on  a  point. the  whole 
body  will  be  in  unstable  equilibrium. 

Center  of  Oscillatioa- Center  of  Percussion,  a6<m< 

Axis  O. — ^The  c^ntgr  of  oscillatioH  P  of  a  mass  ! 
swinging  or  oscillating  about  a  fixed  axis  passing 
through  O.  isa  point  at  which  if  the  whole  mass  were 
coocentrated  the  oscillation  would  remain  the  same. 
The  ctnUr  of  percussion  P  of  the  mass  suspended 
hom  the  axis  at  O,  is  that  point  at  which  if  a  hori- 
zontal force  be  applied  there  will  be  no  shock  at  O. 
The  two  points  P  are  identical.  Let  any  mass  M, 
Pig.  48,  be  suspended  from  an  axis  at  O.  Let  G 
be  the  mi  of  trav  of  the  mass.  C  the  center  of  gyra- 
tioQ,  and  P  the  center  of  oscillation  or  percussion; 
and  let  p^,  f  and  /  be  the  respective  distances  to 
these  pomts  from  the  plane  X;  r  being  the  radius 
of  gyration  of  the  mass  about  O,  and  /  the  radius  of 
oscillation.  Then  will  r  be  a  mean  proportional  be- 
tween yo  and  /.  so  that 

..        e       .„  ..       ,      r'     (radius  of  gyration)*  ^.^ 

radius  of  oscillation  /  -  —  —77-— ^ (47) 

yo       dist  to  cen  of  grav  ^     ' 

To  illustrate:  For  a  rod  of  length  L  and  of  uniform  section,  suspended 

freely  from  iu  upper  end:    >to— y.r*— -3.  and /— |L. 

Note  that  O  and  P  are  interchangeable;  that  is.  if  P  becomes  the  axis, 
then  O  will  be  the  center  of  oscillation  or  percussion. 

The  theory'of  the  compoimd  pendulum  is  based  on  the  above  principles. 

Impact  or  ColUslon. — The  "line  of  impact"  of  two  bodies  in  collision 
i>  a  line  normal  to  the  surfaces  at  the  "  point  of  contact,"  irrespective  of  the 
itlative  motion  of  the  two  bodies.     Impact  is — 
Central,  when  the  line  of  impact  coincides  with  the  line  joining  the  centers 

of  gravity  of  the  two  bodies;  eccentric,  when  it  does  not. 
I>irKt,  when  the  line  of  impact  coincides  with  the  line  of  relative  motion 

of  the  two  bodies;  oblique,  when  it  does  not. 
Central  impact  may  be  either  direct  or  oblique. 
Direct  impcurt  may  be  either  central  or  eccentric. 
In  aU  cases  of  impact,  action  —  reaction. 

Notation. 

—  the  respective  masses, 

—  the  respective  velocities  before  impact, 

—  the  respective  velocities  at  any  given  instant  during  impact. 

—  the  respective  velocities  after  impact. 

—  common  velocity  at  time  of  greatest  compression. 

—  coefficient  of  restitution  in  imperfectly  elastic  contactgle 


«1. 

m^. 

«l. 

C7. 

v". 

xf. 

h. 

Vt, 

304  15.— MECHANICS. 

Central  Impact  Formulas. 
Velocity  at  time  of  greatest  compression,  v— ^— (48) 

tKl  +  fH^ 

^    /«  •     ^    r       .x  .■  veloc  regained  after  compression     v—vi 

Coefincient  of  restitution.  *  —  — -. — r: — -. — r-j — : —— : —  — — 

velocity  lost  during  compression     Ci—v 

^^^ (4g) 

For  perfectly  elastic  bodies,  *  would  =  1 ;  but  as  all  bodies  are  imperfectly 
elastic,  tf  is  always  less  than  unity,  showing  that  there  is  a  loss  of  energy 
during  impact. 

Loss  of  enengy  due  to  inelastic  impact  —  ^  ,   *    r  (Ci  — cj)* (50) 

z  {nti  +  ni2) 

Loss  of  energy  due  to  imperfectly  elastic  impact «  (1—**)  «-? — ~, r(^ — c^i* 

A  \vi%x  +  mi} 

(61) 


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16.— THEORY  OF  STRESSES  IN  STRUCTURES. 


OUTER  AND  INNER  FORCES. 

A  ftnxrttire  is  designed  to  resist  safely  the  loads  which  may  come 
ttpoo  it.  These  loads  (which  include  the  weight  of  the  structure  itselO 
together  with  their  attendant  reactions,  are  called  the  external  or  ouUr 
forcts;  while  the  stresses  which  these  outer  forces  produce  in  the  members 
of  the  structure  themselves,  are  called  the  internal  or  innsr  forces;  thus — 

rwrf—  f^s».^—  i  (*•)    Loads  (-live,  dead,  wind,  snow.  etc.). 
Ooter  forces-  {  .^<^    Reactions. 

hmer  iocces—     (c.)    Stresses  in  the  members. 

Aseumlng  that  the  loads  acting  on  the  structure  are  known,  the  first 
itep  is  to  find  one  or  more  of  the  reactions;  and  from  these  outer  forces  the 
Ortssis  in  the  members  may  be  determined  by  the  use  of  the  analytical  or 
the  graphical  methods,  or  by  the  two  methods  combined.  In  the  operation 
of  fiodmg  the  reactions  and  stresses  it  is  well  to  remember  the  following 
principles: 

PRINCIPLES  OF  STATIC  EQUIUBRIUM. 

Firsi. — The  algebraic  sum  of  the  moments*  of  the  outer  forces  about 
any  point  is  equal  to  zero;  from  which,  considering  right-hand  (clockwise) 
moments  plus  and  left-hand  (un-clockwise)  moments  minus^  or  vice  versa, 
we  have — 

Summation  of  moments— 0:     JAf — 0 (1) 

Second. — ^The  algebraic  sum  of  the  components,  in  any  given  direction, 
of  the  outer  forces  is  equal  to  zero;  from  which,  considering  those  downward 
or  to  the  right,  plus,  and  those  upward  or  to  the  left,  minus,  or  vice  versa, 
we  have — 

Summation  of  vertical  components— 0:     JK— 0 (2) 

Summation  of  horizontal  components —0:     IH  — 0 (3) 

Third. — ^Por  clearness  and  simplicity  of  calculation,  in  the  application 
of  equations  (1).  (2)  and  (3).  the  stresses  in  certain  members  of  the  truss  or 
frame-work  may  temporarily  be  considered  as  outer  forces,  by  cutting  the 
structure  in  two  by  certain  planues  (straight  or  curved)  properly  intersecting 
the  members  in  question — considering  that  portion  of  the  structure  on  one 
Bde  of  the  cutting  plane  (usually  the  left  side)  as  a  complete  structure: 
and  the  stresses  in  the  members  so  cut,  as  outer  forces  acting  on  the  section 
to  produce  eqtiilibrium.  That  is,  these  imaginary  outer  forces  are  the 
ttnsses  to  be  odculated.  (See  Pigs.  1  and  2.)  Uenerally.  only  threet  active 
members  may  be  cut;  thus — 

Cut  three  active  members;  intersection  of  either  two  is  ) 
origin  of  moments  for  calculating  the  stress  in  the  third  > . .  . .  (4) 
member.  ) 


Fig.  1. 

*  The  moment  of  a  force  about  a  given  point,  as  origin,  is  the  product  of 
the  force  and  the  shortest  distance  from  the  origin  to  the  line  of  the  force, 
t  See  "Notes,"  page  726,  for  cutting  of  four  active  members. 


306 


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306  It.— THEORY  OF  STRESSES  IN  STRUCTURES. 

PRINCIPAL  METHODS  OF  CALCULATION. 

Method  of  Moaentt. — ^This  method  of  calculation,  usixig  equation  ( 
is  ustially  employed  in  determining  the  reactions  at  the  points  of  suppa 
the  stresses  in  the  chord  members  of  bridges  and  roofs  and  in  the  web  me 
bers  where  the  chord  members  are  not  parallel;  the  wind  stresses  in  t 
main  vertical  members  of  towers,  buildings  and  similar  structures;  the  coi 
presiive  streaaes  in  masonry  dams;  etc 

Method  of  Shears. — This  method,  using  equations  (2)  and  (8),  is  tisua 
employed  in  calculating  the  stresses  in  the  web  members  of  any  £rame-wc 
connecting  parallel  chords,  as  the  lateral  systems  of  bridges;  the  web  me 
ben  of  .simple  bridge  and  roof  trusses;  the  bracing  of  towers;  the  shi 
in  dams;  etc. 

The  stress  in  any  vtrttcal  web  member  whidi  "takes  tip"  all  the  she 
is  equal  to  the  algebraic  sum  of  the  vertical  components  of  the  outer  for 
to  the  left  of  the  section  cutting  the  member;  and  the  stress  in  any  dioif^ 
member  is  eoual  to  the  vertical  shear  multiplied  by  the  secant  of  ax^k 
inclination  ot  that  tnember  with  the  vertical. 

The  term  "vertical"  may  be  used  in  any  imiformly  specific  directkn 
usually  at  right  angle  with  the  axis  of  the  structure  and  parallel  with  ^ 
direction  of  the  prevailing  outer  forces.     To  epitomize: 

Stress  in  any  member  carrying  all  the  shear— vertical) 
shear  X  secant  of  angle  of  inclination  with  the  vertical. )   *  *  •  * 

The  above  five  laws  are  fundamental  in  the  determination  of  the  sires 
in  any  structure  which  is  statically  determinate. 

Qraphical  Methods. — ^The  most  common  methods  of  determin: 
stresses  is  by  graphics,  which  may  be  performed  by  "moment  diasraxi 
or  by  diagrams  involving  the  principle  of  the  "triangle  of  forcM^'  ( 
Mechanics.  Figs.  31  to  35).  The  latter  is  called  Maxwell's  method  i 
is  the  most  used.     (See  Pigs.  4,  etc.,  following.) 

PRACTICAL  APPUCATION  OF  PRECEDING  PRINCIPLES. 

CASE  A.    LOADS  AND  REACTIONS  VERTICAL. 

Problem. — Find  the  dead-load  stresses  in  a  6-panel  Pratt  truss 
i20-ft.  span.  23  ft.  in  height  center  to  center  of  chords;  assuming  1 
dead  load  per  truss  at  500  lbs.  per  lin.  ft.  and  acting  at  the  lower  pa 
points,  Pig.  2. 


Fig.  2. 

Calculation. — Stresses  are  usually  in  thousand-pound  tmits  and  ca] 
lated  to  the  nearest  hxmdred  pounds;  thus.  64,7-M700  lbs.;M.O— 6400O  I 
64-04  lbs.  .etc.  That  is,  where  the  stress  is  abbreviated  to  the  thouaand-poi 
imit  there  should  be  one  figure  to  the  right  of  the  decimal  point,  wnet 
it  is  a  significant  figure  or  merely  zero,  to  show  that  the  stress  is  in 
abbreviated  form.  The  sign  (  — )  before,  or  (c)  after,  the  stress  indio 
that  the  member  is  in  compression,  as  —64.7  — 04.7c;  while  the  signs  ( 
and  (0  indicate  tension,  as  +04.7- 64.7 1. 

Load  p0T  panel  per  fru55  -  500 X  20 »  10000  lbs. -10.0. 


ct  to  the  Rfc ol ^ -bl -4l. 

of  panel  ^ ^'Kl -H^ 


PRATT  TRUSS  WITH  PARALLEL  

Rgaction  at  Left  Support. — Assuming  the  panel  lengths  as  unity  and 
taking  moments  about  the  right  hand  abutment  B.  using  equation  (1). 
Ijf -0,  we  have. 

i?,X«-10.0(6+4+8+2+l)-0. 

Hence,  teaction  Rt  —  — g^  —  25.0,  acting  upward. 

Umgtks  cf  Members. — ^All  horisontal  or  chord  members  are  20-£t.;  all 
Toticals  (posts  and  end  suspenders)  are  23-ft.;  hence,  all  diagonals  (bars 
and  end   posts)    are 

V20»  +  2y-  30. 48 -ft.    Thus,  hor-  20;  ver-  23;  di|«-  30.48. 

Tngonomeiric  Rixtios. — ^The  angle  oc,  Pig.  2.  is  the  angle  of  inclination 
of  the  diagonal  members  with  the  vertical;  and  its  two  functions,  tan  a 
and  sec  oc,  are  respectively  employed  in  calculating  the  stresses  in  the  chords 
sad  diagmial  members  of  bridiges  with  parallel  chords. 

BSITDINQ  MOMBNTS  AND  ChORD  StRBSSBS: 

Let  O,  Pig.  3,  be  the  origin  of  moments  at  any  panel  point  of  either 
chord,  obtained  by  cutting  three  active 

iQembera.aeeeq\iation(4),andletitbe  R  f| 

required  to  find  the  stress  in  the  oppo-      |*'"*W'T!^ — xA — '  ' 

■te  chord  member  so  cut.     Let  any     1  * 

number  of   panel  loads  Pi  act  to  the  | 
teft  of  O,  and  any  number  of  jpanel 

knds  Pt  act  to  the  right  of  ().  on  »•      « 

the  qjan  Nl;  in  which  F«-  ^ 

^■•length  in  feet  of  one  panel. 
JV^number  of  panels  in  the  span. 

Ml,  a  —number  of  panels  from  Rt  to  P|  and  O,  respectively. 

«2.   6— number  of  panels  from  R^  to  Pt  and  O,  respectively. 

Then.  Bending  moment  at  0-Afo-  ^  ^* '^^  ^^^^^'''"  °  ^ (•) 

And  if  d  represents  the  effective  depth  of  truss,  we  have. 

a>n»  m  chori  member-^'-  j^JL^n^.-^P.  %  t-KT  P.  ,.a^^  ^-  ^^ 

which  are  the  general  equations  for  finding  the  bending  ntioments  and  chord 
screases  without  first  finding  the  reactions. 

Equations  (0)  and  (7)  are.  however,  very  little  used,  and  it  is  probably 
best  for  the  beginner  to  employ  equations  (8)  and  (9),  following,  m  which 
the  reaction  Rt  must  first  be  determined. 
Thai.  Bending  moment  at  O  — Afo-/?i.  al—IPt.  Xtl (8) 

And.  Stress  in  chord  member-  -j2-(/?ia- J  Pi  «i)  tan  a (9) 

in  which  ^—number  of  paAels  from  Pi  to  O, 

Shbars  and  Wbb  Strbssbs! 

Let  O,  Pig.  3.  be  the  line  of  shear  cutting  tistially  two  or  three  active 
members,  including  one  web  member  which  takes  up  all  the  shear.     Then — 

Vertical  shear  at  O^So^Rx-I  Pi (10) 

Streasinwcbnaember-(/e|-JPi)  sec  a (11) 

in  which  oc— angle  of  inclmation  of  web  member  with  the  vertical, 
and  £  Pi —sum  of  all  loads  to  left  of  cutting  line. 

Stresses  in  Chord  Members  by  Method  of  Moments:  JM-0. — In  addi- 
tion to  determining  the  amount  of  stress  in  the  various  members  of  a 
structure,  it  is  of  course  necessary  that  the  kind  of  stress,  whether 
tensile  or  compressive,  be  Imown  in  each  case.  Ortain  rules  may  be  followed 
in  determining  the  anunmt  and  kind  of  stresses  in  statically  determined  struc- 
tures,  as  included  in  tiie  following  steps: 
First. — Draw  a  plane  through  the  structure  cutting  three  active  members. 

including  the  one  to  be  calculated.     The  point  of  intersection  of  any 

two  of  the  members  will  be  the  center  of  moments  tor  determmmg  the 

stress  in  the  third. 

'  ■— Digitized  by  VjOOQ IC 


308 


IQ.— THEORY  OF  STRESSES  IN  STRUCTURES. 


Stcond. — For  the  member  m  question,  find  the  intersection  of  the  other  tr^o 
members  or  "center  oi  moments"  about  which  the  moments  of  the 
outer  forces,  acting  on  the  section  to  the  left  of  the  cutting  plane,  are 
to  be  taken.  These  will  include  the  reaction  at  the  left  abutment;  and 
the  moment  equation,  JAf  — 0,  will  include  also  the  required  stre^ 
asstuned  temporarily  as  an  outer  force  and  acting  at  the  right  of  the 
cutting  plane. 
Third. — ^Take  moments  about  the  center  of  moments,  assuming  that  the 
above  last  mentioned  unknown  force  (the  reqtdred  stress)  is  plus  (-•-) 
and  acts  awav  from  the  section.  All  other  forces  tendine  to  pitxluce 
moments  in  the  same  direction  as  the  above  may  be  considered  as  (H-  ) 
forces  and  their  moments  as  (  +  )  moments;  while  all  other  outer  forces, 
that  is,  forces  tending  to  produce  moments  in  the  opposite  direction 
may  be  considered  as  (— )  forces  and  their  moments  as  (— )  moments. 
Fourth. — K,  in  the  equation  JM —0,  the  result  of  the  nsquircd  stress  is  a 
(  +  )  quantity,  the  member  is  in  tension;  while  if  it  is  a  (  — )  quantity 
the  member  is  in  compression.    Thus, 

Assume  required  stress  as  +5  acting  away  from  the  section f  12) 

If  the  restilt  of  5  is  + ,  the  member  is  in  tension 1 1 3) 

"     "         '*     "Sis—,     "  **        ""compression (14) 

Table  1  is  based  on  the  above  methods  and  rules,  which  will  be  found 
useful  to  the  young  engineer.  The  experienced  engineer  can  usually  tell 
the  kivtd  of  stress  by  inspection,  but  there  are  many  cases  in  complex  struc- 
tures where  the  rules  have  to  be  followed. 


1. — Showing  Calculation  op  Chord  Stresses.  Pig.  2. 


Cut- 
ting 
Plane 


Method 


Equation. 


Calculation. 


Remarks. 


C-C 
d-d 


i-Af-O 


JAf=0 
JAf"0 


(fi-Af-O 


'-c\sM 


Ui  S2-/?i  tana 


Ui  Si  -  /?i  tan  a 

t/2  58-(/?iX2-P&Xl) 

tan  a 
L3  54--(3/?-3F)tana 

L2,St,=  -'i2R-P)  tano 


26.0X.87-+21.7 


21.7/ 


40.0X.87=+34. 

-45.0X.87^ 39. 

-40.0X.87^ 34. 


21.7/ 
.8/ 


;.8,34. 


39  Ic 

8c 


1 

8^34, 


//?i-25.0; 

Itana  — .87 
'Also,  from 

.Si  ~  Sa 

3P-P»X 
2+/'4Xl. 
2R^ktX2 


Stresses  in  Web  Members  by  Method  of  Shears:  IV  ^0. — The  shear 
method  is  usually  adopted  where  a  single  web  member  in  a  panel  takes 
up  all  the  shear,  as  in  Pig.  2,  in  which  top  and  bottom  chords  are  parallel 
and  at  right  angle  with  the  prevailing  outer  forces.  In  such  cases  the 
following  steps  may  be  employed: 

First. — Draw  a  plane,  cutting  the  web  member  in  question  and  also  the 
upper  and  lower  chords.  It  is  clearly  evident  that  the  stresses  in  the 
chords  can  have  no  vertical  component  to  assist  in  "taking  up"  the 
shear,  since  they  are  at  right  angle  with  the  shear,  hence  it  miist  be  taken 
up  by  the  web  or  shear  member. 
Second. — Find  the  algebraic  sum  of  the  vertical  outer  forces  to  the  Utft  of 
the  cutting  plane,  and  this  will  be  equal  in  magnitude  and  opposUe  in 
direction  to  the  vertical  component  of  the  required  stress  in  the  member 
acting  at  the  right  of  the  cutting  plane  to  produce  equilibrium.  If  the 
required  stress  acts  away  from  the  cutting  plane  the  member  is  in  ten- 
sion (4-).  while  if  it  acts  toward  the  cutting  plane  the  member  is  in 
compression  (  — ). 

Table  2  is  based  on  the  above   rules,  although    the    algebraic     siims  i 
giving  direction  can  usually  be  dispensed  with.  .^^^  ^  GoOqIc  i 


d  by  Google 


810 


M,— THEORY  OF  STRESSES  IN  STRUCTURES. 


L2L3,  etc..  or  to  use  entirely  different  letters,  as  F,  G,  H,  etc.;  while  some 
prefer  the  use  of  the  letters  X  and  Y  to  represent,  respectively,  the  upper 
and  lower  outside  spaces  of  the  truss.  There  is,  however,  no  real  principle 
involved  in  these  various  customs. 


ATU: 


m-i' 


k^lZA     L  ♦tt.7  B 


Fig.  5.     Force  polygons  at  joints  (Fig.  4). 

Qraphical  Method. — ^The  principle  of  force  polygons  at  the  joints  of  a 
structure  has  led  to  the  rapid  solution  of  stresses  by  the  graphical  method. 
It  will  be  noticed  that  Figs.  6.  if  "fitted  together."  will  form  the  com- 
plete graphical  stress  diagram  of  half  the  truss — Fig.  6,  showing  the 
complete  stress  diagram  of  the  whole  truss,  the  two  halves  being  sym- 
metrical. 


Fig.  6. 
Hence  if  the  loads  and  reactions  are  laid  off  to  proper  scale,  formins  a 
closed  polygon  of  outer  forces  called  the  load  line,  the  Imes  drawn  parallel 
with  the  members  of  the  skeleton  diagram  of  the  truss  and  properly  inter- 
secting one  another,  will  represent  by  scale  the  actual  stresses  in  the  mem- 
bers. The  following  rules  will  be  found  universal  in  application  for  loads 
and  reactions  in  any  direction  or  applied  at  any  points  of  the  structure. 

GENERAL  RULES  FOR  STRESS  DIAGRAMS. 

Order  of  Coosidering  Forces  Around  Joints. — 
1**.  Draw  skeleton  of  truss  accurately  to  a  good  scale. 
2?.    Show  T  loads  at  top  joints  and  B  loads  at  bottom  joints  of  truss. 

Note. — In  ordinary  cases  where  T  and  B  loads  at  the  abutmemis  are 
vertically  downward  and  opposite  in  direction  to  the  reactions  at  those 
points,  these  loads  may  be  omitted — so  far  as  the  stresses  in  the  trusses 
are  concerned — and  the  reactions  diminished  accordingly:  but  the  total 
reactions  must  be  considered  in  designing  the  supports  themselves.  Where 
the  loads  and  reactions  are  not  in  the  same  straight  line,  both  mvist  be  tn^ 
eluded. 

3*.    Ft  wd  the  react  ions — Ri  —  left-hand:  R2  —  right-hahd. 
4**.     Load-line — reactions  and  loads  forming  closed  polygon  of  outer  forces. 

Note. — Begin  with  one  of  the  reactions  and  draw,  in  the  directions  o| 
the  forces,  the  closed  polygon  of  outer  forces — reactions  and  loads — con-^ 
sidering  them  in  right-handed  (clockwise)  or  left-handed  (unclockwise) 
order  around  the  truss,  as  per  the  following: 


GENERAL  RULES  FOR  STRESS  DIAGRAMS. 


sn 


Omtgr  farces  around  truss  considerid  in  clockwise  order'. 

Beginning  with  Ri — (mainly  for  T  loads,  at  top  of  truss) — 

( Draw  stress  diagram  to  left  of  load  line; 

I  Consider  forces  around  joints  in  clockwise  order 

Beginning  with  R2 — (mainly  for  B  loads,  at  bottom  of  truss) — 
(  Draw  stress  diagram  to  left  of  load  line; 
( Omsider  forces  aroimd  joints  in  clockwise  order 


}.(15) 
}.(!•) 


\0 


For  (16)  For  (17)  For  (19) 

.    Outer  forces  around  truss  considered  in  un-clockwise  order: 
Beginning  with  Rx — (mainly  for  B  loads,  at  bottom  of  truss) — 

{Draw  stress  diagram  to  rijsht  of  load  line;  ) 

Consider  forces  around  jomts  in  im-clockwise  order ) 

Beginmng  with  Rt — (mainly  for  T  loads,  at  top  of  truss) — 

(  Draw  stress  diagram  to  right  of  load  line;  ) 

( Consider  forces  amtmd  joints  in  im-clockwise  order ) 


(17) 


(18) 


For  (16) 


For  (18) 


For  trusses  loaded  with  T  loads,  at  top,  and  B  loads,  at  bottom  chords. 
fl5)  and  (16)  may  be  combined  in  (19);  while  (17)  and  (18)  may  be  com- 
taned  in  (20);  as  folk>WB: 

7".    Outer  forces  around  truss  considered  in  clockwise  order: 

(Beginning  with  /?» or  /?•— (for  both  T and  B  loads)—  1 
Draw  stress  diagram  to  left  of  load  line;  [  (19) 

Consider  forces  around  joints  in  clockwise  order  J 

8°.    Outer  forces  around  truss  considered  in  un-clockwise  order: 

(Beginning  with  Ri  or  Rt—^{{ot  both  B  and  T  loads) — ^1 
Draw  stress  diagram  to  right  of  load  line;  [      (20) 

Consider  forces  around  joints  in  tm-clockwise  order  J 

Remarks. — The  k>ad-line  diagrams  above,  illustrating  (16)  to  (20) 
ituJusive,  simply  show  the  order  of  considering  the  forces  at  the  joints,  but 
not  their  direction.  Note  that  if  the  outer  forces  are  all  vertical,  the  load 
ime  will  be  a  vertical  line. 


Order  of  Comidering  Joints. — So  far,  wc  have  considered  the  order  of 
drawing  the  outer  forces  to  form  the  load-line  polygon;  and  the  order  of 
considering  the  forces  around  the  joints  for  a  stress  diagram  either  to  right 
or  left  of  the  load  line.  We 'will  now  consider  the  order  of  proceeding  from 
one  joint  to  another  of  the  truss  in  drawing  the  stress  diagram;  bearing  in 
nand  that  it  is  sometimes  essential  to  begin  at  the  end  of  the  truss  which 


312 


16.— THEORY  OF  STRESSES  IN  STRUCTURES. 


has  the  larser  reaction,  as  a  stress  diagram  is  simply  a  system  of  triangulation 
and  the  larger  the  initial  base  the  better.  There  are  other  reasons,  how- 
ever, which  must  be  considered:  namely,  the  natiire  of  the  loading  and  the 
general  convenience  of  always  starting  from  the  one  end.  In  trusses  which 
support  moving  loads  the  loads  are  made  to  come  on  from  the  right,  and 
the  left  reaction  is  taken  as  the  initial  base  of  the  stress  diagram.  In  other 
words,  we  usually  start  with  joint  Lq  of  the  truss. 

In  following  from  joint  to  joint  we  must  select  the  one  which  has.  for 
the  given  loading,  only  two  nnknown  stresses  whose  directions  are  known, 
because — ^with  one  force  given,  in  magnitude  and  direction — 

Two  unknown  forces  only,  whose  directions  are  known,  can  be] 
solved  by  a  "triangle  of  forces;"  and  this  fact  determines  the  order  [  (21) 
of  considering  joints.  J 

PRACTICAL  APPUCATION  OF  PRECEDING  GRAPHICAL  RULES. 

Graphical  Solutloii  of  Case  A ;  Loads  at  Bottom  Joints. — DaU:  9  panels 
at  20-ft.-120-ft.  span:  height  of  truss- 23  ft.;  load  per  joint  — 10.000  lbs.; 
reactions,  each —  25.000  lbs. 

Draw  the  truss  very  carefully  to  scale,  large  enough  so  lines  in  the 
stress  diagram  can  be  drawn  parallel  with  the  members  of  the  truss,  with 
sufficient  accuracy. 

In  accordance  with  (17),  beginning  at  the  left-hand  end  of  the  tniss, 
lay  off  consecutively  in  direction  and  mtensity.  by  scale,  the  outer  forces 
/?.-25.0  (upwardj;  Pb,  Pa,  Pz,  P2,  Pi- 10.0+ 10.0+10.0+10.0+ 10.0 
(downward);  and  /?2"26.0  (upward). 

Draw  the  stress  diagrsim  as  per  Pig.  6,  considering  the  order  of  the 
forces  in  un-clockwise  order  around  each  joint  and  noting  that  when  a 
stress  is  drawn  in  direction  away  from  the  joint,  the  member  is  in  tension; 
while  if  drawn  in  direction  toward  the  joint,  the  member  is  in  compression. 
The  arrows  in  Pigs.  6  show  the  direction  of  the  stresses  of  each  polygon 
of  forces,  indicating  the  nature  of  the  stress  in  each  case. 

Table  3  shows  the  order  of  considering  the  joints,  the  given  and 
required  forces  at  each  joint,  and  the  nature  of  the  stresses  in  the  members. 


3. — Graphical  Mbthod  op  Solvino  Casb  A,  Pios.  4,  5  and  0. 


si 

Oto 


c 

^ 

,0 

Porces  (Fig.  4). 

% 

Direction  of  forces  in 
force  polygon. 

From  the 

Toward  the 

• 

0) 

Given. 

To  find. 

joint,  denot- 
ing tension 

joint,  de- 
noting com- 

\ 

2: 

(+). 

pression  (  - ) 

& 

u 

Ri 

LA,  UA 

A 

LA  =+21.7 

UA 33.1 

l^x 

AL,UL, 

LB,AB 

B 

/LB -+21.71 
\AB  -  +  10.0J 

Ut 

UA,AB 

UC,BC 

C 

BC  »+19.9 

UC  —  34i 

k 

CB,BL,L,L, 

LD,CD 

D 

LD  -+34.8   CD  —  5.0 

UC,  CD 

UE,DE 

E 

DE-+  6.6  :c;£— 39.1 

u. 

UE 

EE',  UE' 

E' 

£E'-±  0.0  ]i;£'--89.1 

fPoint 
XE^ET. 

u 

EE'.DE,DL,L,L'. 

LD'M'D' 

ly 

D'£:=-+  6.6  |Li>'-+34.8 

d  by  Google 


d  by  Google 


81i 


16— THEORY  OF  STRESSES  IN  STRUCTURES. 


Reactions  in  Any  Direction. —  The  foregoing  elementarv  principles 
will  apply  to  any  case  of  loading  and  reactions,  whether  vertical  or  oblique; 
rememoering  that  the  load  line  is  a  polygon  of  forces  in  which  the  resultant 
loads  and  resultant  reactions  are  respectively  equal  in  magnitude  and 
opposite  in  direction.  There  are  four  cases,  as  follows: 
Case  A. — Loads  and  reactions  vertical  (these  have  just  been  considered). 

Example. — ^Truss  of  an  ordinary  span  "resting"  on  the  abutments. 
Cast  B. — Resultant  of  loads  oblique;  reactions  oblique  and  parallel. 

Exaa4>le.     Roof  truss  with  both  ends  "fastened  '  to  supports. 
Cast  C. — Resultant  of  loads  oblique;  one  reaction  oblique.  One  vertical. 

Example. — Roof  truss  with  one  "roller"  and  one  "fixed"  end. 
Case  D. — ^The  loads  vertical;  reactions  oblique. 

Example. — ^Three-hinged  arch,  "pressing"  against  abutments. 

Case  B;  Roof  Truss;  Both  Ends  Fixed;  Wind  on  One  Side. — A  roof  truss 
with  both  ends  fastened  to  the  supports,  and  wind  pressxire  on  one  side. 
Pig.  12.  The  assumption  made  here  is  that  the  horizontal  components 
of  Rt  and  R2  are  directly  proportional  to  the  reactions  themselves;  m  other 
words,  the  end  that  has  the  greater  reaction  resists  the  greater  horizontal 
thrust. 


Fig.  12. 

Note. — P  is  the  resultant  of  all  the  T  loads:  Ti  and  Ts  arc  each  one- 
half  of  T2.  7*3  or  T4,  the  last  named  three  being  full  panel  loads.  For  height 
of  truss— 2  panels,  the  resultant  P  cuts  the  lower  chord  2^  panels  from 
the  left-hand  end.  so  that  /?i-6iP-i-8.  and  /?2»-2iP-i-8. 


Fig.  13. 

(18).  Loads  and  reactions,  un-clockwise. 
Forces  around  joints,  un-clockwise. 
Remarks. — ^This  case  is  seldom  used  excepting  perhaps  for  short  spans. 
Case  C,  which  will  next  be  treated,  can  be  applied  tmiversally.  Note  that 
stress  diagram.  Pig.  13.  indicates  that  there  is  no  stress  in  any  of  the  dotted 
web  members  of  the  truss  shown  in  Fig.  12,  6^  being  made  to  include 
the  whole  triangular  space  comprising  the  right-hand  half  of  the  truss. 

Case  C;  Roof  Truss;  One  Roller  End;  Wind  on  Either  Side. — ^Roof  truss 
with  wind  pressure  on  left  side;  two  conditions  as  follows: 
Ca. — Left  end  is  roller  end;  right  end  is  fixed  end.     See  Figs,  li  and  15. 
Cb. — Left  end  is  fixed  end;  right  end  is  roller  end.     See  Figs,  li  and  16. 

Fig.  16  in  the  stress  diagram  for  the    truss   (Fig.    li)    treated    as    per 
Case  Ca.     The  load  line  is  composed  of  P,  R^,  and^j.     P,  the  resultant  of 


REACTIONS  IN  ANY  DIRECTION. 


316 


all  tbe  T  loads,  is  known  in  intensity,  direction  and  position .  passing  through 

T]  Dorxnal  to  the  roof;  Ri  is  known  in  direction  and  position,  passing  vcr- 

.     tically  throtigh  L.     Let  O  be  the  point  of  intersection  of  P  and  R^  and 

'     considenng  it  the  center  of  moments  of  all  the  outer  forces,  we  have,  from 

JAf-0.  that  Rt  must  be  in  the  direction  RO,  passing  through  the  center 

L    (d  moments  O. 

[         The  stress  diagram.  Pig.  15,  is  drawn  by  rule  (18),  page  311: 
Fig.  14 —  (18). — Loads  and  reactions,  un-clockwise. 

Forces  around  joints,  un-clockwise. 
I  Note. — As  the  left  end  is  the  roller  end  the  reaction  Ri  must  be  vertical. 

Fig.  16  is  the  stress  diagram  fc 
the  same  truss,  treated  as  per  Cai 
0>  by  sinciilar  analysis. 

(15).  Loads  axid  reactions,  clod 
wise. 
Forces  axoxmd  joints,  clocl 
wise. 
!  Note. — As  the  right-hand  end 

the  roller  end  the  reaction  R^  mtu 
be  vertical. 

Remarks. — ^The  two  conditio! 
(a)  and  (6)  of  Case  C  are  applie 
ia  practice  to  the  roof  truss  f< 
maximum  wind  stress  in  each  of  it 
m^nbers..  In  addition  to  these  th 
members  of  course  are  designed  fc 
aiow-.  dead-,  and  live-loads,  if  an] 
For  these  latter  cases,  however,  th 
reactions  are  vertical  and  the  grapt 
teal  methods  are  simple.  (See  RooC 
Section  46). 

Com  D.  Thret-hingtd  Arch: 
Loads. — ^Three-hinged  arch  (Pig.  1 
load  P  acting  on  the  left-hand  gii 
panel  froai  the  center  of  the  f 
a  hinged  in  the  center  and  at 
sad  as  there  can  be  no  moments 
tbe  lines  of  reactions  must  pass  t 
foUows: 

(o.)  For  a  load  at  center  of  span,  Ri  takies  the  direc- 
tion LO,  and  R%  takes  the  direction  RO. 
Q>).  For  a  load  at  the  left   of   the   center   as   P,  /?• 
I  takes  the  direction  RO,  intersecting  the  line  oi 

I  the  force  P  at  if ;  whence  Ri  takes  the  direc- 

tkm  LH. 
ic.)   Similarly,  for  a  load  P*  at  the  right  of  the  center, 
R,  takes  the  direction  LO,  intersecting  the  line 
of  the  force  P'  at  if' ;  whence  /?2  takes  the  direc- 
tkm  RH'. 
Pig.  18  is  a  stress  diagram  of  the  arch, 
for  the   load    P,  Case   Db,  above.     For 
th»  load  the  dotted    members.  Fig.  17, 
faa'vv  no  stress. 
(18).  Loads  and  reactions,  un-clockwise. 
Forces  around  joints,  un-clockwise. 
Note. — /?2  and  P  de- 
termine R%. 

Remarks.  —  The  + 
and  —  si^ros  for  the  mem- 
bers indicate  respective- 
ly whether  they  are  in 
tension  or   compression. 


GoogT 


17.— NATURAL  HISTORY  OF  MATERIALS. 

(For  Wbichts  and  Specific  Gravitibs,  Sbb  Sbction  27.) 
A.— CHEMICAL. 

Compositloa  of  Matter. — If  a  drop  of  water  could  be  magnified  to 
Bize  of  the  earth  it  is  estimated  that  the  countless  atoms  of  which  the  d 
is  comp>osed  would  each  appear  to  be  about  the  size  of  a  bird's  egg. 
would  also  be  seen  that  all  the  atoms  would  be  in  groups  of  three,  e 
group  or  molecule  being  composed  of  two  atoms  of  hydrogen  and  on* 
oxygen.  Subject  the  drop  of  water  to  a  galvanic  current  and  it  will  ce 
to  exist  as  water,  being  decomposed  into  its  two  elements — hvdrogen  J 
oxygen.  In  other  wordfs.  the  molecules  forming  the  compound,  water, ' 
become  disintegrated,  all  the  atoms  of  hydrogen  passing  off  as  hydro 
gas,  and  all  the  atoms  of  oxygen  passing  on  as  oxygen  gas.  Conversely 
now  the  two  evolved  gases  are  mixed  and  sufficiently  heated  they  will 
unite  with  explosive  force  into  the  same  molecular  composition  as  befi 
re-forming  the  drop  of  water.  In  the  above  processes,  the  decomposil 
and  recomposition  of  the  substance  water,  none  of  the  atoms  have  b 
divided  or  destroyed. 

Old  Atomic  Theory. — Up  to  about  the  year  1898  the  last  sentence  of 
preceding  paragraph  might  have  been  concluded  about  as  follow^  ; 
generally  accepted:  "Because  the  atom  is  indivisible  and  indestructi 
representing  the  smallest  particle  of  an  element  of  matter;  hence  when 
say  that  matter  is  indestructible  we  mean  simply  that  the  atoms  of  wl 
all  matter  is  composed  are  indestructible." 

Recent  Discoveries. — ^The  recent  discoveries  of  the  Hertzian  ray  and 
practical  use  in  wireless  telegraphy;  of  the  Rontgen  or  X-ray,  by  rocan 
the  Crooke's  or  vacuum  tube.  1895;  of  the  Becqucrel  ray.  cxhibiiing 
radio-activity  properties  of  the  element  uranium,  in  18tf0;  and  later. 
Madame  Curie  and  others,  of  similar  properties  in  the  elements  thorii 
polonium,  radium  and  actinium,  have  resulted  in  shaking  the  old  ato 
theory  of  Dalton,  which  had  lasted  for  a  century. 

The  Corpuscular  Theory. — It  is  now  believed  that  each  atom,  previoi 
supposed  to  represent  the  smallest  particle  of  matter,  is  really  coznposci 
a  great  number  of  smaller  particles  called  corpuscles.  For  instance, 
smallest  and  lightest  atom  known,  that  of  hydrogen,  contains  about 
such  corpuscles;  while  one  of  the  heaviest  atoms,  that  of  radium,  contj 
about  200.000.  It  is  further  submitted  that  these  corpuscles  are  so  mfini 
small  that  the  unoccu[)ied  space  in  the  atom  is  almost  infinitely  great 
comparison,  and  that  they  are  vibrating  or  traveling  through  this  sf 
with  velocities  of  many  thousands  of  feet  per  second.  This  becomes  all 
more  amazing  when  it  is  staled  that  the  diameter  of  a  molecule,  which 
atoms  co.r.pose.  is  in  the  neighborhood  of  asooAs^oo  of  an  inch. 

The  corpuscular  theory  has  been  advanced  m  order  to  explain  sons 
the  recent  discoveries  cited  above.  Kadium,  for  instance,  is  consla: 
iving  off  heat  to  surrounding  objects  without  any  visible  source  of  sup 
'he  heat  is  evidently  furnished  by  the  breaking  up  or  disintegration  ot 
atoms;  i.  e.,  by  the  transformation  of  part  of  the  corpusciilar  enernr  of 
atoms,  into  heat.  The  balance  of  the  energy  is  dissipated  in  the  form 
various  kinds  of  rays.  On  this  theory  the  laws  of  the  conservation  of  cn< 
still  hold,  for  it  has  been  observed  that  all  of  the  radio-active  substa 

fradually  lose  in  weight.  It  is  estimated  that  radium  will  disj^rse  al 
its  mass  in  1500  years,  and  fa  of  it  in  10000  years.  Thorium  and  uran 
act  much  more  slowly,  requiring  in  the  first  instance  about  1000  mil 
years,  and  in  the  second  instance  10000  million  years.  Moreover,  all 
stances  are  supposed  to  be  radio-active  to  some  extent,  i.  e..  their  atoms 
gradually  breaking  up  into  corpuscles  and  the  corpuscular  energy  is  b 
transformed  into  other  kinds  of  energy.  In  line  with  this  argument,  wit 
the  scent  of  flowers  and  of  many  substances. 

Looking  at  the  subject,  then,  from  this  point  of  view  we  may  con! 
matter  as  the  great  storehouse  of  energy;  and  some  idea  of  the  efhcienc 

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CHEMICAL  COMPOUNDS.  821 

C4Hii|NMnids« — ^A  compound  is  a  chemical  tmion  of  two  or  more  elementa 
each  molecale  of  the  compound  being  a  perfect  likeness  in  miniature  o£ 
the  oompotmd  itself.  It  diners  from  a  mixture  in  that  no  chemical  change 
takes  place  in  the  latter,  the  original  molecules  of  each  of  the  substances 
mixed  remaining  intact. 

Compound  substances  are  generally  named  so  as 

(a)  To  denote  the  constituent  elements. 

(b)  To  denote  the  kind  of  molecular  grouping-  of  the  elements. 

(c)  To  denote  the  nature  of  a  resulting  compoimd  by  the  addition  or  sub- 

traction of  some  partictilar  kind  of  element. 

Snple  Combinatioiis* Ides.— Many  of  the  non-metallic  elements 

vben  combined  with  a  simple  basic  one  take  on  the  suffix  ids  or  et,  as,  for 


< 

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as 

chlorine. 

Iron  and  oxygen  form  iron  oxide  (oxide  of  iron). 

Lead  *'    chtorine     *'    lead  chloride  (chloride  of  lead). 

Potasnum"    bromine    "     potassium  bromide  (etc.). 

Hydrogen  "    sulphur     **    hydrogen  sulphide  (sulphuret  of  hydrogen). 

Copper       **    sulphur     "    copper  sulphide  (etc.). 

Btzt  by  reason  of  the  fact  that  two  substances  often  tmite  in  different 
proportions  the  names  of  the  resulting  compounds  are  so  contrived  by 
Latjn  prefixes  and  suffixes  as  to  indicate  quite  directly  its  molecular  com- 
position.   Thus, 

Sa<6oxide  of  copper  C«2  O      Ratio  of  O  is  < 

Protoxide  of  manganese  (  °-  monoxide)  MnO 
DnUoxide  of  lead  Pb  O2 

5rj9M«oxide  of  manganese  Mn^  0%        "  " 

Btfcoxideof  silica  (—dioxide)  SiOt  **  *' 

7*rroxk]e  of  chromnmi  (  — frtoxide)      Cr0%  "  " 

Peroidde  of  Nickel  Ni2  O, 

The  same  prefixes  may  be  applied  to  other  compounds, 
sulphur,  etc 

Acids,  Bases  and  Salts. — ^When  an  acid  and  a  bau  or  alkali  are  brought 
together  chemically  in  the  proper  proportions,  they  neutralize  each  other, 
and  the  resulting  chemical  products  are,  1st,  waier  and  2nd,  salt. 

An  acid  may  be  defined  as  a  substance  containing  hydrogen,  which  it 
readily  exchanges  for  a  metal  when  treated  with  a  metal  or  metal  compoimd 
called  &base. 

A  base  is  a  substance  containing  a  metal  combined  with  hydrogen  and 
oxygen,  which  metal  it  readily  exchanges  for  hydrogen  when  treated  with 
an  acid. 

A  salt  is  a  neutral  substance,  one  of  the  products  of  the  action  of  an 
acid  on  a  base,  the  other  product  being  water, 

Oxides  and  Hydroxidas,^ — An  oxide  is  a  compound  of  oxygen,  more 
especially  with  a  metcU  or  metalloid.  The  principal  classes  of  oxides  are 
i\)  basic  or  metallic  oxides,  and  (2)  acid  oxides  or  acid  anhydrides. 
Examples:  (1),  calcium  oxide  (CaO);  (2),  sulphuric  anhydride  (5  O3). 
A  hydroxide  mav  be  formed  (1)  by  treating  oxides  with  water,  and  (2^  by 
deoomposing  salts  by  the  addition  of  soluble  hydroxides  to  their  solutions. . 
ExampSril),  Ca  0-\-H%0^Ca{0H)2\  (2),  Mg  SO4  +  2  Na  OH^NatSOt^ 
Mg  (OH}i. 

Add  Cotnbinatloos. — ^An  acid  is  a  compound  containing,  in  each  mole- 
Cole,  one  or  more  atoms  of  hydrogen  which  may  be  displaced  by  a  metal  or 
by  a  compound  poss^sing  metallic  functions.  If  the  acid  molecule  contains 
one  hydrogen  atom  it  is  monobcuic;  two  hydrogen  atoms,  bibasic;  three 
hydrogen  atoms,  tribasic;   more  than  one  hydrogen  atom,  polybasic,  etc. 

^in^en  acid  contains  oxvgen  the  suffix  — ic  is  usually  given  to  the 
characteristic  element  of  the  compound,  as  sulphuric  acid  for  HjSOji. 
But  if  two  adds  can  be  formed  with  oxygen  from  the  same  characteristic 
element,  that  one  which  is  the  more  highly  oxidized  has  the  suffix  — ic  while 
the  otlwrr,  the  less  oxidized,  takes  on  the  suffix  — ous.  In  cases  where  more 
than  two  acids  are  formed  by  different  proportions  of  oxygen  the  above  are 


822  17— NATURAL  HISTORY  OF  MATERIALS, 

further  modified  by  the  preffixes  hyper^,  meaninff  over,  and  kypo^,  mean- 
ing under.  Thus  we  may  have  according  to  the  relative  proportions  of 
oxygen  present,  say  in  the  sulphur  acids: 

/lyposulphurous  acid,   Ht  OSjt.     ^Least  proportion  of  oxygen.) 
sulphuroia      **      H3S  Oi.    (Less  proportion  of  oxvgen.) 
hyp4n\x\p\i\3i(ms    "  (Per  otten  used  instead  of  kyptr.) 

Ay^osulphuric        "  (This  is  preferable  to  c.) 

sulphuric        *',      Hi  SO4      (Greater  proportion  of  oxygen.) 
n)      hypitnalphuru:       "      HfSf  Og    (Greatest  proportion  of  oxygen.) 
Salts. — We  have  seen  that  an  acid  contains  one  or  more  atoms  of  hydro- 
gen which  may  be  replaced  by  metallic  atoms  or  basic  radicals.    When  such 
a  change  takes  place  in  an  acid  the  resulting  compotmd  is  a  salt.     The 
names  of  the  salts  so  formed  are  related  to  the  acids  which  produce  them,  as 
ic    acids    form        ate  salts. 

hypo — ^-ous    "  "    hypo        Ue      ** 

Thus,  stdphuric  add  (Hs  SO^)  and  soda  (Na)  form  8tilpha<#  of  soda 
{Na^  SO4) ;  hypasvdphuTOus  acid  {H^  SO^)  and  soda  form  kyposviiphiu  of 
soda.  etc. 

In  line  with  the  above  definition  we  may  say  further  that  any  base  in 
which  one  or  more  of  the  hydrogen  atoms  have  been  replaced  by  non-metallic 
atoms  or  acid  radicals,  is  a  salt. 

A  salt  may  be  formed  by  compounding  a  metallic  oxide  with  an  anhy- 
dride. 

Periodic  Law. — "The  properties  of  the  elements,  as  well  as  the  forms  and 

f>roperties  of  the  compounds,  are  in  periodic  dependence  on,  or  form  periodic 
unctions  of.  the  atomic  weights  of  the  elements."  This  law.  conceived  by 
Newlands  and  later  i>erfectea  by  Mendel^ff,  Meirer  and  othu^  is  a  funda- 
mental law  of  Chemistry  If  the  elements  are  arranged  in  series  on  an 
ascending  scale,  according  to  their  atomic  weights,  this  series  can  be  made 
to  exhibit  Family  Groups  showing;  common  characteristics,  in  much  the 
same  manner  as  the  natural  divisions  or  classifications  ot  the  mineral, 
vegetable  and  animal  kingdoms. 

Table  2  is  such  a  grouping,  by  Meyer.  The  inclined  lines  indicate  a 
spiral  or  continuous  series  if  the  table  were  wrapped  around  a  cylinder. 
The  vertical  columns  show  the  Groups,  I.  II.  III.  etc..  with  sub-divisions  A  and 
B.  Each  group  has  common  characteristics,  while  those  of  the  subnlivisions 
are  still  more  in  common.  The  vacant  spaces  are  for  other  elements,  most  of 
which  have  not  yet  been  discovered  or  their  atomic  weights  determined. 
It  is  a  significant  fact  that  by  means  of  this  law  Mendel^eff  foretold  the 
existence  of  some  of  the  elements  long  before  their  discovery,  and  calculated 
their  atomic  weights  correctly. 


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PERIODIC  LAW, 


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834 


n.— NATURAL  HISTORY  OF  MATERIALS. 


Chemical  SubsUnces  and  Their  Common  Names.— » 

(Knowledge  Year  Book.) 


Alum— Sulphate  of  aluminum  and 
potassium. 

Aqua  fortis— Nitric  acid. 

Aqua  regia  ->  Nitro-hydrochloric  add. 

Calomel  — Hercurous  chloride. 

Carbolic  acid  —  Phenol. 

Caustic  potash  —  Potassium  hydrate. 

Caustic  soda  — Sodiimi  hydrate. 

Chalk  — Calcium  carbonate. 

Copperas  —  Sulphate  of  iron. 

Corrosive  sublimate  —  Mercurous 
chloride. 

Cream  of  tartar— Bitartrate  of  po- 

^    tassium. 

Epsom  salts  —  Magnesium  sulphate. 

Fire  damp  — Light  carbtirctted  hy- 
drogen, methane. 

Glaubers'  salt  —  Sodium  sulphate. 

Grape  sugar  —  Glucose. 

Goulard  water  — Basic  acetate  of 
lead. 

Iron  pyrites  —  Sulphide  of  iron. 

Jewelers'  putty  — Oxide  of  tin. 

Laughing  gas  — Nitrous  oxide. 

Lime  — Calcium  oxide. 

Lunar  caustic  —  Silver  nitrate. 

Mosaic  gold  —  Bisulphide  of  tin. 

Muriatic  acid  —  Hydrochloric  acid. 

Plaster  of  paris— Calcium  sulphate. 


Realgar  — Sulphide  of  arsenic. 

Red  lead  -  Oxide  of  lead. 

Rochelle  salt— Sodium  potassium  tar- 

trate. 
Sal  ammoniac  — Ammonium  chloride. 
Salt,  common  —  Sodium  chloride. 
Salt  of  tartar  (potash)  —  Potassium 

carbonate. 
Saltpetre  —  Potassium  nitrate. 
Salt  of  lemon  —  Oxalic  add. 
Slacked  lime— Caldum  hydrate. 
Soda,  washing  — <^cium  carbonate. 
Soda,  baking— Soditmi  bicarbonate. 
Soda  — Sodium  carbonate. 
Spirits  of  hartshorn  — Solution  of  Am* 

monia. 
Spirits  of  salt  —  Hydrochloric  add. 
Sugar  of  lead  —  Lead  acetate. 
Tartar  emetic  —  Potassium  antimony 

tartrate. 

Verdipris  —  Basic  acetate  of  copper. 
Vermillion  —  Sulphide  of  mcrctuy . 
Vinegar— Dilute  Acetic  acid. 
Vitriol,  blue  —  Oapper  sulphate, 
green  —  Ferrous  sulphate, 
oil  of —  Sulphuric  add. 
white  —  Zinc  sulphate. 
Volatile  alkali  —  Ammonia. 


B.— MINERALOOICAL. 

Minerals  Compose  Rocks. — Mineralogical  substances  include  all  thoa 
natural  objects  which  belong  to  the  Inorganic  Kingdom,  whether  solici 
liquid  or  gaseous.  A  mineral  may  be  defined  as  a  nattiral.  inorganic,  home 
geneous.  chemical  substance ;  while  a  rock  is  made  up  of  one  or  more  zninen 
masses  mixed  in  fairly  constant  proportions  throughout. 

(a)  Hardness. — The  hardness  of  a  mineral  is  its  resistance  to  abraskn 
There  are  ten  recognized  degrees  of  hardness,  typified  by  the  followis 
minerals: 

1.  Taic. — Soft  and  greasy:  easily  scratched  by  finger  naiL 

2.  Gypsum. — ^Not  easily  scratched  by  the  finger  nail. 

3.  Calcite. — Scratches  copper  coin;  is  scratched  by  same. 

i.  Fluorite. — Not  scratched  by  copper;  and  docs  not  scratch  slaai 

6.  ApaiiU. — Barely  scratches  glass;  easily  scratched  by  a  knife. 

6.  Orthoclas0. — Easily  scratches  glass;  barely  scratched  by  a  file. 

7.  Quarts. — Not  scratched  by  a  knife. 

8.  Topas, — Not  scratched  by  a  file. 

9.  Sapphire. — About  Vioo  as  hard  as  diamond. 
10.  Diamond, — Hardest  substance  known. 


(6  to/).  Other  Physical  Characteristics. — Minerals  are  often  identified  ' 
the  above  characteristics  of  hardness  and  also  by  the  kinds  and  degrees 
the  following: 

(b)  tenacity,  (c)  cleavage,  (d)  fracture,  (c)  feel.  (0  taste,  (g)  odj 
(h)  lustre,  (i)  color,  (j)  transparency,  (k)  translucency.  0)  oi>«kQi 
ness,  etc. 


MINERALOGICAL.  826 

a.— Classification  op  Importamt  Mimbral  Spbcibs.* 
L  Native  Elements. 
A  Series. — ^Non-basic  or  electro-positive  elements. 

1.  Gold  Group. — Gold,  silver,  hydrogen,  potassium,  sodium,  etc. 

2.  Iron  Group. — Platinum,  palladium,  mercury,  copper,  iron,  zinc,  lead, 
cobalt,  nickel,  chromium,  manganese,  calcium,  magnfwium,  etc. 

2.  Tin  Group. — ^Tin,  titaniim:i,  eirconiim:i,  etc. 
B  Series. — Elements  generally  electro-negative. 

1.  Arsenic  Group. — Arsenic,  antimony,  bismuth,  phosphorus,  vana- 
dium, etc. 

2.  Sulphur  Group. — Sulphur,  tellurium,  selenium. 

3.  Carbon-Silicon  Group. — Carbon,  silicon,  diamond,  graphite. 
C  Series. — Elements  alwasrs  negative. 

1  Chlorine,  bromine,  iodine. 

2.  Fluorine. 

3.  Oxygen. 

n.  Sulphides. — Sulphides,  tellurides,  selenides,  arsenides,  antimonides,  bis- 
muthides. 

A.  Binary    Compotmds. — Sulphides   and   telltirides  oi    metals   qi   the 

sulphur  and  arsenic  groups. 

(a)  Realgar  Group.     RS.  Realgar,  ^5  5. 

(b)  Orpiment  Group.   Rt  S%.     Orpiment,  ilf*  S% 

St:buite,5fr2<^a 
Bismuthinite.  Bit  St. 

(c)  Tetradymite.  B»t  (r*.  S)s. 

(d)  Molybdenite  Group.    RSf     Molybdenite.  Mo  5a. 

B.  Binary  compounds. — Sulphides,  tellurides,  etc.,  of  metals  of  the  gold 
iron  and  tin  groups. 

1.  Basic  Division. — Dyscrasite.  il£i56;  i4£A56.    Domeykite,  Cmi  i45. 

2.  Proto  Division.    RS  (or  /?2  5),  X  5#,  -R  Te. 

(a)  Galenite  Group.     Argentitc.  i4g«  5.  Crookesite,  (Cms,  7/.  il<)  5#. 

GaTenite,  Pb  S. 

(b)  Blend  Group.     Sphalerite,  Z»  S. 

(c)  Chalcocite  Group. 

S  Cinnabar,  Hg  S  (or  Hgt  5j).  Millerito,  Ni  S, 
Pjrrrhotite,  Ftj  Sh  mostly. 
Greenockite,  Cd  S  (or  Cdt  Sj). 


8.   Deato  or  Pyrite  Division. 

(a)  Pyrite  Group.     Pyrite. 

(b)  Marcasite  Group.  Marcasite,  Fr  5j 
Arsenopyrif 
Sylvanite. 

.  Ternary  Compounds. — Sulpharsenites,  sulphantimonites.  sulphobis- 
muthites. 


(a)    Pvrite  Group.     Pyrite,  F*52.    Chalcopyrite,  Ci*  F#  Sj. 
"  '    Marcasite  Group.  Marcasite,  Fr  Sf. 

Arsenopyrite,  FeAsS^Ft  S2+F0  Ast. 


(a)  Group  I.    R(As,Sb)tS4''RS+(AsSbhSa. 

<b)  Subgroup.    Rt(As,Sb,Bt\S9-ZRS+2iAs,Sb,Bi)iSt. 

(c)  Group  II.    /?,  iSh,  Ash  S5-  2RS+  {Sb,  Ash S». 

id)  Group  III.    RtiAs,  56)2  ^6-  3/?5+  (As,  SbhSt. 

<e)  Group  IV.    R.(As.  Sb.  B*h  57  -  4/25  +  (As.  Sb,  Bi)t  Sf 

to  Group  V.    RtlAs,SbhSg~iRS+(As,SbhSt. 

m.    Cbkuides,  Bromides,  Iodides. 

A.  Anhydrous  Chlorides.    R{Cl,Bi,D\  Rt(Cl,Br,I)',  RCk- 

HaKtc.  NaCl.  Calomel.  HgCl. 

Sylvite.  KCl.  Sal  Ammoniac,  NHtPL 

B.  Hydrotis  Chlorides. 
C    Ozychlorides. 

IV.    Fluorides. 

A.  A«hyd«,u.Fl«oride..   {^;^^:%%fX,F„(„  tNaF+AlF^. 

B.  Hydrous  Fluorides. 

*  Mostly  in  accordance  with  Dana's  Classification.^^ '^'^^^^^^^g'^ 


826  n.— NATURAL  HISTORY  OF  MATERIALS, 

3. — Classification  of  Important  Mikbrals. — Cont'd. 
V.   Oxygen  Compounds. 
a.  Oxides. 

A.   Oxides  of  metals  of  the  gold,  iron  and  tin  groups. 
1.    Anhydrous  oxides. 

(a)  Protoxides.   RO  or  (i^gO).   Cuprite,  Cu%  O.    Zindte.  Zn  O, 

Tenorite,  Cu  O. 

(b)  Sesquioxides,  RO^.    Conindum,  AI 0%.      Hematite.  F#  On. 

(c)  Compounds  of  protoxides  and  sesquioxides,  RR  O^  (or  RO+ROt). 

Spinel  Group.— Spinel,  Mg  Al O^i^Mg  0+Al 0»). 

Magnetite.  Fe  Fe  Otior  Fe^  O4)  '^FeO+F^d. 
Pranklinite,  (Fe,  Zn,  Mn)  (Fe,  Mn)  O4. 
Chromite.  Fe  Cr  O4,  or  (Fe,  Mg,  Cr)  (Al,  Fe, 

Cr)04. 
Uranite.  t/g  0»(U  O2+  2U  Oa). 

(d)  Deutoxides.    RO2. 

2.    Hydrous  oxides.    Targite,  H  2  Ft  Or      Diapose.  H2AI  0«. 
Gothite,  IfzFeOA-' HoFe  Ot+2Fe  Oa. 
Manganite,  H^Mn O^^HMn  Ofl+2 Mn  Oj. 
Limonite,  if*  Ftfj  O^'^Ht  Fe  0^+  Fe  O9, 


B.   Oxides  of  metals  of  the  arsenic  and  sulphur  ^t>ups. 

Arsenolite,  A52  Oz.         Bismite,  BU  O^. 
Molybdite.  Mo  Os.        Tungstitc,  W  O9. 


C.    Oxides  of  the  carbon-silicon  group.  Quartz.  Si  O2. 

.     Tridymite,  Si  0%.  Opal,  Si  0%. 

fi.    Ternary  Oxide  Compoxmds. 
A.  Silicates. 

1.    Anhydrous  silicates.  ^ 

1**  Bisilicates.    R  Si  0%, 

(a)  Amphibole  Group. — Wollastonite,  Ca  Si  Os. 

Pyroxene  ( —  Augitc) .  R  Si  Oz',  R  may 
be  Ca,  Mg,  Fe,  Mn,  Zn,  KOi,  Na^. 

(b)  Amphibole  Section.  Amphibole.  R  Si  Oz  (var.,  Horn- 

Beryl,  Bez  Al  Sin  Oig.  blende). 

2f*  Unisilicates,  Rz  Si  0«. 

.)    Chrysolite  Group. —  Chrysolite,  (Mg,  F*) a  S«04.  Olivene. 
'    Willemite  Group. — Willemite,  Zna  Si  O4. 
Garnet  Group. — R3  RSiz  0^. 
Vesuvianite  Group. 

Epidote  Group. — -Epidotc,  Hz  Coa  Rz  Sia  Oza. 
Mica  Groiip. — Biotite.    Muscovite. 
,     Scapolite  (jroup. 
(m)  Nephelite  Group. 

(n)    Feldspar  Group. — Anarthite.      Labradorite.       Andesite. 
Oligoclase.    Albite.    Orthoclase. 

8*^  Subsilicates. 


(jb)   Andalusite.  Fibrolite,  AlSiO^.    Cyanite,  A/ Si  Oa 

Topaz.  A I  Si  O5.  Euclase,  /fj  Bez  AlSi^  Oiq. 

Datolitc.  Hz  Coz  Bz  Siz  Oiq.  Titamite,  Ca  Tt  Si  O4. 

(c)    Staurolite. 

.    Hydrous,Silicates. — I.     General  Section. 
Bisilicates. — Pectotite;  lanmontite;  okenite;  crysocolla;  alipite. 
Unisilicates. — Calamine;    prenitc. — ^Thorite,  Pyrosmalite. 
Subsilicates. — Allophane. 

II.    Zeolite  Section.  Digitized  by  GoOqIc 


MINERALOCICAL,  827 

3. — Classification  of  Important  Minbrals. — Cont'd. 
Oxygen  Compounds — Cont'd. 

IIL  Msrsarophyllite  Section. 

BisUicstes. — ^Talc;  pyrophylUte;  sepiolite. 
Unisilicates. 

Serpetitine  Group. 
Kaolinite  Group. 
Finite  Group. 
Hydro-mica  Group. 
Subsilicates. 

Chlorite  Group. 

B.  Tantalates.  Columbates. 

C    Phosphates.  Arsenates,  Vanadates,  etc 
Anhydrous. 

Xenotime,  Yt  P%  Os- 
Apatite  Group. — ^Apatite.    Vanadinite. 
Antimonates. 
Hydrous. 

Antimonates. 

Nitrates.     Nitre.  K  N  0»,       Soda  nitre.  Na  7V0». 

D.   Borates.  Boracite.  Af£7  5»6C^08-2Af*8B8  0,4+Af£  Cij. 

Borax.  Nat  fi«  O7+  10  ofl-  2(Na  BOz  +  HBO^  +  9aq. 

B.  TungsUtesC/eirOO.   Molybdates  (i?  AfoO«).Chromates(i?C«0«). 

P.    Sulphates. 

Anhydrous  R  SO4. 

Barite  Group.    Barite,  Ba  SO4.    Anglesite.  Pb  SO4. 
Hydrous.  Mirabilite.  Na^  SO4  + 10  aq. 

Gypsum,  Ca  SO4+ 10  o^.  var..  selenite. 
Epaomite.  Mg  SO4  +7aq. 
Copperas  Group. — Chalcanthite.  Ca  SO4+6  aq. 
Alum  and  Halalrichite  Groups. — Copiatite. 

Aluminite  Al  SOt+  9  aq. 
Telluratcs.— Montanite.  Bit  F#  Oe+  2  aq. 

G.   Carbonates. 
Anhydrous. 

Calcite  Group.    RCOz.    Caldte,  Ca  COi. 

1.  Crystallised:  Iceland  spar.  Fountainblue  limestone. 
Satin  spar. 

2.  Massive:  Granular  (Saccharroidal) :  Marble.  Statu- 
ary  marble.  Shell  marble.  Lithographic  stone, Brec- 
cia marble,  Pudding  stone  marble.  Hydraulic  lime- 
stone. 

Soft  Compact  Lim^tone:  Chalk,  Calcareous  marl. 
Concretionery,  massive:  Oolite. 

a.  Stalactites. 

b.  Stalagmites. 

c.  Calc-sinter.    Travertine.  Calc-tufa. 

d.  Agaric  mineral. 

e.  Rock-meal. 
Dok>miU.  (Ca,  Mg)  COjl. 

Aukerite.  Ca  CQ^  +  Fe  COa+  x  (Ca  Mg  Ct  OJ. 
Magnesite.  MgCOt. 
Siderite.  F#  CDs- 
Rhodochrosite.  Mn  COz. 
Smithsonite.  Zn  COz. 

Aragonite  Group.  ^  j 

Hydrous.  °  a  '^^^  '^y  V^OOg IC 


328  17.— NATURAL  HISTORY  OF  MATERIALS. 

3. — Classification  of  Important  Minerals. — Concl'd. 
VL   Hydrocarbons. 

1.   Simple  (no  oxygen). 

(a)  Marsh  Gas  Series.  CnHta+t.  Includes  liquid  naphthas  and 
more  volatile  parts  of  petroleum;  also  scheercrite  and 
chrismatite. 

Petrolexun. — Mineral  oil.  Kerosene.  Ber^ol,  Erdol. 

(b)  Olefiant  or  Ethylene  Series.  Cn  Hza.  Pittolium  group  of 
liquids  or  pettarsphalts  (mineral  tar)  and  the  paraffines. 
Paraffin  Group. 

(c)  Camphene  Series.    Cn  Hta-A- 

Id)    Benzole  Series.    Cn  Hta-9.    Benzole  liquids, 
(e)    Naphthalin  Series.    Cn  Hin- 12. 

Naphthalin  (found  in  Rangoon  tar). 
2.   Oxygenated. 

Succinate  (amber). 
Appendix  to  Hydrocarbons. 

Asphaltum. — Bitumen,  Asphalt,  Mineral  pitch. — Mixture  of  dif- 
ferent hydrocarbons,  part  of  which  are  oxygenated. 

Following  substances  are  closely  relatea  to  asphaltum: 
Grahamite,  Albertite,  Pianzite,  Wollongongite. 
Mineral  Coal. — Made  up  of  different  kinds  of  hydrocarbons  with 
perhaps,  in  some  cases,  free  carbon. 

1.  Anthracite. 
Bituminous. 

2.  Coking. 

8.  Non-coking. 

4.  Cannel  coal. 

5.  Torbanite. 

6.  Brown  coal. 

7.  Earth  brown  coal. 

(m).  Blowpipe  Characteristics.— The  following  important  flame  colorations 
result  from  the  blowpipes:  Carmine,  from  lithium  compounds;  scarlet,  from 
strontium  compounds;  yellowish  red,  from  calcium  compotmds;  vellow,  from 
sodium  and  all  its  salts;  yellowish  green,  from  barium  compounos,  molybde- 
num sulphide  and  oxide;  pure  green,  from  compotmds  of  tellurium  or  thal- 
lium* emerald  green,  from  most  copper  compounds  with  hydrochloric  acid; 
bluish  green,  from  phosphoric  acid  and  phosphates  with  sulphiiric  acid; 
feeble  areen,  from  antimony  or  ammonium  compounds;  whitish  green,  from 
zinc;  light  blue,  from  arsenic,  selenium  and  lead;  asure  blue,  from  copper 
chloride;  violet,  from  potassium  compounds. 

Some  of  the  Important  Minerals. 

Thb  Gold  Minerals. 
Tellurides. — Sylvanite.  calaverite.  krennerite. 
Ores. — Pyrite,  arsenopyrite,  pyrrhotite,  and  various  sulphides,  etc. 

Thb  Silver  Minbrals. 
Ordinary  silver  ores  contain  less  than   1%  of  the  silver  compounds 
distributed  through  various  minerals. 

Thb  Potassium  Minerals. 
Chlorides. — Sylvite.  camallite,  kainite.   Sulphates. — Kalinite.    Nitrate, — 
Nitre.    The  chlorides  are  the  natural  potash  salts. 
Thb  Sodium  Minerals. 
Chloride. — Halite.    Sulphate. — Mirabilite.    Nitrate. — Soda  nitrate.   Car- 
bonate.—From  Na2  CO3,  H  Na  CO9.   2H^. 

The  Lithium  Minerals. 
Used  in  medicine. 

The  Platinum  and  Iridium  Minerals. 
Metals. — Platinum,  iridosmine.  Arsenide. —  Spcrrylite.  Purified  pltUi- 
num. — ^Used  in  incandescent  lamps,  for  electrical  contact  points,  and  in  the 
so-called  "oxidizing  of  silver."  Iridosmine. — Pointing  gold  pens;  phosphide 
of  iridium  is  used  for  pointing  tools  and  stylograpnic  pens  and  for  kziife 
edges  in  the  most  delicate  balances. 


IMPORTANT  MINERALS.  829 

Thb  Mbrcurt  Minerals. 

Sulphide. — Cinnabar.    C"Ater*<i*.— Calomel. 

Uus. — Mercury  is  used  in  extraction  of  gold  and  silver  from  their  ores; 
giannfacture  of  vermillion;  barometers,  thermometers;  silvering  mirrors; 
mcdiciiie. 

Thb  Coppbr  Minerals. 

Sulphides. — Chalcocite,  bomite,  chalcopyrite.  Sulpho^rsenite. — Enarg- 
ite.  SulpkoantimonUe. — Tetrohedrite.  Oxtdes, — Cuprite,  tenorite.  Basic 
chloride. — Atocamite.  Sulphates. — Chalcanthitc.  Carbonates. — Malachite, 
axurite.    Silicates. — Chrysocolla.  diastase. 

Ores. — Chalcopyrite,  bomite,  native  copper,  cuprite,  malachite,  augite. 

Uses  of  copper. — Electrical  work;  alloys  with  zinc  and  tin,  such  as  brass, 
yellow  metal,  bronze,  bell  metal.  German  silver. 

The  Iron  Minerals. 

Metal. — Iron.  Sulphides  and  arsenides. — Pyrrhotite,  pyrite,  marcasite. 
arBenopjrrite.  Icucopyrite.  Oxides. — Magnetite,  franklinite,  hematite,  menac 
canite.  turgite,  goethite,  melanterite.  Sulphates. — Copiatite,  melanterite. 
Pkosphates. —  Vivianite.  triphylite.  Arsenates. — Scoroditc,  pharmacosiderite. 
Carbonate. — Siderite.    Chr ornate. —QhTomWe. 

Ground  for  paint. — Limonite,  hematite.  Used  as  iron  ores. — Hematite, 
fimonite.  magnetite,  siderite.  For  extracting  sulphur. — Pyrite,  marcasite, 
pyrrhotite.  For  arsenic. — Arsenopyrite.  For  chromium. — Potassium  bi- 
chromate, potassium  chromate,  ferro-chromium.  For  tungsten. —  Wolfram- 
ite, scheelite.  For  gold  and  silver. — Pyrite.  arsenopyrite.  For  nickel. — 
Pyrrhotite. 

Thb  Cadmium  Minerals. 
Sulphide. — Greenoddte,  is  a  yellow  pigment  6i  fixed  color. 

The  Zinc  Minerals. 
Sulphide. — Sphalerate.     Oxide. — Zincite.     Sulphate. — Gostarite.     Car^ 
houates. — Smithsonite.  hydrozincite.    Silicates. — Willemite.  Calamine. 

Ores  of  Bine. — Spalerite,  smithsonite,  calamine,  willemite,  zincite.  Zinc 
oxide  also  made  from  franklinite. 

Uses  of  metallic  sine. — Galvanizing  iron  wire  or  sheets;  manufacturing 
brass;  sheet  zinc,  zinc  diist.    Zinc  white,  a  paint,  is  zinc  oxide  grotmd  in  oiL 

The  Lead  Minerals. 

Ores. — Galenite,  cerussite.     Uses  of  lead. — Manufacture  of  white  lead, 

preparation  of  red  lead,  litharge,  shot,  lead  pipe,  sheet  lead.  Alloys. — ^With 
antimony  for  type,  and,  friction-bearings. 

The  Cobalt  Minerals. 

Sulphides  and  arsenides. — Linnaeite,  cobaltite.  smaltite.  Arsenates. — 
Erythrite. 

CobaU  blue. — Cobalt  and  alumina  compound.  Ainman's  green. — Com- 
pound of  cobalt  and  zinc  oxide. 

The  Nickel  Minerals. 

Sulphides. — Millerite.  pentlandite,  gersdorffite.  Arsenides. — Nicolite, 
cfaloanttiite.  Ar^nate. — Annabergite.  Carbonate. — Zaratite.  Silicate. — 
Gamierite. 

Alloyed  with  copper,  iron  and  arsenic  in  making  German  silver;  with 
copper  (26%  Ni  and  75%  Cu)  in  the  five-cent  piece;  with  steel  in  making 
nickel  steel. 

The  Manganese  Minerals. 

Sulphide. — ^Alabandite.  Oxides. — Braunite.  hausmaunite.  pyrolusite. 
manganrtc,  i)silomelane.    Carbonate. — Rhodochrosite,  wad. 

Alloys  with  iron,  form:  Spiegeleisen,  ferro-manganesc  (for  manufacture 
of  steel).    Used  as  manganese  ores. — Pyrolusite,  psilomelane. 

The  Calcium  Minerals. 
Limestone  and  marble  are  ma^ive  calcite  and  dolomite  and  are  used 
largely  in  building  construction.    Limestone  is  used  for  hydraulic  cements; 
and  gypsum,  for  plaster  of  pans  and  wall  plaster;  also  in  paper  making. 


330  U.^NATURAL  HISTORY  OF  MATERIALS, 

Thb  Magnbsium  Minbrals. 
Calcined  magnesite  is  used  as  a  lining  for  converters  in  the  basic  process 
for  the  manufacture  of  steel. 

Thb  Tin  Minerals. 
Sulphide. — Stannite.     Oxide. — Cassiterite  (ore  of  tin). 
Uses  of  tin. — ^Tin  plate  (sheet  iron  coated  with  tin)  for  making  cans. 
kitchen  utensils,  etc.  Alloy. — Bronze,  bell  metal,  pewter,  solder,  tin  amalgam. 

Thb  Titanium  Minbrals. 
Oxide  of  titanium  used  for  glazing  porcelain. 

Thb  Thorium  Minerals. 
Oxide  of  thorium,  thoria.  constitutes  about  99%  (other  1%  is  cerium 
oxide)  of  the  mantle  of  the  Welsbach  incandescent  gas  lamp. 

Thb  Arsbnic  Minerals. 
Sulphides. — Orpiment,  realgar.  Sources. — ^Prom  arsenides  and  arseno- 
sulphides  of  iron,  cobalt  and  co[)per.  The  white  arsenic  is  a  poisonoxxs 
oxide,  and  is  used  in  dyeing,  medicine,  sheep  washing,  calico  printing,  timber 
preservative,  for  fly  paper,  rat  poisons  and  glass  manufacture.  Paris  green 
IS  an  arsenate  of  copper. 

The  Antimony  Minerals. 
Sulphides. — Stibnite,  kcrmesite.    Oxide. — ^Valentinite. 
Uses. — ^The  sulphide  is  used  in  viUcanizing  rubber. 

Thb  Bismuth  Minerals. 
Uses. — Alloys  with  tin.  lead  and  cadmium,  expand  in  cooling. 

The  Sulphur  and  Tellurium  Minerals. 
Uses  of  Sulphur. — Manufactvire  of  sulphuric  acid.  ^\m powder,  matches, 
rubber  ^oods,  bleaching,  medicines,  etc.     Tellurium  is  closely  related  to 
sulphur  m  a  chemical  way. 

The  Uranium  Minerals. 
A  small  Quantity  of  uranium  in  steel  increases  the  elasticity  and  hard- 
ness.   Ore. — Uraninite  (principal  source  of  radium). 

The  Molybdenum  Minerals. 
Sulphide. — Molybdenite.    Oxide. — Molybdite. 
Uses. — ^The  metal  is  becoming  important  as  an  alloy  with  steel. 

The  Aluminum  Minerals. 

Ores. — Bauxite  is  the  principal  ore. 

Uses  of  Aluminum. — Where  lightness,  strength  and  non-corrosiveness 
are  desirable.  It  is  replacing  sheet  copper  and  zinc  and  is  used  as  bronze 
powder  and  alumina  leaf  for  silvering  letters  and  signs.  It  is  replacing 
copper  wire  as  electrical  conductors.  In  metallurgy  it  is  becoming  important 
in  welding  pipes,  rails  in  place,  and  steel  castings.  By  adding  less  than  1% 
of  aluminum  to  the  melted  metal  it  prevents  blow-holes  in  castings  of  steeU 
copper  and  zinc. 

The  Boron  Minerals. 

Acid. — Sassolite.  Borates. — Borax,  ulexite,  colemanite,  boracitc.  Borax 
is  used  in  welding;  as  a  base  of  enamels  on  metal  or  porcelain;  as  a  flux; 
as  an  antiseptic  in  packing  meat;  for  powders,  soaps,  washing,  dyeing. 
tanning. 

The  Hydrogen  Minerals. 

Water  is  the  most  important,  one-eighth  of  its  volume  being  hydrogen. 
Hydrogen  is  present  in  combination  with  carbon  forming  marsh  gas,  petxv>-> 
leum,  ozocerite,  etc. 

The  Carbon  Minerals. 

Diamond  and  graphite  are  pure  carbon.  It  is  present  in  a  large  numbear' 
of  solid,  hauid  and  gaseous  compounds,  as  natural  gas,  petroleum.  asphaltA^ 
bitumens,  fossil  resins,  mineral  waxes,  coal.  Carbon  is  present  in  all  organic^ 
matter,  entering  with  plant  life  from  the  carbon  dioxide  of  the  air;  and 
exists  to  a  large  extent  in  natural  gas. 


IMPORTANT  MINERALS.    LITHOLOGY.  831 

Tub  Silica  Minbrals. 
A. — Silica. 
B. — ^Anhydrous  Silicates. 

1.    Disilicates  and  polysilicates. 
II.    Metasilicates. 

III.  Orthosilicates. 

IV.  Subsilicates. 
C. — ^Hydrous  silicates. 

I.    Zeolite  Division. 
II.    Mica  Division. 

III.  Serpentine  and  Talc  Division. 

IV.  Kaolin  Division. 
D. — Titano  silicates. 

Somg  of  th€  Mast  Important  Silicates: — 

Graniie, — Contains  syenite,  gneiss,  basalt,  diorite,  andesite.  which  are 
compounds  of  silicates  (usxmlly  three  or  more)  and  usually  quartz,  the 
ieldnpars  and  micas,  pyroxene  and  amphibole. 

Sandstone. — Made  up  of  grains,  mainly  quartz,  with  perhaps  feldspar, 
rnin^   of  Other  mineral: 
siEceotis;  ] 

ferrasinous;  According  to  the  nature  of  the  cement  which  binds  the 

calcareous;         [     grains  together, 
axsill^tceotis;      j 

Bln€sU>n$. — Hard,  durable,  fine-grained  sandstone,  cemented  with  sili- 
oeotis  material. 

SlaU. — Hardened  clay.    Used  mostly  for  roofing,  sinks,  blackboards. 

Fibrous  talc  and  compact  talc. — Used  in  paper  manufacture.  The  latter, 
aoapstone,  is  very  valuable  because  refractory,  for  vise  in  furnaces,  crucibles, 
sinka.  baths,  hearths,  electric  switch-boards,  cooking  utensils;  also  used  in 
paints,  slate  pencils,  crayon,  gas  tips,  as  a  lubricant,  and  in  soap  making. 

Mica. — Muscovite,  phlogopite.  biotite,  have  become  of  great  importance 
as  non-conductors  in  electrical  apparatus ;  also  for  stove  and  f lutiace  doors. 

Asbestos. — This  is  fibrous  amphibole  and  serpentine.  It  is  used  in  the 
rcantifacture  of  incombustible  paper,  cloth,  cement,  boiler  and  steam-pipe 
covering  and  packing  rope  or  yam  for  valves. 

Serpentine. — A  marble. 

Feidspat. — Crushed  and  mixed  with  kaolin  in  the  manufacture  of 
porcelain. 

Quarts. — Used  in  the  manufacture  of  sandpaper,  glass,  porcelain,  hone- 
stones,  oilstones  and  as  a  flux.  Ground  flint  is  used  as  a  scouring  agent  in 
soaps. 

Infusorial  earth. — Calcined  and  made  into  water  filters,  polishing  pow- 
ders, soap  filling  and  boiler  and  steam-pipe  covering. 

Kaoltnite  and  clay. — Clay  is  decomposed  feldspar  and  other  silicates. 
It  lies  in  beds  composed  partly  of  some  hydrous  aluminum  silicates,  as 
kac4inite,  but  is  usually  nuxed  with  quartz,  mica,  undecomposed  feldspar, 
oxides  and  sulphides  of  iron.  The  industry  includes  the  manufacture  of 
comnoon  brick,  paving  brick,  fire-brick,  hydraulic  cement,  earthenware, 
fi'onewarc.  porcelain,  terra  cotta,  sewer  pipe,  drain  tile. 

FuUer's  earth. — ^A  clay  used  in  refining  and  clarifying  mineral  oils. 

Rocks  and  Rock-Fonnations  (Litholofy). 

Composition. — The  chemical  elements  which  enter  chiefly  into  the  com- 
pootion  of  the  rocks  may  be  classed  as  metallic  and  non-metallic,  as  follows: 
Metallic  (basic)  elements. — Aluminum,  magnesium,  calcium,  iron,  sodium 

potassium. 
S'on-metallic   (acidic)   elements. —  Oxygen,   silicon,   carbon,   sulphur,   phos- 
phorus, chlorine,  fluorine,  hydrogen. 

These  are  combined  in  various  ways,  forming  the  numerous  minerals 
-srinch  compose  the  rocks.  Table  4,  following,  gives  a  list  of  the  principal 
rc<Jc-forming  minerals,  arranged  as  per  E.  S.  Dana's  classification.  It  will 
be  seen  that  silica  and  the  silicates  play  a  most  important  part.  The  cal- 
careous group  of  minerals  comprise  mainly  the  lime  and  magnesium  carbon- 
ates, and  the  lime  phosphates  and  sulphates,  so  that  lime  is  a  very  important 
constituent.  Iron  is  found  plentifully  in  most  of  our  heavier  rocks,  being 
associated  principally  with  oxygen,  sulphur  and  carbon.  The  hydro-carbons 
flemish  a  most  tueftd  group  of  substances  to  the  engineer. 


332 


17.— NATURAL  HISTORY  OF  MATERIALS. 


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THE  COMMON  ROCKS. 


836 


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836 


n.— NATURAL  HISTORY  OF  MATERIALS. 


THE  COMMON  ROCKS, 


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THE  COMMON  ROCKS,  839 

Notes  on  Prbcbdino  Tablb. 

Claas  I. — This  group  of  rocks  illustrates  the  formation,  by  various 
cementing  processes,  of  pudding  stone  and  conglomerate  from  ordinary 
beach  pebbles;  limestone  breccia  from  limestone  pebbles;  conglomerate 
from  old  broken  rocks;  and  sandstone  from  sand.  Gravel  consists  of  pebbles 
worn  by  the  action  of  water  to  the  size  not  smaller  than  a  pea,  whue  sand 
is  the  result  of  greater  wear,  the  grains  being  minute.  Snizigle  is  larger 
than  gravel.  Onartz  is  a  large  constituent  of  gravel  owin^  to  its  resistence 
to  abrasion,  hence  old  gravel  is  a  durable  material  for  building  operations. 
Oav  is  mainly  decomposed  feldspathic  rock  in  place.  It  is  made  up  princi- 
pally of  silica  and  alumina,  and  contains  also  lime,  magneisa.  iron  oxides, 
etc    As^a  cement  it  is  called  argillaceous. 

The  rock  cements  are  mostly  argillaceous  (clayey),  carbonate  of  lime 
(calcite),  femiginous  (iron  compounds),  silica,  arenaceous  (sandy-quartz 
sand),  iron  oxide,  etc.  Very  often  they  are  a  combination  of  these  or  per- 
haps consist  of  certain  of  their  elements. 

Cement  gravel  is  partially  formed  rock  composed  of  cemented  gravel 
and  sand.  It  occurs  in  various  degrees  of  hardness  and  is  often  difficult  to 
dasafy  by  the  engineer,  either  as  earth  or  rock.  A  separate  classification  is 
often  preferred,  as  it  is  usually  more  easily  broken  up  by  blasting  than  by 
plowing:  that  is,  powder  is  cheaper  in  some  cases  than  the  specified  "six- 
mule  team." 

Class  II. — ^This  is  a  distinct  group — sandstones.  It  is  composed  of  strat- 
ified grains  of  sand  cemented  together.  The  nature  of  the  cementing  material 
determines  largely  the  hardness  or  crushing  strength  of  the  sandstone,  silica 
being  superior  to  carbonate  of  lime  or  iron  oxide  in  both  strength  and  dura- 
bility. (Quartz  is  the  principal  constituent  of  sandstone;  but  mica,  feldspar, 
hornblende  and  augite  are  often  present.  The  sandstones  lie  midway  between 
the  conglomerates  (pebble  base)  and  the  shales  (indurated  clay  base). 
They  may  also  be  said  to  occupy  a  structural  position  between  almost  loose 
sand,  in  which  there  is  little  or  no  cementing  material,  and  the  consolidated, 
metamorphosed  varieties  which  resemble  granite.  If  the  cementing  material 
is  carbonite  of  lime  and  very  abundant,  it  gradates  into  limestone. 

Of  the  varieties,  quartzite  is  the  hardest;  arkose  contains  much  feldspar: 
freestone,  as  its  name  implies,  is  easily  worked ;  brownstone  is  an  impure 
sandstone,  rather  soft,  and  fotmd  in  Connecticut  and  New  Jersey:  flagstone 
is  shalely  and  used  for  pavements,  and  includes  the  bluestone  variety. 

Class  in. — Slate  is  a  metamorphic  clay  or  shale,  produced  by  great 
h^t  and  pressure.  The  old  cleavage  planes  of  the  shale  are  changed  to 
new  cleavage  planes  in  the  slate,  and  when  these  are  perfect  it  forms  the 
typical  roofing  slate.  Slate  is  quarried  in  Maine,  Vermont,  New  York, 
Pennsylvania,  Maryland,  Georgia,  Minnesota,  California. 

Classes  IV.  and  V. — ^These  two  groups  comprise  mainly  the  limestones, 
marbles  and  dolomites.  Under  Class  III.  it  was  seen  that  a  sandstone  con- 
taining an  abundance  of  calcareous  (carbonate  of  lime)  cement  grades  into 
limestone  when  the  cementing  material  increases  to  such  an  extent  that  it 
really  forms  the  base  of  the  rock,  the  sand  diminishing  in  quantity  and 
becoming  merely  accessory,  forming  the  impurities.  Pure  limestone  is 
carbonate  of  lime,  the  cementing  material  of  many  other  rocks.  Limestone 
ma:^  contain  also  a  small  amotmt  of  carbonate  of  magnesia  and  such  im- 
parities as  silica,  alumina,  ferric  oxide,  etc.  When,  however,  the  propor- 
tion of  carbonate  of  magnesia  increases  to  a  considerable  extent  the 
limestone  grades  into  dolomite.  Further,  if  it  contains  a  large  amount  of 
the  above  so-called  impurities — silica  and  alumina — it  becomes  hydraulic 
lim^rtone.  Coquina  and  tufacious  limestones  in  Class  III.,  and  crinoidal 
limestone  in  Class  IV,  represent  different  sources  of  formation  or  origin. 

Marble  is  a  name  formerly  applied  to  all  limestones  of  crystal  and  granu- 
lar texture,  capable  of  taking  a  polish;  but  it  is  now  commercially  used 
to  apply  to  all  limestones  (even  the  non-crystalline)  which  can  be  polished. 

Girpsum  is  composed  of  one-third  lime  iCa  O),  nearly  one-half  sulphuric 
add  (/f^O^).  and  one-fifth  water.  Alabaster  is  a  pure  white  variety,  while 
sypsite  contains  more  or  less  earthy  impurities.  Plaster  of  paris  is  obtained 
^heating  gypsum  to  above  12?*  C.  (261''  P.).  driving  oflf  about  one-seventh 
01  the  water  of  crystallization,  and  then  grinding  to  Po^*^5oOqIc 


340  17.— NATURAL  HISTORY  OF  MATERIALS. 

Halite,  No.  60,  is  sodium  chloride  (Na  CI)  in  the  crystal  form.  Sodium 
chloride,  common  salt,  plays  a  very  important  part  in  the  manufactiire  of 
some  high  explosives. 

Classes  VI.  and  VII.— -Gneiss  is  a  name  given  to  a  class  of  metamorphic 
rocks  composed  essentially  of  the  same  elements  as  granite,  namely,  ortho- 
clase,  quartz  and  mica,  with  perhaps  pyroxene,  hornblende,  etc.  They 
may  be  either  of  igneous  origin,  like  the  granites  and  syenites,  or  of  sedi- 
mentary origin,  as  the  schists,  presenting  all  graduations  between  these 
two  classes.  As  they  mer^e  from  the  granitic  to  the  schistose  texture  the 
feldspar  disappears.  Gneisses  may  be  granitic  (granite-gneiss),  syenic 
(syenite-^eiss),  homblendic  (hornblende-gneiss),  etc.,  according  to  its 
composition. 

Schist  is  a  term  applied  to  a  metamorphic  rock  of  slaty  appearance, 
and  of  imperfect  crjrstallization.  Thus  we  have  mica  schist,  hornblende 
schist,  staurolitic  schist,  albite  schist,  etc.  A  slate  is  a  schist  of  argillaceous 
character,  forming  a  rather  distinct  class. 

Soapstone.  a  magnesian  silicate,  is  a  talc  schist  and  is  very  useful  tot 
hearthstones,  sinks,  etc. 

Greensand  or  marl  is  composed  mostly  of  glauconite  (a  silicate  of  iron 
and  potash)  and  is  used  as  a  tertilizer. 

Classes  VIII.,  IX.  and  X. — ^These  are  distinctly  igneous  (eruptive) 
rocks,  with  more  or  less  change  in  composition  due  to  age  of  weathering^ 

Lava  from  an  eniptive  volcano  is  molten  rock  which  subsequently 
hardens  in  cooling.  Many  attempts  have  been  made  to  classify  lava  ac- 
cording to  its  composition  or  texture,  but  no  satisfactory  results  have  vet 
been  attained.  In  density  it  varies  from  pumice,  an  extremely  light, 
frothy,  spongy  form  of  obsidian  (rhyolite)  usually,  to  the  heavy,  compact 
basalt,  which  is  usually  the  last  oi  the  lava  flow. 

Obsidian  is  a  volcanic  glass  consisting  approximately  of  silica  (70  per 
cent),  aluminum  (12),  calciimi,  potassium,  sodium,  iron,  etc.  The  prin- 
cipal kinds  of  obsidian  are  rhyolite  and  trachyte. 

Rhyolite  has  about  the  same  chemical  composition  as  granite,  and 
from  it.  through  weathering,  etc.,  the  latter  is  formed.  Soda-rnyolites  con- 
tain much  sodium  oxide;  porphyritic-rhyolites  are  massive  and  compact. 
Pelsite  is  a  rhyolite  which  is  not  porphyritic. 

Trachyte  has  about  the  same  chemical  compositiori  as  syenite,  which, 
like  granite,  is  formed  through  the  action  of  weathering,  changing  slightly 
the  chemical  composition  and,  to  a  marked  degreer  the  texture. 

Basalt  is  a  porphyritic  rock  of  basaltic  or  coltminar  form.  It  is  com- 
posed of  hornblende,  feldspar,  augite,  iron,  and  various  other  miner^s. 
As  it  weathers  very  slowly  it  is  synonymous  with  greenstone,  trap,  "  basalt," 
etc.,  which  comprise  the  so-called  trap  rocks.  Melaphyr  is  a  Tertiary 
basalt. 

C— BOTANICAL. 

About  three-eighths  of  the  area  of  the  United  States,  or  7(K),000.000 
acres,  is  wooded;  and  of  this,  about  14  ^r  cent  comes  unde/  the  United 
States  Forest  Service.  The  rapid  depletion  of  our  timber  iff  a  matter  of 
grave  concern,  calling  for  abundant  National  and  State  reservations.  The 
National  forest  reserves  are  situated  usually  at  the  heads  of  oiu*  tributary 
streams;  serving,  at  the  same  time,  to  equalise  the  "  run-off  "  of  the  pre- 
cipitation, by  retarding  the  melting  of  the  snows  in  the  spring  of  the  year. 

The  following  is  a  classification  of  the  most  important  lumber  trees  of 
the  United  States  and  Canada: 


d  by  Google 


d  by  Google 


d  by  Google 


BOTANICAV-WOOD. 


343 


«. — Classification  of  Important  Trbbs. — Cont'd. 


8p6cte0< 


Height.    Dta.    Principal  Localities. 


The  OTPBttsss  (2).    Genus.  Cham»eq/varU, 


-  White  Oedar." 


atkaC.  Tellowa. 
(C.  nootkatnui*,) 


Lavsoo  Cyiwcas. . . 


1V-%V 

V-2h' 
-4' 

100'-120' 

5'-6' 

150'-200' 

-12' 

Coast.  Mass,  to  Fla.. 
and  west  to  Pearl 
RIv..  Miss. 

8.  W'n  Alaska.  B. 
C.  Cascade  Mts.. 
Wash.,  Oreg. 

CX>ast  Mts.  of  Ore- 
gon and  Cal. 


Finishing ;  shingles, 
cooperage,  leno- 
ing.  Ues. 

Shipbuilding;  In- 
terior finish;  tur- 
nlture. 

Int.  finish  and  floor- 
ing; ties,  fencing; 
shipbuilding. 


The  CTPnnsBs  (3).    Qenus.  TaxodUtm. 


BaldCsrpreas 

iT.  dUtlehmn,) 


i'-y 

-12' 


Del.  to  Fla.;  Gulf 
Coast  to  Tex;  Miss. 
Val.  to  Mo..  Ind.. 
lU. 


Luinber.  flooring, 
shingles,  cooper- 
age, ties,  fencing. 


Bottcnnit.  White  W  . 
(J.  diurea.) 


KaA  W 

U.migra,) 


The  Walnittb.    Genus.  Julians. 


SO'-lOO* 


2'-3' 


New  Brunswick  to 

Del.  and  to  Dak.; 

Mid.  West:  Ga.. 

Ala. 
Ontario  to  Fla. ; 

west  to  Nebr.  and 

Texas. 


Cabinet  work;  Inte- 
rior finish. 


Cabinet  work;  in- 
terior finish;  ship 
building. 


The  HiCKORiKB.    Genus.  Hicoria. 


,  Shagbark 


SMUwrkH. 

H 

(ff.  ovaia.) 

BIgSlwBbark  H... 
(H.  tocteioM.) 

Ptgout.  WlilteH.. 
(ff,  glabra,) 


Moekienrat  H..  Big  Bud 
H- 

(H.  alba.y 
Xetmeir  H. 

(H.  mifristieaeformU.} 
Feean  H- 


Btueraat  H..  Swamp  H. 
IH.  minima,) 

iTater  H..  Bitter  Pecan. 
(H.  apiaHea.) 


70'-90' 
-120' 

3'-4' 

120' 

-3' 

80'-90' 

3'-4' 

50*- 80' 

-100' 

80'- 100' 

-3' 
-2' 

100'-170' 

4'-«' 

60'- 100' 

2'-3' 

50'-80' 
-100' 

-2' 

Me.  to  Del.  to  Fla.; 

N'n  Ala.,  Miss.; 

west  to  Mln.,  Neb. 

south  to  Texas. 
Ohio  Basin.  Middle 

West,  and  South 

East. 
Me.  to  Fla..  west 

thro  Ont..  Mich.. 

Neb.  South  to  Tex- 
as. 
Ontario  to  Fla.; 

west  to  Kan.  and 

Tex. 
E'n  8.  C^r. ;  Cen.  Ala. 

Miss.,  to  S'n  Kan. 
S'nill..  Ind..  la.; 

Miss.  Riv.  States 

to  Cen.  Ala. 
Me.  to  Fla.;  Ontario 

to  Minn..  Neb.  and 

Tex- 
Swamp  regions.  Va. 

to  Tex. :  north 

along  Miss.  R.  to 

lU. 


Agric  Imp. ;  wagons 
and  ax-handles. 


Agrlc.  Imp.;  wag- 
ons; ax-handles. 


Agric.  Imp. ;  wag- 
ons; tools. 


Agric.  Imp. ;  wag- 
ons; ax-handles. 


Lumber  and  fuel. 


Fuel;  valuable  nut 
tree. 


Hoops  and  fuel. 
Fencing,  fuel. 


Coctonwood. 


Ooooowood 

(P.  fremontU.} 


Tlio  PoPLAiu.    Genus.  Populus. 


60'-100' 
-160* 


7'-8' 


Quebec  to  N.W.  Ter- 
ritory; south  to 
Fla.;  west  to  N.M. 

California,  from  Sac- 
ramento south; 
E'ly  to  Col..  Tex,  ize 


Shelter  and  shade 
in  prairie  States. 

Shade  tree;  fuel. 

j  by  Google 


844  n.— NATURAL  QISTORY  OF  MATERIALS. 

6. — Classification  op  Important  Trbbs. — Cont'd. 


SpeolM. 


Helebt.    DIa.    Prfndpal  Localities. 


The  Poplars.    Genus.  Popuita.— Continued. 


Aspen.  Quaking  Asp. 
(P.  tremvkrtdes.) 


BalmofOUead 

(P.  baUamifera.) 

Black  Cottonwood . . 
(P.  trichocarpa.) 


Black  W 

(S.  Hiffra.) 
Golden  Osier., 

(S.  alba.) 


40'-l«0' 


Newfoundland  to 
Alaska;  south  to 
N.  J. :  west  to 
Penn..  Ky..  Neb., 
Rocky  Mts..  Cosst 
Range. 

Newf'dl'd  to  Alaska 
S.  toN.  Y.;W.to 
Mich..  Neb..  Idaho. 

West  coast,  Alaska 
to  S'n  Cal. 


The  Willows.    Genus,  Salix, 


40'-60' 

-3' 

-120' 

4O'-«0' 

r 

Me.  to  Fla. ;  Rocky 

Mts.:  Cal. 
Eastern  N.  America. 


The  Birches.    Genus.  Beiuia. 


Shelter  and  shade; 
now  rapidly  spread 
over  Rocky  Mt. 
areas  swept  by 
llres. 

Shade  and  shelter. 


Woodw  ware :  staves 
of  sugar  barrela. 


Canoe  B.,  Paper  B. 
iB.  paptfri/era.) 


YellowB..  Grey  B. 
(fi.  luua.) 


Beech 

(P.  Americana.) 


Chestnut 

(C.  derUata.) 


Chinquapin 

(C  pumUa.) 


«0'>70'  2' -3'    Labrador  to  Alaska: 
south  to  Long  Id.; 
Penn..  Cent.  Mich. 
Minn..  Neb.,  Black 
HHls.  Mont..  N.W7 
Wash. 
Gulf  of  St.  L.  to  Del., 
to  N.  Car.,  to  Tenn. 
to  Minn. 

The  Bebchcs.    Genus.  Fagu». 

7 C- 80'  1 3' -4'  I  N.  Scotia  to  L.  Hur- 
-nc  on;  N'n  Wis.; south 

to   Fla..    Mo.   and 

Tex. 


The  CHCSTNtJTB.    Genus.  Casunua. 


ec-ioo 


3'-4' 

-12' 


S'n  Me.  to  Mich.: 
south  to  Ind..  Del.; 
to  Ala.,  Miss. 

Penn.  to  Fla. ;  west 
to  Ark.  and  Texas. 


Pacific  Post  O..  Oregon 
White  O 

(Q.  Qorryana.) 
Live  O 

(Q.  virglniana.) 

White  O 

(Q.  aiba.) 


Burr  O..  Mossy-Cup  O. . 
(Q.  macrocarpa.) 

Swamp  O..  Overcup  O. . 
(Q.  Ivrata.) 


The  Oaks.    Genus,  Qwreut. 
White  Oaks. 


Vancouver  Id.;  W'n 
Wash..  Oreg..  and 
Cal. 

Coast  and  Idands. 
Va.   to   Fla.;   Gulf 
and  Lower  Cal. 

S'n  Me.  to  Fla. ;  west 
to  Minn..  Kan.  and 
Tex. 

Nova  Scotia  to  Mon- 
tana ;  s'tb  to  Penn. 
Tenn.  and  Tex. 

Maryland  to  Fla; 
west    to     Missouri 
and  Tex. 


60' -70' 
-100' 

2'-3' 

40'-75' 

3'- 4' 

60'- 1 00' 
-150' 

3'-4' 
-8' 

70'-180' 

6'-7' 

70'- 100' 

2'-3' 

Letter  papa*:  bark 
for    canoes,     and 
various    camp 
arUdee. 


Furniture,  boxee. 
wheel  hobs,  fueL 


Chairs,  shoe-tasta. 
plane-stocks,  tool 
handles;  fuel. 


Int.  finish,  furni- 
ture, ties,  feoelnc:. 
fuel. 

Large  sises  for  ttOB 
and  fencing. 


Cabinet  work.  wa«w 
ons,  ship  buOdlBK^ 
cooperage,  fuel. 

Exoolent  lumber; 
ship  building. 

Construction  ;riili»>    ; 

bunding.  Ues.  la^ 

finish,  cabinet 

work. 
Cons. ;  shlpbufldlias;. 

ties.  Int.  finish. 

cabinet  work. 
Confounded  oom> 

mercially  with 

Q.  alba,  above. 


BOTANIC AL-^WOOD. 
6. — Classification  of  Important  Trbbs. — Cont'd. 


345 


White  Oaks.~00Dtiniied. 


FtwiO^  IroaO. 

(Q,  wdnor.y 

Gbestout  O..  Tftn-bark  O 

TeOovO 

{Q.  aewminala,) 
Swop  White  O 

(Q.  fkinkmotda.) 

GovO..  Basket  O...., 
IQ.  wtiehauxH.) 


Live  O..  Maul  O..  Oold- 

capO 

(Q.  eknfoUpU.) 

Pm  O^  Swamp  Spanish 
O. 

(Q.  palustrU.) 
Beda 

tQ.rybra.) 

SearletO 

(Q.  eoecima,) 

Texan  CRed)  O 

(Q.  Textuta.) 

BlaacO..  Yellow  O.... 
{Q^  peUatna,) 

SpanWiO 

tQ.  diffeiata.) 

WaterO 

WKofwO 

{Q.pkeao$.} 


Aorel  O..  Shinxle  O. . . 
CO.  ImbrUarta.) 


40'-50' 
-100' 

eC-TO' 
-100' 

80*- 1 00* 
-l«0' 
•O'-TO' 
-lOO* 

60'-i00' 


3'-4' 
-7' 


2'-3' 


Mass,  to  Fla.;  west 
to  Missouri  aod 

Maine  to  Tenn.; 

Mts.  in  Qa.  and 

Ala. 
Vt.  to  Minn.;  south 

to  Ala.  and  Tex. 
Me.  to  Oreat  Lakes 

and  la.:  south  to 

Md.,  Qa..  Kt..  Ark. 
N'nDel.  toila.: 

west   to    HI..    Mo. 

and  Texas. 


Black  Oaks. 


40'-50' 

3'-5' 

70'-80' 
-120' 
70'-80' 
-150' 

2'-3' 

-5' 

3'-4' 

70'-80' 

2'-3' 

50'- 100' 
-200' 

7'-8' 

70'-80' 
-150' 

3'-4' 

70'-80' 

2'-3' 

60'-80' 

2'-3r 

70'-80' 

2'-3' 
-4' 

50'-60' 
-100' 

3' 
-4' 

W'n    Slopes  Sierras 

and  Coast  Mts.. 

Oreg..     and     Cal. 

Ari2..  N.  M. 
Mass.  to  Del.;  west 

to  Wis.  and  Ark. 

N.SootlatoMlnn.; 

south  to  Ga..  Tenir. 

and  Kan. 
Me.  to  Fla.;  west  to 

Ohio    Val..    Minn. 

Neb..  Mo. 
Iowa  to  Ind. ;  south 

to  Fla.  and  Texas. 

Me.  to  Fla. ;  west  to 
Minn..  Kan..  B'n 
Tex. 

N.J.  to  Fla.;  west  to 
Mo.  and  Tex. 

Del.  to  Fla.;  west 

thro    Qulf    States, 

Ky.,  Tenn..  Ark.  to 

Tex. 
N.Y.  to  Fla.;  Quit 

States  to  Tex.; 

N'l7  In  Mo.,  Ky., 

Tenn. 
Penn.  toOa.;weet 

to  Nebr.  Mid  Ark. 


Ties,  fencing,  fuel; 
cooperage. 

Cooperage,  wheels, 
fraclng.  ties. 

Cooperape.  wheels, 
fencing,  ties. 

Cooperage,  boat- 
building, fencing, 
ties.  fuel. 

Fencing,  ties,  fuel; 
bark  tar  tanning. 


Wagons  and  agrle. 
imp.;  most  val. 
OakonPac 
Coast. 

Cooperage;  int.  fin- 
ish; shingles,  clap- 
boards. 

Interior  finish;  fur- 
niture; bark  for 
tanning. 

Interior  fluJsh;  fur- 
niture. 

Lumber.  Miss.  Val.. 
better  than  Q.  ru- 
bm. 

Fuel.    Bark  used 
In  medicine,  dye- 
ing, tanning. 

Light  construction, 
and  fuel ;  bark  for 
tanning. 

Fuel. 


Whfte  E..  American  B  . . 
(27.  mmeriama.) 

*?nL&r^ 

n>4«rK       

itJ.  eroMiifoUa,) 

The  Elms.    Genus,  Ubntts. 

Newfoundland  to 

Fla. ;  west  to  Rocky 

Mts. 
Ontario  to  Dak., 

Nebr.;   south    to 

Fla.;  west  to  Tex. 
S'n  Ark.,  Miss,  and 

Tex, 


The  Swz£T  GuacB.    Genus.  Liquidambar. 


75'-125' 

6'-ll' 

eo*-?©' 

2' 

-80' 

2'-3' 

iwectCBIIsted.. 


80*- 140' 


4'-5' 


Conn,  to  Mo. ;  south 
to  Fla.  and  Tex. 


Clapboards;  fellies 
for  wheels;  some 
construction. 

Clapboards  and 
shingles;  some 
construction. 


Wheel  hubs,  saddle 
trees,  flooring, 
cooperage. 

Fencing,  ties,  whed 
hubs,  agric.  Im- 
plements. 

Fencing  and  fud. 


Furniture,  int.  fin- 
ish, shingles,  fruit 
boxes,  paving 
blocks,  ties. 


346 


n.—NATURAL  HISTORY  OF  MATERIALS. 


6. — Classification  of  Important  Trbbs. — Concl'd. 


Specials. 


Height. 


PrioolpalLooaUttos. 


Red  M..  Scftriet  M.. 
Swamp  M 

(A.  rutfrum.) 
SnverM..  SoftM.... 

{A.  taccJUainwn.) 

Oregon  M..  Broadleaf  M . 
(A.  machrophyUtan.) 

Sugar  M..  Rock  M..  Hard 
M 

{A,  8acehannn.) 
Black  H..  Black  Sugarlf . 

{A.  nigrum.) 


The  Mapubb.    Qenus.  Acer. 


Eastern  and  Middle 
States.    Lower 
MlsBlJisippl.    Texas. 

New  Brunswick  to 
Dak. '.south  to  Fla. 
and  Oklohoma. 

South  Coast  Alaska 
to  San  Diego.  Oal. 

Great  Lakes  to  New- 
foundland, to  Fla., 
to  Neb.,  to  Tex. 

Dak.  to  Vt..  to  Va,, 
Ky..  Mo..  Kan. 


80'- 1 20* 

3'-41' 

90'-120' 

3'-4' 

SC-IOC 

2'-3' 

TS'-iaC 

r-3' 

-SO* 

-3' 

Tool  handles.  osTB, 
(uralture.  woodcor 
ware:  fuel. 

Cheap  furniture 
and  flooring. 

Interior  finish,  fur- 
niture, ax-  and 
broom-handles. 

Buildings,  flooring, 
furniture*  boats, 
fuel. 

BulldlngB.  flooring, 
furniture, 
fuel. 


The  Ashes.    Genus.  FraxinuM. 


White  A 

{F.  americana.) 

Black  A 

(F.  ntgra.) 

Bine  A 

(F.  gvadraitQulata.) 
Oregon  A 

(F.  oregana.) 

Green  A 

(F.  Umeeolata.) 


-120' 
80'- 90' 


60'-70' 

12U' 
70'-80' 


6'-6' 

2'-3' 
-4' 


N.  Scotia  to  Fla.; 
west  to  Minn..  Tex- 
as. Ohio  R.  Val. 

Va.  to  Del.  to  Mani- 
toba. lU..  Mo..  Kan. 

Mich,  to  Mo.,  to 

Kan.  to  Ark. 
Coast,  Puget  Sound 

to  San  Frandsoo; 

Sierras. 
L.  Champl'n  to  Fla. 

west  to  Arts..  Utah, 

Tex. 


Int.  finish,  stairs; 
tool  handles,  oars, 
furniture. 

Furniture,  fencing, 
barrel  hoops,  cabi- 
net work. 

Flooring,  tod    han- 
dles, vehldes. 

Int.  finish,  furni- 
ture, wagons, 
ooopert^e,  fuel. 

Int.  finish,  stairs; 
tool  handles,  oars, 
furniture. 


Intbrbstino  Facts  About  Trbbs. 

Some  of  the  Tallest  Trees.— Big  Tree  (350  ft.).  Redwood  (325  ft.). 
Sugar  Pine  (300  ft.),  Douglas  Spruce  (300  ft.),  Western  Hemlock  (260  ft.). 
Western  Larch  (250  ft.). 

Some  of  the  Best  Timber  Trees. — Longleaf  Pine,  Douglas  Spruce, 
White  Pine,  Norway  Pine,  Shortleaf  Pine,  Live  Oak  (Q.  virgtniana). 

Some  of  the  Best  Lumber  Trees. —  All  the  timber  trees  make  good 
lumber.  In  addition  we  may  name:  Most  of  the  Pines.  Spruces,  Hem- 
locks, White  Fir^  Redwoods.  Sitka  Cypress,  Lawson  Cypress,  some  of  the 
Walnuts  and  Hickories,  many  of  the  Oaks.  Some  ot  the  Oaks,  Ashes. 
Chestnuts,  Maples,  and  Walnuts  are  used  for  interior  finish.  > 

Ages  of  Trees  at  Mo/Krt/y.— White  Pine.  250  yrs.;  White  Oak,  200  yrs, ; 
Chestnut,  176  yrs.;  Beech,  100  yrs.;  Elms,  90  yrs.;  White  Ash,  80  yrs.; 
Birches,  60  yrs. 

Relative  Rapidity  df_  Growth. — Silver  Maple,  White  Elm,  Red  Maple^ 
Sugar  Maple,  Chestnut.  Red  Oak.  Pin  Oak,  Scarlet  Oak.  White  Ash.  Whit<? 

Some  Important  Tree  Products — Tar,  Rosin  and  Turpentine  arc  ol> 
tained  from  the  resin  or  sap  of  the  longleaf  pine.  Pine  tar  is  also  obtaineiJ 
by  the  burning,  or  rather  smouldering,  of  the  limbs  and  knots  of  the  longle&j 
pine.  The  dry  distillation  of  woods  produces  wood  vinegar  (used  foi 
dyeing),  acetic  acid  (which  is  made  into  vinegar),  and  wood  alcohol.  T>w 
latter  may  also  be  obtained  from  sawdust,  and  is  destined  to  become  a  mosi 
valuable  product  for  heating  and  power.     Wood  charcoal  is  also  a  valuabil^ 

Eroduct.     All  are  familiar  with  the  products  of  the  Balsam  and  the  StiffEti 
[aole     Wood  pulp  is  used  in  making  paper. 


CLASSIFICATION  OF  ANIMALS.  147 

D.— ZOOLOGICAL. 

Foreoote. — So  far  as  known  there  are  about  350,000  living  species  of 
animals,  and  50.000  extinct  specimens,  making  a  grand  total  of  about 
400^000.  The  latest  and  most  logical  classification  of  the  animal  world, 
by  Parker  and  Haswell,  comprises  12  grand  divisions  or  Phyllums,  arranged 
according  to  structure — beginning  with  the  lowest  forms,  the  Protozoans  or 
unioellular  animals,  and  ending  with  the  highest  forms,  the  Mammals  with 
Han  at  the  head  of  the  scale.  In  the  evolution  of  the  species  the  lower 
forms  of  life  have  played  an  important  part  in  the  development  of  the 
higher,  just  as  today  the  whole  animal  kinjsdom  forms  a  valued  adjimct  to 
the  devek>pment  and  uses  of  man. 

Among  the  insecU  we  have  the  honey-bee;  the  5ift-worm;  the  cochineal, 
fbtmd  on  certain  species  of  cactus,  for  useful  and  harmless  dye;  the  lac  for 
dtgOac;  the  galls  of  the  ^all-fly  for  ink.  etc. 

Many  uhes,  tncludmg  the  swora-fish,  codfish,  sunfish,  etc.,  yield  oil. 
Oil  is  atoo  yielded  by  many  reptiles,  by  the  whale,  walrus,  manatee,  etc. 

The  whale,  narwhal  and  elephant  furnish  us  with  ivory;  the  seal,  beaver, 
and  other  fur-bearing  animals,  with  furs;  the  alligator,  goat,  and  many 
quadrupeds,  with  skins  for  leather;  the  latter,  also,  with  horns  and  tallow; 
the  sheep,  with  wool;  sea-fowl,  with  guano;  etc.,  etc. 

A  considerable  percentage  of  the  animal  world  supplies  us  with  food; 
and  a  few  animals  produce  useftil  work. 

The  following  classification  is  now  recognized  by  scientists  as  the  most 
logical  that  has  ever  been  submitted. 

l.'-CLASSIFICATION  OF  ANIMALS. 
(After  Parker  and  Haswell.) 


JS  3  ^ 

U  09  ^ 

a.  PniOMOM*     (Unicellttlar  animals.) 
I.   Protocoa  (Protozoans).     One  cell;  or  several  cells  of 
same  kind. 

1.  RJuMopoda  (Amoeba,  etc.).     With  retractile  pseudopodia. 

2.  Myc0totoa  (Slim^.     Terrestrial  protozoa,  plasmoidal. 
3l  Mastigophora.     Without  cilia,  or  sucking  tentacles. 

4.  SporoMca.     Without  appendages*  internal  parasites. 

5.  Infusoria.     With  sucking  tentacles. 

$.   MttMMoa.     (Multicellular  animals.) 
n.  Porlfera  (Sponges).     Fixed;  body-wall   perforated, 
pores. 
L  Por^^ra. 

(a).  Cakarea.    With  skeleton  or  calcareous  spicules. 
(b).  Non-Cakarea.     Where   skeleton   exists,    composed    of   siliceous 
spicules. 
in.  Corieaterata   (Polyps,  etc.).     Radial    structure;   diges- 
tive cavity  Imed. 
I.  Hydrosoa  (Hydroids,  etc.).     More  than  two  rays;  single  cavity. 

3.  Scyfhotoa  (Jellyfishes).     Many  radii;  cavitv  divided  by  radial  partitions. 
X  Acttnozoa.     Colonies  or  attached  individuals. 

(a).  ZooiOAarta  (Sea- Anemones.  0>rals.  etc.).     Numerous  tentacles, 

usually  in  5's. 
(&).  Alcyonaria  (Sea-rans.  Red  (^rals.  etc.).     Eight  tentacles. 
1  Cttnophcfa.     With  two  radii,  and  rows  of  sucking  tentacles. 

IV.  Platyhelmintbes      (Platworms).     Body     composed     of 
loose  cells. 

1.  TurbtUaria  (Planarians).     Body  covered  with  celia;  one  opening  to  ali- 

mentary tract. 

2.  TremaUxia  (Flukes).     Parasitic,  imsegmented;  adult  without  celia. 
3l  C^stoda  (Tapeworms).     Without  mouth  or  alimentary  canal. 

4.  Xemwrtinea.     C^amivorous  and  aquatic ;  with  mouth,  arm»,  and  food  canal. 
Palagtmemertinea. 


348  IT.^NATURAL  HISTORY  OF  MATERIALS. 

7. — Classification  of  Animals. — Cont'd. 


V.  Nemathelminthcs    (Round    worms).     Usually — oiouth. 

arms,  alimentary  tract. 

1.  Ntmatoda  (Threadworms).     With  intestinal  canal;  parasitic. 

2.  Acanthoc0phala.     Parasitic;  no  mouth  or  intestines. 

3.  Ckaetognaiha  (Arrow  worms).     Developed  nervous  system;  spiny. 

VI.  Trochdintothes    (Wheel-animalcules).     Larva  in   tro- 
chosphere  form. 

1.  Rotifera.     Microscopic. 

2.  DinophiUa.     Minute;  with  5  to  8  segments,  usually  ciliated. 

3.  Gastrotricha.     Minute;  ciliated  on  ventral  surface. 

VII.  MoUnscoida   (Sea-Mats  and   Brachiopods).     Aquatic 

1.  Polyzoa  (Bryozoans).     Form  colonies  connected  by  one  organic  sub- 

.    stance, 
(a).  Ectoprocta.     Anus,  external. 
(b).  Endoprocta.     Anus,  internal;  bud,  forming  colonies. 

2.  Pkoronida.     Worm-like;  bom  from  ova,  not  by  buds. 

8.  Brachiopoda  (Lamp-shells).     Body  enc.  in  shell  of  two  valves,  usually 
on  a  stalk. 

VIII.  Echinodermata      (Echinodenns).       With     intestinal 
walls. 

1.  Asteroidga  (Starfish).     Star-shaped;  furrows  under  the  arms. 

2.  Ojfhiuroidta  (Bnttle  Stass) .     Arras  not  grooved. 

3.  Echinoidta  (Sea-Urchins).     Body,  globxuar:  armless. 

4.  HoloihuToidea  (TrepangsK     Worm -Tike;  with  tentacles  about  mouth. 
6.  Crinoidea  (Crinoides).     Sessile;  with  cup-shaped  body.* 

6.  Cystoidea  (Fossil).     Globular  and  stalk^  (sessile). 

7.  Blastoidea  (Fossil).     Ovate;  stalked. 

IX.  Annulata     (Worms).     Bilaterally   segmented;   without 

jointed  legs. 

1.  Chaetopoda  (Annelids).     Composed  of  scries  of  metamereS.  bearing  cirrL 

(a)    Polycha^ta    (Marine    Annelids).     Sexes    distinct;    ovaries    and 

testes,  many. 
(6)    Oligochaeta  (Fresh  water  and  terrestrial).     Sexes  united;  ovaries 

and  testes,  few. 

2.  MyMostomida  (Crinoides).     Unsegmcnted. 

3.  Geph^ea  (Marine).     Sessile;  adult,  without  external  segmentation. 

4.  Archi-Annelida  ((;ften  Parasitic).     Minute;  marine,  segmented  (faintly). 

5.  Hirundinea  (Leeches).     With  ventral  suckers. 

X.  Arthropods    (Insects,  Crustaceans,  etc.).     Symmetrical, 

segmented. 

1.  Crustacta   (Crustaceans).     Aquatic,   gill   bearing;   two   pairs  antennae, 

usually. 

(a)    Entomostraca  (Water-Fleas,  etc.).     Varied  number  of  appendages. 

(6).  Malacostraca  (Crabs,  Crayfish,  etc.).     With   19  pairs  of  appen- 
dages. 

2.  Trilcbila  (Extinct  Trilobites).     With  head,  thorax  and  abdomen. 

3.  Onychophora  (Peripatus).     With  series  of  short  walking  appendages. 

4.  Myriapoda  (Centipedes  and  Millipedes).     Segments,  each  with   1  or   2 

pairs  of  legs. 

6.  Insecta  (Insects).     With  six  thoracic  l€«s,  and  tisually  with  wings. 

6.  Arachntda  (Spiders,  Scorpions,  etc.).     Air-breathing;  without  antexmske. 


ZddLOGICAL.  349 

7. — Classification  of  Animals. — Conduded. 


3  3  3-^      fS 

U  CO  CO  04 

XI.  Molliisai    (MoUiisks).     Unsegmented;    muscular    loco- 

motion. 

1.  PfUcvfoda  (Bivalves).     Gills  leaf-like;  two-valvcd  shell. 

2.  Amphtfuura  (Chitons).     Symmetrical  bi-laterally:  anus  at  end  of  body. 
2.  Gastropoda  (Gastropods).     Unsym.  body;  shell  (it  any)  univalve. 

(a).  Strepton4ura  (Limpets,  Whelks,  etc.).     Visceral  commissures  like 

a  fijKure  8. 
(6).  Enikyneura  (Pulmonates  Nudibranchs,  etc.).     Vis.  com.  not  like 

a  ngure  8. 

4.  Scaphopoda  (Marine).     Mouth-lobes  formed  into  a  tube. 

(<x).  Scaphopoda  (Tusk-shells.) 

(6).  Rhodop9.     Mmute;  no  shell;  with  sucking  tentacles. 

5.  Cephalopoda   (Cuttle-fish).     Mouth  surrotmded   by  arms;  foot  funnel- 

shaped. 
(a).  Dibranckiata  (Squids,  Octopods).    Two  sym.  branchiae;  tubular 

fimnel. 
ib).  Tetrabranckiata  (Nautilus,  Ammonites).    Four  branchiae;  multi- 

kx:ular  shell. 

XII.  Chordata    (Chordates).     Animals  having  a  notochord. 
L                  {A).   Adelochorda    (Balanoglossus.    etc.).     Marine;    with    noto- 
chord as  larvae. 

2.  iB).  Urochorda  (Ascidians).     Marine;  having  a  notochord  when 

larvae. 
(O.  Verttbrata  (Vertebrates).     Sym.  bilaterally;  having  a  back- 
bone. 
(/).     Acrania   (Branchiostomidae,  Amphioxus,  etc.).     Without  a 

head. 
(11).  Craniata  (Fishes,  Reptiles,  Birds,  Mammals). 
1.  CycJostomata  (Lcunprcys).     Eel-like,  without  lower  jaw;  mouth,  suctorial. 

Cartilaginous    skeleton; 

•us;  four  pairs  of  gill  slits. 

sh). 

nals    with    apparatus    for 

1.  leavae,  lungs  when  adult. 

4.  idermal  skeleton  of  scales. 

i. 

h  prolonged  tail  of  many 
vertebrae. 
(6).  Neorniihes  (Modem  Birds).     Tail  vertebrae  compacted. 
8.  Mammalia  (Mammals).     Suckle  their  young;  clothed  with  hair,  more  or 
less, 
(a).  Protoihtria  (Didelphia).     Mammals  with  oviducts  separated. 
(6).  Thtria  (Monodelphia).     Mammals  with  oviducts  more  or  less 
tmited. 
{hi).   Mttatheria  (Marsupials).     Rudimentary  birth;  shel- 
tered in  pouch. 
(6s) •   Eutheria  (higher  Mammals).     Bom  in  uterus;  no 
pouch. 


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18.— EXPLOSIVES. 


An  explosive  is  a  mixture  which,  mnder  certain  disturbing  influences, 
enters  into  rapid  chemical  reaction,  forming  expansive  ^ases  and  evolving 
much  heat.  The  substances  mixed  may  be  solid  or  liquid.  Explosives 
mav  be  classified  according  to  the  nature  of  the  mixture,  whether  mechan- 
ical or  chemical. 

(M).     MECHANICAL  MIXTURES. 

In  mechanical  mixtures  the  component  elements  remain  intact  until 
a  high  temperature  is  reached,  when  they  chemically  react  and  pass  off  as 
gases  (mostly),  causing  the  explosion. 

Nitrate  Mixtures. — ^This  class  comprises  the  mixture  of  a  nitrate, 
embodyingoxygen,  with  some  base  yielding  carbon  and  usually  containing 
sulphur.  The  explosion  occiu^  when  the  oxyven  leaves  the  nitrate  ana 
combines  with  the  carbon,  having  a  greater  affinity  for  the  latter.  Gun- 
powder is  typical  of  this  class. 

Qiuipowder. — ^This  is  the  oldest  and  one  of  the  most  common  of  explo- 
sives. It  consists  of  a  mixture  of  saltpetre  ( —  nitre  =•  potassium  nitrate  =■ 
KNO^,  charcoal  (  —  carbon)  and  sulphur  in  various  proportions  according 
to  the  nature  of  tne  explosion  desired.  The  black  powder,  formerly  used 
almost  exclusively  in  U.  S.  ordnance,  was  comix>sed  of  75  parts  saltpetre, 
16  parts  charcoal  and  10  parts  sulphur;  while  the  brown  or  sporting  powder 
contains  much  more  charcoal  and  considerably  less  sulphur,  the  proportions 
being,  79  parts  saltpetre.  IS  parts  charcoal  and  3  parts  sulphur.  These  are 
now  being  superseded  by  the  smokeless  powder. 

Blastinf  Powder. — ^This  is  made  slower  acting  than  the  gunpowder  by 
reducing  the  proportion  of  saltpetre  to  66  parts,  charcoal  forming  15  parts, 
and  sulphur  19  parts.  Sodium  nitrate  or  Chili  saltpetre  is  now  commonly 
tised  instead  of  the  more  expensive  potassium  nitrate. 

Assuming  the  weight  of  powder  at  62.6  lbs.  per  cu.  ft.  (spec.  grav.  — 
unity),  the  following  table  gives  the  weight  of  powder  in  a  hole  one  ft.  deep 
and  of  various  diameters: 


1.— Weight  of  Powder  in 

A  Hole  One  Foot  Dbbp. 

Diam. 

Weight. 

Weight    (Avoir.) 

'  Diam. 

Weight. 

Weight 

(Avoir.) 

Ins. 

Lbs. 

Lbs.            Ozs. 

Ins. 

Lbs. 

Lbs. 

Ozs. 

.0862 

0    —       1.4 

24 

2.131 

2    — 

2.1 

.1332 

0    —       2.1 

3 

3.068 

3    — 

1.1 

.1917 

0    —       3.1 

3i 

4.176 

4    — 

2.8 

.2610 

0    —       4.2 

4 

6.464 

5    — 

7.8 

1 

.3409 

0    —       6.6 

4i 

6.903 

6    — 

14.5 

n 

.6326 

0    —       8.6 

6 

8.622 

8    — 

8.4 

I 

.7670 

0             12.3 

H 

10.312 

10    — 

6.0 

1 

1.044 

1     —       0.7 

6 

12.27 

12    — 

4.4 

2 

1.364 

1     —      6.8 

6J 

14.40 

14    — 

6.4 

Note. — Weight  in  lbs.  =  0.3409 X  (diam.  of  hole  in  ins.)»;  therefore  it 
is  proportional  to  the  square  of  the  diameter  of  the  hole. 

Other  Nitrate  Explosive  Mixtures. — ^The  following  mixtures  are  analo- 
gous to  gunpowder  in  exploding  at  high  temperattires: 
Amide. — ^Ammonium  nitrate,  potassium  nitrate,  charcoal. 
Azotine. — Sodium  nitrate  (69),  carbon  (16),  sulphur  (12).  petroleum  (4). 
Carbo-azotine. — Potassium  nitrate  (61),  soot  (26),  sulphur  (14). 

QCA  Digitized  by  VjOOQIC 


MECHANICAL  AND  CHEMICAL  MIXTURES.  851 

Diortxitm. — Potawinm  nitrate  (50),  soditim  nitrate  (35),  tulpfaur  (12).  hard 

■awdust  (13). 
Jokniu. — PotK^um  nitrate  (76),  sulphtir  (10),  lignite  (19),  sodium  picrate 

(3).  potassium  chlorate  (2). 
Pgtraiiie. — Potassium  nitrate  (64),  charcoal  (30).  crude  antimony  (0). 
PyroUu. — Potassium  nitrate  (51),  sodium  nitrate  (16),  sulphur  (20),  saw- 

dttft  (11).  charcoal  (2). 
Chlorate  Explosive  MIxtarM. — Potassium  chlorate  is  a  constituent  in 
each  of  tlie  following  explosives,  which  are  considered  rather  unsafe  on 
accoont  of  spontaneous  or  premature  reaction: 
AspkaJtne. — Potassium  chlorate  (54),  potassium  nitrate  and  sulphate  (4), 

bran  (42). 
Ekrhardt    P. — Potassium    chlorate,    cream   of   tartar,  powdered   nutgalls, 

tannin. 
Ftmtoitts  P. — Potassium  chlorate,  potassium  picrate. 
Hors^ky    P. — Potassium  chlorate   (6),   nutgalls   (1),   charcoal   (1),   nitro- 

glyc«9rin  (72).     (This  is  a  dynamite.) 
iiichalowoski  Blasting  P. — Potassium  chlorate   (50),   manganese  dioxide 

(5).  bran  (45). 
Oriental  P. — Potassium  nitrate  and  crude  gamboze,  potassium  chlorate. 
Pyronomt. — Potassium  nitrate  (69),  sulphur  (9).  charcoal  (10),  antimony 

(8).  potassium  chlorate  (5).  rye  flotir  (4),  potassium  chromate. 
Radtarock. — Potassitun    chlorate     (79),     mono-nitrobenzine     (21).     Fresh 

mixed. 

(b).     CHEMICAL  COMPOUNDS. 
,        Nitro-cotetitatioa   Explosive    Mixtures. — ^The   following  are  examples 
'  of  nitric  acid  treatment  of  the  hydrocarbons,  producing  compounds  yrhich 

ax  hish  temperatures  become  unstable: 

Amumomit0S. — Ammonium  nitrate   (88),  di-nitro  napthalin   (12). 

B€Ui$e. — ^Ammonium    nitrate    (5),    meta-di-nitrobenzine    (1),    potassium 
nitrate. 

Bwlinttto  P. — Picric  acid  (10),  sodium  (10),  potassium  chromate  (8). 

ExiraJ^t0. — Ammonium  nitrate,  potassium  chlorate,  naphthalin. 

Jaogiu. — Nitro-naphthalin.  nitro-phenol,  sodium  nitrate. 

Reburitt. — Ammonium  nitrate,  chlorinated  di-nitrobenzine. 

RomuU. — ^Ammonium  nitrate,  potassium  chlorate,  naphthalin. 

S^curitt. — ^Ammonium  nitrate,  di-nitrobenzine. 

Voimfy  P. — Potassium  nitrate,  sulphur,  nitro-naphthalin. 

Nitric  Acid  Compomids. — ^When  certain  vegetable  tissues,  called  cellu- 
lose, notably  cotton,  are  treated  with  nitric  acid  the  resulting  cellulose 
mtzate  is  a  very  high  explosive.  The  stronger  treatments  produce  gun- 
cotum  and  the  weaker,  pyroxylin.  Similarly,  when  the  animal  compounds 
^fmA»*in  or  glycerine,  are  treated  with  nitric  acid  there  results  nitroglycerin, 
a  moat  powerful  explosive.  Dynamite  consists  of  some  absorbent  soaked 
with  nitroglycerin  to  protect  the  latter  from  decomposition  and  premature 
ccplockm. 

Ovacottoa. — ^Tkis  is  made  bv  soaking  cotton,  or  other  form  of  cellulose, 
ia  nitric  acid  (one  part)  and  sulphuric  acid  (three  parts)  for  about  a  day, 
aad  then  thoroughly  washing.  The  resulting  product  is  from  60  to  85  per 
cem  heavier  than  the  cellulose,  depending  upon  the  proportion  and  strengths 
of  the  adids  and  the  general  treatment.  It  is  the  safest  explosive  known 
C3  general  handling  and  shipment.  It  is  exploded  hy  percussion  when  con- 
£sMd  and  highly  compressea,  but  if  ignited  bums  quietly  without  explosion. 

Guncotton  is  used  as  an  agent  in  various  mixtiues  containing  nitrates 
c^  which  the  following  are  examples: 

GiyoxUint. — Guncotton,  saltpetre,  nitroglycerin, — in  form  of  pellets. 
f^^^teniiU. — Guncotton,  saltpetre. — in  form  of  cartridges.  jOOQ Ic 
'Samite. — Guncotton,  bariiim  nitrate, — in  form  of  cartridges.  ^ 


352  IS.— EXPLOSIVES. 

Detonatioii. — In  our  classification  of  the  variotis  explosives  under  the 
two  headings,  Mechanical  Mixtures  and  Chemical  Compounds,  we  are  con* 
fronted  with  the  great  natural  law  of  gradation,  which  is  universal.  For 
instance,  there  are  some  animate  objects  which  the  naturalist  is  unable  to 
classify  distinctly  as  plants  or  animals,  bordering  on  the  division  line  and 
having  some  of  the  common  attributes  of  both  great  orders  in  nature.  So 
with  explosives.  Up  to  1864,  when  Alfred  Nobel,  a  Swedish  engineer, 
began  to  put  some  of  the  higher  explosives  to  practical  use,  the  great  prin- 
ciple of  '  detonation  "  or  instantaneous  explosion  by  "  ^ock  '  was  but 
vaguely  known.  His  investigations  with  nitroglycerin  led  to  the  discovery 
that  many  explosives  heretofore  treated  by  ordmary  combustion  were  fai 
more  powerful  when  subjected  to  "perciission,  "which  converted  the  substance 
immediately  into  gas.  In  his  experiments  with  nitroglycerin  he  tised  i 
percussion  cap  charged  with  fulminate  of  mercury  as  an  mitiatory  explosivei 
Detonation  is  essential  in  the  higher  class  of  explosives  as  gtmcotton.  nitroi 
glycerin,  dynamite,  etc. 

The  following  are  some  of  the  guncotton  preparatiox»  resulting  froni 
Nobel's  discovery: 

Blasting  gelatin. — Guncotton  absorbed  in  nitroglycerin. 
Gelatin  dynamite. — Blasting  gelatin  and  an  absorbent. 
Fbrcite. — Blasting  gelatin  (SO),  absorbent  (60). 
Gelignite.— BUiStins  gelatin  (65).  absorbent  (36). 

Smokeless  Powders  contain  guncotton,  nitratej^carbonate,  ^  nitrogly 
cerin,  and  various  other  substances  of  like  nature.  The  product  is  a  hom 
like  substance,  which  is  cut  into  chords  or  grains. 

Nitroglycerifi. — ^To  the  engineer,  this  is  one  of  the  most  useful  and  most 
powerful  explosive  agents.  It  is  prepared  by  treating  glycerin  with  stron] 
nitric  and  sulphuric  acids,  producing  the  chemical  compound,  Cs  Hs  N^  Ot 
In  its- pure  liquid  form  it  bums  quietly,  producing  carbon  dioxide,  hydrogen 
nitrogen  and  water.  But  when  gradually  heated  to  180°  C.  or  when  sub 
jected  to  violent  percussion  it  explodes,  developing  gases  from  1200  to  1401 
times  the  volume  of  the  liquid,  which  in  turn  are  further  expanded  bv  th| 
great  amount  of  heat  evolved,  to  about  10,000  times  the  original  bulk 
Nitroglycerin  when  mixed  with  infusorial  earth  as  an  (inert)  absorben 
forms  dynamite,  which  is  sold  under  various  trade  names. 

Djmamlte. — As  the  liquid  nitroglycerin  is  liable  to  explode  by  heat  a 
decomf>osition,  it  is  rendered  safer  by  being  combined  with  some  protcctini 
absorbent.  The  absorbent  may  be  inert  or  active,  naturally  dividing  th 
dynamite  into  two  classes.  The  second  class  comprises  by  far  the  mor 
important,  as  follows: 
Atlas  P. — Nitroglycerin  (75),  wood  fibre  (21),  sodium  nitrate  (2),  magn< 

sium  carbonate  (2),      Also  lower  grades. 
Carbonite. — Nitroglycerin  (26),  wood  dust  (40),  sodium  nitrate  (34),  sodiui 

carbonate  (1). 
Dualin. — Nitroglycerin  (40),  wood  dust  (30),  potassium  nitrate  (20). 
Giant  P. — Nitroglycerin  (40),  resin  (8),  kieselguhr  (8),  sulphur  (6),  soditU 

nitrate  (40). 
Hercules  P. — Nitroglycerin    (40),   wood   fibre   (11),   sodium  nitrate    (4^ 

sodium  chloride  (1),  magnesium  carbonate  (1). 
Judson  P. — Nitroglycerin  (5),  cannel  coal  (15),  sulphiu"  (16),  sodium  fl 

trate  (64). 
Lithofracteur. — Nitroglycerin  (54),  kieselguhr  (17),  sulphur  (7),  bariiun  n 

trate  (15),  wood  dust  (2),  manganese  (2),  soda  (2),  bran  (1). 
Meganite. — Nitroglycerin    (60),   nitrated   wool  and  vegetable   ivory    (2^ 

soditmi  nitrate  (20). 
Rhexite. — ^Nitroglycerin  (64),  decomposed  wood  (11),  wood  dust  (7),  aodim 

nitrate  (18). 
Safety  nitro    P.— Nitroglycerin  (69),  wood  fibre  (13).  sodium  nitrate  (18 
Sk>«i>.— Nitroglycerin    (68),   wood   dust    (4),   kieselguhr    (20).    potassiul 

nitrate  (8). 


DYNAMITE.  363 

VigoriU. — ^Nitroslycerin  (68),  kieselguhr  (20),  potassium  nitrate  (7),  car- 
bonate, etc.  (5). 

Vukan  P. — Nitxx)glycerin  (30),  charcoal  (11),  sulphtir  (7),  sodium  nitrate 
(62). 

Umixed  ExplotiTCt.— There  is  a  cerUin  class  of  explosives  called  Pan- 
clastxtes,  consisting  of  two  ingredients  which  separatelv  are  inexplosive  but 
when  mixed  are  considered  fully  as  powerful  as  dynamite.  They  are 
shipped  separatelv  and  mixed  at  the  site  when  needed  imr  use.  The  prin- 
dpai  ingrraients  of  the  mixture  are  nitrc^en  tetroxide  and  carbon  disulphide. 
They  are  not  generally  recommended  for  ordinary  use  by  the  class  of  men 
usually  employed  in  blasting. 

Penhadon  Ca^f. — Fulminate  of  mercury  enters  into  the  composition 
used  for  percussion  caps  and  electric  fuses  employed  in  detonating  charges 
of  djmamite  in  blasting  operations.  It  is  prepared  by  adding  alcohol  to  a 
nitnc  add  solution  of  mercury. 

(c).    The  Handling  and  Use  of  Dynamite. 

Dynamite  as  invented  by  Noebel  in  1867  consisted  of  nitroglycerin 
absorbed  by  a  porous,  inert  solid.  The  best  absorbent  was  found  to  be  a 
nticeous^imusonal  earth  known  as  Ideselguhr,  obtained  in  Hanover,  Ger- 
many. When  dried  it  is  an  impalpable,  white  powder  of  cellular  structure, 
and  IS  capable  of  absorbing  three  times  its  weight  of  nitroglycerin,  giving 
the  resultant  dvnamite  the  appearance  and  consistency  of  heavy  brown 
sugar.  Coupled  with  its  absorbent,  nitrc^lycerin  is  thus,  in  the  form  of 
dynamite,  free  from  the  danger  of  spontaneous  explosion,  and  detonation 
from  shodcs  of  a  moderate  nature.  In  the  loose  powdered  form,  dynamite 
loses  none  of  its  explosive  properties  when  exposed  to  natural  temperatures; 
i.e.,  it  explodes  readily  by  the  action  of  the  fulminating  mercury  primer 
or  cap.  On  the  other  hand,  when  the  powder  is  compressed  into  cartridges 
and  the  temperature  is  reduced  to  between  60°  and  i2°  F.  it  freezes  and, 
like  frosen  nitroglycerin,  is  inexplosive.  It  loses  only  a  small  percentage 
of  its  explosive  power  on  being  saturated  with  water,  hence  its  great  value 
in  submarine  work.  If  unconnned  and  ignited  by  a  name  (360°  Jr )  it  bums 
freely  and  quietly  withqut  explosion. 

Dynamite  is  usually  compressed  in  sticks  or  cylinders  called  cartridges, 
varying  from  |  to  2  ins.  in  dia.  and  about  8  ins.  long,  more  or  less;  or  they 
are  sold  in  any  size  and  length  ordered.  The  sticks  are  wrapped  separately 
in  paper,  and  packed  in  boxes,  in  layers  cushioned  with  sawdust;  usually 
SO  lbs.,  or  35  lbs.,  to  the  box. 

In  "  freezing  "  weather  these  cartridges  have  to  be  "  thawed  "  out. 
The  term  "  freezing  "  applies  to  any  temperature  that  chills  the  dynamite, 
usually  in  the  neighborhood  of  46°  P,  sometimes  lower  and  sometimes 
.Usher,  depending  upon  the  grade,  the  quality  of  the  absorbent,  and  the 
nature  of  the  exposure.  The  *'  thawing  of  d3mamite  consists  in  slightly 
vanning  it  to  take  off  the  chill.  It  sometimes  requires  a  temperature  of 
iff  or  60°  P  to  do  this  effectively,  and  it  must  not  be  allowed  to  chill  again 
vhile  being  carried  to  the  drill  holes  and  loaded.  The  usual  method  of 
thawing  dynamite  is  by  a  small  out -door  fire,  but  the  disadvantages  of  this 
plan  are:  (1)  waste  of  time  in  thawing,  (2)  greater  or  less  danger  attached 
to  it,  (3)  inefficiency  of  thorough  thawing  so  that  the  dynamite  will  explode 
»ith  the  greatest  effect.  In  a  pamphlet  "  Thawing  Dynamite  "  published 
by  the  Aetna  Powder  O).,  of  Chicago,  is  an  illustration  of  a  Thaw  House 
about  7x10  ft.,  fitted  with  steam  coils  and  shelves  for  thawing.  The  shelves 
Itave  a  capacity  of  about  600  lbs.  of  dynamite,  and  about  1000  lbs.  more 
can  be  stored  in  the  house  in  boxes.  The  special  caution  for  sweeping 
and  cleaning  merits  careful  attention. 

In  preparing  the  charge,  the  fulminating  cap,  to  which  the  safety  fuse 
has  been  attached,  is  inserted  in  the  top  of  the  cartridge,  the  neck  of  which 
ii  tied  around  the  fuse  with  a  string,  and  the  charge  placed  in  the  hole  and 
Bred.     If  an  electric  blasting  machine  is  used,  a  special  cap  is  required. 

Many  of  the  dynamites  are  put  up  in  two  grades.  No.  1,  and  No.  2, 
tJae  former  containmg  as  high  as  76%  N.-G.  Some  of  the  powders  are  fur- 
sisbed  in  several  grades,  ranging  from  75  down  to  20%  N.JG.  In  ordering 
"iynamitc  it  is  necessary  to  state  the  percentage  of  nitroglycerin  required, 
vbether  30,  40,  60,  60.  75%,  imless  the  name  ot  the  desired  brand  if  known. 


354  l8.-'EXPLOSIVES. 

2.— Sous  OF  THB  Most  Common  Commercial  Dtnamitbs. 

(Note. — ^The  percentages  of  nitroglycerin  are  shown  in  parenthcsc 
Aetna   powder.    No.   1  (65).   No.   2  XX  (50).   No.  3  (40).  No.  3  X  (3 

No.  4  X  (25).  No.  5  (15). 
Atlas  powder.  A  (75),   B  +  (00).   B  (50).  C  +  (45),  C  (40),  D   +  (2 

D  (30).  E  +  (25). 

E  (20).  P  +  (15).  I  Carbonite  (25). 

Colonia  powder  (40).  |   Dualin  (40  to  50). 

Dynamite— Nobel's  Kieaelguhj^-Old  No.  1  (75),  Old  No.  2,  (40),  OM  I 

3,  (25). 
Portnte  (49).  I  Oelignite  (62i). 

Giant  powder.  No.  1  (75).   New  No.  1  (50).  No.  2  extra  (45),  No.  3  (4 

No.  2  c  (33).  No.  XXX  (27).  No.  M  (20). 
Giant  powdei--Nober»— No.  2  (20).     |   Hecla  powder.  No.  1  XX  (75). 
Herxmles  powder.  No.  1  XX  (75).  No.  1  (65),  No.  2  SSS  (55).  No.  2  SS  (£ 

No   2  S  (46).  No.  2  (40).  No.  3  S  (35),  No.  8  (30).  No.  4  S  (25),    No. 

(20). 


Horsley  powder  (72). 

Judson  powder,  PPP  (20),  FF  (15). 

Rcndrock  (40). 

Vigorite  (30  to  68). 


Judson  giant  powder.  No.  2  (4( 
Lithofracteur  (64). 
Stonite  (68). 
Vulcanite  (30). 


A  List  of  Permissible  Explosives  for  Use  in  Coal  Mines. — ^Pollow 
brands,  tested  prior  to  Oct.  1,  1009:  Aetna  coal  powder  A,  AA,  B.  C;  Bii 
minite  No.  1;  Black  Diamond  Nos.  8,  4;  Carbonite  Nos.  1,  2.  3,  1-L. 
2-L.  P.;  Coalite  Nos.  1.  2-D:  Coal  Special  Nos.  1.2;  Collier  dynamite  N 
2.  4.  5*  Gyant  A  low-flame  dynamite,  C  low-flame  dynamite;  Masui 
M.L.  F.;  Meteor  dynamite;  Mine-iteA,  B;  Manobel;  Tunelite  Nos.  5,6,7 


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19.— PRESERVATIVES. 

PAINTS. 

A  paint  consists  of  a  pi^rment.  vehicle,  drier,  and  (ustially)  solvent. 
Sometitnes  the  pigment  is  ground  alone  and  then  mixed  with  the  vehicle 
sad  drier  but  usually  they  are  ground  together,  and  sealed  in  kegs  or  cans 
for  shipment. 

Pfgnients. — ^The  following  are  the  most  important  to  the  engineer: 

Whitg  kad,  consisting  of  a  mixture  of  lead  hydrate  and  lead  carbonate,  is 
universally  employed  for  white  paint.  It  is  often  adulterated,  however, 
vhh  heavyspar.  gypmim,  chalk,  clay,  sulphate  of  lead,  etc..  which  renders 
it  more  or  less  inferior. 

Wkfie  »iuc  or  zinc  oxide  is  used  for  white  paint;  often  adulterated  with 
heavyspar. 

Lampblack  (mainly  carbon)  is  one  of  the  best  pigments  for  black  paint 
and  for  printer's  ink.  It  is  obtained  by  btu^ng  substances  rich  in  carbon, 
with  a  low  flame,  that  is,  to  incomplete  combustion,  so  the  carbon  will  not 
be  burned.  For  this  purpose  resin,  ozokerite,  the  by-product  hydrocarbons 
from  oil  refineries,  variotis  kinds  of  oils  gas,  etc.,  are  used. 

Bonthiack  and  ioory  black  are  obtained  by  heating  bones  with  exclusion 
of  air. 

Graphite  is  becoming  one  of  our  most  useful  paint  pigments,  especially 
as  a  protection  to  iron  and  steel    from  rust. 

Iron  oxides  give  brownish  colors  varying  to  red,  yellow,  etc.,  depending 
upon  the  natural  ores,  as  ochres,  bole,  pozzuole  earth,  sienna  earth,  etc 
nae  ground  ores  are  often  adulterated  with  heavyspar,  gypsum,  clay,  etc., 
ior  cheapness  and  shading  of  colors. 

Red  lead  (red  oxide  or  minium)  is  more  highly  oxidized  than  white 
lead  or  litharge  and  is  obtained  by  properly  heatmg  the  latter  in  a  furnace 
or  oven,  in  contact  with  the  air,  to  a  certain  temperature  (about  40()°  to 
50(P  C).  It  is  used  as  a  red  pigment  and  is  also  a  very  durable  cement  for 
gkjs  azid  for  water  pipes.  Commercially,  as  a  pigment,  it  is  often  adulter- 
ate! with  brick  dust,  red  bole,  heavyspar,  oxide  of  iron,  etc. — the  last 
Darned  being  particularly  objectionable. 

Verdigris  is  a  pigment  usually  mixed  with  white  lead  to  produce  a  green 
I^int.  It  is  made  by  exposing  thin  copper  plates  to  the  air  in  contact  with 
acetic  acid. 

Ochre  is  a  clay  containing  oxide  of  iron,  and  when  dried  and  ground  is 
oaed  as  a  pigment.  It  is  usually  of  a  yellowish  color  but  by  burning  it 
gradually  changes  to  red  by  the  oxidation  of  the  iron  present. 

Umber  differs  from  ochre  in  containing  a  quantity  of  oxide  of  manganese 
m  the  clay  in  addition  to  the  oxide  of  iron.  The  unbumed  or  "  raw  "  umber 
is  dried  and  ground  as  a  pigment  for  brown  paint:  while  the  calcined  or 
"  burnt  "  timber  yields  a  reddish  brown  color. 

Sienna  is  a  ferruginous  earth  like  ochre,  the  imbumed  of  '*  raw  "  sienna 
prodticine  a  vellowish-brown  pigment;  if  "  burnt "  (before  being  ground) 
a  jriekls  a  reddish-brown  pigment. 

Asbestos  is  a  fibrous  hornblende  (amphibole)  or  crysotile  (serpentine) 
of  various  colors  as  white,  gray,  red,  green  and  black.  Its  value  m  paint 
Hes  in  its  fireproofing  qualities  when  applied  to  wood,  or  other  inflammable 
matcxiaL 

Vriddef — ^A  vehicle  in  paint  corresponds  to  lime  paste  in  common 
mortar,  forming  the  binder  when  dry.  in  calcimine,  the  pigment  is  zinc- 
white  and  the  vehicle  glue-sizing  diluted  with  water;  tintmg  is  produced 
by  adding  the  various  coloring  matters.  For  common  paints  linseed  oil  is 
uzuveraally  j  referred  as  a  vehicle,  although  any  kind  of  varnish  may  be  used. 

Digitized  by  VjOOQ  IC 

355  ^ 


850 


19.^PRESERVATIVES. 


Linsttd  oil  is  obtained  from  the  seed  of  common  flax,  by  ( 1)  cold  pressure, 
(2)  hot  pressure.  (3)  extraction.  The  first  named  process  produces  the 
food  oil;  the  second  and  third,  the  article  of  commerce.  The  method  of 
extraction  is  by  the  use  of  some  solvent  as  benzine,  naphtha,  etc.  Carbon 
disulphide  yields  fully  50^  more  oil  than  the  cold-drawn  process,  but  is 
objectionable  when  used  with  a  lead  pigment  because  the  retained  sulphur 
turns  it  dark.  "  Boiled  "  linseed  oil  is  used  as  a  vehicle  for  paints  beoause 
drying  is  facilitated  and  it  acts  better  with  the  pigment.  Linseed  oil  is 
often  adulterated  with  other  oils  as  those  of  mustard  seed,  rape  seed,  hemp 
3eed,  cotton  seed,  etc.  The  engineer  usually  specifies  "  pure  "  ra^r  or 
boiled  linseed  oil.  the  former  being  often  preferred  ahm  as  a  ooatins  for 
steel  when  it  leaves  the  shop. 

Driers,  such  as  compotmds  of  lead,  manganese  and  zinc,  are  simply 
oxidising  agents  for  converting  the  oils  from  "  vehicles  "  into  "  binders.*^' 
Among  the  most  common  are  litharge,  red  lead,  lead  acetate,  oxides  of 
manganese,  borate  of  manganese,  oxide  of  sine,  etc.,  or  their  various  mix> 
tures.  These  act  as  agents  in  conveying  oxygen  from  the  air  to  the  oils, 
thus  drying  them. 

Solvents. — A  good  solvent  is  slow  to  evaporate  and  flows  sufficiently 
to  efface  the  brush  marks. 

Turpentine  is  the  best  solvent.  It  is  a  repeated  distillation  of  the 
resinous  sap  of  certain  coniferous  trees,  and  dissolves  readily  the  various 
substances  used  in  paints.  Only  the  pure  turpentine  should  be  accept- 
ed. It  is  composed  entirely  of  carbon  and  hydrogen,  but  when  exposed 
to  the  air  it  absorbs  oxvgen  and  turns  yellow.  It  should  be  kept  air-tisht 
and  away  from  the  light.  Turpentine  has  no  substitute.  Benzine,  kero- 
sene and  some  other  oils  are  sometimes  used  either  alone  or  as  adulter- 
ants, but  should  be  shunned. 

House  Paints. — ^White  is  obtained  from  white  lead*,  black,  from  launp- 
black:  red,  from  red  lead  (50)  and  red  ochre  (50);  green,  from  verdigris  (7^) 
and  white  lead  (26);  chocolate,  from  Spanish  brown  (96)  and  lampblack  <4)  ; 
stone  color,  from  white  lead  (00)  and  burnt  umber  (1);  lead  color,  frxxai 
white  lead  (08)  and  lampblack  (2). 

The  following  table  shows  how  various  colors  may  be  produced  by  a 
simple  combination  of  two  other  colors.  To  produce  "  shades  "  of  &xxy 
color  add  black;  to  produce  "  tints  "  add  white: 


Red. 

YeUow. 

Blue. 

Orange. 

Purple. 

Green. 

Red 

Yellow 

Orange. 

Blue 

Purple. 

Green. 

Orange 

Purple 

Russet. 

Green 

Olive. 

Citrine 

— 1 

1 

Note. — Yellow  and  red  produce  orange;  yellow  and  blue,  green; 
and  orange,  russet;  etc. 

Special  Paints. — These  are  made  by  mixing  substances  having  af>«cj 
properties,  with  the  pigments:  ^ 

AlHtninum  paint  is  made  from  powdered  aluminum  and  contains 
91%  metallic  aluminum.  6%  aluminum  oxide,  1J%  silica.  1%  >K^«^t| 
Gas  or  air  is  forced  under  pressure  into  the  molten  metal  which  is  vigOTx>\ii 
stirred,  and  forms  a  powder  in  setting.  This  powder  is  crushed  and  ri 
through  sieves  and  polished.  About  2  lbs.  of  the  powder  is  mixeti  ^ 
one  gallon  of  varnish  composed  of  1.5  galls,  turpentine.  J  gall,  palest, 
varnish.  4  oz.  palest  terebine.  4  oz.  carbonate  of  magnesia.  The  " 
allowed  to  settle  and  the  clear  varnish  is  drawn  off. 


•*«^t^?^ 


PAINTS,     VARNISHES.     PLATING,  357 

BroHMt  paint  is  made  hy  mixing  filings  of  copper,  brass,  etc.,  with  the 
pigment,     it  is  used  in  pamting  iron  and  other  materials. 

Copper  paint,  mercury  paint,  arsenic  paint  and  paris-green  paint  are 
poitcmous  to  marine  life  and  are  used  in  painting  ships  bottoms.  The 
copper  pcunt  is  formed  b^  mixing  salts  of  copper  with  the  pigment.  The 
ocners  axe  formed  by  mixmg  merctu-y,  arsenic,  and  pans  green,  respectively, 
with  the  pigments  used. 

VARNISHES,  LACQUERS,  ETC 

Vanrfshca^ — A  Tarnish  consists  of  a  gum  or  resin  dissolved  in  "  spirit  " 
or  in  oil,  with  peiiiapts  some  coloring  matter  added.  The  resinous  sub- 
stances are  amber,  anim^,  copal,  mastic,  resin,  sandarac.  shellac,  for  the 
%hter  colors:  and  asphaltum  and  pitch  for  the  dark  colors.  The  solvents 
are  "  spirits.'  as  ethyl  alcohol,  wood  (methyl)  alcohol,  ether,  benzol,  chloro- 
ionn.  carbon  disulphide.  coal  oils  (light),  turpentine:  or  "  oils,"  as  linseed, 
poppy,  nut.  hemp,  castor,  walnut,  cotton-seed.  The  coloring  matter  is 
aloes,  dragon's  blood  (a  resin),  tumeric,  sanders-wood,  saffron,  anotto, 
indigo.  The  name  of  the  varnish  usually  takes  its  name  from  the  solvent, 
as  spirit  varnishes  and  ail  varnishes. 

Lacqacring  is  the  varnishing  of  polished  metal  surfaces,  as  brass.  The 
lacquer  is  an  alcoholic  solution  af  shellac  with  some  coloring  matter  added 
to  9ve  the  desired  tint.  Being  transparent  or  nearly  so,  the  brass  effect 
is  visible  while  the  metal  is  at  the  same  time  preserved  from  discoloring 
or  oxidi^ng. 

Japaiming  is  varnishing  with  japan,  a  black  varnish  made  with  asphal- 
tum (mostly)  dissolved  in  turpentine. 

QALVANIZINO  AND  TINNING. 

Qalvanteing  consists  in  dipping  the  iron  or  steel  sheets,  rods,  boltSf 
wire,  etc,  in  a  bath  of  molten  zinc.  The  coat  is  naturally  very  durable 
cmless  exposed  to  sulphurous  smoke  or  other  similarly  destructive  chemical 
agents. 

Tfaiflinc  consists  in  immersing  the  iron  or  steel  sheets  in  molten  tin  and 
taUow.  ^n  plate,  so  called,  is  merely  the  thin  metal  sheet  coated  with  tin. 
Teme  plate  is  made  by  dipping  the  iron  or  steel  sheets  into  a  bath  of  tin 
and  lead,  being  less  expensive  than  tin  plate  and  much  inferior  to  it.  It 
is  used  largely  for  roofing. 

ELECTRO-PLATINQ. 

This  branch  of  Electro-Chemistry  was  evolved  from  discoveries  made 
by  Jacobi  in  1838.  By  its  use  we  are  enabled  to  plate  the  cheaper  and  less 
durable  metals  with  durable  metal  coatings.  The  agent  employed  is  the 
electric  current. 

Electro-Chemistry  is  that  branch  of  chemistry  which  treats  of  the 
fhemiral  changes,  produced  by.  or  producing,  electricity  or  electrical  encnjy. 
It  embraces  the  subjects  of  ( 1)  Electrolysis,  the  decomposition  of  a  chemical 
oompoiind  called  an  electrolyte  into  its  constituent  parts  by  an  electric 
current:  and  (2)  Electro-Metallur^.  the  deposition  of  certain  metals,  as 
gold,  silver,  copper,  etc.,  from  their  solutions  by  means  of  the  slow  action 
of  an  electric  current.  All  electrolytes  are  either  acids,  bases  or  salts,  and 
all  electro-chemical  reactions  produce,  or  are  produced  by,  these  three 
classes  cd  compounds.  The  transformation  of  chemical  energy  into  elec- 
trical energy  is  through  a  system  termed  a  voltaic  or  galvanic  cell  or  battery, 
two  or  more  cells  in  combination  forming  a  battery. 

Electrolyds  — ^When  an  electrolytic  substance  is  subjected  to  the  action 
of  an  electric  current  it  decomposes  into  ions,  the  cottons  (electropositive 
ions)  seeking  the  "  cathode  "  or  negative  pole,  and  the  anions  (electro- 
XMsative  ions)  seeking  the  "  anode  "  or  positive  pole.  Thus,  when  water 
is  decomposed  the  hydrogen  atoms  (cations)  are  attracted  to  the  negative 
pole,  while  the  oxygen  atoms  (anions)  collect  at  the  positive  pole. 

Electre-Metalliirgy  is  an  electrolytic  process  by  which  the  metal  in  an 
Qie  is  separated  from  its  impurities.  It  is  one  of  the  common  processes,  the 
others  being:  Smelting  or  heating  of  the  ore;  Amalgamation,  by  the  use  of 
niexcury;  and  Extraction  by  chemkal  solutions.  tized  by  UoOQLc 


358  19.^PRESBRVATIVES, 

Elcctro-PUtiiig  embodies  all  the  preceding  principles.  The  article  to 
be  plated  must  first  be  cleaned  thoroughly.  It  is  dipped  in  a  cleansing 
solution  and  then  thoroughly  rinsed  with  water  so  that  none  of  the  solution 
will  remain.  If  necessary  it  is  then  placed  in  a  scouring  tray  before  going 
to  the  plating  vat.  where  it  is  susp>enaed  in  the  plating  solution  from  copper 
rods  by  means  of  short  "  slinging  "  wires  of  copper.  The  electric  current 
used  for  depositing  the  metal  from  the  plating  solution  may  be  obtained 
from  any  sotirce  which  is  convenient,  either  from  a  battery  or  dvnamo. 
The  following  are  some  of  the  solutions  used  for  electro-plating:  VorgoJd 
plating,  a  solution  of  gold  cyanide  and  potassium  cyanide;  for  stiver,  a 
solution  of  silver  cyanide  and  potassium  cyanide;  for  copcer^  an  ammoniacal 
solution  of  copper  and  potassium  cvanide;  for  nicktl,  tne  double  sulphate 
of  nickel  and  ammonia,  or  the  double  salt  of  nickel  and  ammonia;  for orass. 
liquid  ammonia  and  potassium  cyanide  added  to  a  nitric  add  solution  ot 
brass.  Various  other  metals  may  be  used  for  plating,  as  iron,  tin,  lead, 
platinum,  bronze,  etc. 

Gold  and  silver  may  be  deposited  in  excellent  condition  on  a  large 
number  of  the  metals  and  allovs.  Copper  ihay  be  deposited  on  steel,  iron, 
tinned  iron,  zinc;  also  on  leaa  and  tin,  and  their  alloys;  it  is  to  be  noted 
also  that  when  any  of  these  metals  are  to  be  gold-,  silver-,  or  nickel-plated 
it  is  best  to  plate  them  with  copper  first,  as  copper  plating  adheres  more 
firmly  to  them,  and  in  turn  is  adhered  to  more  firmly  by  the  desired  coat- 
ings. Nickel  may  be  deposited  on  most  of  the  common  metals,  including 
German  silver,  brass,  and  alloys  of  the  soft  metals. 

PRESERVATION  OF  STEEL  AND  IRON. 

Oiling,  Painting,  Asphalting,  etc. — Many  engineers  specif y  that  structtiral 
material  on  leaving  the  shop  shall  simply  be  coated  with  pure  boiled  linseed 
oil  instead  of  being  painted.  This  is  doubtless  good  practice,  as  the  oil 
penetrates  the  skin  of^the  metal  sufficiently  to  preserve  it  temporarily  from 
rust  and  does  not  cover  up  any  possible  miperfections.  which  zaay  be  de- 
tected readily  before  erection.  Among  the  best  paints  are  the  lead  paints 
and  the  carbon  painu.  On  ordinary  structures  they  should  last  at  least 
ten  years  if  properly  applied.  Some  of  the  best  paint  companies  guarantee 
their  paints  for  that  period.  Graphite  paint  and  asphalt  paint  are  also 
lajtgely  used.  One  gallon  of  paint  will  cover  600  sq.  ft.  and  upward  of 
metal,  two  coats;  costing  about  A  to  A  ct.  per  sq.  ft.;  or  say,  2  to  3  cents 
per  100  lbs.  of  metal,  for  ordinary  structures.  For  light  bridges  the  cost 
per  100  lbs.  would  be  greater;  for  heavy  bridges  and  buildings,  about  2 
cents.     This  is  exclusive  of  labor  in  painting. 

Iron  or  steel  thoroughly  imbedded  in  cement  or  cement  concrete  is 
permanently  protected  from  rust,  but  not  from  electrolysis. 

For  water  pipes  the  following  are  used:  Asphalt,  coal  tar  (inferior). 
Smith's  durable  metal  coating,  Sabin  process.  The  last  named  is  a  process 
of  applying  asphalt  varnish,  the  pipe,  after  dipping,  being  baked  for  several 
hours  at  a  temp,  of  400**  to  600**,  thus  producing  an  enamel  coating. 

Mill  Scale  on  structural  steel,  can  effectively  be  removed  at  the  mill: 
(1)  by  "  pickling  "  or  cold  rolling,  at  an  expense  of  say  80  cents  to  $2  .00 
per  ton:  (2)  by  the  sand  blast  at  a  cost  of  about  i  less;  (3)  by  steel  scrapers 
and  wire  brushes  at  considerably  less  expense  if  only  ordinary  cleaninc;  is 
desired.  Engineers  differ  as  to  the  advisability  of  using  the  s&nd  blast. 
The  following  opinions  are  expressed  in  Report  of  Committee  E  on  Pre- 
servative Coatings  for  Iron  and  Steel,  Proceedings  A.  S.  T.  M.,  Vol.  VI: 
Mr.  Phelps  Johnson,  Eng'r  Dominion  Br.  Co.,  Limited,  says:  "  In  my  ex- 
perience I  have  foimd  that  an  exposure  to  the  weather  for  three  or  four 
months  will  ordinarily  loosen  nearly  all  the  mill  scale  adhering  to  rolled 
material,  and  have  considered  that  the  subsequent  removal  by  steel  bru^ies 
of  the  slight  coating  of  nist  powder  that  is  formed  leaves  the  material  in 
the  best  practicable  shape  for  receiving  the  paint.  I  am  of  the  opinion 
that  the  exposure  to  the  weather  may  be  prolonged  to  say  24  months  without 
appreciable  waste  of  metal  or  injurious  pitting  or  roughening  of  the  surfaces, 
and  that  there  is  but  slight  increase  in  the  labor  necessary  to  brush  the  sur- 
face clean  for  painting."  Mr.  Gustav  Lindenthal,  Consulting  Engineer, 
says:  **  Mill  scale  is  simply  the  magnetic  iron  oxide,  which  is  insoluble  in 
most  acids,  and  an  excellent  preservative  of  the  metal  tindemeath,  al>9vays 
provided  that  it  adheres  tightly  to  the  surface  of  the  metaL  ...  I 
consider  the  xise  of  the  sand-blast  for  the  cleaning  of  metal  surfaces  not  only 


PRESERVATION  OF  IRON  AND  TIMBER,  369 

,  btxt  detriinental.    .    .    .    The  problem  of  painting  iron  and  steel 

is  not  yet  lolved.  in  spite  of  the  volumes  of  papers,  discussions  and 
neports  on  investigations  which  encumber  the  bookshelves."  Mr.  A.  H. 
Sabin.  Chemist,  says;  "  For  best  work,  the  cleaning  of  structural  steel 
voric  by  the  use  of  the  sand  blast  is  probably  the  simplest  and  most  satis- 
factory way  to  have  it  done.     The  great  objection  to  this,  as  to  all  such 

work,  ts  the  cost For  ordinary  work,  the  wire  brush  is  an  efficient 

means  of  getting  rid  of  loose  scale  and  dirt;  but  it  is  practically  worthless 
for  removing  thick  rust  or  anything  which  adheres  closely.  Much  of  such 
material  may  be  removed  by  steel  scrapers,  but  deeplv  corrugated  spots 
flhoukl  be  cleaned  out  thoroughly  with  a  chisel,  and  then  well  brushed." 
Mr.  George  B.  Thackray,  Structural  Engineer.  Cambria  Steel  Co..  says: 
"  Send  blasting  is  almost  useless  and  impracticable,  as  I  have  seen  sand 
hbBting  done,  exposing  the  metal  surface,  which  was  soon  covered  with  a 
thick  coat  of  nist  before  the  painters  could  reach  it.  although  both  the 
•and  blasters  and  painters  were  working  with  expedition." 

Mr.  Leonard  M.  Cox,  Civil  Eng'r.  U.  S.  Navy,  in  describing  the  pro- 
tective coating  on  the  floating  dry  dock  "  Dewey."  says:*  **  The  selection 
of  a  protective  coating  for  the  dodc  was  made  the  subject  of  careful  study. 
Samples  of  a  number  of  the  best  known  paints  on  the  market,  exclusive 
of  the  oxide  raunts,  were  applied  to  test-plates  and  subjected  to  difTcrcnt 
conditions.  Three  plates  were  coated  with  each  sample,  one  was  exposed 
to  the  weather  at  the  company's  works,  a  second  was  suspended  half  m  air 
and  half  in  water,  and  a  third  was  submerged  in  the  water  of  Chesapeake 
Bay.  The  tests  extended  over  a  period  of  2  years,  during  the  construction 
of  the  doc^.  and  resulted  in  the  cnoice  of  a  mixture  of  red  lead,  white  zinc 
and  Unseed  oil  in  the  following  proportions:  100  lbs.  of  red  lead.  15  lbs.  of 
zinc  ground  in  oil.  and  5  galls,  of  linseed  oil.  It  is  only  fair  to  state  that  in 
these  tests  a  graphite  paint  manufactured  in  Detroit  showed  as  good  results 
as  the  red  lead,  but  was  not  used  because  of  the  lack  of  available  data 
bearing  on  its  behavior  in  salt  water. 

"  As  the  pontoons  have  more  or  less  water  in  their  bottoms  at  all  times, 
except  when  self-docked,  it  was  very  necessary  to  provide  adequate  pro- 
tection for  their  floors.  Experiments  with  Bitumastic  Enamel  led  to  its 
application  to  the  whole  of  the  interior  floors,  and  to  all  vertical  bulkheads, 
braces,  etc.,  to  a  height  ofl  12  ins.  The  process  of  applying  tbi8*mixture 
ronsists  in  a  careful  cleaning  and  drying  ol.the  metal,  one  coating  of  a  solu- 
tion, the  fiinction  of  which  is  to  provide  a  surface  to  which  the  enamel  will 
adhere,  and  a  final  heavy  coating  of  enamel,  from  i^i  to  i  in.  in  thickness, 
appliea  hot. 

"  Great  care  was  taken  to  rid  the  hull  plating  of  mill  scale.  The  speci- 
Scation  provided  that  all  loose  scale  should  be  removed  by  hammering, 
•craping,  and  brushing  with  wire  brushes,  and  to  make  its  removal  easier 
and  surer,  no  paint  was  applied  until  a  short  time  before  launching.  Nearly 
all  the  material,  therefore,  was  exposed  to  the  weather  in  the  yard  for  periods 
ranging  from  12  to  24  months.  The  existence  of  mill  scale  on  the  com- 
pleted structure  has  such  an  important  bearing  on  the  subject  of  corrosion 
that  the  additional  expense  entailed  by  pickling  would  be  a  good  investment 
m  the  way  of  insurance,  and  it  is  recommended  that  specifications  for  future 
docks  include  this  requirement.  It  was  also  noticed  that,  in  the  process 
<tf  weathering,  the  mill  scale,  where  covered  with  paint,  adhered  closely 
and  could -not  be  removed  without  the  use  of  the  hammer  and  chisel.  This 
scale,  of  course,  will  come  off  in  time,  and  for  this  reason  the  requirement 
that  all  contact  surfaces  be  given  one  coat  of  paint  before  assembling, 
sixrald  be  limited,  so  as  to  apply  to  rolled  shapes  only." 

PRESERVATION  OF  TIMBER. 

8o«rces  of  Decay. — Decay  may  be  due  to  (1)  "wet  rot."  caused 
by  the  attack  of  certain  large  fungi  which  may  enter  the  pores  of  standing 
tiniber  or  of  timber  tised  in  damp  places;  (2)  fermentation,"  or  decompo- 
sition of  the  celluloee  tissues  by  the  putrifying  sap.  which  takes  place  in 
onaeaaoned  timber:  (3)  "  dry  rot."  which  occurs  in  so-called  seasoned 
timber,  caused  by  the  fungus  Meruiius  hchrymans  which  can  operate  only 
in  the    presence  of  some    moisture;  (4)  insect  larvae  and  forest  worms; 

♦  Page  146^701.  LVIII.  Trans.  A.  S.  C.  E..  in  Paper  No.  1042.  entitled 
"The   Naval  Floating  Dock — its  advantages,  design  and  construction." 


860  19.-'PRESERVATIVES. 

(5)  sea  worms,  as  the  teredo  (Teredo  navalis),  limnoriaand  other  x 
wood  borers  which  inhabit  pure  salt  water  and  attack  woodwork  exposed 
to  same.  These  sea  worms  were  formerly  confined  to  southern  waters,  but 
have  gradually  worked  their  way  northward.     (Not  present  in  freshwater.) 

POIng  and  timber  grillage  for  submarine  work  need  not  be  seasoned 
or  treated  with  preservatives  when  below  the  action  of  the  teredo,  as  timber 
will  last  thus  for  centuries.  Piling  in  ordinary  foundation  work  is  prac- 
tically preserved  from  contact  with  the  atmosphere  and  the  destructive 
elements,  by  being  sealed  in  the  surrounding  moisture.  It  is  customary 
to  leave  the  bark  on  piles  when  driven  in  the  water  and  to  peel  them  when 
land  driven.  If  exposed  to  teredo  the  piles  are  peeled  and  treated  with 
some  preservative.  They  may  be  copper  sheeted,  creosoted,  tarred,  kvan- 
ized,  wrapped  with  tarred  paper  or  other  similar  preparation  secured  by 
vertical  strips  of  wood.  Specially  constructed  piles  are  sometimes  usea. 
made  up  of  strips  of  scantling,  on  the  principle  that  teredo  will  not  cross 
a  seam  between  two  strips;  the  composite  pile  thus  made  bein^  sometiznes 
treated  also  with  a  surface  preservative.  The  process  of  encircling  piles 
with  tight  casings,  pumping  out  the  water,  and  then  applying  steam,  has 
proved  to  be  expensive. 

Creosoting  consists  in  impregnating  the  wood  with  creosote  oil  (con- 
taining carbolic  acid,  cresylic  acid,  etc.)  which  is  obtained  from  coal-tar 
distillations.  The  timber  to  be  treated  is  placed  in  large  iron  cylinders, 
hermetically  sealed  and  filled  with  steam  at  a  low  pressure,  which  softens 
and  warms  up  the  sap  and  woody  fibres.  The  steam  b  then  expelled  and 
a  partial  vacuum  produced  (one-half  atmosphere)  with  the  air  puni(>s. 
thus  expunging  the  sap  in  the  cells  of  the  wood.  The  creosote  oil  is  then 
turned  into  the  cylinders  and  by  means  of  hydraulic  pressure  is  forced  into 
the  wood.  There  are  many  variations  in  the  process.  Creosoting  is  uni- 
versally recognized  as  one  of  the  best  and  most  practical  preservatives 
known.  Timber  should  be  framed  before  treatment  as  the  suxface  satura- 
tion is  strongest.  Ordinary  ties,  6x8 — 8,  usually  absorb  about  25  pounds 
of  creosote,  costing  from  40  to  60  cents  apiece.  Piling  or  timber  exposed 
to  the  teredo  require  much  more  oil.  The  cost  or  creosoting  piling  may 
be  assumed  at  20  cents  upward  per  lin.  ft. ;  and  timber  $1 6 .  upward  per 
M.  B.  M.  Creosoting  probably  ranks  first,  and  bumettising  second,  as  a 
timber  preservative,  on  a  commercial  scale. 

One  valuable  point  to  be  noted  in  creosoting  is  that  the  hard  and  expen- 
sive woods  like  oak  and  longleaf  pine  do  not  absorb  the  creosote  ou  as 
rapidly  nor  as  thoroughly  as  do  the  softer  and  less  expensive  woods  like 
beech;  so  that  the  soft  woods,  thoroughly  impregnated,  really  outlast  the 
harder  ones. 

For  a  good  description  of  a  creosoting  plant  see  the  article  entitled 
••  New  Tie  and  Timber  Preserving  Plant  of  the  A.  T.  &  S.  P.  Ry,  at  Somer- 
ville,  Texas,"  Eng.  News,  May  3,  1906. 

Bamcttizing  is  similar  in  method  to  creosoting.  The  solution  used  is 
chloride  of  zinc,  a  compound  of  zinc  and  hydrochloric  add.  The  results 
are  inferior  to  creosoting,  especially  for  bridge  timbers.  For  ties,  the 
comparison  is  not  so  marked.  The  cost  of  bumettizing  is  about  i  to  i  that 
of  creosoting.  but  much  depends  upon  the  uses  for  which  the  timber  is 
required.  As  water  leaches  out  the  zinc  chloride  in  a  comparatively  ^ort 
time  when  the  treated  timber  is  constantly  submerged,  it  is  evident  that 
bumettizing  will  not  do  for  piling.  It  even  loses  its  strength  in  posi- 
tions exposed  to  heavy  rains. 

Miscellaneous  Notes. — Where  timber  is  used  in  construction,  the  first 
proper  guard  against  the  actions  of  decay  is  the  selection  of  the  right  kind 
of  wood.  Cedar,  redwood,  juniper,  cypress,  etc.,  are  best  able  to  resist 
ordinary  decay,  due  to  alternate  wetness  and  dryness,  hence  their  special 
usefulness  for  fencing,  telegraph  poles,  ties,  shingles,  etc.  Decay  is  some- 
thing that  enters  the  wood  at  some  time  or  other,  either  during  the  period 
of  growth  or  subsequently.  There  is  little  doubt  that  if  a  timbor  is  cut 
from  a  perfectly  healthy  tree  and  its  surface  hermetically  sealed  so  as  to 
keep  the  interior  in  a  constant  state  of  either  extreme  moisture  or  dryness, 
it  will  last  for  thousands  of  years.  The  earliest  and  most  primitive  method 
of  preserving  wood  was  that  of  charring  the  surface,  practiced  before  the 
dawn  of  hwtory.  Subsequently,  it  was  discovered  that  piling  kept  con- 
stant] v  moist  would  last  for  centuries:  and  that  the  life  of  timber  wouki 


TIMBER  PRESERVATION.  861 

be  prokmsed  greatly  if  kept  dry  from  the  influences  of  the  weather,  etc. 
Witoess  some  of  our  old  covered  wooden  bridges,  and  the  wooden  joists  of 
our  cokmial  houacs. 

In  the  West  where  wooden  bridges  are  common  there  are  four  principal 
methods  employed  to  prolong  the  life  of  the  structure:  (1)  Wooden  covenng 
(not  common);  (2)  seasoning  the  timber  to  12  or  15  per  cent  of  moisture, 
aad  painting:  (3)  covering  the  upper  stuiaces  of  chords  and  end  posts 
with  galvanized  iron  (#  22  to  #  27),  allowing  the  sheets  to  lap  a  few  inches 
down  the  sides;  (4)  treating  the  timber  before  erection,  or  painting  it  after 
erection,  with  a  liquid  preparation  known  as  carbolineum  avenarius.  This 
oreparation  is  also  much  us^  in  preserving  flooring  and  wooden  paving 
Uocks. 

A  coating  of  coal  tar  forms  a  good  preservative  on  any  material,  wood. 
iron  or  stone,  but  its  appearance  is  often  objectionable.  Note  the  tise  of 
tarred  paper  for  roofing. 

Copper  sheeting  for  piles  and  ships'  bottoms  is  very  effective  against 
the  action  of  sea  worms. 

It  is  claimed  that  the  life  of  wooden  posts  can  be-  lengthened  by  boring 
sa  auger  hole  in  the  top.  filling  same  with  salt,  and  sealing  with  a  wooden 
phs.  Probably  the  more  effective  method  is  to  bevel  the  tops  of  the  posts, 
ana  plane  and  paint  them.  Posts  of  all  kinds  which  set  in  the  grotmd  mav 
be  paints  with  tar  for  a  short  distance  above  and  below  the  ground  level, 
and  an  additional  covering  of  metal  may  also  be  used.  Telegraph  poles 
are  frequently  treated  in  this  manner,  and   their  life  greatly  lengthened. 

Chloride  of  zinc  is  often  used  for  the  preservation  of  timber,  and  as  a 
dinnfectant. 

Creosote  oil  tends,  if  anything,  to  pr0s^rv€  railway  spikes  in  ties;  it  also 
has  a  detfrrtMt  effect  on  the  ravages  of  the  teredo  on  piling. 

Creosote  and  zinc  chloride  together  forms  Rutgen  s  process. 

Barshall  or  Hesselmann  process — zinc  chloride  and  glue. 

Kyanizing — corrosive  sublimate. 

SEASONING  OF  TIMBER. 

The  following  is  a  digest  of  Bulletin  No.  41,  Bureau  of  Forestry,  U. 
S.  Department  of  Agriculture,  issued  in  1903,  comprising  an  article  entitled 
"  Seasoning  of  Timber."  by  Hermann  von  Schrenk,  in  charge  of  Mississippi 
Valley  Laboratory,  Bureau  of  Plant  Industry: 

Distribotioii  of  Water  in  Timber. — (a)  Local  Distribution.— Water  may 
occxir  in  wood  in  three  conditions:  (1)  It  forms  the  greater  part  (over  90 
per  cent)  of  the  protoplasmic  contents  of  the  living  cells;  (2)  it  saturates 
the  walls  of  all  cells;  and  (8)  it  entirely  or  at  least  partly  fills  the  cavities 
cf  the  lifeless  cells,  fibers,  and  vessels;  in  the  sapwood  of  pine  it  occurs  in 
an  three  forms;  in  the  hcartwood  only  in  the  second  form,  it  merely  satur- 
ates the  walls.  Of  100  pounds  of  water  associated  with  100  pounds  ot  dry- 
TQod  substance  taken  from  200  pounds  of  fresh  sapwood  of  white  pine, 
about  35  potmds  are  needed  to  saturate  the  cell  walls,  less  than  5  poimds 
are  contained  in  living  cells,  and  the  remaining  60  pounds  partly  fill  the 
cavities  of  the  wood  fibers.  This  latter  forms  the  sap  as  ordinarily  under- 
wood. It  is  water  brought  from  the  soil,  containing  small  quantities  of 
nsoeral  salts,  and  in  certain  species  (maple,  birch,  etc.),  it  also  contains 
at  certain  times  a  small  percentage  of  sugar  and  other  organic  matter. 
These  organic  substances  are  the  dissolved  reserve  food,  stored  during 
winter  in  the  pith  rays,  etc.,  of  the  wood  and  bark;  generally  but  a  mere 
trace  of  them  is  to  be  foimd.  From  this  it  appears  that  the  solids  contained 
in  the  sap,  such  as  albumen,  gum.  stigar,  etc.,  can  not  exercise  the  influence 
OT  the  strength  of  the  wood  which  is  so  commonly  claimed  for  them. 

The  irood  next  to  the  bark  contains  the  most  water.  In  the  species 
vhkfa  do  not  form  heart  wood  the  decrease  toward  the  pith  is  gradual,  but 
*here  this  is  tormed  the  change  from  a  more  moist  to  a  drier  condition  is 
uually  quite  abrupt  at  the  sapwood  limit.  In  longleaf  pine,  the  wood  of 
the  outer  1  inch  of  a  disk  may  contain  60  per  cent  of  water,  that  of  the 
next,  or  second  inch,  only  35  per  cent,  and  that  of  the  heartwood  only  20 
per  cent.  In  such  a  tree  the  amount  of  water  in  any  one  section  varies 
^^h  the  amount  of  sapwood,  and  is  therefore  greater  for  the  upper  than 
the  lower  cuts,  greater  for  the  limbs  than  stems,  and  greatest  of  all  in  the 
roots. 


362  19.— PRESERVATIVES. 

Different  trees,  even  of  the  same  kind  and  from  the  same  place,  differ 
as  to  the  amotmt  of  water  they  contain.  A  thrifty  tree  contains  more  water 
than  a  stunted  one,  and  a  young  tree  more  than  an  old  one.  while  the  wood 
of  all  trees  varies  m  its  moisture  relations  with  the  season  of  the  year. — 
Timber.  By  Filibert  Roth  (Bull.  10,  Division  of  Forestry,  U.  S.  Dcpt. 
of  Agriculture,  1895.) 

(b)  Seasonal  Distribution. — It  is  generally  supposed  that  trees  contain 
less  water  in  winter  than  in  summer.  This  is  evidenced  bv  the  popular 
saying  that  "  the  sap  is  down  in  the  winter."  This  is  not  always  the  case. 
Some  trees  contain  as  much  water  in  winter  as  in  summer,  if  not  more. 
The  average  weight  of  lodgepole  pine  ties  of  the  same  sir«  cut  at  Bozeman. 
Mont.,  in  June,  1902,  was  167  lbs.;  in  July.  144  lbs.;  in  Au^.,  150  lbs.;  in 
Sept.,  157  lbs.;  in  Oct.,  164  lbs.  It  is  probable  that  this  mcrease  would 
keep  up  throughout  the  winter. 

Relatioa  of  Water  to  Decay  in  Timber. — ^Low  forms  of  plant  life  called 
fvmgi  grow  in  wood,  and  by  so  doing  disintegrate  and  dissolve  portions  of 
the  wood  fiber.  As  a  result  of  this,  the  wood  changes  in  its  physical  prop- 
erties and  is  called  decayed.  When  the  fungus  has  extracted  a  sufficient 
amount  of  material,  it  forms,  on  the  outside  of  the  wood,  fruiting  bodies 
known  as  ptmks  or  toadstools,  containing  spores,  which  are  blown  about 
and  infect  sovmd  wood.  One  of  the  most  common  of  these  wood-destroying 
fungi  is  called  the  Lentinus  lepidens.     The  conditions  necessary  for  the 

Ewth  of  these  fungi  are  (1)  water,  (2)  air.  (3)  organic  food  materia],  and 
a  certain  amount  of  heat.  The  wood  fiber  and  the  organic  substances 
nd  in  the  living  cells  of  sapwood,  such  as  albuminous  substances,  starch, 
sugar  and  oils,  form  the  food  supply  necessary  to  start  the  growth  of  the 
fimgus  threads.  A  further  requirement  is  oxygen;  no  growth  will  take 
place  under  water  or  in  the  grotmd  at  depths  of  2  feet  or  more,  the  depth 
varying  with  the  character  of  the  soil.  The  best  examples  of  this  necessity 
for  oxygen  can  be  foimd  in  the  way  in  which  fence  posts  and  telegraph  and 
telephone  poles  decay  at  points  just  at  or  just  below  the  surface  of  the 
ground,  where  there  is  a  balance  between  the  supply  of  air  and  of  "water. 
For  practical  purposes  water  is  the  most  important  factor.  Without 
water  no  fungus  growth,  and  consequently  no  decay,  is  possible.  **  Dry 
rot,"  a  form  of  decay  in  which  the  wood  turns  to  a  dry,  brittle,  charcoaV- 
like  substance,  is  commonlv  supposed  to  take  place  without  any  water. 
But  such  is  not  the  case.  The  atmospheric  moisture  is  sufficient  to  penriit 
growth  of  the  dry-rot  ftmgus  even  if  no  moisture  is  contained  in  the  "wood. 
Too  much  water  will  prevent  fungus  growth,  because  it  shuts  off  the  air 
supply.  The  amount  of  water  necessary  for  ftmgi  growth  is  very  small; 
and  wood  freely  cut  contains  more  than  enough,  at  aU  seasons  of  the  year. 

What  Seasooing  Is. — (a)  Differtncs  Between  Seasoned  and  Utiseason^ 
Timber. — Seasoning  implies  other  changes  besides  the  evaporation  of  w^ater. 
Although  we  have  as  yet  only  a  vague  conception  as  to  the  exact  nature  of 
the  difference  between  seasoned  and  unseasoned  wood,  it  is  very  probable 
that  one  of  these  consists  in  changes  in  the  albuminous  substances  in  the; 
wood  fiber,  and  possibly  also  in  the  tannins,  resins,  and  other  incrusting' 
substances.  Whether  tne  change  in  these  substances  is  merely  a  dicing 
out,  or  whether  it  consists  in  a  partial  decomposition,  is  as  yet  undetertnined. 
Exposure  to  the  wind  and  air,  however,  brings  about  changes  in  the  wood 
which  are  of  a  nature  that  the  wood  becomes  drier  and  more  permeable. 
When  seasoned  by  exposure  to  live  steam,  similar  changes  may  take  place. 
The  water  leaves  the  wood  in  the  form  of  steam,  while  the  organic  cona- 
pounds  in  the  walls  probably  coagulate  or  disintegrate  under  the  hishi 
temperature. 

(6)  Manner  of  Evaporaiian  of  Water. — ^The  evaporation  of  water  froxn 
timber  takes  place  largely  through  the  ends,  i.e.,  m  the  direction  of  tfaue 
longitudinal  axis  of  the  wood  fibers.  From  the  other  surfaces  it  take^ 
place  very  slowly  out  of  doors,  but  with  great  rapidity  in  a  kiln.  The  rat« 
of  evap.  differs  with  the  kind  of  timber  and  its  shape.  Thin  boards  axK5 
beams  dry  faster  than  thick  ones;  sapwood,  faster  than  heartwood;  amd 
pine,  faster  than  oak.  Recent  tests  (not  altogether  conclusive)  shuiowed 
little  difference  in  rate  of  evap.  from  sawed  and  hewn  ties.  Air-drying 
out  of  door  takes  from  two  months  to  a  year,  depending  on  kind  of  timt>e| 
and  climate.  Wood  which  has  been  air-dried  will  absorb  water  in  scoalj 
quantities  after  a  rain,  or  during  damp  weather,  and  lose  most  of  it 


SEASONING  OF  TIMBER.  863 

when  a  few  warm,  drv  days  follow.  When  soaked  in  water,  seasoned 
timber  absorbs  it  rapidly.  It  first  enters  the  wood  through  the  cell  walls, 
and  when  these  are  soaked  it  will  fill  the  cell  lumen  completely. 

Seasoning  «nd  Preservative  Treatment. — (a)  Seasoning  and  the  Leach- 
ing of  Salts. — Where  timber  is  chemically  treated  with  salts  dissolved  in 
water,  it  is  absolutely  necessary  to  season  it  after  the  treating  process,  for 
two  reasons:  First,  to  prevent  the  rapid  leaching  out  of  the  salts  pressed 
into  the  wood;  second,  to  prevent  subsequent  decay.  In  the  case  of  ties, 
the  leaching  out  takes  place  very  rapidly  when  they  are  laid  immediately 
after  treatment. 

(b)  Seasoning  and  the  Processes  of  Preservation. — ^The  object  of  timber 
treatment  is  to  get  certain  chemical  compounds  into  the  wood  with  as 
moch  thoroughness  as  possible.  Because  of  its  peculiar  structure,  wood 
will  not  allow  of  the  penetration  of  Hquids  into  its  mass  as  docs  a  sponge. 
The  solution  must  work  its  way  into  the  wood  fibers  through  walls  of  wood 
substance.  If  a  water  solution  is  used  for  the  impregnating  material,  it 
ought  to  fill  every  cell  and  permeate  every  wall,  at  least  of  the  sapwood. 
The  most  successful  method  for  timber  treatment  (excepting  the  boiling 
process)  so  far  used  consists  in  pressing  the  solution  into  the  wood.  If  the 
wood  cells  and  the  walls  are  already  full  of  water,  it  is  evident  that  there 
wiQ  be  great  difficulty  in  making  the  water  already  in  place  give  way  to  the 
wlution.  When  the  walls  and  cell  cavities  are  free  from  water  the  process 
of  absorption  of  a  solution  is  facilitated.  Besides  this,  prior  seasoning 
not  only  brings  about  a  reduction  in  the  amount  of  water,  but  also  results 
in  a  partial  disintegration  of  the  albuminous  substances  which  offer  more 
or  less  resistance  to  the  entrance  of  solutions.  The  steaming  of  wood 
before  treatment  with  solutions  can  never  replace  seasoning,  as  it  can  do 
DO  more  than  drive  of!  part  of  the  water,  unless  the  temp,  of  the  steam  is 
sufficiently  high  to  injure  certain  portions  of  the  wood  fiber  itself. 

Advantages  of  Seasoning. — ^The  four  principal  advantages  of  seasoning 
timber  may  be  enumerated  as  follows:  ( 1)  Seasoned  timber  lasts  much  longer 
than  unseasoned;  (2)  Seasoning  before  cnemical  treatment  greatly  increases 
its  eflfectiveness,  ana  seasoning  after  treatment  prevents  the  rapid  leaching 
out  of  the  salts  introduced  to  preserve  the  timber:  (3)  The  saving  of  freight 
due  to  a  decrease  in  weight  oi  35  to  40%  is  sometimes  a  considerable  item, 
even  when  compared  with  the  total  cost  of  the  timber;  (4)  Seasoning  allows 
tile  tase  of  k>wer  grade  or  softer  timbers,  so  that  red  and  swamp  oak  and 
beech  are  now  being  substituted  for  white  oak,  loblolly  pine  for  longleaf 
pine,  hemlock  and  tamarack  for  oak  and  pine,  etc.;  besides,  the  softer 
woods,  being  more  porous,  are  more  easily  treated  chemically. 

To  prevent  checking  and  splitting  of  timbers  while  seasoning,  many 
English  roads  tise  S  irons,  whicn  are  driven  into  the  ends  of  timbers  that 
begin  to  show  such  tendencies.  Pig.  1  shows  one  of  these  irons  of  meduim 
size,  and  Pig.  2  shows  the  method  of  applying  same.  The  effect  is  a  great 
saving. 


UngfftofPi€oe$.lS 

~4J3 '^^ 


r 


^^ 


~3lV3 /^ 

/Diam.m/!l$ 
*^.— --' 

Fig.  1.  Fig.  2. 

Horn  Timi»er  b  Seasoned. — (a)  Kiln  Drying. — ^The  French  Eastern  Ry. 
maintaiiis  at  Amague  a  plant  for  completing  the  drying  of  its  ties  after 
they  have  been  seasoned  in  the  open  air,  which  consists  of  four  kilns.  The 
Btrticttires  are  about  50  ft.  lon£^  by  46  ft.  wide,  and  contain  two  pairs  of 
hot-air  galleries,  each  pair  of  which  is  provided  with  an  independent  furnace 
and  can  be  operated  as  a  separate  kiln.  The  air  enters,  at  first  cold,  from 
the  outside  into  a  lower  chamber  of  the  furnace,  and  becomes  gradually 


364  19.— PRESERVATIVES. 

heated  in  its  upward  progress.  It  is  at  last  discharged  into  a  hot-air  cham- 
ber which  occupies  all  the  upper  part  of  the  kiln.  Prom  this  it  is  carried 
down  to  the  galleries  in  which  the  ties  are  dried  by  four  vertical  pipes, 
having  a  cross  section  of  18  by  18  ins.  Two  pipes  open  into  each  gallery, 
at  the  end  of  which  the  trams  bearing  the  ties  pass  out  after  the  drying 
has  been  complete.  Each  tram  carries  about  40  ties  slightly  separated 
from  each  other,  so  that  all  the  faces  may  be  in  direct  contact  with  the  hot 
air  in  the  galleries  of  the  dry  rooms  ana  with  the  tar  oil  in  the  cylinders. 
The  four  kilns  in  all  contain  16  galleries,  with  a  c^Cpacity  of  6  trams  each. 
in  all  80  small  trams.  It  is  thus  possible  to  drv  about  3200  ties  at  once. 
With  an  annual  output  of  400,000  ties,  seventy-two  hours  would  be  allowed 
for  the  average  drying  period.  The  temperature  of  the  galleries  is  at  the 
maximum  of  30°  to  36*  C.  at  the  entrance,  and  70**  to  80**  C.  at  the  delivery. 
As  the  trams  are  taken  from  the  cylinders  one  at  a  time,  the  drying  is  pro- 
gressive, and  the  wood,  for  this  reason,  is  less  liable  to  split  or  warp.  To 
turn  out  400,000  ties  the  furnaces  of  the  four  dry  rooms  consumed  about 
20O  tons  of  nne  coal  and  250  tons  of  the  trimming,  from  show  machines, 
and  wood  trash  and  chips  from  the  wood  yard.  This  mixture  develops  a 
sufficient  heat  and  offers  the  additional  advantage  of  not  wearing  out  the 
fire  boxes  by  a  two  intense  heat.  The  expense  for  fuel  is  about  one-fifth 
of  a  cent  for' each  tie. 

(b)  S0asoning. — Seasoning  of  timber  has  been  carried  on  in  a  practical 
way  tor  many  years  in  Europe.  Most  of  the  European  railroads  season 
their  ties  for  many  months  before  they  treat  them.  The  Eastern  French 
Railway  piles  its  ties  in  open  piles  11.4  ft.  high,  8.8  ft.  wide,  and  8.8  to 
65 . 6  ft.  long.  The  ties  are  about  5  ft.  apart.  The  ties  are  laid  grillage 
fashion  and  spaced  4  ins.  apart,  except  the  two  top  tiers  which  are  inclined 
(in  the  same  direction)  to  shed  water.  At  Amague,  where  kiln  drying  is 
subsequently  used,  oak  ties  are  allowed  to  remain  in  piles  for  15  to  20  months; 
and  beech  ties,  6  months.  Thev  are  then  kiln  dried  for  from  60  to  80  hours 
at  a  temp,  b^inning  at  36°  and  gradually  brought  to  75°  C.  Finally,  they 
are  treated  with  tar  oil. 

(c)  Seasoning  by  Steaming. — Steaming  is  at  best  a  makeshift  and  unless 
modified  materially  it  can  never  replace  open-air  seasoning,  supplemented 
possibly  by  kiln-drying.  However,  it  ought  to  last  longer  than  unsteamed, 
and  where  it  is  necessary  to  secure  partially  seasoned  wood  the  steaming 
may  do.  The  use  of  the  vacuum  pump  does  not  materially  improve  matters, 
for  it  is  not  possible  to  maintain  a  sufficiently  high  temperature  in  a  cylinder 
in  which  enough  of  a  vacuum  exists  to  insure  the  complete  removal  of  all 
the  water.  [With  the  present  state  of  our  knowledge  the  injurious  effect 
upon  timber  from  high-temperature  steam  is  not  definitely  known.] 

(d)  Seasoning  by  Immersion  in  Water. — It  is  very  probable  that  im- 
mersion of  timber  for  long  periods  in  water  materially  hastens  subsequent 
seasoning.  The  tannins,  resins,  albuminous  materials,  etc.,  which  axe 
deposited  in  the  cells  of  the  fibers  of  green  wood,  and  which  prevent  rapid 
evaporation  of  the  water,  imdergo  changes  when  under  water,  probaoly 
due  to  the  action  of  bacteria  which  can  hve  without  air,  and  in  the  course 
of  time  many  of  these  substances  are  leached  out  of  the  wood.  The  cells 
thereby  become  more  and  more  permeable  to  water,  and  when  the  wood  is 
finally  brought  into  the  air  the  water  escapes  very  rapidly  and  very  evenly. 

(ff)  Seasoning  by  Boiling  in  Oil. — It  is  sometimes  claimed  that  all  season 
ing  preparatory  to  treatment  with  a  substance  like  tar  oil  might  be  done 
away  with  by  putting  the  green  wood  into  a  cylinder  with  the  oil  and  heat- 
ing to  226°  F.,  thus  driving  off  the  water  in  the  form  of  steam,  after  which 
the  tar  oil  would  penetrate  readily  into  the  wood.  This  is  the  basis  of  the 
so-called  *'  Curtiss  process  "  of  timber  treatment.  But  the  same  obiection 
made  for  steaming  holds  here,  i.e.,  in  order  to  get  a  temperature  of  il2^  F. 
in  the  center  of  the  treated  wood  the  outside  temperature  would  haye  to 
be  raised  so  high  that  the  strength  of  the  wood  might  be  injured  seriously. 
A  company  on  the  Pacific  coast  which  treats  red  fir  piling  asserts  that  it 
avoids  this  danger  by  leaving  the  green  timber  in  the  tar  oil  at  a  temp. 
which  never  exceeds  226°  P.  for  from  6  to  12  hours,  until  there  is  no  ftirther 
evidence  of  water  vapor  coming  out  of  the  wood.  The  tar  oil  is  then  run 
out,  and  a  vacuum  is  created  for  about  an  hour,  after  which  the  oil  is  run 
in  again  and  is  kept  in  the  cylinders  under  100  lbs.  pressure  for  from  10  to 
12  hours,  until  the  required  amount  of  absorption  has  been  reached  (about 
12  lbs.  per  cu.  ft.). 


TIMBER  SEASONING.    CREOSOTE  OIL.  S0< 

Conclwloiis  and  RecommeiidAtioiu. — ^Timber  seasoning  is  a  practical 
method  for  increasing  the  length  of  life  of  both  untreated  and  treated  tim- 
ber.  At  the  same  time  it  forms  the  most  important  preliminary  step  to 
successful  chemical  treatment.  The  cost  of  seasoning  is  insignificant, 
while  the  returns  amotmt  to  a  considerable  sum  in  the  end.  With  the 
increased  cost  and  scarcity  of  timber  every  step  leading  toward  a  more 
economic  use  of  our  supply  ought  to  receive  attention.  It  is  perhaps  too 
soon  to  draw  final  conclusions,  but  the  following  general  recommenda- 
tions can  confidently  be  made: 

(1)  Green  timber  should  be  piled  in  as  open  piles  as  possible  as  soon  as 
it  is  cut,  and  so  kept  until  it  is  dry.  In  the  case  of  ties  the  7  by  2  form  of 
pile  (tiers  with  7  and  2  ties  alternating)  is  the  best.  No  timber  should  be 
treated  chemically  until  it  is  dry. 

(2)  Timber  treated  with  a  preservative  dissolved  in  water  should  be 
ptled  after  treatnient  for  several  months  at  least  to  allow  the  water  pressed 
mto  the  wood  with  the  salt  to  evaporate.  Under  no  circumstances  should 
timber  fmhly  treated  with  a  water  solution  be  expose^^  to  weathering 
influences. 

CREOSOTE  IN  WELL-PRESERVED  TIMBERS. 

The  following  is  a  digest  of  Forest  Service  Circtdar  98,  U.  S.  Dcpt.  of 
AgncuHure,  issued  May  9.  1907,  comprising  an  article  entitled  "  Quality 
and  Character  of  Creosote  in  Well-Preserved  Timbers."  by  Gellert  Alleman, 
Prof,  of  Chem.  in  Swarthmore  College: 

"  Of  the  various  preservative  proc«scs  for  timber,  those  using  coal- 
tar  creosote  are  the  most  efficient,  and.  in  the  long  nm.  are  frequently  the 
most  economical  as  compared  with  the  less  expensive  metallic-salts  pro- 
cesses. Moreover,  creosoted  wood  can  be  used  for  some  purposes,  as  for 
salt-water  piles,  for  which  wood  treated  with  metallic  salts  is  but  slightly 
more  durable  than  untreated  timber.  Recent  reports  on  the  service  of 
creosoted  railroad  ties,  and  of  salt-water  piles,  have  shown  that,  while 
proper  treatment  gives  excellent  results,  mucn  of  this  timber  was  not  treated 
properly  and  has  not  lasted  as  it  should.  It  is  imperative  that  we  should 
Know,  as  completely  as  possible,  just  what  constitutes  efficient  creosote 
treatment.  This  depends  on  three  things — the  amount  of  creosote,  its 
character,  and  the  thoroughness  with  which  it  penetrates  the  timber.  The 
propNcr  anx>imt  of  creosote  will  depend  upon  the  intended  use  of  the  timber. 
For  instance,  piles  which  must  resist  the  attacks  of  marine  borers  need  more 
creosote  than  telephone  poles,  and  those  in  warm  waters  require  more  than 
those  in  cooler  waters. 

*'  The  sort  of  creosote  best  suited  to  prevent  decay  and  the  inroads  of 
marine  borers  can  be  ascertained  only  by  many  careful  experiments.  The 
best  means  for  securing  a  maximum  penetration  of  the  oil  is  a  problem 
compb'cated  by  many  factors  such  as  wood  structure,  moisture,  etc.  One 
way  of  approaching  this  problem  involves  a  study  of  the  nature  of  the 
creosotes  present  in  timbers  which  have  given  long  service.  The  results  of 
a  series  oi  analyses  of  the  oils  present  in  such  timbers  forms  the  most  im- 
portant part  of  this  paper.  A  brief  account  of  the  source  and  composition 
of  coal-tar  creosote  precedes  the  description  and  discussion  of  the  experi- 
ments. 

Maunifacttire  and  Composition  of  Creosote^ — (a)  Sourct  and  Composition 
of  Coal  Tar. — When  certain  varieties  of  coal  are  heated  in  an  oven  or  retort, 
in  the  absence  of  sufficient  air  for  their  combustion,  the  coal  is  decomposed 
and  gas,  tar,  and  coke  are  formed.  The  gas  and  tar  rise  from  the  heated 
mass  and  the  coke  remains  in  the  retort.  Coke  and  illuminating  gas  are 
manufactured  in  this  way.  Where  coke  is  the  main  product  desired  the 
"beehive  "  oven  is  used  and  the  gas  and  tar  are  not  collected,  but  when 
the  volatile  materials  are  to  be  collected  the  "  by-product  "  oven  is  used. 
In  making  illuminating  gas  the  coke  and  tar  are  regarded  as  by-products, 
and  one  of  the  problems  of  managament  is  how  to  dispose  of  these  by- 
Iffodncts  to  advantage. 

Coal  tar  is  an  extremely  complex  mixture  of  organic  compounds,  vary- 
ing with  different  coals  and  with  different  treatments  of  the  same  coal, 
which  will  yield  at  the  same  plant  various  qualities  of  coke,  ^as  and  tar, 
depending  on  the  amount  of  neat  applied,  the  quantity  of  air  admitted. 
and  the  season  of  the  year.  With  a  low  heat  a  relatively  small  amount  of 
93m«  and  tar  is  evolved  and  the  tar  contains  larpe  quantities  of  compounds 
of  the  Dara€&n  series;  but  with  a  high  temp,  much  larger  amounts  of  gas 


366 


19.— PRESERVATIVES, 


and  tar  are  obtained  and  the  predominant  compounds  of  the  tar,  in  nearly 
all  cases,  are  those  of  the  aromatic  series,  as  benzine,  toluene,  phenol,  naphtlu^ 
lin,  anthracene,  etc. 

(6)  Production  of  Cr$osott  from  Coal  Tar. — ^The  first  distillation  of 
crude  tar,  in  which  several  separate  fractions  are  usually  taken,  is  made 
in  laiKe  iron  retorts  holding  from  10  to  30  tons.  The  forms  of  the  retorts 
and  the  manner  of  controlling  the  distillation  vary  more  or  less  in  different 
work.  In  some  cases  the  stul  is  provided  with  a  thermometer  enclosed  in 
an  iron  tube  srcewed  into  the  still  nead;  in  other  cases  the  time  for  changing 
the  receiver  for  various  fractions  is  judged  solely  by  the  specific  gravity 
and  other  properties  of  the  distillates. 

In  Germany  the  fractions  are  frequently  taken  as  follows:  The  teznp. 
is  that  registered  by  the  thermometer  in  the  tar  at  the  beginning  of  the 
distillation,  but  free  from  the  oil  and  indicating  the  temp,  of  the  vapor 
passing  over  when  anthracene  oil  begins  to  distil:  First  light  running  up  to 
110°  C.;  light  oils,  110°  to  210°  C;  carbolic  oils,  210°  to  240°  C;  heavy  or 
creosote  oils,  240°  to  270°  C;  anthracene  oils,  270°  to  400°  C. 

At  many  English  works  the  following  fractions  are  taken  with  the 
thermometer  placed  as  in  the  German  procedure  just  cited:  Light  naphtha 
up  to  110°  C;  light  oil,  110°  to  170°  C;  carbolic  oils.  170°  to  226*  C;  creosote 
oils,  225°  to  270°  C;  anthracene  oils.  270°  to  360°  C. 

These  temperatures  are  by  no  means  universally  accepted  in  the  r»- 
pective  countries,  and  one  or  more  fractions  are  often  omitted;  when,  for 
example,  it  does  not  pay  to  extract  carbolic  acid,  or  when  the  demand  for 
anthracene  is  limitea. 

Owing  to  the  variable  constitution  of  the  tar  and  to  the  different  tem- 
peratures between  which  fractions  are  taken,  the  products  of  this  prelim- 
inary separation  are  ferquently  widely  different  in  physical  character  and 
chemical  composition.  In  distilling  according  to  the  German  method 
given  above,  the  "  firet  runnings  "  and  "  light  oils  "  contain,  among  other 
things,  benzene,  toluene,  and  the  xylenes;  the  "  carbolic  oils  "  contain 
phenol,  the  creosotes,  and  some  naphthalin;  the  "creosote  oils."  small 
quantities  of  phenols,  naphthalin.  anthracene,  and  many  other  hydro- 
carbons; the  *  anthracene  oils,"  anthracene,  acridene,  etc.  The  residue 
in  the  still  is  either  soft  or  hard  pitch,  according  to  the  point  at  which  the 
distillation  is  stopped.  When  tne  anthracene  oil  is  completely  distilled, 
the  residue  is  largely  hard  pitch  or  carbon,  and  this  is  used  as  a  bnqtiette 
binder  and  in  the  manufacture  of  electric  light  carbons.  When  the  dis- 
tillation is  stopped  at  an  earlier  stage, sott  pitch  is  obtained  which  contaasa 
a  considerable  qtiantity  of  the  high-boiling  tar  constituents;  and  is  used 
for  roofing  and  for  builders'  paper.  At  present  there  is  almost  no  market 
in  America  for  hard  pitch,  whereas  the  demand  for  soft  pitch  for  roofing 
is  very  great,  which  explains  why  the  distillation  of  tars  is  not  carried  so 
far  here  as  in  some  foreign  works. 

(c)  Statistics  of  Production  and  Importation  of  Creosote. — The  folIo'vHns 
table  gives,  approximately,  the  amount  of  Coal  Tar  produced  in  the  U.  S., 
also  the  amount  of  Creosote  Oil  produced  and  imported,  in  millions  oC 
gallons,  for  the  years  named: 


Coal  Tar. 

1 

Creosote  OiL 

c 

1 

From 

Gas 

Works. 

From 
By- 
pro- 
duct 
Ovens. 

Total. 

MUl- 

ions 

of 

Gals. 

Price 

per 

Gallon. 

Pro- 
duced 
in  U.S. 

Im- 
por- 
ted. 

Total 
Mill- 
ions 
of 
Gals. 

Price, 

per 

Gallon. 

1 

18^8 

24.38 
40.80 
41.73 
43.64 

4.02 
22.15 
27.77 
36.38 

28.40 
62.95 
69.50 
80.02 

3.7cts. 
3.49" 
3.04" 
2.73" 

if 

|b 

Oh  O 

1903 
1904 
1906 

4  00 
4.85 
5.80 

3.71 
3.78 
7.75 

7.71 

8.63 

13.55 

5. Sets. 
6.3  " 
6  4  •• 

CREOSOTE  OILS,  3«7 

rhe  estimate  for  1903  includes  the  tar  produced  at  1956  "  by-pxxxluct  " 
ovens,  assuming  8 . 5  gallons  of  tar  per  ton  of  coal  coked.  It  is  generally 
oated  that  12.5  gallons  per  ton  of  coal  may  be  obtained  from  gas  works, 
that  the  general  average  from  gas  works  and  from  ovens  is  a  little  over 
aUons.  Moreover,  it  is  usually  assumed  that  the  average  coal  tar  pro- 
d  in  this  country  contains  at  least  10%  of  oils  which  can  be  used  as, 
dded  to,  creosote  oil. 

d)  Composition  of  Commercial  Crtosoit. — ^Technically  speaking,  the 
ion  of  oil  passing  over  between  240**  and  270**  C.  during  the  first  dis- 
ion  of  the  crude  coal  tar  is  known  as  '*  creosote  oil,"  ^eavy  oil,"  or 
td  oil  of  coal  tar."  In  practice,  however,  the  oily  residues  which 
in  after  extracting  carbolic  acid,  naphthalin,  and  anthracene  from 
iranous  distillates  m  which  they  occur  are  added  to  the  creosote  oil, 
in  consequence,  many  of  the  creosote  oils  of  commerce  contain  con- 
able  amounts  of  materials  having  boiling  points  higher  than  270**  C, 
krwer  than  240**  C.  As  a  matter  of  fact,  it  is  the  practice  at  nearly 
^tilling  plants  to  add  to  the  *'  creosote  well  "  or  tank  all  those  oils  and 
ues  which  cannotprofitably  be  worked  over  and  used  to  greater  com- 
ial  advantage.  Tne  solvents  which  are  used  in  the  ptirification  of 
thalin  and  of  anthracene  are  sometimes  added  to  the  "  creosote  well," 
this  accounts  for  the  occasional  presence  of  paraffin  oil  in  creosote, 
"he  "  creosote  well  "  or  tank  is  usually  constructed  of  steel  plates, 
s  fitted  with  inclosed  steam  coils  at  the  bottom,  in  order  that  the  solid 
rials  crystallizing  out  can  be  melted  before  the  oil  is  delivered  to  tank 
tank  steamers,  or  barrels.  A  stirring  device  is  also  frequently  used 
cux«  uniformity  in  quality  of  suipply. 

"he  creosote  oil  of  commerce  contains  phenol  (carbolic  acid),  the  ortho, 
.  and  para  cresols,  naphthalin,  the  oc  and  p  methyl-naphthalins  (the 
BT  being  a  liquid,  the  latter  a  solid  melting  at  33°  C),  anthracene, 
snthracene,  arcidene,  and  small  quantities  of  certain  high-boiling 
;  and  adds.  When  first  distilled,  creosote  has  a  distinct Iv  fluorescent 
uunce,  and  is  light  green  in  cloor.  There  is  strong  evidence  for  the 
:  that  some  of  the  individual  constituents  in  creosote  oil  combine  with 
other  and  probably  form  new  products. 

.t  certain  works,  carbolic  acid  is  extracted  and  the  creosote  oil  coming 
such  places  is  low  in  "  tar  acids;"  at  other  places,  naphthalin  is  ol 
dcrable  commercial  importance  and  the  creosote  oils  obtained  from 
works  contain  little  naphthalin.  Usually  anthracene  separates 
napthalinj  and  in  the  event  that  the  latter  is  frozen  out,  the  former 
o  lacking  m  the  oil  which  is  placed  on  the  market.  In  America  the 
ote  oils  usuallv  contain  large  amotmts  of  naphthalin,  very  small 
mts  (about  5%)  of  phenols  or  cresols,  and  practically  no  anthracene 
he  reason  previously  mentioned).  It  is  evident  that  these  variations 
mufacttu^  result  in  creosotes  differing  greatly  in  physical  and  chemical 
rrties;  some  are  rather  thin  oils,  some  are  almost  entirely  solid  with 
thalin,  and  some  are  heavy  oils  with  a  large  proportion  of  nigh-boiling 
ituenta. 

he  different  sorts  of  oils  are  believed  to  have  different  preservative 
a  when  injected  into  timber,  but  there  is,  unfortunately,  a  lack  of 
rmity  of  opinion.  Some  investigators  have  advocated  oils  rich  in 
>ls,  some  tnose  containing  much  naphthalin,  some  those  containing 
ximum  of  the  high-boiling  compounds.  But  little  has  been  published 
e  subject. 

jMlyscs  of  the  Creosote  Extracted  from  Timber  Well  Preserved  after 
Service. — ^To  determine  what  is.  in  fact,  a  good  oil,  a  natural  way  is 
Amine  the  composition  of  those  oils  which  have  protected  treated 
>r  satisfactorily.  This  can  be  done  by  extracting  and  analyzing  the 
pom  timbers  the  exact  history  of  whose  service  is  Known.  The  writer 
essor  AUeman)  secured  from  various  sources  a  number  of  creosoted 
*n  which  had  been  in  varied  and  extended  use  under  markedly  different 
tic  conditions.  The  oils  from  these  timbers  were  extracted  and  ana- 
with  the  following  results: 

§ndii  of  Ou  Anaiy$#5.— The  results  of  the  analyses  of  the  creosote 
cted  from  37  different  samples  of  wood  are  given  m  Table  1 .  following. 
cnajority  of  these  samples  were  obtained  from  various  Er^tnsh  com- 
s  using  creosoted  wood.  Such  details  as  could  be  learned  concemmg 
iatory  of  tie  timbers  arc  given  in  the  footnotes.  r^^^^T^ 

Digitized  by  VjOOv  IVL 


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CREOSOTE  OILS  I 


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870  l^^PRESERVATIVES, 

Glasgow  and  Southwbstbrn  Railway,  Scotland: 

Tie  No.  106  taken  out  of  the  Main  Line  February  12,  1906,  near 
Milliken  Paric;  put  in  during  1889.  Creosoted  with  2i  gallons  ol  gas- 
works creosote  of  1 .010  specific  gravit^r  at  60**  F. 

Tie  No.  104  taken  out  of  the  Main  Line  February  6,  1905,  near 
Elderslie  Station;  put  in  during  1887.  Creosoted  with  about  2i  gallons 
of  oil  to  the  tie. 

Tie  No.  113  taken  from  the  Main  Line  April  16,  1905,  near  Elder- 
slie Station:  put  in  during  1887.  Creoeoted  tnat  same  year  with  about 
2i  gallons  of  oil  to  the  tie. 

Tie  No.  109,  same  history  as  No.  100. 
Grbat  Western  Railway,  Hbath  Division.  England: 

Pile  No.  118  was  in  salt  water  at  New  Milford  47  years;  not  decayed, 
but  attacked  bv  Limnoria. 

Tie  No.  lOi  was  in  sidings  at  Eastern  Depot,  Swansea,  for  42  years. 

Tie  No.  106  served  for  20  years  in  the  Main  Line  at  Hirwain  (Vale 
of  Neath),  and  afterwards  was  used  as  a  fence  post  for  18  years. 

Memel  pile  No.  1  was  in  a  tidal  river  at  Lougnor  for  53  yean.  Treat- 
ed with  crude  coal  tar  and  not  analyzed. 

Memel  pile  No.  2  was  in  salt  water  at  Llanelly  Docks  for  58  years. 
Treated  with  crude  coal  tar  and  not  analyzed. 
London  and  Northwestern  Railway  Company,  England: 

Ties  No,  103  and  No.  110  installed  in  the  road  for  permanent  way 
purposes  in  1886;  removed  February,  11,  1905.     They  were  creosoted 
with  blast  furnace  Scotch  oil  in  1886. 
Northeastern  Railway  Company.  England: 

Paving  blocks  Nos.  88  and  89  removed  in  perfect  conditkm  after 
beixig  in  use  at  Hull  for  20i  years. 

Tie  No.  114  was  under  water  for  20  years,  and  afterwards  used  as 
a  tie  under  piles  of  timber  in  the  dockyard  for  10  years,  a  total  service 
of  30  years. 
City  Engineer,  Hull  Corporation,  Hull,  England: 

Paving  blocks  Nos.  90  and  91  laid  with  close  joints  in  1894;  re- 
moved in  February.  1905,  in  perfect  condition.  Paving  block  No.  02 
consisted  of  three  broken  blocks  laid  with  open  joints  in  1892;  not 
decayed  when  removed  in  1905.  Treated  with  creosote  and  pitdi  on 
the  outside;  not  analysed. 
Maryport  and  Carlisle  Railway  Company,  England: 

Ties  Nos.  108  and  137  creosoted  in  1881,  placed  in  track  1882,  and 
removed  in  1905.    Tie  No.   137  was  not  analyzed. 
Highland  Railway  Company,  Scotland: 

Ties  Nos.  2,  3.  and  41  were  in  service  in  a  gravel  ballast,  damp  bed, 
for  20  years,   20  years,  and  22  years,  respectively.     These  ties  were 
seasoned  two  years  before  treatment  and  stacked  six  months  after 
creosoting  before  being  placed  in  the  track. 
North  British  Railway  Company.  Scotland: 

Tie  No.  101  was  in  the  track  21  years;  No.  102,   21  years;  No.  112, 
14  years;  No.  100,  14  years  (not  analyzed).    These  tics  were  taken  out 
at  different  parts  of  the  system. 
Clyde  Navigation  Trust,  Glasgow: 

Pile  No.  116  is  from  the  part  of  the  pile  which  was  above  high-water 
level,  and  was  therefore  exposed  to  the  air. 

Pile  No.  1 1 1  is  from  the  part  of  the  pile  between  high  and  low  water. 
It  was  therefore  exposed  to  the  wash  of  the  water. 

Pile  No.  117  is  from  the  part  of  the  pile  which  was  always  under 
water. 

Pile  No.  4  is  from  the  part  which  was  buried  m  the  ground. 

Pile  No.  5  is  from  the  part  of  a  pile  above  high  water;  creosoted 
with  8  pounds  per  cubic  foot. 

Tie  No.  8  was  laid  in  slag  in  the  year  1888. 

Tie  No.  9  is  a  part  of  a  Baltic  redwood  tie  laid  in  1889.  It  was 
bedded  in  concrete  and  causewayed  over  with  granite  seta.  Both  of 
these  ties  were  creosoted  with  2^  gallons  of  gas  creosote  of  not  leas  than 
1 .010  specific  gravity  at  61**  F. 

Pile  No.  116  is  from  a  part  of  pile  No.  5  between  high  and  low 
water;  not  analyzed;  creosoted  with  8  pounds  per  cubic  foot. 


CREOSOTE  OILS  EXTRACTED  FROM  TIES,  ETC. 


371 


NOKPOLK  CrBOSOTING  COMPANY^  NORPOLK.    Va.: 

Pile  No.  81,  section  of  a  creosoted  pile  put  in  Santiago  Harbor 
Cuba.  April.  1887;  taken  out  in  perfect  condition  November.  1902. 

Pile  No.  82,  section  of  a  creosoted  pile  put  in  Tampico  Bay  in  May. 
1891;  taken  out  in  perfect  condition  October,  1902. 

Pile  No.  83,  section  of  a  pile  treated  with  croesote  and  resin;  re- 
moved after  seven  years  badly  attacked  by  Teredo. 

Pile  No.  84,  section  of  a  creosoted  pile  put  in  a  drydock  at  Newport 
NcwSj  Va.,  May,  1881;  removed  in  good  condition  October,  1901. 

Pile  No.  86,  section  of  a  creosoted  pile  in  service  for  17  years  at 
Newport  News,  Va. 

Tie  No.  86  was  in  the  track  for  22  years  at  Houston.  Texas. 
Intsrnational  Crbosotino  and  Construction  Company.  Galveston, 
Tbx.: 

Piles  Nos.  50  and  61  were  in  Galveston  Bay  for  29  years. 

Paving  block  No.  62  was  in  service  in  the  street  at  New  Orleans,  La., 
fcM-  84  years. 

Paving  block  No.  63  was  in  service  in  Galveston  for  29  years. 

Paving  blocks  Nos.  64  and  66  were  in  use  at  Galveston  for  9  years. 
They  showed  poor  service. 
Bbu.  Tblbphonb  Company: 

Conduit  pipe  No.  67  was  in  service  as  conduit  at  Philadelphia.  Pa., 
for  14  years;  removed  in  perfect  condition  to  make  extensions  of  service. 

In  the  following  Table  (2)  the  87  samples  described  above  are  grouped 
in  classes  and  the  average  results  of  all  the  well  preserved  timbers  are  given 
for  each  class: 


2. — Analyses  of  Extracted  Oils. 


Aver- 
age 
serv-n 

Creo- 
sote 
to  the 

Distillation  o(  extracted  oil. 

Bamplea. 

To 

205* 

245<» 

270" 

320- 

Resi- 
due 
above 
420«» 

a 

Solid 
naph- 
tha- 
lln 
from 
distil- 
lates. 

Solid 
an- 
thra- 
cene 

^ 

ice. 

cubic 
foot. 

205«» 

a 

to 

2450 
0. 

to 

270* 
C. 

to 
820» 

a 

to 
0. 

oil 

distil- 
lates. 

1 

Yn. 

Un. 

% 

% 

% 

% 

% 

% 

% 

% 

Cmt. 

i9ecoss-tles 

21.84 

9.6« 

0.025 

12.07 

13. 8S 

23.80 

24.69 

26.27 

I.IS 

23.47 

0.65 

f  EogUsh  pOes.  . 

43.0fl 

9.19 

.46 

16.92 

16.31 

21.06 

22.77 

23.04 

19.95 

.61 

6  American  pfles. 

20. 2C 

15.64 

.67 

30.28 

15.82 

18.49 

13.21 

21.43 

26.93 

43.27 

4  paving  blocks  . 

23. 6C 

15.70 

.29 

21.34 

21.39 

18.73 

19.40 

18.64 

12.52 

40.40 

.52 

1  paving  Mock 

ppor  service... 
t  eoodolt  pipe  . . 

9,0(1 

5.77 

9.62 

14.41 

19.27 

41.74 

11 . 2.1 

3.4(1 

14.00 

8.74 

5.08 

27.23 

10.46 

27*68 

19.03 

9.93 

23.17 

14.28 

Average  of  36 

timbers  giv- 

ing good  ser- 

net. 

24.90 

11.18 

.36 

■  7.37. 6.. 8| 

22.00 

21.71 

23.09 

6.98 

27.81 

.50 

Diicassioa  d  the  Analytical  Results.— (a)  Quantity  of  Oil  FCund.— 
The  average  figures  show  that  the  quantity  ot  creosote  in  these  long-service 
timbers  was  not  excesuve.  Practically  nothing  is  known  of  the  amount 
of  oil  which  was  injected  into  the  various  samples.  Six  of  the  ties.  Nos. 
8,  e,  104,  106,  109,  and  113.  were  said  to  have  received  2\  (English)  gallons 
of  creosote  eadi  or  10.60  lbs.  of  oil  per  cu.  ft.,  assuming  the  spec.grav.  of 
the  oil  at  1 .06  and  the  volume  of  each  tie  at  2 i  cu.  ft.  The  average  amount 
present  was  8.66  lbs.  l*he  American  piles  (all  set  in  warm  water,  those 
Urthest  north  being  on  the  Virginia  coast)  show  a  much  higher  content 
of  oil  than  the  English  samples.  For  the  (having  blocks,  there  is  a  con- 
siderable contrast  between  the  quantity  of  oil  present  in  those  which  gave 
good  service,  and  the  sample  which  was  short  lived.     The  difference  m 


872  19.''PRESERVATIVES. 

service  was  doubtless  due  to  two  factors,  the  quantity  and  the  quaHty  o€ 
the  injected  creosote:  it  is  impossible  to  say  which  had  the  greater  influence. 

In  general,  the  results  tend  to  show  that  10  lbs.  of  creosote  per  cubic 
foot  is  ample  for  railroad  ties,  and  that  piles  reqxiire  from  10  to  20  Iha., 
according  to  the  location  in  which  they  are  to  be  placed.  If  a  creosote 
contains  much  light  oil,  a  proportionately  larger  quantity  must  be  tised. 

(b)  Character  of  the  Extracted  Creosote. — A  difficulty  in  the  proper  inter- 
pretation of  the  results  of  the  analyses  arises  from  our  ignorance  of  the 
quality  of  the  oil  used  in  treating  the  various  timbers.  It  is,  therefore. 
possible  to  believe  that  the  materials  which  have  volatilised  from  the  tim- 
bers have  created  an  antiseptic  environment  which  has  been  a  most  im- 
portant factor  in  preserving  the  wood.  Aside  from  this,  however,  the 
ajialjrses  furnish  a  strong  ai^rument  in  favor  of  the  use  of  heavy  oils.  For 
example,  tie  No.  6  had  seen  but  14  years'  service,  two-thirds  the  avera^re 
of  the  ties,  and  doubtless  would  not  have  suffered  decay  for  many  years  to 
come,  yet  it  does  not  contain  more  light  oil  than  the  average  of  the  tie  group, 
but,  on  the  contrary,  the  creosote  from  this  specimen  was  over  half  recovered 
as  solid  anthracene  oil.  If  the  constituents  present  in  the  timbers  repre- 
sented a  non-efficient  residue  from  which  the  efTective  light  oils  had  evap- 
orated, we  should  expect  to  find  a  relatively  iiigh  proportion  of  light  oils 
in  this  tie  which  haa  seen  a  shorter  term  of  service.  The  natural  inter- 
pretation of  the  results  is  that  it  is  the  heavy,  high-boiling  compoxinds 
which  stay  in  timber  and  are  an  efficient  barrier  to  the  entrance  ox  'virater 
and  to  the  attacks  of  fungi  and  borers. 

The  creosotes  recovered  contained  practically  nothing  which  boiled 
below  205**  C.  The  general  average  shows  that  32.9%  of  the  oils  distilled 
below  270*  C,  and  66.95%  above — that  is,  two-thirds  above  and  one- 
third  below  this  rather  high  temperature.  Another  noticeable  fact  is  the 
large  amount  of  soUd  anthracene  oil  recovered  from  the  distillates  of  many 
samples,  the  highest  being  67%.  . 

A  distinctive  feature  of  the  creosotes  from  American  piles  was  the 
quantity  of  naphthalin  which  they  contained.  The  average  from  this  class 
of  timbers  was  nearly  26%,  and  one  sample  showed  over  48%.  It  appears 
probable  that  the  creosotes  used  in  treating  these  timbers  contained  much 
more  naphthalin  than  the  oils  applied  to  the  English  piles.  The  results 
indicate  that  this  substance  possesses  value  for  timber  treatment,  although 
it  probably  is  inferior  to  anthracene  oil.  It  is  worth  noting  that  these  Ions* 
lived  American  piles  contained  more  anthracene  oil  than  naphthalin. 

Perhaps  the  most  striking  thing  is  the  disappearance  of  the  tar  acids. 
It  is  certainly  conservative  to  place  the  original  tar-acid  content  at  5%. 
Yet  the  extracted  oils  showed  but  one  tenth  of  this  amoimt.  It  is  possible 
that  the  compotmds,  on  account  of  their  hydroxvl  groups,  have  underirone 
chemical  changes  during  the  many  years  that  they  have  been  exposed  to 
varying  amounts  of  water  and  air,  to  the  reactive  lignin  portion  of  the 
wood,  and  to  the  numerous  compounds  present  in  creosote.  On  the  other 
hand,  these  phenol  bodies  have  been  volatilised  or  been  washed  from  the 
timbers. 

It  appears,  therefore,  that  light  oils,  boiling  below  205**  C,  will  not 
remain  in  timber,  but  that  heavy  oils,  containing  a  high  percentage  of  an- 
thracene oil,  will  remain  almost  indefinitely  and  protect  the  wood  from 
decay  and  boring  animals.  It  is  probable  that  naphthalin  stays  in  'vrood 
for  many  years,  but  whether  it  is  as  valuable  as  anthracene  oil  is  an  open 
question.  The  value  of  the  tar  acids  has  apparentlv  been  overestimated 
by  many  persons,  for  although  it  has  not  been  proved  that  they  are  value- 
less, they  have  been  shown  to  possess  poor  staying  qualities. 

EXCERPTS  AND  REFERENCES. 

The  Protectloii  of  Ferrk  Structures  from  Corrosion    (By  M.  P.  Wood. 

Trans.  A.  S.  M.  E..  1901;  Eng.  News,  Sept.  16,  1901.— (1)  Iron  OxMe 
Pigments. — ^To  neutralize  the  sulphur  element  natural  to  the  ore  or  devel- 
oped in  roasting,  it  is  the  common  practice  to  add  carbonate  of  lime  Cco- 
mon  chalk)  to  the  amount  of  5  to  10%  by  weight  of  the  iron  oxide. 
(2)  Boiled  Oil  vs.  Pigment  Coatings. — Many  engineers  have  abandone<i  the 
use  of  iron  oxide  and  other  imcertain  patent  paint  compounds,  but  still 
adhere  to  the  use  of  oil  for  the  first  coating.  The  writer  believes  tl^t  a 
good  pigment  paint  is  much  better  than  oil  coating.  Asphaltum  Coatlass. — 
ITie  so-called  asphaltum  paints  in  general  have  thus  far  proved  to  be  Quite 
as  mettective  protective  coatings  as  any  of  the  iron  oxide  or  miscellaxaeoua 


MISCELLANEOUS  PRESERVATION.    COSTS.  878 

eompOMiKl  paints.  Lhiifxl  OIL — ^Diactisset  the  proceaeca  of  eztractixis  the 
oil.  etc  P^Uoting  at  the  Milt — ^£>oes  not  advocate  painting  the  iron  or 
itecl  just  after  it  has  left  the  rolls  or  hammer,  and  while  hot;  but  just 
bc^se  ascembling. 

Tha  Paifltinr  and    Sand-Blast  Cleaniiiff  of  Steel  Bridses  and  Viaducts 

(By  Geo.  W.  LUly.  Enars.  Qub,  Columbus.  O.,  Feb.  1.  1M2;  Eng.  News, 
April  24.  11M)2).~--Raw  Linseed  OU  is  said  to  make  a  better  binder  than 
boiled  linseed  oil,  but  it  sets  so  slowly  that  in  certain  locations,  such  as 
Tiaducts  subject  to  the  blast,  smoke  and  steam  from  locomotives,  its  use 
is  inadvisable,  because  it  will  be  filled  with  cinders  and  otherwise  seriously 
iajured  before  it  is  dry.  The  Pigments  most  commonlv  used  for  anti-rust 
paints  on  steel  may  be  classed  under  the  names  red  lead,  iron  oxide,  carbon 
and  graphite.  Each  of  these  has  had  its  champion  among  men  who  have 
had  oonisiderable  experience  in  the  use  of  paints,  while  the  experience  of 
many  experts  has  lea  to  the  conclusion  that  "red  lead,  oxide  of  iron,  carbon 
and  graphite  all  give  results  which  average  about  the  same."  Mixing  and 
ApHyinc  tbe  paint. — All  paints  should  be  thoroughly  mixed  by  machmenr 
and  subsequent  grinding  with  a  burr-stone  mill  u  possible.  But  red  lead, 
which  is  inclined  to  settle  and  harden  somewhat  in  the  mixture  and  make 
it  difficult  to  spread  and  also  diminish  the  coherence  of  the  coating  made 
by  it,  can  be  quite  thoroughly  mixed  by  hand  when  the  facilities  for  ma- 
chine mixing  are  not  at  hand;  and  this  is  advisable  in  most  cases,  for  the 
reason  that  it  is  usually  impossible  to  have  it  mixed  at  the  time  it  is  needed 
except  it  be  done  by  Hand.  All  painting  should  be  done,  if  possible,  when 
the  temperattire  of  the  atmosphere  is  above  55**  P.,  when  little  trouble  will 
be  experienced  in  spreading  red  lead  or  any  other  of  the  commonly  used 
paints.  If  painting  is  done  when  the  temperattire  is  lower  than  this,  the 
paint  shoula  be  warmed  up  by  placing  it  in  a  vessel,  which  is  set  in  water 
heated  to  a  temperature  of  13u*  to  150**  P.,  and  each  painter  should  be 
frequently  supplied  with  warm  paint  when  the  paint  in  his  bucket  becomes 
cool.  Cwuiins  tlw  Stod  Before  Paintiiif . — Before  any  paint  or  other  coat- 
ing of  any  kind  is  permitted  to  be  applied  to  the  iron  or  steel  of  a  bridge  or 
viaduct,  all  the  scale,  rust,  dirt,  grease  and  other  foreign  substances,  as 
well  as  dead  paint,  should  be  removed  from  its  surface,  so  that  the  coating 
may  come  into  intimate  contact  with  the  clean  surface  of  metal,  and  thus 
give  Uie  best  condition  for  firm  adhesion  of  the  coating  to  the  metal.  The 
sand-blast  has  been  given  sufficient  trial  to  make  it  reasonable  to  say  that 
such  cleaning  as  is  necessary  on  new  work  at  the  shops — that  is,  removal 
of  mill  scale  and  some  rust  and  grease — can  be  done  at  about  i  ct.  per 
sq.  ft.  of  steel  surface  cleaned,  and  possibly  a  little  less.  On  this  basis  the 
cost  per  ton  for  cleaning  steel  plates  woula  be:  Por  plates  1'  thick,  49  cts.; 
J' thick,  98  cU.;  i^  thick,  $1.96.  For  shapes:  7' I-beams,  weighing  17.5 
lbs.  per  ft.,  $1.35  per  ton;  12*  I-beams  at  50  lbs.  per  ft.,  80  cts.;  the  heavier 
sectioxiB  costing  less  and  the  lighter  sections  costing  more  per  ton.  The 
average  cost  for  cleaning  most  plate  girder  bridges  would  probably  be 
about  $1  per  ton;  and  the  cost  for  a  truss  bridge  might  vary  from  $1 
per  ton  for  heavy  bridges  to  81.75  per  ton  for  light  bridges.  This  article 
contains  an  illustrated  description  of  the  Newhouse  sand-blast  machine 
used  in  cleaning  viaducts  at  Columbus,  O. 

Craosotinf  Wooden  Poles  for  Electric  Line  Work  (By  W.  E.  Moore. 
Read  before  Nat'l  Elec.  Lt.  Ass'n,  at  Cincinnati.  O.,  May  20.  1902;  Eng. 
News.  May  29,  1902).— 4ron  Poles  or  creosote  poles  are  as  yet  seldom  used 
by  lighting  companies,  though  iron  Pples  are  extensively  used  for  street 
railway  purposes.  Wooden  Poles. — Wooden  poles  are  usually  of  cedar, 
beart-eawed  pine,  cypress,  juniper  or  redwood,  and  arc  prenerally  used  on 
accotmt  of  low  cost  and  the  comparative  safety  with  which  workmen  may 
handle  the  live  wires  when  standing  on  the  cross-arms,  as  wood  is  a  fair 
insulator.  Red-cedar  and  white-cedar  poles,  while  they  have  a  compara- 
tively long  life,  have  now  become  so  scarce  that  it  is  extremely  difficult  to 
•ectue  them  in  sufficient  numbers  of  suitable  sizes  for  electric  light  lines  at 
any  price  in  the  Eastern  or  Southern  market,  though  there  is  yet  a  con- 
siderable supply  of  white  cedar  in  the  Northwest.  Heart-sawed  pine  poles 
have  a  somewhat  longer  Hife  than  cypress,  ranging  from  8  to  9  years;  but 
sap  pine,  though  readily  secured  in  sticks  of  suitable  size  and  necessary 
length,  is  never  used,  on  accotmt  of  its  rapid  decay.  Study  of  Preservation 
of  Poles.— The  Augusta  Ry.  and  Elec.  Co.  began  about  9  years  ago  to  study 
the  problem  of  treating  poles.    The  first  exi>eriment  consisted  m  cnamng 


874  19.— PRESERVATIVES. 

the  butts  of  the  poles,  up  to  about  1  ft.  above  the  earth  line,  and  then  satu* 
rating  them  with  a  coal-tar  paint;  but  this  was  found  to  be  of  little  service. 
Painting  the  poles  with  various  brands  of  preservative  compounds  soM 
under  various  trade  names  was  then  tried,  but  with  little  or  no  benefici&l 
results.  In  the  nleantime  the  poles  then  in  use,  almost  entirely  of  cypress, 
continued  to  rot  out  after  an  average  life  of  about  6  or  6  years.  Creosotiiig 
Plant.— Consists  of  a  steel  cylinder  O'  dia.  and  102'  long,  with  heavy  cast- 
iron  heads,  securely  supported  on  hinges  and  arranged  to  be  clamped 
against  a  fibrous  gasket  on  the  head  of  a  cylinder  so  as  to  resist  a  hydro- 
static pressure  of  150  lbs.  There  is  a  narrow  gage  railway  throtigh  it,  with 
tracks  continuing  bevond  ends  of  cylinder,  Which  has  a  series  of  l"  pipes 
laid  from  end  to  end  and  covering  the  bottom,  and  supplied  with  steam 
from  an  80  H.  P.  return  tubular  boiler,  the  steam  being  superheated  to  a 
temperature  of  400^  to  600^.  To  the  cylinder  is  also  connected  a  direct- 
acting  vacuum  pump,  14'  x  24*.  and,  again,  a  direct-acting  oil-pressure 
pump,  10*  X  18^  Method  of  Treatmeat. — Is  fully  described.  Cost  of 
Treaaneiit.-— Cost  of  average  size  (say  34  ft.  long,  8*  dia.  at  top)  cypress 
pole,  from  $1.76  to  $2  each;  and  cost  of  creosoting,  about  $20  per  M.  B.  M.. 
or  about  twice  the  first  cost  of  pole.  Assumed  that  life  of  treated  pole  will 
be  prolonged  4  to  0  times  that  of  untreated.  Effect  of  Creosoting,  on  Line- 
men« — Disaf^reeable  in  handling:  dangerous  to  linemen  when  handling 
wires  carrymg  1000  to  3000  volts,  as  the  creosoting  lowers  the  electric 
resistivity  of  the  timber. 

Sand-Blast  aeaning  of  Structural  Steel  (By  Geo.  W.  Lilly.  Tians. 
A.  S.  C.  E.,  Vol.  L). 

Creosoting  Works  of  the  Western  Ry.  of  France  (By  T.  M.  Merklen. 
May  n\unber  of  "Revue  Generale  des  Chemins  de  Per;"  Eng.  News,  July  27, 
1905). — ^Fvill  description  of  Plant,  Method  of  Treatment,  and  illustrated 
Method  of  Piling  Ties  for  Seasoning. 

Tie  and  Timber  Preserving  Plant  of  the  A.  T.  A  S.  F.  Ry.  at  Sotner^ 
vlUe,  Texas  (Eng.  News,  May  3,  1906). — Description  of  Creosoting  Process, 
Seasoning,  Inspection  and  Maricing,  Creosoting  Plant,  Experimental  Plant. 
Tanks,  Cxages  and  Pipe  System,  etc.    Ulustrated. 

The  Inspection  of  Treatment  for  the  Protection  of  Timber  by  the 
Injection  of  Creosote  Oil  (By  H.  R.  Stanford.    Trans.  A.  S.  C.  E..  Vol.  Lvi). 

Coal  Tar  Paints  (Eng.  News,  Aug.  16,  1906).  —  Discussions  and 
references  to  other  articles. 

Corrosion    of  Steel  in  Reinforced  Cinder  Concrete    (By  W.  H.  Pox. 

Eng.  News,  May  23,  1907). — Following  conclusions  from  results  of  experi- 
ments: In  no  case  was  any  evidence  found  underneath  the  collars  of  neat 
cement  which  surrounded  a  portion  of  each  steel  specimen .  To  secure  a  dense 
homogeneous  cinder  concrete,  a  thorough  tamping  is  necessary.  A  rich 
mixture,  either  a  1:1:3  or  one  in  which  the  proportion  of  cement  to  agKre- 
gate  is  larger,  should  be  used  in  all  cases.  The  greatest  care  should  be  taken 
m  mixing  the  materials,  and  it  may  be  necessary  to  resort  to  the  seeminsly 
impractical  method  of  coating  the  reinforcement  with  grout  before  placing 
in  the  concrete. 

Cleaning  Steelwork  by  Sand-Blast    and    Painting  by  Compressed  Air 

(By  De  Witt  C.  Webb.  Eng.  News.  Sept.  19,  1907).— Plant.— Following 
outfit,  purchased  at  cost  of  |2090,  delivered  at  U.  S.  Naval  Station,  Key 
West,  Fla.:  1  hor.  gasoline  engine,  20  H.  P.;  1  air  compressor,  capac.  90  ft^ 
of  free  air  per  min.  compressed  to  pres.  of  30  lbs.  per  sq.  in.  in  one  sta^e, 
belt  connected  to  engine;  1  rotary  cutjulating  pump,  belt  connec.  to  ennne ; 
1  galv.  steel  water  tank;  1  air  receiver,  18^x  54';  (above  all  mounted  on 
steel  framed  wagon  with  wooden  housing.)  2  sand-blast  machines,  at  capsur.; 
of  2  cu.  ft.  of  sand  each;  2  paint  spraying  machines,  one  a  hand  machix>e 
of  i-gal.  capacity  for  one  operator,  the  other  of  10-gal.  capac.  for  t^ro 
operators;  100  hn.  ft.  of  sand-blast  hose;  200  lin.  ft.  of  pneumatic  hose 
for  sand-blast  machines;  400  lin.  ft.  of  pneu.  hose  for  painting  machines^ 
4  khaki  helmets,  with  mica-covered  openings  for  the  eyes;  200  lin.  ft.  oi 
2f  galv.  pipe.  Cost  of  Cleaning. — 2000  sq.  ft.  of  previously  untouche<3 
surface  was  thoroughly  cleaned  and  7000  sq.  ft.  of  hand  cleaning  was  slU 
gone  over  and  mvich  improved  at  a  total  cost  for  labor  of  $97.68,  and  fott 
gasoline  (at  19  cts.  per  gal.)  of  $16.15.    Cost  of  Patatifl«.— The  coal-t&xi 


MISCELLANEOUS  PRESERVATION.     COSTS.  376 

paint  originated  by  A  C.  Cuiminifham  was  used  (see  Eng.  News,  July  12, 
1906),  prepared  with  the  foUowing  proportions  (by  volume):  coal  tar 
(A  parts),  kerosene  oil  (1),  Portland  cement  (1);  cost,  15  cts.  per  gallon. 
Shed  "A"  required  64^  gsib.  for  9000  sq.  ft.  or  1  gal.  to  140  sq.  ft.,  at  cost 
for  labor  of  $28.16.  and  for  gasoline  of  $3.80.  Shed  "B"  required  86  gals, 
for  12500  sq.  ft.  or  1  gal.  to  145  sq.  ft.,  at  cost  for  labor  (including  cleaning, 
painting,  moving,  setting  up  and  removing)  of  $460,  and  for  gasoline,  $81. 

Paints  for  Concrete  (By  G.  D.  White.    Proc.    A.  S.  T.  M..  Vol.  IX, 
1S09). — With  discusaions. 

Comparison  of  Varioas  Processes  of  Preservinc  Timber    (By  G.  B. 

Shipley,  Eng.  News,  Oct.  14. 1903). — ApproximaU  cost  of  treating  ties,  exclud- 
ing ro^tv: — Burnetizing  process:  about  Hb.  dry  zinc  per  cu.it..  $0.12  (>er 
tie.    Wellnouse  process:  about  i-Ib.  zinc  per  cu.  tt.  plus  glue  and  tannin, 


IOLl6per  tie.  Card  process:  about  IHhs.  creosote  and i-lb.  dry  zinc  per  cu. 
tt.,  10.18  per  tie.  Rueping  process:  about  6-Ibe.  creosote  per  cu,  ft..  $0~" 
per  tie.   Lowry  process:  about  6-lbs.  creosote  per  cu.  ft..  $0,225  per 


tt.,  $0.18  per  tie.  Rueping  process:  about  6-Ibe.  creosote  per  cu.  ft..  $0,225 
per  tie.  Lowry  process:  about  6-lbs.  creosote  per  cu.  ft.,  $0,225  per  tie. 
Absorption  process:  about  6-lbs  creosote  per  cti.  ft.,  $0.23  per  tie.    Pull  cell 


process:  about  10-Ibe.  creosote  per  cu.  ft.,  $0.3%  per  tie.  The  above  costs 
are  based  on  creosote  oil  at  $0.07  per  gal.  and  dry  zinc  chloride  at  $0.04  per 
lb.  It  costs  about  i-cent  per  tie  to  handle  in  the  yard.  Timber. — The  cost 
of  crcosoting  timber  with  10  lbs.  of  creosote  per  cu.  ft.  will  be  about  $8  per 
WOO  ft.  B.  11.,  and  for  each  additional  pound  of  creosote  used  add  about 
10.75  per  1000  ft.  B.  M.  based  on  creosote  oil  at  $0.07  per  gal.  Bumetizing, 
l-Ib.  dry  zinc  chloride  per  cu.  ft.,  $4  per  M.  B.  M. 


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20.— LUMBER  AND  LUMBERING. 

Stiimi>ase. — ^The  following  is  a  digest  of  Forest  Service  Circular  97, 
U.  S.  Dcpt.  of  Agricultiire,  issued  April  24,  1907,  and  entitled  "  The  Timber 
Supply  of  the  United  States,"  by  R.  S.  Kellogg.  Forest  Inspector: 

The  percentage  of  the  total  lumber  cut  furnished  by  the  principal  regions 
since  1850,  according  to  census  figures,  is  as  follows: 

1. — Gbographical  Distribution  of  Total  Lumbbr  Product. 


Year. 

North- 
eastern 
States. 

Lake 
States. 

Southern 
States. 

Pacific 
States. 

1850 

Percent. 
54.5 
86.2 
36.8 
24.8 
18.4 
16.0 

Percent. 
6.4 
18.6 
24.4 
33.4 
36.3 
27.4 

Percent. 
13.8 
16.5 
9.4 
11.9 
15.9 
25.2 

Percent, 
8.9 

I860 

6.2 

1870 

8.8 

1880 

3.5 

1890 

7.3 

1900 

9.6 

The  principal  estimates  of  the  stumpage  of  the  U.  S.  made  since  1880 
are  given  in  Table  2.  The  first,  by  Saigent  (1880),  in  addition  to  beins 
too  low  for  almost  every  species  considered,  with  the  possible  exoeption  ot 
the  hardwoods,  is  notable  for  its  omission  of  Douglas  spruce — which  exists 
today  in  greater  quantity  than  any  other  of  our  valuable  timbers— and 
yellow  pine,  another  important  species.  The  next  estimate,  that  of  Hotdi- 
kiss  (1898),  does  not  go  mto  details.  The  next  estimate,  by  Gannett  (1900). 
was  most  carefully  prepared.  That  by  Femow  (1902)  is  a  legional  esti- 
mate. Long's  estimate  (1903)  does  not  cover  cypress,  sugar  pine,  or  hard- 
woods. Its  principal  pomt  of  interest  is  that  it  differs  so  radicallv— about 
38% — from  that  of  the  census  of  1903  upon  the  stumpage  of  yelk>w  pine. 
The  last  estimate  given  in  the  table  is  that  published  in  the  "American 
Lumberman,"  Sept.  23,  1905.  It  is  based  primarily  upon  census  data, 
with  the  addition  of  some  species  and  with  increased  figiires  for  others: 
2. — Estimates  op  Stumpaob  op  the  UNrrED  States. 


Kind  ol  Timber. 

Census, 
1880. 

HotchklSB, 

1898. 

Census. 
1900. 

Femow, 
1902. 

Long, 
1903. 

American 
Lumber- 
man, 1905. 

White  pine 

M  b-rd  ft. 
87.7&5.000 

M  board  ft. 

M  board  ft. 
60,000.000 

M  board  ft. 

M  b'rd  ft. 
60.000.00U 

M  board  ft. 

Eastern  and 
northern  pine. 

55.000.000 

300.000.000 
75.000.000 
100.000.000 
350,000,000 

Southern  yellow 

pine 

Eastern  spruce. . 
Eastern  hemlock 
Douglas  flr 

237,141.500 
12.265,000 
20.165.000 

300.000.000 
50.000.000 
100.000.000 
300,000.000 
125.000.000 
65.000.000 
75.000.000 

187.260.000 
I8.22i.0u0 
66.571.000 
260,000,000 
138,000,000 

Western  ycl.plnc 
Cypress 

250.000.000 

♦2.153,600 
25,825.000 
22,800.000 

6S.OOQ1OOO 

Redwood 

75.000,000 
27.640,000 

TSIOOQIOOO 

Cedar 

Bugar  ploe..  . . . 

25,000,000 

50.000000 

Other  conifers. .. 

12,600.000 

250,000.00t 

Total  conifers . 
Total  bardw'ds 

420.605.100 
435,685.000 

1.090.000,000 
300.000.000 

822,682.000 

1.570.000.00t 
400.000.000 

Region: 
Northern  States 

100.000.000 

500.000,000 
70U.000.000 
800.000.000 



Soutbcm  States 

300.000,000 



Western  States. 

. .. .» 

Pacinc  States... 

1.000.000.000 



Total I8.'i6.290.100i  1.400.000,000 

1.390.000.000 

2.000.000.000 

822.682.000 

1. 970.000.000 

*  Florida  and  Alabama  only. 


376 


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STUMP  AGE-    LUMBER  PRICES, 


377 


The  "  Pacific  Lumber  Trade  Journal,"  in  the  issue  of  Tanuwy,  1907, 
save  the  following  estimate  of  the  stumpage  of  the  Pacific  Coast,  including 
Idaho.  Montana,  and  British  Columbia: 

3. — BsTiiiATBD  Stumpage  op  California,  Orbgon.  Washington,  Idaho, 
Montana,  and  British  Coluubia. 


Kind  of  timber. 

M  board  feet 

Kind  of  Umber. 

M  board  feet 

nnnnilMf  nr 

374.064.1U2 
175.586,520 
78.961.383 
75,000,000 
60,848.259 
50,000.000 

i  Spruce 

25.419.215 

Western  and  yellow  pine. 

T^rrh 

5,078,601 

Miscellaneous  and  bard- 
woods. 

Redwood 

5.700,000 

Hemlock 

Total 

Sqfir  pine 

850,668.080 

This  total  is  credited  by  States  as  follows: 

M  board  feet.  M  board  feet. 

Oregon 225,000.000        British  Columbia 150.000.000 

Washlnirton 195,658.080        Idaho  and  Montana 100.000.000 

CSiUfoniJa 180.000.000 

The  present  annual  cut  of  some  of  the  principal  woods  is  as  follows: 
Whilt  Ptru — about  3  billion  feet  in  the  Lake  States  and  1  billion  feet  in 
other  States;  Ygllow  Piru — about  12  billion  feet,  or  a  little  more  than 
one-third  the  total  cut  of  all  species,  and  it  is  evident  that  within  10  to  15 
years  there  will  be  a  most  senous  shortage;  Spruce — about  Ijt  billion  feet, 
of  which  Maine  furnishes  about  one-third;  Hemlock — about  3  billion  feet, 
of  which  Penn.,  Mich.,  and  Wis.  furnish  about  three-fourths  (the  cut  of 
both  eastern  spruce  and  eastern  himlock  is  decreasing,  while  that  of  western 
spruce  and  hemlock  is  increasing);  Douglas  Spruce — about  4 J  billion  feet 
(If  billion  feet  in  1900);  Western  Yellow  Pine— about  1  billion  feet,  two- 
thirds  of  which  is  in  the  Pacific  Coast  States;  Redwood — about  450  million 
feet,  and  increasing*  Cypress — about  760  million  feet,  with  Louisiana 
supplying  about  66%;  Hardwoods — about  6  billion  feet,  consisting  of 
approximately  43%  oak,  12%  poplar,  9%  maple,  and  lesser  amounts  of 
numerous  other  species. 

To  engineers  who  are  basing  cost  of  proposed  work  on  former  estimates 
which  are  incomplete  in  detail,  the  .accompanying  diagram,  Fig.  1,  may  be 


Time -"Year©. 
Fig.   1.     Range  of  Lumber  prices,  IBS7  to  1907r^oOQle 


878  20.— LUMBER  AND  LUMBERING, 

of  interest  as  showing  the  marked  advance  in  the  prices  of  lumber  during 
the  past  20  years,  and  especially  during  the  last  decade. . 

Loninc* — (a)  How  Ttms  Grow. — ^The  section  of  an  ordinary  tree, 
thn>ugh  the  trunk,  discloses  first  the  heartwood  at  the  center,  next  the 
sapwood.  and  between  the  sapwood  and  the  bark  we  find  the  ccunbium. 
If  we  call  the  bark  the  "  coat  '  of  the  tree,  we  may  call  the  cambium  the 
(continuous^  "  undergarment."  for  it  clothes  every  portion  of  the  woody 
fiber  from  tip  of  root  to  end  of  stem,  terminating  m  the  leaves  which  are 
really  an  extension  of  the  cambitmi  itself.  This  slimy  covering  carries 
the  ufe  blood  or  sap  of  the  tree.  It  has  no  definite  thickness  as  it  grad- 
ually merges  into  the  bark  on  the  one  hand  and  into  the  woody  fiber  (sap- 
wood)  on  the  other.  If  the  tnink  or  limb  of  a  tree  is  completely  girdled, 
expoung  the  cambium  to  the  air,  that  portion  of  the  tree  aix>ve  the  girdle 
will  die.  as  if  amputated. 

A  tree  breathes  mainly  through  its  leaves,  and  partly  through  the  pores 
of  the  bark.  The  sap,  containing  various  mineral  substances  as  ix>tassium, 
calcium,  iron,  sulphiir.  magnesium,  phosphorous  and  nitrogen,  ascends 
from  the  roots  to  the  leaves,  and  is  here  met  by  the  free  oxygen  and  carbonic 
acid  (CO2)  which  the  leaves  breathe  from  the  air.  Various  compounds, 
mainly  starch  {CtHitPbit  are  formed  in  these  chemical  laboratories  through 
the  agency  of  the  sim,  and  these  new  products,  in  solution,  circulate  back 
with  the  sap,  build  up  the  woody  fiber  of  the  tree  and  produce  growth  of 
trunk,  roots,  branches,  leaves,  and  buds,  generally.  When  the  carbon 
dioxide  is  breathed  into  the  leaves,  much  of  the  water  of  the  sap  is  thrown 
off  into  the  air,  and  this  exhalation  is  called  transpiration,  a  process  similar 
to  the  perspiration  of  animals.  Some  trees  will  transpire  considerably 
more  than  a  hundred  gallons  of  water  in  a  day.  When  daylight  ends, 
starch-making  ceases,  but  the  building  up  of  the  woody  fibers  goes  on 
throughout  the  night. 

Trees  grow  radially  outward.  Drive  two  spikes,  spaced  vertically, 
into  the  trunk  of  a  tree  and  note  that  the  space  does  not  increase  percep- 
tibly  as  the  tree  grows  taller.  The  trunk  expands  in  diameter  as  the  aelicate 
cells  near  the  cambium  become  thickened  with  starch  from  the  down-flow 
sap  into  the  woody  fiber,  and  the  up-flowing  8ap*is  forced  outward  through 
newer  tubes.  Finally  the  walls  of  the  sapwood  become  hardened  with 
mineral  deposits  and  form  heartwood.  The  alternate  semi-annular  rings 
are  due  to  siunmer  and  winter  growth.  With  the  fall  of  the  leaves  the 
breathing  takes  place  through  the  pores  of  the  bark,  and  in  winter  the  tree 
practically  sleeps  or  hibernates. 

(6)  Btst  Tim*  for  Cutting  Timber. — We  usually  speak  of  '*  winter  cut  " 
timber  as  the  best,  and  some  give  as  a  reason,  that  it  contains  less  moisture. 
This  is  hardly  the  case.  On  the  contrary,  some  authorities  claim  that  many 
woods  contain  quite  as  much  if  not  more  moisture  in  winter  than  in  summer. 
The  principal  reasons  why  winter  cut  timber  should  be  preferred  arc  that 
it  is  harder  and  denser;  not  so  susceptible  to  the  attacks  of  forest  fungi: 
and  capable  of  being  more  perfectly  seasoned.  The  most  rapid  growth 
of  timber  is  in  the  early  summer,  and  this  is  the  poorest  time  tor  cutting. 
Winter  and  late  fall  cutting  seasons  are  the  best. 

{c)  Volume  of  Standing  Timber. — ^The  amount  of  standing  timber  on  a 
certain  tract  is  usually  estimated  by  a  "  cniiser."  This  is  done  in  various 
ways  depending  upon  the  accuracy  required.  For  any  individtial  tree, 
the  contents  is  assumed  equal  to  the  area  of  base  multiplied  by  one-halt 
the  height. 

(d)  Transportation  of  Logs. — ^The  "  felling  "  of  trees  is  a  very  important 
operation,  often  producing  splits  and  cracks  which  reduce  the  grade  of  the 
timber.  After  felling,  the  bark  is  removed  and  it  is  cut  into  the  desired 
lengths  for  mill  logs,  spars,  poles,  piles,  tiea.  etc.  Mill  logs  are  usually  in 
even  lengths,  from  12  ft.  upward,  generally  from  16  to  34  ft.  They  arc 
dragged,  rafted,  fiumed,  or  shipped  (by  logging  trains)  to  the  mill.  Ocean 
rafts  are  sometimes  made  up  at  an  expense  of  many  thousands  of  dollars, 
and  towed  himdreds  of  miles  to  save  the  cost  of  rail  transportation.  These 
rafts  are  cigar  shaped,  composed  of  the  longest  obtainable  logs,  arranged 
scientifically  with  "  broken  joints,"  and  well  boimd  with  heavy  chains 
for  strength  in  resisting  the  action  of  the  heavy  seas.  If  this  method  is 
contemplated,  it  is  wise  to  estimate,  ordinarily,  that  one  raft  in  every  two 
or  three  is  liable  to  be  "  broken  up  "  and  lost.  Successful  rafting  of  this 
kind  has  been  performed  from  Astoria,  Oregon,  to  S^  Prandsco,  and  from 
Nova  Scotia  to  Jersey  City,  N.  J.  r   ^^-r^ 


>  S^  Prandsco, 
byTjOOgle 


SAWING.    SEASONING.    BOARD  MEASURE.  879 

(#)  Scaling  Logs. — ^The  determination  of  the  number  of  thotisand  feet 
of  himber  in  k>RS,  as  a  basis  for  selling,  is  usually  made  at  the  mill  by  an 
official  scaler.  The  diam  of  the  small  end  is  meastu^ed  in  ins.  by  a  scale 
rule.  4  ins.  deducted,  and  the  balance  squared.  The  result  is  the  number 
of  ft.  B.  M.  for  a  log  16  ft.  in  length-proportionate  for  logs  of  other  len^hs. 
Where  logs  are  defective  a  reouction  is  made  depending  upon  the  judg- 
ment of  the  scaler. 

Sawinc  the  logs  up  into  rough  lumber,  such  as  "  sticks  "  (general  term 
for  large  dimension  timber),  posts,  beams,  joists,  ties,  scantling  (small 
dimension  stuff),  bocuds,  shingles  and  laths,  is  done' with  the  various  saws, 
as  band,  circular  (single  or  double),  slab,  gang,  shingle,  and  lath  saws. 
Rough  lumber  should  be  furnished  "  full-dimension  "  but  not  necessarily 
to  exact  dimension,  as  ordered.  When  exact  dimensions  are  required  the 
Itunber  should  be  ordered  "  sized." 

**Siziiic"  consists  in  rtmning  the  rough  lumber  through  the  planer  or 
"sticker,"  so  ga^^ed  that  when  planed  it  shall  be  exactly  to  ordered  dimen- 
sions, la  ordering  say  12'x  12*  to  be  planed  on  all  sides,  we  generally 
say  ir  X  12*  5  4  j;  if  on  on#  side.  12*  x  12'  5  1  *;  etc. 

Plaaiai:  costs  the  purchaser,  ordinarily,  from  $1.60  to  $2.00  per  M, 
but  it  is  often  desirable  to  order  planed  lumber  where  rough  lumber  might 
answer;  thus,  with  so-called  "  permanent "  wooden  structures  like  Howe 
truss  bridges,  for  instance,  the  cost  of  framing  with  planed  lumber  is  less 
than  with  rough,  and  the  life  greater,  to  say  nothing  of  the  appearance. 
Rough  dimension  stuff  which  is  to  be  planed  is  usually  ordered  about  {' 
large  for  each  dimension,  dei>ending  upon  size  of  piece;  less  for  smaller 
pieces. 


Id — After  being    sawed,    lumber    should    be    seasoned  more 

or  less  thoroughly  before  being  used.  K  "  open-stacked  "  under  roof 
tbeher  for  three  months  or  longer  it  is  in  fairly  good  condition  for 
ordinary  outside  construction,  but  for  so-called  thoroughly  dried  lumber 
a  year  or  two  is  required.  Heavy  timbers  of  coiuve  rec^uire  longer  periods. 
Kiln-dried  lumber  is  the  common  practice  and  is  verv  satisfactory  if  properly 
(loQe,  and  the  temperature  of  the  iciln  is  not  too  high.  If  steam  is  admitted 
the  temperature  may  be  from  160**  to  170**  F.  for  the  harder  woods  and 
from  17fr*  to  180**  for  the  softer  kinds,  as  pine.  In  dry  kilns  the  temper- 
ature should  be  lower.  The  harder  woods  are  preferably  stacked  in  the 
open  air  for  some  months  before  being  placed  in  the  kilns,  or  they  may  be 
immediately  kiln  dried  at  low  temperatures.  (See  also  "Seasoning  of 
Timber,"  under  Preservatives,  page  861). 

Board  Measure. — One  ft.  B.  M.  of  lumber  is  equiva\ent  to  a  board  1  in. 
thick.  12  ins.  wide,  and  1  ft.  k>ng,  or  i^  cu.  ft.;  hence  1000  ft.  B.  M.  (« 1 M. 
B.  Mo  contains  83^  cu.  ft. 

The  following  Table  (4)  of  board  measure  embraces  all  the  sizes  ordin- 
arily used  in  constructionj  and  gives  the  ft.  B.  M.  for  lengths  from  1  to  9. 
whxJi  may  be  used  decimally  for  any  lengths.  Interpolation  may  be 
resorted  to  for  dimensions  not  m  the  table,  but  this  will  rarely  be  necessary. 
Another  method  is  to  find  the  ft.  B.  M.  for  dimensions  2  or  more  times  as 
large  or  small,  and  then  factor  the  results  accordin^^Iy.  Note  that  for  this 
porme  the  list  of  1-inch  stuff  is  very  comprehensive. 

Where  (exact)  results  are  required  to  decimal  places  beyond  those  in 
the  table — which  will  rarely  be  the  case — a  casual  inspection  will  in  most 
cawa  suffice  Thus,  1.083-1.083^3,  3.167-3.16^6.  1.042-1.0416^6, 
etc.  The  "  character  "  of  the  decimal  for  any  particular  length  may  gen- 
erally be  determined  by  examining  other  decimals  in  the  same  line,  showing 
whether  the  decimal  rcpresenU  Oths.  8ths.  12ths.  16th8,  etc. 


d  by  Google 


d  by  Google 


BOARD  MEASURE. 


381 


4. — Pbbt  Board  Mbasurr- 

-Enoinebrs*  Tablb.— Continued. 

111 

Length  10  Feet. 

1 

5^a 

1       • 

2 

3 

4 

s 

6 

7 

8 

9 

1  xM 

1.6<7 

3.333 

5.000 

6.667 

8.333 

10.00 

11.67 

13.33 

15.00 

1  x20 

••x2l 

1.750 

3.500 

5.250 

7.000 

8.750 

10.50 

12.25 

14.00 

15.75 

••x21 

••x22 

1.833 

8.667 

5.500 

7.333 

9.167 

11.00 

12.83 

14.67 

16.50 

••x22 

•*X23 

1.917 

3.833 

5.750 

7.667 

9.583 

11.50 

13.42 

15.33 

17.25 

••x23 

••XM 

2.000 

4.000 

6.000 

8.000 

10.000 

12.00 

14.00 

16.00 

18.00 

••X24 

!S!t 

.1302 

.2604 

.8906 

.5208 

.6510 

.7812 

.9115 

1.042 

1.178 

lixl* 
••xl 

.1983 

.3125 

.4688 

.6250 

.7813 

.9375 

1.0938 

1.250 

1.406 

••xit 

.1823 

.3646 

.5469 

.7292 

.9115 

1.0937 

1.276 

1.458 

1.641 

"xl 

"xl 

.2083 

.4167 

.6250 

.8333 

1.0417 

1.250 

1.468 

1.667 

1.875 

••x2 

••xJi 

.2344 

.4688 

.7031 

.9375 

1.172 

1.406 

1.641 

1.875 

2.109 

••x2i 

1^ 

.2604 

.5208 

.7813 

1.0417 

1.302 

1.563 

1.823 

2.083 

2.344 

lix2| 

.286S 

.8729 

.8694 

1.146 

1.432 

1.719 

2.005 

2.292 

2.578 

••x2| 

••^ 

.3125 

.6250 

.9375 

1.250 

1,563 

1.875 

2  188 

2.600 

2.813 

••x3 

••X3J 

.3046 

.7292 

1.0937 

1.458 

1.823 

2.187 

2.662 

2.917 

3.281 

••x3| 

••X4 

.4167 

.8333 

1.250 

1.667 

2.083 

2.500 

2.917 

8.333 

3.750 

••x4 

Iiz4} 

.4688 

.9375 

1.406 

1.875 

2.344 

2.813 

3.281 

3.750 

4.219 

lix4» 

•^5 

.5208 

1.0417 

1.563 

2.083 

2.604 

3.125 

3.646 

4.167 

4.688 

••x5 

••xH 

.5729 

1.146 

1.719 

2.292 

2.865 

3.438 

4.010 

4.583 

5.166 

••X5* 

•xT 

.6250 

1.250 

1.875 

2.600 

3.125 

3.750 

4.376 

5.000 

6.625 

••x6 

•17 

.72«2 

1.458 

2.188 

2.917 

3.646 

4  375 

5.104 

5.833 

6.562 

••x7 

l|x8 

.8333 

1.667 

2.500 

3.333 

4.167 

5.000 

6.833 

6.667 

7.500 

ljx8 

•19 

.9375 

1.875 

2.813 

3.750 

4.688 

5.625 

6.563 

7.500 

8.438 

••x9 

"xlO 

1.0417 

2.083 

3.125 

4.167 

5.208 

6.260 

7.292 

8.833 

9.375 

••xlO 

••xll 

1.146 

2.292 

3.438 

4.683 

5.729 

6.875 

8.021 

9.167 

10.313 

••xll 

••xl2 

1.260 

2.500 

3.750 

5.000 

6.250 

7.500 

8.750 

10.00 

11.25 

••xl2 

•11} 

.1875 

.3750 

.5625 

.7500 

.9375 

1.125 

1.313 

1.500 

1.688 

lixll 

.2188 

.4375 

.6563 

.8750 

1.0938 

1.313 

1.631 

1.750 

1.969 

••xH 

••X2* 

.2500 

.5000 

.7500 

1.0000 

1.250 

1.500 

1.760 

2.000 

2.250 

••x2 

•^ 

.2813 

.5625 

.8438 

1.1250 

1.406 

1.688 

1.969 

2.250 

2.531 

■■^ 

.3125 

.6250 

9375 

1.250 

1.663 

1.875 

3.188 

2.500 

2.813 

Iix3f 

.3438 

.6875 

1.0313 

1.375 

1.719 

2.063 

2.406 

2.750 

3.094 

Iix2f 

'W 

.3750 

.7500 

1.125 

1.600 

1.875 

2.260 

2.625 

3.000 

3.375 

••x3 

"X3i 

.4375 

.8750 

1.313 

1.750 

2.188 

2.625 

3.063 

3.500 

3.938 

••x31 

•x? 

.5000 

1.0000 

1.500 

2.000 

2.600 

3.000 

3.500 

4.000 

4.500 

••X4 

•14i 

.5625 

1.125 

1.688 

2.250 

2.813 

8.375 

3.938 

4.500 

5.063 

••X4i 

lix5 

.6250 

1.250 

1.875 

2.500 

8.125 

8.750 

4.376 

5.000 

5.635 

lix5 

•*X6J 

.6875 

1.875 

2.063 

2.760 

3.438 

4.125 

4.813 

5.500 

6.188 

••X5J 

"2r 

.7500 

1.500 

2.2&0 

3.000 

3.780 

4.500 

5.250 

6.000 

6.750 

••x6 

••x7 

.8750 

1.760 

2.625 

3.500 

4.375 

6.250 

6.125 

7.000 

7.875 

••x7 

••x« 

1.0000 

2.000 

3.000 

4.000 

5.000 

6.000 

7.000 

8.000 

9.000 

••x8 

ihcf 

1.125 

2.250 

3.375 

4.500 

6.625 

6.760 

7.875 

9.000 

10.125 

lix9 

"xiO 

1.250 

2.500 

3.760 

5.000 

6.260 

7.500 

8.760 

10.000 

11.25 

••xIO 

•*XI2 

1.500 

3.000 

4.500 

6.000 

7.500 

9.000 

10.500 

12.00 

13.60 

••xl2 

2x2 

.3333 

.6667 

1.000 

1.333 

1.667 

2.000 

2.333 

2.667 

3.000 

2  x2 

"X2i 

.3750 

.7500 

1.125 

1.500 

1.875 

2.250 

2.625 

3.000 

3.375 

•*x2t 

2x2i 

.4167 

.8333 

1.250 

1.667 

2.083 

8.500 

2.917 

3.333 

3.750 

2X2* 

••x3 

.4583 

.9167 

1.375 

1.833 

2.292 

2.760 

3.208 

3.667 

4.125 

••x2t 

••3^ 

.5000 

1.0000 

1.500 

2.000 

2.500 

8.000 

3.600 

4.000 

4.500 

••x3 

••xH 

.5833 

1.167 

1.750 

2.338 

2.917 

8.500 

4.083 

4.667 

5.250 

••x3J 

••X4 

.6667 

1.333 

2.000 

2.667 

8.338 

4.000 

4.667 

5.333 

6.000 

••x4 

2x4| 

.7500 

1.500 

8.250 

8.000 

8.750 

4.500 

5.250 

6.000 

6.760 

2x4i 

••x? 

.8333 

1.667 

2.500 

3.333 

4.167 

5.000 

5.833 

6.667 

7.600 

••x5 

•*xH 

.9167 

1.833 

2.760 

3.667 

4.583 

5.600 

6.417 

7.333 

8.250 

••X6* 

••xT 

1.0000 

2.000 

3.000 

4.000 

5.000 

6.000 

7.000 

8.000 

9.000 

••x6 

•*X7 

1.167 

2.833 

3.500 

4.667 

5.833 

7.000 

8.167 

9.33^ 

10.500 

••x7 

niniti- 

0 

382 


20— LUMBER  AND  LUMBERING. 


4. — Pbbt  Board  Mbasurb — Enginbbrs*  Tablb. — Continued. 


III 

Length  In  Feet. 

III 

1 

2 

3 

4 

8 

6 

7 

8 

9 

2x8 

1.333 

2.667 

4.000 

5.333 

6.667 

8.000 

9.333 

10.667 

12.00 

2  x^ 

'*x9 

1.500 

3.000 

4.500 

6.000 

7.500 

9.000 

10.600 

12.00 

U.50 

••xf 

••xlO 

1.687 

3.338 

5.000 

6.667 

8.333 

10.00 

11.67 

13.33 

15.00 

••xlO 

•*xll 

1.833 

3.667 

5.500 

7.333 

9.167 

11.00 

12.83 

14.67 

16.50 

••xll 

••xl2 

2.000 

4.000 

6.000 

8.000 

10.00 

12.00 

14.00 

18.00 

18.00 

••XI2 

S  xM 

2.833 

4.687 

7.000 

9.333 

11.67 

14.00 

16.S3 

18.67 

21.00 

2  xU 

••xl5 

2.500 

5.000 

7.500 

10. 000 

12.50 

15.00 

17.50 

20.00 

22.60 

•*X15 

••xl6 

2.887 

5.333 

8.000 

10.67 

13.33 

16.00 

18.67 

21.33 

24.00 

••Xl6 

Hx2i 

.6208 

1.0417 

1.563 

2.083 

2.604 

3.125 

3.646 

4.167 

4.688 

2«x2^ 

••x2f 

.5729 

1.146 

1.719 

2.292 

2.865 

3.438 

4.010 

4.683 

6.15« 

••X2| 

SixS 

.8250 

1.250 

1.875 

2.500 

8.125 

3.750 

4.875 

6.000 

6.625 

2ix3 

"xsi 

.7292 

1.458 

2.188 

2.917 

8.646 

4.375 

6.104 

6.833 

6.663 

"xJi 

••x4 

.8333 

1.667 

2.500 

3.333 

4.167 

6.000 

6.833 

6.667 

7.500 

••x4 

••x44 

.9375 

1.875 

2.813 

3.750 

4.688 

5.625 

6.563 

7.500 

8.438 

••X41 

••x5 

1.043 

2.083 

3.125 

4.167 

5.208 

6.250 

7.292 

8.333 

9.375 

"XS 

2iz4 

1.148 

2.292 

3.438 

4.583 

6.729 

6.875 

8.021 

9.167 

10.313 

2|x3i 

••xe 

1.250 

2.500 

8.750 

6.000 

6.250 

7.500 

8.750 

10.000 

11.25 

•xT 

••x7 

1.458 

2.917 

4.375 

5.833 

7.292 

8.750 

10.208 

11.67 

13.13 

••x7 

"x8 

1.687 

3.333 

6.000 

6.667 

8.333 

10.00 

11.67 

13.33 

15.00 

••xS 

••«» 

1.875 

3.750 

5.625 

7.500 

9.375 

11.26 

13.13 

15.0U 

16.88 

•'x9 

2ixl0 

2.083 

4.167 

8.250 

8.333 

10.417 

12.50 

14.58 

16.67 

18.75 

21x10 

••xl2 

2.500 

5.000 

7.500 

10.000 

12.50 

15.00 

17.50 

20.00 

22.50 

••XI2 

"xU 

2.917 

5.833 

8.750 

11.67 

14.58 

17.50 

20.42 

23.33 

26.25 

•'XI4 

"xl5 

3.125 

6.250 

9.375 

12.50 

15.63 

18.75 

21.88 

25.00 

28.1  J 

••xl5 

••xl6 

3.333 

6.667 

10.000 

13.33 

16.67 

20.00 

23.33 

26.67 

30.00 

••xl6 

3  x3 

.7500 

1.500 

2.250 

3.000 

8  750 

4.500 

6.250 

6.000 

6.750 

3  X3 

•'x3J 

.8750 

1.750 

2.625 

3.500 

4.375 

5.250 

6.125 

7.000 

7.875 

••x3J 

••x4 

1.0000 

2.000 

3.000 

4.000 

5  000 

6.000 

7.000 

8.000 

9.000 

•'X4 

••x4i 

1.125 

2.250 

8.375 

4.500 

5.625 

6.750 

7.875 

9.000 

10.125 

••X4J 

••x5 

1.250 

2.500 

8.750 

5.000 

6.250 

7.500 

8.750 

10.000 

11.25 

'•X5 

3  xH 

1.875 

2.750 

4.125 

5.500 

6.875 

8.250 

9.626 

11.00 

12.38 

ZxH 

"x6 

1.500 

3.000 

4.500 

6.000 

7.500 

9.000 

10.500 

12.00 

13.50 

••X6 

••x7 

1.750 

3.500 

6.250 

7.000 

8.750 

10.500 

12.25 

14.00 

15.75 

'•x7 

"x8 

2.000 

4.000 

6.000 

8.000 

10.000 

12.00 

14.00 

16.00 

18.00 

••x8 

••x» 

2.250 

4.500 

6.750 

9.000 

11.25 

13.50 

15.75 

18.00 

20.25 

••x9 

3  xlO 

2.500 

5.000 

7.500 

10.000 

12.50 

15.00 

17.50 

20.00 

23.50 

3x10 

••xll 

2.750 

5.500 

8.250 

11.00 

13.75 

16.50 

19.25 

22.00 

24.76 

••xll 

••xI2 

3.000 

6.000 

9.000 

12.00 

15.00 

18.00 

21.00 

24.00 

27.00 

••xl2 

•'xl3 

3.250 

6.500 

9.750 

13.00 

16.25 

19.50 

22.76 

26.00 

29.25 

••XI3 

••xll 

3.500 

7.000 

10.500 

14.00 

17.50 

21.00 

24.60 

28.00 

31.60 

••X14 

3  xl5 

3.750 

7.500 

11.25 

15.00 

18.75 

22.50 

26.25 

30.00 

33.76 

3x16 

••xl6 

4.000 

8.000 

12.00 

16.00 

20.00 

24.00 

28.00 

32.00 

36.00 

••XI6 

••xl8 

4.500 

9.000 

13.50 

18.00 

22.50 

27.00 

31.50 

36.00 

40.50 

••xl8 

3ix3i 

1.021 

2.042 

3.063 

4.083 

5.104 

6.125 

7.146 

8.167 

9.188 

HtH 

••X4 

1.167 

2.333 

8.500 

4.667 

5.833 

7.000 

8.167 

9.333 

10.667 

••X4 

8ix4i 

1.313 

2.625 

3.938 

6.250 

6.563 

7.875 

0.188 

10.500 

11.813 

Hx4» 

"x5 

1.458 

2.917 

4.375 

5.833 

7.292 

8.750 

10.208 

11.67 

13.13 

'•x« 

"xH 

1.604 

3.208 

4.813 

6.417 

8.031 

9.625 

11.23 

12.83 

14.44 

•'X5i 

••x6 

1.760 

3.600 

6.250 

7.000 

8.750 

10.500 

12.25 

14.00 

16.76 

••X6 

"x? 

8.043 

4.083 

6.125 

8.167 

10.208 

12.25 

14.29 

16.32 

18.38 

••x7 

8}x8 

2.333 

4.667 

7.000 

9.333 

11.67 

14.00 

16.33 

18.67 

21.00 

Hx» 

•*X9 

2.625 

5.250 

7.875 

10.500 

13.13 

15.75 

18.38 

21.00 

23.63 

••x9 

••xio 

2.917 

5.833 

8.750 

11.67 

14.58 

17.50 

20.42 

23.33 

26.25 

••xlO 

••xu 

3.206 

6.417 

9.625 

12.83 

16.04 

19.25 

22.46 

25.67 

28.88 

*'xn 

•*X12 

3.500 

7.000 

10.500 

14.00 

17.50 

21.00 

24.50 

28.00 

31.50 

••xl2 

BOARD  MEASURE. 


888 


4. — Pbbt  Board  Mbasurb — Enginbbrs*  Tablb. — Continued. 


Length  ta  Feet. 

ill 

Si£ 

pis 

1 

3 

3 

4 

8 

6 

7 

8 

9 

r 

3JX14 

4.0SB 

8.167 

12.25 

16.33 

20.42 

24.60 

28.58 

32.67 

36.75 

34x14 

•xlS 

4.375 

8.750 

13.18 

17.60 

21.88 

26.25 

30.63 

35.00 

39.38 

••xl5 

'•xli 

4.M7 

9.333 

14.00 

18.67 

23.33 

28.00 

32.67 

37.33 

42.00 

••xl6 

••xlT 

4.»58 

9.917 

14.88 

19.83 

24.79 

29.75 

34.71 

39.67 

44  63 

••xl7 

"xlS 

5.2M 

10.500 

15.76 

21.00 

26.36 

31.50 

36.75 

42.00 

47.25 

•118 

4x4 

1.333 

2.667 

4.000 

5.833 

6.667 

8.000 

9.333 

10.67 

13.00 

4x4 

"X4J 

1.500 

3.000 

4.500 

6.000 

7.500 

9.000 

10.500 

12.00 

13.50 

•144 

"xS 

1.6C7 

3.333 

5.000 

6.667 

8.333 

10.00 

11.67 

13.33 

15.00 

••x5 

"x5| 

1.833 

3.667 

5.600 

7.333 

9.167 

11.00 

12.83 

14.67 

16.50 

••X54 

"rf 

i.too 

4.000 

6.000 

8.000 

10.000 

13.00 

14.00 

16.00 

18.00 

fx6 

4x« 

3.1C7 

4.833 

6.600 

8.667 

10.83 

13.00 

15.17 

17.33 

19.50 

4x64 

-^ 

2.333 

4.667 

7.000 

9.333 

11.67 

14.00 

16.33 

18.67 

21.00 

'•X7 

'*xa 

2.667 

5.333 

8.000 

10.667 

13.33 

16.00 

18.67 

21.33 

24.00 

••x8 

••xf 

3.000 

6.000 

9.000 

12.00 

15.00 

18.00 

21.00 

24.00 

27.00 

••x9 

**xlO 

3.333 

6.667 

10.000 

13.83 

16.67 

20.00 

23.83 

26.67 

30.00 

•110 

4x11 

3.M7 

7.833 

11.00 

14.67 

18.83 

22.00 

25.67 

29.33 

33.00 

4X11 

•*X12 

4.000 

8.000 

12.00 

16.00 

20.00 

24.00 

28.00 

32.00 

36.00 

•112 

•*X14 

4.667 

9.333 

14.00 

18.67 

23.33 

28.00 

33.67 

37.33 

42.00 

•114 

•*xl5 

5.600 

10.000 

15.00 

20.00 

25.00 

30.00 

35.00 

40.00 

45.00 

•115 

••xU 

5.33$ 

10.67 

16.00 

21.33 

26.67 

32.00 

37.33 

42.67 

48.00 

••xl6 

4X18 

6.00O 

12.00 

18.00 

24.00 

30.00 

36.00 

42.00 

48.00 

54.00 

4x18 

4^X4^    1.M8 

3.375 

5.063 

6.760 

8.438 

10.13 

11.81 

13.50 

15.19 

44x44 

••X5      1.876 

3.750 

5.626 

7.600 

9.876 

11.26 

13.13 

15.00 

16.88 

••x6 

"X$i 

2.063 

4.125 

6.188 

8.250 

10.313 

12.38 

14.44 

16.50 

18.56 

••X54 

•xT 

2.250 

4.600 

6.760 

9.000 

11.35 

13.60 

16.75 

18.00 

20.26 

••x6 

4|x«» 

2.438 

4.876 

7.813 

9.760 

12.19 

14.63 

17.06 

19.60 

21.94 

44x64 

••X7 

2.625 

5.250 

7.876 

10.600 

13.13 

15.75 

18.38 

21.00 

23.63 

••x7 

•18 

3.000 

6.000 

9.000 

12.00 

15.00 

18.00 

21.00 

24.00 

27.00 

••x8 

"X» 

3.375 

6.750 

10. 125 

13.50 

16.88 

20.25 

23.63 

27.00 

30.38 

•19 

•-xlO 

3.750 

7.600 

11.26 

16.00 

18.75 

22.60 

26.25 

30.00 

33.75 

•110 

4ixll 

4. 125 

8.250 

12.38 

16.50 

20.63 

24.76 

28.88 

33.00 

37.13 

44x11 

■112 

4.500 

9.000 

13.50 

18.00 

22.50 

27.00 

31.50 

36.00 

40.50 

••xl2 

•114 

5.250 

10.500 

15.75 

21.00 

26.25 

31.50 

36.75 

42.00 

47.25 

••xl4 

••xIS 

5.625 

11.25 

16.88 

22.60 

28.13 

33.75 

39.38 

45.00 

50.63 

••xl5 

•IIS 

6.000 

12.00 

18.00 

24.00 

30.00 

36.00 

42.00 

48.00 

54.00 

••xl6 

4ixl8 

6.T50 

13.50 

20.25 

r.oo 

33.75 

40.60 

47.26 

54.00 

60.75 

44x18 

5x5 

2.083 

4.167 

6.250 

8.333 

10.42 

12.50 

14.58 

16.67 

18.75 

5  x5 

••x5J 

2.202 

4.5» 

6.876 

9.167 

11.46 

13.76 

16.04 

18.33 

20.63 

••x54 

•1« 

2.500 

5.000 

7.600 

10.000 

12.50 

15.00 

17.50 

20.00 

22.50 

••x6 

'1« 

2.708 

5.417 

8.136 

10.83 

13.64 

16.25 

18.96 

21.67 

24.37 

••x6J 

5X7 

2.017 

6.833 

8.750 

11.67 

14.68 

17.60 

20.42 

23.33 

26.25 

8  x7 

••X7J 

3.126 

6.250 

9.375 

12.60 

15.63 

18.75 

21.88 

25.00 

28.13 

••x74 

••x8 

3.333 

6.667 

10.000 

13.83 

16.67 

20.00 

23.33 

26.67 

30.00 

••x8 

"x9 

3.760 

7.600 

11.25 

15.00 

18.75 

22.50 

26.25 

30.00 

33.76 

••x9 

"xlO 

4.167 

8.333 

12.60 

16.67 

20.83 

25.00 

29.17 

33.33 

37.50 

•110 

Szll 

4.58S 

9.167 

13.75 

18.33 

22.92 

27.50 

32.08 

36.67 

41.25 

5  xll 

'113 

5.000 

10.000 

15.00 

20.00 

25.00 

30.00 

35.00 

40.00 

45.00 

•112 

••Xl4 

5.833 

11.67 

17.60 

23.83 

29.17 

35.00 

40.83 

46.67 

52.50 

••xl4 

•115 

6.250 

12.60 

18.75 

25.00 

31.25 

37.50 

43.75 

50.00 

56.25 

••xl5 

•in 

6.667 

13.33 

20.00 

26.67 

33.33 

40.00 

46.67 

53.33 

60.00 

••xl6 

5X18 

T.800 

15.00 

22.60 

30.00 

37.60 

45.00 

52.50 

60.00 

67.50 

5  XI8 

Hx5i 

2.621 

5.042 

7.663 

10.08 

12.60 

15.13 

17.65 

20.17 

22.69 

5JX5J 

"xT 

2.750 

6.500 

8.250 

11.00 

13.75 

16.50 

19.25 

22.00 

24.75 

••x6 

••x«| 

2.979 

5.958 

8.938 

11.92 

14.90 

17.88 

20.85 

23.83 

26.81 

'!*•* 

17 

3.208 

0.417 

9.626 

12.83 

16.04 

19.25 

22.46 

25.67 

28.88 

••x7 

HH.— LUMBER  AND  LUMBERING, 


4. — Fbbt  Board  Mbasurb — Bnginbbrs'  Tablb. — Continued. 


Lent  m  in  Feet. 

I 

2 

3 

4 

5 

6 

7 

8 

9 

^ 

3.438 

6.875 

10.313 

13.75 

17.19 

20.63 

24.06 

27.60 

30  94 

c8 

3.667 

7.333 

11.00 

14.67 

18.33 

22.00 

25.67 

29.33 

83.00 

c9 

4.125 

8.250 

12.38 

16.50 

20.63 

24.75 

28.88 

33.00 

37.13 

clO 

4.583 

9.167 

13.75 

18.33 

22.92 

27.50 

32.08 

36.67 

41.25 

Ell 

5.042 

10.083 

15.13 

20.17 

26.21 

30.26 

25.29 

40.33 

45.38 

cl2 

5.500 

11.00 

16.60 

22.00 

27.50 

83.00 

38.60 

44.00 

49.50 

(14 

6.417 

12.83 

19.25 

26.67 

32.08 

38.60 

44.02 

61.33 

67.75 

(15 

6.875 

13.75 

20.63 

27.60 

34.38 

41.25 

48.13 

65.00 

61.88 

116 

7.333 

14.67 

22.00 

29.33 

86.67 

44.00 

51.33 

58.67 

66.00 

cl8 

8.250 

16.60 

24.75 

33.00 

41.25 

4».60 

57.75 

66.00 

74.25 

k6 

3.000 

6.000 

o.ooe 

12.00 

15.00 

18.00 

21.00 

34  00 

27.00 

K6i 

3.250 

6.500 

9.750 

13.00 

16.25 

19.60 

22.75 

26.00 

29.25 

k7 

3.500 

7.000 

10.600 

14.00 

17.60 

21.00 

24.60 

28.00 

31.50 

k7» 

3.750 

7.500 

11.25 

15.00 

18.75 

22.60 

26.25 

30.00 

33.76 

c8 

4.000 

8.000 

12.00 

16.00 

20.00 

24.00 

28.00 

33.00 

36.00 

c9 

4.500 

9.000 

13.50 

18.00 

22.60 

27.00 

31.60 

36.00 

40.80 

KlO 

5.000 

10.000 

15.00 

20.00 

25.00 

30.00 

35.  UO 

40.00 

46.00 

Kll 

5.500 

11.00 

16.50 

22.00 

27.60 

83.00 

38.50 

44.00 

49.50 

KI2 

6.000 

12.00 

18.00 

24.00 

30.00 

36.00 

42.00 

48.00 

54.00 

K14 

7.000 

14.00 

21.00 

28.00 

36.00 

43.00 

49.00 

56.00 

63.00 

115 

7.500 

15.00 

22.50 

30.00 

37.60 

45.00 

52.50 

60.00 

67.50 

KI6 

8.000 

16.00 

24.00 

32.00 

40.00 

48.00 

56.00 

64.00 

72.00 

IC18 

9.000 

18.00 

27.00 

36.00 

45.00 

64.00 

63.00 

72.00 

81.00 

i6i 

3.521 

7.042 

10.56 

14.08 

17.60 

21.13 

24.66 

28.17 

31.69 

17 

3.792 

7.683 

11.38 

15.17 

18.96 

22.75 

26.54 

30.33 

34.13 

r7J 

4.063 

8.125 

12.19 

16.25 

20.S1 

24.38 

28.44 

32.60 

36.66 

X8 

4.033 

8.667 

13.00 

17.83 

21.67 

26.00 

30.33 

34.67 

39.00 

x9 

4.875 

9.750 

14.63 

19.50 

24.38 

29.25 

34.13 

39.00 

43.88 

XlO 

5.417 

10.833 

16.25 

21.67 

27.08 

32.60 

37.92 

43.83 

48.78 

Ell 

6.958 

11.92 

17.88 

23.83 

29.79 

35.75 

41.71 

47.67 

53.63 

xl2 

6.600 

13.00 

19.50 

26.00 

32.60 

39.00 

45.50 

52.00 

58. 5C 

114 

7.583 

15.17 

22.75 

30.33 

37.92 

45.50 

53.08 

60.67 

68.28 

Xl5 

8.125 

16.25 

24.38 

32.50 

40.63 

48.75 

56.88 

65.00 

73.13 

X16 

8.6C7 

17.33 

26.00 

34.67 

43.33 

62.00 

60.67 

69.33 

78.  OC 

118 

9.760 

19.60 

29.25 

39.00 

48.76 

68.50 

68.26 

78.00 

87.7! 

X7 

4.083 

8.167 

12.25 

16.33 

20.42 

24.50 

28.58 

82.67 

36.7! 

17* 

4.375 

8.750 

13.13 

17.60 

21.88 

26.25 

30.63 

36.00 

39.3f 

x8 

4.667 

9.333 
10.600 

14.00 

18.67 

23.33 

28.00 

82.67 

37.33 

42.0( 

x9 

5.250 

15.76 

21.00 

26.25 

31.60 

36.75 

42.00 

47.2! 

KlO 

5.833 

11.67 

17.50 

23.33 

29.17 

35.00 

40.83 

46.67 

62.5( 

111 

6.417 

12.83 

19.25 

25.67 

32.08 

38.60 

44.92 

61.33 

57.7! 

xI2 

7.000 

14.00 

21.00 

28.00 

35.00 

42.00 

49.00 

66.00 

63. 0( 

113 

7.583 

15.17 

22.75 

30.33 

37.92 

45.50 

63.08 

60.67 

68.2! 

KM 

8.167 

16.33 

24.50 

32.67 

40.83 

49.00 

57.17 

65.33 

73. 6< 

115 

8.750 

17.50 

26.25 

35.00 

43.75 

62.50 

61.36 

70.00 

78.7! 

116 

9.833 

18.67 

28.00 

37.33 

46.67 

56.00 

65.33 

74.67 

84.0( 

118 

10.600 

21.00 

31.50 

42.00 

52.50 

63.00 

73.60 

84.00 

94. 5< 

174 

4.688 

9.375 

14.06 

18.75 

23.44 

28.13 

32.81 

87.60 

42. 1< 

18 

6.000 

10.000 

15.00 

20.00 

25.00 

30.00 

36.00 

40.00 

45. 0( 

184 

6.313 

10.63 

16.94 

21.25 

26.66 

31.88 

37,19 

42.60 

47.81 

19 

5.625 

11.25 

16.88 

22.60 

28.13 

33.75 

39.88 

45.00 

50.62 

llO 

6.250 

12.60 

18.75 

25.00 

31.25 

37.60 

43.76 

60.00 

56.2! 

111 

6.875 

13.75 

20.63 

27.60 

34.38 

41.25 

48.13 

65.00 

61.81 

112 
113 

7. BOO 
8.126 

15.00 
16.26 

22.50 
24.38 

30.00 
32.60 

37.60 
40.63 

4.').  00 
48.75 

62.60 
66.88 

60.00 
65.00 

67.54 
73.1: 

BOARD  MEASURE, 


885 


4- — Pbbt  Boakd  Mbasurb — Enoinbers*  Tablb. — Continued. 

ill 

Lanctta  In  Feet. 

tu 

aSe 

1 

2 

a 

^ 

8 

0 

7 

• 

7iXl4 
••X15 
••X16 
••X18 
tz8 

8.750 
9.275 
10.000 
11.25 
5.323 

17.50 
18.76 
20.00 
22.50 
10.67 

26.25 

28.12 
30.00 
33.75 
16.00 

35.00 
37.60 
40.00 
45.00 
21.38 

43.75 
46.88 
60.00 
56.25 

26.67 

52.50 
56.25 
60.00 
67.60 
32.00 

61.26 
66.63 
70.00 
78.75 
37.33 

70.00 
76.00 
80.00 
90.00 
42.67 

78.76 
84.38 
90.00 
101.25 
48.00 

7ixl4 
"xl6 
••xl6 
••X18 
8x8 

••xf 
"xlO 
••xll 
"xiz 

5.607 
6.000 
6.667 
7.333 
8.000 

11.33 
12.00 
13.38 
14.67 
16.00 

17.00 
18.00 
20.00 
22.00 
24.00 

28.67 
24.00 
26.67 
29.33 
32.00 

28.38 
30.00 
33.38 
36.67 
40.00 

34.00 
36.00 
40.00 
44.00 
48.00 

39.67 
42.00 
46.67 
51.33 
56.00 

45.38 
48.00 
53.33 
58.67 
64.00 

51.00 
54.00 
60.00 
66.00 
72.00 

8x8J 
••x9 
"xlO 
"xll 
••xl2 

8  xl3 

"X14 
••Xl5 

"xie 

••xl8 

8.607 
9.383 
10.000 
10.67 
12.00 

17.33 
18.67 
20.00 
21.33 
24.00 

26.00 
28.00 
30.00 
32.00 
36.00 

34.67 
87.33 
40.00 
42.67 
48.00 

43.33 

46.67 
50.00 
53.33 
60.00 

62.00 
66.00 
60.00 
64.00 
72.00 

60.67 
65.33 
70.00 
74.67 
84.00 

69.38 
74.67 
80.00 
86.33 
96.00 

78.00 
84.00 
90.00 
96.00 
108.00 

8x12 
••xl4 
••xl5 
••X16 
••xl8 

••xlO 

"Xll 

6.021 
6.375 
6.729 
7.083 
7.792 

12.04 

12.75 
13.46 
14.17 
15.58 

18.06 
19.13 
20.19 
21.25 
22.38 

24.08 
25.50 
26.92 
28.33 
31.17 

30.10 
31.88 
33.65 
35.42 
38.96 

36.13 
38.25 
40.38 
42.50 
46.76 

42.15 
44.63 
47.10 
49.58 
54.64 

48.17 
61.00 
53.83 
56.67 
62.34 

64.19 
67.38 
60.56 
63.75 
70.18 

••xll 

8»xl2 
••xl3 
••XI4 
••xl5 
•'xl6 

8.500 
9.208 
9.917 
10.63 
11.33 

17.00 
18.42 
19.83 
21.25 
22.67 

26.50 
27.63 
29.76 
31.88 
34.00 

34.00 
36.83 
39.67 
42.60 
46.33 

42.50 
46.04 
49.58 
53.13 
56.67 

51.00 
55.26 
59.50 
63.75 
68.00 

59.60 
64.46 
69.42 
74.38 
79.33 

68.00 

73.67 
79.33 
85.00 
90.67 

76.50 
82.88 
89.25 
95.63 
102.00 

8ixl3 
••xl3 
••xl4 
"xl6 
•■xl6 

HXI7 
••X18 
»  X9 

12.04 
12.75 
6.750 
7.125 
7.500 

24.08 
25.60 
13.50 
14.25 
16.00 

36.12 
38.26 
20.26 
21.38 
22.50 

48.17 
51.00 
27.00 
28.60 
30.00 

60.21 
63.75 
33.75 
35.63 
37.50 

72.26 
76.50 
40.50 
42.75 
45.00 

84.29 
89.25 
47.25 
49.88 
52.60 

96.33 
102.00 
54.00 
57.00 
60.00 

108.38 
114.75 
60.75 
64.13 
67.50 

8U17 
••xl8 
9  x9 

••in 

9  xU 
••xl2 
•'Xl3 

•xu 

••xl5 

8. 250 
9.000 
9.750 
10.50 
11.25 

16.50 
18.00 
19.50 
21.00 
22.60 

24.75 
27.00 
29.25 
31.60 
33.75 

33.00 
36.00 
39.00 
42.00 
46.00 

41.26 
46.00 
48.75 
52.50 
56.50 

49.50 
54.00 
58.50 
63.00 
67.50 

57.75 
63.00 
68.25 
73.50 
78.76 

66.00 
72.00 
78.00 
84.00 
90.00 

74.25 
81.00 
87.75 
94.50 
101.25 

9  Xll 
••xl2 
••xl3 
•'xl4 
"xl6 

9  xl« 
••Xl7 
••xl« 
"X20 
91X9* 

12.00 
12.75 
13.50 
15.00 
7.621 

24.00 
25.50 
27.00 
30.00 
15.04 

36.00 
38.25 
40.60 
45.00 
22.56 

48.00 
51.00 
64.00 
60.00 
30.08 

60.00 
63.75 
67.50 
75.00 
37.60 

72.00 
76.50 
81.00 
90.00 
45.13 

84.00 
89.25 
94.50 
105.00 
52.65 

96.00 
102.00 
108.00 
120.00 

60.17 

108.00 
114.75 
121.50 
135.00 
67.69 

9X16 
•'xl7 
••xI8 
"x20 
0ix9* 

HxlO 
••xll 
••xl2 
••xl3 
••Xl4 

7.917 
8.708 
9-500 
10.29 
11.08 

15.83 
17.42 
19.00 
20.58 
22.17 

22.75 
36.13 
28.60 
30.88 
33.25 

31.67 
34.83 
38.00 
41.17 
44.33 

39.58 
43.54 
47.50 
51.46 
55.42 

47.50 
52.25 
57.00 
61.75 
66.50 

55.42 
60.96 
66.50 
72.04 
77.58 

63.33 
69.67 
76.00 

82.34 
88.67 

71.25 
78.38 
85.50 
92.63 
99.75 

9ixl0 
"xll 
"X12 
■•xl3 
"xl4 

9ixl5 
••xl6 
••xl7 
••xl8 
•'x20 

11.88 
12.67 
13.46 
14.25 
15.83 

23.76 
25.33 
26.92 
28.50 
31.67 

35.63 
38.00 
40.38 
42.75 
47.50 

47.60 
60.67 
53.83 
57.00 
63.33 

59.38 
63.33 
67.29 
71.25 
79.17 

71.25 
76.00 
80.75 
85.50 
95.00 

83.13 
88.67 
94.21 
99.75 
110.83 

95.00 
101.33 
107.67 
114.00 
126.67 

106.88 
114.00 
121.13 
128.25 
142.50 

9ixl5 
••xl6 
••xl7 
•'xl8 
••x20 

10x10 
••xll 
•'xll 
••xl3 
••xU 

8.333 
9.167 
10.00 
10.83 
11.67 

16.67 
18.33 
20.00 
21.67 
23.33 

25.00 
27.50 
30.00 
32.50 
36.0lf 

38.33 
36.67 
40.00 
43.38 
46.67 

41.67 
45.83 
50.00 
54.17 
58.33 

50.00 
55.00 
60.00 
65.00 
70.00 

58.33 
64.17 
70.00 
75.83 
81.67 
Digitize 

66.67 
73.. 33 
80.00 
86.67 

75.00 
82.50 
90.00 
97.50 
105.00 

10x10 
"xll 
"xl2 
••xl3 
"X14 

886 


20.— LUMBER  AND  LUMBERING. 


4. — Feet  Board  Measure — Enginbbrs'  Table. — Continued. 


Lengthln  Feet. 

ifl 

1 

2 

3 

4 

9 

6 

7 

8 

9 

5la 

10x15 

12.50 

25.00 

37.60 

60.00 

62.60 

76.00 

87.60 

100.00 

112.50 

10x15 

••xl« 

13.33 

26.67 

40.00 

53.33 

66.67 

80.00' 

91.38 

106.67 

120.00 

"xie 

••xl7 

14.17 

28.33 

42.60 

66.67 

70.83 

86.00 

99.17 

113.83 

127.60 

••xl7 

••xl8 

15.00 

30.00 

46.00 

60.00 

76.00 

90.00 

105.00 

120.00 

135.00 

••xia 

••x20 

16.67 

33.33 

60.00 

66.67 

83.33 

100.00 

116.67 

133.83 

160.00 

••x20 

11x11 

10.08 

20.17 

80.26 

40.83 

50.42 

60.60 

70.68 

80.67 

90.76 

llxll 

••xl2 

11.00 

22.00 

33.00 

44.00 

68.00 

66.00 

77.00 

88.00 

99.00 

••X13 

••xl3 

11.92 

23.83 

u 

47.67 

69.68 

71.6a 

83.48 

96.33 

107.25 

"xW 

••xU 

12.83 

25.67 

51.88 

64.17 

77.00 

80.83 

102.67 

115.60 

••xI4 

••xl5 

13.76 

27.60 

41.25 

66.00 

€8.76 

82.60 

96.26 

110.00 

123.76 

"X16 

11x16 

14.67 

29.33 

44.00 

68.67 

78.83 

88.00 

103.67 

117.33 

133.00 

lIxU 

••xl7 

15.58 

31.17 

46.76 

62.33 

77.92 

93.60 

109.08 

124.67 

140.26 

••xlT 

••xl8 

16.50 

33.00 

49.60 

66.00 

82.50 

99.00 

115.60 

132.00 

148.60 

••X18 

••x20 

18.33 

36.67 

55.00 

73.33 

91.67 

110.00 

128.33 

146.67 

165.00 

'•x30 

12x12 

12.00 

24.00 

36.00 

48.00 

60.00 

73.00 

84.00 

96.00 

108.00 

13x13 

12x13 

13.00 

26.00 

39.00 

52.00 

66.00 

78.00 

91.00 

104.00 

117.00 

12x13 

••xl4 

14.00 

28.00 

42.00 

56.00 

70.00 

84.00 

98.00 

113.00 

126.00 

••xl4 

••xl5 

15.00 

30.00 

45.00 

60.00 

76.00 

90.00 

106.00 

120.00 

135.00 

••xl5 

••xl6 

16.00 

32.00 

48.00 

64.00 

80.00 

96.00 

112.00 

128.00 

144.00 

••xlC 

••xl7 

17.00 

34.00 

51.00 

68.00 

85.00 

102.00 

119.00 

136.00 

153.00 

"xl7 

12x18 

18.00 

36.00 

64.00 

72.00 

90.00 

108.00 

126.00 

144.00 

163.00 

12x18 

'•x20 

20.00 

40.00 

60.00 

80.00 

100.00 

120.00 

140.00 

160.00 

180.00 

**X20 

••x22 

22.00 

44.00 

66.00 

88.00 

110.00 

132.00 

154.00 

176.00 

198.00 

'•xaj 

••x24 

24.00 

48.00 

72.00 

96.00 

120.00 

144.00 

168.00 

192.00 

216.00 

••x24 

13x13 

14.08 

28.17 

42.26 

56.33 

70.42 

84.60 

98.68 

112.67 

121.76 

13x18 

13x14 

15.17 

30.33 

45.60 

60.67 

75.83 

91.00 

106.17 

121.33 

136.50 

13x14 

••xl6 

16.25 

32.50 

48.75 

65.00 

81.25 

97.60 

113.76 

130.00 

146.26 

••xl5 

••xl« 

17.33 

34.67 

52.00 

69.33 

86.67 

104.00 

121.33 

138.67 

156.00 

'•xl« 

••xl7 

18.42 

36.83 

55.25 

73.67 

92.08 

110.60 

128.92 

147.83 

165.75 

**xl7 

••xl8 

19.50 

39.00 

68.50 

78.00 

97.60 

117.00 

136.60 

156.00 

176.60 

"X18 

13x20 

21.67 

43.33 

65.00 

86.67 

108.33 

130.00 

151.67 

173.33 

196.0t 

13x20 

'•x22 

23.83 

47.67 

71.50 

95.33 

119.17 

143.00 

166.83 

190.67 

214.60 

••x22 

•'x24 

26.00 

52.00 

78.00 

104.00 

130.00 

156.00 

182.00 

208.00 

234.00 

••x24 

14X14 

16.33 

32.67 

49.00 

65.33 

81.67 

98.00 

114.33 

130.67 

147.00 

14x14 

••Xl6 

17.50 

35.00 

52.60 

70.00 

87.60 

105.00 

123.60 

140.00 

167.60 

••Xl5 

14X16 

18.67 

37.33 

56.00 

74.67 

93.33 

112.00 

130.67 

149.33 

168.00 

14x18 

••xl7 

19.08 

38.17 

57.25 

76.33 

95.42 

114.50 

133.58 

152.67 

171.75 

'•xl7 

••xl8 

21.00 

43.00 

63.00 

84.00 

105.00 

126.00 

147.00 

168.00 

189.00 

••xl8 

••x20 

23.33 

46.67 

70.00 

93.33 

106.67 

140.00 

163.33 

186.67 

210.00 

••x20 

••x22 

25.67 

51.33 

77.00 

102.67 

128.33 

164.00 

179.67 

206.83 

231.00 

••X21 

14X24 

28.00 

56.00 

84.00 

112.00 

140.00 

168.00 

196.00 

224.00 

258.00 

14x24 

15X15 

18.76 

37.60 

56.26 

75.00 

93.75 

112.50 

131.25 

150.00 

168.76 

15x18 

••xl6 

20.00 

40.00 

60.00 

80.00 

100.00 

120.00 

140.00 

160.00 

180.00 

"xl« 

•'X17 

21.25 

42.50 

63.75 

85.00 

106.25 

127.50 

148.75 

170.00 

191.36 

••xl7 

••xl8 

22.50 

45.00 

67.60 

90.00 

112.50 

136.00 

157.50 

180.00 

203.60 

••xl8 

15x19 

23.75 

47.60 

71.26 

95.00 

118.75 

142.50 

166.26 

190.00 

213.75 

15x18 

••x20 

25.00 

50.00 

75.00 

100.00 

125.00 

150.00 

175.00 

200.00 

225.00 

••x20 

••x22 

27.50 

55.00 

82.50 

110.00 

137.60 

165.00 

198.60 

220.00 

247.50 

Vx22 

••x24 

30.00 

60.00 

90.00 

120.00 

150.00 

180.00 

210.00 

240.00 

270.00 

•'X24 

16x16 

21.33 

42.67 

64.00 

86.33 

106.67 

128.00 

149.38 

170.67 

193.00 

18x18 

16x17 

22.67 

46.83 

68.00 

90.67 

113.83 

136.00 

158.67 

181.83 

204.00 

18x17 

•'XI 8 

24.00 

48.00 

72.00 

96.00 

120.00 

144.00 

168.00 

192.00 

216.00 

••xl8 

'•x20 

26.67 

53.33 

80.00 

106.67 

133.33 

160.00 

186.67 

213.33 

240.00 

•'X28 

••x22 

29.33 

68.87 

88.00 

117.33 

146.67 

176.00 

205.33 

234.67 

264.00 

••x22 

••x24 

32.00 

64.00 

96.00 

128.00 

160  00 

192.00 

224.00 

256.00 

288.00 

••x24 

GRADING  OF  LUMBER— YELLOW  PINE. 


887 


4. — ^Pbbt  Board  Mbasurb — Enoinbbrs' Tablb. — Concluded. 


had 

III 

Length  In  Feet. 

III 

1 

2 

3 

4 

5 

6 

•  7 

8 

9 

JTX17 
"Xl« 
••XI9 

"xai 

•X22 

17x24 
18x18 
"Xlf 

"xai 
••xai 

UX24 

aiio 
••x» 

"U4 

ax2a 

22x24 
24ZM 

24.08 
25.60 
M.tt 
28.33 

81.17 

34.00 
27.00 
38.50 
30.00 
33.00 

30.00 
».33 

30.67 
40.00 
40.33 

44.00 
48.00 

48.17 
61.00 
63.83 
66.67 
63.33 

68.00 
54.00 
57.00 
60.00 
66.00 

72.00 
60.67 
73.33 
80.00 
80.67 

88.00 
96.00 

72.25 
76.60 
80.75 
86.00 
93.50 

102.00 
81.00 
85.50 
90.00 
99.00 

108.00 
100.60 
110.00 
120.00 
121.00 

133.00 
144.00 

96.33 
102.00 
107.67 
113.33 
124.67 

136.00 
108.00 
114.00 
120.00 
133.00 

144.00 
133.33 
146.67 
160.00 
161.33 

176.00 
192.00 

120.42 
127.60 
134.68 
141.67 
165.83 

170.00 
135.00 
142.50 
150.00 
166.00 

180.00 
166.67 
183.33 
200.00 
201.67 

220.00 
240.00 

144.60 
153.00 
161.50 
170.00 
187.00 

204.00 
162.00 
171.00 
180.00 
198.00 

216.00 
200.00 
220.00 
240.00 
242.00 

264.00 
288.00 

168.58 
178.50 
188.42 
198.33 
218.17 

238.00 
189.00 
199.50 
210.00 
231.00 

252.00 
233.33 
256.67 
280.00 
282.33 

308.00 
836.00 

192.67 
204.00 
215.33 
226.67 
249.33 

272.00 
216.00 
228.00 
240.00 
264.00 

288.00 
266.67 
293.33 
320.00 
322.67 

353.00 
384.00 

216.75 
229.50 
242.25 
255.00 
280.50 

306.00 
243.00 
256.50 
270.00 
297.00 

324.00 
300.00 
330.00 
360.00 
363.00 

896.00 
432.00 

17x17 
••xl8 
••xl9 
••x20 
'•x23 

17x24 
18x18 
••X19 
••x20 
••x22 

18x24 

20x20 
••x22 
••x24 
22x22 

22x24 

24x24 

of  Lombor. — ^Attention  is  here  called  to  Forest  Service  Bulle- 
tin 71.  U.  S.  Dept.  of  Agriculture,  entitled  **  Rules  and  Specifications  for 
the  Grading  of  Lumber,  adopted  by  the  Various  [181  Lumber  Mantifacturing 
Associations  of  the  U.  S."     Compiled  by  B.  R.  Hodson,  1006. 

The  American  Society  for  Testing  Materials  has  undertaken  the  very 
difficult  task  of  recommending  Standard  Specifications  for  the  Giading  of 
Structural  Timber.  The  report  of  the  Committee  for  1006  will  be  found 
in  VoL  VI  of  the  proceedings,  page  120.  and  is  discussed  tmder  three  head- 
ings: (1)  De&utions  of  structural  timber,  (2)  Standard  defects,  and  (3) 
^sndazd  names  for  structural  timbers.  Among  the  standard  defects  are 
the  following:  Sound  ibi^f— solid  across  its  face,  and  as  hard  as  the  siuroimd- 
ing  wood;  loost  knot — not  firmly  held  in  place  by  growth  or  position;  pith 
ioot— sound  knot  with  pith  hole  not  more  than  \  m.  in  dia  in  the  center; 
rotUn  knot — not  as  hard  as  the  surrounding  wood;  pin  knot — sound  knot 
not  over  i  in.  in  dia.^  hrg€  knot — sound  knot  more  than  H  ins.  in  dia.; 
spik€  knot-—onc  sawn  m  a  lengthwise  direction;  pitch  pockets — openings  in 
grain  of  wood  containing  more  or  less  pitch  or  bark  (small  when  not  over 
1  in.  wide,  standard  when  not  over  |  in.  wide  or  3  ins.  long,  large  when  over 
I  in.  wide  or  3  ins.  long):  wang — ^bark  or  lack  of  wood  on  edge  of  timber; 
skakgs — splits  or  checks  between  annular  rings;  rot,  dot*,  and  red  heart — 
white  or  red  rotten  spots,  dark  discolorations  not  found  in  sound  wood,  etc. 

Clasiifficatioo  aad  Inspection  of  Yellow  Pine  hvan\>tt»*'— General  Rules. — 
All  Itimber  must  be  sound,  commercial  longleaf  yellow  pine  (pine  combining 
IsTBe  coarse  knots,  with  coarse  grain,  is  excluded  tmder  these  rules),  weu 
msntifactnred,  full  to  size  and  saw  butted,  and  shall  be  free  from  the  follow- 
ing defects:  Unsound,  loose,  and  hollow  knots,  wormholes  and  knot  holes, 
through  shakes  or  round  shakes  that  show  on  the  surface;  and  shall  be  square 
edge  unless  otherwise  specified.  A  through  shake  is  hereby  defined  to  be 
through  or  connected  from  side  to  side,  or  edge  to  edge,  or  edge  to  side. 
In  the  measurement  of  dressed  lumber  the  width  and  thickness  of  the  lumber 
before  dresssngmust  be  taken — ^less  than  one  inch  thick  shall  be  measured 
as  one  inch.  The  measurement  of  wane  shall  always  apply  to  the  lumber 
in  the  rough.  Where  terms  one-half  and  two-thirds  heart  are  used  they 
shall  be  con^rued  as  referring  to  the  area  of  the  face  on  which  measured. 

*  Interstate  rules  of  1005.  Adopted  by  the  Georgia-Florida  Sawmill 
AModation,  Georgia  Interstate  Sawmill  Association,  South  Carolina  Lum- 
ber Association,  New  Yoric  Lumber  Trade  Association  of  New  York  City, 
Yellow  Pine  Exchange  of  New  York  City,  The  Lumbermen's  Exchange 
of  Philadelphia.  The  Lumbermen's  Exchange  of  Baltimore. 


888  70.-— LUMBER  AND  LUMBERING. 

In  the  dressing  of  lumber,  when  not  otherwise  specified,  one-eighth  : 
shall  be  taken  oflf  by  each  planer  cut.     All  lumber  grading  higher  than  1 
grade  for  which  it  is  sold  shall  be  accepted  as  of  the  grade  sold. 

shall  embrace  four,  five  and  six  quarter  i 

i]  inches  in  width,  excluding  lixO.     Porexamp 

1  and  5;  ljx8,  4,  —"<  *      n^^*  •ti.ii  ^.^nW*. 

a  .  by  over  0  ins. 

a  ins.  wide.     Plat 

1  ess  by  over  6  ini 

9  jy  6  and  over  in  ^ 

s  d  under  0  ins  in 

C  le:  2x2.  2x3.  2x4 

a  hall  embrace  all 

I  For  example:  da 

1  21  ins.  in  thicki 

I  and  2}  x7.  and 

J  s  1  in.  and  up  ii 

1  inly.     For  exam] 

trj    u  uiB.  ckuu  UK*  **iuc.  B«v*cd  OU  tWO  sidcS  Okxijr.  i 

Inspection. — Standard  lumber  shall  be  sotmd,  sap  no  objection.  Wane  i 
may  be  allowed  i  of  the  width  of  the  piece  measured  across  face  of  wane, 
extending  \  of  the  length  on  one  comer,  or  its  equivalent  on  two  or  more 
comers,  provided  that  not  over  10%  of  the  pieces  of  any  one  size  ^all  Aow 
such  wane.  Merchantable  sizes  under  0  ins.  shall  show  some  heart  the  entire 
length  on  one  side;  sizes  9  ins.  and  over  shall  show  some  heart  the  entire 
length  on  two  opposite  sides.  Wane  may  be  allowed  i  of  the  width  of  the 
piece  measured  across  face  or  wane,  and  extending  \  of  the  length  of  the 
piece  on  one  comer  or  its  equivalent  on  two  or  more  comers,  provided  that 
not  over  10%  of  the  pieces  of  any  one  size  shall  show  such  wane.  Prime 
lumber. — Flooring  shall  show  one  heart  face,  free  from  through  or  round 
shakes  or  knots  exceeding  one  inch  in  dia  or  more  than  four  in  a  board  on 
the  face  side.  Boards  7  ins.  and  xmder  wide  shall  show  one  heart  face: 
over  7  ins.  wide  shall  show  }  heart  on  both  sides;  all  free  from  round  or 
through  shakes,  large  or  imsound  knots.  Plank  7  ins.  and  under  wide 
shall  show  one  heart  face;  over  7  ins.  wide  shall  show  }  heart  on  both  sides; 
all  free  from  round  or  through  shakes,  large  or  unsotmd  knots.  Scantling 
shall  show  three  comers  heart,  free  from  through  or  round  shakes  or  un- 
sotmd knots.  Dimension  sizes  of  Prime  lumber. — ^All  square  lumber  shall 
show  }  heart  on  two  sides  and  not  less  than  \  heart  on  two  other  sides. 
Other  sizes  shall  show  )  heart  on  face  and  show  heart  f  of  length  on  edges, 
excepting  when  the  width  exceeds  the  thickness  by  3  ins.  or  over;  then  it 
shall  show  heart  on  the  edges  for  \  the  length.  Stepping  shall  show  3  comers 
heart,  free  from  shakes  and  all  knots  exceeding  4  in.  in  dia,  and  not  more 
than  6  in  a  board.  Rough  Ed^e  or  Flitch  shall  be  sawed  from  good  heart 
timber,  and  shall  be  measured  m  the  middle  on  the  narrow  face,  free  from 
injurious  shakes  or  imsound  knots.  Wane  on  not  over  5%  of  the  pieces 
jn  any  one  size,  shall  be  allowed  as  on  merchantable  quality. 

Rules  for  Orading  Fir,  Spruce,  Cedar,  and  Hemlock  Lnmber.* — Gengral 

Instructions. — ^All  lumber  graded  with  special  reference  to  its  suitability 
for  the  use  intended ;  therefore  each  piece  is  considered  and  its  grade  deter- 
mined by  its  general  character,  including  the  sum  of  all  its  defects.  "Yard 
Ltunber  "  (dimension,  common  boards,  finish,  etc.)  is  graded  from  the  face 
(best)  side,  except  that  when  lumber  which  is  dressed  one  side  only  is  graded 
from  the  dressed  side.  Factory  lumber  (for  doors,  sashes,  etc.)  which  miist 
show  on  both  sides,  is  always  graded  from  the  poorest  side.  Defects  are 
taken  in  connection  with  the  size  of  the  piece,  wider  and  longer  pieces 
carrying  more  defects  than  smaller  pieces  in  toe  same  grade.  Grade  is 
determmed  at  time  of  shipment  and  cannot  be  reconsidered  after  further 
working;  a  i^ipment  of  any  grade  to  consist  of  a  fair  average  of  that  grade. 
Material  not  conforming  to  standard  sizes  shall  be  governed  by  special 
contract.  Standard  lengths  for  all  lumber  are  multiples  of  two  feet,  except 
that  the  standard  lengths  for  flooring,  ceiling,  siding,  rustic,  and  finish  ax« 

*  Rail  shipments.  Digest  of  rules  adopted  March  80,  1900,  by  the 
Pacific  Coast  Lumber  Manufacturers'  Association,  Southwestern  Wash- 
ington Lumber  Manufacturers'  Association,  Oregon  and  Washiziston 
Ltunber  Manufacturers'  Association. 

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MO  TO.'-LUMBER  AND  LUMBERING. 

Sprucb. 
Nanus  and  Grades. — FlooriM  is  classed  as  Clear,  "A,"  and  "  B;**  Pin- 
ish,  as  First  and  Second  Clear,  Third  Clear,  Selects;  Ceiling,  as  Clear.  "  A." 
and  "  B;"  Partition,  as  Clear,  **  A,"  and  **  B;"  Porch  Decking,  as  Olear, 
•*A,"  and  **  B;"  Bevel  Siding,  as  Clear,  "A,"  "  B,"  and  **  C;"  Factory 
Stock,  as  Select  and  Better,  No.  1  Shop,  No.  2  Shop. 

Rbd  Cbdar. 
Nanus  and  Grades. — Bevel  Siding  is  classed  as  Clear.  **  A,"  and  •*  B;" 
Ceiling,  as  No.  1,  No.  2.  No.  8;  Finish,  as  No.  1.  No.  2.  No.  3;  CorrusAted 
Decking,  as  No.  2  and  Better;  Flooring,  as  No.  1,  No.  2.  No.  3. 

Hbmlock. 
In  a  general  way  the  rules  for  grading  Fir  and  Spruce  lumber  are  applied 
to  Hemlock. 

Shingles.-^ — Ptrhctions. — 18  inch,  random  widths,  five  butts  must 
measuire  2  A  mch  plump  in  thickness  when  green,  or  2^  inches  after  drjrins. 
Must  be  well  manufactured,  strictly  clear  in  every  resect,  and  00%  vertical 
grain.     Will  not  admit  any  shingle  narrower  than  8  inches. 

Pug0t  A. — Same  thickness  as  Perfections.  Must  be  well  manufacttared ; 
will  aomit  sound  knots  8  inches  from  butt,  16-inch  shims;  also  admits 
slash-grain  shingles,  otherwise  must  be  clear.  Will  not  admit  shingles 
narrower  than  2  inches. 

Eurtka. — 18  inch,  random  widths,  five  butts  must  measure  2 A  inclies 
in  thickness  when  green,  or  2  inches  after  drying.  Must  be  well  manu- 
factured, strictly  clear  in  every  respect,  and  90  per  cent  vertical  sradzi. 
Will  not  admit  any  shingles  narrower  than  3  inches. 

SkagU  A. — Same  thickness  as  Eureka.  Must  be  well  manufactured. 
Will  admit  sound  knots  8  inches  from  butt;  16-inch  shims.  Also  admit 
slash-grain  shingles:  otherwise  must  be  clear.  Will  not  admit  shizislea 
narrower  than  2  inches. 

Extra  Clear. -^16  inch,  random  widths,  five  butts  must  measure  2 A 
inches  in  thickness  when  green,  or  2  inches  after  drying.  Must  be  -well 
manufactured,  strictly  clear  in  every  respect,  and  90  per  cent  vertical 
grain.     Will  not  admit  any  shingles  narrower  than  2  inches. 

Choice  A. — Same  width  and  thickness  as  Extra  Clear.  Must  be  'vreU 
manufactured.  Will  admit  sound  knots  6  inches  from  butt;  also  slash- 
grain  shingles,  wane  edge,  sap,  14-inch  shims,  i-inch  knotholes  or  worm 
holes  6  indbes  from  butt;  otherwise  must  be  clear. 

Extra  M*  — 16-inch  ramdom  widths,  six  butts  must  measure  2A  inches 
green,  or  2  inches  after  drying;  must  be  well  manufactured.  Wm  admit 
sound  knots  10  inches  from  butt;  otherwise  must  be  strictly  clear,  and  00 
per  cent .  vertical  grain.    Will  not  admit  any  shingles  narrower  than  2  snchea . 

Standard  A. — Same  width  and  thickness  as  Extra  *A*;  must  be  well 
manufactured.  Will  admit  sound  knots  6  inches  from  butt,  slash-srain 
shingles,  wane  edge,  sap,  14-inch  shims,  i-inch  knot  holes  or  more  holes  6 
inches  from  butt;  otherwise  must  be  clear. 

Shingles  with  the  following  defects  are  culls,  and  must  not  be  put  in 
any  of  the  above  grades:  Rot,  worm  holes,  except  as  above  provided,  che^c. 
shake,  stub  comers,  tapering  edges,  rou^,  waney,  or  unevenly  sawn. 

Eighteen  inch,  5  to  2}  inch  shingles,  must  be  packed  20  courses  per 
bunch.  5  bunches  to  the  M.  Eighteen  inch,  5  to  2  mch.  and  16^ch  shin.. 
gles.  must  be  packed  25  courses  to  the  bunch,  4  bunches  to  the  M.  All  shin* 
gles  must  be  packed  in  the  regulation  frame,  full  20  inches  in  width,  cu&d 
no  opening  of  more  than  i\  inches  is  admissible  in  any  one  course. 

All  shingles  to  be  packed  as  closely  as  possible.  Bands  should  not  l>e 
shorter  than  19i  inches  in  length.     Every  bimch  of  shingles  must  be  branded* 

Dimension  shingles  are  packed  24  courses  in  each  bunch. 

t  Oregon  and  Washington  Lumber  Manufacturers*  Aiiodatioii. 


LOG  RULES.   SHIPPING  WEIGHTS.  891 

EXCERPTS  AND  REFERENCES. 

Qnphlcal  ComMrison  of  Varioiis  Log  Rules  (By  A.  H.  Morse.  Eng. 
News,  April  9,  1908).— According  to  The  Woodman  s  Handbook,  by  Prof. 
H.  S.  Graves,  published  as  Bulletin  36  of  the  Biueau  of  Forestry,  U.  S. 
Dept.  of  Agric.,  Wash.,  D.  C,  more  than  30  different  "log  rules"  are  in  use 
in  the  U.  S.  All  these  rules  profess  to  accomplish  the  same  thing,  viz..  to 
provide  means  for  ascertaining  the  number  of  board  feet  of  1-in.  lumber 
which  can  be  sawn  from  a  log  of  given  dia.  and  length;  that  is,  to  give  the 
"icale'*  of  a  log  in  board  feet.    This  article  compares  the  principal  log  rules. 

A  Table  of  Lumber  WeighU  (Eng.  News.  May  5, 1910)  .—The  following 
table  of  weights  of  lumber  represents  the  commercial  classification,  taken 
from  the  reports  of  the  secretaries  of  the  "^^Euious  lumber  associations,  and 
are  accepted  by  the  trade  in  place  of  actttal  weights. 

Shipping  Weights  in  lbs.  per  1000  ft.  B.  M. 


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21.— METALLURGY. 

Iroa  Ore* — Hematite  (FetOz),  an  ore  abundant  around  Lake  Superior, 
in  Alabama,  etc.,  furnishes  five-sixths  of  the  iron  manufactured  m  the 
United  States;  with  limonite  (one-ninth),  and  magnetite  (one-sixteenth), 
next  in  order.  Most  of  the  ore  has  to  be  prepared  for  the  blast-furnace. 
Thus,  "  sorting  "  the  ore  from  foreign  fragments;  "  washing  "  away  the 
earthy  matter:  "  concentrating  "  the  crushed  ore  by  magnetic  "  separators;'* 
"  calcinating  '  or  driving  off  the  volatile  matter  by  heat;  etc.,  are  methods 
usually  employed.  Iron  ore  contains  from  35  to  65%  of  iron^  the  balance 
being  oxygen,  phosphorus,  sulphur,  silica  (sand),  and  other  impurities. 

Pig  Iron  is  the  cast  iron  product  from  a  blast  furnace.  The  furnace  Is 
shaped  like  a  lamp  chimney,  and  the  charge  is  introduced  at  the  top:  layers 
of  ore,  limestone,  fuel,  ore,  limestone,  fuel*,  etc.,  in  regular  sequence.  By 
forcing  a  current  of  hot  air  at  the  bottom  of  the  furnace  into  the  heated 
mass  a  series  of  chemical  reactions  take  place,  producing  molten  iron, 
molten  slag,  and  gases.  The  molten  iron  is  drawn  off  after  the  slag  and 
run  into  moulds  or  (cast)  pigs.f  From  pig  iron  all  kinds  of  iron  and  steel 
can  be  made.  Among  the  uses  to  which  pig-iron  may  be  put  are  the  follow- 
ing: 

(a)    Directly  without  refining,  for  foundry  work. 

(6)     Refined  by  elimination  of  silica  and  phosphorus,  then  removal  o£ 


carbon  by  dry-puddling,  for  wrought  iron  (not  used  in  U.  S.). 

ic)  Wet  puddling,  in  removal  of  silica,  phosphorus  and  cacbon,  for 
soft  structural  and  blacksmith  iron. 

(d)  Acid  Bessemer,  in  removal  of  silica,  manganese  and  carbon,  for 
rails  and  structural  steels  (mild). 

(e)  Basic  Bessemer,  in  removal  of  silica,  manganese,  carbon  and  phos- 
phorus, for  rails  and  structural  steels  (mild). 

if)  Krupp  washing,  and  Siemens-Martin  process,  for  structural  steels 
(mild). 

(g)  Charcoal  hearths,  for  wrought  iron;  cementation  furnace,  foe 
shear  steel;  crucible,  for  high  grade  tool  steel. 

Cast  Iron. — In  foimdry  work,  for  ordinary  castings,  the  melt  from 
the  cupola  is  much  more  certain  in  composition  than  the  direct  casting 
from  the  unrefined  pig.  It  gives  a  closer  grain  and  somewhat  increas^ 
strength.  A  good  casting  contains  about  3 . 5  per  cent,  carbon,  1 . 6  per 
cent,  silicon,  not  over  0 . 7  per  cent,  phosphorus,  0 . 6  per  cent  manganese, 
and  a  trace  of  sulphur.  It  shows  a  gray  fracture,  can  be  workea  easily 
with  chisel  and  file,  completely  fills  the  mold,  chills  with  a  smooth  surface. 
has  no  blow  holes,  shrinks  Uttle  in  cooling.  Large  castings  should  contain 
less  silicon  than  small;  shrinkage  may  be  decreased  by  lowering  the  man- 
ganese; to  increase  the  strength  the  carbon,  silicon  and  manganese  are 
lowered  and  phosphorus  eliminated  as  far  as  possible. 

The  above  chemical  properties  may  be  varied  to  suit  the  special  pur- 
poses for  which  the  castings  are  intended.  Mr.  Heniy  Souther.t  in  Vol.  V, 
Proc.  A.  S.  T.  M.,  pa^e  218.  says  with  reference  to  Hard  Cast  Iron  whicii 
had  given  complaint  m  the  machine  shop;  '*  Cast  iron  that  chills  may  be 
called  hard  in  the  truest  sense  of  the  word.  ...  In  the  last  five  or  six 
years  three  separate  complaints  of  hard  iron  have  reached  the  writer  and 
proved  of  so  baffling  a  character  that  in  each  case  visits  were  made  to  the 
machine  shops.  ...  It  developed  [citing  one  particular  case]  that 
small  drills,  J-in.  or  thereabout,  were  standing  up  with  this  iron  just  as 
well  as  any  other,  but  the  larger  drills  in  the  neighborhood  of  }-m.  and 
J-in.  were  dulling  exactly  as  though  the  iron  were  ch^ged  with  emery. 

*  Charcoal,  coke  or  anthracite  coal. 

t  Pig  iron  contains  about  93%  of  pure  iron,  3  to  5%  of  carbon  (pure 
coal),  also  some  silicon,  phosphorus,  sxilphiu",  etc. 
J  State  Chemist,  Hartford.  Conn. 

302  ^  , 

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IRON  AND  STEEL.  113 

The  edges  were  beh]|r  gioiind  off  and  would  last  only  a  fraction  of  the  time 
nsaal  for  the  same  dnfis  in  the  same  machine.  Here  was  an  unusual  con- 
dition, thin  iron  working  easilv,  thick  iron  on  the  same  castings  working 
with  diflSculty.  The  chemical  results  were  normal,  except  manganese: 
Silicon  2.50,  phosphorus  .70,  sulphur  about  .08,  total  carbon  S.oO  and 
cuuQganese  .10.  .  .  .  Inasmuch  as  the  only  abnormal  part  in  the  anal* 
JUS  was  shown  in  the  manganese,  that  element  was  suspected,  althotigh 
then  seemed  to  be  no  metallurgical  reason  for  doing  so.  Means  were  takax 
to  raise  it  to  the  neighborhood  of  .60.  and  as  soon  as  this  was  done  the 
difficulty  disappeared  in  the  machine  shop  and  has  not  reappeared  after 
some  months.  .  .  .  This  leads  to  the  belief  that  there  must  be  some 
caiWe  of  iron  or  carbide  of  silicon  that  forms  in  the  absence  of  a  reasonable 
anxnmt  of  manganese,  and  that  does  not  form  with  manganese  present.'* 

Cast  Stodd — *Steel  for  castings,  may  be  made  by  the  open-hearth, 
cnidble  or  Bessemer  process.  Castings  to  be  annealed  unless  otherwise 
specified.  Ordinary  castings,  those  in  which  no  physical  reouirements 
are  specified,  shall  not  contain  over  0.40%  carbon,  nor  over  0.08%  phos- 
(diorns.  Castings  which  are  subjected  to  phYsical  test  shall  not  contain 
over  0.05%  phosphorus,  nor  over  0.05%  smphur. 

Tested  castings  shall  be  of  three  classes:  Hard.  Medium,  and  Soft,  with 
minimum  physical  requirements  as  follows: 

Hard.  Medium.  Soft. 

Tensilestrength,  lbs.  persq.  in 85000.  70000.  60000. 

Yieldpoint.            *'       "  ^'     '* 88250.  31500.  27000. 

Ekjngation,  per  cent  in  two  ins 15.  18.                 22. 

Contraction  of  area,  per  cent 20.  25.                80. 

For  determinixig  the  above  physical  properties,  standard  turned  specimens 
r  in  dia.  and  f'  gauged  len^h  shall  be  used. 

For  bending  test,  a  specimen  I'xK  shall  bend  cold  aroimd  a  dia.  of  1' 
without  fracture  on  outside  of  bent  portion,  through  an  angle  of  90°  for 
"Medium  "  or  120^  for  "  Soft  "  castings. 

Malleable  Casttags. — ^An  ordinary  casting,  unless  it  is  too  large,  may 
be  made  malleable  by  decarburization.  The  original  casting  is  preferably 
*'  white,"  indicating  that  is  is  low  in  carbon,  and  should  practically  be  free 
from  sulphur  and  phosphorus.  The  castings  are  packed  in  a  pot  (or  retort) 
with  oxide  of  iron,  usually  .hematite,  placed  in  a  furnace,  and  kept  at  an 
orange  or  rwi  heat  for  about  a  wcck^  and  then  cooled  very  slowly.  The 
carbon  in  the  casting  mostly  unites  with  the  oxygen  of  the  ore,  passing  off 
as  carbonic  oxide.  The  casting  is  thus  rendered  malleable  like  crude  wrought 
iron.  Malleable  castings  are  used  for  pipe  specials  which  have  to  be 
threaded;  for  wood -stave  (water)  pipe  shoes;  and  in  general  for  deUcate 
castings  which  are  liable  to  be  subjected  to  various  kinds  of  stress. 

Wrought  Iroik — ^Wrotight  iron  is  purified  pig  iron.  Although  it  is 
made  "  directly  "  from  the  ore  the  "  indirect  "  process  is  generally  used. 
The  pig  iron  is  oxidized  in  a  puddling  furnace  whence  the  silicon,  mangan- 
ese, phosphorus  and  carbon  impurities  are  removed.  As  with  malleable 
cast  iron  the  light  grades,  containing  the  least  carbon  and  those  practically 
free  from  sulphur  and  phosphorus,  are  selected.  The  wet-puddling  process, 
in  a  reverboratory  furnace,  is  the  practice  in  the  United  States.  A  grav 
onrefined  iron,  containing  more  silica  than  the  white,  is  used,  mixed  with 
a  large  quantity  of  hematite  or  magnetite  of  high  ^rade  used  as  reagents 
for  oxidizing  the  impurities— the  carbon  passing  off  in  the  resulting  carbon 
dioxide,  and  the  other  impurities,  in  the  slag.  The  following  shows  the 
per  cent,  of  composition  of  the  pig  and  of  the  resulting  muck-bar  (puddle 
bar),  in  a  typical  case: 

Car^        g^^        Silicon.        ^^^       Sulphur. 

Pig  (before  melting).  2.55%         5.15%         3.20%         0.95%         0.057o 
Muck-bariron 0.65*^         0.15"  0.10"  0.10"  0.01" 


•  Synopsis  of  Specifications  adopted  by  letter-ballot  oLthe  A.  S. 

i   Sept.    1,     1905.  Digitized  by  V^OOgie 


T.  M 


394 


21.— METALLURGY. 


The  objection  to  this  process  is  the  enonnous  cost  of  fuel.  The  xnucik 
bars  are  re-heated  and  xolled  into  merchant  bar— principally  demanded 
by  the  blacksmith.  (Soft  or  mild  steels  are  generally  replaong  wroueht 
iron.) 

Mr.  George  Schuhmann,  in  the  **  Pilot "  (official  publication  of  the 
P.  &  R.  Ry.  Dept.),  April.  1906,  sajrs: 

"  The  purer  the  iron  the  higher  is  its  melting  point.  Pig  iron  melts  at 
about  2100  degrees  F.^steel  at  about  2500  degrees,  and  wrought  iron  at 
about  2800  degrees.  The  temperattire  in  the  puddling  furnace  is  liish 
enough  to  melt  pig  iron,  but  not  high  enough  to  keep  wrought  iron  in  a 
liquid  state;  therefore,  as  soon  as  the  small  particles  of  utm  become  purified 
they  partly  congeal  (come  to  nature),  forming  a  spongy  mass  in  which 
small  globules  of  iron  are  in  a  semi-plastic  state,  feebly  cohering  with  fluid 
cinder  filling  the  cavities  between  them.  This  sponge  is  divided  by  the 
puddler  into  lumps  of  about  200  lbs.  ecu:h;  these  lumps  or  balls  are  taken 
to  a  steam  hammer  or  a  squeezer,  where  thev  are  hanunered  or  squeezed 
into  elongated  blocks  (blooms]),  and  while  still  hot,  rolled  out  between  the 

Euddle  rolls  into  bars  3  to  6  inches  wide,  about  f-inch  thick,  15  to  30  ft. 
>ng.  These  bars  are  called  puddle  bars  or  muck  bars,  and,  owing  to  the 
large  amount  of  cinder  still  contained  therein,  they  have  rather  rough 
surfaces.  The  muck  bars  are  cut  up  into  pieces  from  2  to  4  ft.  long  and  piled 
on  top  of  each  other  in  so-called  piles  "  varying  from  100  to  2000  lbs., 
according  to  the  size  product  desired.  These  piles  are  heated  in  heating 
furnaces,  and  when  white  hot.  are  taken  to  the  rolls  to  be  welded  together 
and  rolled  out  into  merchant  iron  in  the  shape  of  either  sheets,  plates, 
bars,  or  structural  shapes  as  desired.  When  cold  this  material  is  sneared 
and  straightened,  and  is  then  ready  for  the  market. 

After  leaving  the  puddle  ftunace.  wrought  iron  does  not  undergo  any 
material  change  in  its  chemical  composition,  and  the  only  physical  change 
is  an  expulsion  of  a  large  portioxi.  of  the  cinder;  the  small  cinder-coated 

? globules  of  iron  are  welded  together  and  the  subsequent  rolling  back  and 
orth  will  elongate  these  globules,  giving  the  iron  a  fibrous  structiuie,  and 
reheating  and  rerolling  will  drive  these  fibers  closer  together,  thus  increas- 
ing the  strength  and  ductility  of  the  metal. 

Sted  — For  structural  work,  steel  has  almost  entirely  superseded  wrought 
iron,  being  stronger  and  more  cheaply  manufactured.  The  latter,  however, 
is  still  used  largely  for  undergrouna  pipes,  because  better  able  to  resist 
decomposition  by  the  natural  elements  and  also  electrolysis.  The  following 
typical  analyses  of  the  products  of  the  four  principal  processes  of  structural 
steel  manufacture  are  here  shown  for  approximate  comparison,  being  in 
no  way  absolute: 


Acid  Bessemer. 

Basic  Bessemer 

Acid  Open 
Hearth. 

Basic 

Open 

Hearth, 

Softs. 

Rail  S. 

Softs. 

Med. 
H'dS. 

Softs. 

Rails. 

Combined  carbon 
Silicon 

.12%      .43% 
.04          .06 
.05          .06 

.04 
.04 
.50 
.04 

-.IP" 

.04 
.04 
.70 
.04 

.12% 

.OS*" 
.06 
.60 
.04 

.43% 

.01 

.06 

.07 

.80 

.04 

.14% 

Sulphur 

.04 

Phosphorus 

Manganese 

Arsenic 

.06 
.06 
.04 

.07 
.60 
.05 

.06 

1.20 

.04 

These  processes  consist  in  decarburieing  and  purifying  the  pig  iron  to 
a  practically  pure  liquid  wrought  iron;  recharging  the  liquid  with  carbon 


and  manganese  where  necessary;  and  casting  it  into  ingots, 
described  as  briefly  as  possible. 


They  will  be 


Acid  Bessemer  Process. — ^Thc  molten  iron  or  pig  from  the  blast  furnace 
(direct  process)  or  the  cupola  (indirect  process)  is  poured  into  an  **  acid  " 
hned      converter,  '  in  the  bottom  of  which  are  a  number  of  small  holes 


STEEL— PROCESSES  OF  MANUFACTURE.  896 

tbfou^  which  air  is  forced  into  the  metal.  The  air  oxidizes  to  imptiritiea — 
carixm,  silicon,  manganese,  etc. — the  heat  of  combustion  from  tne  carbon 
and  sulphur  m^iritAining  the  metal  in  a  fluid  condition.  *  The  "  acid  " 
kiing  is  a  hifl^y  refractory,  siliceous  (about  93  per  cent,  silica)  material. 
Tfai^  renooves  tne  carbon,  silicon  and  manganese,  but  is  incapable  of  taking 
the  phosphorus  and  sulphur  away  from  the  metaJ;  hence  the  pig  iron  used 
must  practically  be  free  from  these  two  latter  elements,  as  they  are  not 
allowed  to  enter  largely  into  steel.  The  impurities  being  thus  removed  it 
ts  sow  liquid  wrought  iron.  Carbon,  for  strength  and  hardness,  and  man- 
for  malleability  in  rolling,  are  added — the  latter  in  the  form  of 


S{Hegeleisen  or  ferro-manganese.  It  is  now  steel  and  is  poured  into  molds 
for  cooling  down  into  ingots.  These  ingots  are  charged  into  the  soaking 
vst  or  vertical  furnace  to  equalize  before  bein^  rolled  mto  blooms.  Later, 
the  bkxmis  are  (re-heated  and)  rolled  into  rails  or  into  the  various  stnic- 
tnnl  shapes  desired. 

Basic  Bessener  Process. — Pig  iron  that  is  too  high  in  phosphorus  (2 . 6 
to  3.0  per  cent.)  for  the  acid  Bessemer  process  mav  be  converted  into  steel 
by  the  basic  Bessemer  process  provided  it  is  low  (below  0.60 per  cent.)  in 
sificon.  The  **  basic  "  lining  of  the  **  converter  is  made  from  a  pure 
tnagnfiian  limestone  (dolomite)  containing  about  20  per  cent,  of  magnesia. 
but  not  over  1  or  2  per  cent,  of  silica.  The  pig  is  usually  remelt^  in  the 
cupola  and  transfeired  to  the  converter — hard-burned  limestone  low  in 
Sa)^  being  added  as  a  flux — ^where  air  is  introduced  as  in  the  acid  process. 
The  impurities  in  the  metal  are  burned  out,  the  phosdhorus  furnishing  the 
heat  ami  uniting  with  the  lime  to  form  phosphate  ot  lime.  The  liouid  is 
ixm  almost  a  chemically  pure  iron,  and  is  recarburized  as  in  the  acid  Besse- 
mer process.  The  floating  slag  when  cooled  and  ground  is  used  as  a  fertil- 
iser or  for  cement. 

This  process  is  not  used  much  in  the  U.  S. 

Add  Open  Hearth  Process.— This  process,  like  the  acid  Bessemer. 
ciUls  for  a  pig  low  in  sulphur  and  phosphorus  because  neither  is  eliminated. 
The  Siemens  furnace  is  a  laive  hearth  built  of  refractory  siliceous  material 
<m  which  the  metal  is  mtUea,  bv  the  combustion  of  gas  admitted  into  the 
furnace  alternately  with  air.  No  solid  fuel  is  used.  A  typical  pig  iron 
vould  contain  about  the  following:  (Carbon  S.6  per  cent.,  sihcon  2.2,  sul- 
phur O.OS,  phosphorus  0.035,  manganese  0.76. 

This  process  is  particularly  adapted  to  producing  steels  high  in  carbon 
and  to  the  exact  percentages  specified. 


Open  Hearth  Process. — In  this  process  the  lining  of  the  hearth 
I  made  from  the  "  basic  "  material — magnesian  limestone — and  like  the 
base  Bessemer,  a  high  phosphoric  pig  is  used,  say  about  as  follows:  Phos- 
I^UHns.  1 .  80  per  cent. ;  silicon,  not  over  1 .  50;  sulphur,  not  over  0 .  60; 
manganese,  1 .75:  carbon,  3.50.  Iron  and  steel  scrap  is  also  added  to  the 
meh.  The  method  is  about  the  same  as  for  the  acid  O-H  process,  the  im- 
parities being  separated  from  the  bath  partly  by  the  air  admitted  and 
partly  by  the  addition  of  iron  oxides.    The  product  is  an  excellent  steeL 

CeneaCatioa  Process. — ^This  process  is  still  employed  in  making  high 
grade  carbon  steels  for  tools,  cutlery,  etc.  "  Cement  bars  "  are  made  from 
the  purest  and  best  grade  iron  (usually  the  Swedish)  heated  in  contact  with 
carbon  (charcoal)  to  a  red  heat  maintained  for  a  week  or  more.  The  product 
is  called  "  cement  steel  "  or  "  blister  steel."  '*  Shear  steel  "  is  made  from 
cement  steel  by  cutting,  piling,  heating  and  rolling  the  cement  bars — 
"  double  shear  steel  "  being  simply  a  duplication  of  the  process.  *'  Crucible 
steel  •*  or  *'  cast  steel  "  is  made  from  blister  steel  by  cutting  up  and  melting 
the  bars  in  a  black-lead  pot,  and  cooling  in  the  form  of  ingots. 

Shear  sted  is  used  for  pbws  and  cheap  edge  tools,  but  not  for  high 
grade  tools. 

.  CrodMe  cast  sted,  made  by  melting  the  blister  steel  of  the  cementa- 
tion process  in  crucibles,  is  a  high  grade  steel,  used  for  the  best  tools.  In 
order  to  avoid  the  permanent  set  of  internal  stresses  in  castings,  due  to 
unequal  shrinkage  m  cooling,  they  are  "  annealed  "  by  being  spradually 


896 


21.— METALLURGY. 


heated  to  temperatures  between  800*  (for  high  carbon  steel)  and  900*  (for 
low  carbon  steels).  Crucible  steel  is  **  tempered  "  for  different  uses,  de- 
pending upon  the  percentage  of  carbon  present,  as  follows: 


Name 

of 

Temper. 

Per  cent. 

of 
Carbon. 

Burning. 

Welding. 

Temper. 

Remarks. 

Razor  .. 
Saw-file 

1.5 

1.376 

1.26 

1.125 

1. 

0.876 
0.76 

Easy. 

Very  difficult. 

Extremely  hard. 

Razors,  etc 
Saws,  etc. 

Tool 

Possible. 

Extreme  care  re- 

Spindle. 

Medium. 

quired  in  weld- 
Marine  turn- 

Chisel . . 

Quite  easy. 

ing  tools,  cut- 
ters, etc. 
Cold  chisels,  hot 

Set 

Little. 
Very  little. 

sets.  etc. 
Cold  sets,  etc 

Die 

Not  easy. 

Easy. 

tools  as  dies. 

Steels  very  low  in  carbon  can  easily  be  welded  but  not  tempered.  Steel 
with  carbon  above  i  per  cent,  can  be  tempered  by  heating  to  a  high  heat, 
and  then  quenching  in  water  or  other  liquid. 

Open  Hearth  Cast  Stecl^^ — The  acid  open  hearth  is  generally  preferred. 
The  cast  steel  produced  is  adapted  to  machinery  castings  for  steel  vessels, 
cars,  etc.;  it  contains  from  one-sixth  to  one-half  of  one  per  cent,  carbon. 

Harveyized  steel  plates  for  armor  are  mild  steel  plates,  face-hardened 
on  one  side  by  carburization  and  sudden  chiHing;  the  other  side  may  remain 
as  mild  steel  or  be  decarburized  into  a  softer  metal. 

Manganese  steel  is  a  steel  containing  about  14  per  cent,  manpranese, 
and  is  made  by  melting  ferro-manganese  with  carbon  steel.  It  is  very 
tough  and  hard,  capable  of  being  forced.  It  is  used  principally  for  car 
wheels,  stamp  heads  and  jaws  for  crushmg  machines;  also  for  crossing  frogs. 

Vanadium  steel  is  used  for  crusher  jaws,  gear  wheels,  etc.  (See  also 
page  809.) 

Chrome  steel  is  made  by  melting  ferro-chrome  with  bar  iron,  in  a  cru- 
cible. It  is  very  hard  and  can  be  forged  readily.  Contains  about  1 .8  per 
cent,  chromiiun  and  0.7  per  cent,  carbon. 

Nickd  sted  is  produced  by  adding  nickel  ore  to  the  carbon  steel  in  the 
open  hearth  bath,  thus  increasing  the  strength  and  elasticity.  It  is  used  in 
armor  plate  manufacture;  and,  with  the  probable  future  reduction  in  cost, 
will  doubtless  be  used  in  steel  bridges,  especially  of  long  spans,  in  the  near 
futtu-e.     (See,  also,  pages  398  and  399.) 

Tungsten  steel  is  very  hard,  difficult  to  forge,  and  is  used  for  cutting- 
tools. 

Alloys. — ^An  alloy  is  a  mixture  of  two  or  more  metals  by  fusion.  The 
number  of  possible  mixtures,  taking  into  consideration  the  varying  pro- 
portions, is  infinite,  but  the  principal  alloys  useful  to  the  engineer,  are  to 
a  certain  extent  limited  ana  well  known.  From  a  mechanical  point  of 
view  the  most  useful  metals  for  alloys  are:  copper  (Cu),  tin  (Sn),  zinc  (Zn), 
lead  (Pb),  antimony  (Sb),  nickel  (Ni),  bismuth  (Bi),  aluminum  (Al),  iron 
(Pe),  etc.,  about  in  the  order  mentioned.  Cu  is  by  far  the  most  useful  and 
may  be  classed  as  the  primary  metal;  with  Sn,  Zn,  Pb,  and  Sb,  •eoondaiy; 
and  Ni,  Bi,  Al,  Fe,  etc.,  tertiary,  as  follows: 
Fe    Sn    Al 

^^     Cu     Sb  nr^r^n]^ 

Ni      Zn     Bi  Digitized  by  V^OOglC 


ALLOYS— STEEL,  BRONZE,  BRASS,  ETC, 


897 


Bating 


iCu,  Sn,  X)  is  the  name  generally  given  to  those  alloys  con- 
chieny  of  copper  and  tin.  with  the  former  metal  largely  in  excess. 
>Uowing  are  some  of  the  principal  bronzes  and  their  uses: 


Name. 

Composition  (parts). 

Remarks. 

Copper. 

Tin. 

Other  metals. 

Iff^al  B. 

95 
91 
90 
89 
88 
82 
68 

5 

9 

10 
11 
12 
18 
32 

Coin  B 

Gtm  B 

For  navy  ordnance. 

Statuary  B 

Valve-metal 

Zinc  (2). 

Bell-metal 

Specolmn-metal. . . 

Phosphor  bronze  is  a  bronze  containing  a  small  percentage  (Z±)  of 
I>hosphorus  properly  introduced  during  fusion.  It  matoially  increases  the 
strath  and  hardness  of  the  metal  and  renders  it  less  susceptible  to  oxida- 
tion and  the  action  of  the  elements  generally.  Phosphor  bronze  is  used  for 
beavy  journal  bearings  in  the  best  machinery,  and  for  wire. 

JAancaaese  bronze  (Cm.  Sn,  Mn)  is  a  bronze  containing  a  small  per- 
centage (1  +  )  of  manganese,  rendering  the  material  tough  and  non-corro- 
sive. It  is  largely  used  for  propeller  blades.  A  good  mixture  is  Cu  (88), 
S»(10),M«(21. 

AInnlnnm  bronze  (Cm,  A  I),  so-called,  is  usually  composed  of  Cu  (90) 
and  Al  (10)  although  these  proportions  may  be  varied  greatly.  It  has  a 
high  tensile  strength  and  is  not  easily  corroded. 

Sflkon  bronze  (Cm,  Sn,  Si)  is  used  for  castings  and  for  telefrraph  wires. 
It  is  an  excellent  conductor  of  electricity  and  has  ^reat  tensile  strength. 
The  proportion  of  dlicon  is  from  3  to  5  per  cent.  Tm  may  or  may  not  be 
used  with  the  copper. 


MS  (Cm,  Zn,  X)  includes  the  alloys  which  are  composed  mainly  of 
copper  and  zinc     The  principal  ones  are  tabularized  as  follows: 


Name. 

(imposition  (parts). 

Remarks. 

Copper. 

Zinc. 

Other  metals. 

Valve-metal 

83 
76 

70 

67 
60 
58 
58 
56 

50 

60 

15 
25 

30 

33 
40 
40 
40 
42 

50 

20 

Tin  (2). 

Brazing-metal 

Flanges     for     copper 

pipe. 
Works  well  under  ham- 

mer. 

Huntz-metal 

Delta-metal 

Iron. 

Tin,  lead,  iron. 

Tobin  "  Bronze  **  . 

Thurston-metal.  . . 
Brazing-metal 

Tin  (2). 

Thiuwton's  maximum 

is  67.  42,  1. 
Solder  for  copper  pipe 

(jerman  nlver 

Nickel  (20). 

flanges. 

,rrih(^00^]C 

398 


21.— METALLURGY. 


TiiHbase  Alloys. — 


Composition  (parts). 

Name. 

Tin. 

Zinc. 

Lead. 

Other 
Metals. 

Remarks. 

Babbitt-metal . . 

89 

85 

67 
50 

(56,8 
15 

Used  for  machinery 

Pewter 

bearings. 

Contains  antimony,  cop- 
per and  bismuth. 

Solder 

33 

50 

1 

t                    

Lead-base  Alloys.- 


Composition  (parts). 

Name. 

Lead. 

Tin. 

Anti- 
mony. 

Bis- 
muth. 

Remarks. 

White-metal 

88 
86 

"io  ' 

12 

Fusible  plug 

4 

For  steam  boilers 

Alxene,  a  new  metal  alloy  composed  of  aluminum  and  zinc,  is  said  to  be 
as  strong  as  cast  iron,  much  more  elastic,  does  not  rust  easily,  and  takes  a 
very  high  polish.  It  is  a  German  product.  Future  results  of  investi|nUioiis 
are  awaited  with  interest.  The  present  proportions  of  the  alloy  are  a  parts 
alimiinum  and  1  part  zinc.  It  is  capaSle  of  filling  out  the  most  delicate 
lines  and  figiires  of  forms  in  casting. 

EXCERPTS  AND  REFERENCES. 

MaUeaUe  Cost  Iron  (By  H.  E.  Diller.  Tl.  of  the  Am.  Foimdrymen's 
Assn.;  Eng.  News.  Dec.  11.  1902). — "Malleable"  can  be  made  up  to  60  000 
lbs.  per  sq.  in.,  though  this  is  not  advisable  as  the  shock-resisting  qualities 
arc  sacrificed.  Yet  as  specifications  become  more  severe  the  general  quality 
of  this  class  of  castings  will  be  improved  until  we  get  a  more  reliable  article, 
and  which  can  better  resist  the  encroachments  of  the  steel  casting.  The 
article  discusses  the  methods  of  manufacture. 

Manafactnre  and  Properties  of  Nickel-Steel  (By  A.  L.  Colby.  Proc. 
A.  S.  T.  M.,  1903;   Eng.  News.  Aug.  20,  1903.)— Modtdiis  of  Elasticity.— 

Young's  modulus  is  practically  the  same  for  both  tool  steel  containing 
1.40%  carbon  and  the  mildest  steel  used  in  boilers.  Their  modulus  of  elas- 
ticity is  in  fact  rarely  found  to  be  below  29.000.000  or  above  31,000,000 
and  is  generally  taken  at  29,500.000  or  30.000,000  in  engineering  calcula- 
tions. The  high  nickel-steels,  especially  those  containing  20%  nickel  or 
over,  have  a  lower  mod.  of  elas.  than  carbon-steel*  but  nickel-steels  con> 
taining  say  4%  of  nickel  or  less,  such  as  are  applicable  for  shafting,  forgings» 
bridge  construction,  rails,  etc..  have  the  same  mod.  of  elas.  as  carbon  steels, 
viz.,  in  the  neighborhood  of  29,000,000  lbs.  per  sq.  in.,  many  authorities 
claiming  that  this  is  true  of  even  5%  nickel-steel.  Tensile  Streiiftli  and 
Elastic  Limit. — Nickel-steel  is  chiefly  distinguished  from  carbon-steel  by 
its  proportionately  high  elastic  limit.  If  3%  nickel  is  alloyed  with  an  open- 
hearth  steel  of  0.25%  carbon,  it  produces  a  metal  equal  in  tensile  strength 
to  a  simple  carbon-steel  of  0.45%  carbon,  but  having  the  advantageous 
dxictilitjf  of  the  lower  carbon-steel.  On  low  carbon-steels  not  annealed. 
ttiSL^^^*^***''^  °^  ^*^^  1%  of  nickel  up  to  6%  causes  approx  .  an  increase  ot 
6000  lbs.  per  sq.  in.  in  the  elastic  limit,  and  4000  lbs.  in  the  ultimate  or 


MISCELLANEOUS— NICKEL  STEEL,  ETC.  809 

tensile  strength.    The  influence  of  nickel  on  the  elastic  limit  and  ultimate 
increases  with  the  percentage  of  carbon  present;    high  carbon 


tadKl-steels  showing  a  greater  gain  than  low  carbon  nickel  steels.  Other 
Prapcrtks  Discussed. — ^Effect  of  compression;  rigidity;  cold  and  quench 
bendmg  tests;  hardness;  resistance  to  torsion;  resistance  to  wear  or 
abrstakm;  expansion;  effect  of  punching  and  shearing;  segregation. 

Notes  on  the  Metannm  of  Steel  (By  Bradlev  Stoughton.  Trans. 
A-  S.  C.  E..  Vol.  LIV,  Part  E). — See  pages  398  to  40«  of  Transactions  for 
112  references  to  this  subject. 

Yafluufiom  Steel  Alloys  (By  J.  Kent  Smith.  Soc.  of  Chemical  Ind- 
dtatry,  Liverpool;  Eng.  News,  May  24,  1906). — The  vanadium  steel 
industry  is  altogether  an  English  indtistry,  80%  of  the  production  being 
used  for  the  construction  dt  motor  cars  and  omnibuses.  The  chrome- 
vanadiuxn  steels  containing  10  to  20%  vanaditmi  show  the  most  remarkable 
properties,  the  highest  test  yet  obtained,  after  special  treatment,  being  a 
maximuni  breaking  strength  of  103  tons  per  sq.  m.  The  nickel-vanaditmi 
steels  are  also  of  great  strength,  but  show  a  k>wer  resistance  to  dynamic 
sad  torsional  tests. 

MaMuiese  Brome  (By  C»  R.  Spare.    Proc.  A.  S.  T.  M..  Vol.  XIII. 
B).— Properti       


UW8)  .—Properties  of,  with  discussions. 

Vaaadliun  Structural  Steel  (By  G.  L.  Norris.  Eng.  Rec.,  June  4, 1910). 
— ^Table  of  results  of  tests  of  ansles  made  from  three  different  heats  of 
cfarome^vanadium  steel.  "The  Sest  chrome-vanadium  steels  for  rolled 
shapes  have  from  0.18  to  0.25%  carbon,  0.25  to  0.40%  manganese.  0.4  to  0-9% 
chrome,  and  0.15  to  0.20%  vanadium." 


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22.— BUILDING  STONES  AND  CEMENTS. 

(For  Wbights  and  Specific  Gravities,  See  Section  27.) 
This  class  of  materials  comprises  all  the  non-metallic  minerals  of  con- 
struction, including  (I)  Natural  stones.  (II)  Cements,  and  (III)  Artificial 
stones: 

L   NATURAL  BUILDING  SrONES. 

These  may  be  classified  in  three  divisions,  as  follows: 

A.  Crystalline  siliceous  rocks,  or  those  of  the  igneous  types  containing 

much  silica,  as  granites  and  sienites. 

B.  Calcareous  rocks,  or  those  consisting  mainly  of  Ume,  as  UmestonoB 

and  marbles. 

C.  Fragmentary  rocks,  as  sandstones  and  slates. 

A.    Crystalline  Siliceous  Rocks. 

Qraiiite.^>ranite  is  an  igneous  rock  of  granular  and  acid  compc»sition 
and,  contrary  to  former  belief,  is  now  supposed  to  be  forming  today,  from 
fusion,  deep  in  the  earth's  crust.  It  is  composed  mainlv  of  orthoclase, 
quartz,  mica  and  usually;  feldspar,  the  following  chemical  analvsis  being 
typical:  Silica  (70).  alumina  (15}.  iron  oxides  (4),  sodiimi  oxide  (4),  potaa- 
sitmi  oxide  (4),  lime  (2),  magnesia  (1). 

Depending  upon  the  material  presence  in  quantity,  with  qtaartz,   of 
muscovite,  hornblende  or  augite,  we  have  respectively* 
Muscovite  granUe,     (Muscovite  is  a  kind  of  mica.) 
Hornblende  granite, 
Augite  granite. 

If  the  granite  loses  its  quarts  it  grades  into  Sientte. 

If  ^t£^  feldspar  is  laigely  replaced  by  lime-soda  feldspar  it  further 
grades  into  Dtorite. 

Granite  is  one  of  the  most  useful  of  building  stones,  but  it  is  hard  to 
work  and  cracks  when  subjected  to  great  heat  as  evidenced  by  the  Boston 
fire  of  1871  on  the  Boston  post  office  building,  and  by  the  recent  Baltimore 
fire. 

Basalt. — ^This  term  is  applied  to  rocks  of  basaltic  lava  origin,  oompri- 
nng  the  so-called  trap  and  the  common  greenstone.  The  basalts  are  very 
hard,  heavy,  and  durable  as  building  stone,  the  principal  objection  to  their 
general  use  being  the  difficulty  of  working  them,< — quarxying  and  cutting. 
Basalt  blocks  are  used  principally  as  paving  stone.  lesisting  wear  and  tear 
to  a  remaricable  degree. 

Trap. — ^This  includes  a  very  wide  range  of  extremely  hard,  crystalline 
rocks,  and  is  sometimrs  applied  outside  the  range  of  basalt.  They  are 
fine  grained  and  usually  dark-green  in  color.  Broken  trap  rock  makes  an 
excellent  base  for  osncrete. 

Greenstone. — When  trap  is  altered  by  the  oresence  of  hornblende, 
chlorite,  eptdote,  etc.,  it  merges  into  grreenstone,  the  green  color  being  im- 
parted by  the  hornblende. 

B.  Calcareons  Rocks. 

Limestone. — Pure  limestone  is  carbonate  of  lime  (CoCOj),  but  ther« 
is  sometimes  present  also  carbonate  of  magnesia  (AfgCOs)  and  certain  so- 
called  impurities,  as  alumina,  silica,  iron,  etc.  Carbonate  of  lime  OCaO, 
CO^  is  a  compound  of  lime  (CaO)  and  carbonic  acid  (COj),  the  lime  being 
an  oxide  of  calcium. — an  alkaline  earth  of  specific  gravity  3.18.  Lrime- 
stone  and  chaUc  are  examples  of  carbonate  of  hme  in  the  amorphous  condi- 
tion, while  marble,  aragonite  and  Iceland  spar  are  varieties  in  the  crystalline 
form. 

400  ^  I 

Digitized  by  VjOOQ  IC 


NATURAL  BUILDING  STONES, 

>f  Ume  is  abtmdantlY  present  in  both  the  organic  c 

(,  the  great  beds  of  limestone  being  thus  provided  vn 

sources  in  their  formation.     The  following  are  importa 

formed  of  the  fossil  remains  of  the  crinoid  species 

as  indicated  by  fragments  of  the  coral  stems.     Th 

[  Indiana,  Iowa  and  Kansas. 

posed  of  cemented  fragments  of  shells  and  corals  fox 

be  sea  on  the  coast  of  Florida. 

Lceous  rock  composed  mainly  of  sea  shells  of  the  or 

id  extensively  on  the  coast  of  England  and  seems 

I  limestone;  not  used  as  a  building  stone. 

mestone  containing  carbonate  of  Ume  {CaCO^  and  c 

.  {MgCOz)  in  large  proportions.     It  may  be  cither  cr 

>us   (massive).     The  massive  varieties  containing  ii 

;par.     Dolomite  is.  foimd  in  Vermont.  Rhode   Islai 

rsey,  Missouri. 

•A   limestone   containing   carbonate  of   lime    {CaCC 

sia  |^AfirCOa)t  silicon  dioxide  (5t0a)  and  alumina,  havi 

dening  tmder  water  after  it  has  been  burned. 

m  of  calcium  carbonate  (46%)  and  clay,  with.perhi 
able  as  a  building  stone.  Occurs  in  New  Jersey,  K 
irginia  and  the  Carolinas. 

limestone  deposit  formed  at  the  mouths  of  springs  a 

e  may  be  considered  as  a  high  grade  limestone,  cr; 
and  capable  of  being  polished.  Those  composed  who 
e  are  white,  whUe  the  various  colorings  in  most  of  1 
the  presence  of  foreign  matter.  Most  of  our  marble 
t,  altnough  it  is  obtained  in  many  other  states  as  Mas 
:,  Tennessee,  Maryland.  Georgia,  Pennsylvania,  Arizoi 

L. 

ign  marbles  imported  to  this  cotmtry  are  the  followii 

and  gold,  Carrara,  Landscape,  Nero  antico. 

xratelle,  Griotte. 

»  antico,  Parian,  Pentellic,  Rosso  antico. 

idian  marble. 

C.  Fragmentary  Rocks. 

idstone  may  be  called  a  "  sand  conglomerate,"  form 

As  a  building  stone  the  cementing  material  is  qu 
i,  the  whole  mixture  having  been  subiected  to  gn 

Sandstones  when  thoroughly  dried  will  absorb  abc 

weight  of  water;  and  in  cold  countries  where  buildii 
le  action  of  the  frost  it  is  best  to  present  the  folial 
the  weather,  in  order  to  prevent  flakmg  or  frost  chippii 

quarried,  usually  lying  in  situ  in  layers  of  greater 
uniform.  A  channelling  machine  is  used  in  cutting  ( 
the  thickness  being  determined  by  the  strata. 
c,  obtained  from  Berea,  Ohio,  is  a  prritty  stone  ^ 
ind  general  masonry  construction.  It  is  a  grayish  sto: 
me,  quarried  in  New  York  (Medina)  is  largely  us 
St.  It  is  reddish  and  argillaceous. 
York)  sandstone  is  very  hard  and  durable  (sometin 
\  reddish  yellow  stone,  found  in  New  York,  Virgir 
ligan. 

lley  sandstone  is  a  Triassic  brownstone,  and  a  very  i 
me. 

dstone  is  also  Triassic. 

ndstone  composed  mainly  of  quartz  sand  with  silicec 
brmation  is  the  best.  If  metamorphosed  into  quartz 
■der  and  more  durable.  ^,g,^.^^^  ^^  GoOglc 


402  n.—BUILDING  STONES  AND  CEMENTS. 

The  best  test  of  a  sandstone  is  to  expose  it  to  the  action  of  frost  as  in 
actual  construction.  This  is  the  case  with  all  the  foregoing,  which  have 
been  well  tried  and  tested  practically.  An  artificial  freezing  is  sometimes 
applied  to  specimens  from  new  quarries,  which  tests  their  power  of  re- 
sisting frost  action.  It  consists  in  boiling  the  specimen  10  or  15  times 
in  a  strong  solution  of  soda  sulphate,  exposing  it  to  the  action  of  the 
air  for  some  hours  after  each  boiling.  The  absorbed  salt  expands  in  crys- 
tallising,  similar  to  frost  action,  flaking  the  specimen  to  a  greater  or  less 
extent. 

Flagstones  are  thinly  bedded  sandstones,  the  cleavage  being  parallel 
with  the  beds  (usually).  Bluestone  is  a  variety  found  m  Pennsylvania, 
New  York  and  New  Jersey. 

Slate. — Slate  is  formed  from  shale  under  great  pressure  and  heat.  The 
cleavage  planes  may  or  may  not  be  identical  with  the  original  shale  folia- 
tion, but  usually  crosses  them  at  different  angles,  and  even  at  right  angle 
to  the  bedding  as  in  that  at  Slatington.  Penn. 

Rooting  slate  is  a  true  slate,  being  a  hard,  compact  rock  apparently  not 
affected  by  the  weather.  It  may  be  laid  on  boarding  or  on  terra  ootta 
roonng,  the  lower  edge  of  each  third  layer  overlapping  the  upper  edge  of 
the  first  by  an  inch  or  more.  Japanned  malleable  iron  nails  are  used  to 
avoid  rust.  Vermont  and  Pennsylvania  furnish  most  of  the  slate  quarried 
in  the  United  States.  It  is  also  distributed  throughout  the  South,  North- 
west and  California. 

II.    CEMENTS. 

Materials  with  Cemeotiiiff  Properties  may  be  mineral,  vegetable  or 
animal  substances,  either  pure,  mixed,  or  transmuted.  The  following 
substances  have  cementing  9uaJities:  Mineral. — Quartz,  calcite  and  the 
iron  ores;  specifically,  silica^  lime,  plaster  of  pans,  sal  ammoniac,  sulphur, 
iron  borings,  brick  dust,  isinglass,  clay,  red  lead,  white  lead,  asphaltum, 
alum,  copal,  chalk,  paraffin,  gypsum,  etc.  Vegetable.— Gum,  resin,  wax 
and  vegetable  albumen;  specifically,  balsam,  india  rubber,  rosin,  starch. 
rice  flour,  wheat  flour,  mastic,  etc.  Animal. — Albumen,  gelatin  ana 
glycerin;  specifically,  white  of  egg,  lac,  shellac,  skim  milk,  cheese,  beeswax. 
stearin,  dextrin,  etc.  Gelatin  is  obtained  by  boiling  animal  substances  as 
sldns,  hoofs,  etc.,  in  water. 

The  Solvents  most  common  in  the  mixing  of  cements  are  water,  alcohol. 
naphtha,  vinegar,  turpentine,  linseed  oil,  benzine,  petroleum,  glycerin, 
ammoniti,  etc. 

In  the  present  discussion,  cements  are  classed  'under  Miscellaneous 
Cements,  and  (Builders)  Cements. 

MISCELLANEOUS  CEMENTS. 

Boiler  cement. — ^To  stop  cracks  and  leaks  in  boilers  and  stoves.  Dry 
powdered  clay  (6  parts),  iron  filings  (1  part);  mix  to  a  paste  with  pure 
boiled  linseed  oil. 

Coppersmith's  cement. — ^To  mend  leaky  joints  in  copper  boilers.  Bul- 
locks blood  thickened  with  quicklime;  use  immediately. 

Fireproof  cement. — ^To  mend  stone.  Fine  river  sand  (20),  litharge  (2>, 
quicklime  (1) ;  mix  to  a  thin  paste  with  linseed  oil. 

Flour  cement. — For  general  paste.  To  J  pint  water  add  1  tablespoonfol 
wheat  flour  slowly,  stirring  rapidly;  heat  until  it  boils,  stirring.  Adding 
a  little  powdered  alum  to  the  water  strengthens  the  paste;  a  little  brown 
sugar  and  corrosive  sublimate  will  preserve  it  from  turning  mouldy. 

Gas  Fitters*  cement. — Resin  (4}),  beeswax  (1);  melt,  and  stir  in  Vene- 
tian red  (3);  pour  into  iron-  or  oiled  paper  molds. 

Iron  cement. — ^For  closing  joints  of  iron  pipes.  Mix  cast-iron  borix« 
or  turnings  (80)  with  sal-ammoniac  (2),  and  flowers  of  sulphur  (1).  La 
using,  add  enough  water  to  moisten;  stir,  and  ram  into  joints.  The  sulphur 
is  sometimes  omitted. 

Glue  cement.— GrtLc  (1),  melted  with  water  Oeast  possible),  and  mixed 
with  black  resin  (1)  and  red  ochre  (\). 

Steam-PUte  cement.— Grind  good  linseed  oil  varnish  with  equal  weights 
of  white  lead,  manganese  oxide,  and  pipeclay.  C^r^r^n\o 


tized  by  Google 


CEMENTS.  403 

Kk^im's  Marhk  ctnmtt. — For  stucco  work;  will  not  stand  weather. 
Baked  gypsum  or  plaster  of  pans  steeped  in  a  saturated  solution  of  alum 
aad  then  recaldned  and  rediiced  to  powder.  To  use,  mix  with  water  the 
tame  as  plaster  of  pans. 

For  a  complete  list  of  cements  and  their  preparation  see  The  Scientific 
American  Cyclopedia  of  Receipts,  Notes  and  Queries;  also  Coolies'  Cyclo- 
pedia of  Praictical  Receipts. 

(BUILDERS)  CEMENTS, 

Caldoin  (Ca)  is  a  light-yellow  metal  whose  specific  gravity  is  1.58. 
and  which  oxidizes  at  ordinary  temperatures,  hence  it  does  not  occur  pure 
b  nature,  but  is  found  abundantly  as  a  component  of  calcite  (CaCO*), 
Kypsum,  dolomite,  aelenite.  aragonite.  Calcite  or  carbonate  of  lime  is  the 
pnndpal  constituent  of  limestone,  marble  and  chalk.  Calcltmi  as  a  base 
plays  a  nsost  important  part  in  the  limes*  mortars  and  cements  used  in  con- 
stntctkxL. 

Lime  (CaO).  as  its  symbol  implies,  is  an  oxide  of  calcium,  and  may  be 
obtained  bv  placing  calcium  in  contact  with  water,  whence  the  latter  is 
decomposea,  forming  lime  and  hydrogen  gas  (which  latter  escapes).  Lime 
is  a  white,  alkaline  powder,  of  specific  gravity  8.16.  It  may  be  obtained 
also  by  heating  pure  carbonate  of  lime  or  calcite  {CaCOs^CaO+CO^, 
whence  the  carbonic  acid  (C02)  is  driven  ofF,  leaving  the  lime.  This  is  a 
pure  lime  and  not  the  more  or  less  impure,  commercial  article  known  to 
the  engineer. 

Comnioa  Ume  is  a  more  or  less  impure  lime  obtained  by  calcinating 
common  limestone,  composed  mainly  of  CaCOs,  in  kilns  or  furnaces,  thereby 
driving  off  the  carbonic  acid  and  organic  impurities.  Its  purity  is  dependent 
mainly  upon  the  mineral  purity  ofthe  carbonate  which  is  burned.  Quick' 
Utm  or  biimed  lime  ^CaO+ impurities)  is  the  name  given  to  it  as  it  comes 
inm  the  kilns.  In  this  state  it  is  white  and  has  a  specific  gravity  of  3.16. 
Slacked  Ume  is  quicklime  which  has  been  slacked  by  exposure  to  the  air. 
whence  the  term  '*  air  slacked  "  in  contradistinction  to  water  slacked. 
Iq  the  former  case  it  absorbs  carbonic  acid  and  moisture  from  the  air. 
Water  slacked  or  simply  common  alacked  lime  is  a  calcium  hydroxide 
(Co/fjOa).  Its  specific  jjravity  is  2.1  or  about  two-thirds  that  of  quick- 
lime, showing  that  slacking  increases  its  btUk  about  one-half.  "  Fat  hme  " 
is  obtained  from  limestone  containing  6  per  cent  or  less  of  impurities,  and 
whoi  these  latter  amount  to  6  per  cent  the  Ume  is  poor. 

Commoa  Lime  Mortar. — This  is  composed  of  common  lime  mixed  with 
the  required  amotmtof  sand,  and  freshly  slacked  to  a  smooth  paste.  The 
proportions  of  the  mixture  of  lime,  water  and  sand  vary  according  to  the 
quality  of  the  lime  and  the  class  of  work  for  which  it  is  intended.  An  aver- 
age proportion  for  brickwork  is.  by  bulk.  1  of  lime.  2  to  3  of  sand.  It  will 
not  set  under  water  and  is  used  only  where  in  contact  with  air  it  can  set 
slowly  by  absorbing  carbonic  acid  (and  some  moisture).  Lime  mortar  may 
contain  any  proportion  of  sand  or  even  no  sand. 

For  a  fat  lime  and  a  good  quality  of  cement  the  adhesive  properties  of 
the  resulting  mortar,  after  being  set,  are  about  as  follows  for  various  mix- 
tores,  calling  that  of  pure  lime  paste  unity: 

Lime.     Sand.     Cohesion.  .^ 


J    0 

1.00 

:    0.5 

.905 

:    1. 

.82 

:    1.5 

.745 

:    2 

.68 

:    2.5 

.625 

:    3 

.58 

:    3.5 

.545 

:    4 

.52 

Lime  Plaster. — ^This  consists  approximately  of  1  part  quicklime,  2  parts 
sand,  and  to  each  100  lbs.  of  the  resulting  mortar  about  |  bushel  of  cow- 
hair  or  other  fine  fibre  is  sometimes  added  to  give  it  coherent  strength. 
ft  is  applied  on  wooden  or  metal  laths.  Many  patent  plasters  are  manu- 
Ujcturea  in  slabs  at  the  factories  and  shipped  ready  to  he>put  in  place. 
They  are  often  compounds  of  gypsum.  Digitized  by  LjOOg IC 


404  22.— BUILDING  STONES  AND  CEMENTS. 

Plaster  of  Paris. — When  gypsum,  a  hydrated  sulphate  of  lime  (CaS04  + 
2H^),  is  heated  sufficiently,  part  of  its  water  of  crvstallisation  is  driven 
ofT,  leaving  the  resulting  composition  iCaSO^±-hH^,  called  plaster  oi 
pans.  This  is  one  of  the  simplest  of  the  mineral  cements,  and  in  addition 
to  its  value  in  the  arts  it  is  used  for  cementing  slabs  of  marble  in  building 
construction.  This  consists  in  simply  mixing  the  plaster  of  paris  to  a  creamy 
paste  and  applying  it.  Its  setting  consists  in  taking  on  water,  again  crys- 
tallizing into  the  hydrate,  gypsum.  Plaster  of  paris  is  a  useful  constituent 
in  many  of  the  dehcate  cements.  Its  strength  may  be  incrrased  bv  mixing 
with  it  a  solution  of  thin  glue,  albumen  (white  of  egg),  or  vegetable  gum. 
Many  architectiiral  ornaments  are  made  of  plaster  oi  paris  mixed  with 
about  cm  equal  amount  of  paper  pulp  and  a  solution  of  size. 

Hydraulic  Lime. — As  common  lime  is  made  by  burning  common  lime- 
stone, so  is  hydraulic  lime  obtained  in  a  similar  way  from  hi^draulic  lime- 
stone, which  contains  a  large  amount  of  silica  and  alumina.  In  boming. 
these  latter  combine  with  part  of  the  lime,  forniing  lime  silicates  and  aln- 
minates,  the  other  portion  of  the  lime  remaining  uee.  The  silicates  and 
aluminates  possess  the  power  of  hardening  under  water.  It  is  used  in 
high-class  masonry  construction  in  Europe,  being  replaced  by  cements 
in  the  United  States. 

Hydraulic  Cement. — ^These  cements  are  capable  of  hardening  undet 
water — containing  a  large  amoimt.  25  to  50  per  cent.,  of  silica  and  alumina. 
They  may  be  classed  as  natural,  Portland  (semi-natural),  and  slag  (arti> 
ficial  or  puzzolanic)  cements. 

Natural  Cement  is  obtained  by  simply  burning  the  natural  hydraulic 
limestone  at  a  low  temperature,  and  grinding  the  clinker  very  fine.  It  is 
manufactured  in  Ulster  County,  N.  y7;  Louisville,  Ky.;  Cumberland.  Md.; 
Utica,  Dl.,  and  Milwaukee,  Wis.  The  limestone  contains  much  clay,  which 
supplies  the  required  silica  and  alumina.  The  product  as  shipped  is  com.- 
posed.  approximately,  of  lime  (42  parts),  silica  (28}.  altmiina  (id),  iron  oxide, 
magnesia  and  impurities  (20).  This  cement  is  usually  ^  called  Ronum 
cement  in  Europe,  and  RosendaU  cement  in  the  U.  S.  It  is  cheaper  than 
Portland  cement,  gains  strength  more  slowly,  and  sets  more  quickly-. 

Portland  Cement. — C^ood  Portland'cement  contains  the  usual  hjrdraulic 
cement  ingredients  about  as  follows,  namely,  lime  (62),  silica  (23).  alumina 

i8),  and  other  impurities  including  iron  oxide,  magnesia,  s;ilphuric  acid  (7). 
t  is  prepared  by  selecting  such  natural  materials  that  when  mixed,  ground, 
and  calcined,  the  product  will  be  the  required  compound  as  above.  Thus, 
the  proper  silicates  and  aluminates  of  lime  are  obtained  from  a  mixture  of 
argillaceous  limestones  of  different  chemical  composition:  from  relatively 
pure  limestone  and  clay  or  chalk  and  clay;  and  from  marl  and  clay.  The 
resulting  clinker  is  then  ground  to  a  powder.  Sand-ground  cement,  as  its 
name  indicates,  is  a  mixture  of  sand  and  Portland  cement  ground  toother. 
It  increases  the  bulk  of  the  "  cement  "  considerably  without  reducing;  its 
strength,  provided  the  ratio  of  sand  to  cement  is  not  greater  than  1  to  1. 
and  the  grinding  is  done  properly,  and  with  a  good  auality  of  sharp,  siliceous 
sand.  Portland  cement  is  stronger  than  Rx)6endale,  sets  more  slowly,  but 
acquires  its  strength  more  rapidly. 

Slag  Cement. — ^This  is  made  by  grinding  furnace  slag  with  Hme,  the  slag 
containing  the  other  necessary  ingredients — silica  and  alumina  (also  a 
small  percentage  of  impurities).  It  is  not  employed  to  any  great  extent  in 
the  United  States. 

Bitumen. — Bitumen  is  a  mineral  pitch  comprising  the  various  class  of 
substances  known  as  asphalt,  maltha,  petroleum,  naphtha,  natural  gas, 
etc.  Bitumen  is  decomposed  vegetable  matter  comprising  mainly  cax^on 
and  hydrogen,  but  containing  also  oxygen,  sulphur  and  nitrogen  in  small 
proportions.  Bituminous  substances  are  found  associated  with  the  carbon- 
iferous rocks  in  pre-volcanic  regions.  Thus  we  have  bittuninous  coal, 
-limestone,  -sandstone,  -shale,  etc. 

Asphalt. — ^This  is  one  of  the  principal  bitumens  and  is  supposed  to 
have  been  formed  by  the  hardening  of  its  allied  liquid  substances.  Tr»tUha 
^^^^^l^^")  *"^  pretroleum.  Pitch  Lake  is  a  lake  of  asphalt  on  the  island 
of  Tnnidad,  and  is  controlled  by  the  Trinidad  Asphalt  Co.  of  Philadelphia. 
Its  product  is  of  the  finest  quality,  and  supply  apparently  inexhaustible. 
Aspnait  IS  a  natural  cement;  its  composition  is  practically  unalterable 


HYDRAUUC  CEMBNTS^NATURAL.  PORTLAND.        406 

when  exposed  to  the  natural  elements;  and  it  is  quite  plastic  and  practically 
watCT-proof.  Thus,  it  forms  an  excellent  road,  pavement  and  roofing  ma- 
terial, and  as  a  coating  preservative  for  water  pipes  it  is  unexcelled.  Asphalt 
cement  is  simply  the  refined  asphalt  tempered  generally  with  the  residue 
from  petroletim  oil.  Asphalt  mastic  is  prepared  b]^  mixing  asphalt  cement 
with  sand  and  perhaps  crushed  limestone,  or  by  mixing;  maltha,  the  poorer 
quality  of  bitumen,  with  natural  rock  asphaJt.  The  mixture  is  heated,  and 
cooled  in  molds  ready  for  use.  Asphalt  concretg  consists  of  broken  stone 
or  gravel  with  asphalt  su»tic  used  as  a  binder. 

Manafactnre  off  Porfland  Cement. 

Raw  Maicrials. — ^The  materials  used  in  the  manufacture  of  Portland 
cement  are  carbonate  of  lime  and  clay:  occurring  either  more  or  less  naturally 
mized.  as  in  the  argilbceous  limestones;  or  separate  in  natural  beds,  as 
the  dialk  deposits  of  England  and  the  various  clav  deposits  common  in 
many  countries.  In  England,  chalk  is  the  principal  form  of  carbonate  of 
Bme  empk>ved,  and  this  is  mechanically  mixed  with  estuary  mud.  In 
Germany,  the  chief  material  is  "  mergel  "  (marl),  a  limestone  rock  of  greater 
or  less  hardness,  containing  clay;  also  "  weisenkalk,"  a  pure  soft  marl 
composed  mainly  of  carbonate  of  lime.  In  the  United  States  the  marls 
amilar  to  those  of  Germany  are  found  in  Ohio,  Indiana,  Michigan  and  New 
York,  and,  mixed  with  clay,  are  largely  used  in  the  manufacture  of  Portland 
cement;  but  most  of  our  cement  is  made  from  certain  limestones  containing 
sufficient  clay  and  nearly  free  from  magnesia,  and  found  in  certain  localities, 
as  PhilHpaburg,  N.  J.,  and  Lehigh  Co.,  Penn. 

The  three  distinct  operations  in  the  manufacture  of  Portland  cement 
sre  (1)  PulTcriring  and  mixing  the  raw  materials,  (2)  Calcination  or  burning, 
(1)  Grinding  the  clinker.    These  are  discussed  as  follows: 

Poivwiziiic  and  Mixing. — ^There  are  two  processes  in  use  for  mixing 
the  raw  materials  preparatory  to  calcination.  These  are  known  as  the 
"  wet  "  process  ana  the  **  dry  "  process,  each  naturally  adapted  to  the 
dass  of  materials  to  be  mixed. 

Wet  Process. — ^This  process  is  used  for  such  materials  as  chalk,  soft 
marl  and  clay,  which,  by  the  admixture  of  a  large  quantity  of  water  in  a 
"  wash  mill,'  can  be  reduced  to  a  homogeneous  creamy  condition  of  "  slip  " 
or  "  shxrry."  The  most  recent  practice  in  the  United  States  is  to  grind 
the  mixture  in  a  liquid  state,  run  it  into  tanks  where  it  is  kept  continually 
ttimd.  aad  thence  to  the  rotary  tubular  furnaces  where  it  is  calcined. 

Dry  Process. — ^This  process  is  particularly  adapted  to  the  treatment  of 
argillaceous  limestones  or  limestones  containing  sufficient  clay  so  that  very 
Imle  mechanical  mixing  is  necessary;  notably  the  limestones  of  Phillips- 
bmg,  N.  J.f  Lehigh  Co.,  Penn.,  and  of  some  localities  in  the  West.  Such 
material  is  run  into  a  "  grinding  machine  "  where  it  is  ground  to  a  greater 
or  less  degree  of  fineness,  depending  upon  the  relative  admixture  of  car- 
bonate of  lime  afid  clay:  i.e.,  if  they  occur  intimately  mixed  in  the  same 
rock  in  the  right  proportion,  very  little  grinding  is  required.  The  process 
becomes  very  expensive,  however,  when  an  almost  pure  limestone  rock 
and  a  dayey  shale  form  the  ingredients  to  be  mixed,  in  which  case  they 
must  first  be  crushed  to  the  sire  of  small  pebbles,  then  mixed  and  ground 
to  an  impalpable  powder  to  produce  an  intimate  blending. 

Calcination. — After  pulverizing  and  mixing,  the  material  is  conducted 
to  the  rotary  tubular  furnace,  where  it  is  burned  at  a  temperature  of  about 
IMO^  P.  Such  a  furnace  consists  of  a  steel  tube  usually  from  60  to  100  ft. 
kmg.  and  0  to  10  ft.  in  diameter,  and  lined  with  fire  brick.  It  is  arranged 
to  rotate  on  rollers  and  is  placed  on  a  grade  of  about  5%.  The  raw  mixture 
to  be  calcined  is  introduced  at  the  higher  end  of  the  tubular  furnace  and.  as 
the  latter  revolves,  the  heated  material  forms  into  small  balls  which  slowly 
gravitate  to  the  lower  end,  fall  into  a  conveyer,  and  are  carried  to  the 
clinker  storage-room.  The  degree  of  burning  is  one  of  the  most  important 
considerations  in  cement  manmacture. 

Qrindbif  tlie  Cflnker. — After  calcination,  the  resulting  clinker  passes 
to  the  "  ball  mills  "  where  it  is  broken  up  into  sand,  with  a  small  proportion 
of  dust.  It  then  goes  to  the  *'  pulveriser,"  where  it  is  reduced  to  the  re- 
quired fineness  of  powder — cement. 


4M  22.— BUILDING  STONES  AND  CEMENTS. 

CdDMlt  Tcftliic* 

Requisite!  of  a  Cement, — The  principal  requisites  of  a  cement  are  that 
when  combined  with  other  materuds  of  construction  it  shall  possess  the 
necessary  resistance  to  disintegration,  that  is.  (1)  strength  to  resist  safely 
the  loads  which  may  come  upon  it.  and  (2)  endurance  to  withstand  safely 
the  continuous  or  repeated  stresses  to  which  it  ma^  be  subjected,  with  the 
element  "  time  "  included.  Certain  factors  affectmg  these  qualitiea  in  a. 
cement  will  now  be  considered. 

Chtmical  Composition  is  one  of  the  most  important  factors  entering 
into  both  the  strength  and  endurance  of  cement;  nence.  the  raw  materials 
should  be  selected  m  the  proper  proportions  to  give  the  required  chemical 
mix  in  the  finished  product.  The  elements  calcium,  silicon,  aluminuni, 
carbon  {and  hydrogen)  all  unite  with  oxygen,  forming  oxid^.  the  exact 
chemical  composition  being  very  complex,  and  varying  greatly  with  different 
cements.  Any  foreign  matter  thus  becomes  an  adulterant,  tending  to  pre- 
vent "  set  "  or  hardening  of  the  cement. 

S9t  or  Hardsning  of  cement  takes  place  when  water  is  introduced  into 
the  anhydrous  cement  powder.  It  then  becomes  a  hydratcd  compound  in 
the  form  of  an  artificial  stone.  In  Trans.  A.  S.  C.  E..  Vol.  LIV,  Part  P, 
pp.  48-52,  Mr.  R.  L.  Humphrey  says:  **  This  hydration  or  crystallization 
begins  with  the  addition  of  water,  and  it  is  doubtful  whether  it  ever  ceases. 
....  Upon  the  addition  of  water,  it  begins  immediately  to  hydrate 
in  the  from  of  fine  needle-like  crystals,  and  it  is  the  intermeshing  of  these 
crystals  that  produces  the  hardening.  They  can  be  seen  forming  under  a 
microscope  immediately  upon  the  addition  of  water  to  cement.  The  action 
is  analogous  to  the  formation  of  crystals  from  a  saturated  salt  solution. 
If  water  is  added  to  a  cement  that  has  commenced  to  set,  and  it  is  again 
mixed,  the  crystals  already  formed  will  be  broken  up.  and  the  mass  weak- 
ened by  this  retempering.  Successive  repetitions  will  spradually  destroy  all 
bond,  and  the  cement  having  set  or  crystallized,  the  mass  will  become  like 
so  much  inert  sand."  The  phenomenon  of  hardening,  then,  "  is  purely  a 
chemical  one  and  is  the  result  of  the  mechanical  intermeshing  of  the  crystals 
of  silicate  of  lime,  etc..  which  are  formed  by  the  hydration  of  the  cement 
powder." 

It  will  thus  be  seen,  from  the  above,  that  cement,  cement  mortar,  and 
concrete  should  be  placed  in  the  work  immediately  after  mixing,  and  should 
not  subsequently  be  disturbed. 

Ratg  of  StUing  or  time  of  setting  in  an  important  feature  in  construction 
work.  It  is  necessary  that  the  cement  should  not  be  so  "  quick-setting  " 
as  to  prevent  proper  manipulation  of  the  mix  and  placing  it  in  the  structttre, 
nor  so  *'  slow-setting  "  as  to  require  extra  time  to  set,  thereby  retarding 
the  work.  The  term  "  set  "  is  here  used  in  the  sense  of  "  initial  set  "  or 
that  point  of  crystallization  where  any  disturbance  or  displacement  of  the 
material.would  eflfectually  weaken  it.  Both  *'  initial  set  "  and  **  final  set  " 
or  "  hard  set  "  are  indefinite  terms  because  crystallization  or  hardening  is 
a  continuous  process  which  goes  on  indefinitely.  Cements  which  do  not 
set  in  two  hours  are  considered  slow-setting.  Chi  the  other  hand.  10  to  30 
minutes  is  usually  allowed  any  cement  for  manipulation  and  placing,  before 
initial  set  should  appear.  The  rate  of  setting  of  cement  may  be  increased 
by  the  addition  of  lime,  or  plaster  of  paris  or  gypsum,  but  the  resultant 
strength  is  thereby  decreaseci. 

Finentss  is  absolutely  necessary  to  the  thorough  crystallization  and 
consequent  hardening,  previously  described.  If  the  grains  are  coarse  the 
crystals  and  their  intermeshing  will  be  imperfect,  which  will  also  be  the 
case  if  the  cement  powder  does  not  contain  the  proper  mix  of  the  raw  ma- 
terials, and  the  right  degree  or  calcination.  An  ideal  cement  is  one  in 
which  the  clinker  has  been  pulverized  to  a  "fiour"  or  impalpable  powder, 
thoroughly  anhydrous,  and  containing  elements  in  such  proportion  Uiat 
when  water  is  added  the  hydrated  comp>ound  will  form  into  mnumerable 
perfect  crystals,  with  no  free  matter  to  obstruct  their  formation.  Of  course 
this  ajndition  can  never  be  realized  because  (1)  the  grinding  or  pulver- 
izing IS  never  carried  to  such  an  extreme  degree,  and  (2)  all  cements  contain 
more  or  less  free  matter,  as  excess  of  lime,  magnesia,  iron,  etc.  These  two 
classes  ot  imperfections  aflFect  the  strength  of  the  cement,  and  the  second 
Class  also  afiects  its  *  soundness  "  and  consequently  its  endurance. 


CEMENT  TESTING.  407 

Semidngss  is  a  negative  term  used  to  express  the  property  which  a 
cement  has  of  not  unduly  expanding,  contracting,  checking  or  cracking 
during  setting,  hardening  or  crystalhzation.  Such  deformations  are  due 
to  "  active  "  impurities  in  the  cement,  such  as  free  magnesia,  lime,  sulphur 
trioxide.  etc.,  which  produce  internal  stresses  and  thereby  impair  both  its 
Arength  and  durability.  The  class  of  impurities  above  mentioned  should 
not  be  confused  with  certain  "  inactive  "  or  inert  impurities  or  adultera- 
dooa  which  affect  only  the  strength  of  the  cement  and  not  its  endurance. 

Inaciim  Adulterants  are  present  to  a  greater  or  less  extent  in  nearly  all 
cement,  the  effect  being  simply  to  reduce  its  strength  and  commercial 
Tahie.  Other  inert  adulterants,  as  sand,  in  sand-cement  mortar,  and  sand, 
broken  stone,  gravel,  etc.,  in  concrete,  are  added  to  or  mixed  with 
cetaeat  purely  on  the  grounds  of  economy,  i#  order  to  increase  the  bulk  of 
the  cementing  material,  allowing  its  strength  to  be  impaured  to  a  point 
consistent  with  necessary  safety. 

Method  of  Tcstliif  Cement.— The  following  is  a  digest  of  the  standard 
method  of  testing  cements,  submitted  as  a  progress  report  by  a  Committee 
of  the  Am.  Soc.  of  Civil  Engineers  in  190S  and  1904,  and  adopted  by  the 
Am.  Soc  for  Testing  Materials  in  1904: 

Selection  of  Sample. — Generally,  one  barrel  in  every  ten  to  be  sampled. 
the  sample  to  be  a  fair  average  of  contents  of  package;  it  shall  be  paraed 
throogh  a  sieve  having  20  meshes  per  lin.  in.  to  remove  lumps  before  testing. 
In  obtaining  sample  from  barrels  or  bags,  an  auger  or  a  sampling  iron 
dwuld  be  used,  reaching  from  side  to  center. 

A  chemical  analjrsis,  if  required,  may  be  made  in  accordance  with  the 
method  outlined  in  thejoumal  of  the  Society  of  Chemical  Industry,  pub- 
Ished  Jan.  16.  1902.  The  determination  of  the  principal  constituents  of 
cement — silica,  alumina,  iron  oxide  and  lime — is  not  conclusive  as  an 
issdication  of  quality. 

Spectfic  Gravity. — ^This  is  most  conveniently  made  with  Le  Chatelier's 
apparatus,  which  consists  of  a  flask  (D),  Fig. 

I.  of    120  cu.   cm.    (7.32  cu.  ins.)   capacity,  ^^ — ^ 

the  neck  of  which  is  about  20  cm.   (7.87  ins.)  *  N^ 

long.  In  the  middle  of  this  neck  is  a  bulb  (C),  U   ^ 

above  and  below  which  are  two  marks  (F)  S      ! 

and  (E).  The  volxime  between  these  marks  is  nrt . 

20cu.  cm.  (1.22  cu.  ins.).     The  neck  has  a  \)l%, 

dia.  of  about  9  mm.  (0.35  in.),  and  is  gradu-  IriS  § 

ated  to    tenths    of    cu.   centimeters    above  1 1 

the  mark  (P).     Benzine  (62^  Baum6   naph-  Ij^  ; 

♦Jha).  or  kerosene  free  from  water,  should  be  Jl     ■ 

used  in  making  the  determination.  y  Vj 

The  specific  gravity  can  be  determined  in  [  iL 

two  ways:  1st,  the  flask  is  filled  with  either  of        ^  ^»^^>^^>^ 

these  liquids  to  the  lower  mark  (E) .  and  64  gr.  I. 

(2^  oz.)  of  powder,  previously  dried  at  100**  C.  (212**  F. ,  »»*«  w*/v*^«  to  the  temp, 
of  the  hquid.  is  gradually  introduced  through  the  funnel  (B)  [the  stem  of 
which  extends  into  the  nask  to  the  top  of  the  bulb  (C)],  until  the  upper 
mvk  (F)  is  reached.  The  difference  in  weight  between  the  cement  remain- 
ing and  the  original  quantity  (64  gr.)  is  the  weight  which  has  displaced 
20  cu-  cm.  tnd,  the  whole  Quantity  of  powder  is  introduced,  and  the  level 
of  the  liquid  rises  to  some  division  of  the  graduated  neck.  This  reading 
;^us  20  cu.  cm.  is  the  volume  displaced  by  64  gr.  of  powder. 

The  specific  gravity  is  then  obtained  by  the  formija:  Specific  gravity  — 
weifldbt  of  cement -i- displaced  volume. 

The  flask,  during  the  operation,  is  kept  immersed  in  water  in  a  jar  (A), 
in  order  to  avoid  variations  in  the  temperature  of  the  liquid.  Results 
from  different  trials  should  agree  within  (i.Ol.  The  apparatus  is  conven- 
iently cleaned  by  inverting  the  flask  over  a  glass  jar.  and  snaking  it  vertically 
until  the  liquid  starts  to  flow  freely,  repeating  the  operation  several  times. 

More  accurate  determinations  may  be  made  with  the  picnometer. 

Fineness. — ^The  fineness  is  determined  by  measuring  the  residue  retained 
on  certain  sieves,  those  known  as  No.  100  and  No.  200  being  recommended 
for  this  purpose.  The  sieves  should  be  circular,  about  20  cm.  (7.87  ins.) 
in  dia.,  0  cm.  (2.36  ins.)  high,  and  provided  with  a  pan  5/cm.  IJUPJ^  ^"^-^ 
deep,  and  a  cover.  i  ed  by  V^OOg  IC 


408  22.^BUILDING  STONES  AND  CEMENTS. 

The  wire  cloth  should  be  woven  from  brass  wire  having  a  dia.  of  0 .  0045 
in.  for  No.  100  sieve,  and  0 .  0024  in.  for  No.  200  sieve.  It  should  be  mounted 
on  the  frames  without  distortion;  the  mesh  should  be  resiilar  in  spacing  and 
be  within  the  limits:  96  to  100  meshes  per  lin.  in.  for  No.  100,  and  188  to 
200  for  No.  200.  For  the  test,  50  to  100  grams  (1 . 76  to  3.52  oz.)  dried  at 
a  temperature  of  212^  P.  prior  to  sieving,  should  be  used. 

The  coarsely  screened  (and  dried)  sample  is  weired  and  placed  on  the 
No.  200  sieve,  which,  with  pan  and  cover  attached  is  held  in  one  hand  in  a 
slightly  inclined  position,  and  moved  forward  and  backward,  at  the  same 
time  striking  the  side  gently  with  the  palm  of  the  other  hand,  at  the  rate  of 
about  200  strokes  per  min.,  and  contmued  tmtil  not  more  than  ^  of  1% 
passes  through  after  1  minute  of  continuous  sieving.  The  residue  is 
weighed,  then  placed  on  the^o.  100  sieve  and  the  operation  repeated. 
The  results  should  be  reported  to  the  nearest  A  of  !%•  The  work  may 
be  expedited  by  placing  m  the  sieve  a  small  quantity  of  large  shot. 

Normal  Consistency. — ^The  use  of  the  proper  percentage  of  water  in 
making  the  pastes*  from  which  pats,  tests  offsetting  and  briquettes  are 
made,  is  exceedingly  important,  affecting  the  results  vitally.  No  method 
is  entirely  satisfactory,  but  the  following  is  recommended: 

ViCAT  Nbbdlb  Tbst. 

The  apparatus  used  is  known  as  the  Vicat  needle,  which  consists  of  a 

frame  (K).  Pig,  2.  bearing  a  movable  rod  (L).  with  a  cap  (A)  at  one  end« 

and  at  the  other  the  cylinder  (B).  1  cm.  (0.39  in.)  in   dia.;  the   cap,  rod 

and  cylinder  weighing  300  gr.  (10.58  oz.).     The  rod,  which  can  be  held 


Fig.  2. 
in  any  desired  position  by  a  screw  (F),  carries  an  indicator,  which  moves 
over  a  scale  (graduated  to  centimeters)  attached  to  the  frame  (K).  The 
paste  is  held  by  a  conical,  hard-rubber  ring  (I),  7  cm.  (2.76  ins.)  in  dia- 
at  the  base,  4  cm.  (1 .57  ins.)  high,  resting  on  a  glass  plate  (J),  about  10 
cm.  (3.94  ins.)  square. 

In  making  the  determination,  the  same  quantity  of  cement  as  will 
subsequently  be  used  for  each  batch  in  making  the  briquettes  (but  not  less 
than  500  grains)  is  kneaded  into  a  paste,  as  described  under  **  Mixing," 
and  quickly  formed  into  a  ball  with  the  hands,  completing  the  operation 
by  tossing  it  six  times  from  one  hand  to  the  other,  maintained  6  ins.  apart; 
the  ball  is  then  pressed  into  the  rubber  ring  through  the  laiger  opening, 
smoothed  off,  and  placed  (on  its  large  end)  on  a  glass  plate  and  the  smaller 
end  smoothed  off  with  a  trowel ;  the  paste,  confined  in  the  ring,  resting  on 
the  plate,  is  placed  imder  the  rod  bearing  the  cylinder,  which  is  brought  in 
contact  with  the  surface  and  quickly  released. 

The  paste  is  of  normal  consistency  when  the  cylinder  penetrates  to  a 
point  in  the  mass  10  mm.  (1 .  39  in.)  below  the  top  of  the  ring.  Great  care 
must  be  taken  to  fill  the  ring  exactly  to  the  top. 

The  trial  pastes  are  made  with  varying  percentages  of  water  tmtii  the 
correct  consistency  is  obtained. 

The  Committee  has  recommended,  as  normal,  a  paste  the  consistency 
of  which  is  rather  wet,  because  it  believes  that  variations  in  the  amount  ctf 
compression  to  which  the  briquette  is  subjected  in  moulding  are  likely  to 
be  less  with  such  a  paste. 

*  The  term  "  paste  "  is  here  used  to  designate  a  mixture  of  cement  and 
water,  and  the  word  "  mortar  "  a  mixture  of  cement,  sand  and  water. 


CEMENT  TESTING. 


409 


H&vtns  determiiied  tn  this  manner  the  proper  percentage  of  water 
reqtrired  to  produce  a  paste  of  normal  consistency,  the  proper  percentage 
'or  the  coortars  may  be  obtained  from  an  empirical  formula,  which  the 
Ccmmittee  bopes  to  devise;  but  temporarily  the  following  Table*  may  be 

Pbscbmtaob  of  Watbr  for  Sfandard  Sand  Mortars. 


Neat. 


One  Cement, 

Three  Standard 

Ottawa  Sand. 


Neat. 


One  Cement. 

Three  Standard 

Ottawa  Sand. 


One  Cement, 

Three  Standard 

Ottawa  Sand. 


15 
16 
17 
18 
19 
20 
21 
22 


8.0 
8.2 
8.3 
8.5 
8.7 
8.8 
0.0 
0.2 


23 
24 
25 
25 
27 
28 
29 
30 


9.3 

9.5 

9.7 

9.8 

10.0 

10.2 

10.3 

10.5 


31 
32 
33 
34 
85 
86 
37 
38 


10.7 
10.8 
11.0 
11.2 
11.5 
11.5 
11.7 
11.8 


1  to  1 

1  to  2 

1  to  3 

1  to  4 

1  to  5 

Cement .  .  ,  ,   , 

500 
500 

333 
666 

250 
750 

200 
800 

167 

Sand   

833 

Timte  of  Setting. — The  object  of  this  test  is  to  determine  the  time  which 
has  elapsea  from  the  moment  water  is  added  until  the  paste  ceases  to  be 
Suid  and  plastic  (called  the  "  initial  set  "),  and  also  the  time  required  for 
it  to  acquire  a  certain  degree  of  hardness  (called  the  "  final  "  or  "  hard  set  "). 
TI»  former  of  these  is  the  most  important,  since,  with  the  commencement 
of  setting,  the  process  of  crystallisation  or  hardening  is  said  to  begin.  As 
a  disturbance  of  this  process  roa^  produce  a  loss  of  stren^h.  it  is  desirable 
to  complete  the  operation  of  mixing  and  moulding,  or  incorporating  the 
fflortar  into  the  work,  before  the  cement  begins  to  set. 

It  is  ustial  to  measure  arbitrarily  the  beginning  and  end  of  the  setting 
by  the  penetration  of  weighted  wires  of  given  diameters.  For  this  purpose 
the  Vicat  needle,  already  described,  should  be  used.  In  making  the  test, 
a  paste  of  normal  consistency  is  moulded  and  placed  under  the  rod  (L), 
Fig-  2.  as  described  under  *'  Normal  Consistency;"  this  rod,  bearing  the 
cap  (D)  at  one  end  and  the  needle  (H),  1  mm.  (0. 039  in.)  in  dia..  at  the  other, 
wrigTiing  300  gr.  ( 1 0 .  58  or.).  The  needle  is  then  carefully  brought  in  contact 
vith  the  surface  of  the  paste  and  quickly  released.  The  setting  is  said  to 
have  commenced  when  the  needle  ceases  to  pass  a  point  5  mm.  (0 .  20  in.) 
above  the  upper  sxu^ace  of  the  glass  plate,  and  is  said  to  have  terminated 
the  ntoment  the  needle  does  not  sink  visibly  into  the  mass. 

The  test  pieces  should  be  stored  in  moist  air  during  the  test;  this  is 
accomplished  by  placing  them  on  a  rack  over  water  contained  in  a  pan  and 
covered  with  a  damp  cloth,  the  cloth  to  be  kept  away  from  them  by  means 
of  a  wire  screen ;  or  they  may  be  stored  in  a  moist  box  or  closet.  Care  should 
be  taken  to  keep  the  needle  clean,  as  the  collection  of  cement  on  the  sides 
of  the  needle  retards  the  penetration,  while  cement  on  the  point  reduces  the 
area  and  tends  to  increase  the  penetration. 

The  determination  of  the  time  of  setting  is  only  approximate,  being 
maiteriaUy  affected  bv  the  temperature  of  the  mixing  water,  the  temper- 
ature and  humidity  of  the  air  during  the  test,  the  percentage  of  water  used, 
and  the  amount  of  nvmlding  the  paste  receives. 

Standard  Sand. — ^The  Ojmmittee  recognizes  the  grave  objections  to  the 
standard  ouartz  now  generally  used,  especially  on  account  of  its  high  per- 
centage of  voids,  the  difficulty  of  compacting  in  the  moulds,  and  its  lack 
of  umformity.  It  recommends,  for  the  present,  the  natural  sand  from 
Ottawa.  HI.,  screened  to  pass  a  sieve  having  20  meshes  per  lin.  in.,  and  re- 

*  Prepared  by  the  Committee  on  Standard  Spedfications' for  Cements 
as  a  temporary  expedient.  '^ed  by  ^^^JUy  le 


410  ^.—BUILDING  STONES  AND  CEMENTS. 

tained  on  a  sieve  havins  30  meshes  per  lin.  in.;  the  wires  to  have  diameters 
of  0.0165  and  0.0112  m..  respectively,  i.e..  half  the  width  of  the  opening 
in  each  case.  Sand  having  passed  the  No.  20  sieve  shall  be  considered 
standard  when  not  more  than  1%  passes  a  No.  30  sieve  after  one  minute 
continuous  sifting  of  a  500-gram  sample.  The  Sandusky  Portland  Cement 
Co..  of  Sanduslry.  O.,  has  agreed  to  undertake  the  preparation  of  this  sand, 
and  to  furnish  it  at  a  price  only  sufficient  to  cover  the  actual  cost  of  prep- 
aration. 

Form  of    Briquttu. —  While  the  form  of  the  «    ..^    3*  •j 

briquette  recommended  by  a  former  Committee  of  !i.'*.tj:T*J '*• 

the  Society  is  not   wholly   satisfactory,  this  Com-  jk'..  /.3'- ->i  | 

mittee  is  not   prepared    to    suggest    any    change.  :  1  \  j 

other  than  rounding  off  the  comers  by  curves  of  IP^^^JJ^""^^! 

i-in.  radius.  Pig.  3. 

Moulds. — ^The  moulds  should  be  made  of  brass, 
bronze,  or  some  equally  non-corrodible  material, 
having  sufficient  metal  in  the  sides  to  prevent 
spreading  during  moulding.  Gang  moulds,  as 
stiown  in  Fig.  4,  are  preferred  to  single  moulds, 
since  the  greater  quantity  of  mortar  that  can  be 
mixed  for  simultaneous  moulding  tends  to  pro- 
duce   greater  uniformity    in    the    results.      They  _^, 

should  be  wiped   out   with   an   oily   cloth   before  i« \.y.. 

using. 

Mixing. — All  proportions  should  be  stated  by  P*-  3. 

weight;  the  quantity  of  water  to  be  used    should 

be  stated  as  a  percentage  of  the  dry  material.    The  jt  • 

metric  system    is    recommended    because    of   the  gr-^yr'^vr^^v/^'*-^      M 
convenient  relation  of   the  gram    and    the  cubic  ■^^;^£}^;^£2Ci-:C:x*="^ 
centimeter.     The  temperature  of  the  room  and  the 
mixing  water  should  be  as   near  70®  P.   as  it   is  n  «    i 

practicable  to  maintain  it.  '^^*  *• 

The  sand  and  cement  should  be  thoroughly  mixed  dry,  and  on  some 
non -absorbing  surface,  preferably  plate  glass.  If  an  absorbing  surface  is 
used  it  should  previously  be  dampened.  The  quantity  of  material  to  be 
mixed  at  one  time  depends  on  the  number  of  test  pieces  to  be  made;  about 
1000  gr.  (35.28  oz.)  makes  a  convenient  quantitv  to  be  mixed,  especially 
by  hand  methods.  The  material  is  weighed  and  placed  on  the  mixing  table, 
and  a  crater  formed  in  the  center,  into  which  the  proper  percentage  of  clean 
water  is  poured;  the  material  on  the  outer  edge  is  turned  into  the  crater  by 
the  aid  of  a  trowel.  As  soon  as  the  water  has  been  alMorbed.  which  ^hoxild 
not  require  more  than  one  minute,  the  operation  is  completed  by  vigorously 
kneading  with  the  hands  for  an  additional  li  minutes,  the  process  being 
similar  to  that  used  in  kneading  dough.  A  sand-glass  affords  a  convenient 
guide  for  the  time  of  kneading.  During  the  operation  of  mixing,  the 
hands  should  be  protected  by  gloves,  preferably  of  rubber. 

Moulding. — ^Having  worked  the  paste  or  mortar  to  the  proper  con- 
sistency it  is  at  once  placed  in  the  moulds  by  hand,  being  pressed  m  firmly 
with  the  fingers  and  smoothed  off  with  a  trowel  without  ramming.  It  should 
be  heaped  up  on  the  upper  surface  of  the  mould,  and,  in  smoothing  off, 
the  trowel  should  be  drawn  over  the  mould  in  such  a  manner  as  to  exert 
a  moderate  pressure  on  the  excess  material.  The  mould  should  be  tamed 
over  and  the  operation  repeated.  A  check  upon  the  uniformity  of  the  mix- 
ing and  moulding  is  afforded  by  weighing  the  briquettes  just  prior  to  im- 
mersion, or  upon  removal  from  the  moist  closet.  Those. varjring  in  wei^t 
more  than  3%  from  the  average  should  be  rejected. 

Storage  of  the  Test  Pieces. — During  the  first  24  hours  after  moulding, 
the  test  pieces  should  be  kept  in  moist  air  to  prevent  them  from  drying  out, 
A  nooist  closet  or  chamber  is  so  easily  devised  that  the  use  of  the  damp 
cloth  shotUd  be  abandoned  if  possible.  Covering  the  test  pieces  with  a 
damp  cloth  is  objectionable,  as  commonly  used,  because  the  cloth  may  dry 
out  unequally,  and.  in  conseouence.  the  test  pieces  are  not  all  ooaintained 
imder  the  same  conditions.  Where  a  moist  closet  is  not  available,  a  doth 
may  be  uced  and  kept  imiformly  wet  by  immersing  the  ends  in  water,  and 
being  kept  from  direct  contact  with  the  test  pieces,  by  xiifians  of  a  wire 
screen  or  some  similar  arrangement.  D,g,,i,3d  by  GoOglc 


CEMENT-^TESTING,  SPECIFICATIONS.  411 

A  moist  ck)6et  consults  of  a  soapstone  or  slate  box,  or  a  metal  lined 
vooden  box — the  metal  lining  being  covered  with  felt  and  this  felt  kept 
vet.  The  bottom  of  the  box  is  so  constructed  as  to  hold  water,  and  the 
sdei  are  provided  with  cleats  for  holding  glass  shelves  on  which  to  place 
tile  briquettes.    Care  should  be  taken  to  keep  the  air  in  the  closet  uniformly 


After  24  hours  in  moist  air.  the  test  pieces  for  longer  periods  of  time 
ihoiikl  be  immersed  in  water  maintained  as  near  70^  P.  as  practicable; 
they  may  be  stored  in  tanks  or  pans,  which  should  be  of  non-corrodible 
materiaL 

TrmsiU  Sirtnfth. — ^The  tests  may  be  made  on  any  standard  machine. 
A  solid  nsetal  clip,  as  shown  in  Fig.   6,  is  recommended.  - — 

This  cHp  is  to  be  used  without  cushioning  at  the  points  of 
contact  with  the  test  specimen.  The  bearin|E  at  each  point 
of  contact  should  be  i  in.  wide,  and  the  distance  between 
the  centers  of  contact  on  the  same  clip  should  be  li  ins. 

Test  pieces  should  be  broken  as  soon  as  they  are  re- 
moved from  the  water.  Care  should  be  observed  in  cen- 
termg  the  briquettes  in  the  testing  machine,  as  cross- 
stains,  produced  by  improper  centering,  tena  to  lower 
the  breaking  strength.  The  load  should  not  be  applied 
too  suddenly,  as  it  may  produce  vibration,  the  shock  from 
which  often   breaks     the    briquette  before    the    ultimate 

ttrtoph  is  reached.     Care  must  be  taken  that  the  clips  and  ^, 

the  sides  of  the  briquette  be  clean  and  free  from  grains  Pig.  6. 
of  sand  or  dirt,  which  would  prevent  a  good  bearing.  The  load  should  be 
appHed  at  the  rate  of  600  lbs.  per  minute.  The  average  of  the  briquettes 
of  each  sample  tested  should  be  taken  as  the  test,  excluding  any  results 
^ikh  are  manifestly  faulty. 

CoHStoHcy  of  Volume, — The  object  is  to  develop  those  qualities  which 
tend  to  destroy  the  strength  and  durability  of  a  cement.  As  it  is  highly 
essential  to  determine  such  qualities  at  once,  tests  of  this  character  are  for 
the  most  part  made  in  a  very  short  time,  and  are  known,  therefore,  as 
acctkraitd  ttsts.  Pailure  is  revealed  by  cracking,  checking,  swelling  or 
disintegration,  or  all  of  these  phenomena.  A  cement  which  remains  per- 
fectly sound  IS  said  to'  be  of  constant  volume. 

Tests  for  constancy  of  volume  are  divided  into  two  classes:  (1)  normal 
tesu,  or  those  made  in  either  air  or  water  maintained  at  about  70**  F  .  and  (2) 
accelerated  tests,  or  those  made  in  air,  steam  or  water  at  a  temperature  of 
115^  P.  and  upward.  The  test  pieces  should  be  allowed  to  remain  24  hours 
in  moist  air  before  immersion  in  water  or  steam,  or  preservation  in  air. 

Por  these  tests,  pats,  about  7i  cm.  (2.95  ins.)  in  dia.,  \\  cm.  (0.49  in.) 
thick  at  the  center,  ana  tapering  to  a  thin  edge,  should  be  made,  upon  a 
dean  glass  plate  [about  10  cm.  (3.94  ins.)  square],  from  cement  paste  of 
normal  consistency. 

Normal  Test. — ^A  pat  is  immersed  in  water  maintained  as  near  70^  P. 
as  possible  for  28  days,  and  observed  at  intervals.  A  similar  pat  is  main- 
tained in  air  at  ordinary  temperature  and  observed  at  intervals. 

Accelerated  Test. — ^A  pat  is  exposed  in  any  convenient  way  in  an  atmos- 
phere of  steam,  above  boiling  water,  in  a  loosely  closed  vessel,  for  3  hours. 

To  pass  these  tests  satisfactorily,  the  pats  should  remain  firm  and 
hard,  ami  show  no  signs  of  cracking,  distortion  or  disintegration.  Should 
the  pat  leave  the  plate,  distortion  may  be  detected  best  with  a  straight-edge 
appued  to  the  surface  which  was  in  contact  with  the  plate.  In  the  present 
state  of  our  knowledge  it  cannot  be  said  that  cement  should  necessarily  be 
condemned  simply  for  failure  to  pass  the  accelerated  tests;  nor  can  a  cement 
be  consadered  entirely  satisfactory  simply  because  it  has  passed  these  tests. 

SpedlicaiUoiis  for  Cement  (A.  S.  T.  M.). 

The  following  specifications  were  adopted  by  the  American  Society 
for  Testing  Materials.  Nov.  14.  1904: 

Oeneral  Condltioiis. — (1)  All  cement  shall  be  inspected.  (2)  Cement 
may  be  inspected  either  at  the  place  of  manufacture  or  on  the  work.  (3) 
In  order  to  allow  ample  time  for  inspecting  and  testing,  the  cement  should 


be  stored  in  a  suitaole  weather-tight  bufiding  having  the  fk>or  properly 
r  raised  from  the  grotmd.     (4)  The  cement  shall  be  stored  in  such 


bk>dced  or  i 


413  22,— BUILDING  STONES  AND  CEMENTS. 

a  manner  as  to  permit  easy  access  for  proper  inspection  and  identification 
of  each  shipment.  (5)  Every  fadlitv  shall  be  provided  by  the  contractor 
and  a  period  of  at  least  twelve  days  allowed  for  tne  inspection  and  necessary 
tests.  (6)  Cement  shall  be  delivered  in  suitable  packages  with  the  brand 
and  name  of  mantifacture  plainly  marked  thereon  (7)  A  bag  of  cement 
shall  contain  94  potmds  of  cement  net.  Each  barrel  of  Portland  cement 
shall  contain  4  bags,  and  each  barrel  of  natural  cement  shall  contain  8  bags 
of  the  above  net  weight.  (8)  Cement  failing  to  meet  the  7-day  require- 
ments may  be  held  awaiting  the  results  of  the  28-day  tests  before  rejection. 
(9)  All  tests  shall  be  made  m  accordance  with  the  methods  proposed  by  the 
Committee  on  Uniform  Tests  of  Cement  of  the  American  Society  of  Civil 
Engineers,  presented  to  the  Society  January  21,  1903,  and  amended  January 
20.  1904,  with  all  subsequent  amendments  thereto.  [See  '*  Method  m 
Testing  Cement,"  page  407.] 

(10)  The  acceptance  or  rejectioo  shall  be  based  on  tlie  following  re- 
qiurements: 

(11)  Natural  Cement.— Definition.— This  term  shall  be  applied  to  the 
finely  pulverized  product  resulting  from  the  calcination  of  an  argillaceous 
limestone  at  a  temperature  only  suifficient  to  drive  of!  the  carbonic  add  gas. 

(12)  Specific  Gravity. — ^Thc  specific  gravity  of  the  cement  thoroughly 
dried  at  100°  C.  shall  not  be  less  than  2.8. 

(13)  Finetuss. — It  shall  leave  by  weight  a  residue  of  not  more  than 
10%  on  the  No.  100,  and  30%  on  the  No.  200  sieve. 

(14)  Time  of  Setting. — It  shall  develop  initial  set  in  not  less  than  10 
minutes,  and  hard  set  in  not  less  than  30  minutes  nor  more  than  3  hours. 

(15)  Tensile  Strength. — ^The  minimum  requirements  for  tensile  strsn^:th 
for  briquettes  one  inch  in  cross  section  shall  be  within  the  following  limits, 
and  shall  show  no  retrogression  in  strength  within  the  periods  specified:* 

Age.  Neat  Cement.  Strength. 

24  hours  in  moist  air 50-100  lbs. 

7  days  (1  day  in  moist  air.  6  days  in  water) 100-200  ** 

28  days  (1  day  in  moist  air,  27  days  in  water) 200-800  " 

One  Part  Cement.  Three  Parts  Standard  Sand. 

7  days  (1  day  in  moist  air,  6  days  in  water) 25-  75  ** 

28  days  (1  day  in  moist  air,  27  days  in  water) 75-150  " 

(16)  Constancy  of  Volume. — Pats  of  the  neat  cement  about  8  ins.  in 
diameter,  i-in.  thick  at  center,  tapering  to  a  thin  edge,  shall  be  kept  in 
moist  air  for  a  period  of  24  hoiu«.  (a)  A  pat  is  then  kept  in  air  at  normal 
temperature,  (b)  Another  is  kept  in  water  maintained  as  near  70°  P.  as 
practicable. 

(17)  These  pats  are  observed  at  intervals  for  at  least  28  days,  and,  to 
satisfactorily  pass  the  test,  should  remain  firm  and  hard  and  show  no  signs 
of  distortion,  checking,  cracking  or  disintegrating. 

(18)  Portland  Cement. — ^Definition. — ^This  term  is  applied  to  the  finely 
pulverized  product  resulting  from  the  calcination  to  incipient  fusion  of  an 
intimate  mixture  of  properly  proportioned  argillaceous  and  calcareous 
materials,  and  to  which  no  addition  greater  than  3%  has  been  made  sub- 
sequent to  calcination. 

(19)  Specific  Gravity. — ^The  specific  gravity  of  the  cement,  thorotagrUy 
dried  at  100°  C,  shall  not  be  less  than  3.10. 

(20)  Fineness. — It  shall  leave  by  weight  a  residue  of  not  more  than 
8%  on  the  No.  100,  and  not  more  than  25%  on  the  No.  200  sieve. 

(21)  Time  of  Setting. — It  shall  develop  initial  set  in  not  less  than  80 
minutes,  but  must  develop  hard  set  in  not  less  than  one  hour  nor  naore 
than  ten  hours. 


•  For  example,  the  minimum  requirement  for  the  24-hour  neat  cement 
test  should  be  some  specified  value  within  the  limits  of  50  and  100  lbs.,  and 
so  on  for  each  period  stated.     [The  consumer,  when  ordering,  may  fix  the 

""""'■-'  b,  Google 


min.  value.] 

Digitized 


CEMENT— SPECIFICATIONS.  418 

(3S)  TensUt  Sttengih. — ^The  minimum  reqtdrements  for  teasik  ttrengtli 
kx  briquettes  one  inch  square  in  section  shall  be  within  the  following  limits. 
ud  shall  show  ao  retrogression  in  strength  within  the  periods  spedned;* 

Age.  Neat  Cement.  Strength. 

24  hours  in  moist  air 150-200  lbs. 

7  days  CI  day  in  moist  air,  6  days  in  water) 450-650  ** 

28  days  (1  day  in  moist  air,  27  days  in  water) 550-650   ** 

One  Part  Cement,  Three  Parts  Sand. 

7  days  (1  day  in  moist  air,  6  days  in  water) 150-200  ** 

28  days  (1  day  in  moist  air,  27  days  in  water) 200-300  ** 

(23)  Constancy  of  Volume. — Pats  of  neat  cement  about  3  ins.  in  diam- 
eter, \'in.  thick  at  the  center,  and  tapering  to  a  thin  edge,  shall  be  kept  in 
moist  air  for  a  period  of  24  hours,  (a)  A  pat  is  then  kept  in  air  at  normal 
temperature  and  observed  at  intervals  for  at  least  28  days,  (b)  Another 
pat  IS  kept  in  water  maintained  as  near  70**  P.  as  practicable,  and  observed 
at  intervals  of  at  least  28  days,  (c)  A  third  pat  is  exposed  in  anv  con-  * 
Teoient  way  in  an  atmosphere  of  steam,  above  boiling  water,  in  a  loosely 
dosed  ve«el  for  five  hours. 

(24)  These  pats,  to  satisfactorily  pass  the  requirements,  shall  remain 
firm  aiid  hard  and  show  no  signs  oi  distortion,  checking,  cracking  or  dis- 
integrating. 

(25)  Sulphuric  Acid  and  Magnesia. — ^The  cement  shall  not  contain 
more  than  1.75%  of  anhydrous  sulphuric  acid  (50s),  nor  more  than  4% 
of  magnesia  (MgO). 

Specifications  for  Cement  (Engrs.  U.  S.  A.). 

The  following  spedficationsf  are  from  Professional  Papers,  No.  28, 
Corps  of  Engineers,  U.  S.  A. 

(Ji)  American  Portland  Cement. — Shall  be  dry  and  free  from  lumps; 
the  oUcined  product  to  contain  at  least  1.7  times  as  much  lime,  by  weight, 
as  of  the  materials  which  give  the  lime  its  hydraulic  properties;  and  to  be 
finely  pulverized  after  said  calcination,  with  subsequent  additions  or  sub- 
stitutions for  regulating  certain  properties  of  technical  importance  not  to 
exceed  2%  of  the  calcined  product. 

The  cement  to  be  put  up  in  strong,  sound  barrels,  well  lined  with  paper, 
or  in  stout  cloth  or  canvas  sacks;  each  package  to  be  plainly  labeled  with 
zuune  of  brand  and  of  manufacturer.  Bidders  will  state  the  brand  which 
they  propose  to  furnish.  The  average  weight  per  barrel  shall  not  be  less 
than  375  lbs.  net.     Four  sacks  shall  contain  one  barrel  of  cement. 

Tests  may  be  made  of  the  fineness,  specific  gravity,  soundness,  time  of 
setting,  and  tensile  strength  of  the  cement. 

(7)  Fineness. — ^Ninety-two  per  cent  of  the  cement  must  pass  through 
a  seve  made  of  No.  40  wire,  Stubb's  gauge,  having  10,000  openings  per 
square  inch. 

(8)  Specific  Gravity, — The  specific  gravity  of  the  cement,  as  determined 
from  a  sample  which  has  been  carefully  dried,  shall  be  between  3.10  and 
3.25. 

(9)  Soundness. — ^To  test  the  soundness  of  the  cement,  at  least  two  pats 
of  neat  cement,  as  taken  from  the  package,  mixed  for  five  minutes  with 
about  20  per  cent  of  water  by  weight  shall  be  made  on  glass,  each  pat  about 
3  inches  in  diameter  and  one-half  inch  thick  at  the  center,  tapering  thence 
to  a  thin  edge.  The  pats  are  to  be  kept  under  a  wet  cloth  until  finally  set, 
when  one  is  to  be  (>laced  in  fr^  water  for  twenty-eight  days.  The  second 
pat  will  be  placed  in  water  which  will  be  raised  to  the  boiling  point  for  six 

*  For  example,  the  minimum  requirement  for  the  24-hour  neat  cement 
test  should  be  some  specified  value  within  the  limits  of  150  and  200  lbs., 
and  so  on  for  each  period  stated.  [The  consumer,  when  ordering,  may  fix 
the  minimum  values.] 

tA  digest  from  the  Report  of  Majors  W.  L.  Marshall  and  S.  S.  Leach, 
and  C^t.  Spencer  Crosby,  Board  of  Engineer  Officers,  on  testing  Hydraulic 
Cements,  with  specifications  for  the  several  classes;  Second-Edition,  with 
Corrections,  190l  Digitized  by  CjOOQIc 


414  22.— BUILDING  STONES  AND  CEMENTS. 

hotira,  then  allowed  to  cool.  Neither  should  show  distortion  or  cracks. 
The  boiling  test  may  or  may  not  reject  at  the  option  of  the  engineer  officer 
in  charge. 

(10)  Time  of  Setting. — ^The  cement  shall  not  acqiiire  its  initial  set  in 
less  than  forty-five  minutes  and  must  have  acquired  its  final  set  in  ten 
hours. 

(The  following  paragraph  will  be  substituted  for  the  above  in  case  a 
quick-setting  cement  is  desired: 

The  cement  shall  not  acquire  its  initial  set  in  less  than  twenty  nor  more 
than  thirty  minutes,  and  must  have  acquired  its  final  set  in  not  less  than 
forty-five  minutes  nor  in  more  than  two  and  one-half  hours.) 

The  pats  made  to  test  the  soundness  may  be  used  in  determining  the 
time  of  setting.  The  cement  is  considered  to  have  acquired  its  initial  set 
when  the  pat  will  bear,  without  being  appreciably  indented,  a  wire  one- 
twelfth  inch  in  diameter  loaded  to  weigh  one-fourth  pound.  The  final 
set  has  been  acquired  when  the  pat  will  bear,  without  being  appreciably 
indented,  a  wire  one  twenty-fourth  inch  in  diameter  loadea  to  weigh  1 
potmd. 

(11)  Tensile  Strength. — Briquettes'  made  of  neat  ceiaent,  after  being 
kept  in  air  for  twenty-foxir  hours  under  a  wet  cloth  and  the  balance  of  the 
time  in  water,  shall  develop  tensile  strength  per  sq.  in.  as  follows:  7  days, 
450  lbs;  28  days.  540  lbs.  Briquettes  made  of  1  part  cement  and  8  parts 
standard  sand,  by  weight,  shall  develop  tensile  strength  per  sq.  in.  as  follo'ws: 
7  days.  140  lbs;  28  days.  220  lbs.  (In  case  quick-setting  cement  is  desired, 
the  following  tensile  strengths  shall  be  substituted  for  the  above:  Neat 
briquettes:  7  days,  400  lbs.:  28  da}rs,  480  lbs.  Briquettes  of  1  part  cement 
to  S  parts  standard  sand:  7  days.  120  lbs.;  28  days.  180  lbs.) 

The  highest  result  from  each  set  of  briquettes  made  at  any  one  time,  is 
to  be  considered  the  governing  test.  Any  cement  not  showing  an  increase 
of  strength  in  the  28-day  tests  over  the  7-day  tests  will  be  rejected. 

(A)  Natural  Cement. — ^The  average  net  weight  per  barrel  shall  not  be 
less  than  800  lbs.     (West  of  the  Allegheny  Motmtains  this  may  be  265  lbs  J 

(7)  Fineness. — At  least  80  per  cent  of  the  cement  must  pass  through 
a  sieve  made  of  No.  40  wire,  otubb's  gauge,  having  10,000  openings  per 
square  inch. 

(8)  Time  of  Setting. — ^The  cement  shall  not  acquire  its  initial  set  in  less 
than  twenty  minutes  and  must  have  acquired  its  final  set  in  four  hours. 

(9)  The  time  of  setting  is  to  be  determined  from  a  pat  of  neat  cement 
mixed  for  five  minutes  with  30  per  cent  of  water  by  weight  and  kept  under 
a  wet  cloth  until  finally  set.  The  cement  is  considered  to  have  acquired 
its  initial  set  when  the  pat  will  bear,  without  being  appreciably  indented, 
a  wire  one-twelfth  inch  in  diameter  loaded  to  weigh  one-fourth  pound. 
The  final  set  has  been  acquired  when  the  pat  will  bear,  without  being  appre- 
ciably indented,  a  wire  one  twenty-fourth  inch  in  diameter  loaded  to  weigh 
1  pound. 

(10)  Tensile  Strength. — ^Briquettes  made  of  neat  cement  shall  develop 
the  following  tensile  strengths  per  square  inch,  after  having  been  kept  in 
air  for  twenty-four  hours  tmder  a  wet  cloth  and  the  balance  of  the  time  in 
water:  at  the  end  of  7  days,  90  lbs.;  28  days.  200  lbs.  Briquettes  noade  of 
1  part  cement  and  1  part  standard  sand,  by  weight,  shall  develop  the  follow- 
ing tensile  strengths  pr  sq.  in.:  7  days.  60  lbs.;  28  days,  150  lbs. 

(c)  Puzz(rfan  Cement. — ^The  average  weight  per  barrel  shall  XK>t  be  less 
than  330  lbs.  net.     Four  sacks  shall  contain  one  barrel  of  cement.  j 

(7)  Fineness. — ^Ninety-seven  per  cent  of  the  cement  must  pass  through 
a  sieve  made  of  No.  40  wire,  Stubb's  gauge,  having  10,000  openings  per 
square  inch. 

(8)  Specific  Gravity. — The  specific  gravity  of  the  cement,  as  determined 
from  a  sample  which  has  been  carefully  dried,  shall  be  between  2 . 7  and  2 .  a.J 

(9)  Soundness. — ^To  test  the  soundness  of  cement,  pats  of  neat  cemenM 
mixed  for  five  minutes  with  18  per  cent,  of  water  by  weight  shall  be  madM 
on  glass,  each  pat  about  3  inches  in  diameter  and  one-halt  inch  thick  at  the' 
center.  tai>ering  thence  to  a  thin  edge.     The  pats  are  to  be  kept  under  wet" 

VI J  ""^'^  finally  set,  when  they  are  to  be  placed  in  fresh  water.     They 
should  not  show  distortion  or  cracks  at  the  end  of  twenty-eight  days. 


ARTIFICIAL  BUILDING  STONES.  415 

(10)  Tismt  of  Setting. — The  cement  shall  not  acquire  its  initial  set  in  less 
t^  forty-five  minutes  and  shall  acquire  its  nnal  set  in  ten  hours. 
T^  pats  made  to  test  the  soundness  may  be  used  in  determining  the  time 
^  setting.  The  cement  is  considered  to  have  acquired  its  initial  set  when 
the  pat  win  bear,  without  being  appreciably  indented,  a  wire  one-twelfth 
cdi  in  diameter  loaded  to  one-fourtn  pound  weight.  The  final  set  has  been 
icqmred  when  the  pat  will  bear,  without  being  appreciably  indented,  a 
sire  one  twenty-fourth  inch  in  diameter  loaded  to  1  pound  weight. 

(11)  Ttnsile  Strength, — Briquettes  made  of  neat  cement,  after  being 
bpt  in  air  tmder  a  wet  cloth  for  twenty-four  hours  and  the  balance  of  the 
^Toe  in  water,  ^lall  develop  tensile  strengths  per  square  inch  as  follows: 
After  7  days,  350  lbs.;  28  days,  600  lbs.  Briquettes  made  of  1  part  cement 
and  3  parts  standard  sand,  by  weight,  shall  develop  tensile  strength  per  sq. 
m.  as  follows:  7  days,  140  lbs.,  28  days.  220  lbs. 

III.    ARTIFICIAL  BUILDING  STONES. 

The  following  classification,  which  includes  brick,  is  convenient  in  the 
present  disctisnon: 
il)  Brick,  usually  an  argillaceous  material,  molded  to  the  required  form, 

and  baked. 
[i)  Concrete,  consisting  of  a  matrix  of  cement  and  sand,  properly  mixed 

with  a  stone  aggregate,  in  situ, 
(3)  Block  stone,  a  hydraulic  cement  concrete  specially  treated  and  formed 
in  mgqlds  at  the  factory. 

(I)  Brick. 
A  good  brick  clay  consists  of  a  fairly  pure  hydrated  silicate  of  alumina, 
hat  contains  also  more  or  less  so-called  impurities  as  iron,  manganese,  free 
ibka  (sand),  potash,  lime.  etc.     In  making  bricks  the  clay  is  well  kneaded, 
Qokied,  dried,  and  then  burned  in  kilns. 

Commoa  brick  is  designated  as  *'  clinker."  *'  hard  "  or  "  soft."  denoting 
the  degree  of  burning  in  the  kiln.  Clinker  bricks  have  been  overbumed 
i  aod  usually  have  a  blueish  cast;  they  are  partly  vitrified,  and  brittle.  Hard 
hndkm  are  the  best  burned,  red  bridk.  Soft  bricks  are  those  which  are 
Buler-bumed.  and  are  paler  than  the  hard.  In  addition  to  the  amount 
cf  banting,  the  color  of  brick  is  much  affected  by  the  quantity  of  iron  or 
Bae  in  the  clay;  the  presence  of  iron  peroxide  produces  a  red  brick  while 
Inne  has  a  tendency  to  make  it  yellow.  The  common  standard  of  brick 
a  the  United  States  is  8i'x4'x2i*;  in  England,  8rx4rx2r. 

Face  brick  is  made  from  one  of  more  specially  selected  clays,  mixed  if 
necessary  to  give  the  desired  chemical  properties  and  color.  The  bricks 
■re  pressed  in  the  molding  machine,  hence  the  name  "  pressed  brick." 
T^ey  are  also  sometimes  re-pressed.  The  standard  size  in  the  United  States 
a  8f'x4'x2r. 

QIased  brick  is  a  brick  coated  with  enamel,  a  fusible  salt.  A  common 
^qtiid  glass  for  glazing  is  composed  of  silicic  acid  (23.2  per  cent.),  soda 
(5.9),  potash  (2.5),  water  (65.4).  The  glazing  may  be  in  various  colors 
«Mi  conse<;piently  pretty  patterns  may  be  obtained.  Glazed  bricks  are 
used  in  buildings  and  subways;  they  are  hygienic  as  well  as  ornamental. 
Vitrified  brick. — Vitrification  is  obtained  from  the  thorough  burning 
of  a  highly  nliceous  clay  or  of  a  clay  mixed  with  a  large  amount  of  siliceous 
and. 

Terra  Cotta,  meaning  baked  earth,  is  made  of  a  si^ecially  graded  clay  or 
days  mixed  with  a  certain  amotmt  of  siliceous  sand,  if  necessary,  to  secure 
the  desired  amount  of  vitrification.  After  molding  and  drying,  the  mix- 
tore  IS  baked.  The  surface  of  terra  cotta  may  also  be  glazed  like  that  of 
t^  common  glazed  brick  and  tile. 

Fire  brick  is  used  for  the  lining  of  furnaces,  chimneys,  etc.  It  is  made 
from  the  natural  fire-clay  of  which  large  beds  are  foimd  in  New  Jersey  and 
elsewhere.  It  is  a  high  graded  hydrated  silicate  of  alumina,  containing 
preferably  not  over  4  per  cent,  of  impurities.  The  clay  contains  a  large 
proportion  of  silica  (sand),  and  sometimes  more  is  added  to  insure  its  re- 
nra^rtory  quality.  Tne  manufacture  is  similar  to  that  of  common  brick, 
^ut  Twith  the  fire-clay  the  product  is  vitrified. 

PnviBf  brick  is  not  so  much  vitrified  as  fire  brick.^       ^^  (^or»al(> 

,..     .  ,.  .        J.     .,  Digitized  by  ^^UUyle 

brick  IS  ordinary,  hard  bnck.  ^ 


416  72.'-BUILDING  STONES  AND  CEMENTS. 

(3)  Concrete  (fio-aute). 
(Sbb,  also,  Concrbts  Masonrt,  pagb  439.) 
Concrete*  is  composed  of  a  mairix  possessing  cementing  propel 
Uioroughly  mixed  and  united  with  an  aggregatt  or  base  composed  of  I 
ments  of  hard,  imperishable^mineral  substances,  the  whole  forming  a  I 
compact,  enduring  mass.  The  matrix  is  the  cement-sand-watcr  nw( 
while  the  aggregate  is  the  crushed  rock  or  gravel  base. 

Mixture. — ^The  cement  and  sand  are  thoroughly  mixed  dry  in  the  i 
proportion,  enough  water  being  added  subsequently  to  form  a  pastoj 
wet  sand.     After  this  matrix  has  been  carefully  kneaded,  the  ags 
which  has  previously  been  washed  of  all  dirt  and  other  injurious  : 
is  added,  and  the  whole  mass  thoroughly  mixed.     It  should  be  pd 
pV  fe  immediately  and  tamped,  with  the  water  just  flushing  the  r 

An  ideal  concrete  is  one  in  which  the  entire  surface  of  every  ^ 
sand  is  covered  with  the  mortar  paste,  with  the  f^ns  nearly  touching  i 
other  but  with  no  voids;  and  in  which  also  all  mterstices  of  the  agr*^ 
are  completely  filled  with  the  matrix,  pressing  firmly  against  every  t 
An  unduly  Uurge  proportion  of  cement  may  make  the  mass  tmneo 
strong  and  expensive,  while  too  little  cement  will  render  it  porous  ai 
possibly  too  weak.  Where  great  strength  is  not  essential  a  cheaper  bra 
of  cement  may  be  used  instead  of  the  most  expensive,  perhaps  used 
greater  proportion,  sufficient  to  fill  all  sand  voids,  thus  rendering  the  m* 
non-porous  at  no  greater  cost.  This  is  an  essential  consideration  in  locj 
ities  where  frosts  are  liable  to  work  injuriously  upon  the  mass  of  concrel 
if  porous.  As  with  cement,  in  regard  to  voids  in  the  sand .  so  with  the  matri 
regarding  voids  in  the  a^^regate.  An  excess  of  matrix  means  excessi 
cost,  while  a  deficiency  gives  a  porous  concrete.  The  latter  is  avoided  1 
thorough  tamping  and  proper  flushing,  and  by  varying  the  proportio 
if  necessary. 

Proportions. — ^The  proportions,  by  bulk,  in  mixing  concrete  are  Qsoall 
based  on  1  of  cement,  2  to  8  of  sand,  and  4  to  7  of  aggre^te,  dependi^ 
upon  the  nature  and  class  of  the  work  as  well  as  the  quality  and  icind 
materials  available.  Portland  cement  is  the  best,  and  cosu  more  than  tJ 
other  brands.  It  is  usually  spedfied  in  first  class  work.  In  ordinary  wo: 
it  often  pves  better  results  than  the  cheaper  brands,  at  no  greater  coi 
because  it  **  goes  further  ";  bearing  in  mind  of  course  that  if  scantily  osi 
the  matrix  will  be  more  or  less  porous.  A  greater  proportion  of  sand  a 
be  used  in  the  matrix  if  it  is  fine  and  siliceous,  hence  a  little  money  spc 
on  sand  will  sometimes  save  a  much  greater  sum  on  cement.  Lastly,  rau 
less  matrix  and  consequently  less  cement  is  required  if  the  aggregate 
graded  to  different  sizes,  lessening  the  voids. 

The  voids  in  sand  amotmt.  generally,  to  about  33  or  34%  of  the  gro 
bulk;  in  gravel,  to  about  the  same;  in  broken  sandstone,  to  about  40  to  425 
in  broken  trap,  to  about  45  to  50%.  Generally,  the  percenta|[e  of  voids 
greater  in  the  freshly  broken,  hard,  flint-like  rocks,  and  less  m  the  soft 
rock  which  leave  the  crusher  with  less-defined  edges.  With  gravel,  wh< 
the  edges  have  worn  away,  the  percentage  of  voids  is  the  least,  hence  gra> 
is  the  most  economical  aggregate  to  use  for  concrete  because  less  cemer 
or  mortar,  is  required.  For  the  same  reason,  basalt  or  trap  arc  the  mc 
expensive,  although  far  superior  for  many  purposes. 

Economy  in  cement  may  be  practiced  by  grading  the  size  of  materia 
as  previously  noted;  thus,  a  coarse  and  a  fine  sand  may  be  used  togetfa 
in  forming  the  matrix,  while  the  aggregate  may  consist  of  graded  grav 
or  gravel  and  broken  stone. 


*  Before  hydraulic  cement  became  recognized  as  an  essential  ing: 
dient  in  concrete,  lime  of  greater  or  less  hydraulic  properties  was  usi 
sometimes  mixed  with  hydraulic  cement  or  asphalt,  etc.    Thus, 

Kind  of  concrete.  Mairix,  Auregate. 

Hydraulic  cement  c.      Hydraulic  cement  mortar,      l  Broken    stone, 

"         Ume         *'  "         lime  *'  I  cnished  brick,  slag 

Asphalt     cement    "       Asphalt      cement     "  |  cinders,     pebbles, 

J  gravel,  etc 
"  Concrete  "  is  now  universally  recognized  as  hydiaulic  cement  concrc 


CONCRETE.    BLOCK  STONE,  417 

CcfliciitiSand  lHix.-^To  get  the  proper  proportiod  of  cement  to  sand 
in  the  matrix:  Determine  the  percentage  ot  voids  in  the  sand  by  noting 
the  quantity  c  of  water  re<iuired  to  "  nush  "  to  the  level  in  a  water-ti^t 
box  filled  with  an  5  qiiantity  of  the  sand  to  be  tised;  then  the  proportion 
r  of  cement  to  sand  should  be  about  1.1  c  :  5.  It  is  to  be  noted  that  the 
amotmt  of  cement  required  is  thus  about  10%  in  excess  of  the  voids  in  the 
sand,  which  is  as  it  would  be,  as  the  sand  grains  will  be  coated  with  the 
cement  and  separated  somewhat  from  each  other.  For  example,  using  sand 
with  84%  voids,  the  ratio  of  cement  to  sand  would  be  about  1:2).  In 
practice  this  ratio  is  sometimes  increased  to  1  :  2,  1  :  H,  or  1  :  1,  depending 
upon  the  character  and  importance  of  the  work,  and  also  upon  the  character 
and  guallty  of  the  materials.  A  1  :  2  mix  is  generally  considered  good 
I»actice  for  a  cement  mortar  in  first  class  masonry  work;  while  a  1  :  1  mix 
makes  an  excellent  wearing  surface  when  used  as  a  finishing  coat  for  concrete 
walks.  •-'^ 

CeniMii-SaiiitBrokeii-ctoiie  Mix. — ^To  get  the  proper  proportion  of 
matrix  to  aggregate:  Determine  the  percentage  of  voids  in  the  aggregate  or 
broken  stone  by  notixig  the  quantity  m  of  water  required  to  "  flush  "  to 
the  level  in  a  water-tight  box  filled  with  an  a  quantity  of  broken  stone; 
then  the  proportion  of  matrix  to  aggregate  should  be  about  1.1  m  :  a. 
For  example,  with  46%  voids  in  the  aggregate,  the  ratio  of  mortar  to  broken 
stcme  should  be  about  1  :  2. 

Further,  if  we  assume  the  sand  voids  at  84%.  as  above,  the  cement- 
sand-broken  stone  ratio  would  be  about  1:24:6.  Note  that  the  quantity 
of  sand  in  the  matrix,  slightly  increased,  really  determines  the  bulk  of  the 
matrix  itself  in  estimating  the  above  ratio.  In  practice,  this  ratio  is  som4' 
Umts  increased  to  1:2:4  mix  for  first  class  building  walls,  piers  and 
btittmses;  to  1  :  l|r  :  8  mix  for  columns  and  heavy  beams  of  concrete* 
steel;  and  to  1  :  1  :  2  mix  for  lighter  reinforced  members. 

Sise  of  Broken  Stone. — ^The  size  to  which  the  stone  must  be  crushed 
or  broken  will  be  governed  somewhat  by  the  size  of  the  concrete  mass. 
For  large  bridge  piers,  stone  which  will  pass  through  a  2Hn.  ring  in  anv 
way  is  often  aUowed.  The  most  common  specification,  however,  for  such 
(omidations  stipulates  the  2-in.  ring.  For  certain  classes  of  work  both 
tok  upper  and  a  lower  limit  are  specined;  as  for  instance,  rock  that  will  pass 
through  a  2i-in.  but  not  through  a  1-in.  ring,  called  the  2^ — l'  grade; 
amilarly,  we  may  have  a  2* — f  grade,  a  If* — r  grade,  etc.  Much  refine- 
jnent  in  this  rrapect  is,  however,  unnecessarily  expensive,  excepting  perhaps 
in  building  construction  and  notably  in  concrete -steel  work.  For  the  latter, 
sizes  as  small  as  the  pea-grade  size  are  used  for  reinforced  floors. 

(3)  Block  Stone. 

By  this  is  meant  the  conunonly  named  "  artificial  stone  '*  proper.  It 
is  manufactured  usually  at  the  factory  and  shipped  to  the  site  for  er»:tion. 
Among  the  most  important  kinds  are  the  following: 

BMoo-Colniet. — ^This  was  invented  by  Coignet,  a  Frenchman,  and 
consisted  of  Fortland  cement,  siliceous  hydraulic  cement,  and  clean  sharp 
sand,  thoroughly  mixed  with  a  small  quantity  of  water,  and  placed  in  mokls 
to  set.  for  use. 

Sand  bricks  are  manufactured  from  lime  and  sand  mixed  with  water 
to  the  consistency  of  a  mortar.  This  mortar  is  molded  into  bricks  or  blocks 
ami  then  hardened  by  heating. 

Portland  stone  is  composed  of  a  mixture  of  Portland  cement  with  water 
sad  sand  or  gravel,  placed  in  molds  and  thoroughly  rammed  for  setting. 
It »  made  plain  and  also  ornamental. 

McMortrie  stone  is  made  of  Portland  cement  concrete  to  which  is  added 
a  solution  of  castile  soap  and  a  solution  of  alum,  forming  compounds  of 
ahunina  potash  and  certain  acids,  which  tend  to  "  set  "  the  concrete  quickly. 
It  is  not  attacked  by  the  weather. 

Ransome  stone. — ^The  amegate  consists  of  broken  granite,  grave!  or 
sand;  the  matrix,  a  silicate  of  soda  and  sand  immersed  in  a  hot  solution  of 
chknide  of  cakium.     It  makes  a  very  good  building  stone. 

Serd  stone. — ^The  matrix  consists  of  a  solution  of  magnesium  chloride 
added  to  the  oxide  of  magnesium.  The  aggregate  is  a  finely  crushed  or 
powdered  stone  of  good  quality.  It  is  extremely  hard  and  is  used  for 
unitatkm  marble,  emery  wheels,  etc  ^,g,  .^^^  ^^  GoOglc 


418  22.^BUILDING  STONES  AND  CEMENTS. 

EXCERPTS  AND  REFERENCES. 

Lutet  and  Cements  Useful  to  Enflaeers  (By  S.  S.  Sadtler.  Paper. 
Phila.  Engre.  Club,  June  4,  1»04;  Eng.  News,  Tan.  6,  1905).— Watefv4>roof 
Compositions. — Asphalt  fluid  coatings  are  useful  for  reservoir  walls,  con- 
crete foundations,  brick,  wood,  etc.  Asphalt  only  partly  dissolves  in 
petroleum  naphtha,  but  heated  in  a  steam-jacketed  kettle  and  not  thinned 
out  too  much,  a  mixture  of  the  two  may  be  obtained  in  which  the  part  of 
the  asphalt  not  dissolved  is  held  in  suspension.  Asphalt  is  entirely  soluble 
in  benzol  or  tuluol  which  are  about  the  cheapest  solvents  for  all  the  con- 
stituents of  asphalt.  Tar  and  pitch  are  sometimes  used  in  this  connection, 
but  tar  contains  water,  light  oils,  and  free  carbon,  and  does  not  wear  as 
well  as  good  refined  asphalt;  and  pitch  contains  free  carbon,  which  is  some- 
times objectionable  when  thinned  out  with  a  solvent.  The  asphalt  alone  is 
somewhat  pervious  to  water,  and  this  is  improved  bv  adding  about  one- 
fourth  its  weight  of  paraffin,  and  made  better  if  in  addition  a  little  boiled 
linseed  oil  is  added  also.  For  thicker  compositions,  where  body  is  required, 
asbestos  stone  powder,  cement,  etc.,  may  be  added  as  fillers.  Lutes  oc 
linseed  oil  thickened  with  clay,  asbestos,  red  or  white  lead,  etc.j  are  water- 
proof if  made  thick  enough.  These  are  much  used  for  steam  jomts.  Flax- 
seed meal  made  into  a  paste  with  water  is  often  serviceable,  the  oil  con- 
tained serving  as  a  binder  as  the  water  evaporates.  Oil-Proof  Compost 
tions. — ^The  most  useful  lute  for  small  leaks,  etc.,  is  the  well-known  "hekto 
graph  composition."  as  follows:  Good  glue  or  gelatin  (2  parts),  glycerine  (1), 
water  (7) ;  this  is  applied  warm  and  stiffens  quickly  on  cooling.  Another 
composition:  a  stiff  paste  of  molasses  and  flour.  Another  preparation 
impervious  to  oil  vapors  is  the  "flaxseed  poultice."  mentioned  above,  which 
is  proof  to  oil  vapors.  A  stiff  paste  of  glycerine  and  litharge  makes  one  of 
the  strongest  cements  (oil-proof,  water^proof,  acid-proof,  etc.),  forming  a 
chemical  combination  and  setting  in  a  tew  minutes;  if  a  little  water  is 
added  it  sets  more  slowly,  often  an  advantage;  it  is  mixed  when  required 
for  use.  Plaster  of  Paris  wetted,  by  itself,  or  mixed  with  asbestos,  straw, 
ludr,  etc.,  is  useful.  A  solution  of  silicate  of  soda  made  into  a  stiff  paste 
with  carbonate  of  lime,  hardens  in  6  to  8  hours.  Add-Proof  Compositions. — 
Several  kinds  given.  Other  Proof  Compositions. — ^For  hydrocarbon  gases; 
chlorine;  general  purposes.  Elastic  cements;  marine  glue;  gasket  com- 
positions; leather  cements,  stone,  iron  and  crucible  cements;  etc. 

Cost  of  Portland  Cement. — Portland  cement,  in  and  around  New  York, 
costs  from  $1.10  to  $1.25  per  barrel,  depending  upon  the  guality  and  quan- 
tity required.    The  price  varies  greatly  according  to  locality. 

A  Cement  Which  is  Proof  Against  Sea-Water  (By  S.  B.  Newberry. 
Cement  Age,  Jan.,  1907;  Eng.  News,  Dec.  12,  1907).— ^This  cement  is  an 
iron-ore  cement  and  has  been  manufactured  for  several  years  in  Germany. 
Its  composition,  as  compared  with  an  average  commercial  Portland  is  as 
follows: 

Port.  Ore- 

Gem.  Port. 

Magnesia..  1.6  1.5 

Sulph.  Anhyd.         1.6  1.0 

Alkalies,  etc.  1.0  1.0 


Portland 

Ore-Port 

Cement. 

Cement. 

Silica 

22.0 

20.5 

Alumina 

8.0 

1.5 

IronOxid 

3.5 

11.0 

Lime 

63.5 

63.5 

100.0        100.0 
Important  lihistnitioas — 

Description.  Enff.  Rec. 

A  briquette  storage  tank,  St.  Louis  testing  laboratory  JuL  24,  '00. 


d  by  Google 


23.— QUARRYING. 

1711611  a  qtiany.  of  whatever  nature,  is  proposed  to  be  opened,  the  site 
shouki  be  studied  carefully  with  two  main  points  in  view,  namely,  ( 1)  the 
most  economic  methods  of  mining  the  material,  and  (2)  the  best  ana  cheap- 
est means  of  transporting  the  product  when  mined.  It  is  well  to  remember 
that  of  the  two  methods  of  transportation — ^watcr  and  rail — ^the  former  is 
the  great  "  leveler  "  in  the  equalization  or  adjustment  of  frdght  rates. 
Consideration  must  also  be  had  to  water-supply  and  drainage,  whether  the 
machinery  is  operated  by  electric-  or  steam  power.  On  opening  the  quarry, 
the  surface  stripping,  consisting  of  organic  and  decomposed  mineral  matter, 
should  be  renioved  ahead  of  the  quarrying.  The  cost  of  stripping  and 
renaoving  the  weathered  rock  is  usually  a  very  considerable  item,  and  in 
new  quarries  opened  for  local  work  this  cost  must  be  proportioned  to  the 
total  yardage  required.  * 

Sand  and  Qravtl^ — ^An  ideal  sand  and  gravel  plant  is  one  in  which  the 
bank  is  sufficiently  elevated  to  allow  of  hydraulic  operations.  The  stream 
or  streams  of  water  may  be  furnished  by  gravity  or  by  pumping.  The 
gravel  and  sand  are  slmced  into  revolving  screens  of  two  or  more  sizes 
which  sort  the  material,  and  from  which  it  passes  into  the  bunkers,  ready 
to  be  loaded  on  scows  or  cars.  The  revolving  screens  are  not  very  durable 
and  probably  the  best  are  common  steel  plate,  perforated.  The  holes  are 
puncned  the  required  size  for  sorting  out  the  sand  and  gravel.  The  material 
as  it  passes  into  the  bunkers  is  thoroughly  washed  and  hence  clean  and  ready 
for  use. 

The  C.  O.  Bartlett  and  Snow  Co.,  of  Cleveland,  Ohio,  manufacture  a 
noovable  combined  gravel  digging  and  screening  plant,  operated  on  a  track. 
The  particular  machine  illustrated  in  Eng.  News,  May  12,  1004,  weighs  25 
tons,  is  equipped  with  a  26-HP.  engine  and  boiler,  and  has  a  capacitv  of 
30  to  40  cu.  yds.  per  hour.  *'  The  gravel  and  sand  are  discharged  m)m 
the  elevator  buckets  into  a  belt  conveyor,  which  delivers  to  a  rotary  screen. 
The  screen  discharges  into  bins,  from  which  the  material  is  drawn  off  into 
gondola  cars  or  wagons."  The  fine  dirt,  or  dust,  is  rejected  by  a  belt  con- 
veyor to  a  waste  dump.  The  excavating  buckets  have  a  capacity  of  about 
three-foorths  of  a  cuoic  yard. 

Ri^<ap. — ^This  class  includes  all  rock  which  may  be  irregular  in  size 
and  shape,  and  especially  used  for  '*  filling  "  in  breakwater  construction, 
rodc-fill  dams,  slope  walls,  paving,  and  crushing  into  broken  stone  for 
concrete,  etc.  The  idea  in  blasting  this  material  is  thoroughly  to  loosen 
as  moch  of  it  as  possible  for  the  labor  of  .drilling  and  cost  of  explosives, 
hence  the  blasts  are  usually  heavy  and  deep  seated.  Dynamite  high  in 
oitroKlycerin,  say  75%,  is  best. 

Block  Stone. — Building  stone  is  quarried  in  sizes  considerably  larger 
than  the  finished  dimensions  required,  in  order  to  allow  for  necessary  waste 
in  squaring  and  dressing.  There  are  four  methods  employed,  each  one 
of  ^raich  is  economically  suited  to  the  special  nature  of  the  quarry,  the 
material,  and  the  product  desired. 

Hand  Tools  are  employed  where  the  stone  is  bedded  in  thin  layers  and 
can  be  worked  with  pick,  sledge  and  bar,  and  by  hand-drilling  and  wedging. 
Flagstones,  for  sidewalks,  are  easily  hand -quarried,  being  a  thin-bedd^ 
sandstone;  also  some  limestones,  shales,  etc. 

Channeling  Mackhus  are  used  in  quarrying  blocks  of  sandstone.  Kme- 
stone  and  marble.  In  many  quarries  the  rock  is  bedded  in  various  com- 
mercial thicknesses,  the  channels  are  cut  to  the  required  depth,  and  the 
blocks  are  wedged  off  in  dimensions  as  ordered. 

The  first  method  used  was  that  of  "  broach  channeling  "  which  consists 
Kji  drilling  rows  of  holes  spaced  about  an  inch  apart,  and  then  breaking 
down  theie  spaces  by  means  of  a  tool  called  a  "  broach.'* 


419 


d  by  Google 


420  2Z-^UARRYING. 

The  "  Steel  Gang  **  channeler  consists  of  a  gang  of  tools  or  chisels  ar- 
ranged side  by  side  and  forming  a  narrow  cutter  several  inches  in  length. 
Pig.  1  shows  a  "  swivel  dead  "  channeler,  size  Z,  with  boiler,  manufactured 
by  the  Sullivan  Machinerv  Co..  of  Chicago.  This  company  also  manu- 
factures the  "  rigid-head  channeler,  used  for  vertical  cuttinjs,  and  the 
"  tmdercutting  "  channeler.  used  for  horizontal  cutting;  also  various  special 
types. 


Fig.  1. 

The  many  recent  improvements  in  channeling  machines  have 

dered  them  valuable  not  only  in  quarrying  dimension  stone  but  also 
in  certain  classes  of  rock  excavation,  notably  in  the  excavation  of  chan* 
nels  or  waterways  through  solid  rock,  sinking  of  laree  pits  or  shafts, 
etc.,  for  water  power,  and  in  general  where  the  sides  of  the  finished  work 
are  required  to  be  fairly  smooth  or  regular. 

The  Z  machine,  together  with  all  the  Sullivan  channelers  of  other  types, 
may  be  operated  by  compressed  air  as  well  as  steam.  Air  is  preferable 
under  conditions  necessitating  the  use  of  a  number  of  machines  at  points 
distant  from  the  central  power  plant  and  from  each  other.  In  this  case  a 
suitable  reheater  is  mounted  on  the  machine  to  secure  the  utmost  efficiency. 
The  Z  channeler  used  in  constructing  the  wheel  pits  at  Niagara  Falls  and 
the  great  canal  of  the  Lake  Superior  Power  Co.,  at  Sault  Ste.  Marie,  were 
driven  by  air  as  above  described. 

The  approximate  amount  of  air  at  80  pounds  pressure  necessary  to 
operate  the  Y  and  Z  channelers  is,  without  reheating,  about  850  feet  per 
minute.  The  size  64  machine  will  use  about  300  feet  under  the  same  con- 
ations, while  the  VX  channeler  will  use  approximately  200  feet. 


CHANNEUNG  MACHINES. 


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423  2^-QUARRYlNG. 

Ex|)locives  are  employed  principally  in  auanying  the  harder  rocks, 
as  granite,  syenite,  trap.  etc. ;  but  they  are  used  extensively  also  in  quarr>'- 
ing  sandstone,  limestone  and  marble,  in  the  smaller  quarries  where  cannelng 
machines  have  not  been  introduced.  In  blasting,  the  explosive  mtxst  not 
be  so  violent  as  to  shatter  the  detached  portions  too  much,  hence  a  coarse 
gunpowder  is  mostly  oreferred  instead  of  the  instantaneous  dynamite. 
Where  dynamite  is  used  it  is  generally  of  the  lower  grades,  containLig  say 
30  to  40%  nitroglycerin  for  ordinary  work,  unless  large  masses  of  very 
heavy  rock,  like  granite,  are  to  be  opened  up,  in  which  case  00%  dynamite 
or  even  75%  dynamite  is  sometimes  usecl.  The  liquid  nitroglycerin  so 
useful  in  submarine  blasting  is  seldom  employed  in  quarrying,  being  too 
violent,  as  well  as  dangerous  to  handle.  Large  blocks,  detached  from  the 
quarry  by  blasting,  are  subsequently  broken  up  into  the  required  dimension, 
by  drilling  holes  m  line  and  wedging,  that  is.  by  plug  and  feather. 

Rock  Drillf  used  in  quarrying  may  be  classed  imder  three  heads,  as  follows: 

The  Hammer'  or  "  Jumper  "  Drill,  which  includes  the  smaller  sizes  such 
as  may  be  operated  by  one  man  who  also  wields  the  hammer,  ^ivetghing 
say  4i  lbs.;  and  also  the  larger  sizes  or  jumpers  proper,  which  are  operated 
by  one  man  ttuning  and  with  two  men  striking  (4i-Ib.  and  10-lb.  hammers 
for  two  hand  drilHng.  and  two  10-lb.  hammers  for  three-hand  drilling). 

The  "Chum'*  Drill,  a  heavy  drill  6  to  8  ft.  in  len^h.  operated  usually 
by  two  or  three,  sometimes  six,  men  who  raise  the  dnll,  let  it  fall  into  the 
hole,  catch  it  on  the  rebound,  etc. — the  most  economical  hand  drill  for 
moderately  deep  holes,  when  nearly  vertical. 


Fig.  2. 

The  "  Percussion  "  Drill,  which  is  simply  a  chum  drill  attached  to  the 
piston  of  a  steam-  or  compressed  air  cylinder,  and  by  far  the  most  effective 
drill  for  quarrying,  mining,  tunneling  and  general  rock  excavation.  Pig  2 
illustrates  a  percussion  drill  of  the  Ingersoll-Kand  type  movmtedon  a  "quar- 
ry bar,"  which  arrangement  is  specially  useful  tor  drilling  **  plug  and 
feather  "  holes,  for  "broaching"  in  granite  and  similar  materials,  for  taking 
out  **  key  blocks,"  for  "  lofting  "  work  in  quarryi^gmaterial  with  a  well 
defined  cleavage,  and  for  general  contract  work.  The  "  Light  3-inch  '* 
bars  have  a  length  (over  all)  of  10  ft.,  a  cutting  length  of  8  ft. -4  ins.,  are 
suitable  for  2-2 f  in.  cyl.  dia.  of  drill,  and  weigh,  with  weights  but  without 
drill.  945  lbs.  The  **  Standard  4Hnch  "  bars  have  a  length  (over  all)  of 
12  ft.,  a  cutting  length  of  10  ft.,  au-e  suitable  for  2i-3|  in.  cyl.  dia.  of  drill, 
and  weigh,  with  weights  but  without  drill,  1625  lbs.  The  price  of  the 
Light  bars  is  1175.00  and  of  the  Standard  bars  $250.00. 

Table  2.  page  424,  gives  dimensions  and  weigh ts^L  the iRand  "tittle 
Qiant     percxission  drill  (Fig.  3).  Digitized  byVjOOglc 


ROCK  DRILLS.  423 

*  Perciipsion  drills  may  be  mounted  on  the  "  tripod,  "  which  is  a 
most  oommon  method;  oq  the  "  column  "  or  vertical  bar;  and  on  the  "  gad- 
der "  or  adjustable  carnage  designed  especially  for  quarry  work  where 
parallel  holes  are  to  be  drilled  in  any  plane.  "  Used  in  connection  with  the 
channeW  it  is  applied  in  '  lofting.'  or  drilling  the  horizontal  undercutting 
boles  in  material  which  has  been  channeled.  Used  in  '  plug  and  feather 
work/  it  breaks  the  large  blocks  cut  free  by  the  channelers.  (See  page 
46.) 

"  I  Air,  used  directly  in  spHtting  granite  and  creating  working 


beds  in  the  qiiarry,  is  a  recent  novelty  practised  successfully  by  the  North 
Carolina  Gninite  Corporation  at  Mt.  Airy,  N.  C,  and  described  fully  in 
"  liine  and  Quarry  "f  of  May.  1005.  The  guarry  consists  of  a  solid  mass 
of  granite  without  cleavage  planes  or  beds  m  any  direction  and  the  com- 
pressed air  is  used  to  create  artificial  beds  to  which  to  work: 

In  the  center  of  the  sheet  or  area  to  be  lifted,  a  drill  hole  two  or  three 
inches  in  diameter  is  sunk  six  or  eight  feet  in  depth,  depending  on  the 
gnastst  thickness  of  stone  required.  The  bottom  of  the  hole  is  enlarged 
into  a  pocket  by  exploding;  half  a  stick  of  dynamite.  A  small  charge  of 
powder,  about  a  handful,  is  then  exploded  m  the  pocket,  thus  starting  a 
norixontal  crack  or  cleavage  across  its  greater  diameter.  Charges  increas- 
ing in  size  are  now  exploded  in  the  cavity,  the  drill  hole  being  plugged  at 
each  blast,  to  confine  the  powder  gases  and  thus  exert  a  more  or  less  con- 
rtant  force  upon  the  stone.  After  the  cleavage  has  extended  to  a  radius 
of  75  or  100  teet  in  all  directions,  a  pipe  is  cemented  into  the  hole  and  con- 
nected by  means  of  a  globe  valve,  to  the  air  pipe  line  from  an  air  compressor 
Compressed  air  at  70  to  80  pounds  pressure  is  gradually  admitted  and  the 
cleavage  rapidly  extended  until  it  comes  out  upon  the  hillside  in  a  thin 
ed^e.  A  sheet  of  several  acres  in  extent  may  be  raised  in  this  manner, 
anording  a  bed  plane  approximately  horizontal,  to  which  the  quarrymen 
can  work,  thus  securing  stone  of  any  required  thickness.  .  .  .  The 
time  (formcrlyl  required  for  extending  the  cleavage  by  powder  for  100  feet 
was  between  two  and  three  weeks,  while  to  split  the  larger  area,  between 
100  and  225  feet  radius,  required  only  half  an  hour  when  compressed  air 
was  used.  ...  Its  equipment  is  modem  in  every  respect,  and  includes 
35  plugt  drills,  3  Sullivan  tripod  drills,  4  Sullivan  quarry  bars,  15  surfacing 
machines,  and  00  small  hand  tools.  These  are  all  operated  by  air  power 
from  a  Sullivan  Corliss  air  compressor  of  the  two  stage  type,  with  a  piston 
(h^Iaoetnent  of  2000  cubic  feet  of  free  air  per  minute  at  78  r.p.m.,  against 
80  to  100  potmds  terminal  pressure.  The  dimensions  of  the  compressor 
sre  as  follows:  Steam  cylinders,  16  and  28  in.  by  42  in.  stroke;  air  cylinders, 
2%  and  16  in.  by  42-in.  stroke. 

Coat  off  Ooarryhis  Rabble  and  Dimension  Stone  for  the  Buffalo.  N.  Y., 
Breakwater  (By  Emile  Low.  Eng.  News.  Oct.  20.  1904.— Tabulated  costs, 
method  of  <niarrying,  and  plant  used  are  given.  The  cost  for  explosives, 
which  includes  powder,  dynamite  and  fuses,  per  ton  of  stone,  all  kinds, 
quarried  was:  For  May  (1908),  1. Sets.;  July  (1903),  2.0 cts.:  August  (1903), 
2.1  cts.  About  1  lb.  of  powder  was  tised  for  every  7  tons  of  stone  quarried, 
and  1  lb.  of  djmamite  tor  every  67  tons  of  stone.  One  fuse  was  tised  for 
t^rtif  Si  tons  of  stone  quarried.  Total  cost  of  quarrying  1  ton  of  stone, 
^^ing  and  placing  same  aboard  of  scows,  as  follows:  Labor,  33  cts.;  coal, 
4  cts.;  explosives,  2  cts.:  miscellaneous,  5  cts.;  total,  44  cts.  Thisis  exclu- 
Qve  of  cost  of  plant  and  deterioration. 

*  Pneumatic  drills  for  hand  service,  like  pneumatic  riveters,  are  the 
kitest  development  in  rock  drilling  by  machinery.  They  go  by  the  various 
oames  of  "  Little  Jap,"  "  Little  Imp,  *'  and  "  rlug  "  drills,  and  do  remark- 
able work. 

t  Published  by  the  Sullivan  Machinery  0}.,  Chicago. 

i  The  plug  dnil  is  a  pneumatic  power  drill  for  hand  service  similar  to 
other  pneumatic  hand  tools,  as  the  pneumatic  riveter,  etc. 


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24.— STONE  CUTTING. 

'  Thfe  1bllowin£:  is  from  the  report  of  the  American  Society's  Com- 
mittee* to  secure  uniformitv  of  terms.  The  matter  is  re-arransed. 
for    convenience,    in    parallel    coltmins. 


STONES    CLASSED    ACCORDINO 
TO    FINISH. 

All  stones  used  in  building  are 
divided  into  three  classes,  accor- 
ding to  the  finish  of  the  surface. 


I.  Rough  stones  that  are  used  as 
they  come  from  the  quarry. 


II.  Stones    rotighly    squared    and 
dressed. 


III.  Stones  accurately  squared  and 
finely  dressed. 


In  practice,  the  line .  of  separ- 
ation between  them  is  not  very 
distinctly  marked,  as  one  class 
gradually  merges  into  the  next. 


I.  Unsquared  Stones.  —  This 
class  covers  all  stones  which  are 
used  as  they  come  from  the  quairy, 
without  other  preparation  than  the 
removal  of  very  acute  angles  and 
excessive  projections  from  the 
general  figure.  The  term  *'  back- 
ing "  which  is  frequently  applied  to 
this  class  of  stone,  is  inappropriate, 
as  it  proF>erly  designates  material 
used  in  a  certain  relative  position 
in  a  wall,  whereas  stones  of  this  kind 
may  be  used  in  any  position. 


TOOLS  EMPLOYED. 

The   Hand   Hamnwr,   weiehins 
from  2.to  6  pounds  is  used  in  dril- 

Tf  1  nuuu  nonwrxr 


Fig.  1. 

ling    holes,    and    in    pointing    and 
chiseling  the  harder  rocks. 

The   Plu£,   a   truncated   wedge 
of  steel,  and;  the  Feathers  of  haJf- 


PKjgand 

Fig.  2. 
rotind  malleable  iron  are  used  for 
splitting  tmstratified  stone.  A  ro\r 
of  holes  is  made  with  the  Drill  on 
the  line  on  which  the  fracture  is 
to  be  made;  in  each  of  these  holes 
two  feathers  are  inserted,  and  the 
plugs  lightly  driven  between  them. 
The  plugs  are  then  gradually  driven 
home  by  light  blows  of  the  hand 
hammer  on  each  in  succession  until 
the  stone  splits. 


DrtUft. 
Fig.  8. 
The  Double  Pace  Hammer  Is  a 
heavy  tool  weighing  from  20  to  30 
pounds,   used  for  roughly  shaping 


U.tta 


D 


Pig.  4. 

stones  as  they  come  from  the 
quarry  and  for  knocking  off  pro- 
jections. This  is  used  only  for  the 
roughest  work. 


» Trans.   Am.   Soc.  C.   E..   vol.  vi.,  p.  297. 
426 


d  by  Google 


CLASSIFIED  FINISH. 


TOOLS  EMPLOYED,       427 


IL  SqaarMl  Stooet^ — ^This  class 
oorers  all  stones  that  are  roughly 
iquared  and  roughly  dressed  on  beds 
and  joints.  The  dressing  is  usually 
done  with  the  face  hammer  or  ax, 
or  in  soft  stones  with  the  tooth-ax. 
Tlie  distinction  between  this  class 
and  the  third  lies  in  the  degree  of 
closeness  of  the  joints  which  is  de- 
manded. Where  the  dressing  on 
the  joints  is  such  that  the  distance 
between  the  general  planes  of  the 
sorfaces  of  adjoining  stones  is  one- 
half  inch  or  more,  the  stones  proper- 
ly belong  to  this  class. 


(a)  Qoarry-faced  stones  are 
those  whose  faces  are  left  untouched 
ss  they  come  from  the  quarry. 


(b)  PHch-laced  stones  are  those 
oo  which  the  arris  is  clearly  defined 
by  a  line  beyond  which  the  rock  is 
cot  awa3r  by  the  pitching  chisel, 
•o  as  to  give  edges  that  are  approxi- 
nately  true. 


(c)  Drafted  Stones  ase  those  on 
which  the  face  is  surrounded  by  a 
diisel  draft,  the  space  inside  the 
draft  being  left  rotigh.  Ordinarily, 
however,  this  is  done  only  on  stones 
m  whk^h  the  cutting  of  the  joints 
is  such  as  to  exclude  them  from 
this  class. 

In  ordering  stones  of  this  class 
the  specifications  should  always 
^ate  the  width  of  the  bed  and  end 
joints  which  are  expected,  and  also 
now  far  the  surface  of  the  face  may 
project  beyond  the  plane  of  the 
edge.  In  practice,  tne  projection 
varies  between  1  inch  axuf  6  mches. 
It  should  also  be  specified  whether 
or  not  the  facet  are  to  be  drafted. 


The  Fac0  Hammtr  has  one 
blunt  and  one  cutting  end,  and  is 
used  for  the  same  purpose  as  the 


i 


Fig.  6. 
double  face  hammer  where  less 
weight  is  required.  The  cutting 
end  is  used  for  roughly  squaring 
stones,  preparatory  to  the  use^ 
finer  tools. 

The  Cavil  has  one  blunt  and 
one  pyramidal,  or  pointed,  end, 
and  weighs  from  15  to  20  potmds. 


I 


^itwcr:^ 


m    O 


.*-^-^^?avII. 


Fig.  6. 
It  is  used  in  quarries  for  roughly 
shaping  stone  for  transportation. 
The  Pitching  Chisel  is  usually 
of  li-inch  octagonal  steel,  spread 
on  the  cutting  ed^e  to  a  rectangle  of 
|x2i  inches.     It  is  used  to  make  a 


ii 


PHchmgOnMl. 

Fig.  7.  Fig.  8. 

well-defined  edge  to  the  face  of  a 
stone,  a  line  being  marked  on  the 
joint  surface  to  which  the  chisel  is 
applied  and  the  portion  of  the  stone 
outside  of  the  line  broken  off  by  a 
blow  with  the  hand-hammer  on  the 
head  of  the  chiseL 

The  Chisel,  of  rotmd  steel  of 
^  to  i  inch  in  diameter  and  about 
10  inches  long,  with  one  end  brought 
to  a  cutting  edge  from  ^  inch  to  2 
inches  wide,  is  used  for  cutting 
drafts  or  margins  on  the  face  of 
stones. 

The  TooUt  Chisel  is  the  same  as 
the  chisel,  except  that  the  cuttinjg 
edge  is  divided  into  teeth.  It  is 
used  only  on  marbles  and  sand- 
stones. 


The    Splitting    Chisel    is 

chiefly  on  the  softer,  stratified 
stones,  and  sometimes  on  fine  archi- 
tectural carvings  in  granite. 


428 


2i.^ST0NE  CUTTING. 


III.    Cot    Stones.— This 

covers  aU  squared  stones  with 
smoothly  dressed  beds  and  joints. 
As  a  rule,  all  the  edges  of  cut  stones 
are  drafted,  and  between  the  drafts 
the  stone  is  smoothly  dressed.  The 
face,  however,  is  often  left  rough 
when  the  constructions  are  massive. 

Roush-pointed^ — When  it  is 
necessary  to  remove  an  inch  or 
more  from  the  face  of  a  stone,  it  is 


Fig.  12. 
done  .by  the  pick  or  heavy  point 
until  tne  projections  vary  from 
i  inch  to  1  inch.  The  stone  is  then 
said  to  be  rough-pointed.  In  dress- 
ing limestone  and  granite,  this 
operation   precedes  all  others. 

Fine-pointed. — If  a  smoother 
finish  is  desired,  rough  pointing  is 
followed  by  fine  pointmg.  It  is 
done    with    a    fine     point.    Fine 


Fine-Wn*0d. 


Fig.  14. 

Sointing  is  used  only  where  the 
nish  made  by  it  is  to  be  final,  and 
never  as  a  preparation  for  a  final 
finish  by  another  tool. 


Crandalled. — ^This  is  only  a 
speedy  method  of  pointing,  the  eflfect 
being  the   same   as  fine   pointing. 


o^^cJS;^;ii. 


Fig.  16. 
except  that  the  dots  on  the  stone 
are  more  regular.  The  variations 
of  level  are  about  i  inch,  and  the 
rows  are  made  parallel.  When 
other  rows  at  right  angles  to  the 
first  are  introduced,  the  stone  is 
said  to  be  cross-crandalhd. 


The  Mallet  is  used  [Instead  of 
the    hand    hammer,    in     pointing. 


softer 


Ikilkt-. 
Pig.  11. 
chiseling,    etc.]    where    the 
limestones  are  to  be  cut. 

The  Pick  somewhat  resembles 
the  pick  used  in  digging,  and  is 
used  for  rough  dressing,  mostly  on 


Fig.  13. 

limestone  and  sandstone.  Its 
length  varies  from  1 5  to  24  inches. 
the  thickness  of  the  eye  being 
about  2  inches. 

The  Point  is  made  of  round  or 
octagonal  rods  of  steel,  from  J  inch 
to  1  inch  in  diameter.     It  is  made 


Fig.  16. 
about  12  inches  long  with  one  end 
brought  to  a  point.  It  is  used 
tmtil  its  length  is  reduced  to  about 
5  inches.  It  is  employed  for  dress- 
ing off  the  irregular  surface  of 
stones,  either  for  a  permanent  fin- 
ish or  preparatory  to  the  use  of  the 
ax.  According  to  the  hardness  of 
the  stone,  either  the  hand-hammer 
or  the  mallet  is  used  with  it. 

The  Crandall  is  a  malleable- 
iron  bar  about  2  feet  long,  flattened 
at  one  end.     In  this  end  is  a  slot. 


in 


i' 


L 


Oncmdall. 


^Zi' 


Fig.  17. 
3  inches  long  and  |  inch  wide. 
Through  this  slot  are  passed  ten 
double-headed  points  of  i-inch 
squared  steel,  9  mches  long,  which 
are  held  in  place  by  a  key. 


d  by  Google 


430 


2A.-'STONE  CUTTING. 


Bush-hammered. — The  rough- 
nesses of  a  stone  are  pounded  ofT  by 
the  bush  hammer,  and  the  stone  is 
then  said  to  be   "  bushed."     This 


i 


Duah  Hammered. 


Fig.  22. 


The  Bush  Hatmmr  is  a  square 
prism  of  steel  whose  ends  are  cut 
mto  a  number  of  pvramidal  points. 
The  length  of  the  hammer  is  from 


ii 


0 


Fig.  2a. 


4  to  8  inches,  and  the  cutting  face 
from  2  to  4  inches  square.  The 
points  vary  in  number  and  in  sice 
with  the  work  to  be  done.  One 
end  is  sometimes  made  with  a 
cutting  edge  like  that  of  the  ax. 


The  Machint  Tools  used  chiefly 
are  the  saws,  planers,  grinders, 
polishers,  etc. 


kind  of  finish  is  dangerous  on  sand- 
stone, as  experience  has  shown 
that  sandstone  thus  treated  is  very 
apt  to  scale.  In  dressing  lime- 
stone which  is  to  have  a  bush- 
hammered  finish,  the  usual  sequence 
of  operation  is  (1)  roiigh-oomting, 
(2)  tooth-axing,  and  (3)  bush- 
hammering. 

Rubbed.  —  In  dressing  sand- 
stone and  marble,  it  is  very  common 
to  give  the  stone  a  plane  surface 
at  once  by  the  use  of  the  stone-saw. 
Any  roughnesses  left  by  the  saw  are 
removed  by  rubbing  with  grit  or 
sandstone.  Such  stones,  therefore, 
have  no  margins.  They  are  fre- 
quently used  in  architecture  for 
string-courses,  lintels,  door- jambs, 
etc.;  and  they  are  also  well  adapted 
for  use  in  facing  the  walls  of  lock- 
chambers  and  in  other  localities 
where  a  stone  surface  is  liable  to 
be  rubbed  by  vessels  or  other 
moving  bodies. 

Diamoad  Panels.  —  Sometimes 
the  si>ace  between  the  margins  is 
stmk  immediately  adjoining  them, 
and  then  rises  gradually  until  the 
four  planes  form  an  apex  at  the 
middle  of  the  panel.  In  general, 
such  panels  are  callled  diamond 
panels,  and  the  one  just  described 
IS  called  a  sunk  diamond  panel. 
When  the  stu^ace  of  the  stone  rises 
gradually  from  the  inner  lines  of 
the  margins  to  the  middle  of  the 
panel,  it  is  called  a  raised  diamond 
panel.  Both  kinds  of  finish  are 
common  on  bridge  quoins  and 
similar  work.  The  details  of  this 
method  should  be  given  in  the 
specifications. 


EXCERPTS  AND  REFERENCES. 

Pneumatk  Stone-Dressing  Machines  tX  the  Wachusett   Dam,  CUntoa, 

MaM.    (Eng.  News,  June  30,  1904). — Illustrations  of  the  Kotten  and  the 
Dallett  pneumatic  stone-dressing  machines.    No  costs  are  given. 


d  by  Google 


25.— MASONRY. 


Kindt  of  Masoanr. — I.  Stone  masonry;  11.  Brick  maaonry:  III.  Coocrete 
masonry;   IV.   Reinforced-concrete  masonry.     In  addition  to  the  above 
we  may  aba  bave:  V.  Mixed  ntasonrv;  VI.  Concrete-block  maaonry;  etc 
(For  Masonry  Arches,  see  Sec.  44,  Arches,  page  763.) 

Classificatiok  of  Railroad  Masonry. 

(By  Committee*  of  Am.  Ry.  Eng.  &  M.  W.  Assn. — See  Proceedings,  Vol  7. 

. 19060 


Kind. 


Material. 


Description 


Manner 
of  Work. 


Dressing. 


Joints  or 
Beds. 


Face  of 
Surface. 


Bridge, 
axid  Re- 
taining- 
WaU 


Arch. 


Colvert. . . 


Dry. 


Stone 

Concrete 

Stone 

Concrete 

Brick 

Stone 

Concrete 
Stone 


Dimension 
Ashlar 

Rubble 

(Reinforced 
^  Plain 
/  Rubble 

Ashlar 

Rubble 

/  Reinforced 
(Plain 


No.  1 

5  Rubble 
I  Dry 

{Reinforced 
Plain 
Rubble 

Rubble 


Coursed 

SCotu^ed   ) 
Broken-  V 
cotirsed) 

Uncoursed 


Coursed 


Uncoursed 


'  English 

Bond 

Flemish 

Bond 

Uncoursed 


Uncoursed 


Smooth 

( Smooth 
<  Fine  p'tcd 
i  R'gh  p'ted 

R'gh-p'ted 
ScabbWd 


( Smooth 
(  Finc-p'tcd 

( Rough-p't 
\  Scabbled 


[  R'gh-p'ted 
[  Scabbled 


( Smooth 
(  Rock-feed 

( Smooth 
I  Rock-feed 


Rock-faced 


( Smooth 
\  Rock-f'ced 


Rock-faced 


Rock-faced 


I.  STONE  MASONRY. 
DcfiaMoiis  of  Parts  of  Wall.t— Fav.  the  front  surface  of  a  wall;  Back. 
the  inside  surface.  Facing,  the  stones  which  form  the  face  or  outside  of 
the  wall;  Backing,  the  stones  which  form  the  back  of  the  wall;  Filling,  the 
interior  of  the  wiul.  Batter,  the  slope  of  the  surface  of  the  wall :  as,  1  on  12  — 
1  inch  horizontal  to  1  foot  vertical.     Course,  a  horizontal  layer  of  stone  in 


♦  Prowess  report.     Published  b^ 
t  See  Trans.  Am.  Soc.  C.  E 
Sec  24.  Stone  Cutting. 


by  permission. 

Vol.  VI.,  as  previously  referred  to  under 


431 


Digitized 


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432 


26.-'MASONRY. 


the  wall.  If  the  stones  of  each  layer  are  of  equal  thickness  througfaottt  it 
is  termed  "regular  coursing;"  if  the  thicknesses  are  unequal,  the  term 
"  random  "  or  "  uneoual  coursing  "  is  applied.  Joints,  the  mortar  layer 
between  the  stones.  The  horizontal  joints  are  called  "  bed-pints."  or  sim- 
ply "  beds;"  the  vertical  joints  are  sometimes  called  "  bvulds."  Usually 
the  horizontal  joints  are  called  "  beds  "  and  the  vertical  ones  **  joints. 
Coping,  a  projecting  course  of  heavy  stones  on  the  top  of  the  wall  to  protect 
it.  (A  "  weathered  "  coping  is  one  whose  top  is  beveled  so  as  to  act  as  a 
rooO.  Pointing,  a  better  quality  of  mortar  put  in  the  face  of  the  joints 
to  help  them  resist  weathering.  Bond,  the  arrangement  of  stones  in  ad- 
jacent courses.  Stretcher,  a  stone  whose  greatest  dimension  lies  parallel  to 
the  face  of  the  wall.  Header,  a  stone  whose  greatest  dimension  lies  per- 
pendicular to  the  face  of  the  wall.  Quoin,  a  comer  stone;  a  header  for  one 
face  and  a  stretcher  for  the  other.  Dowels,  straight  bars  or  pins  of  iron 
which  enter  a  hole  in  the  upper  side  of  one  stone  and  also  a  hole  m  the  lower 
side  of  the  stone  next  above  (for  lateral  stability).  Cramps,  bars  of  iron 
havixig  the  ends  turned  at  right  angles  to  the  body  of  the  bar.  which  ends 
enter  holes  in  the  upper  side  of  adjacent  stones. 

Definitions  of  Kinds  of  Masonry.* — (Por  classification  of  Stones,  see 
Sec.  24.  Stone  Cutting). 

Rubble  Masonry. —  Masonry   composed    of    un- 
squared  stone.  Fig.  1 

Uncoursed  rubble. — Masonry  composed  of  un-' 
squared  stones  laid  without  any  attempt  at  regular 
cotu-ses.     Pig.  1.  c 

Coursed  rubble. — Unsquared-stone  masonry  which  is 
leveled  off  at  specified  heights  to  an  approximately 
horizontal  surface  (as  at  a,  b,  etc..  Pig.   1).  Pig.  i. 

{Squared  rubble. — Rubble  masonry  in  which  the  stone  may  be  required 
to  be  roughly  shaped  with  the  hammer,  so  as  to  fit  approximately.) 

Squared-Stone  Masonry. —  Masonry  in  which  the  stones  are  roushly 
squared  and  roughly  dressed  on  beds  and  joints.  (If  the  joints  are  as  small 
as  about  one-half  inch  the  classification  might  come  under  that  of  Ashlar). 

There  are  five  kinds. 

Regarding  character  of  face: 
Quarry-faced  masonry. — Face  of  stone  is  left  as  it  comes  from  the  quarry. 
Pitch-faced  masonry. — Face  of  stone  is  roughly  dressed. 


r 


SE 


rrTT 


31 


3 


B 


rTTT 


Pig.  4. 


Fig.  2.  Fig.  8. 

Regarding  character  of  course: 
Range-work   (Fig.    2). — Masonry  laid   in  continuous  courses  throughout. 
Broken  Range-work  (Fig.  3)  .—Masonry  laid  in  courses  non-continuousor  broken. 
Random-work    (Fig.  4). — Masonry  not  laid  in  courses  at  all. 

Ashlar  Masonry. — "  Cut-stone  masonry."  or  masonry  composed  of  any 
of  the  various  kinds  of  cut  stone  mentioned  under  Stone  Cutting,  Sec.  2%. 
From  its  derivation  ashlar  apparently  means  large,  sqiuu«  blocks;  but 
practice  seems  to  have  made  it  synonymous  with  "  cut-stone,"  and  this 
secondary  meaning  has  been  retained  for  convenience. 

Fig.  5  represents  the  face  of  an  ashlar  wall,  coursed  throughout. 
Broken  Ashlar  (Fig.  6). — Cut-stone  masonry  in  which  the  joints  are  not 
continuous. 


*  See  Trans.  Am.  Soc.  C.  E.,  Vol.  VI..  as  previqGSly^referred  to  uzMier 
Sec.  24.  Stone  Cutting.  °  9' '^^^  byVjOC 


STONE  MASONRY— SPECIFICATIONS. 


433 


I  .  I   .  I   .  I 


^ 


I  I   I   I   I 


ri 


ffl 


Pig.  5.  Pig.  6. 

Small  Ashlar. — Cut-stone  masoniy  in  which  the  stones  are  less  than  one 
foot  in  height;  seldom  iised. 

Rou^  Adtlar. — ^A  term  sometimes  given  to  squared  stone  masonry,  either 
"  qoarry-^aced  "  or  "  pitch-faced  "  when  laid  as  rangt-ufork,  but  it  is 
more  logical  and  more  expressive  to  call  such  masonry  squargd  rangg^vork. 
Dtmensitm  Stands. — Cut-stones,  all  of  whose  dimensions  have  been  fixed 
in  advance.  If  the  specifications  for  ashlar  masonry  are  so  written  as  to 
prescribe  the  dimensions  to  be  used,  it  will  not  be  necessary  to  make  a  new 
class  of  such  stones. 

Range-woxic.  whether  of  squared  stones  or  of  ashlar,  is  usually  backed 
up  with  rubble  masonry,  which  in  such  cases  is  specified  as  Cotuved  Rubble. 

Whatever  terms  are  employed  in  common  use  to  various  classes  of 
masonry,  it  is  not  safe  to  trust  to  them  alone  in  preparing  specifications 
for  construction,  but  every  specification  should  contam  an  accurate  des- 
cription ci  the  character  and  ouality  of  the  work  desired.  Whenever 
practicable,  samples  of  such  kind  of  cutting  and  masonry  should  be  pre> 
par^  beforehand,  and  exhibited  to  the  persons  who  propose  to  undertake 
the  work. 

Spedficationsfor  Stone  Masonry. — ^The  following  is  a  Committee  Report* 
(amoidments  included)  submitted  to  the  Am.  Ry.  Eng.  and  M.  W.  Assn., 
March  1906,  but  has  not  formally  been  approved  by  the  Association. — See 
Proceedings,  Vol.  7. 

Gbnbral. 

Stone. — 1.  Stone  masonry  shall  be  built  of  the  kinds  specially  designated, 
with  such  arrangements  of  courses  and  bond  as  shown  on  the  drawings  or  as 
directed.  The  stone  shall  be  hard  and  durable,  free  from  seams  or  other 
imperfections,  of  approved  quality  and  shape,  and  in  no  case  have  less  bed 
than  rise,  ana  shall  be  laid  on  their  broadest  beds,  well  bonded  and  solidly 
bedded.  When  liable  to  be  affected  by  freezing,  no  unseasoned  stone  shall 
belaid. 

Dressing. — 2.  Dressing  shall  be  the  best  of  the  kind  specified  for  each 
class  of  work.  8.  Bedff  and  joints  or  builds  shall  be  square  with  each  other, 
and  dressed  true  and  out  of  wind.  Hollow  beds  will  not  be  allowed.  4. 
All  stones  shall  be  dressed  for  laying  on  natural  bed.  5.  Marginal  drafts 
should  be  neat  and  acctuate.  6.  Pitching  shall  be  done  to  true  lines  and 
exact  batter. 

Mortar. — 7.  The  sand  and  cement  shall  be  mixed  dry  and  in  small 
batches  in  proportions  as  directed,  on  a  suitable  platform,  which  must  be 
kept  clean  and  free  from  all  foreign  matter;  then  water  is  to  be  added,  and 
the  whole  remixed  until  the  mass  of  mortar  is  thoroughly  homogeneous, 
and  leaves  the  hoe  clean  when  drawn  from  it.  It  shall  not  be  retemperea 
after  it  has  begun  to  set.  Mechanical  mixing  to  produce  the  same  results 
may  be  permitted. 

Laytng. — 8.  All  stones  shall  be  laid  on  natural  beds.  Each  stone  shall 
be  settled  into  place  in  full  bed  of  mortar.  9.  No  stone  shall  be  dropped 
or  slid  over  the  wall,  but  shall  be  placed  without  jarring  the  stones  already 
had.  10.  No  heavy  hammering  snail  be  allowed  on  the  wall  after  a  course 
is  laid.  11.  If  a  stone  becomes  loose  after  the  mortar  is  set,  it  shall  be 
relaid  with  fresh  mortar.  12.  Each  stone  shall  be  cleansed  and  dampened 
before  laying.  13.  Stones  shall  not  be  laid  in  freezing  weather  unless 
allowed  by  tne  engine^.  If  allowed,  they  shall  be  free  from  ice,  snow  or 
frost  by  warming,  and  laid  in  mortar  made  of  heated  sand  and  water,  or, 
with  proper  precautions,  mixed  with  brine  in  proportions  of  one  lb.  of  salt 
to  18  galls,  of  water,  when  the  temperature  is  32®  F.  Add  one  ounce  of 
salt  for  every  degree  of  temperature  below  32**  F.  14.  Stones  shall  be  laid 
to  exact  lines  and  levels  so  as  to  give  the  required  bond  and  thickness  of 
mortar  in  beds  and  joints. 


courtesy 


•  Published  by  permission  of  the  Executive  Commi£tee)/^through  the 
rtesy  of  Mr.  K  H.  Fritch,  Secretary.  ^zed-byKLJt^«. 


434  ii.^MASONRY. 

Pointing. — 16.  Mortar  in  beds  and  ^ints  of  exposed  faces  shall  be 
removed  to  a  depth  of  not  lees  than  one  in.  before  it  has  set.  No  pointing 
shall  be  done  until  the  wall  is  complete  and  mortar  set.  nor  when  frost  is 
in  the  stone.  Wet  the  joints  and  fill  again  with  mortar  made  of  equal 
parts  sand  and  Portland  cement.  It  shall  be  pounded  in  with  "  set -in  '* 
or  calking  tool,  and  finished  with  a  beading  tool  the  width  of  the  joint, 
used  with  a  straight-edge. 

Classification. 

16.  Stone  masonry  shall  be  classified  under  the  following  heads:  Bridge 
and  Retaining  Wall  Masonry,  Arch  Masonry,  Culvert  Masonry,  and  Dry 
Masonry. 

Bridge  and  Retaining  Wall  Masonry. 

17.  Bridge  &nd  Retaining  Wall  masonry  shall  consist  of  two  classes: 
(a)  Ashlar  (either  coursed  or  broken-coursed),  and  (b)  Rubble. 

(a)  Ashlar  Masonry  in  Bridges  and  Retaining  Walls. 

18.  In  Ashlar  masonry  in  bridges  and  retaining  walls  (either  coursed 
or  broken-coursed),  the  stone  shall  be  large  and  well-proportioned.  19.  No 
course  shall  be  less  than  14  ins.  nor  more  than  30  ins.  thick;  the  thickness 
of  courses  to  diminish  regularly  from  bottom  to  top. 

Dressing. — 20.  The  beds  and  joints  or  builds  of  face  stones  shall  be  fine- 
pointed,  so  that  the  mortar  layer  shall  not  exceed  i  in.  in  thickness  when 
the  stones  are  laid.  21.  Joints  in  face  stones  shall  be  full  to  the  square 
for  a  depth  equal  to  at  least  i  the  height  of  the  course,  but  in  no  case  less 
than  12  ins. 

Facing  or  Surface  Finish. — 22.  The  exposed  surface  of  each  face  stone 
will  be  rock-facea,  and  the  edges  pitched  to  true  lines  and  exact  batter; 
the  face  to  have  no  projections  over  3  ins.  beyond  the  pitch  lines.  23.  A 
chisel  draft  li  ins.  wide  shall  be  cut  at  each  exterior  comer.  24.  No  holes 
for  stone  hooks  shall  be  permitted  to  show  in  exposed  surfaces.  They 
must  be  handled  with  clamps,  keirs,  lewis  or  dowels. 

Stretchers. — 25.  Stretchers  shall  be  not  less  than  4  ft.  long,  and  to  have 
at  least  1}4  times  as  much  bed  as  thickness  of  the  course. 

Headers. — 26.  Headers  shall  be  not  less  than  4  ft.  in  length.  They 
shall  occupy  one-fifth  of  the  face  of  the  wall,  and  no  header  shall  have  less  than 
18  ins.  width  of  face,  and  when  the  course  exceeds  18  ins.  height,  the  width 
of  face  shall  be  not  less  than  the  height  of  course.  Headers  shall  hold  the 
size  in  the  heart  of  the  wall  that  they  show  on  the  face,  and  be  so  arranged 
that  a  header  in  a  superior  course  snail  be  placed  between  two  headers  in 
a  course  below;  but  no  header  shall  be  laid  over  a  ^int,  and  no  joint  shall 
cover  a  header.  They  shall  be  similarly  disposed  in  the  back  of  the  wall, 
interlocking  with  those  in  the  face  when  the  thickness  of  the  wall  will  admit. 
When  the  wall  is  too  thick  to  admit  of  such  arrangement,  stones  of  not  less 
than  4  ft.  iij  length  shall  be  placed  transversely  in  the  heart  of  the  wall  to 
bond  the  two  opposite  sides  of  it. 

Backing. — 27.  Backing  shall  be  large,  well-shaped  stone^  roughly 
bedded  and  jointed;  the  bed  joints  not  to  exceed  1  in.,  and  vertical  jomts 
generally  not  to  exceed  2  ins.  No  part  or  portion  of  vertical  joints  shaU 
have  a  greater  dimension  than  6  ins.,  which  void  shaU  be  thoroughly  filled 
with  spalls  full  bedded  in  cement  mortar  or  filled  with  concrete.  At  least 
one-half  of  the  backing  stones  shall  be  of  the  same  size  and  character  as 
the  face  stone  and  with  parallel  beds.  28.  When  face  stone  is  badced 
with  two  courses,  neither  course  shall  be  less  than  8  ins.  thick.  29.  When 
the  wall  is  3  ft.  thick  or  less,  the  face  stone  shall  pass  entirely  through  and 
no  backing  be  allowed.  30.  If  the  engineer  so  directs,  the  backing  may  be 
entirely  of  concrete,  or  back  laid  with  headers  and  stretchers,  as  specified 
above,  and  heart  of  wall  filled  with  concrete. 

Bond. — 31.  The  bond  of  stone  on  face,  back  and  heart  of  wall  shall  not 
be  less  than  1 2  ins.  Backing  shall  be  laid  to  break  joints  with  the  face  stone 
and  with  one  another. 

Coping. — 32.  Coi>ing  shall  be  dimension  stone,  holding  full  size  through- 
out, proportioned  for  its  loading,  as  marked  on  the  drawings.  33.  The  beds, 
joints  and  top  shall  be  fine-pointed.  34.  The  location  of  jomts  shall  be  deter- 
mined by  the  position  of  the  bed  plates,  and  must  be  shown  on  the  drawings. 

Locks. — 35.  When  required ,  in  the  judgment  of  the  engineer,  coping 
stones,  stones  in  the  wings  and  abutments,  and  stones  on  piers  shall  be 
secured  together  with  iron  clamps  or  dowels,  their  position  beiag  indicated 
by  the  engmeer.  Digitized  byVjOOQTe 


d  by  Google 


436 


^^MASONRY. 


(6)  Slope  Walls. 

67.  Slope  walls  shall  be  built  of  such  thiclnww  and  slope  as  may  be 
required  by  the  engineer.  No  stones  shall  be  used  which  do  not  reach 
through  the  wall.  Stones  shall  be  placed  at  right  angles  to  the  slopes. 
This  wall  is  single-faced  and  built  with  steep  dope  sim\iltaneoualy  with 
the  embankment  which  it  is  to  protect. 

Quantity  of  Masonrv  in  Abutments. — ^Tables  1  and  2,  following,  were  cal- 
culated from  Fig.  7.  Table  1  gives  the  quantities  of  masonry  and  steel  in 
one  abutment  of  various  heights,  and  Table  2  is  a  supplementary  table  to 
facilitate  the  reduction  of  these  quantities  to  weights. 

1. — OuANTrriBS  IN  Onb  R.  R.  Masonry  ♦Right  Abutments  of 
Various  Heights  k.      (See  Fig.  7.) 


Height  h 

At 

Az 

A3 

\ 

F, 

>2 

Fj 

F4 

Ri 

R, 

«, 

«4 

of  Base  of 
Rail 

U 

asonr 

f  Alxn 

« 

Masonry /» 

Steel  Rati  In 

above 

Found 

Atlon. 

FoundatloQ. 

FoundaUoa. 

Top  of  1 
Founda- 

^   "O 

M    .■ 

tit 

M    .• 

M 

M    .^ 

i^    ,  m 

m  .ti 

'm 

^    .«! 

tion. 

Ih 

||S 

«   •■§ 

Wi 

W- 

Bi 

P^ 

Ft. 

A^S 

%H 

^^5 

A«S 

%h 

4^5 

4«5 

8 

31.2 

48.4 

64.8 

78.8 

29.6 

44.2 

57.8 

68.4 

288. 

394. 

509. 

608. 

9 

38.8 

68.8 

78.6 

94.5 

33.2 

48.5 

62.8 

74.1 

308. 

421. 

541. 

643. 

10 

47.6 

70.8 

94.0 

112. 

37.0 

53.0 

68.0 

80.0 

330. 

460. 

675. 

•M. 

11 

67.7 

84.2 

111. 

131. 

41.0 

67.7 

73.4 

88.1 

364. 

481. 

611. 

719. 

12 

69.0 

99.2 

130. 

163. 

46.2 

62.6 

79.0 

92.4 

380. 

614. 

649. 

760. 

13 

81.6 

116. 

150. 

175. 

49.6 

67.7 

84.8 

98.9 

406. 

649. 

689. 

803. 

14 

95.4 

134. 

172. 

200. 

64.2 

73.0 

90.8 

106. 

438. 

586. 

731. 

843. 

15 

111. 

153. 

195. 

227. 

59.0 

78.5 

97.0 

113. 

470. 

625. 

ns. 

895. 

16 

127. 

174. 

220. 

255. 

64.0 

84.2 

103. 

120. 

504. 

666. 

821. 

944. 

17 

144. 

196. 

247. 

285. 

69.2 

90.1 

110. 

127. 

540. 

709. 

869. 

995. 

18 

163. 

220. 

275. 

317. 

74.6 

96.2 

117. 

134. 

678. 

754. 

919. 

1048. 

19 

183. 

246. 

305. 

351. 

80.2 

103. 

124. 

142. 

618. 

801. 

971. 

1103. 

20 

205. 

273. 

336. 

386. 

86.U 

109. 

131. 

150. 

660. 

860. 

1026. 

1160. 

21 

227. 

301. 

369. 

423. 

92.0 

116. 

138. 

158. 

704. 

901. 

1081. 

1219. 

22 

251. 

331. 

404. 

462. 

98.2 

123. 

146. 

166. 

750. 

954. 

1139. 

1280. 

23 

276. 

363. 

440. 

503. 

105. 

130. 

154. 

175. 

798. 

1009. 

1199. 

1343. 

24 

302. 

396. 

478. 

546. 

111. 

137. 

162. 

184. 

848. 

1066. 

1261. 

1408. 

20 

330. 

430. 

517. 

691. 

118. 

145. 

170. 

193. 

900. 

1125. 

1325. 

1475. 

26 

359. 

466. 

558. 

637. 

125. 

152. 

178. 

202. 

954. 

1186. 

1391. 

1544. 

27 

389. 

603. 

601. 

686. 

132. 

160. 

187. 

211. 

1010. 

1249. 

1450. 

1615. 

28 

420. 

542. 

645. 

736. 

140. 

168. 

196. 

220. 

1068. 

1314. 

1529. 

1688. 

29 

453. 

583. 

691. 

787. 

147. 

177. 

205. 

230. 

1128. 

1381. 

1601. 

1783. 

30 

487. 

625. 

738. 

840. 

155. 

185. 

214. 

240. 

1190. 

1450. 

1675. 

1840. 

31 

522. 

668. 

787. 

895. 

163. 

194. 

223. 

260. 

1264. 

1521. 

1751. 

1919. 

32 

558. 

713. 

838. 

952. 

171. 

203. 

233. 

260. 
271. 

1320. 

1694. 

1829. 

2000. 

33 

596. 

760. 

890. 

1011. 

180. 

212. 

243. 

1388. 

1669. 

1909. 

20S3. 

34 

634. 

808. 

944. 

1072. 

188. 

221. 

253. 

282. 

1458. 

1746. 

1991. 

2168. 

35 

675. 

857. 

999. 

1135. 

197. 

231. 

263. 

293. 

1530. 

1825. 

2075. 

2255. 

36 

716. 

908. 

1056. 

1199. 

206. 

240. 

273. 

304. 

1604. 

1906. 

2161. 

2344. 

Above  f/1,  -    I (A-5)«+3.2*.      F,  »  0.W+  l.9h+  8.      /?t  -**+»  +  200. 
by    J^2  -    l(/»-6)^+5.2fc.      Fa  -  0.l/i«+  2.6fc+17.      J?a  -  fc»  +  lOfc  +  250, 
For-  \A^  -  0.8fc»  +  0.2^+12.      F,  -  0.1^«+  3.3fc+25.       R9  "  h*  +  I5h  +  ZO. 
mulas;  U«  -  0.«»«-4-  0.4A+18.      F4  -  O.IAH-  A.Oh+20.      i?4  -  *»  +  18fc  +  «0. 
♦  For  "skew"  abutments,  multiply  quantities  in  table  by  secant  of  "skew- 
angle  ,    I.e..  angle  which  face  of  abut .  makes  with  a  right  anglt  to  center  line. 


MASONRY  IN  ABUTMENTS.   BRICK  MASONRY.  487 

2. — ^Tablb  for  PiHDiNo  Wbiohts  of  Ouantitibs  in  Tablb  I. 


Viembt  of  Haaonry, 
In  1000  LIM. 


•   5}  cu.ft. 


Mas.  at  Mas.  at 

ISSLbe. 


per 
cu.ft 


Weight  of  Steel 
laLbfl. 


mi.bl^^*^ 


per 
ou.  ft. 


60  Lbs. 
per  yd. 


Ralla  atRalla  at 


65  Lbs. 
per  yd. 


70LbB. 
per  yd 


*Ex. — A  maaonry  abut- 
ment contains  384  cu.  yd& 
masonry  at  155  •  bs.  per  cu. 
ft.,  and  832  lin.  ft.  steel 
rallsat651bfl  per  (1  in)  yd. 
Find  the  welRht  or  load 
which  the  abutment  alone 
produces  on  the  pile  founda- 
tion. 


3.9IS 
7.830 
11.745 

15.660 
19.57S 
23  490 

27.405 
31.320 
35.235 


10       89.150 
100     391.5 


400 
500 


1174.5 
15M. 

1957.5 


4.1 
8.370 
12.555 

16.740 
20.925 
25.110 

29.295 
33.480 
37.665 

41.850 
418.5 
837. 

1255.5 

1674. 

2092.5 


4.32 
8.64 
12.96 

17.28 

21. 

25. 

30.24 
34.56 
38.88 


43.20       200. 


432. 
664. 

1296. 
1728. 
2160. 


1000  ^15. 


20. 
40. 
60. 

80. 
100. 
120. 

140. 
160. 
180. 


2000. 
4000. 

6000. 
8000. 
10000. 


21.67 
43.33 
65. 

86.67 
108.33 
130. 

151.67 
173.33 
195. 

216.67 
2167. 
4333. 

6500. 
8667. 
10833. 


23.33 
46.67 
70. 

93.33 
116.67 
140. 

163.3.3 
186. 67{ 
210. 

233. 
2333. 
4667. 


7000. 
9333.    % 
11667.     9 


Ftjf.7. 


*Ams. — From  columns  1.  3  and  6  In  above  table  we  have:    Weight  -■  (masonry) 
ie07.O4X  1000-1- (steel)  18460- 1,625.500  lbs.- 812.75  tons. 


II.   BRICK  MASONRY. 


Bond. — ^The  terms  *'  header  "  and  **  stretcher  "  are  used  in  brickwork 
as  in  stonework.     The   '  bond  "  of  a  brick  wall  depends  upon  the  arrange- 
ment  of  headers  and  stretchers,  in  the  same  or  m 
adjacent  courses. 

English  Bond  (Fig.  8). — Alternate  entire  courscsi; 


i:;=;i; 


of  headers  and  stretchers. 

Modified  English  Bond. — Each  course  consisting 
entirely  of  headers  or  of  stretchers,  but  not  alter- 
nating as  above;  usually  one  course  of  headers  to 
every  four  to  six  courses  of  stretchers.  (Where  wall 
is  laid  with  one  course  of  headers  to  every  two  or 
three  courses  of  stretchers  it  is  generally  classed  as 
English  bond). 

Flemish  Bond  (Fig.  9). — Each  course  made  up  of 
altemate  headers  and  stretchers. 

English  bond  is  considered  the  strongest. 


II    II    IE 


=v 


r^ 


^ 


zl 


rz 


II     II     L 


ft 


■;■  ■■■  ■; 


^ 


II  11  I   i: 


Fig.  8. 


Brickwork  is  well  adapted  to  all  kinds  of  II 
masonry  construction  where  excessive  strength  and  jj; 
massive  weight  (as  bridge  abutments,  piers,  dams.  II 
etc,  which  call  lor  concrete  and  stonework)  are  not  ■*— 
particularly  essential.  Hence  its  use  in  building- 
walls  (incltiding  the  upper  stories  in  tall  buildings) 


I    I.    ,1    I 


III 


XI 


in 


nr 


nr 


lEII 


HI 


a 


nc 


I  I      II 


rrT, 


III! 


Fig. 


The 


^  ..  _  „    9. 

tunnel  linings,  small  arches,  culverts,  (street  paving),  sewers,  etc. 
convenience  in  handling  and  laying  brick,  in  forming  arches  and  rounding  " 
comers,  makes  it  p«uticularly  useful  in  these  classes  of  construction.  In 
fire^resisting  qualities  it  is  superior  to  any  natural  building  stone,  with  the 
exception  possibly  of  sandstone,  and  is  equal  to  the  latter  in  this  respect. 


488 


26.— MASONRY. 


and  infinitely  superior  to  it  (i.e.,  to  most  varieties)  as  regards  frost  action 
and  absorption  of  moisture.  Generally  speaking,  when  compared  "witli 
stonework,  brick  masonry  lies  between  ashlar  and  common  rubble  masonry, 
both  in  cost  and  strength.  Regarding  cost,  the  writer  has  witnessed  the 
price  of  common  building  brick  fluctuate  during  the  past  year,  in  Broolclyn. 
between  $16  and  $7  per  thousand.  It  is  perhaps  essential  to  note  here  that 
while  the  higher  price  was  maintained  the  builders  resorted  largely  to 
rubble  and  concrete  construction,  which  finally  brought  the  trust  price  to 
the  lower  figure.  This  may  illtistrate  also  that  the  "  cost  of  woric  '  obtained 
from  any  source  must  be  used  with  judgment  in  connection  with  the  details 
furnished  therewith,  and  with  the  prevailing  local  conditions. 

The  Mortar  used  in  brick  masonry  may  vary  considerably,  depending 
upon  the  class  of  work.  For  instance,  the  best  mortar  usually  specified  is 
composed  of  1  part  Portland  cement,  and  2  parts  clean,  sharp  sand,  where 
the  structure  is  exposed  to  considerable  stress;  while  for  the  most  ordinary 
brickwork,  1  part  fresh,  well-slaked  lime  and  2*  to  3  parts  sand,  will  ans^wer. 
Between  these  limits  we  may  have  various  mixtures  of  Portland  oexnent. 
natural  cement,  common  lime,  and  sand.     Thus: 


Class  A 
*'    At 

1  Port.  Cem. 
1     ••       •* 
1     "       *• 

Nat.  Cem. 

Com. 

Lime. 

2 
2 

Clean. 

sharp  Sand. 

"    A^ 

"     B 

1    ;;   ;; 
1    ••    " 

*•    Bt 

"     B« 

••   C 

1  *• 

•| 

'*    Ct 

**    C9 

"     D 

1     "       *• 
1     "       " 
1     "       " 
1     *•       •• 

1    ••    " 
1    "    •• 
1    "    " 

'*    Dt 

**     Da 

**    E  etc 

1  Lime  paste 

•*    F  etc 

1    *•    " 

Class  A  is  used  in  superior  building  construction,  for  raiboad  masonry 
in  general,  tvmnel  lining,  and  sewers;  class  £,  for  building-work  of  the  very 
highest  class;  class  C,  for  common  brickwork  as  in  buildings.  Where  cement 
and  lime  come  in  barrels.  *'  barrel  "  measure  may  be  used  in  determining 
the  "  parts  "  of  cement,  lime  and  sand.  Fire  bnck  should  be  laid  in  fire- 
clay mortar.     Colored  mortar  is  used  for  pressed  brick  facing. 

Pressed-brick  masonry,  for  facing,  requires  less  mortar  per  cubic  yard 
of  masonry  than  the  common-brick  backing,  because  pressed  bricks  are  a 
little  larjger  than  the  common  (which  are  8ix4x2i  standard)  to  allow  for 
thinner  joints. 

For  any  kind  of  masonry,  the  bricks  should  be  wet  before  laying  (except 
perhaps  in  freezing  weather — unless  special  care  is  taken  to  warm  the  water 
and  sand),  and  thoroughly  bedded  in  mortar,  and  pressed  or  shoved  into 
place. 

3. — OuAMTiTiBS  OP  Brick  and  Mortar  in  Brick  Masonry. 
(Brick,  standard  size — 8ix4x2J.) 


i^ 

No.  of 

No.  of 

Cu.  Ft.  of 

Cu.  Yds.  0^ 

Cu.  Yds.  of 

Cu.  Yds.  of 

M  0 

Brick  per 

Brick  per 
Cu    Yd.  of 

Masonry. 

Masonry 

Mortar  per 
Yd.  of 

Mortar  per 

.5^ 

Cu.  Ft.  of 

per  1000 

per  1000 

1000 

tro 

Masonry. 

Masonry. 

Brick. 

Brick. 

Masonry. 

Brick. 

zero. 

23.3 

628.4 

43.0 

1.69 

.000 

.000 

»^ 

21.1 

568.6 

47.5 

1.76 

.006 

.167 

H 

19.1 

616.6 

62.3 

1.94 

.180 

.366 

% 

17.4 

471.0 

67.8 

2.12 

.260 

.630 

H 

16.0 

430.9 

62.6 

2.32 

.314 

.728 

H 

14.6 

395.4 

68.3 

2.63 

.871 

.939 

This  table  is  calculated  for  massive  masonry  construction;  allowance 
should  be  made  for  thin  walls — bricks  to  increase  andnrnpilait  to  dimini^ 
slightly  per  volume  of  masonry.  Digitized  by  V^OOQLc 


BRICK  MASONRY.    CONCRETE  MASONRY,  439 

IlL  CONCRETE  MASONRY. 

.  No  other  class  of  masonry  is  so  generally  employed,  especially  for  mas- 
sive construction,  as  concrete.  It  is  almost  universally  used  for  footings 
of  heavy  stnictures  such  as  abutments,  walls  and  i^iers  for  bridges,  revet- 
ments (Weakwaters) ,  dams,  and  builaings;  while  it  often  enters  largely, 
aomctina^  wholly,  into  these  structures  themselves. 

Concrete  footings  are  often  reinforced  with  steel  rails  or  I-beams,  in 
otie  or  more  tiers,  to  distribute  the  loads  (either  above  or  below)  more 
uniformly.  Such  construction  may  be  said  to  form  the  connecting  link 
between  plain-  and  reinforced  concrete.     See  Sec.  50,  Foundations. 

Rock  Cmshers  are  now  almost  wholly  employed  in  breaking  stone  for 
concrete,  in  place  of  hand -breaking.  By  the  last-named  method  a  laborer 
is  osually  coimted  upon  to  break  about  one  cu.  vd.  of  trap  or  from  2  to  8 
CO.  yds-  of  limestone,  in  sizes  to  pass  through  a  2-in.  ring,  in  a  10-hr.  day. 
Hudi  depends  upon  the  size  ana  shape  of  the  rip-rap  stone  received  for 
liaeaking.  On  the  other  hand,  the  capacities  of  machines  nm  up  to  several 
bundred  tons  per  day.  A  cubic  yard  of  broken  trap  rock,  assuming  45% 
voids,  will  weigh  about  185x27x.55  =  about  2750  lbs.  or  1|  tons;  while  a 
cubic  yard  of  limestone,  assuming  87i%  voids,  will  weigh  about  the  same. 
Unscreened  broken  stone,  especially  of  the  softer  kinds,  has  less  percentage 
<rf  voids  than  the  screened.  The  softer  rocks  in  crushing  assume  a  more 
rounded  form,  and  break  into  more  variable  sizes,  both  of  these  conditions 
tending  to  reduce  the  i>ercentage  of  voids.  Spheres  of  uniform  size,  as 
cannon  balls,  may  be  piled  in  large  piles  in  pyramidal  form  so  that  the 
percentage  of  voids  will  approach  the  lower  hmit  of  25.963%  voids. 

Permanent  crushers,  often  with  extensive  plants,  are  frequently  installed 
at  quarries.  For  this  purpose,  the  gyratory  type  of  crusher  is  preferred, 
a  smgle  machine  being  able  to  turn  out  as  high  as  2000  tons  or  more  per 
lO-hr.  day.  Such  a  machine  would  weigh  in  the  neighborhood  of  50  tons, 
have  a  receiving  opening  of  say  Ux5  ft.,  and  reguire  about  150  H.  P.  to 
operate.  The  smaller  machines  are  less  economical  in  the  use  of  power. 
A  machine  of  \  the  above  capacity  would  require  about  |  the  power  to  oper- 
ate, and  would  weigh  about  30  tons;  a  machine  of  \  the  above  capacity 
wouW  require  about  f  the  power,  and  weigh  about  20  tons;  \  the  capacity, 
I  the  power,  and  weigh  about  10  tons,  etc.  The  above  H.  P.'s  include 
pofwer  required  to  operate  elevators  and  screens. 

Portable  crushers  are  furnished  as  low  as  about  4  tons  in  weight,  with 
openings  for  7x10  in.  stone,  capacity  50  to  60  tons  per  10-hr.  day.  and  re- 
quiring about  8  H.  P.  to  operate.  Small  machines  cost  about  $8.50  to 
19  per  capacity  in  tons  per  10  hr.  day.     Large  machines,  from  17  to  18. 

Hand  crushers,  costing  about  $30,  will  receive  stone  up  to  about  lix 
?ins. 

The  best  crushers  have  jaws  of  manganese-steel,  or  other  steel  of  equal 
hardness. 

Concrete  Mixers,  or  machines  for  mixing  concrete,  are  indispensable 
at  the  present  day  on  work  of  any  magnitude.  They  may  be  divided  into 
two  classes,  namely,  **  fixed  "  mixers,  and  "  mechanical  "  mixers. 

Fixed  or  Gravity  Mixer  consists  of  a  steel  trough  fixed  on  an  incline  of 
say  4  to  4i  ins.  horizontal  to  1 2  ins.  vertical,  and  some  provided  with  internal 
projections  in  the  form  of  steel  pins  or  baffle  plates,  which  deflect  and  "  mix  " 
the  material,  fed  at  the  upper  end,  as  it  descends.  These  mixers  are  econ- 
omically used  in  lining  the  bottoms  and  sides  of  reservoirs  and  in  work  of 
similar  character  where  the  mixing  can  be  done  at  an  elevation  above  the 
place  for  depositing  the  concrete. 

Mecliaiiical  Mixers  are  of  two  types: "  continuous  "  mixers,  and  "  batch  " 
mixers.  The  continuous  mixers  are  provided  with  plows,  shovels,  or  pad- 
dles -which  mix  the  material  as  fast  as  delivered,  ana  discharge  the  mixture 
continuously.  Portable  machines  of  this  type  arc  used  economically  for 
stxeet  woxk. 

Batch  mixers  of  the  rotary  type  are  the  most  generally  used.  These 
machines  with  engine  (gasoline),  or  engine  and  boiler  (steam),  are  mounted 
on  skids  or  on  wheels,  are  very  compact,  and  have  a  capadty  of  about  200 
batcfa»  per  10-hr.  day,  each  batch  ordinarily  containing  i  yd..  |  yd.,  or 
I  yd^  depending  on  tnie  "  size  '"  of  the  mixer.     They  are,  however,  made 


440  25.— MASONRY. 

in  sizes  ranging  from  2  cu.  ft.  up  to  2  cu.  yds.  The  number  of  H.  P.  re- 
quired is  equal  to  size  of  batch  in  cu.  yds.  multiplied  by  15,  about.  Many 
of  the  machines  measure  the  proportions  of  the  ingredients. 

The  Proportions  of  Portland  Cement,  Sand  and  Broken  Stone  are«  1  :  2  to 
4  :  4  to  8,  depending  upon  the  equality  of  materials  used  and  of  the  resultinK 
concrete  required.  A  good  mix  is  1  :  2i  :  6.  while  1  :  8  :  6  is  perliaps 
most  common  for  ordinary  work.  In  the  construction  of  the  Mississippi 
jetties,  the  block  concrete  was  made  with  the  following  proportion:  Portlazul 
cement,  1,  sand  2i,  clean  gravel  li,  broken  stone  5;  the  resulting  mass 
was  about  li  yds.  of  concrete  per  yd.  of  broken  stone.  Common  lime 
may  be  added  to  cement  to  increase  the  bulk  of  the  "  cement  '*  paste. 
and  consequently  of  the  mortar,  where  concrete  is  not  to  be  placed  under 
water  and  where  it  is  not  subjected  to  excessive  stress;  but  as  common 
lime  has  no  hydraulic  properties,  its  addition  to  cement  in  mortar  is  simply 
the  addition  of  so  much  inert  matter,  like  sand,  when  the  concrete  is  depos- 
ited tmder  water. 

A  common  custom  of  late  is  to  designate  concrete  by  the  proportion  of 
cement  to  sand  assuming  that  the  volume  of  broken  stone  shall  be  twice 
that  of  the  sand.  Thus.  1  to  2  matrix  would  mean  1  cement.  2  sand,  and 
4  broken  stone,  or  1  :  2  :  4  mix;  1  to  2|  matrix,  a  1  :  2)  :  5  mix.  etc  This 
abbreviation,  unless  explained  (which  explanation  would  tend  to  nullify 
the  advantage  of  abbreviation  itself)  is  apt  to  lead  to  error.  The  propor- 
tion of  broken  stone  to  sand  need  not  necessarily  be  in  the  ratio  2:1.  In 
the  case  of  broken  limestone,  where  the  crushed  rock  is  graded,  and  also 
where  gravel  is  used,  especially  with  broken  stone,  the  ratio  may  be.  say. 
21  :  1.  2|  :  1.  etc.  In  all  large  work  the  percentage  of  voids,  and  conse- 
quently the  proportions,  should  be  determined  by  experiment  for  the 
classes  of  materials  used.  See  page  417,  where  the  method  of  determining 
voids,  etc.,  is  given. 

In  Mixing  by  hand,  the  cement  and  sand  are  thoroughly  mixed  dry  on 
a  clean  platform,  enough  water  is  added  to  make  a  stiiTpaste,  the  broken 
stone  (wet  and  i>reviously  washed  clean)  is  then  spread  over  the  mortar 
and  the  whole  thoroughly  mixed  by  shoveling  into  another  pile,  and  re- 
shoveling  as  often  as  necessary.*  Concrete  should  be  mixed  in  small 
batches  and  placed  immediately,  as  the  cement  may  set  appreciably  within 
30  to  40  minutes  after  water  is  applied,  and  all  subsequent  disturbaiu^ 
may  tend  to  weaken  the  mass. 

Placing,  Spreading  and  Ramming  are  operations  which  should  closely 
follow  one  another  rapidly.  The  concrete  may  be  delivered  in  barrows, 
cable  buckets,  carts  or  chutes,  the  last  named  being  the  cheapest  under 
favorable  conditions.  Spreading  consists  in  pushing  over  the  top  of  each 
batch  dumped,  so  as  to  present  a  fairly  level  bed  for  the  next  layer.  The 
layers  are  usually  specified  to  be  from  6  to  9  ins.  in  thickness.  Kamniing 
compacts  concrete  trom  6  to  25%  and  makes  it  stronger  by  bringing  the 
ingredients  more  intimately  together,  so  that  crystallization  takes  place 
more  firmly.  Rxunmers  are  round  wooden  blocks  or  logs  about  4  ft.  long, 
ring-shod  at  the  lower  end  and  provided  at  the  upper  end  with  handles 
for  one-man  or  two-man  manipulation. 

Ramming  should  bring  the  concrete  to  a  rather  firm  state  with  a  flush 
of  water  at  the  top,  but  should  not  continue  for  an  tmdue  length  of  time  ao 
as  to  weaken  its  setting*  "Dry"  concrete  naturally  requires  more  ramming 
than  a  *'  wet  "  mixture.  Before  depositing  a  new  layer,  the  top  of  the 
preceding  layer  should  be  wetted,  after  allowing  not  less  than  12  hrs.  for 
It  to  set.  Where  a  layer  is  not  wholly  completed  at  the  end  of  a  day's 
work,  its  edge  should  be  left  rough  (not  smooth)  for  the  next  day's  joining. 
'•  Medium  "  concrete  is  between  **  dry  "  and  wet."  The  advantage  of 
medium  concrete  is  that  it  can  be  rammed  better  than  "  wet,"  whue  at 
the  same  time  possessing  some  of  the  good  qualities  of  the  latter. 

Subaqueous  Concrete  has  seldom  been  deposited  with  entire  satisfaction 
even  in  still  water  to  an^  great  depth,  but  in  moderate  depths  this  has  been 
accomplished  with  quite  favorable  results.  The  essential  principle  in 
depositing  concrete  under  water  is  to  convey  it  properly  through  the  water 
so  that  the  mix  will  not  be  disturbed  by  '*  wash.       Examinations  by  divers 

*Some  engineers  and  most  builders  prefer  to  spread  the  (wet)  gravel 
una  broken  stone  on  the  dry  cement-sand  mix  before^weater  is  added. — See 
ijerman  Specifications,  pages  442. 443.  ized  by  dOOQ Ic 


CONCRETE— MIXING,  PLACING, 


441 


hvr^  in  many  cases  dkcloeed  "  streaky  concrete,'*  with  cement,  sand  and 
matrix  more  or  less  separated  by  wash,  owins  to  their  different  specific 
gnvities  axni  fineness.    The  result  of  this  lack  of  homogeneity  is  a  reduction 
U  ttreq|th,  hence  ^reat  care  shotild  be  taken  to  insure  as  little  disturbance 
as  poanble  in  placmg  the  material.     Under  no  drcumstanoes  should  con- 
crete be  dtmiped  loosely  into  water  and  allowed  to  settle  in  place.    The 
three  principal  methods  most  comnx>nly  used  are: 
(\)  Depositing  through  closed  chutes  or  tubes. 
(3)  Depositing  by  means  of  specially  arranged  buckets. 
(3)  Depositing  in  sacks  or  in  bags. 

The  first  method,  by  chute,  is  seldom  used.  The  tube  may  be  of  any 
section,  foadually  enlarising  toward  the  bottom  to  avoid  clogging  of  the 
ooQcreteled  continuously  at  top  of  tube.  The  tube  is  suspended  vertically 
with  the  lower  end  at  the  bottom,  and  is  moved  laterally  as  the  concrete 
laEA  into  place.  The  principal  objection  to  this  method  is  the  washing 
vhich  the  concrete  receives  m  its  descent. 

The  second  method,  by  buckets,  has  been  used  with  greater  or  less  suc- 
cess. One  of  the  most  recent  uses  of  this  method  was  in  the  construction 
of  a  8000-ft.  pier  at  Superior  Entry,  Wis.,  by  the  Government,  in  about 
33ft  of  water.*  The  steel  buckets  (Pig.  10)  about  4  ft.  cubes,  open  at  the 
tGrp.  were  provided  with  canvas  covers,  quilted  with  strips  of  sheet  lead, 
to  fold  over  the  concrete  and  prevent  wash.  The  buckets  when  lowered 
were  tripped  by  a  latch.  Mr.  Clarence  Coleman.  Asst.  Engr.  in  charge, 
states  that  the  examinations  of  concrete  lowered  23  ft.  and  raised  again  in 


.Skto  of  Bucket 
Willi  \jto^  Hon^m^  doivn. 


Side  of  Budwt. 


Fig.  10. 


the  bucket  showed  the  concrete  to  be  in  good  condition;  and  that  dis- 
coloration of  the  water  from  cement  was  seldom  noticed  during  the 
descent  of  the  bucket. 

The  tiiird  method,  by  bags,  has  been  used  extensively  in  both  this 
country  and  in  Europe.  Mr.  W.  M.  Patton,  in  his  "Treatise  on  Foundations, "t 
page  108.  says:  **Perhaps  the  best  mode  of  depositing  concrete  under  water 
IS  to  fill  open  sacks  or  gunny  sacks  about  two-thirds  to  three^fourths  full 
of  the  concrete  or  mortar,  and  deposit  these  in  place,  arranging  them  in 
ooorses,  where  practicable,  header  and  stretcher  system,  and  ramming 
each  course  as  laid;  the  bagging  is  close  enough  not  to  allow  the  cement  to 
be  washed  out,  but  at  the  same  time  open  enough  to  allow  the  whole  mass 
to  be  umted  and  to  become  as  compact  as  concrete  itself.    The  writer  used 

♦  See  Vol.  8.  Part  4,  of  Report  of  Chief  of  Engineers.  U.  $r;A>oolp 
-  " r  John  Wiley  &  Sons,  New  York.        fze^by-vjuoy  IL 


t  Published  by  J 


442  25.^MASONRY. 

this  method  in  the  foundation  of  a  pier  over  100  feet  high,  and  hasalsl 
adopted  this  plan  in  other  works  of  less  magnitude,  but  never  has  the  rei 
been  satisfactorv  when  deposited  under  water  in  any  other  manner/' 

Sub-Foandatioat  are  prepared  by  dredging,  if  necessary,  and  drivim 
piles  and  cutting  them  on  near  the  river  bottom.  Before  concrete  is  dei 
posited,  molds  are  constructed  of  timber  and  sunk  in  place  to  give  form  U$ 
the  concrete  pier.  The  inside  faces  of  the  molds  are  of  course  smoothi 
lined,  the  timber  frames  being  ouUide.  Long  adjustable  bolu  or  turn-* 
buckle  rods  are  convenient  to  use  with  colla^ible  sides,  where  the  saniA 
molds  are  to  be  used  over  again.     See  Sec.  50,  Fotmdations. 

Cefnent  Qroat  (either  pure  cement,  or  1  cement  and  say  1  sand)  may  bet, 
injected  into  a  quick-sana  or  ^avel  foundation  bed  to  form  a  sub  founda- 
tion. The  grout  is  pumped  mto  vertical  iron  pipes  perforated  with  holei 
at  the  bottom  to  allow  it  to  ooze  through  into  the  natural  bed  material. 
The  pipes  should  extend  downward  throtigh  the  soft  material  to  bed  rock  of 
other  firm  sub-stratum. 

Qerman  Speclfflcatioat  for  GMcrete. — ^The  following  is  a  digest  of  portions 
of  the  report  of  standing  committee  of  the  German  Concrete  Society  asi 
adopted  by  that  Society  and  entitled  "  Specifications  for  Designing,  Con- 
structing and  Testing  Concrete  Structures."  These  specifications  were 
brought  to  the  attention  of  Eng.  News  by  L.  S.  Moisseiff.  and  published 
under  date  of  Nov.  9,  1905. 

/.  General. — Specifications   apply  to  concrete  construction  in  seneral. 
and  to  use  of  Portland  cement  in  particular.     Concrete  is  termed      wet  ** 
or  "  dry;"  shall  be  capable  of  bein^  tamped  to  acqtiire  the  necessary  den- 
sitv   to   develop   the   required   resistance.     //.  Ptanning  and  Destpting. 
III.  Construction.     (A)    General.     (B)    Superintendence    and    workmen. 
(C)  Building  Materials  and  their  Working,     (a)  Materials:  Cement  which 
fulfils  the  requirements  of  the  standard  specifications  for  Portland  cenoent 
shall  be  used  exclusively.     Quick  setting  cement  shall  not  be  used  £or 
concrete  except  in  special  cases.     (The  setting  of  the  concrete  is  affected 
by  the  temperature  and  moisture  of  the  air  and  the  temperature  of  the  water 
used.     High  temperature  accelerates  setting:  low  temperature  retards  it. 
In  the  presence  of  water  pressxue  the  use  ot  quick  setting  cement  is  fre- 
quently necessary.)     "  Sand  "  includes  land-,  river-  and  sea-sand,  as  well 
as  broken  or  crushed  products,  from  fine  grains  to  0.28  in.  in  dianoeter 
(includes  granulated  furnace  slag  of  proper  consistency).     "  Gravel,"  from 
0.28  in.   up.     "Gravel-sand,"  the  natural  mixture  m>m  excavations  or 
beds  of  streams.     The  sand,  gravel  and  broken  stone  shall  be  suitable 
(loam,  clay  and  similar  admixtures  have  an  injurious  effect  if  they  adhere 
to  the  sand  and  stone;  but  if  they  are  finely  distributed  in  the  sand,  without 
adhering  to  the  ^ains.  they  are,  as  a  rule,  harmless  and  may  even  sometimes 
increase  the  resistance),  and  shall  not  contain  vegetable  matter  or  other 
impurities.     (The  stone  or  gravel  used. shall,  as  a  rule,  have  at  least  the 
same  resistance   as   the  hardened   mortar.     Stone  not  weather-resisting, 
soft  sandstone,  underbtunt  brick  shall  not  be  used  for  concrete.     Slas  is 
variable  and  ^ould  be  tested).     According  to  the  thickness  of  the  concrete 
body,  gravel  up  to  2  ins.  in  dia.  may  be  used.     (Clean  stones  of  large  size 
of  good  compressive  resistances  and  weathering  qualities  may  be  embedded 
in  the  concrete  up  to  40%  of  the  total  volume  il  the  character  and  dimen- 
sions of  the  member  allow  it  and  provision  be  made  for  the  proper  distri- 
bution of  such  stones  in  the  concrete  as  well  as  for  the  use  of  a  sufficiently 
wet  concrete  to  surround  them  completely.)     For  *  broken  stone.**   only 
hard  rocks,  unaffected  by  the  weather,  shall  be  used.     As  a  rule,  the  broken 
stone  shall  also  be  of  different  sizes  of  stones  as  the  concrete  mass  can  then 
be  worked  easier  and  better,  and  gives  a  denser  and  stronger  concrete. 
The  sizes  of  the  stones  vary  with  the  thickness  of  the  concrete  mass.      The 
largest  stones  shall,  according  the  their  use,  pass  in  any  direction  throush 
a  nn^  of  2 . 4  to  2 . 8  ins.  diameter,  or  through  a  square  of  2  to  2 . 4  on  a  siae^ 
Particles  of  sizes  smaller  than  0 .  28  in.  down  to  stone  dust  shall  be  considered 
as  sand.     The  "  water  "  used  shall  be  clean,  etc.      Marshy  water  is   in- 
jurious,    (b)    Preparing   the  concrete:   In  proportioning  the  materials,    it 
the  cement  be  measured  by  volume  it  is  understood  that  it  is  emptied  into 
the  measuring  vessel  without  dropping  and  the  latter  is  not  shaken.      To 
convert  volumes  into  weights,  a  cuDic  foot  of  Portland  cement  shall  be  t«ken 
as  87.6  lbs.      Gravel-sand  and  mixed  broken  stone  may  in  many  cases  be 
used  without  being  separated.     Tests  shall  then  be  made  by  sieving   to 
determine  the  proiK>rtions  of  the  sand  in  the  gravel  or  the  stone  dvtst  in 


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444  25.— MASONRY. 

The  Preservative  Qualities  of  Cement,  witk  regard  to  iron  or  steel 
imbedded  in  the  concrete,  are  pretty  clearly  established.  Iron  exposed 
to  pure,  dry  air,  or  in  moist  air  free  from  carbonic  oxide,  and  at  ordinary 
temperatures,  wiU  not  rust.  Rust  is  formed  through  the  combined  agency 
of  carbonic  acid  and  moisture,  and  as  carbonic  aad  has  a  greater  aifinity 
for  the  cement  mortar,  the  iron  will  not  be  attacked  while  the  former  is 
present,  and  encases  it  in  a  thorough  manner.  The  few  isolated  cases 
recorded  where  rust  has  been  found  must  be  explained  on  the  theory  of 
some  defect  in  workmanship  or  materials,  as  they  stand  out  in  m&rked 
contrast  with  practically  all  the  accepted  results  of  investigation  on  this 
subject.  Perhaps  the  most  notable  instance  of  what  may  indirectly  be 
called  a  long-time  test  was  the  finding  of  a  small  piece  of  "  bright  "  ixxm  in 
mortar  taken  from  the  base  of  the  Egyptian  obelisk  (of  granite,  70  ft.  long, 
weighing  200  tons,)  re-erected  in  Central  Park,  New  York  City,  1881. 
Numerous  instances  may  be  cited  of  iron  being  found  in  perfect  condition 
after  from  10  to  25  years'  service  in  mortar  or  concrete  (both  stone  and  cin- 
der) entering  into  various  kinds  of  construction,  both  m  and  out  of  v^ater 
(salt  and  fresh).  To  insure  absolute  protection,  the  bright  rods  niuiy  be 
coated  with  fresh  cement  when  placed;  and  it  is  well  to  remember  that  they 
should  be  embedded  thoroughly  in  the  concrete,  the  latter  to  be  a  wet 
mixture,  or  a  medium,  well  rammed,  (the  former  preferred)  to  guard  against 
voids. 

The  Fire-Resisting  Qualities  of  Concrete  and  concrete-steel  construction 
in  buildings  were  illustrated  in  the  Baltimore  fire,  in  1901.  Although  no 
construction  was  found  to  be  really  fireproof,  it  was  noticeable  that  con- 
crete made  from  steam-boiler  cinders  and  Portland  cement  seemed  to  act 
the  best;  and  that  stone  concrete  stood  fully  as  well  as,  if  not  better  than, 
terra  cotta.  Results  of  other  tests,  specially  made  for  com[>arison,  point 
to  the  same  conclusion.  We  may  safely  say,  then,  that  reinforced  concrete 
has  all  the  fire-resisting  qualities  which  may  be  expected  in  the  best  materials 
of  construction  of  the  present  day. 

The  Proportions  used  in  mixing  concrete  for  reinforced-concrete  con- 
struction almost  invariably  range  from  1  cement,  2  sand,  and  4  broken 
stone  or  gravel  or  cinders,  to  a  1  :  8  :  6  mix.  Portland  cement  should  be 
used.  Clean,  sharp  sand  is  usually  specified,  but  some  engineers  claim 
that  sand  well  worn  and  rotmded  is  best,  and  also  cheapest  as  the  voids  are 
less,  requiring  less  cement.  A  1  :  8  :  6  mix  is  suitable  for  column-  and  wail 
construction;  a  1  :  2}  :  5  mix,  for  girders;  and  a  1  :  2  :  4  mix  for  the  lighter 
construction  as  fioor  slabs  and  small,  shallow  beams  subject  to  direct  impact 
from  live  load.  The  broken  stone  is  also  graded,  say,  from  i  in.  upwautl 
to  conform  somewhat  with  the  above  proportions,  the  finer  stone  being 
used  with  the  1:2:4  mix,  for  the  thinner  masses. 

Calculation  of  Beams. — ^The  following  analysis  assumes  that  the  resist- 
ing moment  of  the  beam  is  made  up  of 
two  moments:  (1)  that  above  the  neutral 
axis,  due  to  the  concrete  area  in  com- 
pression; and  (2)  that  below  the  neutral 
axis,  due  to  the  steel  area  in  tension,  no 
account  being  taken  of  the  concrete  inx 
tension.  This  is  in  accordance  with  the 
best  practice  at  the  present  time. 

Notation. 

Let  k  -height  of  beam,  in  ins.  (Fig.  11);  Pig.  11. 

6 —  breadth  of  beam,  in  ins.; 
X  —  X  =  neutral  axis ; 

cf= depth  to  center  of  reinforcement,  below  top  of  beam,  in  ins.; 
A  — cf— distance  from  bottom  of  beam  to  center  of  reinforcement,  in  ins. 
(either  d  or  k—d  may  be  fixed  arbitrarily);^ 
/  IB  allowable  compressive  stress  in  lbs.  per  S9.  in.  on  concrete  to  be 
used  with  tne  straight-line  equivalent  (instead  of  the  stress    .«: 
to  due  to  the  actual  stress-strain  diagram — shaded) :  ©  • 
*/2  moe.  —  720  lbs.  per  sq.  in.  for  good  1:2:4  concrete. "8  ^ 
♦/amos.-GOO     "     ^'     '^     "       ••      ^'         1  :  2J  :  6       "          t?^ 
^/2mos.-600    • *•        1:3:6       "         ^^ 

*  These  values  are  about  10%  greater  than  the  vahaes  of  i«  which  would 
be  used  with  the  exact  stress-strain  ctirve.       Digitized  by  V^OOglC 


REIN. -CONCRETE  BEAM  FORMULAS.  445 

F-aJlowable  tensile  stress  in  lbs.  per  sq.  in.  on  the  steel  rods 

(15000  for  buildings): 
a— sectional  area  of  the  steel  rods,  in  sq.  ins.; 
ik— ratk>  of  raodulii  of  elasticity  of  steel  and  concrete: 

Ar»13  for  steel  and  good    1:2    :  4  concrete. 

ik-14 1  :  2J  :  6 

*-15    ••     "       ••       ••       1:3:6 
V— distance,  in  ins.,  from  top  of  beam  to  neutral  axis. 
Jf'— bending  moment — resisting  moment,  inch-lbs. 
AT-       "  "        -        "  "  ft.-lbs. 

Gtrm'al  Formulas: 

Raisting  moment,  Af'-  i  /  6  y«+aF  (d-y) (1) 

For  conditions  of  equilibrium,  the  algebraic  sum  of  the  horizontal  forces  at 
any  section  must  eoual  zero  (JH—O),  hence  we  have,  neglecting  the 

tension  in  concrete,  below  the  neutral  axis,  a  F—  \fby (2) 

Prom  the  ratio  k  of  the  moduli!  of  elasticity  of  the  materials,  and  the  relative 

position  of  the  neutral  axis,  we  have,  kf{d—y)'^Fy  .'.  ydv.7^. . . .  (8) 
Combining  (2)  and  (3),  we*have: 


.(4) 


Distance  to  neutral  axis,  y —-r- («/l-i — r — l)     

Breadth  of  beam.  b^^id-y) (id) 

Area  of  steel  rods,  a*-  ^urJ  — 7 (**) 

£M  (a—y) 

Also,  from  (2),  a-y-^ (4c) 

Depth  to  center  of  rods,    d-y  (l  +  ^\ (id) 

Combining  (1)  and  (2)  we  have: 

Stress  in  the  concrete,        f  —  g~7\izr~^  ^^'  P®*"  ^Q*  i° (*) 

Stress  in  the  steel, ^"^  a(3d-y)     "     ^^ 

Also,from(2),    F-^^ (6o) 

The  following  values  of  /t  niay  be  asstuned  for  the  three  standard  con- 
crete mixes:    (See  Table  4,  next  page.) 
Concrete. 

Uix.                Time.  Ultimate.  Factor  4.  Factor  5.  Factor  6. 

1:2:4               1  mo.  /-2400.  /-600.  /-480.  /-400. 

2mos.  2880.  720.  676.  480. 

Smos.  8000.  750.  600.  500. 

Omos.  8600.  900.  720.  600. 

I:2i:6             1  mo.  2200.  550.  440.  367. 

",                 2mos.  2640.  660.  528.  440. 

8mo8.  2750.  688.  550.  458. 

6mos.  8300.  825.  660.  550. 

1:3:6              1  mo.  2000.  500.  400.  333. 

2mos.  2400.  600.  480.  400. 

dmos.  2500.  625.  500.  417. 

6mos.  8000.  750.  600.  500. 


*  Equation  (3)  gives  y  when  a  is  unknown ;  it  is  directly  proportional  to  d. 

t  Pen*  use  with  straightiJine  formulas  adopted  above.  The  values  of 
fo,  or  actual  maximum  compression  on  the  outer  element  af>  the  concrete, 
wiU  be  about  9%  less.  '-^^  by^aOgTe 


446 


26.^MASONRY. 


4. — Propbrtibs  of  Rbin.-Conc.  Bbajcs  1*  Widb  (6—1)  and  of  Various 
Dbpths.  d  OR  h.  (Pig.  11,  page  444.) 

DaU:  (>>ncrete.  1:8:6;  age,  2  mos. ;  /»  600.     Steel.  F->  15000.     ib  -»  15. 
Pactor  of  safety.  4.     Por  factor  of  6,  mult.  Af'  of  table  by  ,1,;  for  6,  by  f 


Area  a 

of  Steel 

RaUo 

Rods. 

a 

Sq.  Ins. 

d 

Maxi- 
mum 
Depth 

In^. 


2 
3 
4 
5 
6 
7 
8 
9 

10 
11 
12 
14 
16 
18 
20 
22 
24 


32.8 

.75 

73.8 

1.125 

131.2 

1.50 

205.8 

1.875 

295. 

2.25 

402. 

2.625 

525. 

3.00 

664. 

3.375 

820. 

3.75 

902. 

4.125 

1181. 

4.50 

1608. 

5.25 

2100. 

6.00 

2668. 

6.75 

3281. 

7  50 

3970. 

8.25 

4725. 

9.00 

1.5 
2.71 
3.87 
5. 

6.12 

7.22 

8.32 

9.41 

10  5 

11.58 

12.66 

13.73 

15.87 

18. 

20.12 

22  24 

24.35 

26.45 


Approx. 

Ratio 

a+h. 

Ins. 


Lin.  ¥t. 
of  Beam, 
at  160 
Lbs.  per 
Cu.  Ft, 
Lbs. 


.0050 
.0055 
.0058 
.0060 
.0061 
.0062 
.0063 
.0064 
.0064 
.0065 
.0065 
.0066 
.0066 
.0067 
.0067 
.0067 
.0068 
.0068 


1.56 

2.82 

4.03 

5.21 

6.38 

7.62 

8.67 

9.80 

10.94 

12.06 

13.19 

14.30 

16.53 

18.76 

20.96 

23.17 

25.36 

27.66 


Pormulas  for  above  table,  reduced  from  General  Formulas,  preceding, 
are:  y-fd;  a-  .02X|>'=-  .0075d;  Jlf'  =  8.203  ^.  These  values  will  vary, 
of  course,  with  variations  in  the  values  of  /,  F,  and  k. 

Sttgfetted  Formulas  for  Reinforced  Concrete  Constmction  (From 
Majority  Report  of  Special  Committee  of  Am.  Soc.  C.  E.  on  Concrete  and 
Remforced  Concrete.  Proc.  Am.  Soc.  C.  E..  Feb.,  1909). — These  formulas 
are  based  upon  the  assumptions  and  principles  given  in  the  chapter  on  De- 
sign (see  Trans.  A.  S.  C.  E..  Vol.  LXVI).  For  Working  Strbssbs,  see: 
Sec.  31.  Beams,  page  585;  Sec.  32,  Columns,  page  609. 

A.    Standard  Notation. 

A.    Rectangular  Beams. 

/.  —  tensile  unit  stress  in  steel. 

/,= compressive  unit  stress  in  concrete. 
£•  — modulus  of  elasticity  of  steel. 
E,  —  modulus  of  elasticity  of  concrete. 

n -£.-*-£,. 
Af  "-moment  of  resistance,  or  bending  moment  in  general. 

A —  steel  area. 

6— breadth  of  beam. 

d  «•  depth  of  beam  to  center  of  steel. 

k  —  ratio  of  depth  of  neutral  axis  to  effective  depth,  d, 

«— depth  of  resultant  compression  below  top. 

f --ratio  of  lever  arm  of  resisting  couple  to  depth,  d. 
jd— d  — «— arm  of  resisting  couple. 

p  — steel  ratio  (not  percentage). 

1-Beamt. 

6 -width  of  flange, 
fr*— width  of  stem. 
<  — thickness  of  flange. 


d  by  Google 


FORMULAS  FOR  REINFORCED  CONCRETE, 


447 


mma  Refarforc«d  for  Coaipmtioa. 
^'— area  of  compressive  steeL 
f'— steel  xatio  for  compressive  steel. 
U  <*tmit  compressive  stress  in  steeL 
C— total  compressive  stress  in  concrete. 
C— total  compressive  stress  in  steel. 
J*— depth  to  center  of  compressive  steel, 
s-o  depth  to  restiltant  td  C  and  C, 


y-toUl  shear. 
v->  shearing  tmit  stress. 
K—bond  stress  per  unit  area  of  bar. 
0-B  circumference  or  perimeter  of  bar. 
Jo^sum  of  the  perimeters  of  all  bars. 


A  » total  net  area. 
A.—area  of  longitudinal  steel. 
Ar->area  of  concrete. 

P->total  safe  load. 

B.     PottlCULAS. 

Rscfsntnlsr  Beams. 

.     /a 

V      — 


Fig.  12. 
Position  of  neutral  axis. 

Arm  of  resisting  couple, 


1, 


/-1-f*. 


For  U"  15  000  to  16  000  and  /«- 600  to  650,  /  may  be  taken  at  \\ 

2pf. 
k 


Fiber  stresses.   /.-  —  -_-. 


,     _2M_     2pf. 


Fig.  18. 


by  Google 


448 


25.— MASONRY. 


Cas0  I.    Wh*n  ihs  ntuiral  axis  lus  in  tk*  flange,  use  the  formulas  f  or 
rectangular  beams. 

Cas0  II.    When  the  neutral  axis  lies  in  the  stem. 

The  following  formulas  neglect  the  compression  in  the  stem: 

Position  of  neutral  axis, 

2ndA  +  bfi 
*^  "  2nA+2bt  ' 
Position  of  resultant  compression, 

Zkd-2t     t_ 

3' 

Arm  of  resisting  couple, 


/.- 


2kd-t 
jd^d-s. 

Mkd 


Fiber  stresses. 

-     ■         U   ±_ 

Aid      '•     bt{kd-\t)jd     n'  k-l 

(For  approximate  results,  the  formulas  for  rectangular  beams  may  l>e 
used.) 

The  following  formulas  take  into  account  the  compression  in  the  stem; 
they  are  recommended  where  the  flange  is  small  compared  with  the  stem. 

Position  of  neutral  axis. 


Position  of  resultant  compression, 

{kdt^-mb+ijkd-tnt+k)  (kd-i)y/ 

'"  t{2kd'-t)b  +  ikd-t)^i/ 

Arm  of  resisting  couple. 

Fiber  stresses, 

.      Ji_  2  Mkd 

^'"Ajd       "^  [i2kd-t)bt+ihd'-t)*l/]jd' 

c    Beams  Reinforced  for  Comprwiloa. 


: i.i.M- 

t-r — 


I 
I 

I 
I 

J± 


Fig.  14. 


Position  of  neutral  axis, 


Position  of  resultant  compression. 


Arm  of  resisting  couple, 


jd^d  —  Z.       Digitized  by  VjOOQIC 


REIN.-CONC.  FORMULAS.   MIXED  MASONRY.  449 

Fiber  stresBes 

,  6Af* 


!  k-£ 

A   Sbmu,  Bond,  and  Web  RciiJorcMMot 

hi.  the  following  formula,  ib  refen  only  to  the  bars  constituting  the 
IcQsion  rexnforoement  at  the  section  in  question  and  /  d  is  the  lever  arm  of 
the  resisting  couple  at  the  section. 

For  rectangular  beams, 

V 

V 

[For  approximate  results,  /  may  be  taken  at  {.] 

The  stresses  in  web  reinforcement  may  be  estimated  by  using  the 
pvUowing  formulas: 

Vertical  reinforcement. 

Reinforcement  incUned  at  75^, 

W  which  P>- stress  in  nngle  reinforcing  member,  K  — proportion  of  total 
hear  assumed  atf* carried  by  the  reinforcement,  and  5  — horizontal  spacing 
tC  the  reinforcing  members. 

The  same  formulas  apply  to  beams  reinforced  for  compression  as  re- 
Buds  shear  and  bond  stress  for  tensile  steel.  ■ 

For  T-beams, 
I  V_  V 

^"l/jd*     ^"id.Io' 

P^or  approximate  results,  /  may  be  taken  at  }.] 

e.    Cdanos. 

Total  safe  load, 

P-/,(A.  +  i»yl.)-M(l  + («-!)/»). 
I     Unit  stresses, 

f  -,  P 

I  ^'     i4(l  +  (n-l)p) 

V.  MIXED  MASONRY. 

The  object  of  using  mixed  masonry  is  to  give  a  substantial  looking, 
kushed  face,  using  a  better  class  of  masonry  for  this  purpose,  and  using  a 
^eai>er  quality  for  interior  and  back  of  wall.  Strictly  speaking,  most 
Qasonry  is  more  or  less  mixed — ashlar  backed  with  rubble,  face-brick 
acked  with  common  brick,  etc.;  but  the  term  "  mixed  masonry  "  is  gen- 
ially restricted  to  stone  facing  with  brick  backing. 

The  bond  between  stone  and  brick,  or  stone  and  concrete,  is  often  a 
tonrce  of  weakness.  When  interior  brick  walls  are  joined  to  stone  face- 
sails,  iron  "  cramps  "  are  generally  employed. 


460  IS.^MASONRY. 

VI.— CONCRETE-BLOCK  MASONRY. 

Solid  concrete  blocks  are  often  used  in  submarine  work,  as  fo 
in  breakwater  construction,  in  preference  to  laying  the  concret 

Hollow  concrete  blocks  are  made  in  many  shapes  and  are  usee 
ing  construction.  The  completed  wall  should  generally  be  not 
two-thirds  solid,  although  in  some  places  as  much  as  40-  to  50  p4 
voids  is  allowed.  The  surface  of  the  blocks  should  be  rich  in  ce 
have  a  finer  aggregate  than  the  interior.  The  best  blocks  are 
machine  under  heavy  (usually  hydraulic)  pressure.  The  writer 
many  blocks  turned  out  by  the  small,  portable  machines  in  wl 
tamping  is  reqiuredj  and  the  results  were  invariably  inferior.  1 
are  laid  in  the  wall  in  cement  mortar,  and  sometimes  iron  cramp 
for  bonding  them  together.  Outside  cement  plaster  or  stucco  oi 
quality  may  be  laid  directly  on  the  blocks,  and  gives  a  finished  a{ 
Inside  plaster  should  not  be  laid  without  furring  and  lathing,  if  \ 
are  porous  or  inferior  in  quality  on  account  of  moisture  and  frc 
the  blocks  have  been  waterproofed. 

Specifications  for  Hollow  Concrete  Building  Blocks. — ^The  fo 
from  the  Rules  and  Regulations  ifovemin^  the  use  and  manu 
Hollow  Concrete  Building  Blocks  in  the  City  of  Philadelphia — 
Building  Inspection. 

Ruks  and  Regulations. 

1.  Hollow  concrete  building  blocks  may  be  used  for  building 
or  less  in  height,  where  said  xxae  is  approved  by  the  Bureau  ol 
Inspection;  provided,  however,  that  such  blocks  shall  be  comp< 
least  1  part  stantlard  Portland  cement,  and  not  to  exceed  5  ps 
coarse,  sharp  sand  or  gravel,  or  a  mixture  of  at  least  1  part  Portia 
to  5  parts  crushed  rock  or  other  suitable  aggregate.  -  Providec 
that  this  section  shall  not  permit  the  use  of  hollow  blocks  in  ps 
Said  party  walls  must  be  built  solid. 

2.  All  material  to  be  of  such  fineness  as  to  pass  a  }-in.  ring  a 
from  dirt  or  foreign  matter.  The  material  composing  such  bl 
be  properly  mixed  and  manipulated,  and  the  hollow  space  in  s 
shall  not  exceed  the  percentage  given  in  the  following  table  foa 
height  walls,  and  in  no  case  shall  the  walls  or  webs  of  the  block 
thickness  than  J  of  the  [height.  The  figures  given  in  the  tal 
represent  the  percentage  of  such  hollow  space  for  different  heig 

Stories.        1st.       2nd.     8rd.      4th.      5th.      6th. 

land  2 33         33       

3  and  4  . . .       25         33         33         33       

5  and  6  . . .       20         25         25         33         33         S3 

3.  The  thickness  of  walls  for  any  building  where  hollow  conci 
are  used  shall  not  be  less  than  is  required  by  law  for  brick  walls. 

4.  Where  the  face  only  is  of  hollow  concrete  building  blocl 
backing  is  of  brick,  the  facing  of  hollow  concrete  blocks  must  b 
bonded  to  the  brick  either  with  headers  projecting  4  ins.  into 
work,  every  fourth  course  being  a  heading  cotirse,  or  with  appi 
no  brick  backing  to  be  less  than  8  ins.  Where  the  walls  are  ma* 
of  hollow  concrete  blocks,  but  where  said  blocks  have  not  the  s: 
as  the  wall,  every  fifth  course  shall  extend  through  the  wall, 
secure  bond.  All  walls,  where  blocks  are  used,  shall  be  laid  up  ii 
cement  mortar. 

5.  All  hollow  concrete  building  blocks,  before  beinff  tised  h 
struction  of  any  building  in  the  City  of  Philadelphia,  shall  hav 
the  age  of  at  least  3  weeks. 

6.  Wherever  girders  or  Joists  rest  upon  walls  so  that  there  a 
trated  load  on  the  block  of  over  2  tons,  the  blocks  supporting  th 
joists  must  be  made  solid.  Where  such  concentrated  load  shal 
tons,  the  blocks  for  2  courses  below,  and  for  a  distance  extendi: 
18  ins.  each  side  of  said  girder,  shall  be  made  solid.  Where  the  1 
J^'l  from  the  girder  exceeds  5  tons,  the  blocks  for  3  courses  bene 
DC  made  solid  with  similar  material  as  in  the  blocks.  Whereve 
accreased  m  thickness,  the  top  course  of  the  thicker  wall  to  be 


Digitized 


by  Google 


SPECNS  FOR  HOLLOW  COSCRETE  BLOCKS.  451 

7.  Provided  alwajrs,  that  no  wall,  or  any  part  thereof,  composed  of 
hollow  concrete  blocks  shall  be  loaded  to  an  excess  of  8  tons  per  superficial 
foot  of  the  area  of  such  blocks,  including  the  weight  of  the  wall,  and  no  blocks 
diall  be  Qsed  that  have  an  average  crushing  at  less  than  1000  pounds  per 
square  inch  of  area  at  the  age  of  28  days;  no  deduction  to  be  made  in  figtinng 
tl»  area  for  the  hollow  spaces. 

8.  All  piers  and  buttresses  that  support  loads  in  excess  of  5  tons,  shall 
be  built  of  solid  concrete  blocks  for  such  distance  below  as  may  be  required 
by  the  Bureau  of  Building  Inspection.  Concrete  lintels  and  sills  shall  be 
reinforced  by  iron  or  steel  rods  in  a  manner  satisfactory  to  the  Bureau  of 
BuJding  Inspection,  and  any  lintels  spanning  over  4  feet  six  inches  in  the 
clear  shall  rest  on  solid  concrete  blocks. 

9.  Provided,  that  no  hollow  concrete  building  blocks  shall  be  used  in 
the  construction  of  any  building  in  the  City  of  Philadelphia,  tmless  the  maker 
of  said  blocks  has  submitted  his  product  to  the  full  test  required  by  the 
Bureau  of  Building  Inspection,  and  placed  on  5le  with  said  B.  of  B.  I.  a 
certificate  from  a  reliable  testing  laboratory  showing  that  samples  from  the 
lot  of  blocks  to  be  used  have  successfully  pa^ed  the  requirements  of  the 
B.  of  B.  L,  and  filing  a  full  copy  of  the  test  with  the  Bureau. 

10.  A  brand  or  mark  of  identification  must  be  impressed  in,  or  otherwise 
pcmanently  attached  to,  each  block  for  purpose  of  identification. 

11.  No  certificate  of  approval  shall  be  considered  in  force  for  more  than 
four  months,  unless  there  be  filed  with  the  B.  of  B.  I.,  in  the  Cityof  Phila., 
at  least  once  every  four  months  following,  a  cert  ificate  from  some  reliable  phys- 
ical testing  laboratory  showing  that  the  average  of  three  (3)  specimens 
tested  for  compression,  and  three  (3)  specimens  tested  for  transverse  strength, 
comply  with  the  requirements  of  the  B.  of  B.  I.;  samples  to  be  selected 
either  by  a  Building  Inspector  or  by  the  laboratory,  from  blocks  actually 
going  into  construction  work.  Samples  must  not  be  furnished  by  the 
oootractors  or  builders. 

12.  The  manufacturer  and  user  of  any  such  hollow  concrete  blocks  as 
are  mentioned  in  this  regulation,  or  either  of  them,  shall,  at  any  and  all 
times,  have  made  such  tests  of  the  cements  used  in  making  such  blocks,  or 
soch  further  tests  of  the  completed  blocks,  or  of  each  of  these,  at  their  own 
expense,  and  under  the  supervision  of  the  B.  of  B.  I.,  as  the  Chief  of  said 
Bureau  shall  require. 

13.  The  cement  used  in  making  said  blocks  shall  be  Portland  cement, 
and  must  be  capable  of  passing  the  minimum  requirements  as  set  forth  in 
the  "  Standard  Specifications  for  Cement  "  by  the  American  Society  for 
Testing  Materials. 

14.  Any  and  all  blocks,  samples  of  which,  on  being  tested  under  the 
direction  of  the  B.  of  B.  I.,  tail  to  stand  at  28  days  the  tests  required  by  this 
regulation,  shall  be  marked  **  condemned  "  by  the  manufacturer  or  user, 
and  shall  be  destroyed. 

15.  No  concrete  blocks  shall  be  used  in  the  construction  of  any  building 
within  the  City  of  Phila.  until  they  shall  have  been  inspected,  and  average 
samples  of  the  lot  tested,  approved  and  accepted  by  the  Chief  of  Building 
In^>ectoi8. 

Mtihod  of  Testing  Hollow  Blocks. 

t.  These  regulations  shall  apply  to  all  such  new  materials  as  are  used 
in  building  constniction,  in  the  same  manner  and  for  the  same  purposes 
as  stones,  brick,  concrete  are  now  authorized  by  the  Building  Laws,  when 
said  new  material  to  be  substituted  departs  from  the  general  8hai>e  and 
dimensions  of  ordinary  building  brick,  and  more  particularly  to  that  form 
of  building  material  known  as  "  Hollow  Concrete  Block,"  manufactured 
from  cement  and  a  certain  addition  of  sand,  crushed  stone,  or  similar 
materiaL 

i.  Before  any  such  material  is  used  in  buildings,  an  application  for 
its  use  and  for  a  test  of  the  same  must  be  filed  with  the  Chief  of  the  B.  of  B.  I. 
A  description  of  the  material  and  a  brief  outline  of  its  manufacture  and 
pn^xjrtions  of  the  materials  used  must  be  embodied  in  the  application. 

8.  The  materia]  must  be  subjected  to  the  following  tests:  Transverse, 
Compression.  Absorption.  Freezing,  and  Fire.  Additional  tests  may  be 
called  for  when,  in  the  iudmnent  of  the  Chief  of  the  B.  of  B.  I.,  the  same 


462  2S.— MASONRY. 

•may  be  necessary.  All  such  tests  mtist  be  made  in  some  laboratory  of 
recognized  standing,  tmder  the  supervision  of  the  Engineer  of  the  B.  of  B.  1. 
The  tests  will  be  made  at  the  expense  of  the  applicant. 

4.  The  results  of  the  tests,  whether  satisfactory  or  not.  must  be  placed 
on  file  in  the  B.  of  B.  L  They  shall  be  open  to  inspection  upon  apphcAtioa 
to  the  Chief  of  the  Bureau,  but  need  not  necessarily  be  published. 

5.  For  the  purposes  of  the  tests,  at  least  20  samples  of  test  i^ieoes 
must  be  provided.     Such  samples  must  represent  the  ordinary  commercial 

rduct.  They  may  be  selected  from  stock  by  the  Chief  of  the  B.  of  B. 
or  his  representative,  or  may  be  made  in  his  presence,  at  his  discretloii. 
The  samples  miist  be  of  the  regular  size  and  shape  used  in  oonstnurtion. 
In  cases  where  the  material  is  made  and  used  in  special  shapes  and  tonxts, 
too  large  for  testing  in  the  ordinary  machines,  smaller  sized  specimezis 
shall  be  used  as  may  be  directed  by  the  Chief  of  Building  Inspei^ioii.  to 
determine  the  physical  characteristic  specified  in  Section  3. 

6.  The  samples  may  be  tested  as  soon  as  desired  by  the  applicant.  \yut 
in  no  case  later  than  60  days  after  manufacture. 

7.  The  weight  per  cubic  foot  of  the  material  must  be  detennined. 

8.  Tests  shall  be  made  in  series  of  at  least  five,  except  that  in  the  fire 
tests  a  series  of  two  (four  samples)  are  sufficient.  Tcaasverse  tests  shall 
be  made  on  full  sized  samples.  Half  samples  may  be  used  for  the  cruslims, 
freezing,  and  fire  tests.  The  remaining  samples  are  kept  in  reserve,  in.  c»ise 
unusual  flaws  or  exceptional  or  abnormal  conditions  make  it  neoessarsr  to 
discard  certain  of  the  tests.  All  samples  must  be  marked  for  identification 
and  comparison. 

0.  The  Transverse  test  shall  be  made  as  follows:  The  samples  shall  be 
placed  flatwise  on  two  rotmded  knife  edge  bearings  set  parallel  Seven  ir><^h^^ 
apart.  A  load  is  then  applied  on  top,  midway  between  the  supports,  and 
transmitted  through  a  similar  roimded  knife  edge,  until  the  sample  ia 
ruptured.  The  modulus  of  rui)ture  shall  then  be  determined  by  mtilti- 
plying  the  total  breaking  load  in  pounds  by  twenty-one  (three  tunee  the 
distance  between  supports  in  inches)  and  then  dividing  the  result  thtzs 
obtained  by  twice  the  product  of  the  width  in  inches  by  the  square  of  the 

depth  in  inches:   R—  2~b~di'    ^°  allowance  should  be  made  in  figuring  the 

modulus  of  rupture  for  the  hollow  spaces. 

10.  The  Compression  test  shall  be  made  as  follows:  Samples  must  be 
cut  from  blocks  so  as  to  contain  a  fuU  web  section.  The  sample  must  be 
carefully  measured,  then  bedded  flat-wise  in  Plaster  of  Paris,  to  secure  a 
uniform  bearing  in  the  testing  machine,  and  crushed.  The  total  brealcin^ 
load  is  then  divided  by  the  area  in  compression  in  square  inches.  No 
deduction  to  be  made  for  hollow  spaces;  the  area  will  be  considered  as  the 
product  of  the  width  by  the  length. 

11.  The  Absorption  test  must  be  made  as  follows:  The  sample  is  first 
thoroughly  dried  to  a  constant  weight.  The  weight  must  be  carefully 
recorded.  It  is  then  placed  in  a  pan  or  tray  of  water,  face  dowuwaixT, 
immersing  it  to  a  depth  of  not  more  than  one-half  inch.  It  is  again  caref  ally- 
weighed  at  the  following  periods:  Thirty  minutes,  four  hours,  and  forty- 
eight  hours,  respectively,  from  the  time  of  immersion,  being  replaced  xz& 
the  water  in  each  case  as  soon  as  the  weight  is  taken.  Its  compressi^ve 
strength,  while  still  wet,  is  then  determined  at  the  end  of  the  forty-eisht 
houra  period,  in  the  manner  specified  in  section  10. 

12.  The  Freezing  test  is  made  as  follows:  The  sample  is  immersed,  as 
described  in  section  11,  for  at  least  four  hours,  and  then  weighed.  ^  It  is 
then  placed  in  a  freezing  mixture  or  a  refrigerator,  or  otherwise  8ubject««l 
to  a  temperature  of  less  than  15  degrees  P.  for  at  least  12  hours.  It  a  th«c& 
removed  and  placed  in  water,  where  it  must  remain  for  at  least  one  hotar, 
the  temperature  of  which  is  at  least  150  degrees  P.  This  operation  la 
repeated  ten  (1())  times,  after  which  the  sample  is  again  wei^ied  while 
stxil  wet  from  the  last  thawing.  Its  crushing  strength  shotild  then  l^e 
determined  as  called  for  in  section  10. 

^3.  The  Fire  test  must  be  made  as  follows: — ^Two  samples  are  plaoe<i 
»  *  T^  furnace  in  which  the  temperature  is  gradually  raised  to  I  TOOdegneea 
f.  ihe  t^  piece  must  be  subjected  to  this  temperature  for  at  least  9Q 
minutes.     One  of  the  samples  is  then  plunged  in  cold  water  (sboot    ^O 


SPECNS  FOR  HOLLOW  CONCRETE  BLOCKS,  453 

to  00  degrees  P.)  and  the  resalts  noted.     Tbe  second  sample  is 

permitted  to  cool  gradually  in  air,  and  the  resiilts  noted. 

14.  The  following  requirements  must  be  met  to  secure  the  acceptance 
of  the  materials:  The  Modulus  of  Rupture  for  concrete  blocks  at  38  days 
old  must  average  150  and  must  not  fall  below  100  in  any  case.  The  ultimate 
compressive  strength  at  28  days  must  average  1000  lbs.  per  s<^.  in.,  and 
must  not  fall  below  700  in  anv  case.  The  percentage  of  absorption  (being 
the  weight  of  water  absorbed  divided  by  the  weight  of  the  dry  sample), 
most  not  average  higher  than  15%  and  must  not  exceed  25%  in  any  case. 
The  reduction  of  compressive  strength  must  not  be  more  than  83i%,  except 
that  when  the  lower  figtuv  is  still  above  1000  lbs.  per  sq.  in.,  the  loss  m 
ttreogth  ma/  be  neglected.  The  freezing  and  thawing  process  must  not 
cause  a  loss  m  weight  greater  than  10%,  nor  a  loss  in  strength  of  more  than 
33)%:  except  that  when  the  lower  fixture  is  still  above  1000  lbs.  per  sq.  in., 
the  loss  in  strength  may  be  neglected.  The  fire  test  must  cause  the  material 
to /hsintesrate. 

15.  The  approval  of  anv  material  is  given  only  under  the  followixig 
conditions:  a.  A  brand  mane  for  identification  must  be  impressed  on.  or 
otherwise  attached  to,  the  material,  b.  A  plant  for  the  production  of  the 
material  must  be  in  full  operation  when  the  official  tests  are  made.  c.  The 
naott  of  the  firm  or  corporation  and  the  responsible  officers  must  be  placed 
on  file  with  the  Chief  of  B.  of  B.  I.,  and  changes  in  same  promptly  reported. 
d.  The  chief  of  the  B.  of  B.  I.  may  require  full  tests  to  be  repeated  on  sam- 
ples selected  from  the  open  maricet  when,  in  his  opinion,  there  is  any  doubt 
as  to  whether  the  product  is  up  to  the  standard  of  these  regulations,  and 
tbe  manufacturer  must  submit  to  the  B.  of  B.  I.,  once  in  at  least  every  4 
months,  a  certificate  of  tests  showing  that  the  average  resistance  of  3  sped- 
xaa»  to  cross  breaking  and  crushing  are  not  below  the  requirements  of  these 
regulations.  Such  tests  must  be  made  by  some  laboratory  of  recognised 
standing,  on  samples  selected  either  by  a  Building  Inspector  or  the  labora- 
tory, from  matdial  actually  going  mto  construction,  and  not  on  ones 
furnished  by  the  manufacturer.  0.  In  case  the  results  of  tests  made  under 
this  condition  (li.)  should  show  that  the  standard  of  these  regulations  is 
not  maintained,  the  approval  of  this  bureau  to  the  manufacturer  of  said 
blodcs  will  at  once  be  suspended  or  revoked. 

EXCERPTS  AND  REFERENCES. 

PermettbiUty    of   Concrete   Under   Hifh   Water  Pressures  (By  J.  B. 

Mclntvre  and  A.  L.  True.  Thesis,  Thayer  School  of  Civ.  Engr..  April,  1902; 
Eog.  News^  June  26,  1902). — Extensive  tables  of  tests,  ttsing  different  pro- 
portions of  concrete,  and  presstues  of  20,  40.  and  80  lbs.,  time  2  hours. 
"Oi  the  various  mixtures  we  may  safely  choose  either  1:2:4  or  1:2.5:4,  on 
account  of  their  simplicity  and  the  ease  with  which  they  may  be  propor- 
timed,  either  for  hand  or  machine  mixing.  In  extreme  cases  however. 
it  might  be  advisable  to  use  one  of  the  richer  mixtures." 

Notes  oa  Concrsto  Construction  in  Oovemment  Portificatlofls— With 

DaU  (Reoort  of  Chief  of  Engrs.  of  U.  S.  A.  for  1902;   Eng. 
.--Subj  •  •— '•• 


1003).— Subjects  treated  are:   "Tests  to  show  suitability  of 

jf  sand  for  use  in  concrete,"  by  Cap1>.  Harry  Taylor;   **Damp 

VrooBaaga  for  ceilings  of  gun  emplacements,"  bv  Maj.  G.  W.  Ooethals; 
"Damp  proofing  sunken  magazines  and  rooms,  by  Col.  P.  C.  Hains; 
"Stoppage  of  leaks  in  concrete  with  linseed  oil,"  by  Caot.  E.  W.  Van  C.  Lucas; 
"Stoppage  of  leaks  in  concrete  with  asphaltum  and  oil."  by  Maj.  W.  T. 
Rosaeu  and  (}apt.  S.  Crosby;  "Asphaltum  and  alum  and  lye  waterproofing," 
by  Capt.  W.  C.  Lan^^tt*  A  sliding  rupture  caused  by  tarred  paper  water- 
pfoc^ng."  by  Maj.  W.  T.  Rossell  and  Capt.  S.  Crosby. 

The  Efficieiicy  of  Concrete-Mixing  Machines  (By  Clarence  (x>leman. 
&ig.  News,  Aug.  27.  1903^.— The  Necessity  of  Thorough  Mixing.— The 
amount  of  cement  as  determined  for  any  concrete  should  always  be  weighed, 
xMt  measured,  as  the  volume  of  cement  is  a  variable.  The  entire  amount 
of  cement  should  be  added  before  mixing  is  commenced,  and  then  mixed 
dry  before  water  is  added.    The  proper  amount  of  water  to  be  added  re- 

r'  BS  judgment  after  visual  inspection,  as  the  hygrometric  condition  of 
sand  is  a  variable;   hence  the  entire  mass  of  the  materials  should  be 
plainly  visible  to  the  person  adding  the  water.     Proportion  of   Water  In 


454 


iS.—MASONRY. 


Concrete. — Gives  a  table  sho^ 


ymrying 


le  showiiifl  the  strength  of  mortar  due  to  varj 
proportions  of  water.    Classtficattoa  of  Machines. — Batch  Mixers  (7  types 
"    *'     "      •  'Con- 


described);    Continuous  Mixers  (5  types  described). 
Crete  Mixers. — ^Descriptions  with  illustrations. 


Comparison  of 


The  Method  of  Finishing  the  Concrete  Surfaces  of  Philadelphia 
Bridces  (By  H.  H.  puimby.  Eng.  News.  Feb.  4,  1904J.— Remove  the  forms 
while  the  concrete  is  still  green,"  and  simply  wash  toe  surface  with  water, 
squirting  it  on  with  a  nozzle  if  tne  work  is  soft  enough,  or,  if  harder.  usin« 
a  scrubbmg  brush.  If  the  cement  is  too  hard  to  wash  off  it  mtist  be  cut  by 
hard  rubbing  with  a  brick  or  a  wooden  float  and  sand,  using  plenty  of  water. 
The  removal  of  the  cement  exposes  the  sand  and  grit  or  pebbles  or  stone — 
whatever  the  aggregate  may  be — ^leaving  a  surface  that  is  mostly  stone, 
and  is  probably  as  little  subject  to  discoloration  and  cracks  as  stone,  and 
as  durable  as  any  plastic  material  can  be  made. 

Tests  of  Adhesion  and  Initial  Stress  of  Steel  In  Concrete  (By  S.  W. 

Emerson.    Eng.  News,  Mar.  10,  1904). — Diagrams  showing  results  of  tests. 

Materials  Required  to  Make  Different  Classes  of  Concrete  for  Coa- 
netkut  Ave.  Bri<lie.  Wash.,  D.  C.  (By  W.  J.  Douglas  and  A.  W.  Dow.  Bng. 
News.  Mar.  10,  1904).— 


Class 

A. 

B. 

B. 
1:2J:8:3 
4.5 
11.25 
1A.3 
13.5 
37.66 

c 

Mixture  (cem.,  sand,  gravel,  stone) 

Oment,  cu.  ft 

Sand,  cu.  ft 

Gravel,  cu.  ft 

l:2:0:4i 

4.5 

9.0 

0.0 
20.25 
21.4 

l:2i:0:6 

4.5 
11.25 

0.0 
27.0 
27.66 

1:3:10:0 

4.5 

13.5 

45  0 

Broken  Stone,  cu.  f t 

Yielded,  rammed  concrete,  cu.  ft 

0.0 
45.0 

Note  that  4.5  cu.  ft.  (Vulcanite)  cement- 1  bbl.  - 4  bags- 378.25  lbs. 

French  Qovemnien%  Rules  for  the  Design  and  Constroctiofi  of  Re- 
inforced Concrete  (Eng.  News,  Mar.  21,  1907). — ^Discussion  of  formulas,  etc. 

Exnanslon  Joints  In  Concrete  Structures,  with  Special  Reference  to 
Block  Construction  In  Drydocks  and  Reservoirs  (L.  P.  Bellinger.  Eng.  News, 
May  2,  1897).— Bright  wood  Reservoir,  Wash.,  D.  C— Dimensions,  415  x 
800  X  20  ft.  deep;  plain  concrete  with  a  vertical  outer  face  and  a  sloping 
inner  face  of  concrete;  the  vertical  outer  face  having  a  heavy  earth  em- 
bankment asainst  it.  The  concrete  wall  was  built  in  alternate  sections  not 
exceeding^  60  ft.  long.  Vertical  key  ways  6  ins.  square,  4  of  which  was  in 
each  section,  were  built  for  expansion  joints  and  first  filled  with  aphalt. 
The  concrete  proportions  were  1:2}:  5.  In  placing  the  fresh  concrete  on 
that  which  was  already  set,  the  surface  was  carefully  washed  and  rirJi 
mortar  was  placed  in  order  to  make  a  joint.  The  forms  were  left  on  from 
one  to  two  days  to  harden;  surfaces  which  were  to  be  exposed  to  the  air 
or  water  had  a  face  of  1:2  mortar,  6  ins.  thick,  placed  at  the  same  time  the 
concrete  backing  was  placed.  The  concrete  floor  was  laid  in  two  lasrers. 
each  5  ins.  thick,  and  laid  in  blocks  15  ft.  square.  In  the  joints  was  placed 
a  3-ply  felt,  up  to  bevels,  which  topped  off  each  joint.  After  the  shrinkage 
cracks  appeared,  these  bevels  were  nm  full  of  asphalt  and  then  2  ins.  of  1:2 
mortar  was  troweled  over  everything.  The  experience  with  this  reservoir 
is  interesting  since  the  asphalt  m  the  key  ways  cracked  and  leaked  in  cold 
weather,  and  in  warm  weather  ran  out  beneath  the  water  surface.  The 
asphalt  was  finally  taken  out  and  replaced  with  carefully  selected  puddling 
clay  and  rammed  into  the  key  ways.  The  contraction  of  the  concrete 
permitted  this  material  also  to  run  out  through  the  expansion  joints  into 
the  reservoir  and  caused  leaks  to  appear  through  the  embankment.  After 
this  occtured,  the  puddling  clay  was  taken  out  and  plain  loam,  with  clay. 
sand,  grass  roots,  dirt  and  fibrous  material,  were  rammed  into  the  ^y 
'^ays-  This  material  has  successfully  prevented  leaks  up  to  the  present 
time.  .Other  Data. — About  a  dozen  other  works  described;  also  Expnnaioo 
Jomts  m  Drydocks  (illus.);  Bkxrk  Construction;  Key  Ways,  etc. 


MISCELLANEOUS  DATA.  455 

The  Um  of  Reinfofced  Concrete  in  Engineerinf  Structures  (Trans. 
A-  S,  C.  E.,  Vol.  LXI). — Discussions  by  E.  P.  Goodrich,  Edwin  Thacher, 

5.  E.  Thompson,  W.  H.  Biirr,  T.  K.  Thompson,  and  others. 

TrsveUnc  Concrete  Mixers  (Eng.  News,  Aug.  5.  1900). — Illustrated:  U. 

6.  Steel  Mixer  Co. 

The  Bonding  of  New  to  Old  Concrete  (By  E.  P.  Goodrich.  Trans.  A.  S. 
C  E.,  VoL  LXlV.,  Sept.,  1  »©»).— Article  contains:  Literature  on  the  sub- 
ject; patented  processes;  published  experiments;  Goodrich's  experiments. 

Xaidng  Concrete  Waterproof  (By  Ira  O.  Baker.  The  Univ.  of  HI. 
"Technogragh,"  No.  28.  1908-0«;  Eng.  News,  Oct.  7,  1909).— Description 
o{  aiam-and-soap  waterproofing  compotmd,  etc. 

The  Compressive  Strength  of  Colce  Concrete  (By  J.  M.  Lewis^  Eng. 
[Rec,  Oct.  30,  1909). — (^mparison  of  tests  of  concrete  columns  made  with 
stone  and  with  coke  cinder.  Weight  of  coke-cinder  concrete,  97  lbs.  per 
;ca.  ft.;  stone  concrete,  150  lbs.  per  cu.  It. 

IssDuritles  in  Sand  for  Concrete  (Informal  Discussion — ^Trans.  A.  S.  C. 
[E..  VoL  LXV..  Dec..  1909).— Sand  tests,  washing,  etc. 

Office  Methods  in  a  Concrete  Designing  Office  (Eng.  Rec..  June  1 1,  1910). 
— -niustrations:  Beam  design  sheet,  half  of  column  design  sheet,  tjrpical 
detaila  for  T-stimips,  upper  part  of  splice  rod  detail  sheet,  upper  part  of 
;l>eain  detail  sheet. 

The  Effect  of  AllcaU  on  Concrete  (By  G.  G.  Anderson.  Transi  A.  S.  C. 
E.,  Vol.  LXVIL.  June.  1910). 

Corrosion  of  Iron  Embedded  in  Concrete  (By  G.  P.  Shaffer.  Eng.  Rec. 
Jaly  80,  1910). — Gives  results  of  tests  at  Mass.  Inst.  Tech.,  obtaining  some 
«ku  on  the  effect  of  currents  of  low  potential  on  embedded  steel. 

Computation  of  Reinforced  Concrete  Flat  Slabs  (By  L.  P.  Brayton.  Eng. 
Rec,  Aug.  27.  1910). — Comparison  with  the  McMillan  method. 

Exterior  Treatment  of  Concrete  Surfaces:  Committee  Report  to  the  Natl 
Asa.  Cement  Users  (Eng.  News.  Sept.  15.  1910). — (a)  Effect  of  material  and 
vorkmanship  on  surface,  (b)  Removal  of  surface  in  various  ways,  (c) 
Coating  surfaces  in  various  wa3rs.  (d)  Defects,  blemishes  of  various  sorts, 
tad  remedies,     (e)  Costs. 

Investigations  on  the  Slip  of  Rods  Imbedded  in  Concrete  Beams  ("Armitier 
Beton."  Sept.,  1910;  Eng.  Roc,  Nov.  12. 1910). — Gives  the  slip  at  lour  points 
of  the  beams  under  incremental  twin  loadings.  Beams  are  12  x  12-ins., 
74-iii.  span.     Rod,  0.94  in.  dia. 

OH-Mixed  Concrete  as  a  Waterprooffaig  Material  (By  T.  W.  Symons, 
Eng.  News.  Dec  15,  1910). — "The  peculiarly  waterproof  and  watcr-repellant 
quality  of  this  oil-concrete,  combined  with  its  strength  and  greater  density 
renders  it  a  material  remarkably  adapted  to  such  canal  structures  as  culverts, 
locks,  the  canal  prism  troughs  crossmg  the  Irondequoit  Valley  and  the  Me- 
dina Gorge,  to  the  core  walls  of  earthen  dams  like  that  at  Hinckley,  etc." 
Oil  to  the  amount  of  about  10%  of  the  weight  of  the  cement  gives  very 
'Satisfactory  restdts.  The  oil  costs  about  6  to  7  cents  per  gallon,  or  about 
40  to  50  cents  per  cu.  yd.  of  concrete;  or  about  60  to  70  cents  more  per  cu. 
^.  of  concrete  (incluoing  handling  and  incorporation)  than  plain  concrete, 
m  place. 

Specifications  for  Scrubbed  Concrete  Surface  (By  H.  H.  Quimby.  Paper 
before  Annual  Conv.  of  Nafl  Cement  Users,  New  York,  Dec  10.  1910;  Eng. 
Kew»,  Dec  22,  1910). — Sent  by  that  Convention  to  a  letter  ballot  of  the 
AsBociation  to  be  adopted  as  a  standard  of  the  Association.     ^OOQLc 


456  iS.—MASONRY, 

SofM  impofftaot  lUwttnudoiu. 

Description.  Bng.  News. 
Spec,  for  plain  and  rein.-conc.  and  steel  rdn.,  A.  R.  £.  &  M.W.AApr.  14,  *  1 C 

Stand.  Spec.  (Assn.  of  Am.  Steel  Mf'rs)  cone.  rein.  bars.  June  15.  'If 

Ens.  Rec. 

Standard  forms  for  a  reinforced -concrete  viaduct  Feb.   IS,  '(H 

Plant  for  washing  and  screening  concrete  aggregates  '  ~  *" 

A  traveling  shed  for  cold-weather  viaduct  concreting 
Tests  of  bond  between  steel  and  concrete. — H.  C.  Berry  _ 

Analysis  of  concrete-bridge  failures. — C.  R.  Young  Apr.    16,  'If 

Clips  and  rods  for  tying  concrete  to  steel  members  Sept.     S,  'II 

Diagram  of  bending  moments  in  concrete  coltumif  and  beams  Oct.    1 5,  *  U 


ae  S<l,  '01 
7  10.  •« 
t.    4.  'M 


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26.— STEREOTOMY. 

This  term  in  Its  broadest  sense  includes  the  subject  of  Stone  Cutting 
(lee  cage  426.).  but  it  is  here  restricted  to  the  preparation  of  the  drawings 
■ad  Hcetches  of  the  dimension  stones,  which  enter  into  the  masonry  structure, 
previoushr  designed. 

The  drawings  of  the  simpler  shapes  may  be  ordinary  sketches  in  mo- 
jectioo,  diowing  the  principal  faces  with  dimensions  thereon,  or  descriptions 
of  ame;  but  isometric  Tiews  should  be  shown  of  the  more  complex  shapes. 
The  dimenaions  of  the  shapes  may  be  obtained  (1)  by  analytic  calculation, 
^2)  by  pcoiection  and  development.  (3)  by  Descnptive  Geometry.  All  these 
metbods  commonly  enter  into  the  case  of  a  single  structure.  Only  a  few 
tatU  can  be  given  here,  but  these,  it  is  hoped,  wOl  serve  to  illustrate  a  more 
extended  application. 

,       WsB  of  Bidldifig. — Pig.  1  illustrates  the  simple  method  of  showing  the 

I  dimenaions  of  stones  on  the  Elevation  plan.    These  dimensions  are  usually 

given  on  the  drawing  to  ctnter  of  joint  with  a  note  on  plan  to  that  effect,  as 


480 


"%'    . 


Wtj 


Its  t; 


286 


167    >;      168   -^ 


Pig.  1. 

"ADow  for  A'  joints."  The  thickness  of  joint  may  vary  from  about  H'  up- 
ward, depending  upon  the  quality  of  the  masonry;  A'  is  common  for  public 
.  buildings.  In  engineering  structures  K  is  about  the  minimum,  and  from 
J'  for  dimension  work.    Note  that  in  Fig.  1 


that  up  to  ' 


each  stone  i4  num- 


bered. Pig.  3  is  an  isometric  view  of  stone  No.  63  (not  shown  in  elevation) 
ot  the  water-table.  All  the  dimensions  L.  H,  A,  W  and  w  should  be 
Priced  directly  on  the  drawing.  L  and  H  may  be  "finished  dimensions" 
fflcethe  others,  or  they  may  be  distances  to  center  of  joints.  Proper  notes 
wottld  be  made  showmg  which  system  is  used. 

Stone  Arch. — Pig.  8  illustrates,  briefly,  two  methods  of  showing  the 
<uxnen8ions  of  the  voussoirs  for  the  stone  cutter.  Those  shown  in  the  end 
^  View  (face  of  arch)  are  in  planes  perp  to  axis  of  arch,  whether  for  right- 
<»  «kew  arch.  The  measurements  shown  may  be  (1)  to  center  of  joints  as 
per  the  "numbered"  vouissoirs,  or  (2)  actual  dimensions  as  per  the  "lettered" 
^titsoirs  (Fig.  3).  Isometric  views  of  stones  "4"  and  "I  assume  the  arch 
to  be  skewed  or  oblique,  with  coursing  joints  parallel  with  axis  of  arch. 
(Such  a  construction  is  alkiwable  only  for  slight  skew,  for  small  arches,  or 
culverts.     When  the  skew  is  considerable,  especially  for  large  spans,  the- 


457 


Digitized 


by  Google 


468  i^.—STEREOTOMY. 

construction  should  be  as  per  Figs.  6  or  7,  page  764.  Section  44.) 
obliquity  of  faces  of  end  voussoirs  may  be  shown  directlv  on  the  end  i 
arch  by  measurements  in  the  corners  a,  b,  c,  showing  the  projection  c 
comtrs  beyond  a  right  section  passing  through  the  comers  o,  assun 
sero.     These  projections  may  be  obtained  graphically  as  illxistrate< 


Fig.  3. 

should  appear  also  on  the  isometric  views.  A  plan  of  soffit  and  also  ( 
of  arch  should  also  be  submitted  showing  the  coursing  joints,  leni 
voussoirs  (at  least  near  ends  of  arch),  and  other  information.  l*he  1 
finish  desired  should  be  marked  plainly  on  plans. 


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27.— WEIGHTS  AND  SPECIFIC   GRAVITIES 
OF  MATERIALS. 

(For  Strength  and  Resistance  of  Materials,  see  Sec.  28.) 

DEFINITIONS. 

Man  (Af)*"  Matter. — If  two  separate  quantities  of  matter  will  balance 
each  other  in  vacuuo  they  are  said  to  have  equal  masses;  and  this  regard- 
less of  kind  of  matter,  volume,  or  temperature.  The  only  stipulation  is  that 
they  shall  be  affected  by  the  same  gravity  acceleration  g,  and  this  neces- 
sarily obtains  when  they  are  counterpoised  at  the  same  time,  at  the  same 
elevation  above  sea  level,  and  at  the  same  parallel  of  latitude  or  place. 

Mass* :- z — -: — ;  or  Af  —  —  ,  the  usual  formtUa. 

gravity  acceleration  g 

The  **u6H^  off  mass*'  (Aft)  ma^  be  a  definite  and  standard  quantity  of 
matter.  For  instance,  if  a  certain  quantity  of  a  particular  metal  occupies 
one  cubic  inch  (Ci),  and  weighs  one  standard  pound  (W^i)  at  a  point  on  the 
earth  where  the  gravity  acceleration  (^ j)  corresponding  to  Wu  is  equal  to. 

say.  32.16,—  then  its  mass  (Af )  is  equal  to  — ^  =•   ^  ._  lb.      Hence,  the  unit 

gl  ^.10 

of  mass  (Ml)  of  the  metal  would  be  equal  to  32.16  cubic  inches,  or  82.16  lbs. 
at  that  particular  locality. 

The  "unit  of  mass"  is  equal  to  g  pounds. 

Qmvfty  Acceleration  (^).— The  value  of  g  increases  with  the  latitude  of 
the  place,  and  decreases  with  the  elevation  above  sea  level.  The  following 
fonnola*  gives  the  value  of  g  for  any  latitude  and  elevation: 

f- 32.172-0.082  cos  21-0.000003  h (1) 

where  ^—acceleration  in  ft.  per  sec,  per  sec; 
A —  latitude  of  the  place  in  degrees; 
A  — elevation  in  feet  above  sea  level. 
From  this  formula  the  values  of  g  and  y/g  (used  !n  Hydraulics)  are  as 
follows,  for  various  latitudes,  at  sea  level: 

Latitude       0*  10*  20*  30*  40*  46* 

J    32.090     82.095      32.109      82.131      32.158      32.172 
V2g      8.011        8.012        8.014        8.016        8.020        8.021 
The  value  of  g  may  be  designated  as  the  intensity  of  gravity. 

Weight  (UO-Af^--The  weight  of  a  body  depends  upon  its  mass  (Af) 
and  upon  the  intensitv  of  gravity  {g).  If  the  mass  is  constant  the  weight 
will  vary  directly  with  g.  Prom  the  preceding  table  we  see  that  a  mass 
weighing  32.131  lbs.  in  latitude  30*.  would  weigh  32,172  lbs.  in  latitude  45*; 
that  is.  the  weight  of  the  same  mass  would  increase  41  lbs.  in  15*  of  latitude, 
or  a  little  more  than  21  lbs.  per  ton.  This  is  so  small  as  to  be  practically 
negligible  in  engineering  calculations,  and  we  generally  assume  for  g  its 
value  in  latitude  40*.  namely,  g  — 32.16.  It  is  to  be  noted,  then,  that  the 
wieghts  per  cubic  foot  of  substances  8[iven  in  the  subjoined  tables  are  practi- 
cally constant,  in  so  far  as  the  intensity  of  gravity  alone  is  concerned,  in  all 
portions  of  the  country. 

♦  In  C.  G.  S.  (Ontimeter-Gram-Second)  System,  adopted  by  the  British 
Association,  the  value  of  g  in  centimeters  is  sometimes  given:  jf'  —  980.6056— 
15028  cos  2  l-.000008ir.  See  also  formula  for  g  under  Simple  Circular 
Pendulum  Mechanics,  page  287. 


459  Digitized  by  dOOg  IC 


460  VJ—WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS. 

Voltime  (V). — ^The  tmit  of  volume  generally  used  in  the  United  States 
18  the  cubic  foot,  and  weights  are  ^ven  in  pounds  per  cubic  foot.  The 
effect  of  tem(>erature  upon  any  mass  is  to  increase  its  volume  (ice  excepted) ; 
hence,  in  giving  the  weights  of  those  substances  which  expand  materiallv 
with  heat,  the  temperature  should  be  stated.  This  is  true  especially  with 
gases  and.  to  a  mucui  less  extent,  with  liquids.  But  with  ordinary  materials 
of  engineering  the  temperature  effect  on  volume  is  so  slight,  within  the 
natural  range  of  the  thermometer,  as  to  be  negligible. 

The  volume  of  any  mass  is  inversely  as  its  density;  thus,  V—  •^. 
Then  for  any  unit  mass  the  volume  and  density  are  reciprocals  of  each  other. 

Density  (D). — ^The  density  of  any  body  is  the  mass  of  a  tmit  of  its 
volume;  thus  in  the  equation  Af  —  VI>,  if  K—  1,  Af -=D.  If,  now,  this  unit 
mass  is  increased,  say  by  temperatiuv,  to  two  units  of  volume,  then  will 
its  density  be  equal  to  \M,  or  60  per  cent  of  what  it  was.  If,  on  the  other 
hand,  the  imit  mass  is  decreased,  say  by  pressure,  to  f  its  original  volume, 
then  will  its  density  be  1.25  M. 

The  relative  density  of  a  substance  is  called  its  specific  gravity,  when 
referred  to  water  (at  maximum  density — 4°  Centigrade). 

Specific  Gravity  (s.  g.). — ^The  specific  gravity  of  a  substance  is  its  rela- 
tive density,  to  a  unit  standard.  More  definitely,  it  is  the  ratio  of  the 
weight  of  a  given  volume  of  the  substance  to  the  weight  of  the  same  volume 
of  distilled  water  at  4*^  (39.1  F.),  its  maximum  density,  equal  to  62.424 
pounds  per  cubic  foot,  and  considered  as  imity.  Moreover,  the  specific 
gravities  of  other  substances  than  water  are  assumed  to  be  taken  at  0^., 
or  if  not  they  are  reduced  by  corrections  to  that  temperature.  These  arc 
the  standards  of  physicists. 

Experimenters,  especially  in  the  field  of  engineering,  have  not  always 
reduced  their  results  to  the  above  standards,  but  have  variously  employed 
as  standard  units,  uncorrected. 

Water  at         0"  C.  or      82*  F..  equal  to  62.416  lbs.  per  cu.  ft. 

(      ••       ••  40c.   "  SQ.l'^F..      "      •'   62.424 ) 

"       •*  IS.Se^'C.   "      60<»F.,      ••      "   62.366 

"       ••        16<»C.   •*  60.8*»F.,      *'      •'   62.861    "      " 

*•       "  I6.6rc.   ••      62«F.,      "      ••   62.866 

And  for  the  substances  experimented  with,  the  temperatures,  when  stated, 
have  been  as  varied  as  the  above.  Hence,  in  the  subjoined  tables  of  specific 
gravities,  extreme  accuracy  cannot  be  expected  in  many  cases,  but  they  are 
suflficiently  exact  for  all  ens^inecring  purposes. 

Specific  gravity -^weight  in  grams  per  cubic  centimeter. 

METHODS  FOR  OETERMININO  SPECIFIC  GRAVITY. 
Solids  Heavier  than  Water. — A  common  method  for  determining  the 
specific  gravity  of  a  solid  heavier  than  water  is  to  weigh  it  in  air  and  then 
weigh  it  in  water;  that  is.  while  still  in  the  scale  it  is  immersed  in  water, 
where  its  weight  will  be  found  to  be  less.  The  specific  gravity  may  then 
be  expressed  by  the  following  formula,  when  temperature  reduction  is  not 
considered : 

W 
Specific  gravity-  ^^j^ZT^ ^^^ 

In  which  W^— weight  of  the  substance  in  air; 

«;«»      *'        **  **  '*  when  immersed  in  water; 

W— w-^loss  of  weight"  by  immersion. 
Solids  Lighter  than  Water  may  be  determined  by  finding  the  weight  (W) 
in  air,  as  above,  and  then  the  buoyancy  or  minus  weight  («/)  in  water, 
when  completely  immersed.     Formida  (2)  then  reduced  to  (3),  as  follows: 

Specific  gravity -ppqp-^ (3) 

In  which  tw'=«  —a»  — force  required  to  immerse  the  body. 

Displacement  Method. — Thi^  consists  in  immersing  the  substance  to  be 
determmed,  in  a  vessel  full  of  water.    Hence, 

cj       .-  .^  weight  of  the  substance  ,m^ 

Specific  gravity  —  — r~- — j -r: — ; j (*) 

weight  of  water  displaced 

Porous  substances  whose  specific  gravities  are  to  be  determined  should 
be  painted  with  a  thin  coat  ot  varnish  before  being  immersed,  in  order  to 
-»xclude  all  moisture. 


METHODS  FOR  DETERMINING  SPECIFIC  GRAVITY.     461 


may  have  two  specific  gravities,  namely,  in  hulk 
tod  in  granuk.  Substances  which  are  affected  by  water  should  be  weip^hed 
m  some  other  liquid  which  will  not  affect  them  and  whose  specific  gravity  is 
known.  Akohol,  turpentine  and  benzine  are  often  used  for  this  purpose. 
Then,  the  specific  gravity  obtained  with  respect  to  the  particxilar  hquid 
must  be  tnuJti  plied  by  the  specific  gravity  of  the  liquid  itself,  to  find  the 
true  specific  gravity. 

For  determining  the  specific  gravity  of  cement,  see  description  of 
method,  page  407,  under  Building  Stones  and  Cements,  Sec.  22. 

Liqoids.* — The  practical  determination  of  the  specific  gravities  of 
liquids  may  be  made  with  instruments  called  hydromtters.  Tliey  consist 
osually  of  a  ^lass  tube  (or  wire)  so  arranged  that  it  will  stand  vertically 
when  partly  immersed  in  a  liquid.  The  depth  of  immersion,  registered 
by  a  scale  on  the  tube,  or  the  weight  required  to  immerse  the  tube  to  a 
certain  fixed  mark  upon  it,  with  reference  to  the  surface  of  the  liquid  in 
srhich  it  is  immersea,  is  the  basis  on  which  the  specific  gravity  is  deter- 
mined. "Scale"  hvdrometers  are  of  variable  immersion  and  constant 
wdght;   "fixed-mark"  hydrometers  are  of  constant  im«  ^ 

mersion  and  variable  weight.  Some  hvdrometers  are 
specially  adapted  to  determining  liquids  heavier  than 
water;  and  some  to  determine  liquids  lighter  than 
water.  Again,  some  hydrometers  are  immersed  in  the 
fimnd  whose  specific  gravity  is  to  be  determined;  while 
others  are  immersed  m  a  standard  liquid,  and  are  pro- 
vided with  a  cup  at  the  top  of  the  tube  to  receive  the 
liquid  which  is  to  be  determined.  Other  forms  of  instru- 
ments, perhaps  not  strictly  hydrometers,  are  used  to  de- 
termine the  purity  or  adulteration  of  various  liquids,  as 
spirits,  solutions,  milk,  urine,  etc.  The  relative  density  to 
some  standard  of  purity  is  the  basis  of  the  determination. 

Beaimi^s  hydrometer,  Fig.  t,  is  a  "scale"  hydrometer 
of  variable  immersion,  whicm  is  immersed  in  the  liquid 
to  be  determined.  The  graduation  of  the  scale  for 
liquids  lighter  than  water  is  different  than  for  those 
heavier  than  water.  The  graduation  is  standardized  by 
the  depth  of  immersion  (1)  in  pure  water  for  one  point  on 
the  scale,  and  (2)  in  a  saline  solution  of  known  strength 
for  another  point.  The  distance  between  the  two  points 
is  then  graduated,  and  the  graduation  extended  be- 
yond either  point  when  necessary.  The  lower  end  of  the 
tube  is  loaded  with  mercury,  and  a  bulb  is  blown 
above  it.  -  .«».  -. 

The  following  relations  exist  between  Beaum^'s  Hydrometer  scale  and 
the  corresponding  Specific  Gravity  desired: 


Beaum^  (deg.). 


Liquid  heavier  than  water . 
Liquid  lighter  than  water. . 


1.000 


10 


1.070 
1.000 


20 


1.152 
.936 


30 


1.246 
.880 


40 


1.357 
.830 


50 


1.490 
.785 


60 


1.652 
.746 


Many  hydrometers  now  record  the  specific  gravities  directly. 

Twedddl's  hydrometer  is  a  scale  hydrometer  for  determining  liquids 
heavier  than  water.    It  is  graduated  in  degrees  D**  such  that 
e       .^            .,        5I?«+1000 
Specific  gravity  = -^ (5) 

Rousseau's  densimeter  is  for  variable  immersion  in  a  standard  liquid. 
It  is  constructed  somewhat  similar  to  Beaume's  (Pig.  1)  but  has  in  addi- 
tion a  tube  or  cup  at  the  top  of  the  stem  which  contains  the  liquid  to  be 
determined.  Hence,  it  is  specially  adapted  to  determining  specific  gravities 
of  small  quantities  of  liquids. 

*  The  specific  gravity  of  a  liquid  may  be  obtained  directly  by  weighing 
equal  volumes  of  the  liquid  and  of  water,  dividing  the  weight  of  the  former 
by  that  of  the  latter. 


4«2   2:1— WEIGHTS  AND  SPECIFIC  GRA  VITIES  OF  MA  TERIALS. 

Nicholson's  and  Fahrenlieit's  hydronetert  are  hydrometers  of  constant 
immersion  and  variable  weight.  They  differ  from  the  above.  For  instance, 
Nicholson's  hydrometer  consists  of  a  hollow  metal  float,  always  submerged, 
below  which  is  suspended  a  dish  loaded  with  weights.  Above  the  float  is 
supported  a  shallow  dish  on  a  thin  vertical  wire.  On  this  wire  is  a  mark 
which  is  brought  to  the  surface  of  the  liquid  by  the  weights  in  the  upper 
and  lower  dishes.  These  weights  determine  the  specific  gravity  of  the 
liquid  in  which  the  hydrometer  is  immersed. 

Refinements.— In  laboratory  work  where  great  refinement  is  necessary 
the  exact  determination  of  specific  gravities  involves  quite  intricate  formulas 
and  extremely  careful  observations.  The  formulas  include  reduction  of 
weighings  to  vacuuo,  and  various  temperature  reductions. 

Oases. — ^When  we  speak  of  the  specific  gravity  of  a  gas  we  must  have 
clearly  in  mind  its  prtssure  and  Umperature,  and  to  what  standard  it  is 
referred.  The  specific  gravity  of  a  unit  mass  of  gas  varies  directly  as  its 
density  and  inversely  as  its  volume.  For  constant  temperature  the  density 
varies  directly  as  the  pressure,  for  constant  pressxire  the  density  varies 
inversely  as  the  temperature,  meaning  of  course  the  temperature  above 
absolute  zero.* 

The  "standard**  pressure  of  the  gas  determined  is  taken  at,  or  reduced 
to,  one  "standard"  atmosphere.  Now  a  standard  atmospheric  pressure  is 
about  14.7  lbs.  per  square  inch,  near  enough  for  all  practical  engineering 
work.  But  it  is  not  a  fixed  quantity.  In  French  unUs  it  is  assumed  as  a 
pressure  equivalent  to  a  column  of  mercury  at  0**  C.  (32**  P.),  760  m  m  (  >  0. 70 
meter—  29.921  ins.)  in  height,  and  acted  upon  by  an  intensity  of  gravity,  g, 
equal  to  that  of  Paris.  This  value  of  g  has  been  determined  as  equal  to  an 
acceleration  of  980.94  e  m  («  9.8094  meters—  32.183  ft.)  per  sec.  Now  the 
specific  gravity  of  mercury  at  0**  C.  is  taken  at  13.596  (Regnault's  determin- 
ation, 13.5959;  commonly  assumed  at  13.6);  hence  the  pressure  of  a  stand- 
ard atmosphere  at  Paris— 76 X  13.596— 1033.3  grams  per  sq.  centimeter  — 
10.333  kilograms  per  sq.  meter  (-14.697  lbs.  per  sq.  m.  — 2116.37  lbs.  per 
sq.  ft.).  It  is  thus  seen  that  the  atmospheric  pressure  may  be  stated  in 
terms  of  a  column  of  mercury,  or  as  a  pressure  per  unit  of  area;  and  that  these 
values  are  dependent  on  the  temperature  (mainly  affecting  the  density  of 
the  mercury,  and  very  slightly  the  air),  the  specific  gravity  of  the  mercury 
(afTected  by  temperature  and  value  of  g),  the  value  of  £  (affected  by  latitude, 
and  elevation  obove  sea  level),  the  latitude,  and  the  distance  above  sea 
level.  In  view  of  this,  English  tmits  are  often  used,  with  round  units  of 
16**  C,  30  ins.  of  mercury,  and  14.7  lbs.  per  sq.  ft.    Thus: 

In  English  units  the  "standard"  pressure  is  often  assumed  equivalent  to 
a  column  of  mercury  at  60°  to  62°  F.  (16°  C).  30  inches  (762  milli- 
meters) in  height,  and  acted  upon  by  an  intensity  of  gravity  g  equal 
to  that  at  45°  latitude.  This  gives  a  pressure  practically  the  same  as 
that  derived  from  the  French  standard,  namely,  14.7  lbs.  per  sq.  in. 

The  standard  temperature  of  the  gas  whose  specific  gravity  is  determined 
should  be  taken  at  or  reduced  to  0°  C.  (32°  F.)  for  French  units,  or  60*  to 
62°  F.  (16°  C.)  for  English  imits.  The  temperature  reduction  should  be 
stated  in  all  cases. 

The  standard  substance  referred  to  in  determining  the  specific  gravities 
of  gases  is  air  at  0°  C.  (32°  F.),  with  the  barometer  at  760  m  m  (29.021  ins,) 
or  one  standard  atmospheric  pressure.  Sometimes  air  at  60°  or  62°  F.  is 
used.  The  specific  gravity  of  the  air  multiplied  by  the  sp  grav  of  the  ^as 
referred  to  it  =  the  sp  grav  of  the  gas  with  reference  to  water.  Water  at  its 
maximum  density,  4°C.,  is  the  standard,  but  sometin^s  60*  or  62°  P.  is 
used. 

One  cubic  foot  of  air  at        0°  C.  (    32°  P.)  weighs  0.0807  lb. 

' 4°  C.  (39.1°  P.)       "       0.0796" 

15.56°  C.(    60°  P.)       "       0.0764" 

16°  C.  (60.8°  P.)       "       0.0763" 

16.6rC.  (    62°  F.)       "       0.0761" 

"    water"         0°  C.  (    32°  F.)       "     62.416     " 

"         4°  C.  (39.1°  P.)       "      62.424     " 

15.56°  C.(    60°  P.)       "      62.366     " 

"      "       16°  C.  (60  8°  P.)       "      62.361     " 

16.6rC.  (    62°  P.)       "      62.856     " 

*  Absolute  zero  (no  heat)  is  273. r  C.  below  0°  C,  or  460.  T  P.  below  0*  P. 


GASES— AIR, 


463 


OASES. 

L— Weight  of  a  Cubic  Foot  of  Dry  Air  at  Various  Temper aturbs.* 
(At  Atmospheric  Pressure— 14.7  lbs.  per  sq.  in.) 


Temper- 
tture 

Weight 
(Ltw.) 

Temper- 
ature 
(Deg.F.) 

Weight 
(Lbfc) 

Temper- 
ature 
(Deg.  F.) 

Weight 
(Lbs.) 

Temper- 
ature 
(Deg.  F.) 

Weight 
(Lbe.) 

0 

.08«3 

50 

.0779 

100 

.0710 

150 

.0662 

1 

.0862 

51 

.0777 

101 

.0708 

151 

.0650 

2 

.0900 

52 

.0776 

102 

.0707 

152 

.0649 

3 

.0858 

53 

.0774 

103 

.0706 

153 

.0648 

4 

.0850 

M 

.0773 

104 

.0705 

164 

.0647 

6 

.0854 

65 

.0771 

105 

.0703 

155 

.0646 

1 

.0852 

56 

.0770 

106 

.0702 

156 

.0645 

T 

.0851 

57 

.0768 

107 

.0701 

157 

.0644 

8 

.0849 

58 

.0767 

108 

.0700 

168 

.0643 

f 

.0847 

59 

.0766 

109 

.0698 

159 

.0642 

10 

.0845 

60 

.0764 

110 

.0697 

160 

.0641 

11 

.0843 

61 

.0763 

111 

.0696 

161 

.0640 

13 

.0842 

62 

.0761 

112 

.0695 

162 

.0639 

U 

.0840 

63 

.0760 

113 

.0694 

163 

.0638 

U 

.0838 

64 

.0758 

114 

.0692 

164 

.0637 

IS 

.0838 

65 

.0757 

115 

.0691 

165 

.0636 

le 

.0834 

66 

.0755 

116 

.0690 

166 

.0635 

17 

.0833 

67 

.0754 

117 

.0689 

167 

.0634 

18 

.0831 

68 

.0752 

118 

.0688 

168 

.0633 

19 

.0829 

60 

.0761 

119 

.0686 

169 

.0632 

n 

.0828 

70 

.0750 

120 

.0685 

170 

.0631 

21 

.0828 

71 

.0748 

121 

.0684 

171 

.0630 

23 

.0824 

72 

.0747 

122 

.0683 

172 

..0629 

33 

.0823 

73 

.0745 

123 

.0682 

173 

.0628 

24 

.0821 

74 

.0744 

124 

.0680 

174 

.0627 

35 

.0819 

75 

.0743 

125 

.0679 

175 

.0626 

» 

.0817 

76 

.0741 

126 

.0678 

176 

.0625 

27 

.0810 

77 

.0740 

127 

.0677 

177 

0624 

28 

.0814 

78 

.0739 

128 

.0676 

178 

.0623 

29 

.0812 

79 

.0737 

129 

.0675 

179 

.0622 

30 

.0811 

80 

.0736 

130 

.0674 

180 

.0621 

31 

.0809 

81 

.0734 

131 

.0672 

181 

.0620 

32 

.0807 

82 

.0733 

132 

.0671 

182 

.0619 

33 

.0806 

83 

.0732 

133 

.0670 

183 

.0618 

34 

.0804 

84 

.0730  . 

134 

.0669 

184 

.0617 

35 

.0803 

85 

.0729 

135 

.0668 

185 

.0616 

U 

.0801 

86 

.0728 

136 

.0667 

186 

.0615 

37 

.0799 

87 

.0726 

137 

.0666 

187 

.0614 

38 

.0798 

88 

.0725 

138 

.0665 

188 

.0613 

39 

.0796 

89 

.0724 

139 

.0663 

189 

.0612 

40 

.0795 

90 

.0722 

140 

.0662 

190 

.0612 

41 

.0793 

91 

.0721 

141 

.0661 

191 

.0611 

43 

.0791 

92 

.0720 

142 

.0660 

192 

.0610 

43 

.0790 

93 

.0719 

143 

.0659 

193 

.0609 

44 

.0788 

94 

.0717 

144 

.0658 

194 

.0608 

45 

.0787 

96 

.0716 

145 

.0657 

195 

.0607 

U 

.0785 

96 

.0715 

146 

.0656 

196 

.0606 

47 

.0784 

97 

.0713 

147 

.0655 

197 

.0605 

4$ 

.0782 

98 

.0712 

148 

.0654 

198 

.0604 

49 

.0781 

99 

.0711 

149 

.0663 

199 

.0603 

50 

.0779 

100 

.0710 

150 

.0652 

.00 

.0602 

*  For  comparison  of  Fahrenheit  with  Centigrade  scale  see  Table  3. 


454  tt— WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS. 


2. — ^Weights  and  Spbcitic  Gravitibs  of  Gasbs. 


Substance  under  1  atmosphere. 


Name. 


Temp. 


Relative 
Density 
to  Air. 


Relative 
Density 

to  Water. 

tSp.  Grav. 


Weight 

per 

Cubic 

Foot. 

Lbs. 


Cocf.  of 
Expan- 
sion per 
Desrree 
tCent. 


Air.  dry  (see  Table  1).. 

Ammonia. 

Binoxide  of  Nitrogen. . 

Carbonic  add 

Carbonic  oxide 

Chlorine 

Cyanogen 

Hydrogen 

Marsh  gas 

Nitrogen 

Olefiant  gas 

Oxygen 

Protoxide  of  nitrogen.. 

Steam  (ideal) 

Sulphurous  acid 


(TC. 


(TC. 


1.0000 

.6967 
1.0388 
1.52901 

.9569 
2.4216 
1.8064 

.06926 

.559 

.97137 

.985 
1.10562 
1.5269 

.6221 
2.1930 


.001.298,2 
.000.769.7 
.001.348.4 
.001.977,4 
.001.234.4 
.003.182.8 
.002.380.2 
.000.089.57 
.000,727.0 
.001.256.15 
.001.274.0 
.001,429.8 
.001.969.7 
.000.804.5 
.002.728.9 


.08071 
.04805 
.08387 
.12345 
.07706 
.19558 
.14547 
.00559 
.04539 
.07842 
.07953 
.08926 
.12297 
.05022 
.17036 


.003666 


.003699 
.003667 


.008877 
.003664 


.003665 


.003900 


*  Air   at    (f  C.  tmder  760  m  m  of  mercury  at  Paris,  unless  otherwise 
stated. 

t  Water  at  4^  C.  under  760  m  m  of  mercury  at  Paris,  unless  otherwise 
stated. 

Specific  gravity  of  a  substance  is  its  weight  in  grams  per  cubic  centi- 
meter. 

%  Coti.  of  expansion  for  low  temperatures  approaches  ^-- -  per  degree  C. 

1 


492.7 


per  degree  P. 


d  by  Google 


UQUIDS— WATER, 


466 


LIQUIDS. 

3. — Weight  or  a  Cubic  Foot  or  Watbr  at  Various  Tbicpbraturbs. 


De«.C 

.    Add: 

.0 

.06 

.11 

.17 

.» 

.28 

.33 

.39 

.44 

.50 

D€*.F. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

• 

32 

62.416 

62.416 

62.416 

82.417 

62.417 

62.417 

82.417 

82.417 

82.418 

62.418 

.56 

33 

.418 

.418 

.418 

.419 

.419 

.419 

.419 

.419 

.420 

.420 

1.11 

34 

.420 

.420 

.420 

.420 

.420 

.421 

.421 

.421 

.421 

.421 

I.«7 

35 

62.421 

62.421 

62.421 

62.421 

62.421 

82.422 

62.422 

82.422 

62.422 

62.422 

2.23 

36 

.422 

.422 

.422 

.422 

.422 

.423 

.423 

.423 

.423 

.423 

2.78 

37 

.423 

.423 

.428 

.423 

.423 

.423 

.423 

.423 

.423 

.423 

a.s3 

38 

.423 

.423 

.423 

.423 

.423 

.423 

.423 

.424 

.424 

.424 

2.89 

39 

.424 

♦.424 

•.424 

.424 

.424 

.424 

.424 

.424 

.424 

423 

4.44 

40 

62.423 

62.423 

62.423 

62.423 

82.423 

62.423 

62.423 

82.423 

62.423 

62.423 

5.00 

41 

.423 

.423 

.423 

.423 

.423 

.423 

.423 

.423 

.423 

.423 

5.56 

43 

.423 

.423 

.423 

.423 

.423 

.423 

.  422 

.422 

.422 

.422 

6.11 

43 

.422 

.422 

.422 

.421 

.421 

.421 

.421. 

.421 

.420 

.420 

6.67 

44 

.420 

.420 

.420 

.420 

.420 

.420 

.419 

.419 

.419 

.419 

7.21 

45 

12.419 

62.419 

62.419 

82.419 

62.419 

62.419 

62.418 

82.418 

62.418 

62.418 

7.78 

46 

.418 

.418 

.418 

.417 

.417 

.417 

.417 

.417 

.416 

.416 

8.33 

47 

.416 

.416 

.416 

.415 

.415 

.415 

.414 

.414 

.414 

.413 

8.89 

48 

.418 

.413 

.413 

.412 

.412 

.412 

.  412 

.412 

.411 

.411 

9.44 

49 

.411 

.411 

.410 

.410 

.410 

.410 

.409 

.409 

.409 

.408 

10.00 

50 

62.406 

62.408 

82.407 

62.407 

62.407 

62.407 

82.406 

82.406 

62.406 

62.405 

10.56 

51 

.406 

.406 

.404 

.404 

.404 

.404 

.403 

.403 

.403 

.402 

11.11 

52 

.402 

.402 

.401 

.401 

.400 

.400 

.400 

.399 

.399 

.398 

11.67 

53 

.398 

.398 

.397 

.397 

.396 

.396 

.396 

.395 

.395 

.394 

12.22 

54 

.394 

.394 

.393 

.393 

.392 

.392 

.392 

.391 

.391 

.390 

12.78 

55 

62.390 

62.390 

62.389 

62.389 

62.388 

62.288 

62.388 

62.387 

62.387 

62.386 

13.33 

56 

.386 

.386 

.386 

.385 

.384 

.384 

.383 

.383 

.382 

.382 

13.89 

57 

.381 

.381 

.380 

.880 

.879 

.279 

.379 

.378 

.878 

.377 

14.44 

58 

.377 

.3n 

.376 

.376 

.375 

.375 

.374 

.374 

.373 

.373 

15.00 

59 

.372 

.371 

.371 

.370 

.370 

.369 

.368 

.368 

.367 

.367 

15.56 

t60 

62.366 

62.366 

62.365 

62.364 

62.364 

82.363 

62.362 

62.362 

62.861 

62.361 

tl6.11 

61 

.360 

.360 

.359 

.369 

.358 

.358 

.358 

.358 

.357 

.357 

16.67 

t62 

.856 

.354 

.354 

.363 

.353 

.852 

.351 

.351 

.350 

.350 

17.22 

63 

.349 

.348 

.348 

.347 

.346 

.346 

.345 

.344 

.343 

.343 

17.78 

64 

.342 

.341 

.341 

.340 

.340 

.339 

.338 

.338 

.837 

.337 

18.33 

65 

62.336 

62.335 

62.335 

82.334 

62.333 

62.333 

82.332 

82.331 

62.330 

62.330 

18.89 

66 

.329 

.328 

.328 

.827 

.326 

.326 

.325 

.324 

.323 

.323 

19.44 

67 

.322 

.821 

.321 

.820 

.819 

.319 

.818 

.817 

.316 

.318 

20.00 

68 

.315 

.314 

.314 

.313 

.312 

.312 

.311 

.310 

.309 

.309 

20.56 

69 

.306 

.307 

.306 

.306 

.305 

.304 

.303 

.302 

.302 

.301 

21.11 

70 

62.300 

62.299 

62.299 

62.298 

62.297 

62.297 

62.296 

62.295 

62.294 

62.294 

21.67 

71 

.293 

.292 

.291 

.291 

.290 

.289 

.288 

.287 

.287 

.286 

22.22 

'72 

.285 

.284 

.283 

.283 

.282 

.281 

.280 

279 

.r9 

.278 

22.78 

73 

.277 

.276 

.275 

.275 

.274 

.273 

.272 

.271 

.271 

.270 

23.33 

74 

.269 

.268 

.267 

.267 

.266 

.265 

.264 

.263 

.263 

.262 

a.89 

76 

62.261 

62.260 

62.259 

62.259 

62.258 

82.257 

82.256 

62.256 

62.255 

62.254 

24.44 

76 

.253 

.252 

.251 

.250 

.249 

.249 

.248 

.247 

.246 

.246 

25.00 

77 

.244 

.243 

.242 

.241 

.240 

.240 

.239 

.238 

.237 

.236 

25.56 

78 

.235 

.234 

.233 

.233 

.232 

.231 

.230 

.229 

.229 

.228 

26.11 

79 

.227 

.226 

.225 

.224 

.223 

.222 

.221 

.220 

.219 

.218 

26.67 

80 

62.217 

62.216 

62.215 

62.214 

62.213 

62.213 

62.212 

82.211 

82.210 

62.209 

27.22 

81 

.208 

.207 

.206 

.206 

.204 

.204 

.203 

r  .202 

.201 

.200 

27.78 

82 

.199 

.198 

.197 

.196 

.195 

.194 

.193 

.192 

.191 

.190 

28.33 

83 

.189 

.188 

.187 

.186 

,185 

.184 

.183 

.182 

.181 

.180 

28.89 

84 

.179 

.178 

.in 

.176 

.175 

.174 

.173 

.172 

.171 

.170 

•  ifAJdmum  deortty.  at  about  39.1  F.  or  4''  C. 
t  'OrdfnaiT"  temperatores  used  for  deterralnlDR  specific  graTlties.  about  OO"  to 
apy^oiyO.    For  seieotlOc  determinations.  0«  C.  is  referred  to  as  sUndard. 


d  by  Google 


.44 

.8 

62.161 

62 

.151 

.141 

^ 

.131 

.120 

62.109 

62 

.098 

.086 

.075 

.063 

62.051 

63 

.038 

.026 

.013 

.000 

61 

61.988 

61 

.975 

.962 

.949 

.936 

61.922 

61 

.910 

.896 

.882 

.863 

61.854 

61 

.840 

.836 

.812 

.797 

61.783 

61 

.768 

.753 

.737 

.722 

61.706 

61 

.690 

.674 

.658 

.641 

61.624 

61 

.608 

.591 

.574 

.558 

61.542 

61 

.528 

.509 

.483 

.476 

61.4S9 

61 

.442 

.425 

.408 

.290 

d  by  Google 


4M   Tn^WElGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS. 


4 — ^Wbiohts  and  Spbcific  Gravitibs  ot  Liquids. 
(AatboritaUT«.    See  alao  Table  5.) 


RdaUye 
Density 
to  Water 
at  4"  a 
Sp.Or. 

Relative 
Density 
to  Water 
at  60"  to 

62"  F. 
(-16"C.). 

Weight 
per  Cubic 
nPoot. 
Lbs. 

•OoeLof 
Expansion 
perbecree. 

Name. 

Temp. 

Oent. 

Add,  aoetlo 

60»F. 

4«G 

0»C. 

60"  F. 

0»G 

60»F. 

0»C. 

60-F. 

0»C. 

«»C. 

60"  F. 

60"  F. 

60"  F. 

60"  F. 

60"  F. 

60"  F. 

0"C. 

0»CJ. 

o"a 

0»C 
0»C. 
60"  F. 
0»CJ. 
0"C. 

o»a 

1.065 

66.41 

anenous 

carbonlo  Olquld)  . 
fluorto 

0.830 

61.810 
93.64 
77.406 
74.83 
88.642 
97.16 
114.923 
49.502 
60.82 
61.96 
57.87 
58.24 
55.81 

1.600 

hydrocWorlc 

murlatlo 

1.240 

* 

1.200 

nitric          

1.420 

.00110 

phosphorto 

sulphuric 

AIoolM)!.  pure  (absolute). 
96  per  cent 

1.558 

1.841 
0.798 

. 00063 

.00104 

.815 
.833 
.930 
.934 
.894 

50  per  cent 

Avninonia 

Benslne 

.69 
.90 
1.060 
2.960 
1.293 
1.525 

Bensde 

Blood 

66.169 
184.775 
80.714 
95.197 
68.48 
62.049 
44.508 
121.477 

Bromine       .....*...•• 

.00104 

Oart>on  bisulphide 

fThlorofonn 

.00114 

.00111 

cider 

1.018 

Qaret       

0.994 
0.713 
1.946 

Ether 

.00015 

Bthvlle  Iodide 

Qasollne 

CHyoerine         ......... 

0"G 
0"CJ. 

o"a 

0"C. 
60"  F. 
60"  F. 
60"  F. 
0"CJ. 
60"  F. 
60"  F. 
0"C. 
0"C. 
60"  F. 
60"  F. 
60"  F. 
60"  F. 
0"a 
60"  F. 
60"  F. 
60"  F. 
0"C. 

o"a 
o"a 
o"a 
4"  a 
o"a 

60"  F 
60"  F. 

1.260 

18.598 

3.342 

1.029 

78.664 
848.84 
208.62 

64.234 

52.88 
59.92 
■57.87 
52.185 
58.31 
52.88 
57.118 
62.186 
57.62 
56.93 
58.12 
58.37 
64.309 
58.12 
68.87 
67  37 
66.119 
89.077 
52.186 
63.672 
62.424 
62.416 
63.98 
77.33 

Mercury 

.00618 

Methylene  iodide 

Mnk.. 

Nairiitha  (oO) 

.848 
.961 
.928 

Oil,  castor 

lemon 

0.852 

Unseed 

.936 
.848 

naphtha. . .  .• 

olive 

0.915 
0.836 

petroleum 

poppy .....,., 

.924 
.913 
.932 
.936 

rape-seed 

iKKmme  ........... 

spindle 

turpenUne 

0.870 

.00090 

walnut 

.936 

.936 
.920 

wood 

whale  (sperm) 

Oxygen  Olquld) 

Pentane 

0.899 
0.626 
0.836 
1.020 
1.000 
0.999 

Urine                 

Water,  dlstflled 

distilled 

sea 

1.036 
1.240 

Dead  sea 

*For  moderate  temperatures. 


d  by  Google 


UQUIDS^MISCELLANEOUS. 


469 


&. — ^Wbigbts  and  Sfbcivic  ORArxras  or  Miscbllanbous  Liquids.* 
(Bee  alio  Table  4.) 


Spedflo 
Gravity. 


[Wt.  Lbi.H 

per     I 

Cu.  Ft.  I 


Name. 


Specific 
Gravity. 


Wt.  Lbfc 

per 
Cu.  Ft. 


Acid.   Benzole 

atrlc 

Conoentnted 
Fboapborfc 
(aoUd) 

Aledbol.  Pure.  60». . 

40% 

25% 

10% 

5% 

Affimoola,  28% 

Aqua  fortta.  double  . 
■Ingle  .. 

Bttomni.  'liquid .' .'.'.' 
Brandy 


.667 
J.  034 
1.621 

2.800 

.794 

.863 

.961 

.970 

.986 

.992 

.891 

1.300 

1.200 

1.034 

.848 

.934 


41.69 
64.48 
94.85 

174.61 
49.51 
53.82 
59.30 
60.49 
61.49 
61.86 
55.66 
81.07 
74.83 
64.48 
52.88 
57.62 


Ether.  AoeUc 

Muriatic.... 
Sulphuric... 

Honey 

GO.  Aniae-eeed 

Codfish 

Palm 

Sunflower 

Spirit,  rectified 

Tar 

Vinegar 

Water  (See  Table  8) 

Wine.  Burgundy  . . . 

Champagne.. 

Madeira 

Port 


.866 

.845 

.716 

1.450 

.986 

.923 

.969 

.926 

.824 

1.015 

1.080 

1.000 

.992 

.997 

1.038 

.997 


54.00 
52.69 
44.59 
90.42 
61.49 
57.56 
60.43 
57.75 
51.38 
63.30 
67.35 
62.36 
61.86 
62.17 
64.73 
62.17 


•  Bawd  on  weight  Of  water  at  62. 36  Iba.  per  cubic  foot.  he.,  at  16<*C.  <'*60.8»F.) 


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470    ^—WEIGHTS  AND  SPECIFIC  GRA  VITIES  OF  MATERIALS. 


^ 


>%r^ 


I 


toie^to^ 


—  CO        CO        •*        -HO»Oi        tOMO  — MCO        Oftr^NOV 


CVOOOm        t«« 


SOLIDS.     MISCELLANEOUS. 


471 


ss's 


lo     ioaiAe<e<oior»^  t«r*QO 


ror-o-^c*-*  — - 


e     e^eo'^'HW 


«'V»>Me9e9m<9«4t« 


^|:&- 


pi"^    8    "S  o  & 
•a  ^     V     6  c  M 

il  *  lis 
s^  s  111 

^-ll  vis 


•O       0  0 


d  by  Google 


472   ^—WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS. 

7. — ^AvBRAGB  Weights  and  Specific  Gravities  of  Woods. 
General  Table. 
[See  also  Table  6.] 


Name  of  Spedes. 


.42—1.01 
.66—1.26 


.31— 

.65—1. 

.52—1. 


12 


.92—1.26 


.48— 
.32— 
.61— 
.63— 


Alder 

Apple 

Aah.  Orecn 

Mountain 
White.... 

Bamboo 

Beecb 

Birch  

Box.  Brazilian. 

Dutch 

French . . . 

Cedar.    Rod... 

White.. 

Cherry 

Chestnut 

Cork 

CypresB,  Bald 

Douglas  "  Fir  "  (See  Spruce,  Douglas) 

Ebony 

Elm,  Cedar 

Willie 

••  Fir  "  Washington  (See  Spruce.  Doug- 
las)   

Gum,  Sweet 

Hackmatack 

Hemlock 

Hickory.   Blttemut  . 

Mockemut  ^    r    -^ 

Nutmeg 
Pecan 
Pignut 
Shagbark 
Water 
(Average  of  above  Hickories) 

Juniper 

Larch 

Lignum- Vltae 1.1ft— 1.38 

Logwood 

Mahogany,    Honduras 

Spanish 56 — 

St.  Domingo 

(Average  of  above  Mahoganies) 

Maple 63—1.06 

Oak.  Ck)w 


s  S  ^ 


Overcup 

Post 

Red 

Spanish 

Texan 

Water 

White 

WUlow 

YeUow 


-6    %   ^ 

Q 


(Average  of  above  Oaks.  say). 

African 

Canadian ] . '. . 

Dantzlc 


•Dry. 


Spec. 
Grav. 


.56 
.76 
.62 
.55 
.62 
.36 
.74 
.65 
1.03 
1.04 
1.33 
.53 
.37 
.66 
.63 
.24 
.46 

1.24 

•  .74 
.64 


.59 
.61 
.42 
.77 
.85 
.78 
.78 
.89 
.81 
.73 
.80 
.57 
.55 
1.28 
.91 
.56 
.86 
.72 
.71 
.75 
.74 
.74 
.80 
.73 
.73 
.73 
.73 
.80 
.72 
.72 
.75 
.82 


Wt.ln 
Lbs.  per 


Cu. 
Ft. 


Ft. 
B.  M. 


Green. 


,1- 


¥t.  In 
bs.  per 


34.3 

2.86 

46.8 

3.90 

38.7 

3.23 

34.3 

2.86 

38.7 

3.23 

22.6 

1.87 

46.2 

3.86 

40.6 

3.38 

64.3 

5.36 

64.9 

5.41 

83.0 

6.92 

33.1 

2.76 

23.1 

1.92 

41.2 

3.43 

39.3 

3.28 

15.0 

1.25 

28.7 

2.39 

77.4 

6.45 

46.2 

3.85 

33.7 

2.81 

36.8 

3.07 

38.1 

3.17 

26.2 

2.19 

48.1 

4.01 

53.1 

4.42 

48.7 

4.06 

48.7 

4.06 

55.6 

4.63 

60.6 

4.21 

45.6 

3.79 

49.9 

4.16 

35.6 

2.97 

34.3 

2.86 

79.9 

6.66 

66.8 

4.73 

35.0 

2.91 

63.1 

4.42 

44.9 

3.75 

44.3 

3.69 

46.8 

3.90 

46.2 

3.85 

46.2 

3   85 

49.9 

4.16 

45.6 

3.79 

45.6 

3.79 

45.6 

3.79 

45.6 

3.79 

49.9 

4.16 

44.9 

3.75 

44.9 

3.75 

46.8 

3.90 

61.2 

4.27 

54.3 

4.53 

47.4 

3.96 

.82 
1.10 


51.2 
68.7 


Ft. 
B.1C 


52.4        4.37 


61.2 
58.7 


76.2 
46.' S' 


1. 


2S 


o 

50.6 


♦  A  wood  is  considered  "dry"  when  it 
cent  of  moisture. 


contains  not  more  than  15  per 


WOODS. 


478 


r. — ^Atbraob  Wbiobts  and  Spbcivic  Gravitxbs  of  Woods— Conddded. 
~  Gbnbral  Tablb. 

[See  also  Table  8.] 


Dry. 

Oreeo. 

Name  of  Speelea. 

Spec. 
Orav. 

Wt.  to 
Lbs.  per 

Spec. 
Orav. 

Wt.  to 
Lbcper 

Cu. 
Ft. 

Ft. 

B.M. 

Co. 
Ft. 

Ft. 
B.M. 

Oak— <?onUaued. 

Enslhih 

.93 
1.17 

.7« 
1.07 

.67 
.63 
.63 
.61 
.50 
.51 
.44 
.38 
.52 
.52 
.45 
.38 
.53 
.44 
.40 

.51 

.59 
.70 
.58 
.49 

58.1 
73.0 
47.4 
66.8 

41.8 
39.3 
38.1 
38.1 
31.2 
31.8 
27.5 
23.7 
32.5 
32.5 
28.1 
23.7 
33.1 
27.6 
25.0 
31.8 

36.8 
43.7 
36.2 
30.6 

4.84 
6.09 
3.95 
6.57 

9.49 
3.28 
2.76 
3.17 
2.60 
2.66 
2.29 
1.98 
2.71 
2/71 
2.34 
1.98 
2.76 
2.29 
2.08 
2.65 

3.07 
3.64 
3.02 
2.55 

1.16 

71.8 

6.98 

(heart  of  oak) 

James  River r  -  - 

Uvc         

1.26 
UOl 

78.7 
63.0 

6  55 

OrecoQ  "  Pine  "  CBee  Spruee.  Douglas) 
IW 61—1.07 

5.25 

Plne.Ciiban                          ,    ^ 

'LoUoUy                       S    •£    '^ 

Lomdeaf  (Yellow)     ati^^^'^ 

IBS?           s  1^ 

(ATerage  of  above  Ptnes.  say) 

.60 

.75 

37.5 
46.8 

3.12 
3.90 

8ncar ,  ,  , 

.58 

36.2 

3.02 

pooiarT!^:.;. !.!!!.!;;!!:::     ; 

Wblte .; 

IttKlwoo^  4 1 —  87 

.82 

51.1 

4  27 

Spnwe.  Qdlfonila 

flvnunon 

.63 

39.3 

3.28 

TSr^..:::::::::::::::::::::::" 

Wstirat.  Black 

WBIoir 

Note  that  treated  timbers  will  weigh  from  6  to  20  lbs.  per  cu.  ft.  more 
than  the  untreated  timbers,  well  seasoned.  Beech,  well  treated,  will  receive 
18.5  Iba.  per  cu.  ft.  of  zinc  chloride  solution  or  about  A  that  quantity  of 
creosote  oil;  pine,  about  the  same  quantities,  usually  a  uttle  less;  and  oaks 
about  I  the  above  quantities.  In  general,  the  harder  woods  mcrease  in 
weight  Ibm  than  tb«  softer;  exact  quantities  depend  upon  the  specifications. 


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474    V— WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS. 


8. — Weights  and  Specific  Gravities  op  Building  Stones. 

Masonry  and  Cements. 

(Average  Values.) 


Name  of  Material. 

Specific 
Gravity. 

Wt.  per 

Cu.  Ft. 

Lbs. 

Wt,lnLbs.per- 

Cu.  Yd. 

Cu.  In. 

Brlok.  Chrome 

2.803 
2.643 
2.403 
2.403 
2.163 
2.163 
1.922 
1.602 
1.442 

(1.04) 
(1.36) 

2.70 
2.79 
2.88 
2.88 

175. 
165. 
150. 
150. 
135. 
135. 
120. 
100. 
90. 

65. 

86. 

100. 

4725. 
4455. 
4050. 
4050. 
3645. 
3645. 
8240. 
2700. 
2430. 

1755. 
2295. 

.1013 

Magnesia 160—170 

PreoBed  (hard) 

.0155 
.0868 

Paving  and  Fire 

0868 

Lime— sand 130—140 

Prcned 

.0781 
0781 

Common,  buQdlng 

.0694 

Soft,  bunding 

0579 

Light,  Inferior 85—  95 

.0621 

Cement   Oooee  or  granular) 

Natural  (Roaendale)  . . .       55—  75 

Portland 75—  96 

"       shaken,  usually  taken  at . . 

Cement   (solid) 
Natural.  Illinois.  Utlca 

Kansas,  Fort  Scott 

Maryland,  Cumberland 

Round  Top 

Minnesota.  Austin 

3.15 

. 

Mankato 

2.87 
3.12 
3.04 
2.98 
2.95 

New  York.  Akron 

Rosendale 

Pennsylvania.  Lehigh 

f (General  averase.  say) 

(184.1) 

(4971.) 

(Specifications  A.  8.  T.  M.,  1904)2 . 8  mln. 

(Report  U.  8.  Engrs..  1 902)        2 . 5 — 2 .  8 

(Extreme  limits  for  good)           2 . 7 — 3 . 2 

PorUand 

(General  average,  iav). 

3.15 

(196.6) 

(5308.) 

(Specifications  A.  S.  T.  M..  1 904)  3 . 1  mln. 

(Extreme  limits  for  good)           3.0—3.2 

Puzcolan  or  slag 

(Oeneral  average,  say) 

2.85 

(177.9) 

(4803.) 

(Report  U.  8.  Engrs..  1902)        2.7 — 2.  8 

(Extreme  limits  for  good)           2 . 7 — 2 . 9 

Blended,  Natural  (50)  and  PorUand  (50). 

say                           .            ...        .        ,    ,    t    ,    t         t    r    -    t   -    r    -   t    T    »   - 

3.05 

(190.4) 

(5141.) 

Cement  (In  barrels),  weight  per  bbl.,  net: 
Spec.  U.  S.  Enffineers,  1902: 
Natural 300  lbs.,  mln. 

West  of  Allegheny 
Mts.  may  be  . .  .265    • 

i 

1 

Portland    48ack8  @  93.751bs.375    ' 

1 

Puziolan  4  Kicks  @  82.50    "  333     *          '* 

Spec  Am.  Soc.  T.  M.,  1904: 
Natural     3  bags  ^  94  lbs....  282  lbs.  mln. 

PorUand    4 bags  @  94   "     ..376    " 

Foreign: 
Enffllsh  PorUand            400  to  430  lbs 

German  PorUand.  gross 400  to  440  " 

net      ....             376  " 

♦Specific  Gravity  Equivalent  for  any  Weight. 
Water  at  4°  C. 


Weight.  Spec.  Grav.  Weight.  Spec.  Grav.   Weight.  jSpec.  Grav 


.016  02 
.032  04 
.048  06 


.064  08 
.080  10 
.096  12 


.112  14 
.128  16 


9  .144J8 


BUILDING  STONES.    MASONRY.    CEMENTS. 


475 


8. — Weights  and  Spbcitic  Gravitibs  op  Building  Stones, 
Masonry  and  Cements — 0)ntinued. 
(Average  Values.) 


1 

Namn  of  Matpiial 

Specific 
Gravity. 

Wt.  per 

Cu.  Ft. 

Lbs. 

Wt,  In  Lbs.  per- 

Cu.  Yd. 

Cu.In. 

Oeooit  Mortar  (oement-aand-water-mlx) 
FttHand.  aay 

1.68 

1.68 

2.33 

(2.00) 

(1.76) 

(1.36) 

(1.79) 

(1.2) 

(1.6) 

3.77 
3.68 
2.63 
2.84 
2.66 

2.69 
2.63 
2.66 
2.72 
2.70 
2.61 
2.68 
2.65 
2.66 
2.74 
2.67 
2.65 
2.70 
2.64 
2.683 
(1.79) 
(2.00) 

(.96) 
(2.08) 
3.12 
1.60 
2.56 
2.58 
3.67 
2.48 
2.51 
2.67 
2.70 
2.34 
2.54 

3.53 
2.76 
2.67 
2.32 

2.71 
2.71 

2.71 

105. 

105. 
145. 
125. 

no. 

85. 
112. 

76. 
100. 

172.9 
167.3 
164.2 
177.3 
166.0 

167.9 

164.2 

166.4 

171.0 

168.5 

162.9 

167.3 

165.4 

166.0 

171,0 

166.7 

165.4 

168.5 

164.8 

167.5 

112. 

125. 

60. 
130. 
(196.) 
100. 
159.8 
161.1 
160.4 
164.8 
156.7 
166.7 
168.5 
146.1 
158.6 

157.9 
172.3 
166.7 
144.8 

189.2 
169.2 

2835. 

2835. 
3915. 
3375. 
2970. 
2295. 
3024. 

.0608 

.0608 
.0839 

Rtsumng  Votume  o1  Mix: 
1  cement..   1  sand   —1.5:   l  cement.    2 

WKi«-3.3: 
I  eemait,  3  sand   -3.1;   1  cement,    4 
WKi-3.8. 
Ooocrete.  Onder 100— HO 

Stone 130—150 

dry 166—120 

Loose,  dry 80—90 

Muddy,  say 106—120 

packed 

(^wtaand 

(>natte.  GalUonila.  Penryn  (hornblende)   . . . 

Roddln  (muBcovite) 

Colorado.  Geoi^etown  (blotlte) 

CXMinectlcut,  Greenwich 

New  Ixmdon 

CSeorgla,  Uthomla  and  Stone  Moun- 
tain     

Maine.  Fox  Island 

1                           HaUowell 

Maryland.  Port  Deposit 

Massachusetts,  Qufncy  (hornblende) 

Rockport 

Mlnnesoto 2.6fr— 2.69 

New  Hampshire,   CToncord 

Keene 

New  York 2.71—2.76 



Rhode  Island,  Westerley 

Vermont.  Barre 

Wisconsin.  Athelstane 

Montello 

1      fAmrftff*^  Of  above  Oranitm.  hav) 

4523. 
3024. 
3376. 

1620. 

3510. 

(5265.) 

2700. 

.0969 

Gam.  Dry,  ssy 

;             Wet,  say    

i  IJoe  Ooose  or  granular) 

Pmhlr  burned  (nnlckilme) .......  ^ ., . 

SUked 

LlBie(solld) 3.09—3.16 

Ltaie  Mortar 

0579 

Umestone.   nilnols,  Jollet 

Lemont...   2.51—2.65 

Quincy 

IndlftfMk,  nodfnnt 

Salem 



Bowling  Oreen 

MlchUcan.  Marquette 

Micnigan.«arq«e^^^.       ..   ... 

!                    Mbmesota.  Fron- 

tenac  2.42— 2. 03 

Stmwater 

Winona 

Missouri.  Oanton 

New  York,  OanaJoharte 

2.69—2.73 

Oobdskin 

Glens  Falls           * 
2.70—2.72 

,  ,(.--(7vr. 

476   21— WEIGHTS  AND  SPECIFIC  GRA  VITJES  OF  MATERIALS. 

8. — Weights  and  Spscinc  Gravitibs  of  Buildino  Stonbs, 

Masonry  and  Cbmbnts— Continued. 

(Average  Values.) 


i^ 


Name  of  MateiiaL 

Spedfle 
Gravity. 

Cu-K 
Lbs. 

Wt.  in  Lbs.  per  - 

C5u.Yd. 

Ou.In. 

LUnestoDO— Continued. 

New  York— Continued. 

K<ngirt/wi         

2.69 
3.75 
2.6 

2.76 
2.73 
2.76 
2.87 
2.87 
2.66 
2.77 
2.80 
2.71 
2.71 
2.72 
2.67 
2.65 
2.71 
2.84 
2.24 
2.00 
1.60 
1.68 
2.33 
8.64 
2.56 

2.63 
2.48 
2.24 
2.60 
2.56 

2.50 
2.72 
2.40 
(1.60) 
(1.98) 
(1.52) 
(1 .  86) 
2.73 
2.43 
2.23 
2.34 
2.50 
2.49 
2.17 
2.54 
2.26 
2.41 
2.60 
2.49 
2.41 
2.60 
2.62 
2.71 
3.70 
2.68 
2.34 
2.21 
2.11 

167.9 
171.7 
l«3.S 

171.7 

170.4 

172.3 

179.2 

179.2 

166.0 

173. 

174.8 

169.2 

169.2 

171.0 

166.7 

166.4 

169.2 

177.3 

140. 

125. 

100. 

105. 

146. 

165. 

160. 

168. 
156. 
140. 
162. 
160. 

156. 
170. 
150. 
100. 
124. 
95. 
115. 
170.4 
151.7 
139.2 
146.1 
156.1 
155.4 
135.5 
158.6 
140.6 
160.4 
163.8 
155.4 
150.4 
162.3 
163.6 
169.2 
168.5 
167.8 
146.1 
138.0 
131.7 

T«ake  ChAmplftln  .... 

Marble.  California,  Colton 

4388. 

.0949 

Qeorgla,  Tate 

New  York.  Gouvemeur 

PleasantTlUe 

TiirkiO^o^ 

Vennoot,  Dorset 

(Average  of  above  Marbles,  say) 

4671. 

.1001 

African 

Blscasran 

Brltlah 

Carrara.,... 

EKVDtlan 

French 

Italian  (whit?) 

Parian 

Masonry.  Brick.  Pressed 

3780 
3375. 
2700. 
283l>. 
3916. 
4455. 
4320. 

4266. 
4185. 
8780. 
4374. 
4320. 

4212. 
4590. 
4050. 
2700 
3348. 
2666. 
3105. 

.0810 

Medium 

.0723 

Soft 

.0679 

Concrete,  (binder 

.0608 

Stone 130—150 

Granite.  Dressed,  for  Buildings. . . . 

Bridges 

Dams 
2.50—2.56 

Rubble  in  cement 

dry,  say 

.0839 
.0955 

Limestone,  Dressed,  for  BuOdlngB  . 

Bridges . . . 

Dams 
2.47—2.63 
MarWc.  Dressed,  for  Buildings 

Band.  Fine,  dry 1.40—1.70 

.0938 

"!0984 
.0668 

wet 1.90—2.05 

Coarse 1.40—1.65 

Mixed,  coarse  and  fine 

aii.nf1«tnnA  rnJirnmlA..  Anfff>l  Tidund 

Colorado.  Fort  CoHlns 

Manltou             .     ... 

Trinidad  

Connecticut.  Portland  2  36 — 2.63 

Msssachusetts.  Long  Meadow .... 
Miohlsan  Marouette             

Portage  EIntry 

MInnniota.  Fond  du  Tat 

New  Jersey.  BdlevlUe  2.26—2.56 
New  York.  Albion      .  . 

Medina...  2. 40 — 2.58 

Hulberton 

Potsdam 

Oswego 

Oxford 

Portage 

Warsaw 

Qeveland , 

Massinon .,. 

BUILDING  STONES.   MASONRY.   CEMENTS. 


477 


8. — Wbigbts  and  Spbcitic  Ghavitibs  ow  Builiumo  Stonbs, 

Masonry  and  Cbmbnts — Concluded. 

(Average  Values.) 


Nmme  of  MaterlaL 

Spedflc 
Gravity. 

Wt.per 

CU.K 

Lbs. 

Wt.  in  Lbs.  per  - 

Cu.  Yd. 

Cu.In. 

aaDdfltone-^OooUnued. 

2.66 

2.60 

2.22 

2.61 

2.47 

2.81 

2.80 

2.78 

2.8 

2.76 

2.81 

2.88 

2.95 

3.00 

3.03 

2.86 

2.96 

185*. 

LumberrUlv 

WiMOfUlii,  FOfMl  4u  Lac 

Virginia,  BrlBlow» 

Uvence  of  above  SandstODes,  lay) 

Sbte.  New  York.  Qfanvflle 2.78—2.84 



.0891 

FeDDsylvanla.  aatlngton 

^ 

VermoDt,  Rutland.. T...  2.76 — 2.80 

(Avense  of  above  Slates,  say)   2.75—2.85 
Aortifa.  sacala 

4725. 

.1013 

Rngland.  Omnwall 

Wflsh 

109,  mnnesota.  Daltrth 

Taylors'  Fails 

New  Jetsev.  Jknter  Qtv 

New  York.  Staten  Idand 

(Avoage  of  above  Trap  rocks,  say) 

4996. 

.0171 

d  by  Google 


478    27— WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS, 


9. — Gbnbral  Table  op  Wbiohts  and  Spbcific  Gravities  op 
Materials. 
(Average  Values.) 


Nanie  of  Substanoe- 


Spec 
Qrav. 


Wt.  per 

Cu.Ft.  1 

Lbs.    I 


Name  of  Substance. 


Spec.  Wt.  p» 
Orav.  Cu.  FL 
Lbs. 


Add  (Sec  Table  4) 

Agate 2.5—2.8 

Air  (See  Table  2) 

Alabaster.  Calcareous 

—2.8 
Ojrpseous 
2.3— 

Alcobol  (See  Table  4) 

Alder  (See  Table  7) 

Alloys  (See  Brass,  Bronse. 

etc.) 

Alum 

Aluminum.  C^ast 

Hammered  . . 

Drawn  wire.. 

Pure 

Sheet 

Aluminum  bronxe 

Amalgam...   13.7—14.1 

Amber 

Ambergris 

Ammonia  (See  Table  4) . . 
Anthracite  (Solid) 

1.4  —1.7 
Antimony.  C»st 

6.«7— 6.74 

Pure 

Apatite 3.16—3.22 

Apple-tree  (See  Table  7) . . 
Aqua  fortis   (See  Table 

5) 

Aragonlte 

Arsenic.   ..     6.7—6.8 
Asbestos....     2.1—  3.1 

paper 

Ash  (See  Table  7) 

Ashes.  Coal  packed  .  6 — .  8 

Asphalt.  Paving 

Asphaltum.  Natural 

l.I—  1.8 
Atmospheric  air  (See 

Table  2) 

Ballast,  brick  and  gravel 
Bamboo  (See  Table  7) . .  . 

Barium 

Banrtes 

Basalt  (See  Trap) 

Beech  (See  Table  7).    .   , 

Beef  fat 

Beeswax 

Benzine 

Beer 

Beton  (See  CJoncrete) 

Birch  (See  Table  7) 

Bismuth,  Cast 

9.76—9.90 
Bitumen    (See   Ashphal- 

tum) 

Blood 

Bone 1 .  8 —  2.0 

Borax i.7__  i   g 

Boxwood  (See  Table  7) . . 

Brass.  Cast       7.8 —  8.8 

Rolled 


2.76 
2.61 


172.3 
162.9 


34.3 


1.72 
2  66 
2.76 
2.68 
2.67 
2.67 
7.7 
13.9 
1.08 
.87 
.894 

1.55 

6.71 

6.80 

3.19 

.75 


107.4 
160. 
171.7 
167.3 
166.7 
166.7 
480. 
868. 
67.4 
54.3 
55.8 

96.8 

419. 
424.5 
199. 
46.8 


3.0 
5.76 
2.8 
1.2 


18.7 
360. 
175. 

75. 


(.7) 
1.6 


44. 

100. 


(1.79) 
.36 
47 


4.45 

2.96 
.74 
.92 
.96 
.69 

1.034 


112. 
22.5 
29.3 

278. 

185. 
46.2 
57.4 
60. 
43.1 
64.4^ 


.65 
9.82 


40.6 
613. 


1.06 

1.9 

1.75 


66.2 
118.6 
109.2 


8.4 
8.6 


524. 
530. 


Brass.  Sheet 

Wire 

Brick  (See  Table  8) 

Brickwork  (See  Masonry, 

Table  8) 

Bromine 

Bronse.  Aluminum 

Coinage 

Oun  Metal 

8.15—8.95 

Ordinary 

Bushel  of  Produce,  etc 
pound  per  U.  8.  bu.— 


do 
do 
do 
do 
do 
do 


.95 


8.7 


1.24445 
24 
32 
40 
48 
56 

Butter 

Butternut  tree 
Cadmium...   8 

QUdte 2.6—2.8 

C^alclum 

camphor 

Caoutchouc 

(Carbon  (See  Diamond) . 

Carbon  bisulphide 

Carbonic  acid  (liquid) . . 

Castor  oU 

Cedar  (See  Table  7) 

Cement  (See  Table  8) . . . 

Chalk 2.2—2.8 

Champagne 

Ciharcoal.  Birch 

Oak  and  Fir  . . . 

Pine 

Powdered 

Cherry  (See  Table  7) . . . 
Chestnut  (See  Table  7) . 

C:iilorotorm 

(Thromlum 

Oder 

Cinnabar 

Qaret 

aay.  Dry 

Moist,  loose  1.7 — 2. 
Moist,  packed 

2.0—2.4 

with  gravel 

CX>al.  Anthradte  (solid)  . 

Lump 

Broken 

Egg 

Stove  (average)  . . 

Nut 

Pea 

Buckwheat 

Bituminous  (solid). . 

Loose... 

C^obalt  .     .   8.51—8.54 

0>ke.  Solid.  Natural  . . . 

Pressed 

Loose.  .^28 — 36 

Digitized  by  VjOC 


8.6 
8.54 


530. 
533. 


2.96 

7.7 
8.66 

8.6 
8.4 


.94 
.38 

8.65 

2.7 

1.58 
.99 
.93 


186. 
480. 
540.6 

537. 
524. 

.80366 
1.00000 
19.29 
26.71 
33.14 
38.57 
45.00 
6r.7 
23.7 

540. 

168.5 
98.6 
61.8 
58. 


1.293 
.830 
.961 


80.7 
61.8 
69.9 


2.6 

.997 
(.64) 
(.45) 
(.30) 
(1.38) 

.66 

.63 
1.525 
6. 
1.018 
8.1 

.994 
1.52 
1.9 

2.2 

2.5 
1.65 
(1.04) 
(1.02) 
(.99) 
(.96) 
(.93) 
(.90) 
(.88) 
1.33 
(.83) 
8.62 
(l.O) 
1.4 
.6 


162.3 

62.2 

84. 

28. 

19. 

86. 

41.2 

89.9 

96.2 
312. 

63.5 
606. 

62.2 

95. 
119. 

137. 
156. 

96.8 

65. 

64. 

62. 

60. 

68. 

66. 

56. 

83. 

52. 
632. 

62. 

87. 

32. 


GENERAL  TABLE. 


479 


9. — General  Table  of  Weights  and  Specipic  Gravities  of 
Materials— Continued . 

(Average  Values.)         


Name  of  Sabstanoe. 


Concrete  (See  Tftble  8) . . .. 
Copper.  Out.  8.6 — 8.9 
Drawn  wire 

8.8—9.0 
Hammered 

8.9—9.0 

Melted 

RoOed8.9— 9.0 

Sheet 

Cork 

CreoM>teofl.   1.04—1.10 

Cypress  (See  Table  7) 

DdU  Metal  (Copper  60. 
sine.   34-44.  iron   2-4. 

Un  1-2) 

Diamond...  3.45—8.60 

Do(fwood 

Dolomite  (See  Limestone) 
DouKlas  "  Fir  *'  (See  Table 


Earth  (See  Table  8). . 
Ebony  (See  Table  7) . 
E(W 


Spec 
Orav. 


Wt.  pel 

Cu.Ft. 

Lbs. 


8.89 

8.95 
8.22 
8.95 
8.89 

.24 
1.07 

.46 


8.6 
3.52 
.75 


1.24 
1.09 


550. 
555. 

559. 

513. 

559. 

555. 
15.0 
66.8 
28.7 


537. 
(220.) 
46.8 


Name  of  Subetanosu 


31.8 


77.4 
68.0 


Elder  pith 

Elm  (See  Table  8) 

Em«tdd 

Emery 

Ether  (See  Table  5)  . .  . 
Ethyllc  Iodide  (Table  4) . 

Fat.   Beef 

Hog 

Mutton 

Feldspar 

Filbert  tree 

Fir  (See  Table  7) 

Flint , 

Gaaon.  of  liquid 

1  pound  per  U.S.  gal- 
lon—   , 

0.13368   pound   per 

U.  S.gaUon- 

Gamboge 

Garnet 3.75—4.20 

German  stiver  8. 4—8. 7 
Glass.  Oown 

Ck)mmon  Window  . . . 


Spec 
Grav. 


.076 


Wt.  per 

Cu,Ft. 

Lbs. 

4.7 


2.7 

4.0 
.713 

1.946 
.92 
.94 
.93 

2.60 
.60 


2.59 


.120 

.016 
1.2 
4.2 
8.55 
2.50 
2.50 


(168.5) 
250. 

44.5 
121.5 

57.4 

58.7 

58. 
(162.) 

37.5 


(162.) 


7.4805 

1 . 0000 
75. 
(262.) 
(534.) 
156. 
1.56 


Window  Glass. 
(a^     Official  Pricea  Current  American  Pittahure  Plate  C,\as&  Co. 


d  by  Google 


480    27— WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIAL 


9.— Gbnbral  Tablb  of  Wbiobts  and  Spbcivic  Gratitibs  of 

MATBR1AL8 — Continued. 

(Average  Values.) 


Name  of  Subetanee. 


Spec 
Orav. 


Wt 
Cu 

L 


QlaflB— Continued. 

Flint 

Flooring.  tbJcJc . . 

Oreen , 

OpUcal 

Plate 

White 

Window 

OnelflB  (See  Table  8) 

Gold.  Caat 

Native,  bammered 
Pure 
Granite  (See  Table  8). ..  , 

Graphite 

Gravel  (See  Table  8) 

Greenstone  trap 

Grindstone 

Gum  Arabic   1.32—1.44 

goods 

Raw  (Caoutchouc  - 

India  rubber)   

Gun  Metal  (bronze) 

Gunpowder  (granular)  . . . 

Gutta  percha 

Gsrpeum,  Pure,  unbumed 
(Calcined.  1  lump 
Powder,  aoild 
loose 
shaken 
Plaster  of  parls 

2.1—2.4 
(See  Plaster) . . . 

Hackmatack 

Hemlock      

Hickory  (See  Table  7) . .  . 

HoUy 

Honey 

Horn 

Hornblende...  3.0 — 3.5 

Human  body 

Ice 88— .92 

melting 

India  rubber 

Iodine 

Iridium,  pure 

Iron,  Oist 

Wrought,  purest .  . . 
average  .. 

Molten 

Ivory 

Juniper  tree 

Kaolin 

Lava.  Basaltic 

Trachytlc 

Larch 

Lard 

Lead,  Commercial."  Cast '. 
^  Sheet. 

Pure 

Molten 

Lignite,  perfect... 
Llgnum-Vltac.  l .  i g— i ' aij 
Lime  (See  Table  8)V;/^ 


187. 
168. 
167. 
215. 
175. 
180. 
166. 


258 

4 
60 


1202. 
1211. 
217. 


2.26 


141. 


185. 
134. 

86. 

94. 

68. 

58. 
537. 

62.4 

61. 
144. 
112. 
159. 

60. 

64. 

140. 


38.1 
26.2 


47.4 
90.5 

105.5 

203. 
66.8 
67.4 
57.4 
58. 

309. 
1320. 

450. 

485. 

480. 

433. 

117. 
35.6 

137. 

181. 

150. 
34.3 
58.7 

710. 

712. 

713. 

649. 
80.5 
79.9 


LlmestoneOee  Table  8) . 

Linden  tree 

Unseed  oU  (See  Tables) 

Lithium 

Locust 

Logwood 

MagnesUu  solid 

loose 

Magneslte 

Magnesium,  pure 

Magnetic  Iron  ore 

Mahogany  (See  Table  7) 

Manganese,  pure 

ore.  Mack  . . 
red... 
Maple  (See  Table  7)..  .. 
Marble  (See  Table  8)... 

Mart 1.7—2.6 

Masonry  (See  Table  8)  . . 

Mastic  (resin) 

Mercury.  Solid. -40"  F. 

Llquld+32»  F. 

+  60»   F. 

212»   F. 

Methylene  Iodide 

Mica 2.65—3.15 

MUk 

Mcriybdenum.  pure 

Mortar.  Cement 


Mud 105—120 

Mulbeny  tree 

Nickel 8.8—0.2 

Nitric  add  (See  Table  4). 

Commwdal 
Oak  (See  Table  7)..  . 
Ochre 

Table  4) 

(See  Table  4)  . . 

ones   1.9 — 2.6 

....   2.1—2.2 


ree 

nm  Iron 

ne  dust,  shaken 

eticlron 

ron  (specular) . . 
ic 


.76—1.15 


I  Pear  tree  (See  Table  7)  . 

Peat,  pressed    .  60 — .  85 

Pentane 

Petroleum  (See  TaMe  4) . 

Pewter 

Phosphorus 

Pine  (See  TaMe  7) 

Pitch 

Plaster  (burned  Gypmmi) 

Cement 

Keene's  cement 
of  Parts 

iiz.d  by  Google 


.60 
.136 

.585 
.71 
.91 
3.2 
(1.74) 
3.0 
1.75 
(5.0) 


8  00 
3.46 
4.0 

.75 
2.77 
2.1 


.85 
16.632 
3.698 
13.680 
13.37(1 
3.349 
2.90 
1.029 
8.63 
1.68 
1.60 
(1   79) 
.75 
8.8 
1.42C 
1.22 


3.5 


.918 
2.36 

2.16 

1.34 
.71 

3.9 

2.66 

6.0 

6.2 

3.9 
11.8 
.95 
.88 
.67 
.72 
.626 
.836 
11.6 

1.77 


1.12 


GENERAL  TABLE, 


481 


0.— Obnbral  Tablb  ov  Weights  and  Spbcific  Gravitibs  09 

Materials — Continued. 

(Average  Values.) 


Spec. 
Qrav. 


Wt.  L 

Cu.Ft.| 
LbcL 


Name  of  Sobstanoe. 


Spec 
Orav. 


Wt.  per 

Cu.Pt 

Lbs. 


Flacter — Continued. 

Parian  eement . . 

Stucco 

Average  for  above: 
Qypanm.  unbumed 
Calcined, 
lump  .. 
powder, 
looae. 
•baken 
Sand  (1)  plaster  (2). 

dry 

QrdJnaij  plaster .... 
(See  Gypsum) 
Platinum.  Cast 

19.6—20.3 

Native 

Pure '. 

RoUed  

(Average,  use) 

Bum  tree 

Plumbago 

Poplar 

Poppy  on  (See  Table  4) . . 

Porcelain  China 

Porphyry 

Portland  eement  (See  O- 

ment) 

Potash  

Potasif  um 

Pumice  stone 

(Quarts  OTBtal.  pure 

2.61—2.71 

(idlnoetree 

Rape-seed  oU 

Bed  lead 

•Ream 

Rocli  crystal  (ballte)  .... 

Rock  Elm 

Roaendale    cement    (Bee 

CSonent) 

Rosewood 

*Raaln 

Ruby 

Salt.  CommoD,  solid 

loose, 
packed 
Coarse,  Sjrraeusc  . . . 
Turk's  Island 
78—80 

Fine,  Liverpool 

Saltpetre.  Chfll 

Kail 

Sand  (See  Table  8) 

Sandstone  (See  Table  8) . . 

Sapphire .' 

Selenium 


2.30 
1.80 


.97 
1.03 


1.52 
1.76 


19.96 
16.0 
21.50 
22.07 
2M50 
.78 
2.1 
.38 
.924 
2.3 
2.76 


144. 
112. 


60, 
64. 


95. 
110. 


1245. 
1000. 
1342. 
1378. 
1342. 
48.7 
131. 
23.7 
57.6 
244. 
172.3 


2.05 
.865 
.92 

2.66 

.71 

.913 

8.94 

1.089 

2.69 

.80 


128. 
54. 
57.4 

166. 

44.3 

56.9 
558. 

68. 
168. 

50. 


.73 
1.1 
3.9 
2.20 

(.96) 
(.72) 

(1.25) 
(.78) 
2.26 
2.05 


45.6 
68.7 

(243.) 

137. 

60. 
45. 

78. 

49. 
141. 
128. 


Serpentine.. 
Shale 


2.5—2.8 


3.95 
4.5 


(246.6), 
281. 


SUIdc  add.  orystaUlne . 

powder 

SOver 

Slag 

Slate  (See  Table  8) . .  . . 

Smalt 

Snow,  freshly  fallen 

wet 

Soapstone 

Sodium 

Spar.  (Calcareous 

Fdd- 

Fluor 

Heavy..    4.4—4.6 

Spelter 

Spindle  ofl , 

Spirit,  rectified 

Spruce  (See  Table  7) 

Sted.  average 

(Handbook  calcula- 
tions)!  

Wire 

Strontium 

Sulphur 

Sulphuric  Add 

Sycamore 

Talc  (steatite) 

Black 

Tallow 

Tamarack 

Tar,  average 

Teak 

Tdlurlum.  pure 

Tiles,  solid..    1.9—2.5 

hollow  (variable) . 

Tin,   Cast 

Rolled...  7. 3— 7.6 

Molten 

Topaz 

Trap  rock  (See  Table  8) . 

Tungsten 

Turpentine 

Type  metal,  cast 

Uranium 

Urine 

Vinegar  

Walnut.  Black 

Walnut  oU 

Water      (See     Tables  3 
and  4) 

Dead  Sea 

DIstUled  40  C 

0«»  C 

Mediterranean..   .. 


165. 
162. 
166. 
162. 
137. 
655. 
40: 


73 

978 

74 

70 

40 

43 

1 

936 

824 


162. 
8. 

50. 
170. 

61. 
171. 
168.5 
212. 
277. 
443. 

58.4 

51.4 


490. 

489.6 

490.4 

168.6 

125. 

114.9 
36,8 

170. 

181. 
58. 
23.7 
62.4 
43.7 

381. 

137. 


456. 
462. 
439. 
(220.) 
185. 
1100. 

54.3 
652. 
142. 

63.7 

67.4 
36.2 

68.1 


77.33 
62.42 
62.42 
64.23 


♦  Resin  is  the  liquid  sap  of  the  Longleaf  Yellow  Pine;  rosin  is  the  hard, 
brittle  substance  which  remains  after  the  turpentine  has  been  extracted. 

t Based  on  bar  1  in.  sq.  and  1  ft.  long  weighing  3.4  lbs.;  or  plate  12  ins. 
sq.  and  I  in.  thick  weighing  40.8  lbs.;  that  is,  2  per  cent  heavier  than  iron 
at  484)  I^.  per  cu.  ft. 


482     21— WEIGHTS  AND  SPECIFIC  GRA  VITIES  OF  MA  TERIALS. 

9. — Gbnbral  Tablb  op  Weights  and  Spbcipic  Gravitibs  of 

Matbrials — Concluded. 

(Average  Values.) 


Spec. 
Qrav. 

Lbe. 

Name  of  Substance. 

Spec 
Orav. 

Wt  pCT 

Cu.Ft. 

Lbs. 

Water — Continued. 

1.000 

1.026 

.96 

.49 

62.42 

63.98 

60. 

30.6 

Wine.  Madeira 

1.038 
.997 

7.12 
.936 

6.86 

7.1 

7.24 

7.1 

64.80 

Rain  4<*  C      

Port 

62  24 

Sea  (ocean) 

WnlfpAiir^ ,  ,              

445. 

Wax,  Be66 

Wood  oil 

58  4 

Willow 

zinc,  Caat 

428. 

Wine 99—1.04 

Pure 

443. 

Burgundy 

.992 
.997 

61.92 
62.24 

Sheet 

453. 

Champairne 

(Ayenum.  rniv) 

443 

10. — ^Weights  op  Producb.* 
The  following  are  minimum  wtights  according  to  the  laws  of  the  United 
States,  and  adopted  by  a  majority  of  States. : 


Per  bushel. 

a  Apples  (dried) 26  lbs. 

6  Barley 48  *' 

c  Beans  (white) 60  ** 

Beans  (castor) 46  ** 

Blue  grass  seed 44  " 

Bran 20  " 

d  Buckwheat 48  " 

e  Clover  seed 60  " 

Coal 80  " 

/  Com  (on  cob) 70  " 

g  Ck)m  meal 48  " 

A  (>)m  (shelled) 66  " 

t  Flaxseed 66  *' 

Hair  (plastering) 8  " 

Hemp  seed 44  " 

Hungarian  grass  seed. ... 60  " 


Lime  (unslacked) 

Malt 

Millet  seed 60 

/Oats 32 

k  Onions 67 

Peaches  (dried) 33 

/Peas 60 

Peas  (ground) 24 

Potatoes  (sweet) 56 

m  Potatoes  (white) 60 

n  Rye 66 

oSalt  (fine) 66 

o  Salt  (coarse) 60 

p  Timothy  seed 45 

q  Turnips 55 

r  Wheat 60 


Per  bushel. 
. .  30  lbs. 
38    " 


*  The  following  are  the  greatest  and  least  minimum  weights  adopted  by  | 
the  various  States:  Apples  (not  dried),  24  to  67  lbs.  Anthracite  coal,  76  to  i 
80  lbs.  a,  22  to  28  lbs.  6,  47  to  50  lbs.  c,  60  to  62  lbs.  d,  42  to  56  lbs.  | 
e,  60  to  64.  /.  68  to  70.  g,  46  to  50.  h,  52  to  58.  i,  44  to  56.  /,  26  to  32.  i 
k,  48  to  57.  /.  46  to  60.  m.  56  to  60.  n,  54  to  56.  o,  from  50  to  80  lbs. 
Coarse  salt,  in  Penn..  80  lbs.;  in  III.,  50  lbs.  Fine  salt.'m  Penn.,  62  lbs.;  ! 
in  Ky..  and  111..  55  lbs.  p,  42  to  60.  q,  42  to  60.  r,  60  lbs.  per  bu.  in  all  I 
the  SUtes. 


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SPECIFIC  GRAVITY  REDUCED  TO  WEIGHT, 


483 


REDUCTION  TABLES. 

11. — ^Wbight  Equivalbnt  for  any  Spbcipic  Gravity. 
Water  at  4°  C.  and  16*»  C. 


Specific 

Weight  of  any  Substance  Compared  with  Distilled  Water  at — 

Gravity 
of  the 
Sub- 

4*»C.-8    1»F. 

16'' C- 60.8° 

F. 

Per 

Cu.Ft. 

Lbs. 

Per 

Ft.  B.  M. 

Lb«. 

Per 

Cu.  In. 

Lbs. 

Per 

Cu.  Ft. 

Lbs. 

Per 

Ft.  B.  M. 

Lbs. 

Per 

Cu.  In. 

Lbs. 

6.2424 
12.4848 
18.7272 

.5202 
1.0404 
1.5606 

.0036  125 
.0072  250 
.0108  375 

6.236 
12.472 
18.708 

.6197 
1.0393 
1.5590 

.0036  080 
.0072  178 
.0108  267 

24.0696 
31.2120 
37.4644 

3.0808 
2.6010 
3.1212 

.0144  600 
.0180  625 
.0216  750 

24.944 
31.180 
87.416 

2.0787 
2.5983 
8.1180 

.0144  356 
.0180  444 
.0216  533 

43.6968 
49.9392 
56.1816 

8.6414 
4.1616 
4.6818 

.0262  875 
.0289  000 
.0325  125 

43.652 
49.888 
56.124 

3.6377 
4.1573 
4.6770 

.0262  622 
.0288  711 
.0324  800 

1.0 

62.4240 

5.2020 

.0361  250 

62.360 

5.1967 

.0360  889 

Example. — ^What  are  the  weights  per  cu.  ft.,  per  ft.  B.  M.,  and  per  cu.  in., 
w  ft  wood  whose  specific  gravity  is  0.61,  water  at  16**  C.  ? 

Sohition. —  Cu.  Ft.  Ft.  B.  M.  Cu.  In. 

.60  87.416  3.118  .02166 

.01  .624  .052  .00036 


.61  38.040  lbs.  3.170  lbs.  .022011b. 

Note  that  for  the  same  specific  gravity  compared  with  water  at  4**  C. 
&e  resultant  weight  is  1  part  in  1000  greater  tnan  when  compared  with 
^ter  at  16^  C;  that  is,  a  volume  of  water  at  the  lower  temperature  is  ^  of 
J%  h&ivier  than  an  equal  volume  at  the  higher  temperature.  As  the 
ipedfic  gravity  of  many  substances  varies  greatly,  depending  upon  the 
particular  specimens  selected  for  test,  it  will  be  noted  that  water  at  either 
^emperatxire  may  generally  1^  used  as  a  basis  for  calculating  the  weight 
of  the  material.  This  is  esf>ecially  allowable  for  woods,  building  stones  and 
other  natural  materials  subject  to  variable  composition,  texture^and  degrees 
of  moisture.  With  liquids  the  variation  of  the  substance  is  less  marked; 
jKi  with  gases  the  temperature  of  the  water  with  which  it  is  compared 
Bould  always  be  stated,  as  well  as  the  temperature  and  pressure  of  the  gas. 


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484    27— WEIGHTS  AND  SPECIFIC  GRAVITIES  OF  MATERIALS. 


12. — ^Weight  op  Sheets,  Bars  and  Wire,  of  ant  Material 
Prom  its  Specific  Gravity. 
(Water  at  4*»  C.) 


Specific 

Gravity 

of  the 

Material. 

Weight  of 
12^x12* 
Sheet 

tV'  Thick. 
Lbs. 

Weight  of 
1'  Square 

Bar 
1  Ft.  Long. 

Lbs. 

Weight  of 
1'  Round 

Bar 

1  Ft.  Long. 

Lbs. 

Weight  of  1000  Lineal  Ft.  of 

Wire 

in  Dia. 
Lbs. 

Wire 

.01' 

in  Dia. 

Lbs. 

Wire 
.001- 

in  Dia. 

(IMU.) 
Lbs. 

.1 
.2 
.3 

.4 
.5 
.6 

.7 
.8 
.9 

1.0 

.0325  125 
.0650  250 
.0975  375 

.1300  500 
.1625  625 
.1950  750 

.2275  875 
.2601  000 
.2926  125 

.3251  250 

.04335 
.08670 
.13005 

.17340 
.21675 
.26010 

.30345 
.34680 
.39015 

.43350 

.034  047 
.068  094 
.102  141 

.136  188 
.170  235 
.204  282 

.238  329 
.272  376 
.306  423 

.340  470 

.133 
.266 
.399 

.582 
.665 
.798 

.981 
1.064 
1.197 

1.330 

.00340 
.00681 
.01021 

.01362 
.01702 
.02043 

.02383 
.02724 
.03064 

.03405 

.0000  340 
.0000  681 
.0001  021 

.0001  362 
.0001  702 
.0002  043 

.0002  383 
.0002  724 
.0003  064 

.0003  405 

Example. — What  is  the  weight  of 
1000  ft.  of  wire  .02  in.  in  dia..  if  the 
specific  gravity  of  the  drawn  metal  is 
8.9? 


Solution: 
Wt.  is  proportional  to  (diam.)* 
For  wire  .01' dia..  8.0-.2724 
.9-. 08064 

8. 9<-. 80304 
4 

For  wire  .02' dia.  wt.- 1.21216  lbs. 


13. — Weight  per  Cubic  Yard  op  any  Material 
Prom  its  Specific  Gravity. 

Specific  gravity  of  material  X  1685.4       —weight  in  pounds  per  cu.  yd. 
X  .8427«      "        *•  short  tons      '*      *' 

X  .7524-     "        "  long  tons        "      " 


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REDUCTION  TABLES, 


486 


11— COMPARISOM  OF 

Various  Wbiohts,  Capacitibs  and  Volumbs. 

Prom  1  to  9  Units. 

tNumber  of  (^  Ft.  per  - 

Cable  Foot. 
Lba. 

U.aLlqtild 

U.  S.  Bushel 

Square  Yard 

Short  Ton 

Long  Ton 

G&lk» 

(2150.42 

1  In.  Thick 

(2000  Lbs.) 

(2840  Lbs.) 

(231  Cu.  IDB.) 

(}U.IIU.) 

(1296  01.1ns.) 

No. 

No. 

Uw. 

Lbs. 

Lbs. 

.m  S64 

.107  421 

1 

.608  673 

2  488.912 

2  787.581 

1 

.133  681 

1.244  456 

.75 

2  000. 

2  240. 

1.83  333 

.178  241 

1.650  r5 

1 

1  600. 

1  680. 

1.107  138 

.214  842 

2 

1  205  346 

1  244.456 

1  393.791 

2 

.267  363 

2.488  912 

1.50 

1  000 

1  120. 

2.410  m 

.333  263 

3 

1.806  019 

829.637 

929.194 

2fM  067 

.366  482 

3.218  500 

2 

750 

840. 

a 

.401  043 

3.733  368 

2  25 

666.667 

746.667 

1.214  256 

.439  684 

4 

2.410  693 

622.228 

696.895 

4 

.634  734 

4.  on  824 

3 

800. 

560. 

4.017  830 

.537  105 

s 

3.013  365 

497.788 

557.516 

4. 821  384 

.644  526 

« 

3.616  038 

414.819 

464.597 

s 

.668  405 

6.222  280 

8.76 

400. 

448. 

6.333  333 

.712  964 

6.637  100 

4 

375. 

420. 

6.634  MS 

.751  947 

7 

4.218  711 

1         355. 559 

398.226 

« 

.802  088 

7.466  736 

4.50 

1         833.333 

373.833 

6.428  S12 

.859  368 

8 

4.821  384 

311.114 

348.448 

6.666  667 

.891  205 

8.296  875 

S 

800. 

336. 

7 

.935  767 

8.711  192 

5.25 

285.714 

320. 

T.232  076 

.966  789 

9 

5.424  057 

876.546 

809.731 

7.480  519 

1 

9.309  178 

5.610  39 

267. 363 

299.445 

S 

1.069  448 

9.956  648 

6 

250. 

280. 

9 

1.203  129 

11.200 

6.75 

222.222 

248.880 

t.333  333 

1.347  687 

11.615 

7 

214.286 

240. 

10.607 

1.435  938 

13.274 

8 

187.500 

210. 

12.000 

1.604  169 

14.933 

9 

166.667 

186.667 

14.961 

3 

18.618 

11.221 

133.681 

149.722 

32.442 

3 

27.928 

16.831 

89.131 

99.815 

20.t22 

4 

27.237 

22.442 

66.840 

74.861 

37.403 

S 

46.546 

28.052 

53.472 

59.889 

44.813 

« 

55.855 

33.662 

44.560 

49.908 

82.364 

7 

65.164 

39.273 

38.195 

42.778 

I9.844 

8 

74.473 

44.883 

83.420 

37.431 

62.360 

8.336  828 

77.604 

46.770 

32.072 

35.920 

62.434 

8.344  875 

77.684 

46.818 

32.039 

35.884 

63.100 

8.355  035 

77.779 

46.875 

32. 

35.840 

67.325 

9 

83.783 

50.494 

29.707 

33.273 

75. 

10.016 

83.334 

56.25 

26.667 

29.867 

IflO. 

13.368 

134.446 

75. 

20. 

.  22.400 

125. 

16.710 

155.557 

93.75 

16. 

17.920 

ISO. 

20.052 

186.668 

112.50 

13.338 

14.933 

175. 

23.894 

317.780 

131.25 

11.429 

12.800 

200. 

26.736 

248.891 

150. 

10. 

11.200 

222.222 

29.707 

276.546 

166.667 

9 

10.080 

248  889 

33.272 

309.731 

186.667 

8.036 

9 

290. 

23.420 

311.114 

187.50 

8 

8.960 

280. 

37.431 

348.448 

210. 

7.143 

8 

2S.714 

38.195 

355.559 

214  286 

7 

7.840 

330. 

42.778 

398.226 

240. 

6.25 

7 

333.332 

44.660 

414.819 

250. 

6 

6.720 

373.333 

49.908 

464.597 

280. 

8.357 

6 

460. 

53.472 

497.782 

300. 

5 

5.600 

448 

59.889 

557.516 

336. 

4.464 

S 

500. 

66.810 

622.228 

375. 

4 

4.480 

960. 

74.861 

696.896 

420. 

3.571 

4 

««6.6«7 

89.121 

829.637 

500. 

3 

3.360 

746.667 

99.815 

939.194 

560. 
760. 
840. 

2.679 

3 

1000. 

133.681 

1  244.456 

2 

2.240 

1130. 

149.722 

1  393.791 

1.736 

2 

3  000. 

267.362 

3  488.912 

1  500. 

1 

1.120 

3  240. 

299.445 

2  787.581 

1  680. 

.893 

"^«*thtpcr 

Above  value 

»  are  directly  i 

Above  values. 

Inversely  pro- 

Cubic  Poot 

tow 

9igbt  per  cubic 

foot.                 I 

portlonal  to  \ 

vt.  per  cu.  ft. 

*  Inversely  proportional  to  Capacity  or  Volume  per  given  Weight. 
t  Inveiaefar  oxDOortional  to  Weight  per  given  (Opacity  or  Volume. 


28.— STRENGTH    AND    RESISTANCE    OF 
MATERIALS. 

I.    GENERAL  PRINCIPLES. 

The  theory  of  the  resistance  of  beams  is  explained  in  Sec.  15. 
Mechanics,  page  298.  The  following  discussion  is  pertinent  to  the  subjoined 
tables,  and  to  general  working  formulas. 

a.   Stresses  and  Resistance. 

Stress  f"  force  acting  on  any  plane  section  of  a  material,  produced 
either  directly  or  by  transmission;  as,  for  instance,  by  leverage.  It  is 
measured  usually  in  lbs.  per  sq.  in.  (or  lbs.  per  sq.  ft.),  that  is,  in  units  of 
force  per  unit  oi  area.  The  three  primary  stresses  are  tension,  compression 
and  shear.  Transverse  bending  is  accompanied  by  all  three  of  the  primary 
stresses.     Torsion  or  twisting  is  usually  treated  as  shear. 

Strain  e '^  percentage  of  distortion  produced  by  stress.  All  strains  can  be 
reduced  primarily  to  tension,  compression  of  shearing,  although  torsion 
(mainly  ^ear)  is  sometimes  classed  separately. 

Modulus  of  elasticity  E  —  g.  ^^  '  (within  the  "elastic  limit")  —  a  constant, 
otram  e 
This  is  equivalent  to  stating  that  "Stress  is  proportional  to  strain"  (Hooke's 
law),  the  stress  f  being  equal  to  the  applied  load  per  square  inch  of  cross- 
section,  and  the  strain  e,  the  percentage  of  resulting  deformation  of  the 
material  in  the  direction  in  which  the  force  acts.  If  the  material  is  in  ten- 
sion there  obtains  £t  "^  — ,  in  which  ft  equals  tensile  stress  per  sq.  in.;  if  in 

compression,  £•  =— ;  if  in  shear,  E  «— :  if  in  torsion,  £,«---^,     Within 

practical  limits,  the  moduli  of  elasticity  for  tension  and  compre^on  are 
regarded  by  most  engineers  as  equal  for  the  same  class  of  material.*  If 
this  is  true  the  neutral  axis  in  the  beam  under  flexure  (and  also  in  the  ideal 
column  under  concentric  loading)  will  pass  through  the  center  of  gravity 
of  the  section  and  remain  stationary  for  all  safe  loadings.  This  is  funda- 
mental to  the  present  theories  of  beams  and  columns. 

Modulus  of  elasticity  E  is  assumed  to  mean  the  tension  or  compression 
modulus  unless  otherwise  stated  or  characterized,  and  will  be  so  considered 
hereafter.     If  a  weight  is  suspended  at  the  lower  end  of  a  rod  one  inch  in 

cross-section,  producing  an  equal  stress  /  in  the  rod,  then  will  /"  iaaa^^^" 

1  E 

the  rod  is  extended  j^  part  of  its  length,t  i.  e.,  when  »- 0.001;  /  — -cKS 

when  the  extension  is  -Vqq  or  »  — 0.002;  etc.    In  general,  f—Er.    It  is  easy 

to  see,  then,  that  if  these  ideal  conditions  of  elasticity  could  continue  to  the 
point  where  ^  — unity.  /  would  equal  E,  Hence,  the  modulus  or  "coefficient" 
of  elasticity  is  sometimes  defined  as  that  force  which  will  stretch  a  rod  of 
unit  cross-section  to  double  its  length,  based,  of  course,  on  the  original 
length  of  rod  and  on  the  cross-section  remaining  constant.  Long  before 
this  100  per  cent  deformation  can  obtain,  however,  we  reach  the  "elastic 
limit"  or  limit  of  elasticity  of  the  material. 

*  The  modulus  of  elasticity  for  most  materials  varies  more  or  less  with 
the  intensity  of  stress,  and  is  different  for  tension  and  compression  of  the  sanoe 
material,  the  difference  becoming  more  apparent  as  the  stresses  increase. 
Hence^  the  neutral  axis  of  beams  varies  in  position  with  the  amount  of  loading. 

t-*",®  <^*iii**ol  length  is  used  by  the  engineer  for  simplicity,  although 
the  final,  or  some  distorted,  length  might  be  more  applicable. 

486 


KINDS  OF  STRESSES.    •  487 

Elasik  limit,  and  yield  point-^Within  the  elastic  limit  of  the  material 
the  strain  is  proportional  to  the  stress  or  load,  and  when  the  latter  is  re- 
moved the  material  will  return  to  its  original  length,  form  or  position. 
(In  other  words,  a  perfectly  elastic  material  or  a  material  strained  withm 
the  elastic  limit  is  capable  of  transmitting  all  the  energy  that  it  receives, 
Qone  of  it  being  absorbed  in  internal  work.)  If,  however,  the  material  has 
been  strained  (by  stress)  in  excess  of  or  "beyond" 
the  elattic  limit  it  will  begin  to  "yield"  and  the  re- 
sohtng  deformation  will  increase  fnore  rapidly  than 
the  increase  of  stress  or  load.  Hence  the  term  "yield 
point"  used  to  denote  a  point  just  beyond  the  elastic 
hmit  of  the  material.  In  Fig.  1,  which  illustrates 
the  meUiod  of  plotting  the  relation  between  stre6S^ 
and  strain  for  any  material,  y  is  the  yield  point ; 
o-g.L    is    a    straight   line    showing    "stress    pro-  Pig.  1. 

portkmal  to  strain"  within  the  slastic  limit ;  and  u  is  the  position  of  ulti- 
mate strength,  showing  the  relation  between  stress  and  strain  at  the  "break- 
ing point.  The  yield  point  is  often  almost  coincident  with  the  elastic 
limit. 

The  elastic  limit  is  affected  more  or  less  by  static-,  repeated-,  and 
alternating  stresses. 

Ultimate  streofth — ultimate  stress. — ^The  ultimate  strength  of  material 
is  the  ultimate  stress  per  sq.  in.  which  the  material  is  capable  of  resisting, 
ap  to  the  point  of  breaking.  This  is  shown  in  Pig.  1  as  point  u.  In 
testing  materia]  the  stress  is  increased  graduallv  by  incremental  loading. 
and  the  breaking  point  is  always  above  the  yield  point. 

The  ultimate  strength  of  material  may  be  affected  by  the  kind  of  stress 
or  stresses  to  which  it  is  subjected. 

Static  stress,  or  stress  in  one  direction,  tends  to  raise  the  elastic  limit. 

Repeated  stresses,  or  stresses  varying  in  intensity  in  one  direction 
(either  in  tension  or  in  compression,  etc.,  and  never  reversing  or  passing 
through  zero),  tend  to  raise  the  elastic  limit,  sometimes  materially,  even 
when  the  stresses  are  well  below  it;  and  at  the  same  time  they  tend  to 
lower  the  ultimate  strength.  The  latter  will  be  the  more  marked  the  greater 
the  ntimber  of  repetitions  and  the  wider  their  range. 

AHeroating  stresses,  or  stresses  passing  through  zero  from  tension  to 
compression  or  vice  versa,  or  from  positiv^  to  negative  shear,  torsion,  etc.. 
in  a  vibratory  manner,  as  often  occurs  in  actual  structures,  tend  to  act 
injuriously  in  lowering  both  the  elastic  limit  and  the  ultimate  strength. 
Hence,  worlcing  alternating  stresses  should  be  kept  low. 

Working  stress  and  factor  of  safety. — ^The  woridng  stress  is  the  maxi- 
mum (safe)  stress  allowed  by  the  designing  engineer  in  his  calculations, 
and  from  the  previous  discussion  it  will  be  seen  that  its  value  may  vary 
greatly.  In  selecting  the  proper  working  stresses  we  must  consider:  ( 1)  the 
had  of  material,  its  physical  qualities,  and  its  durability;  (2)  the  kind  of 
loading,  and  the  nature  of  the  stresses;  (3)  the  probable  life  of  the  struc- 
tore.  whether  permanent  or  temporary.  In  general,  the  working  stresses 
must  be  well  within  the  elastic  limit  of  the  material^for  any  possible  loading, 
and  during  any  age  of  the  completed*  structure.  The  ratio  of  the  ultimate 
strength  to  the  working  strength  is  called  the  factor  of  safety;  thus. 

T»  ^        £      e^         ultimate  strength 

Factor  of  safety  — ^. . 

working  stress 
The  reason  for  basin^r  the  safety  factor  on  the  ultimate  strength  instead 
of  on  the  elastic  limit  is  that  the  former  is  more  definitely  ascertained; 
but  the  elastic  limit  is  also  considered  to  a  certain  extent,  perhaps  indirectly, 
in  fixing  the  working  stress. 

With  reference  to  the  same  kinds  of  loading  or  stresses,  we  select  larger 
factors  of  safety  for  natural  materials,  as  wood  and  stone,  than  we  do  for 

*  Concrete  and  reinforced  concrete  structures  are  not  considered  "com- 
pleted" until  the  cement  has  set  to  that  degree  of  hardness  consistent  with 
the  woridng  stresses  adopted  and  based  on  the  "age"  of  the  concrete. 
Coocrete  structures  fzrow  stronger  with  age:    wooden  structures,  weaker. 


488       2».— STRENGTH  AND  RESISTANCE  OF  MATERIAL 

manufactured  materials,  as  steel  and  iron.  The  obvious  reason  ft 
that  the  ultimate  strength  of  the  manufactured  material  may  re 
be  expected  to  vary  but  little  from  the  specification,  say  8  to 
metals,  whereas  the  ultimate  strength  of  wood  and  stone,  even  oi 
quality,  may  vary  100%  or  more;  furthermore,  tests  of  metals 
same  heat  will  determine  the  general  character  of  the  material  f 
heat,  while  the  physical  properties  of  nattxral  materials  are  not  < 
termined.  excepting  for  the  particular  piece  under  test.  Again, 
substances,  as  stone,  are  more  tmcertain  than  fibrous  substances, 
weaknesses  are  less  easily  detected;  and  hence  stone  should  ha 
factors  of  safety  than  wood. 

Factors  of  safety  may  be  considered  to  range  from  8.  for  stj 
on  steel,  tmder  favorable  conditions,  up  to  20  or  30.  for  impact 
masonry,  due  to  moving  machinery. 

Resilience  -  work. — If  a  weight  W  is  applied  gradualiy  to 
sectional  area  A,  and  length  /,  equal  to  volume  i4/—V,  the  ela 

W      I 
will  be  equal  ^  "4"X  -p: :  and  as  TV  is  applied  gradually,  the  work 

W  W^l 

in  stretching  the  rod  —  -j-  X  i  *»  ttaF'     ^  '  represents  the  stress  p 

then-r-"^/.  and  the  work  — ^Xi4/;    but  ^47— the  volume  V,  1 

fty 
resilience  or  work  =»  ~ .    This  is  called  the  elastic  rtsilienct  whet 

the  elastic  limit  of  the  material. 

Similarly,  if  a  beam  is  loaded  in  the  middle  with  a  conctntt 

W  applied  gradually,  the  deflection  at  the  center  will  equal  Tsgj 

W  W       W/> 

the  average  load  —  -5- ,  the  total  work  performed " "«"  X  ToWf'    But 

W     I  f 

theory  of  beams,  the  bending  moment  Af  a  ^"^X-n*  equals  Ma.  —  - 

AC  3 

y- ;   and,  substituting  this  value  of  W  in  the  above,  we  have 

H^/*       Pll       PAr*l      P       f* 
Resilience  or  ^o^k  -  ^^  -  ^^  -  -^^^  ---._..  ^i; 

or,  in  terms  of  volume  it  is  equal  to  gn^^J  *  ^  "■  oF  '  ^  *  ^* 

By  the  last  equation  it  can  be  compared  directly  with  the  rea 
a  rod.  The  above  equations  will  represent  Xh^elasUc  resilience  of  t 
for  concentrated  loading  at  the  middle,  when  /  (the  outer  fiber  ; 
sg.  in.)  is  equal  to  the  elastic  limit  of  the  material.  In  general,  the 
of  the  beam  is  obtained  by  multiplying  the  greatest  allowable  : 
applied  load,  by  one-half  the  deflection. 

The  resilience t  of  a  material  may  be  defined  as  the  capacit; 
material  to  absorb  and  give  out  energy,  measured  in  units  6i 
inch-pounds. 

For  ditlerent  kinds  of  stress  we  have  the  following  values  for 
or  work  of  deformation  of  any  material.  By  proper  substitution 
for  the  particular  kind  and  shape  of  the  material  the  r^ilience 
obtained  in  definite  units;  and  tne  result  will  be  the  elastic  resUie 
value  of  /  represents  the  elastic  limit  of  the  material: 

Stress.  Resil 

Tension,  direct,        ---.--..  -£ 

2J 

Compression,  direct,        .......  Jl 

2j 


*  See  Table  1.  Sec.  31,  Properties  and  Tables  of  Beams  and  Gird* 
l,ynh\  if  tK!!^*T***.  °/  »'««(«*»»<^<'  is  the  resilience  of  a  unit  volume  (< 
mch)  of  the  material     It  is  obtained  by  making  V-unity,  in  the  e- 


RESIUENCE    SUDDEN  LOADING.  489 

Strtss. 
Bendins,  in  beam,  £rom  concentrated  load,. 
**  MM.,      uniform  load, 

"  "  rectangular  beam  (bxh),  cancan,  load,  •  ibe^ 

"        unifonn"       -  ^r^ 

i5E 


Rtsilien€$. 

4/V 

16£y» 

^^ 

r.v 

"  beam  with  unif.  longitudinal  bending  moment,  ^  V 


%E 
6f* 


Torsion,  in  solid  rod,       -------  , 

where  V'-voltune  ot  material  under  action,  in  cubic  inches; 
£  — modulus  of  elasticity  of  the  material, 
r  — radius  of  gyration,  in  inches; 

y— distance  from  neutral  axis  to  extreme  outer  fiber,  in  inches; 
/^extreme  outer  fiber  stress,  in  lbs.  per  sq.  in. 

b.  Loading  and  Impact. 
Sodden  Loading.-~In  the  discussion  of  resilience,  the  loading  is  con- 
skiered  as  applied  gradually,  the  restiltant  being  a  static  load;  and  at  no 
^nie  is  the  distortion  greater  than  that  due  to  the  load  statically  applied. 
The  intensity  of  stress  increases  constantly  from  zero  to  a  maximum,  and 
coiuequentlv  the  average  stress  equals  one-half  the  maximum  stress.  If, 
bowever,  a  load  just  "touching"  a  rod  or  beam,  so  as  to  produce  the  least 
tmotmt  of  stress,  is  applied  suddenly  but  without  impact,  that  is,  "let  go." 
the  distortion  will  practically  be  doubled,  and  hence  the  fiber  stress,  deflec- 
tioa,  and  work  performed  will  be  double  that  produced  by  resilience  as  when 
the  load  is  applied  gradually.  For  this  reason  "live  loads"  on  structures, 
and  specially  train  loads  on  bridges,  are  considered  as  "sudden  loads, 
the  working  stresses  for  which  are  usually  but  one-half  the  working  stresses 
lor  dead  or  static  loads. 


t  is  the  energy  of  the  blow  when  one  mass,  possessing  momentum, 
comes  in  contact  with  another  mass.  At  the  instant  of  contact  each  gives 
eoeigy  to  and  absorbs  energy  from  the  other,  and  if  they  were  perfectly 
elasUc  (an  ideal  condition  never  realized  in  practice)  none  of  the  energy 
would  be  dissipated  into  heat. 

The  mathematical  analyses  of  many  operations,  as  pile  driving,  water 
»m  in  pipes,  etc.,  are  dependent  upon  reducing  the  energy  of  the  blow  to  an 
eqmvalent  static  iorce\  but  no  formula  yet  devised  correctly  represents  the 
^Ution.  To  do  so,  it  must  take  into  consideration  the  element  of  distor- 
tion or  distance  (energy  is  a  measure  of  force X distance),  the  inertia  of  the 
Hoisting  mass,  the  loss  of  energy  in  heat,  in  deformation  of  material,  etc. 
Partial  analyses  of  some  of  these  conditions  have  been  attempted,  upon 
certain  assumptions,  but  they  are  of  doubtful  utility  unless  accompanied  by 
data  from  practical  experiments.  The  term  "impact"  is  sometimes  wrongly 
applied  to  "sudden  loading." 

For  discussion  of  pure  Impact,  see  Sec.  15.  Mechanics,  pages  303,  304. 

II.    TABLES  OF  STRENGTH  OF  MATERIALS. 

Comprising  also  Standard  Specifications, 
Treated  under  the  following  heads: 

A.  Woods,  page  490.  C.     Building  Stones,  Cements,  etc.,  page  fi07. 

B.  Metals,  page  406.  D.     Miscellaneous  Materials,  page  512. 


d  by  Google 


400      2S.^STRENGTH  AND  RESISTANCE  OF  MATERIALS. 


A.   Woods. 

1. — Compression  (End)  Tbsts  of  Timbbr. 

(From  Circular  No.  15,  U.  S.  Dep't  of  Agric. — ^Div.  of  Forestry. 

[Pounds  per  square  inch.] 


Specle& 


Num- 

High- 

Low- 

o ^ 

il 

Aver- 

II 
|S- 

ber 

est 

est 

IS 

age 

o( 

single 

single 

of  all 

til 

tests. 

test. 

test. 

tests. 
(8) 

Per 

eeiiL 

1.230 

11.900 

3.400 

8.600 

6.700 

6.900 

53 

41C 

10.60( 

2.80C 

9.500 

6.600 

7.9O0 

61 

33C 

8.50C 

4.50C 

7.60C 

4.800 

6.900 

47 

660 

11.200 

3.900 

8,70tt 

6.400 

6.500 

49 

130 

8.600 

3.200 

6.800 

4.000 

6.400 

49 

IOC 

8.200 

4,30C 

8.1O0 

4.900 

6,700 

64 

17C 

10.000 

4.40( 

8.80C 

5.600 

7.300 

66 

659 

».900 

2.90( 

8.5O0 

4.200 

6.000 

81 

87 

6.20fl 

3.2O0 

6.00( 

4.400 

5.200 

79 

41 

8.900 

4.10( 

8.  IOC 

4.200 

6.700 

38 

21{ 

12.6U(J 

M0( 

11.30C 

6.300 

8.600 

40 

216 

9.100 

3.70C 

8.60C 

6.000 

7.300 

70 

4S 

8.200 

5.900 

8.10C 

6.000 

7.100 

8« 

256 

11.500 

4.60U 

9,80C 

6.600 

7.400 

61 

67 

9.70C 

5.40C 

9.200 

5.500 

7.200 

36 

117 

11.30C 

6.80C 

9.80C 

6.900 

8,100 

62 

4( 

8.600 

6,50C 

8.300 

5.800 

7.300 

6e 

31 

9.200 

6.20C 

9,000 

6.300 

7,800 

76 

153 

11,000 

4.20G 

8.700 

5.500 

7.200 

61 

251 

10.60C 

3,70C 

9,50C 

5.100 

7.700 

61 

137 

13.70C 

5.80C 

10.900 

7.500 

9.500 

79 

75 

12.200 

6,20C 

11.60C 

8.000 

10,100 

66 

H 

10,000 

6.700 

9.60G 

7.000 

8.400 

71 

25 

11.500 

7.300 

11,200 

7,800 

9.600 

60 

72 

12.300 

6.4O0 

U.OOC 

7.100 

8.8O0 

U 

37 

10.50C 

8.80C 

10.40C 

7.300 

9.1O0 

61 

3C 

13.000 

8.701 

12,70C 

8.900 

10.900 

T2 

IS 

8.80C 

4.90C 

8.80C 

5.000 

6.500 

28 

44 

10.600 

6.20( 

lO.lOC 

6.500 

8.000 

66 

87 

9,600 

6.00( 

8.70C 

5.700 

7.200 

46 

IC 

9  8O0 

6.60C 

9.800 

6,600 

8.000 

29 

118 

8.900 

4.600 

8.500 

5.600 

7,100 

60 

Reduced  to  lb  per  cent 

moisture. 

(SeeTable2). 

Longteaf  Pine 

Cuban  Pine 

Shortleaf  Pine 

LobloUy  Pine 

Reduced  to  IZ  per  cent 
motstto'e. 

White  Pine 

Red  Pine 

Spruce  Pine 

Bald  Cypress 

White  Cedar 

Dougias  Spruce  a 

White  Oak 

Overcup  Oak 

Post  Oak 

Cow  Oak 

Red  Oak 

Texan  Oak 

Yellow  Oak 

Water  Oak 

Willow  Oak 

Spanish  Oak 

Shagbark  Hickory. ., 
Mockemut  Hickory. 

Water  Hickory 

Blttemut  Hickory... 
Nutmeg  Hickory  . . . , 

Pecan  Hickory 

Pignut  Hickory 

White  Elm 

Cedar  Elm 

White  Ash 

Green  Ash 

Sweet  Gum 


Per 
cenL 

90 
93 

90 
84 


93 

96 

95 

74 

99 

65 

81 

95 

100 

S9 

94 

9S 

100 

100 

83 

f4 

97 

f  9 

100 

100 

•; 

•5 

100 
8S 

ts 

•« 

IM 
07 


♦  Nos.  correspond  with  similar  numbers  in  Sec.  27,  Weights  and  Specific 
Gravities  of  Materials,  Table  6,  page  470;  also  in  the  five  following  tables, 
o  Actual  tests  on"dry"  material  not  reduced  for  moisture. 


d  by  Google 


TIMBER-COMPRESSION  TESTS. 


491 


2. — ^Factors  to  bb  Added  to  the  strength  factors  of  Southern  Pines 
It  15  per  cent  moisture  in  order  to  reduce  them  to  12  per  cent: 


Ko. 


Species. 


Crusb- 
Ing  end- 
wise. 


Bending— 


At 
elasUo 
limit. 


At 
rup- 
ture. 


Modulus 

of 

eUs- 

tldtjr. 


Crusb- 
ing 


grain. 


Longleaf  Pine  (Pi$nu  paltutris) 
Cuban  Pine  (Pinua  heter&phyUa) 
Sfaortteaf  Pine  (Ffnti*  ecMnaia) 

LobloUy  Pine  {Pima  today 

Reierenoe  to  TaUe 

and  name  of  Column 


Lin.  per 

aq.in. 

1.100 

800 

«00 

900 

Tab.  1. 

Col.  (8). 


Lb».  . 

sq.  in, 

1.600 

1.500 

600 

1.000 

Tab.  b. 

Col.  (8). 


perLbt, 


sq.  w. 

1,700 

1.700 

900 

1.200 

Tab.  4. 

Col.  (8). 


tq.  in, 
180.000 
70.000 
80.000 
100.000 
Tab.  5. 
Ool.  (11), 


Lb$.  per 

tq.in. 

180 

220 

60 

ISO 


3. — Compression  (End)  Tests  op  Green  Timber. 

(Above  40  per  cent  moisture;  not  reduced.) 

[Pounds  per  square  inch.] 


No. 

8peele& 

Number 
of  tests. 

Highest 
single, 
test. 

Lowest 
single 
t«st. 

Average 
ofaU 
tests. 

, 

T^nngl^^r  PJfM»   .  , 

86 

38 

8 

69 

71 

280 

34 

25 

45 

58 

39 

49 

52 

22 

18 

4 

26 

4 

5 

6 

7.300 
6.100 
4.000 
6,500 
4.700 
8.200 
3.400 
7.000 
4.900 
4.900 
6.000 
5.500 
6.100 
6.900 
7.200 
5.600 
5.500 
3.800 
6.200 
3.600 

2.800 
3.500 
3.000 
2.600 
2.800 
1.800 
2.300 
3.200 
2.800 
2.300 
3.100 
2.300 
2.500 
3.500 
4.500 
4.700 
3.700 
3.300 
4.700 
3.000 

4.300 

2 

Cuban  Pine 

4,800 

3 

Sbortleaf  Pine 

3.300 

i 

LoMoUy  Pine  . .         

4.100 

7 

Spruce  Pine 

3.900 

n 

Bald  Csrprefls       

4.200 

A 

White  Cedar 

2.900 

11 
It 

WblteOak 

Overcup  Oak 

5.300 
3.800 

14 

Cbw  Oak    

3,800 

16 

Texan  Oak 

5.200 

19 

Willow  Oak 

3.800 

70 

Spanish  Oak 

3.900 

21 

Shagbark  Hickory 

5.700 

?2 

Mockemut  Hickory 

6,100 

tn 

Water  Hickory 

6.200 

IS 

Nutmeg  Hickory, ,.,,,,-.,.,, 

4.500 

24 

Pecan  Hickory 

3.600 

27 

PiKnut  Hickory 

5.400 

32 

Sweet  Qmn 

3.300 

d  by  Google 


492       2&,— STRENGTH  AND  RESISTANCE  OF  MATERIALS. 


4. — Bbndino  Tbsts  of  Timber  at  Rupturb. 
[Potinds  per  square  inch.] 


SpecleB. 


Num- 
ber 
of 

tests. 


est 
single 
test. 


Low- 
est 

single 
test. 


s 
I: 

n 
It 


Aver- 
age 
o(aU 


(8) 


8 
&. 


Reduced  to  15  per 
cent  moisture. 
{See  TabU  2). 

LoDgieaf  Pine 

Cuban  Pine 

Shortleat  Pine 

LobloUy  Pine 


1.160 
390 
330 
650 


17,800  3.300 

17.000  2.900 

15.300  5.000 

14.800  3.900 


Reduced  to  12  per 
cent  moisture. 


5  White  Pine 

6  Red  Pine 

7  Spruce  Pine 

Bald  Csrpress 

White  Cedar 

Douglas  Spruce  a.  . 

White  Oak 

OvercupOak 

Post  Oak 

Cow  Oak 

Red  Oak 

Texan  Oak 

Yellow  Oak 

Water  Oak 

WlUowOak 

Spanish  Oak 

Shagbark  Hickory . . 
Mockemut  Hickory. 

Water  Hickory 

BIttemut  Hickory. . 

25  I  Nutmeg  Hickory  . . . 

26  Pecan  Hickory 

27  Pignut  Hickory 

28  I  White  Elm 

29  .  Cedar  Elm 

30  White  Ash 

31  Oreen  Ash 

32  Sweet  Gum 


120 

95 

170 

665 

87 

41 

218 

216 


11.100 
12.900 
16.300 
14.800 
9.100 
13.000 
20.300 
19.600 
49|  16.400 


256 

57 

117 

40 

31 

153 

267 

187 


23.000 
16.500 
19.500 
15,000 
16.000 
16,000 
17.300 
23.300 


75  20.700' 


18,000 
19.500 
16.600 
18.300 
30^25.000 
14.000 
19.200 
15.000 
16.000 
14.400 


44 

87 

10 

118 


4.600 
3.100 
3,100 
2.300 
3.500 
3.300 
5,700 
4,900 
5,100 
3.300 
5.700 
8.200 
5*100 
6,800 
3.200 
5.000 
5.700 
5.300 
5,300 
7.000 
6,700 
5.600 
Ll.lOO 
7,300 
6.600 
5.000 
5.100 
5.100 


14.200 
14.600 
12.400 
13.100 


10.100 
12.300 
13.600 
11.700 
8,400 
12.000 
18.500 
14.900 
15.300 
12.500 
15.400 
16,900 
14.600 
15.700 
13.800 
15.600 
20.300 
19.700 
17.300 
19.300 
15.600 
18.100 
24.300 
13.600, 
17.300| 
14.200 
16.000 
12.700 


8.800 
8.800 
7.000 
8.100 


5.000 
4.900 
5.800 
5.000 
4.000 
4.100 
7.600 
6.300 
7.400 
6.500 
9.100 
10.000 
5.700 
7.200 
5,400 
6.900 
9.400 
7.900 
6.400 
8.700 
8.100 
I0.8OO 
11.600 
7.300 
a  500 
6.300 
6.100 
6,000' 


I 


10.900 
11.900 
9.200 
10.10Q 


7.900 
9.100 
10.000 
7.900 
6.300 
7.900 
13,100 
11.300 
12.300 
11.500 
11.400 
13.100 
10.800 
12.400 
10.400 
12.000 
16.000 
15.200 
12.500 
15.000 
12.500 
15.S00| 
18.700 
IO.8OOI 
13.500 
10.800 
11,0001 
9.500 


Per 
cenL 

41 
46 
40 
44 


43 
28 
43 
26 
32 
22 
89 
47 
47 
82 
46 
64 
2S 
4C 
38 
40 
46 
41 
SI 
Sfi 
4fl 
Sfl 
4S 
44 
5C 
87 
SO 
88 


84 
83 
79 
84 


81 
60 

81 
69 
78 
68 
75 
81 
92 
68 
84 
86 
65 
76 
7t 
72 
84 
78 
64 
60 
88 
OS 
77 
78 
86 
77 
60 
70 


o  Actual  tests  on  "dry"  material  not  reduced  for  moisture. 


d  by  Google 


TIMBER^BENDING  TESTS.  493 


5. — Bbkdino  Tests  of  Timber  at  Relative  Elastic  Limit. 
[Pounds  per  square  inch.] 


a  Actxial  tests  on  "dry"  znaterial  not  reduced  for  moisture. 


d  by  Google 


NCE  OF  MATERIALS. 


R08S  Grain,*  and  Shearing 
TH  Grain. 
e  inch.] 


Compres- 

Staearin 

Num- 

sion 

with 

ber  of 

across 

grain  tu 

tests. 

grain. 

reduoei 

(4) 

for 
moistur 

1.210 

1.000 

70C 

400 

1.000 

70C 

,  . 

330 

900 

70C 

690 

I.OOO 

70C 

130 

700 

4O0 

100 

1.000 

SOfl 

175 

1.200 

80C 

650 

800 

50fl 

87 

700 

40fl 

41 

800 

5O0 

218 

2.200 

l.OOC 

216 

1.900 

I.OOO 

49 

3.000 

I.IOO 

256 

1.900 

900 

57 

2.300 

1.100 

117 

2.000 

900 

40 

1.800 

1.100 

30 

2.000 

1.100 

153 

1.600 

9O0 

255 

1.800 

9O0 

135 

2.700 

1.100 

75 

3.100 

1.100 

14 

2.400 

1.000 

25 

2.200 

I.OOO 

72 

2,700 

i.ioo 

37 

2.800 

1.20C 

SO 

3.200 

1.200 

18 

1.200 

800 

44 

2.100 

1.304 

87 

1.900 

1.100 

10 

1.700 

I.OOO 

118 

1.400 

800 

height  of  the  specimen, 
luced  for  moisture. 

tion  of  J.  B.  Johnson,  for  t 
ise,  aside  from  the  actual  val 
iriation  which  may  be  expects 

Timber. — For  want  of  space  tl 
it   close  relations  of  weight 
ns  may  be  shown  analytical] 

re  inch: 

y)  in  potmds  per  cu.  ft.  X 195. 
y)  in  pounds  per  cu.  ft.  X 170. 
inch  (fiber  stress): 
y)  in  poimds  per  cu.  ft.  X  300. 
y)  in  pounds  per  cu.  ft.  X  256. 
p  cubic  foot  are  to  be  used.  fS 
Specific  Gravities,  pages  470, 471 


TIMBER— TENSION,  COMPRESSION,  ETC. 


496 


7.— TiMBBR  IN  Tbnsion,  Comprbssion,  Bbaring,  Bbndino  and 

Shbas. 

Practical  Worldxig  Units  for  Columns.  Beams,  etc.* 

(See  Author's  Column  Formula,  Sec.  82,  Columns,  page  M>.) 

[Note. — Values  in  table  are  in  thousand  pounds  per  square  inch;  hence, 
multiply  by  1000  to  reduce  to  pounds  per  square  inch.    Thus  12,0— 12000.1 


7 

)r. 

Tens. 

1 

Compresrion. 

Beartog. 

Bending. 

Shear 

TbnlMr           Bafet 
Facu 

Zero 
length. 

10 

1 

1 

it 

1 
II 

11 

II 

3 
0 

1 

1 

1 

0 

(1) 

Doaglas  Spmoe  (Ore«.  and 
WsA.  *Plne-  or  "Fir"). 

Longleaf  Pine 

5 
6 

I 
5 
6 

5 
6 

6 
6 

1 
5 
6 

5 
6 

1 
5 
6 
1 
5 
6 
1 
5 
6 
1 
5 
6 
1 
5 

,6 
1 
5 
5 
1 
5 

,6 
I 
5 
8 
1 
5 
6 

5 
6 

(2) 

12.0 
2.4 
2.0 

12.0 
2.4 
2.0 

10.0 
2.0 
1.7 

10.0 
2.0 
1.7 
8.0 
1.6 
1.3 
9.0 
1.8 
1.5 
9.0 
1.8 
1.6 

10.0 
2.0 
1.7 

10.0 

?:? 

1.3 
8,0 
1.6 
1.3 
7.0 
1.4 
1.2 
6.0 
1.2 
1.0 
7.0 
1.4 
1.2 
6.0 
1.2 
1.0 
9.0 
1.8 
1.5 

(3) 

7.6 
1.5 

7.0 
1.4 

'6.6 

'«.V 
1.3 

'5.5 
1.1 

'5.5 
1.1 

'5.5 
1.1 

'7.0 
1.4 

*7.0 
1.4 

'5.6 
1.1 

6.5 
1.1 

(4) 

7.0 
1.4 

6.6 
1.3 

5.0* 
1.0 

'6.0 
1.2 

'5.0 
1.0 

'6.0 
1.0 

■5.0 
1.0 

*6.V 
1.3 

'6.6 
1.3 

'm 

1.0 

'5.0 
1.0 

(6) 

6.6 
1.1 

6.0' 
1.0 

'4.0 
0.8 

'4.6 
0.9 

'4.0 
0.8 

i.'o 

0.8 

'4.0 
0.8 

■5.0 
1.0 

'5.0 
1.0 

'4.0 
0.8 

'4.0 
0.8 

(6) 

8.0 
1.6 
1.3 
8,0 
1.6 
1.3 
6.0 
1.2 
1.0 
7.0 
1.4 
1.2 
5.5 
1.1 
0.9 
6.0 
1.2 
1.0 
6.0 
1.2 
1.0 
7.0 
1.4 
1.2 
7.0 
1.4 
1.2 
6.0 
1.2 
1.0 

(7) 
1.2 

1/4 

i.o 

2.0 
0.8 
6,8 
6.8 
6.8 
6.8 
6.7* 
6.7* 

(8) 

6.0 
1.2 
1.0 
7.0 
1.4 
1.2 
6.0 
1.2 
1.0 
6.5 
1.3 
1.1 
4.5 
0.9 
0.7 
5.0 
1.0 
0.8 
4.5 
0.9 
0.7 
6.0 
1.0 
0.8 
5.0 
1.0 
0.8 
4.0 
0.8 
0.7 
6.0 
1.0 
0.8 
4.5 
0.9 
0.7 
3,6 
0.7 
0,6 
6.0 
1.0 
0.8 
6.0 
1.0 
0.8 
6.0 
1.0 
0.8 

(9) 
1500. 
1600. 
1100, 
1400. 
1000. 
1100. 
1100. 
1400. 
1400. 
1100. 
1100. 
1000. 
1000, 
900. 
1000. 
1200. 

(10) 
0.6 

"0.6' 

Sbortfeaf  Pine 



0.4 

WUte  Oak 

'id 

WUte  Pine 

"  " 

0.4 

Red  Pine 

"iV 

Norvay  Pine 

"6  A 

Guadlan  White  Pine 
(Ottawa) 

Guttdlan  Red  Pine 
(Ootarto)  X . . . . 

"6,4 

"0.4* 

Spnwe  and  Eastern  Fir 

CUUDnla  Spmee 

"0.4' 
"0,4* 

OtfUonIa  Bedwood 

5.5 
1.1 

6.0 
1.0 

4.0 
0.8 

0.8 

0.4 

Htailoek 

5.5 
1.1 

5.0 
1.0 

4.0 
0.8 

0.6 

0.4 

"Tilte  OBdar 

5.5 
1.1 

■5.6 
1.1 

7.0 
1.4 

6.0 
1.0 

5.0 
1.0 

6.5 
1.3 

4.0 
0.8 

'4.0 
0.8 

*6.0 
1.0 

6.0 
1.2 
1.0 
6.0 
1.2 
1.0 

0.7 
6.'7' 
6.9 

0.4 

Bald  Cypress 

*0.4* 

Chotoot         .    . 

0.6' 

d  by  Google 


METALS— TENSION,  COMPRESSION,  ETC, 


497 


S-^Tbmsion,  Couprbssion,  Bbndino,  Shbaring,  btc.  of  Mbtals — Cont'd. 
[Pounds  per  square  inch.] 


MeUL 

Tension 
(Ult.) 

ElasUc 
Limit. 

Oom- 

presBloQ 

(Ult.) 

Bend- 
ing 
(Extr. 
Fiber.) 

Bbeai^ 

tag 

(Ult.) 

Mod- 
ulus of 
Elas- 
ticity. 

Bmue.  Aluminum    (See         / 

•  Chm  (meUI).    U.  B.   Ord- 

25-55 

40  000 

72-78 

75  000 

60  000 

100  000 
50  000 

100  000 
55  000 
75  000 

108  000 
66  000 
80  000 

100  000 
32  000 
25  000 
32  000 

35  000 
(55-65) 
60  000 

36  000 
45  000 
68  000 
85  000 

100  000 
20  ODD 
30  000 
50  000 

nanee,  cop.  9,  tin  I . . 
**  sune  greatij  oompres- 

10  000 

52  000 

10  000  000 

■ed.T .' '. . . . 

If MMnui^^f^  east 

30  000 
80  000 
24  000 

125  000 

loUed 

Phnsplior    

*•          wire......... 

8llooa.caiV.  3%  81 

••           ••6^**   

bardwlret 

ItMn.  cast 

rolled 

40  000 

4  500  000 

cold  roOed 

Copper  bolts 

'6' 666 

10  000 

32  666 
40  000 

<fMPt 

22  000 

30  000 

10  000  666 

pUtes 

rods  (drawn) 

wire  unannesled / 

(hard) 1 

•*    auiealed 

18  000  000 

15  000  000 

1  Ddta  metal,  cast 

'  rolled  plates  . . . . 

amaU  bars 

wire  (bard) 

(Wd,  fast 

4  000 

8  000  000 

wire  (bard) 

QM.  (5).  copper  (1)  part 

(Son  metal  (see  Bronze) 

Ino.  east  (ordinary) | 

sGray  cast 

(say) 
80  000 

15  000 

6  000 

30  000 

18  000 

i  2600' 666 

Ckmunon \ 

Staybolts 

*(*2*7-35> 
32  000 
18000+ 

20  000 

IWrouffbt  (see  Steel)  .... 



* 

*  The  phjrsical  properties  of  gun-metal  vary  greatly  with  the  method  of 
casting,  and  also  with  the  position  of  the  metal  in  the  cast.  The  tenacity 
increases  with  the  specific  gravity  and  pressure;  it  is  greater  at  the  bottom 
of  the  melt  than  at  the  top. 

t  The  relative  conductivity  of  silicon-bronze  wire  to  pure  copper  at  1.00 
varies  from  .95  for  the  soft  wire  down  to  .35  for  the  hard. 

t  Composed  of  about  60  parts  copper,  38  to  40  parts  zinc,  2  to  4  iron, 
1  to  2  tin. 

a  See  Proposed  Standard  Specifications  for  Gray  Iron  (Stings,  p.  498. 

*»  The  Am.  Soc.  for  Testing  Materials  adopted  (by  letter-ballot  on  Nov. 
15,  1904— Vol.  IV,  page  96)  the  following  tests  for  tensile  and  transverse 
itrength  of  malleaole  castmgs:  Tensile  Test.  The  tensile  strength  of  a 
standard  test  bar  (a  bar  1  in.  square  and  1 4  ins.  long,  without  chills  and 
with  ends  perfectly  free  in  the  mold)  for  castings  under  specification  shall 
not  be  less  than  40i000  lbs.  per  sq.  in. ;  and  the  elongation  measured  in  2  ins. 
duUl  be  not  less  than  2i  per  cent.  Transverse  Test.  The  transverse  strength 
of  a  standard  test  bar.  on  supports  12  ins.  apart,  pressure  being  applied  at 
center,  shall  be  not  less  than  3000  lbs.,  deflection  being  at  least  i  inch. 

If  Wrought  iron  is  now  seldom  manufactured  except  for  blacksmith  iron 
and  water  pipes.  Steel  which  often  goes  under  the  double  name  of  "Iron 
and  Steel,  in  specifications,  has  entirely  superseded  iron  for  structural 
work  because  it  is  stronger  and  more  cheaply  manufactured. 


498      2S.— STRENGTH  AND  RESISTANCE  OF  MATERIALS. 

8. — ^Tbnsion.  Comprbssion,  Bbndino,  Sbbaring,  btc.  of  Mbtals — Cont' 
[Pounds  per  square  inch.] 


Metal. 

Tension 
(Ult.) 

Elastic 
Limit. 

C3om- 

presBlon 

(Ult.) 

Bend- 

(Extr. 
Fiber.) 

Shear- 
ing 
(Ult.) 

Modffr 
lusof 
Elas- 
ticity 

Iron— Cont'd. 

Wrought  shapes 

48  000 
50  000 
52  000 
60  000 
80  000 

1  800 
3  200 

2  500 

28  000 
27  000 

46  000 
48  OOU 

44  000 
48  000 

40  000 
40  OOU 

"        bars 

28  OOd  0 

bolts 

Wire,  annealed 

15  000  0 

"      unannealed 

27  000 

26  000  0 

f-flad,  fwit 

1  000  0 

mUled 

wire 

Malleable  castings  (see  Iron) . . . 

*  Nickel 

FlatlnuQk  wire,  unannealed  .... 

53  000 
32  000 
40  000 

annealed 

Silver,  cast 

*  Alloys  with  copper  and  steel.   (See  Steel,  Nickel.) 


Gray  Iron  Casiings.-^Fropoaed  Standard  Specifications,  adopted  I 
letter-ballot  of  the  Am.  Soc.  for  Testing  Materials,  September  1,  190 
Digest: — 1.  Unless  furnace  iron  is  spedned.  all  gray  castings  are  to  1 
made  by  the  cupola  process.  2.  The  sulphur  contents  to  be  as  follo-w 
Light  castings,  not  >.08%;  medium  castings,  not  >.10%;  heavy  casting 
not  >.12%.  3.  "Light  castings  are  those  having  any  section  less  thi 
i  in.  thick;  "heavy"  castings  are  those  in  which  no  section  is  less  than  2  is 
thick;  "medium"  castings  are  those  not  included  under  light  or  heav 
4.  Traiksverse  Test.  The  minimum  breaking  strength  of  the  "Arbitrati< 
Bar"  (a  round  bar  li  ins.  dia.  and  15  ins.  long)  under  transverse  load  shi 
not  be  tmder:  Light  castings,  2500  lbs.;  medium  castings.  2900  Iba 
heavy  castings.  3300  lbs.  In  no  case  shall  the  deflection  be  under  .10  inc 
(The  loads  to  be  applied  at  middle  of  bars  resting  on  supports  12  ins.  apai 
The  deflection  at  rupture.  Two  sets  of  2  bars  each  from  each  heat;  one  s 
from  the  first,  and  the  other  set  from  the  last  iron  going  into  the  casting 
Where  the  heat  exceeds  20  tons,  an  additional  set  of  two  bars  shall  be  cai 
for  each  20  tons  or  fraction  thereof 
above  this  amount.  In  case  of  change 
of  mixture  during  the  heat,  one  set  of 
two  bars  shall  also  be  cast  for  every 
mixture  other  than  the  regular  one. 
Each  set  of  2  bars  is  to  go  into  a  single 
mold.  The  bars  shall  not  be  rum- 
bled or  otherwise  treated,  being  sim- 


ply btished  off  before  testing.)   itnsilt 
Test.    Where  specified,  this  shall  not  f 
run  less  than:  Xight  castings,   18000  ^ 


lbs.   per  sq.  in.;    medium     castings,  q- 

21000  lbs.  per  sq.  in.;  heavy  castings,  "• 

2i000  lbs.  per  sq.  in.    The  tensile  test 

shall  be  made   on  the  "Tensile  Test 

Piece*"    (3i  ins.  long  with  sectional 

diameter  1  in.  rotmd).    6.  The  quality 

of  the  iron  going  into  castings  under 

specification  shall  be  determined  by 

means  of  the  "Arbitration  Bar."  The 

tensile  test  is  not  recommended,  but   „.     .      ,,  ,,,      .. »  ^.        .       ,> 

in   case    it    is  called    for.  the    'Ten-  ^^-  2- — Mold  for  "Arbitration  Bar 

®u®ii^if®^  Piece"  turned  up  from  any  of  the  pieces  of  the  transverse  tc 

shall  be  used.    The  expense  of  the  tensile  test  shall  fall  on  the  purdiaser. 


I 

I 


k.<      'fi 


<3''> 


*  See  Fig.  3.  page  601. 


Digitized 


by  Google 


STEEL— WROUGHT,  CAST,  FORGED,  ETC. 


499 


8.—TBif8ioN.  Coia»RB8siON,  Bbndino.  Sbbarino.  etc.,  or  MSTALS—Cont'd. 
[Potmds  per  square  inch.] 


MetoL 

Tension 
(Ult.) 

Elastic 
Limit. 

Com- 

preflBlon 

(Ult.) 

Bend- 
ing 
(Extr. 
Fiber.) 

Shear- 
ing 
(Ult.) 

Modu- 
lus ot 
Elas- 
Udty. 

SiMl* 

mffl,  fmsanga,  max    , 

142  000 
85  000 
70  000 
60  000 

hftnl 

•*       "Kw^lnm 

ion 

40  000 

70  000 

70  000 

60  00030  000  000 

tforstngt 

•prlngs.  (untempered) .  { 

(65-115) 
90  000 
80  000 
120  000 
180  000 
200  000 
280  000 

3  500 
11   000 
(4-6) 
5  000 

16  ood 

(40-70) 
55  000 
40  000 
60  000 
80  000 
95  000 

*'    cmdble 

extra,  tempered . . . 

Tin,  rut  

1   800 

6  000 

4  000 

Tin  1 0,  antimony  1 

4  000  000 

anccaat { 

rolled 

iooo 

(say) 
18  000 

..r®^" 

13  000  000 

*  High  ult  tens  str  of  steel  was  employed  in  the  following  structures: 
St.  Louis  Br,  10(KM)0;  Plattsmouth  Br.  and  Niagara  Centilever,  80  000; 
Bismarck  Br..  80-90000  comp..  70-80000  tens:  Susquehanna  Br.  (B.  &  O.), 
Ky.  and  Ind.  Cantilever,  and  Van  Buren  Br.,  80000  comp,  70000  tens. 
The  Manufacturers*  Standard  (1903)  employs  three  grades:  Rivet  (48- 
58000),  Railway  Bridge  (56-66000).  Medium  (60-70000);  elastic  limit  not 
kts  than  ijult  str;  percentage  of  elongation.  1 400000 -h  ultimate  strength. 


MatcriaH  (tee  Fig.  5,  page  501). 


Tensile 

EUstlc 

Oontrao- 

OasB  of  Steel 

Strength. 

Limit. 

Elonga- 

Uonof 

boUow  forglngs  In  which 

Forging. 

Lbaper 

Lbs.  per 

tion. 

Area. 

the     physical     qualities 

Sq.  In. 

Sq.  In. 

Percent. 

Percent. 

mentioned  to  the  left  are 
guaranteed. 

Solid  or  Hollow  forelngB. 
no  diameter  or  thickness 

(1) 

95  000 

66  000 

21 

50 

.  of  section  to  exceed  3  Ins. 

Solid  forglngs  of  rectan- 

gular sections  not  exceed- 

Nlekd 

(2) 

90  000 

60  000 

22 

50 

ing  6  ins.  thick:  or  Hollow 
forglngs,     the    walls    of 

Steel 

which  do  not  exceed   6 

Ott- 

Ins.  In  thickness. 

Tmpered. 

Solid  forglngs  of  rectan- 
gular sections  not  exceed- 

(3) 

85  000 

55  000 

24 

45 

ing  10  ins.  thick,  or  Hol- 
low forglngs.  the  waUs  of 
which  do  not  exceed  10 
Ins.  In  thickness. 

[Solid  or  HoUow  forglngs. 

(1) 

80  000 

50  000 

25 

45 

no  diameter  or  thickness 
of  section  to  exceed  1 0  ins. 

Nickel 

Solid  forglngs.  no  diam- 

Steel 

(2) 

80  000 

45  000 

25 

46 

eter  to  exceed  20  Ins..  or 

^"Hwaled- 

thickness  of  secUon  1 5  Ins. 

(3) 

80  000 

45  000 

24 

(Solid    forglngs    over    20 
40    lln8.dlanv^           i 

tizedbyV^OOgle 

600       2S.— STRENGTH  AND  RESISTANCE  OF  MATERIALS. 


Class  of  Steel 
Forging. 

Tensile 
Strengtb 
Lbfl.  per 
Sq.  In. 

Elastic 
Limit. 
LbH.per 
Sq.In. 

Elonga- 
tion. 
Percent. 

Contrac-  Dimensions  of  solid  w 
tlon  of     boUow  forglngs  In  whl 
Area.       the     physical     quall^ 

Percent,   mentioned  to  the  left  i 
guaranteed. 

Carbon 
Steel 
on- 
Tempered. 

(1) 
(2) 

(3) 

90  000 
86  000 

80  000 

55  000 
60  000 

46  000 

20 
22 

23 

46 

45 

40 

Solid  or  HoUow  fondi 
no  diameter  or  thlcki 
of  seotlon  to  exceed  3 
Solid  fbrglngs  of  red 
gular  sections  not  exoe 
Ing  6  Ins.  In  thickneas 

of  which  do  not  exo 
6  ins.  in  tblclcneai. 
Solid  fCrgtngs  or  red 

Ing  10  Ins.  m  thickness 
Hollow  forglngs.  the  w 
of  which  do  not  exc 
llO Ins.  in  thickness. 

Carbon 

Steel 

Annealed. 

(1) 

(2) 
(3) 

80  000 

76  000 
70  000 

40  000 

37  600 
35  000  ^ 

22 

23 
24 

85 

36 
30 

f  Solid  or  HoUowfbrgli 
no  diam.  or  thlcknest 
section  to  exceed  10 
Solid  forglngs.  no  di 
to    exceed    20    ln«., 

r  Solid    forglngs    over 
\  Ins.  dIam. 

Digest  of  Standard  Specirications  for  Steel,  adopted    by  the    Am, 
for  Testing  Materials.   (See  Proceedings,  Vols.  1,  V,  etc.) 


i.    Stand.  Spec,  for  Structural  Steel  for  Bridges. 
ii.  Stand.  Spec,  for  Open-hearth  Boiler  Plate  and 

Rivet  Steel. 

iii.  Standard  Specifications  for  Steel  Rails, 
iv.  Standard  Specifications  for  Steel  Castings.      - 
V.  Standard  Specifications  for  Steel  Axles. 
vi.  Standard  Specifications  for  Steel  Forgings.  - 


Ref. 
Vol.  V. 

Vol.  1. 
Vol.  VI. 
Vol.  V. 
Vol.  V. 
Vol.  V. 


Adopted 
Sept.  1,  19 


Proposed. 
Sept.  1.  19 
Sept.  1.  19 
Sept.  1.  19 


i.   Structural  Steel  for  Bridges. 


1.  Stiel  shall  be  made  by  the  open-hearth  process.    2.  The  cJumical  < 
physical  properties  shall  conform  to  the  following  limits : 


Elements  Considered. 

Structural  Steel. 

Rivet  Steel. 

Steel  Casting 

PhosphorusMax.(|^^*^ 
Sulphur  Max 

0.04  per  cent. 
0.08       " 
0.05      " 

0.04  per  cent. 

0.04 

0.04       " 

0.05  per  oen 
0.08       " 
0.05 

Ult.  tensile  strength    \ 
Lbs.  per  sq.  in.          / 

Elong.:  Min.  per  cent  1 
in  8  ins.  (Fig.  3)        1 

Elong.:  Min.  per  cent  \ 
in  2  ins.  (Pig.  4)        / 

Character  of  fracture 

C:old  bend  without       \ 
fracture                       / 

Desired 
60  000 
1  500  000* 

Ult.  tens.  str. 
22 

Silky 
180  degrees  flat  t 

Desired        / 
50  000        1 
1  500  000 
Ult.  tens.  str. 

Silky         { 
180  degrees  flattl 

Not  less  tha. 
65  000 

18 

Silky  or  fine  sr 
ular 

90®ondia.«=.t 

X  the  thickn< 

(d-S*) 

•See  par.  11.    t  See  par.  12,  13  and  14.    t  See  par.  15. 


STEEL—SPECIFICA  TIONS. 


601 


The  yield  point,  as  indicated  by  the  drop  of  beam,  shall  be  recorded  in 
the  test  reports.  8.  If  the  inU  str  varies  more  than  4000  lbs.  from  that  de- 
toed,  a  re-Ust  may  be  made,  at  the  discretion  of  the  inspector,  on  the  same 
ganse.  which,  to  be  acceptable,  shall  be  within  6000  lbs.  of  the  desired 
tdtimate.  4.  Cktmieal  (mrminatious  for  percentages  of  carbon,  phos- 
phonas,  sulphur  and  managnese  to  be  made  from  test  ingot  at  time  of  pour- 
ing; cneck  analyses  from  finished  material  may  show  25  per  cent  above 
required  limits.  6.  Specimens  for  tensile  and  bending  tests  for  plaits, 
Aap€s  and  bars  shall  be  made  by  cutting  coupons  from  the  finished  product, 
which  shall  have  both  faces  rolled  and  both  edges  milled  to  the  form  shown 
by  Fig.  4:  or  with  both  edges  parallel;  or  they  may  be  turned  to  a  dia  of 
i  in.  for  a  length  of  at  least  9  ins.,  with  enlarged  ends.  6.  Rivet  rods  shall 
be  tested  as  rolled.  7.  For  pins  and  rollers,  specimens  shall  be  cut  from  the 
fiiuahed  rolled  or  forged  bars  in  such  a  manner  that  the  center  of  the  speci- 
men shall  be  1  inch  from  surface  of  bar.  Specimen  for  tensile  test  shaJl  be 
turned  to  the  form  shown  by  Fig.  6;  specimens  Jor  bending  test  shall  be 
I X  #  in.  in  section.  8.  Steel  Castings. 
The  number  of  tests  will  depend  on 
the  character  and  importance  of  the 
/~a^;r»g«  specimens  shall  be  cut  cold 
from  cou|>ons  molded  and  cast  on 
some  portion  of  one  or  more  castings  i^ 
from  each  melt  or  from  the  sink-heads,  ^ 
if  the  heads  are  of  sufficient  size. 
The  coupon  or  sink-head,  so  used, 
shall  be  annealed  with  the  casting  be- 
fore it  is  cut  off.  Test  specimens  to  be 
of  the  form  prescribed  for  pins  and 

rollers.     9.   Material    which    is  to    be     

without  annealing  or  further  treatment  shall 
be  tested  in  the  condition  in  which  it  comes 
fronx  the  rolls.  When  material  is  to  be  an- 
nealed or  otherwise  treated  before  use.  the 
specinoens  for  tensile  test,  representing  such 
material,  shall  be  cut  from  properly  annealed 
ca-  similarly  treated  short  lengths  of  the  full 
section  of  the  bar.  10.  Number  of  tests.  At 
kast  one  tensile  and  one  bending  test  shall  be 
made  &om  each  melt  of  steel  as  rolled.     In,  ^i* 

case  steel  differing  |  inch  and  more  inthick- \y^\[fy/.'.^*Piy".'^li'l^^ 

ness  is  rolled  from  one  meltj  a  test  shall  be  j •  -•    *   i 

fna^y  from 
rial   rolled 


a  irom  one  meit.  a  test  snail  be  h»tw%»y>-p. 
the  thickest  and  thinnest  mate-  L         ^w     t^ 
11.    Elongation.     For    material  l\..A  y *- 


Jen  than  A  inch  and   more  than  f  inch 
( the  '  "      '  —      • 


-^•u^ 


Vjw ?'-"W^ 

following  modifications  will  be 

aOowed  in  the  requirements  for  elongation:  Fig.  5. 

(a)  For  each  t^  in.  in  thickness  below  A  in.,  a  deduction  of  2i  from  the 

specified  percentage. 

(b)  For  each  f  in.  in  thickness  above  f  in.,  a  deduction  of  1  from  the 

specified  percentage. 
IX  Bending  tests  may  be  made  by  pressure  or  by  blows.  Plates,  shapes 
and  bars  less  than  1  in.  thick  shall  bend  as  called  for  in  par.  2.  13.  Full- 
^wed  material  for  eye-bars  and  other  steel  1  inch  thick  and  over,  tested  as 
rolled,  shall  bend  cold  180°  around  a  pin  whose  diam  is  twice  the  thickness 
of  the  bar.  without  fracture  on  outside  of  bend.  14.  Angles  }  inch  and  less 
in  thickness  shall  open  flat,  and  angles  \  inch  and  less  in  thickness  shall 
bend  shut,  cold,  tmder  blows  of  a  hammer,  without  sign  of  fracture.  This 
test  to  be  made  only  when  required  by  inspector.  16.  Rivet  steel,  when 
flicked  and  bent  around  a  bar  of  the  same  diam  as  the  rivet  rod,  shall  give 
a  gradtaal  break  and  a  fine,  silky,  uniform  fracture. 

ii.    Opbn-Hbartr  Boiler  Plate  and  Rivet  Steel. 

1.   Steel  shall  be  made  by  the  open-hearth  process.    2.  Chemical  proper^ 
ties  of  the  three  classes  shall  conform  to  the  following  limits: 

Flange  or  boiler  steel.  Fire-box  steel.  Extra  soft  steel. 
Pfaospborus  shall  /Add         0.06  per  cent,     0.04  per  cent.     0.04  per  cent. 

not  exceed      \Basic        0.04        "  0.03       "  0.04 

Sulphur  shall  not  exceed      0.05       "  0  04       "  0  04 

Manganese  0.30  to  0.60        0.30  to  0.60        0.30  to  0.50 


502      28.STRENGTH  AND  RESISTANCE  OF  MATERIALS. 

8.  Stetl  for  hoiUr  rivets  shall  be  of  the  extra  aoft  class  as  specified  in  pi 
and  4.    4.  Physical  properties  of  the  three  classes  shall  be  as  follows: 

Flange  or  boiler  steel.   Fire-box  steel.    Extra  soft  st 

Tensile  strength,  lbs.  ]  55000  to  66000  62000  to  62000  45000  to  550 

per  s().  in. 
Yield  point,  in  lbs.  per  sq 

in.  s^all  not  be  less 

than 
Elongation,  per  cent  in  8 

ins.,  shall  not  be  less 

than 


I  tens  str  \  tens  str  i  tens  str 


26  26  28 

(see  par.  6)  (see  par.  5)         (see  par.  6 


6.  Ehngcaion.  For  material  less  than  A  inch  and  more  than  f  incl' 
thickness  the  following  modifications  will  be  allowed  in  the  requiremc 
fur  elongation: 

(a)  For  each  i  in.  in  thickness  above  f  in.,  a  deduction  of  1  from 

specified  percentage. 

(b)  For  each  ^^  in.  in  thickness  below  A  in.,  a  deduction  of  2i  from 

specified  percentage. 
6.  Bending  tests.  The  three  classes  shall  conform  to  the  following  bene 
tests;  the  bendins-test  specimen  to  be  li  ins.  wide  if  possible,  and  for 
material  i  in.  in  thickness  or  less,  it  shall  be  of  the  same  thickness  as  i 
of  the  material  from  which  it  is  cut;  but  it  may  be  i  in.  thick  for  mate 
over  f  in.  thick.  (Round  rods  shall  be  tested  of  full  size  as  rolled.):  (c^  1 
specimens  cut  from  the  rolled  material  as  specified  above,  shall  be  subje< 
to  a  cold  bending  test,  and  also  to  a  quenched  bending  test.  The  cold  be 
ing  test  shall  be  made  on  the  material  in  the  condition  in  which  it  is  tc 
used;  and  prior  to  the  quenched  bending  test,  the  specimen  shall  be  hes 
to  a  light  cherry-red  as  seen  in  the  dark  and  quenched  in  water,  the  t 
perature  of  which  is  between  80  and  90°  F.  (d)  Flange  or  boiler  steel.  1 
Dox  steel  and  rivet  steel  (all  three  classes),  both  before  and  after  quenchi 
shall  bend  cold  180**  flat  on  itself  without  fracture  on  outside  of  bend.  7.  Ho 
geneity.  For  fire-box  steel  a  sample  taken  from  a  broken  tensile  test  sp 
men  shall  not  show  any  single  seam  or  cavity  more  than  i  in.  long  in  eil 
of  the  three  fractures  obtained  on  the  test  for  homogeneity  as  descri 
below  in  pvagraph  12.  8.  Test  pieces  and  testing.  The  standard 
specimen  of  8  in.  gauged  length,  chall  be  used  to  determine  the  phys 
properties  specified  in  par.  4  and  6.  The  standard  shape  of  the  test  sp 
men  for  sheared  plates  shall  be  as  shown  in  Fig.  4,  preceding,  the  piece  tc 
of  same  thickness  as  the  plate.  For  other  material  the  test  specimen  t 
be  the  same  as  for  sheared  plates,  or  it  may  be  planed  or  turned  part 
throughout  its  entire  length,  and  in  all  cases  where  possible  two  oppo 
sides  of  the  test  specimens  shall  be  the  rolled  surfaces.  Rivet  rounds  ; 
small  rolled  bars  shall  be  tested  of  full  size  as  rolled.  9.  One  tensile 
specimen  will  be  furnished  from  each  plate  as  it  is  rolled,  and  two  ten 
test  specimens  will  be  furnished  from  each  melt  of  rivet  rotmds.  In  < 
any  one  of  these  develops  flaws  or  breaks  outside  of  the  middle  third  oi 
gauged  length,  it  may  be  discarded  and  another  test  specimen  substitv 
therefor.  10.  For  material  f  in.  or  less  in  thickness  the  bending  test  specit 
shall  have  the  natural  rolled  surface  on  two  opposite  sides.  The  head 
test  specimens  cut  from  plates  shall  be  li  ins.  wide,  and  for  material  nr 
than  \  in.  thick  they  may  be  i  in.  thick'  the  sheared  edges  may  be  mi 
or  planed.  The  bending  test  specimens  lor  rivet  rounds  Miall  be  of  full 
as  rolled.  The  bending  test  may  be  made  by  pr^ure  or  by  blows.  1 1.  i 
cold  and    one  quenched   bending   specimen   will  be   furnished  from  e 

Elate  as  it  is  rolled.    Two  cold   and  two   quenched  bending  specimens 
e  furnished  from  each  melt  of  rivet  rounds.    The  homogeneity  test  for  1 
box  steel  shall  be  made  on  one  of  the  broken  tensile  test  specimens.    12.  ' 
homogeneity  test  for  fire-box  steel  is  made  as  follows:    A  portion  of 
broken  tensile  test  specimen  is  either  nicked  with  a  chisel  or  grooved  c 
machine,  transversely  about  A   in.   deep,   in   three   places  about    2 
apart.    The  first  groove  should  be  made  on  one  side,  2  ins.  from  the  sqtj 
end  of  the  specimen;   the  second.  2  ins.  from  it  on  the  opposite  side;    1 
the  third,  2  ins.  from  the  last,  and  on  the  opposite  side  from  it.    The 
specimen  is  then  put  in  a  vice,  with  the  first  groove  about  i  in.  above 
jaws,  care  being  taken  to  hold  it  firmly.     The  projecting  end  of  the 
sp^cimenis  thra  broken  off  by  means  of  a  hammer,  a  number  of  light  bl 
Deing  used,  and  the  bending  being  away  from  the  groove.    The  spedme 


STEEL-^PECIFICATWNS^RAILS,  ETC, 


503 


broken  at  the  other  two  grooves  in  the  same  way.  The  object  of  this  treat- 
ment is  to  open  and  render  visible  an^r  seams  due  to  failure  to  weld  up.  or 
to  foreign  interposed  matter,  or  cavities  due  to  p;as  bubbles  in  the  ingot. 
After  rupture,  one  side  of  each  fracture  is  examined,  a  pocket  lens  being 
Med  if  necessary,  and  the  lengths  of  seams  and  cavities  determined. 

iii.    Stbbl  Rails. 

1.  Manufactun.  (a)  The  entire  process  of  manufacture  and  testing 
shall  be  in  accordance  with  the  best  current  practice,  and  conform  carefully 
to  the  following  instructions:  (b)  Ingots  shall  be  kept  in  a  vertical  position 
in  the  pit  heatmg  furnaces  until  ready  to  be  rollea.  or  until  the  metal  in 
the  interior  has  time  to  soKdifv.  (c)  No  bled  ingots  shall  be  used,  (d)  Sufifi- 
dent  material  shall  be  discarded  m>m  the  top  of  in^t  to  insure  soimd  rails. 
1  Oumical  composition.  Rails  of  the  various  weights  per  yard  specified 
below  shall  conform  to  the  following  limits  in  chemical  composition: 


60  to  59 
pounds. 
Per  cent. 

60  to  69 
pounds. 
Per  cent. 

70  to  79 

pounds. 
Per  cent. 

80  to  89 
pounds. 
Per  cent. 

90  to  100 
pounds. 
Per  cent. 

Carbon 

Phosphorus,  shall    not  ex- 
ceed   

.35-.45 

.10 

.20 

.70-1.00 

.38-48. 

.10 

.20 

.70-1.00 

.40-.60 

.10 

.20 

.76-1.05 

.43-63 

.10 

.20 

.80-1.10 

.46-66 
.10 

Silicon,  shall  not  exceed 

Manganese x 

.20 
.80-1.10 

S.  One  drop  test  shall  be  made  on  a  piece  of  rail  not  less  than  4  ft.  and 
not  more  than  6  ft.  long,  selected  from  every  fifth  blow  of  steel.  The  test 
shall  be  taken  from  the  top  of  the  ingot.  The  rail  shall  be  placed  head 
upwards  on  the  supports,  and  the  various  sections  shall  be  subjected  to  the 
following  impact  tests  under  a  free  falling  weight: 

Weight  of  Rail— ^bs.  per  yard,  46     to    65;  height  of  drop,  15  ft. 
^  •  ••  66+  to    66        ^^  ••       16    '• 


66+  to  76 
76+  to  86 
86+  to  100 


17 

18 
19 


H  any  rail  break  when  subject  to  the  drop  test,  two  additional  tests 
taken  from  the  top  of  the  ingot  will  be  made  of  other  rails  from  the  same 
bkiw  of  steel,  and  if  either  of  these  latter  tests  fail,  all  the  rails  of  the  blow 
which  they  represent  will  be  rejected ,  but  if  both  of  these  additional  test 
pieces  meet  the  requirements,  all  the  rails  of  the  blow  which  they  represent 
win  be  accepted.  4.  Finishing  temperature.  The  number  of  passes  and 
speed  of  train  shall  be  so  regulated  that  on  leaving  the  rolls  at  the  final  pass 
the  temperature  of  the  rail  will  not  exceed  that  which  requires  a  shrinkage 
allowance  at  the  hot -saws,  for  a  30-ft.  rail  of  100-lb.  section,  of  6H  ins.,  and 
ft  in.  leas  for  each  6-lb.  decrease  of  section.  These  allowances  to  be  decreased 
St  the  rate  of  rht  i°-  for  each  second  of  time  elapsed  between  the  rail  leaving 
the  finishing  roUs  and  being  sawn.  No  artificial  means  of  cooling  the  rails 
shall  be  used  between  the  finishing  pass  and  the  hot -saws.  6.  The  drop 
testing  machine  shall  have  a  tup  of  2000  lbs.  weight,  the  striking  face  of 
which  shall  have  a  radius  of  not  more  than  5  ins.,  and  the  test  rail  shall  be 
plaoed  head  upwards  on  solid  supports  3  ft.  apart.  The  anvil  block  shall 
weigh  at  least  20000  lbs.,  and  the  supports  shall  be  part  of.  or  firmly  secured 
to.  the  anvil.  The  report  of  the  drop  test  shall  state  the  atmospheric  tem- 
perature at  the  time  the  test  was  made.  (The  Am.  Soc.  C.  E.  standard 
nul  section  is  recommended.     See  Sec.  30,  page  660,  and  Sec.  60,  page  1060.) 

iv.  Stbbl  Castings. 
1.  Steel  for  castings  may  be  made  by  the  open-hearth,  crucible  or 
Bessemer  process.  Castings  to  be  annealed  unless  otherwise  s{>ecified. 
2.  Ordinary  castings,  those  in  which  no  physical  requirements  are  specified, 
ihaM  not  contain  over  0.40  per  cent  of  carbon,  nor  over  0.08  per  cent  of 
phosphorus.  3.  Castings  which  are  subjected  to  physical  test  shall  not 
contain  over  0.06  per  cent  of  phosphorus,  nor  over  0.06  per  cent  of  sulphur. 


d  by  Google 


STEEI^-SPECIFICATIONS— FORCINGS,  ETC, 


50S 


5.  Drop  ttst.  One  axle  selected  from  each  melt,  when  tested  by  the  drop 
test  deflcribed  in  par.  9.  shall  stand  the  number  of  blows  at  the  height 
q)edfied  in  the  following  table  without  rupture  and  without  exceeding, 
as  the  result  of  the  first  blow,  the  deflection  given.  Any  melt  failing  to  meet 
these  requirements  will  be  rejected: 


4* 

41 

4A 

41 

41 

61 

61 

Noiober  of  blows 

5 

24 
8* 

6 

26 
8J 

5 

11 

5 
31- 

8 

5 

34 

8 

5 
43 

7 

7 

Hewht  of  drop,  feet 

43 

Defection (njax..  1st  blow),  inches 

6i 

6.  Carbon  steel  and  nickel  steel  driving  and  engine  truck  axles  shall  not  be 
subject  to  the  above  drop  test.  7.  Test  piects  and  testing.  The  standard 
tnrned  test  specimen  (Pig.  6.  page  601),  i  in.  diam.  and  2-in.  gauged 
h.  shall  be  used  to  determine  the  physical  properties  specified  in  par.  4. 


8.  For  driving  and  engine  truck  axles  one  longitudinal  test  specimen  shall 
be  cut  from  one  axle  of  each  melt.  The  center  of  this  test  specimen  shall 
be  half-way  .bet  ween  the  center  and  outside  of  the  axle.  9.  The  points  of 
supports  on  which  the  axle  rests  dtunng  tests  must  be  8  ft.  c.  to  c.\  the  tup 
msst  weigh  1640  lbs.;  the  anvil,  which  is  supported  on  springs,  must  weigh 
17600  lbs.;  it  must  be  free  to  move  in  a  vertical  direction;  the  springs  upon 
whkh  it  rests  must  be  12  in  number,  of  the  kind  described  on  drawing:  and 
the  radius  of  supports  and  of  the  striking  face  on  the  tup  in  the  direction  of 
the  axis  of  the  axle  must  be  6  ins.  When  an  axle  is  tested  it  must  be  so 
placed  in  the  machine  that  the  tup  will  strike  it  midway  between  the  ends, 
and  it  must  be  turned  over  after  the  first  and  third  blows,  and  when  required, 
after  the  fifth  blow.  To  measure  the  deflection  after  the  first  blow  prepare 
a  straight  edge  as  bng  as  the  axle,  by  reinforcing  it  on  one  side,  equally  at 
each  end.  so  that  when  it  is  laid  on  the  axle,  the  reinforced  parts  will  rest 
on  the  collars  or  ends  of  the  axle,  and  the  balance  of  the  straight  edge  not 
touch  the  axle  at  any  place.  Next  place  the  axle  in  position  for  test,  lay 
the  straight  edge  on  it.  and  measure  the  distance  from  the  straight  edge  to 
the  axle  at  the  middle  point  of  the  latter.  Then  after  the  first  blow,  place 
the  straight  edge  on  the  now  bent  axle  in  the  same  manner  as  before,  and 
measure  the  distance  from  it  to  that  side  of  the  axle  next  to  the  straight 
edge  at  the  point  farthest  away  from  the  latter.  The  difference  between 
the  two  meastirements  is  the  deflection.  The  report  of  the  drop  test  shall 
state  the  atmospheric  temperature  at  the  time  the  tests  were  made. 


vi.    Stbbl  Poroinos. 

1.  Steel  forgings  may  be  made  by  the  open-hearth,  crucible  or  Bessemer 
process.  2.  Chemical  properties.  There  will  be  four  classes  of  steel  forgings 
whkh  shall  conform  to  the  following  limits  in  chemical  composition: 


Foi 
of  Soft 
or  Low 
Carbon 
Steel. 


Forgings 
ofCarbon 
Steel  not 
An- 
nealed. 


Per  cent. 


Per  cent 


Forgings 
ofCarbon 
Steel. Oil 

Tem- 
pered or 
Aneal'd. 

Per  cent. 


Loco- 
motive 
Forgings 


Per  cent 


Forgings 
of  hRckel 
Steel.  Oil 

Tem- 
pered or 
Aneal'd. 

Per  cent. 


Phosphorus  shall  not  exceed 

Sulphur  **        "        [\ 

Manganese 

NickcL 


0.10 
0.10 


0.06 
0.06 


0.04 
0.04 


0.06 
0.05 
0.60 


0.04 
0.04 


by'Googu 


,  to  4. 


Digitized 


by  Google 


28 


22 

23 
24 


25      ^ 

25    ^ 
i4     4 


STEEL  FORCINGS.    BRICK,    CEMENT, 


507 


«p*<-w~»««  shall  be  taken  from  a  prolongation  of  the  same  diameter  or  section 
as  that  of  the  foising  back  of  the  large  end  or  collar.  In  the  case  of  hollow 
ibafting,  either  forged  or  bored,  the  specimen  shall  be  taken  within  the 
fimshed  section  prolonged,  half-way  between  the  inner  and  outer  surface  of 
the  wall  of  the  forging.  7.  The  specinun  for  htnding  test,  1 X  i  in.,  shall  be 
cot  as  specified  in  par.  6.  The  bending  test  may  be  made  by  pressure  or  by 
Wows. 

C.    Bidldinc  Stooes,  CemMits,  Etc. 

9. — CoMPRBSSioN,  Tension.  Bbndino,  etc.,  of  Above  Materials. 
[Pounds  per  square  inch.] 


Material. 

CompressloQ. 
(Ult.) 

Tensloii. 
(Ult.) 

Bendlnff. 
(Extr.  Fiber.) 

•BiMMom  (New  York) Use 

Bdck.  soft.  Interior 

12  000 
1  000 

10  000 
U   000 

13  000 
15  000 

6  000 

6  000 

38  000 

1200 

60 

200 

2500 

good  common 

600 

f  Faee,  bard  bUTii«d 

f  0>inm<)l.  hfxl  burned 

1  PaTlng.  5000  to  7000 

Pi^BBd^40dO  to  11000 

Vitrtfled.  tests  od  2*  cubes 

Extira  high  record. 

*High  Records  for  Compressive  Strength  of  Bluestone  (Hudson  R.)- — 
414221b6.  per  sq.  in.;  88000 lbs.  persq.  in.,  at  capacity  of  machine  without 
failing.     Test  made  on  2-in.  cube. 

t  Tests  at  Watertown  Arsenal  (1883) :  Bay  State,  mediimi  burned.  10390 
to  13709;  Pace,  hard  burned,  11060  to  16734;  Ck>mmon,  hard  bttmed.  12995 
to  22361  lbs.  per  sq.  in.  The  direction  of  pressure  was  at  right  angle  to  the 
largest  face.     (For  tests  of  Brick  Piers,  see  page  622.) 

J  A  commission  appointed  by  the  Nat'l  Brick  ManTrs*  Ass'n  (1896)  to 
study  the  best  methods  for  testing  paving  brick  concluded  that  the  "Rattler" 
t«st  was  the  most  valuable;  that  toe  absorption  and  cross-bearing  tests  were 
of  little  use;  and  the  crushing  test  was  useless.  A  standard  rattler  test  was 
formulated  as  follows:  The  rattler  barrel  is  28*  diam.X20' long;  it  is  a 
14-dded  polygon.  suppK^rted  on  trtmnions,  the  shaft  not  being  continuous 
through  tne  barrel;  it  is  built  of  cast  iron  heads  and  either  cast  or  wrought 
iron  staves  0*  wide;  the  space  between  the  staves,  for  the  escape  of  dust, 
not  to  exceed  I'  in  width;  rate  of  rotation  30  revs,  per  min.,  with  28  and  32 
as  limits;  each  test  requiring  1800  revs.,  or  00  mins.  at  standard  speed; 
number  of  brick  per  test  charge,  9  to  12;  an  official  test  to  be  the  average 
loss  in  per  cent  ot  initial  charge  from  two  separate  charges;  the  brick  to  be 
absolutely  dry  when  tested;  each  charge  to  contain,  in  addition  to  the  brick, 
225  lbs.  of  li  in.  cast  iron  cubes  at  0.88  lb.  each  when  new.  and  also  75  lbs. 
cast  iron  shot  2iX 24X 4|ins.  at  about  7  lbs.  each  (to  be  renewed  when  the 
loss  in  weight  is  10%).  The  k>sses  in  the  brick  vary  from  12  to  25%.  Mr. 
Edward  Orton,  Jr.,  (see  Proc.  Am.  Soc.  for  Test'g  Mafls,  Vol.  V,  page  296) 
considers  17%  loss  for  heavy  traffic  streets  and  20%  loss  for  light  residence 
streets  to  constitute  reasonable  limits  for  standard  tests. 


[Pounds  per  square  inch.] 


MaterlaL 


Natural,  neat 

1  oement.  3  ss 

Portland,  neat 

"        1  oesaent.  3  t 


•ii 


I...ES 


Com- 
pression, 
(Ult.) 


Tension 
(Ult.) 


Bending. 
(Extr. 
Fiber.) 


Refer- 
ence. 


1  day. 


TensUe    Strength. 

7  days.  |  28  days. 

50-1  OOl  100-200  200-300 

25-  75   75-150 

150-200(  450-550  650-650 

150-200  200-300 


412. 
413. 


d  by  Google 


CEMENT.    CONCRETE. 


609 


0*  Stom  Coner§t$  Cubis,  1:3:4  mix,  80  days. 
CompressioD  tests  on  6-inch  cubes,  by  Prof.  Edgar  Marbun  (Proc 
Am.  See  Test'g  Mat'ls,  1904),  give  mean  average  values  as  follows: 
Wet,  or  rather  medittm,  mixtures  (amount  of  water  16%  of  combined 
weight  of  cement  and  sand,  the  water  flushing  freely  to  top  during  tamp- 
ing), av.  1650  lbs.  per  sq.  in.,  with  1864  min.  and  2603  max.;  two  cubes 
mixed  "dry"  with  10%  water,  instead  of  16%.  developed  a  compressive 
•tiength.  without  cnishins.  of  2778  lbs.  per  sq.  in.,  the  limit  of  the 
testing  machine  being  100000  lbs. 

d^andiy  Trap-rock  ConcrtU  Cub»s,  1:2.8:4.0  mix. 
(Watcrtown  Arsenal  Tests.) 
These  were  wet,  or  rather  medium,  mixtures  (amount  of  water  16.2% 
of  combined  weight  of  cement  and  sand) : 

2-  8*  cubes  developed  (2630  and  2440).  av.  2535.  lbs.  per  sq.  in.  at  30dys 
2-  8*     "  *•  (3830  and  8300).  av.  8565.  lbs.     "  '       60  ^' 

2-12' cubes        "  (3360  and  3100).  av.  8230.  lbs.     "         "       30  " 

2-12*     ••  "  (3940  and  4780).  av.  4360.  lbs.     "         *'       60  " 

1-12*  cube  "  5170  lbs.     "         "       6mos 


Age.  months. . 


1.     2. 


2. 


1.      2.       6. 


Ratio  of  strength.  S'  cubes. 
12*     •'      . 


1.0    1.40 
1.0    1.35 


1.60. 


0.71 

1.74 


1.0 

1.0  1.19^0.62    0.84  1.0 


NoU  that  the  sist  of  the  cube  seems  to  be  a  function  of  the  crushing 
strength  of  concrete,  as  it  is  with  natural  stoned-granite,  limestone,  etc. 

The  elastic  limit  of  concrete  under  compression  is  about  i  to  }  (say  |) 
the  ultimate  strength. 

Concrete,  Portland.   Tension. 

(Tests  by  Prof.  W.  K.  Hatt,  1901-2.) 

Modulus  of      Elongation  Strength 
Kind        Age  in  Elasticity,  lbs.        " 
Stone.        Days.        per  sq.  in. 
1:2:4  35  2  700  000 

1:2:4  33  2  400  000 

1:2:4  28  1  400  000 

1:2:4  26  1  900  000 


No. 
1 
2 
3 

4 


Average. . . 
1:2:4 


28 


2  100  000 


at  Rupture 

lbs.  per 

1  part  in. 

sq.  m. 

11  660 

300 

8  750 

305 

4  400 

360 

7  700 

280 

7  000 

311 

910 

281 

Where 
Broken. 
At  pin. 


Body 


The  tension  specimens  were  4'  square  in  cross-section,  with  gauged 
length  of  24'.  and  30*  between  centers  of  pins,  through  heads  S'diam. 
The  concrete  was  fairly  dry  concrete  intended  to  be  plastic  after  a 
thorough  ramming.  About  5.5%  of  water  by  weight  was  added  to  the 
mortar.  Prof.  Hatt  says:  These  tension  tests  were  not  satisfactory  for 
determination,  since  the  heads  of  the  bars,  with  some  exceptions,  pulled 
off;  but  it  is  believed  that  the  strength  of  the  body  of  the  bars  did  not 
differ  greatly  from  the  loads  recorded  at  the  point  of  rupture  of  the 
heads.  They  served,  however,  very  well  for  the  determination  of  modu- 
lus of  elasticity. 

The  elastic  limit  of  concrete  imder  tension  is  very  near  the  ult.  str. 

Concrete.  Portland.    Compression.  Tension,  Bending,  and  Shearing.* 

That  some  broad  relations  exist  between  the  compressive  strength, 
tensile  strength,  modulus  of  rupture  (extreme  fiber  stress  due  to  bending) 
and  shearing  strength  of  concrete,  is  quite  probable;  but  it  is  certain 
that  no  constant  ratios  can  be  assigned.  Even  for  the  same  proportions 
of  mixture  the  above  mentioned  ratios  would  vary  with  the  consistency 
of  the  mix  and  the  age  of  the  concrete.  We  have  seen  also  that  com- 
pressive strength  per  sq.  in.  increases  with  the  size  of  the  cube  or  mass. 


*Por  Shearing  values  of  stone  and  concrete, 
VIII.,1908.— By  H.  H.  Quimby. 


see  Proc.  A.  S.  T.  M..  Vol. 


Digitized 


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510      X.^STRENGTH  AND  RESISTANCE  OF  MATERIAL 

bat  we  have  every  reason  to  believe  that  a  like  increment  woiild 
for  tension,  bending  and  shearing,  although  the  compreaaive  at 
cubes  is  influenced  greatly  by  the  shearing  reaistence  of  the 

The  following  ratios  are  approximate  only: 
Compressive  Tensile  Mod.  of  Shearii 

Strength.  Strength.  Rupture.  Streng 

1.00  0.08to0.12  

1.00  1.4tol.8  1.2to 

Coocreta,  Portland.    Modolaa  of  ElatticUy  (E)  of  concrete  increases 

richness  of  the  mixture  and  with  the  age;  it  decreases  (usual] 
stress  increases:  and  is  greater  (usually)  when  the  concrete 
compression  than  when  tmder  tension,  although  for  practical 
of  design  the  latter  distinction  is  seldom  recognized.  Som< 
authorities  assume  the  ratio  of  the  modulus  of  elasticity  of  cc 
that  of  steel  as  1:9  or  230  000  (kilograms  per  sq.  meter^,  mal 
English  units-  3  270  000  (lbs.  per  sq.  in.),  this  viidue  being  us 
calculations  of  reinforced  concrete  beams.  In  American  pra 
high  value  of  E  would  be  assigned  to  a  rich  mixture  of  concrete 
3  to  6  months.     (See  Sec.  25,  Masonry,  page  445.J 

Concrete.  Portland.  Heat  Effect.  The  coefficient  of  linear  exp 
concrete  may  be  assumed,  for  all  practical  purposes,  to  eqyx 
steel,  namelv.  .000000]  per  degree  Fahrenheit,  or  a  change  m 
.01  ft.  per  100  ft.  in  length  for  each  15  degrees  variation  in  ten 
Pahr.  To  this  fact,  the  use  of  reinforced-concrete  is  made  pot 
Heating  tests  on  concrete  prisms,  by  Prof.  Ira  H.  Woolson. 
University,  1905-6.  indicate  a  marked  decrease  in  strength  ant 
of  elasticity  after  the  specimens  had  been  subjected  to  a  temp 
750°  F..  and  a  decided  decrease  in  both  of  these  physical  chan 
after  exposure  to  1500**  F.  It  is  to  be  noted  that  broken 
concrete  stood  the  heating  effect  far  better  than  the  smooti 
gravel  concrete,  which  latter  practically  disintegrated  at  t 
temperature,  maintained  for  2  to  3  hours.  The  specimens  •< 
4'  to  7'  in  size  which  naturally  exposed,  in  the  furnace,  a  p: 
atoly  large  "surface"  to  "mass,  '  and  hence  no  direct  conclustc 
drawn  from  these  tests  as  to  the  fire-resisting  qualities  of  o 
actual  construction.  The  tests,  however,  wowed  the  inf« 
gravel  concrete  under  the  conditions  imposed. 

Concrete,  Natural.  The  compression,  tension,  modulus  of  ni| 
shearing  of  natural  (Rosendale)  cement  concrete  may  be  a: 
alxjut  50%  of  the  values  for  Portland  cement  concrete,  unl< 
ular  brands  of  known  value  are  used. 

Concrete,  Cinder. 

Watertown  Arsenal  Tests  (1903)  for  Eastern  Expanded  Metal 
(12-in.  cubes,  Lehigh  Portland  Oment.) 
Proportions.  Age,  Modulus  of  Elasticity —  ( 

Gem.  Sand.  Cinder.     Days.  At  500  to  1000  lbs.  At  uft.  str.  Ll 
38  1  786  000  1  136  000 

38  1  923  000  1  136  000 

224  1  471  000  1  087  000 

224  1  568  000  468  000 

1     :    2^    :     5 


38 

1  250  000 

893  000 

1  136  000 

1  250  000 

781  000 
1  000  000 
1  000  000 

735  000 

38 
224 
224 

34 

*  893  dob' 

694  000 

34 
220 
220 

'  *694  Obb' 
463  000 

(See  D.  Miscellaneous  Materials. J^t^lft,  page  612.) 


CONCRETE.   GRANITE.    MARBLE.   MASONRY.  611 

0. — Strength  of  Building  Stones.  Cbubnts.  Etc. — Continued. 


Material.      Color  A  Grain. 

(Ult.) 

Tension. 
(Ult.) 

Bending. 
(Extr.  Fiber.) 

OMteaad 
GUlfomla,  Penryn,          Oray;  fine. 

6  000 
6  200 

17  600 

16  000 

18  000 

15  000 

23  000 
21   000 

17  000 

19  000 
27  000 

24  000 
23  000 
13  000 

16  000 

25  000 

20  000 
13  500 

17  733 

12  000 

Rocklln,         White:  fine. 

Colorado.  Qeorgetowii«     Gray;  flue. 

OoonecUcat.  Stony  Creek. 

Pink;  line. 
Georgia.  Utbonla,           Gray;  line. 
Maine.  Fox  Uland.          Gray;  coarse. 

Waldo  County.     Gray;  fine. 
Maryland.  Port  Deposit.  Blutsb-gray. 
MsMaohuaettB.  Qutncy.  Bl.-Gr.;  coarse. 

Rockport.  Greenish. 
Mliuieeota.  E.  St.  aoud.  Oray. 
E.  St.  aoud.  Red. 
Sauk  Rapids.  Gray. 
lOnnirt.  Oranltevllle.      Red;  coarse. 
N.  Hampshire.  Concord.  White:  toe. 
Viniilnla,  Richmond.        Gray;  toe. 

(NoTi.— High  Rec- 
ords for   Compressive 
Strength  ot  Granite 
(Conn.  Val.).— 43300  and 
40840  lbs.  per  sq.  In. ;  aver- 
age of  23  tests  from  same 
quarries  gave  35000  lbs. 
persq.ln.    Tests  made  on 
nominally  2-ln.  cubes, 
prepared  by  sawing  and 
rubbing,  but  not  polish- 
ed.) 

WIseooala.  Atbelstane. 

Montello.       Rd.-Gr.:  toe. 

(Average  ot  above  Gneisses  and  Gran- 
ites)   

UnleaB  tested,  use.  for  good  stone 

1  600 

Material. 

(Ult.) 

Tension. 
(Ult.) 

Bending. 
(Extr.  Fiber.) 

Liaeatooc  (L)  and 
MarMe  (M}  (tested  In  small  cubes). 
Osllfomia.  CMton (AO 

17  000 
5  800 

13  000 
16  500 
11   600 
16  500 

22  000 
20  000 

7  500 
11   500 
25  000 

7  000 
20  000 

11  000 

12  000 

23  000 
12  000 

15  000 
10  500 

8  000 

18  000 

16  000 

14  445 
8  000 

2  500 
2  000 

1  500 

2  000 
1   500 
1   000 

Ooonectlcut.  Canaan.                     (M) 

nunols.  Lemont,           (Dolomite  L) 

Indiana.  Greensborough,                (L) 

Putnamvine.                    (L) 

Kentucky.  Bardstown,                   (L) 

Michigan,  Lime  Island.                   (L) 
Marquette.                      (L) 

Minnesota.  Frontenac  (Dolomite  L) 
SttUwater.  (Dolomite  L) 

Minourf.  Canton,                            {L) 

New  York.  Canajoharle.                 (L) 
Glens  Falls.                   (L) 
Kingston.                      (L) 

(Note.— For  Tensile 
Strengths  of  Granites  and 
Limestones,  see  table  of 
tests  In  "  Baumaterialien- 
kunde."  Aug.  1 . 1 905 :  Eng. 
News,  Oct.  12.  1905.) 

Ohio.  Marblehead.                         (L) 

Pednsylvanla.  OMMhobocken.        (L) 

Montgomery  Co..     (M) 

Vermont.  Dorset.                           (M) 

Wisconsin.  Big  Sturgeon  Bay.        (L) 

Door  County.                (L) 

(At.  of  above  Limestones  and  Marbles) 

Unless  tested,  use.  fbr  good  limestone 
Masoory.  Brickwork.  Cement  mort»r 
SmaU  Brick  Piers. 
Face  brick;  Port.  cem.  1.  sand  2 

800 

1  500 

Nat.  cem..  1  sand  2 

Ume  l.sand  3 

Com.  brick;  Port.  cem.  l.  sand  2 

Nat.  cem.  1.  sand  2 

Lime  l.sand  3 

Concrete  (see  Concrete) 
Stonework.    Squared  stone  work 
from  i  to  i  the  strength  of 

good  ashlar  In  cement. 

/^~> 

, 

bTGoogk 


51S      K.^STRENGTH  AND  RESISTANCE  OF  MATMR. 
9. — Strbnctr  of  Building  Stones,  Cbmbnts.  Etc.- 


Matarliri.            Color  A  QnOn. 

COlt.) 

TeosloD. 
(Ult.) 

QdlfornU.  Ansd  liUiid, 

Orm-gry;  fine. 

4  500 
9  600 

OolorMlo.  lUnltou.       L't  rad. 

OoonecUout.  PortUnd.  R'd>browiL 

18  000 

(NOTB 

lUMaehusetts.  Long  Meadow. 

ordsfor C 

Red;  fine. 

8  500 

Strength    o 

Mlchlsan,  Marquette.  Br.-red. 

6  000 

(Pottsdam. 

Mlnnetota,  Food  du  Lac. 

lbs.  persq.  l 

Red. 

6  500 

of  machine 

New  Jersey.  BeUevflle.  R'd-brown. 

10  000 

Ing.    Test 

New  York.  Medina.      Rd-gr*y:  fine 

II  000 

nomlnallj 

prepared  b^ 
rubbing,  bv 

Rd-br.:  line. 

8  000 

Ohio.  Bere*.                 Gray:  fine. 

9  000 

ed.) 

R'd.-br..  Died. 

12  600 
6  500 
9000 

5  000 

Unless  tested,  use.  for  good  stone 

ISO 

State 

10  000 
5  000 

S  000 

Term  Cotta 

D.   Miacelkuieoas  Mgterials. 

10. — Ultimate  Tension,  Compression,  etc,  of  Miscbu, 
Materials. 

[Pounds  per  sqtutfe  inch.] 
Canvas.    Tensile  strength:  lengthwise.  260;  crosswise.  330. 
Cotton.     Tensile  strength:    belting,  solid,  woven.   7260;    be] 

stitched.  6160. 
Flax.    Tensile  strength:  yam  fiber.  25000;  belting,  solid,  woven 

ing.  folded,  stitched,  6400. 
Glass,  Common  green.     Tension:    thin  plates,  4800;    bars  J* . 

Compression:  small  cubes.  20000:  small  cylinders,  40000.    I 

3000.  ^|od.  of  rupture  (extreme  nber)  4000.  Mod.  of  elastic 
Glass,  Flint  (best).    Tension:   thin  plates.  4200;  bars  i'diam., ! 

pression:  small  cubes,  13000;  small  cylinders,  27000. 
Glass,  Flooring.    Tension.  3000;  compression.  10000;   mod.ofrv 
Ice,  Hard.    Compression.  260. 

Leather,  Ox.    Tension.  3600.    Modulus  of  elasticity,  250000. 
Plaster  of  Paris.    Tension,  70;  compression.  700. 

III.  HEAT  EFFECT  ON  VARIOUS  SUBSTANCES. 

Qeneral  Discussion. — Substances  are  usually  classed  from 
standpoint  as  gases,  liquids  and  solids,  according  to  their  con 
natural  atmospheres  (with  regard  to  both  temperature  and  ores 

A  Gas  may  be  defined  as  a  substance  which  when  enciosei 
vessel  will  assume  the  shape  and  volume  of  the  vessel ;  a  Liquid 
the  shape  of  that  portion  ol  the  vessel  which'Corresoonds  to  the  vt 
liquid  Itself;  while  a  Solid  will  assume  neither  the  shape  nor 
of  an  arbitrary  vessel. 

All  gases  may  be  reduced  to  liquids  by  lowering  the  temper 
gas  sumciently,  and  subjecting  it  to  the  required  pressure. 

The  Critical  Point  or  Critical  Temperaturg  of  a  gas  may  b< 
that  temperature  above  which  it  cannot  be  liquefied,  no  matt< 
the  pressure  exerted  upon  it.  If  the  temperature  of  a  gas  is  aJ: 
the  critical  temperature  it  is  known  as  vaf>or,  and  pressure  alon* 
to  reduce  it  to  a  liquid.  Every  gas  has  its  critical  temperatun 
this  point  a  sudden  change  from  gas  to  liquid  is  accompanied 
change  of  volume — with  a  clear  line  of  demarcation  when  on] 
of  the  gas  is  so  transformed.  ^ 

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^NGTH  AND  RESISTANCE  OF  MATERIALS. 

-Critical  Tbiipbraturb.  Critical  Prbssurb, 
Boiling  Point  and  Prbbzing  Point. 
Gases  and  Liquids. 


Critical 
Temperature 

Critical 

Pressure 

in 

Atmosph's 

Boiling  Point 
at  Atmos. 
Pressure. 

Freezing 
Point. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fah 

+  322* 
+    37 
-140 
+  244 
+  130 
-121 
+   31 
-141 
+  146 
+  268 
+  194 
-120 
+    62 
-236 
+    36 
-   82 
-146 
-115 
+  155 
+  366 
+  233 

+  612* 
+    99 
-220 
+  471 
+  266 
-186 
+    88 
-222 
+  295 
+  614 
+  381 
-184 
+  126 
-391 
+   97 
-116 
-231 
-176 
+  311 
+  689 
+  461 

67 
68 
89 
64 
115 

+  iir 

+  243* 

+    17* 

+  6 

+   78 

-  34 
-187 

-  80 

+  172 
-    29 
-805 
-112 

-130 

-  75 
-190 

-  78 

-2C1 

-Id 

—  31 

77 
85 
94 
55 
86 

-IC 

+   60 
+    37 
-187 

+  140 
+    99 
-805 

cid. . . 

86 
20. 
73 
55 
35 
50 
79 
196 
73 

-253 

-428 

-258 

-4; 

-192 
-181 
-    10 
+  100 
+   66 

-314 
-294 
+    14 
+  212 
+  150 

-214 

-3i 

-100 
0 

-14 

+    3 

I"" 

-|c*  +  32*;  C*  =j(F*  -  32*). 


—Boiling  Points  at  Atmospheric  Prbssurr. 


;. 

Cent. 

Fahr. 

Substance. 

Cent. 

Fa> 

+  117* 
+   56 
+    78 

-  34 
+  131 
+    21 
+  182 
+  437 
+    80 
+  261 
+    80 
+    47 
+    60 
+  746 
+    48 

-  80 
+   60 

-  20 
+    37 
-187 
-253 
+  200 
+  314 

+  243* 
+  133 
+  172 

-  29 
+  268 
+    70 
+  360 
+  819 
+  176 
+  602 
+  176 
+  117 
+  140 
+  1376 
+  118 
-112 
+  140 

-  4 
+    99 
-306 
-423 
+  392 
+  597 

Mercury 

+  358* 
+   66 
+  217 
+  120 
-192 

-  92 
-181 
+  340 
+  407 
+  290 
+  137 
+  108 
+  665 
+  448 
+  310 
+  318 

-  10 
+  167 
+  100 
+  101 
+   66 
+  940 

+  «• 

Methyhc  alcohol 

Naphthalin 

+  11 
+  4' 

Nitric  acid 

+  ?4 

Nitrogen 

-31 

Nitrous  oxide 

Oxygen 

-i: 

—  25 

Phenanthrene 

Phosphate  of  phenyl . 
Phosphorus 

+  64 
+  7< 
+  51 

arbon.  . 

Propionic  acid 

Saturated  brine 

Selenium 

+  2- 
+  21 
+  11 

Sulphur 

+  8; 

idc 

Sulphuric  acid 

•*    (strong) 

Sulphurous  acid 

Turpentine  (oil) 

Water  (distilled) 

"       (sea) 

+  « 

+  64 

+ 

+  s 

+  2 
+  ? 

Wood  alcohol 

Zinc 

+  1 

+  n 

tized  by  Google 

FREEZING  AND  BOIUNG  POINTS,  ETC, 


616 


13.— Mbltino  Poimts  of  Various  Substancbs. 


Cent. 

Fahr. 

Substance. 

Cent. 

Fahr. 

Acetic  find 

+  ir 

-180 

+   63° 
-202 

Lead 

+  326«» 
+  700 

+  617« 

Alcohol 

Magnesium 

+  1292 

Aluminum 

AiniDonia. 

+  625  '+1157 

-  76  1-103 
+  600    +932 
-190  ,-310 
+  600  '+932 
+  120    +248 
+  262    +604 
+  1025  +  1877 

-  12  ,+    10 
+  910    +1670 
+33+91 
+  276    +625 

Margaric  acid 

Mercury 

+   57  '+136 
-    39    -   88 

Antimony 

Aigon 

Nitrobenzine 

+     3  1+   37 

Nitrogen 

-214  '-363 

Arsenic              ....... 

Nitroglycerin 

+     7 
+  150(J 
+   44 
+  1775 
+   60 
+  1015 
+    94 
+    39 
+  982 
+   90 

+   46 

Benzoic  acid 

Palladium 

+  2732 

Bismuth                 .    . 

Phosphorus 

+  111 

Braa. 

Platinum 

+  3227 

Bromine. 

Potassium 

+  140 

Bronze 

Potassium  sulphate . . . 
Rose's  fusible  metal. . . 
Rubidium 

+  1859 

Butter 

+  201 

Cadmiuni 

+  102 

Calcium 

at  red 

-  78 
+  1186 
+  1220 
+  1054 
-169 

-  13 
+  1045 
-258 

-  9 

heat. 
-108 
+  2075 
+  2228 
+  1929 
-272 
+      9 
+  1913 
-432 
+    16 

Silver 

+  1800 

Carbonic  acid 

Sodium 

+  194 

Cftst  iron  white  .... 

Spermaceti 

+   49  '+120 

Copper 

Stearic  acid 

+   70 
+   66 
+  1360 
+  114 
-100 
+   33 
+  229 
-   27 
+    65 
+    68 
+  1550 
+  412 

+  158 

Stearine 

+  131 

Ethylene 

Steel 

+  2462 

Formic  acid 

Sulphur 

+  237 

Gold 

Sulphurous  acid 

Tallow 

-148 

Hydrogen 

+   92 

Hyponitric  acid 

Tin •. . 

+  444 

Ice. 

0  '+   32 
+  176    +349 

Turpentine,  oil  of 

Wax 

Wood's  fusible  metal  . 

Wrought  iron 

Zinc 

-    17 

Indium 

+  149 

Iodine 

+  107 
+  1960 
+  1650 
+   83 

+  225 
+  3642 
+  2822 
+    91 

+  154 

Indium 

+  2822 

Iron,  wrouirht 

+  774 

ESd           ;:: 

Note. — Some  substances,  as  glass  and  iron,  have  no  definite  melting 
point,  passing  gradually  from  the  solid  to  the  liquid  state,  by  what  is  known 
as  vitrwus  fusion. 

Thbruodynamics — Rbpbrbncbs. 

In  Sec.  60,  Steam  and  Gas  Power,  the  following  subjects  are  defined  and 
discussed,  and  may  be  considered  somewhat  pertinent  to  the  present  matter 
in  this  Section: 


British  Thermal  Unit  (B.T.U.) 

Density. 

Entropy. 

Entropy  Dlam^rm. 

External  and  Internal  Work. 

First  Law  of  Thermodynamics. 

Heat. 

Heat  Equivalent  of  External  Work. 

Heat  Equivalent  of  Internal  Work. 

Heat  of  Combustion. 

Heat  of  the  Liquid. 

Heat  of  Vaporization. 

Heating  Power  of  Fuels. 

Uechanical  Equivalent  of  Heat. 


Mechanical  Equivalents  of  Heat 

(Table). 
Pressure  of  Saturated  Steam. 
Specific  Heat  of  the  Liquid. 
Specific  Volume. 

Specific  Volume  of  Saturated  Steam. 
Specific  Volume  of  Water. 
Steam. 

Steam  Tables. 
Thermal  Energy. 
ToUl  Heat. 
Thermal  Units. 
Thermal  Unit  Equivalents  (Table). 


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616      28.— STRENGTH  AND  RESISTANCE  OF  MATERIALS. 

Coefficient  of  Expansion.— The  coefficient  of  expansion  of  a  body  is  th 

rate  of  increase  per  deg .  of  temperattire ,  usuall  y  based  on  the  Fahrenheit  scali 

Let  us  take  a  cube  of  metal,  and  denote  the  length  of  each  edge  by  1 

when  the  temperature  is  f*.    At  the  higher  temperature  of  7*  the  length  < 

each  edge  expands  to  L+x.    Then  we  have— 

At  7^.     Atf*.    Expansion  for  r°- 1*. 
Length  of  each  edge »      L+x;      —  L.  x 

Surface  of  each  face  -    (L  +a?)»;    =L«.     2  Lx  +x* 
Volume  of  the  cube  -    (L  +«)»;    -"L».     dUx+SLx*  +x*. 
Hence  (for  one  degree),  we  have — 

(Exact.)  (Approx.) 

Coef .  of  Linear  Expansion         -  j—  x  ^  -  ~p  (^)  . 

Coef.  of  Surface  Expansion       —  roZ^  ^  — 71 —  "*  T^—t^  l"7 /  * 

Coef.  of  Volumetric  Expansion  —  j^~m  ^  ~' 71 "  T^—f*  \~l)  ' 

The  approximate  results  are  obtained  from  the  assumption  that,  as 

itself  is  so  extremely  small,  any  power  of  x  greater  than  unity  (as  sfl  ac 

*»)  would  be  practically  zero. 

It  is  thus  seen  that  the  Surface  expansion  and  the  Volumetric  expansk 

are,  respectively,  two  and  three  times  the  Linear  expansion. 

14. — COBFFICIBNTS   OP  LiNBAR  EXPANSION  OP  SoLIDS,* 

Average  Values. 


ittiiBc  oi  lemperature  ot  180*'  F=  100°  C. 


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EXPANSION  BY  HEAT,    FRICTION, 


517 


IV.  FRICTIONAL  RESISTANCE  OP  iMATERIALS. 

.  In  1881-4  General  Arthur  Morin,  of  the  French  Artillery,  conducted  a 
series  of  experiments  on  friction,  which  were  published  in  his  "Lecons  de 
Mecanique  Pratique."  The  results  of  these  experiments  have  been 
reprintcKl  extensively  in  various  works  because  of  the  care  with  which  the 
^Ests  were  conducted.  Tables  16,  16  and  17  are  reproduced  here  from 
Joieph  Bezmett's  translation  of  the  above  work.*  Table  16,  from  Rankine's 
Applied  Mechanics,  is  also  added  ip.  order  to  show  that  author's  version  of 
Morin's  tests.  Later  experiments,  notably  those  of  Beauchamp  Tower,  t 
bave  added  to  otir  knowledge  of  the  laws  oi  friction. 

The  three  ftmdamental  laws  of  friction  deduced  by  Morin,  who  experi- 
mented with  pressure  up  to  about  30  lbs.  per  sq.  in.,  are  as  follows: 

1st.  Friction  is  directly  proportional  to  the  pressure;  the  coefficient  of 
uiction  [natural  tang,  of  the  angle  of  repose]  beixig  constant  at  all  pressures. 

2nd.  The  total  friction  and  the  coefficient  of  friction  are  independent 
of  the  areas  in  contact:  the  total  pressure  remaining  the  same.  (This 
naturally  follows  from  the  1st  law.] 

3rd.  The  coefficient  of  friction  is  independent  of  the  velocity  of  one 
torfsuct  on  the  other. 

,  It  is  perhaps  well  to  suggest  here  that  Table  15  be  not  used  with  undue 
reliability,  as  any  jarring  of  the  structure,  the  conditions  of  the  atmos- 
phere, etc,  mi^ht  anect  the  tabular  results.  Table  16  would  be  safer  to 
a«  where  stability  is  desired. 

Mr.  Tower  found  in  experimenting  with  revolving  journals  at  high 
gpeeds  and  under  heavy  pressures,  that  the  coefficient  of  motion,  /,  varied 
oirectly  with  the  square  root  of  the  linear  velocity,  and  inversely  with  the 
pressure.     With  good  oil  the  value  of  /  with  revolving  journals  may  be 

ii»,m<^  o*.  f     Welocity  in  ft.  per  secT 

Msumed  at:         /"  .  .^  y, : — tt : — • 

4  X  Pres.  m  lbs.  per  sq.  m. 

*  "  Fundamental  Ideas  of  Mechanics,"  revised  and  translated  by  Joseph 
Bennett;   D.  Appleton  &  Co.,  New  York,  1860.     Published  by  permission. 
tSee  Proceeoings  of  the  Institution  of  Mechanical  Engineers.  1883. 

16. — Friction  of  Planb  Surpacbs  Which  Havb  Bbbn  Sohb  Timb 
IN  Contact. 
(Morin.) 


Kind  of  Surfaces  In 
Gontact. 


Disposition  of 
the  Fibres. 


CondiUon  of  the 
Surfaces. 


^ 


Oak  on  oak.. 

Oak  on  dm. 
Ctanon  oak. 


Aah.  pine,  beech,  sorb.  1 
onoak / 

Tuined  leather  on  oak  | 

On 
plane 
oak 

Blickearrted         sur- 
leather  or  belt  ]faoe.. 
On 
oak 
drum. 


ParaUd 

Perpendicular 

Wood  upright  on 

wood  flatwise 

Parallel 

PerpendlctUar . .... 

Paralld 

The  leather  flatwise 
The  leather  on  edge. 

Paralld 

Perpendicular 


Without  unguent. 
Rubbed  with  dry  soap 
Without  unguent. 
Moistened  with  water. 

Without  tmguent. 


Rubbed  with  dry  soap 
Without  unguent. 


Moistened  with  water. 


Without  unguent. 


0.62 
0.44 
0.54 
0.71 

0.43 
0.38 
0.69 
0.41 
0.57 

0  53 
0.61 
0.43 
0.79 


31-48 
23-45 
28-22 
35-22 

23-16 
20-48 
34-36 
22-18 
29-41 

27-65 

81-23 
23-16 
38-19 


36-30 


hvG(S^glJ-  ^^'0 


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FRICTION. 


610 


16.— Friction  of  Plans  Surtacbs  in  Motion  upon  Bach  Othbr. 
(Morin.) 


BurlBccs  In  Contact. 


Poiltion  ot  Fibres. 


State  of  Surtaceo. 


S3 


l£ 


Otkonoak. 


QmoQoak. 


Aih.  pine,  beach,  wnd 
pnr  and  aorb.  on  oak  \ 

Iron  on  oak 


Parallel 

Perpendlouiar. , 


Uprlgbt  on  Flatwise 

Parallel 

Perpendlctdar . . 
ParaUd 


Out  Iron  on  oak. 


Copper  on  oak 

Iron  on  dm 

G»t  Iron  on  dm 

Black   curried    leather] 


on  oak. 


Tinned  leather  on  oak 


Tanned  leather  on  cast  \ 
Iron  and  brass j 

Hemp  strips  or  cords  f 

upon  oak 1 

Oak  and  elm  on  castt 

Iron ] 

WU  pear  on  cast  Iron . . 

Iron  upon  Iron 

Iron  upon  cast  Iron  and 

brass 

Out   Iron    upon    oast 

iron  and  brass 

Ckst  Iron  on  east  Iron  ... 

Ion  brass 
on  cast  Iron 
on  Iron 

utk.  dm,  yoke  dm. 
vlld  pear,  cast  Iron. 
Iron.  sted.  sted  brass 
ilkUng  upon  each 
other  or  tbemsdves 

CUcarcoos    ooUte 
calc  ooUte 

HosehdJcalk  oa 

ooUte 

common  brick  on  calc. 

oolite 


Flatwise  on  edffe. . . 


Flatwise  and  on 
edge , 


on  I 


calc 


Paralld 

Perpendicular. 

ParaUd 


Without  unguent. 
Rubbed  with  dry  soap 
Without  unguent. 
Wet  with  water. 
Without  unguent. 


Wet  with  water. 
Rubbed  with  dry  soap 
Without  unguent. 
Wet  with  water. 
Rubbed  with  dry  soap 
Without  unguent. 


Wet  with  water. 
Without  unguent. 
Wet  with  water. 
Unctuous  and  wet 

with  water. 
Spread  with  oil. 
Without  unguent. 
Wet  with  water. 

Without  unguent. 


Wet  with  water. 
Without  unguent. 


Lubricated  In  the 
usual  way  with  tal- 
low, lard,  soft  coom. 
etc 

SIlKhtly  unctuous  to 

the  touch. 
Without  unguent. 


0.48 

0.1 

0.34 

0.25 

0.19 

0.43 

0.45 

0.25 

0.36tO 

0.40 

0.62 

0.26 

0.21 

0.49 

0.22 

0.19 

0.62 

0.25 

0.20 

0.27 

.30to 

.35 

0.29 
0.56 
0.36 

0.23 
0.  15 
0.52 
0.33 

0.38 

0.44 

• 

0.18t 

0.15t 

0.31 
0.20 
0.23 
0.161 

•7 

r  to 

.81 

}0.15 
0.64 
0.67 

0.65 


25-38 
9-05 
18-47 
L4-02 
?0-45 
23-16 
24-14 
14-02 
I9-48tO 
21-48 
31-48 
14-34 
11-52 
26-06 
12-24 
10-45 
31-48 
14-02 
11-19 

15-07 

16-42 
to 

19-17 
16-10 
29-16 
19-48 

12-57 

8-32 

27-28 

18-16 

20-48 

33-45 


8-32 

17-13 
11-19 
1^24 
9-06 

35" 
to 
38-40 


8-32 
82-37 
33-49 

33-01 


*  Stirfacca  worn  when  there  was  no  unguent  (ointment), 
t  The  surfaces  still  being  slightly  unctuous  (oily  or  greasy). 
X  The  surfaces  sKghtljr  unctuous. 

5  When  the  unguent  io  constantly  supplied,  and  uniformly  Jaid^n,  this 
ratio  may  be  lowered  to  0.05.  ^^^^  by  VaC^Dgie- 


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29.— PROPERTIES  AND  TABLES  OF  PLAI 
SURFACES. 

I.— GEOMETRICAL  FIGURES. 

Center  of  gravity  indicated  bv  heavy  dot. 
(Values  are  exact ) 

Notation. 
i4— area  of  figure.     /  —  i4f*  — moment  of  inertia  about  axis  X  —  X; 


V/+i4 —radius  of  gfyration  about  axis  X^X.     S—  —— section  modu 

S|«-— ;    Sj—  — .     aoryo  "  distance  from  axis  considered  to  parallel  j 

through  center  of  gravity. ;  x  —  length  of  strip  of  infinitesimal  width 
distant  y  from  neutral  axis.     All  in  inches. 


Fig.  1. — Any    figure;    neutral    axis 
X—X  through  center  of  gravity. 


/xay  /—    I  xyk 


7 


xy^y 
A 


5,-- 


yi 


X- 


ya 


^Mi^ 


Pig.  2. — Any  figure;  axis  at  base. 

A  -  fxiy       I   -  fxyMy 
Jo  Jo 

JyiA         f^d 
0  Jo 

JFT 


'  xydy 
xay 


s^± 


0-: 


a 


Fig.  S. —  Any    figure;    axisJV'- 
parallel  with  neutral  axis  A'— A*. 


/'  (about  A'-A*') 


I  +  a^A 
'  xy*dy  +  . 


-f-^ 


(I  is  for  neutral  axis  throi 
con  of  gravas  in  Fig.  1;  a  —  p 
dist  between  the  two  axes.) 


throi 


yi'hi 


ya-T 


52-  jf2 


Vis 


-  0.2a6d 


624  ^'  I 

Digitized  by  VjOOQ IC 


d  by  Google 


-^  -  0.707  d 

d*  -  di* 
12 

-  0.118  ((f  -  di») 

r    -1:;^^  -  0.289  (d 
^12 


yi  —  y2 
A  - 
/   - 

51  =  52-' 


rfi) 


^2^ 


Fig.  16. — Square;  axis  at  base. 
'         3  ^»      T 

r ;=:  =  0.677  d  Digitized  t 


5t-5,-f^-0.120«i» 

r   -6^-0.4666 
-  0.264  d 


Pig.  19. — ^Regular  hexagt 
y^  «  ^2  —  0.433d  —  b 
A  (same  as  for  18) 
/  (same  as  for  18) 

GooqIc 


f  (sa&e  as  for  19) 


-0.1(1 


d  by  Google 


538    29.'-PROPERTIES  AND  TABLES  OF  PLANE  SURFACE 


Fig.  25.— Circle. 
d 

yi  -  y»  -  ft  -  J 

5t-5s-^  -0.0962(2« 


^-^-0.25d 


Fig.  26. — Hollow  circle. 

A  -  ir(f ,«  -  f  j»)  -  0.7854  (d»  -  di«) 

7    «  ^  (r,4  _  ^,4)  «  0.0491  W*  -  dt*) 
yi    y»     

Vft*  +  f  2«      \/(i^  +  di* 
^    "  2  "■         4 


Fig.  27. — Semicircle;  axis  at  base, 
il  -  ^  -  1.6708f|« 

/   -  ^*  -  0.3827  n* 

5,-^- 0.8827 f,« 

r   -^-0.5r. 


Fig.  28.--Semicircle;    axis    through 
cen  of  grav. 

A,  I,  S  and  r  same  as  for  27. 


x-Z-V— M-x 


Ffg.  29. — Semicircle;    axis 
cen  of  grav. 

S.-I        '        5.-1 
Vi        yt 

0«  * 


Fig.  80.  —  Circular      sectoa 
throtigh  cen  of  grav. 


a       Sin  a 

yi "  I  ri 

a 

A  -  Ti^a 
[Note.  180«»  -  jc  -  8.1416.) 


«^>X| 


Fig.  81.  —  Circular      haIf-« 
axes  through  cen  of  grav 


4sin*ig  --  sin»g  cos< 

a  —  sin  a  cos  a 

yi  -fisma-yi 

sin' a 

— : ftco 

a  — smacosa 

afj  — fi(l  — cosa)  —  ae, 
i4  —  -^  (a  — sin  a  cos  a) 


yi  -  f  1 8 


Note.— For  transposed  a 
Fig.  3.  For  skeleton  figui 
Figs.  49  to  54.  For  Mensural 
Sec.  11.  page  214. 


GEOMETRICAL  FIGURES.    SKELETON  FIGURES. 


ig.  S. — Ellii>se. 

«-  semi  major  axis 
•>  semi  minor  axis 

d 
,  -  ya  -  o  =  -5- 


[  —  jtod-  -J-  « 
"     4    "    64 


0.7854  loi 
-  0.049  iMi« 


t-Ss-: 


32 
-  0.006  ivd* 


ig,  33. — Hollow  ellipse. 

and  b  "  outer  semi-axes 
and  bt  —  inner  semi-axes 

-  -^  (a>6-a»»6j) 

^^     yx    yt 


-v? 


Note— For  other  propcrtie 
the  Ellipse,  see  Sec.  11.  Mensura 
page^ 


Fig.  34. — Parabolic  half-segni 
axes  X'-X'  and  K'-  K'  pai 
through  cen  of  grav. 


Fig.  86. — Parabolic  spandril;    1 
X'-X'   and    y-y     pa2 
through  cen  of  grav. 
3i.  7. 


-Iw. 


Note.— For  other  propertic 
the  Parabola,  see  Sec.  11,  Mens 
tion,  page  237. 

2^SKELET0N  FIGURES  WITH  THIN  LINES  OF  WIDTH  t 

For  Notation,  Sbb  Pagb  624. 
Center  of  gravity  indicated  by  heavy  dot. 
'alues  are  generally  more  or  less  approx.,  depending  on  thickness  of  lii 


It 


m. 

Yt 


IIX 


J.  36. — Vertical  web  plate. 

^      Ad* 
""   12  ■"  12 

—  -i=  -  0.2894 
V12 

^alocs  exact.) 


K— -b--»i 


X *-— X 

Fig.  37.— Straight  line  about 
lei  axis. 

P< 

A 

--bt 

I 

"Ay^ 

I'  btyt* 

'  Vt  "  "' 


,n!i.l'^l;sT?>^'e'<^'@Ci6§le 


630    2^.— PROPERTIES  AND  TABLES  OF  PLANE  SURFACE 


Wff 


y\  - 


Fig.  38.— Angle.    Tee. 

i4  -  (//,  +  btt 

d^tx 

'  2  {dix  +  6/a) 
'ibh-^dt, 
^'      2{bh-^dhr 

T 

(Errors  m  vy,  y^,  I  and  r  decrease 
as  b  approaches  zero). 


I 
d 


\l 


.Y 


**-b--H 


Fig.  39. — Cross:  yj  -  yj  -  4- 

(f'/i 
^    —  -j2"  (^i°e  b  neglected) 


-VJ 


(Note  that  line  b  is  included  in  A 
and  not  in  /) . 


Fig.  40— -H-section: 


yi  -  ya  -  - 


i4  -  2rfri  +  6^ 

~6~  ^^"®  ^  neglected) 


Ih 


^X 

^yi 


Fig.  41.— Rectangular  celL 
il  -2((f/,+^/a) 


-V? 


Note. — For    squan  cell, 
'2  —  /i  —  /,  we  have, 
A  "idt 
I  "idH 

r   --7=-0.408d 
V6 


Fig.  43.— Channel. 
i4  -  2<iij  +  6/, 

^'       2(i<x  +  bSa 

2  V3  ^2dt^'hbtJ 


SKEU 


Straight 


.iT'x 


-^ 


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630    ^.—PROPERTIES  AND  TABLES  OF  PLANE  SURFACE 


Fig.  88. — Anglo.    Tee. 

A  -  rf/i  +  btt 

rf*/i^  _ 

^*  "  2  idl\  +  bta) 

2bt2±dti_. 
^*"  2{bt2+dti) 

^  (ibtt  +  dtt\ 
'    "■   12  \bt2  +  dti) 

'-^ 

(Errors  in  yi,  y^,  I  and  r  decrease 
as  b  approaches  zero) . 


Fig.  39. — Cross;  yt  —  yj  —  -j. 
/    —  -Tg-  (line  b  neglected) 


■V? 


(Note  that  line  b  is  included  in  A 
and  not  in  /) . 


t.     t. 


*-b*M^^ 


Fig.  40. — H -section;    yi  —  yj  —  — 

i4  =  2dh  +  bt2 

I    =-  -g-  (line  6  neglected) 

■A  Diait 


Fig.  41. — Rectangular  celL 

d 
yi  -  y t  -  J  -  y 

A  -2(ii<t  +  6/a) 

Note. — For    squarw   cell 
/a  —  /i  —  /,  we  have, 
A^idt 
I   "idH 

r    --~=-0.408rf 


Fig.  42. — Channel.    I-beazo 
d 

yi  -  y«  -  y  -  y 

A  -  d/i  +  26«, 


Fig.  43.— Channel. 
A  '~2dH  +  bt2 

dHj 
^*  "  2d/x  +  !?<, 

.(  dh  +  bit  \ 
^^'^  \2dt,^btJ 

J   _  ^  /  <i  .        fe<i<a      \ 
2  V3      2d/,  +  6«a/ 


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5S3    29.— PROPERTIES  AND  TABLES  OF  PLANE  SURFACE: 


a- 


% 


Pig.  Si. — Semi-circtilaLr  arc.  * 
A,  I  and  r  same  as  for  50. 

Fig.  52. — Semi-circular    arc ;      axis 
through  ccn  of  grav.* 

yi  -  fi  (l  -  j)  -  0.a6S4f, 

y,  -  ?^  -  0.«3Wr, 

A  -  xrgt  -  3.1416ri< 

I   -  UU  (|.  - 1^  -  0.2»7«f,»/ 


-V^'  - 


0.306  fi 


(Note  that  1st  can  be  obtained 
from  /so  by  method  explained  under 
Pig.  3;    using   the   mmus  sign,  as 


Pig.  58. — Circular  arc.* 

(.      sin  a\         • 

(sin  a  \ 

—^ coeaj 

A  -2f,a« 


-  riU  (a+si 


a+smacosa  — 


2sinSa\ 


(Note. — The  angle  a  may  be  ex- 
of*;  thus,  180*  —  X, 

90O  -  I-,  etc.) 


pressed  in  terms 
2 


J? 


.4\|« 


Pig.  64. — Circular  arc.* 


Pig.  H-Caniimi4d. 

(sin  a  \ 

XfTi  (1-cosa)  -xi 

A  T|  a  / 

J-  ,    /a  — sinacosar     4j 

/   -ri»/|^ ^2 

Special  Com. 
Por  axis  X'  at  base: 

/    —  -5-  (a  —  sm  a  cos  a) 

V,      sinacosa 
* — 2^r- 

Fig.  65. — Corrugated  sheet, 
ing  corrugations  to  be  c 
curves,  we  have,* 
b  -  Breadth  of  sheet  befort 
gating. 
d 

y.-2- 

/   -  A«««-0.1833(«rt 

r   -d>/S-0.3d5(f 

(Compare  this  with  49.  50, 
that  semi-circular  arcs  wou 
r  -  0.364d.) 


Vt  "-  U  sm  a  —  y2 
•Thickness  of  lines  —  /.  Digitized 


Fig.  56.— Corrugated  sheet. 

yi  -  ya  -  y.    Let 
F  —  area  top  flanges. 

—  area  bottom  flanges, 
W  —  area  of  webs.  Then 
A  -2F-I-W 

(Note. — Thp  above  valu 
holds  true  for  any  inclinatioi 
webs,  from  vertical  to  hor 
the  upper  and  lower  flanges 
equal  areas). 


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534    ^.^PROPERTIES  AND  TABLES  OF  PLANE  SURFACES. 


Fig.  65. — ^I-bcam. 

d 
yi  -  y»  -  J 

bd*-{b-tt)(d-2h)* 
^    "  12 


-VJ 


l«-V>-->! 


Fig.  66. — Channel. 
Properties  same  as  for  65. 


Fig.  68. — ^Tee;  tapered  stem. 


»6/2  + 


(d-h)  (to+U) 


yl»        2:4 

a.  (<i  -  <o)   ((i  -  /2)  (<i  + 
"*■  6A 

ya  —  d  —  yi 

/    »  ^  4.  (^  -  '2)1  <3<q_+ Ji) 
3    "^  12 

->l(yi-/2)» 

Continued  in  next  column. 


2h) 


Pig.  67.—CotUinMed, 
<?  -1  9  -  ^ 

yx  y» 


-b— >5 


=5.i 


Fig.  60. — I-beam;    uneqttal   f 
with  unequal  thicknesses. 

A  -6<2+  W-/a-<o)<i  +  ^)«o 

ya-^-yi 
'    "  3 


*<-bo-> 


Fig.  70. — I-beam;    unequal 
with  equal  thickne 


A  -  (fc  +  6tt)<2+  (d-2/,)«, 
yi-  [y  (fr-fro)+<5irf(6Q-«,) 

y2  "d-yi 


I   - 


feyiM-fcoy^ 


3  ; 

•^»      IT  oj  —  — 

yi  yt 


f    — 

Di^tized 


_  JZ 

byCjV)6gIe 


POLAR  MOMENT  OF  INERTIA-  635 

4.~R01XED  SHAPES. 

(Se«.  also.  Sections  30,  31,  32.  following.) 

In  the  following  illustrations  the  center  of  gravity  is  indicated  by  a 
heavy  dot. 

Values  are  exact  for  shapes  as  outlined.  These  shapes  do  not  show 
Ute  actual  rounded  "  fillets  "  because  the  latter  are  disregarded  in  structural 
c&lculations,  except  in  special  cases. 

The  flanges  of  I-beams  and  standard  channels  slope  at  the  rate  of  2  :  12 
on  their  inner  faces,  equivalent  to  an  angle  of  9**  28'.  The  heavier  sections 
of  I-beams,  channels  and  Z-bars  are  made  by  spreading  the  rolls,  thereby 
increasing  the  width  of  flange;  but  most  angles  are  rolled  in  '*  finishing 
KTooves,  which  maintain  a  standard  width  of  flange  for  various  thicknesses 
of  metal. 

Moment  of  inertia  (/a)  about  inclined  axis.  ^HS'Q.     T        \^Q, 

■--In  the  preceding  illustrations  (Pigs.    1-70)  we  >"'-{■ — ^       ^ 

nave  confined    our   attention    to    moments    of  /^     ^  x  dX-" 

mertia  about  the  coordinate   axes    X  —  X  and  /          J      x;    \ 

'.-y.  one  of  which  is  usually  drawn  parallel  /       ^ll^4.    \ 

'"th  a  principal  line  of  the  figtire,  and  the  other  X" r~~7^  -x.— *.     ^ 

at  right  angle  to  the  first.     It  very  often  hap-  X '"       I             / 

pens,  however,  that  we  wish  to  know  tl\e  value  ^-\                     / 

/«,  the  moment  of  inertia  about  an  .inclined  axis  <t-      \.       {         y 

nuking  an  angle  a  with  the  axis  X  —  X,  Fig.  71.  -rH^^'^^—^-^+k^ 

about  which  latter  axis  U    is  the   moment    of  3'2"q.       }       4^q. 

jnertia.    This  may  be  obtained    from   the   fol-  Y 

lowing  formula:  Fig.  71. 

/a— /x  cos*  a+/y  sin*  a—  2  K  cos  a  sin  a. (1) 

In    which     /«—  I  I yVxdy  — moment  of  inertia  about  axis  X—X; 

IxMx  <fy  — moment  of  inertia  about  axis  Y—Yx 


^-//'' 


/a -"moment  of  inertia  about  axis  a— a\ 
a— angle  between  the  axes  a— a  and  X—X^  the  functions 
of  a  to  be  considered  algebraically;  thus,  sin  a  is  +  in 
the  1st  and  2nd  quadrants,  and  —  in  the  8rd  and  4th; 
while  cos  a  is  -I-  m  the  1st  and  4th,  and  negative  in  the 
2nd  and  3rd.  Hence,  cos*  a  and  sin*  a  are  always 
positive  (+),  while  sin  a  cos  a  becomes  positive  (-f-) 
when  the  axis  a— a  lies  in  the  Ist  and  3rd  quadrants, 
and  negative  (  — )  when  it  lies  in  the  2nd  and  4th. 


-//■ 


xy  dx  (i^r  — double   integration    (summation)    of   dA 

i^dx  dy,  or  D)  multiplied  by  its  axial  distances  x  and 
y  (see  Fig.  71).     Those  portions  of  the  figure  or  surface 
considered  which  lie  in  the  1st  arid  3rd  quadrants  tend 
to  niake  K  positive  (  +  ).  while  those  portions  which 
lie  in  the  2nd  and  4th  quadrants  tend  to  make  K  nega- 
tive (-). 
In  solving  equation  (1)  we  find  the  values  of  Ix,  ly  and  K  from  the 
shape  of  the  plane  fi^^ure  ana  with  the  coordinate  axes  X  —  X  and  Y—Y 
mtersecting  at  the  origin  O.     Then  by  assuming  the  proper  value  for  the 
angle  a  we  may  solve  equation  (1)  for  la.     Values  of  /x  and  ly  for  many 
figures  arc  given  under  the  preceding  illustrations.     We  will  now  explain 
now  K  is  derived. 

VahMi  of  K  in  Equation  (1).— The  value  of  K  is 

Ixydxdy (2) 


^-/f 


"e*ring  in  mind  what  has  previously  been  said  regarding  positive  and 
*»««ative  values.  C^r\t^rs]o 

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63d    ».^PROPERTlES  AND  TABLES  OF  PLANE  SURFACES. 


Secondly,  the  preceding  formula  (2)  may  also  be  expressed: 

iC— A  0^)^ 

In    vrlucik     A  —area  of  tke  figure  or  plane  surface, 

ab—  4-  or  —  distance  from  axis  of  Y—  Y  to  cen  of  grav  c 
yB—  4-  or  —  distance  from  axis  of  X^X  to  cen  at  grave 
all  in  inches.  It  is  evident  that  when  the  cen  of  grav  lies  at  the  orip 
(Pig.  71)  the  value  of  iC  is  zero;  when  in  the  1st  or  3rd  qtiadrants.  it  ii 
and  when  in  the  2nd  and  4th,  it  is  — .  But  the  minus  sign  in  equatiox 
must  also  be  considered,  as  well  as  the  algebraic  value  of  cosa  sin< 
solving  for  la. 

Thirdly,  the  figure  may  be  cut  up  into  smaller  areas,  each  area  h 
multiplied  by  its  respective  coordinate  distances  x  and  y  to  the  cen  of  j 
of  each  area;  thtis. 


X  -  i"  i4i  «,  y,  +  ill  ac,  y,+ i48X3  y8+ 


The  four  following  examples  will  illustrate  the  methods  of  finding 
value  of  K  in  Equation  (1): — 


(1) 


"-n^-'-'i^'-niv-'TT-^- 

Or,  K^hd  •  Y  •  T  "  "I"  (*cco"d  method). 


(2)X-w(6.+|)(-d.-4) 


If,also,6i-0,  /C-- 


6»(i« 


IstQ. 


2ndO. 


(3)K-     ^     -      -2i 


(Compare  with  Fig.  72) 


3rdO. 

4 


But  if  fc=0  and  rfi— 0,  there  will  remain  for  the  2nd  x & 


6,«(i« 


quadrant,   iC— — 


(4)    K^Kx-^Kt+Ki 

~t(d-t)xtyt  +  btXO+i(d-t)(-Xi)(-'yz) 


b^t        ^  d 

— y-.andyi-ys-yi 


But^l—JTs 

K-*  (jbt-^fl)  id>-dt). 


hence 


dbyGoOgh 


Pig.  75. 


ROLLED  SHAPES. 


£37 


Probkm. — (1)  Find  the  moment  of  inertia  la,  about  the  axis  ai  — «i 
of  a  square  beam  of  cross-section  d  Xd,  ai  making 
an  Midword  angle  of  46'*  with  the  axis  X  — A; 
(2)  find  /aa  about  the  axis  a*  —  a^  making  a  dcwn- 
anrd angle  of  45**  with  the  axis  X-X. 

So&rfttm.— /x-/y-y  (Fig.  9). 


K-^  (Fig.  72). 


Then  from  equation  (1): 


(l')/ai--j  (ooe*  a+sin*  o)  —  y  cos  a' sin  a 


'2 


d* 


J  -^    (See  Fig.  14). 


"3' 

d*  d* 

(y)/a2— Y   (co8*a  +  sin'a)  —  Y  cos  a  (  —  sin  a) 

"32   '*"l2* 

Maximum  and  minfanom  values  of  la. — If  a  Z-bar,  angle  or  other  shape 
is  used  as  a  column  or  strut  it  is  essential  that  we  know  the  least  radius  of 
gyration  of  the  section,  and  this  can  be  obtained  from  the  minimum  moment 

of  inertia,  as  r 


-^- 


also  /  min  and  /  max  are  valuable  in  connection  with 

the  resisting  moments  of  beams.     The  following  formulas  give  the  value  of 
a  for  minimum  or  maximum  value  of  la: 

T«.2.-^, : «> 

Moreover,  it  can  be  stated  that  the  axis  say  at—  og  giving  /<ri  a  minimum 
value  will  be  at  right  angle  to  the  axis  say  aj—  02.  giving  /aa  a  maximum 
value.  That  is,  maximum"  and  "  mmimum  axes  intersect  at  the 
origin,  O.  at  an  angle  of  90°.  In  practice  it  is  easy  to  distinjgruish  one  from 
the  other;  thus,  in  Pig.  76,  af  at  is  the  "  minimum  "  axis,  and  a^—  a* 
the  "  maximum."  The  maxima  and  minima  axes  are  called  the  "  principal 
axes,  and  in  this  particular  case  they  happen  to  lie  at  an  angle  of  46°  with 
the  axes  of  X  ana  Y.  Figs.  80  and  81,  following,  show  positions  of  axes 
for  minimum  values  of  /  for  the  Z-bar  and  angle. 

For  a  more  complete  discussion  of  moments  of  inertia  about  inclined 
axes  see  Lanza's  *'  Applied  Mechanics  ";  also  Paper  No.  1020,  Trans.  Am. 
Soc  C.  E..  VoL  LVI.  p.  169.     See  also  Handbook  of  Cambria  Steel  Co. 


Fig.  77.— r-beam. 
A^td  +  2vim+n) 

/x-A[W»+^(^-/*)] 

^y-  AP^  W-«  +  ifi  +  j(fr«- 1*)] 

2Ix2ry 


Rad  of  gyration  r  "•\f'lf  ^ 


Y 


Fig.  78.— (Channel. 
A  -<d+(6-0  (m-w) 

Slope  5  —  t  —  ; 


-[. 


2(6-0 
,  ht* ,  s(b-t)Hb+2t)-\ 


xt   -i6«n-l-'-^-l- 


2  3 


^'-•P^^tittT^Sogle 


i-rOi|--i4«,« 


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ROLLED  SHAPES.    RECTANGLES. 


639 


5^*  MOMENTS  OP  INERTIA  (1)  OP  ^  RECTANGLES. 


Depth 

».- 

-Width  off  Rttctaogto  In  InclMf. 

I&ehes. 
i 

i 

ft 

* 

ft 

i 

ft 

t 

2 
3 

4 

.17 
.66 

1.88 

.21 
.70 
1.67 

.25 

.84 

2.00 

.29 

.98 

2.83 

.33 
1.13 
2.67 

.38 
1.27 
8.00 

.43 
1.41 
3.33 

S 
1 

7 
8 
9 

2.60 
4.50 
7.16 
10.67 
15.19 

8.26 
5.63 
8.93 
18.33 
18.98 

3.91 
6.75 
10.72 
16.00 
22.78 

4.66 

7.88 
12.51 
18.67 
26.58 

6.21 
9.00 
14.29 
21.33 
80.38 

5.86 
10.13 
16.08 
24.00 
84.17 

6.51 
11.25 
17.86 
26.67 
37.97 

10 
11 
12 
13 
14 

20.83 
27.73 
36.00 
45.77 
57.17 

26.04 
34.66 
45.00 
67.21 
71.46 

81.25 
41.59 
54.00 
68.66 
85.75 

36.46 
48.53 
63.00 
80.10 
100.04 

41.67 
56.46 
72.00 
91.54 
114.33 

46.87 
62.39 
81.00 
102.98 
128.63 

62.08 
69.32 
90.00 
114.43 
142.92 

15 
1< 
17 
18 
19 

70.81 
85.83 
108.35 
121.50 
142.90 

87.89 
106.67 
127.94 
151.88 
178.62 

106.47 
128.00 
153.53 
182.25 
214.34 

123.05 
149.33 
179.12 
212.63 
250.07 

140.63 
170.67 
204.71 
243.00 
285.79 

158.20 
192.00 
230.30 
273.38 
321.52 

176.78 
213.83 
255.89 
303.75 
357.24 

20 
21 
23 

n 

24 

166.67 
192.94 
221.83 
253.48 
288.00 

208.33 
241.17 
277.29 
316.85 
360.00 

250.00 
289.41 
332.75 
380.22 
432.00 

291.67 
337.64 
388.21 
443.59 
504.00 

833.33 
385.88 
443.67 
506.96 
576.00 

375.00 
434. 11 
499.13 
570.33 
648.00 

416.67 
482.34 
554.58 
633.70 
720.00 

25 
26 

27 
26 
29 

325.52 
366.17 
410.06 
457.33 
508.10 

406.90 
457.71 
512.58 
571.67 
635.13 

488.28 
549.25 
615.09 
686.00 
762.16 

569.66 
640.79 
717.61 
800.33 
889.18 

651.04 
732.33 
820.13 
914.67 
1016.21 

732.42 
823.88 
922.64 
1029.00 
1143.23 

818.80 
915.42 
1025.16 
1143.33 
1270.26 

20 
32 
34 
36 
38 

562.50 
682.67 
818.83 
972.00 
1143.17 

708.13 
853.33 
1023.54 
1215.00 
1428  96 

843.75 
1024.00 
1228.25 
1458.00 
1714.75 

984.38 
1194.67 
1432.96 
1701.00 
2000.54 

1125.00 
1365.33 
1637.67 
1944.00 
2286.33 

1265.63 
1536.00 
1842.38 
2187.00 
2572.13 

1406.25 
1706.67 
2047.08 
2430.00 
2857.92 

40 

44 

46 
48 

1333.33 
1543.50 
1774.67 
2027.83 
2304.00 

1666.67 
1929.88 
2218.33 
2634.79 
2880.00 

2000.00 
2315.25 
2662.00 
3041.75 
3456.00 

2333.33 
2701.13 
3105.67 
3548.71 
4032.00 

2666.67 
3087.00 
3549.33 
4055.67 
4608.00 

3000.00 
3472.88 
3993.00 
4562.63 
5184.00 

3333.33 
3858.75 
4436.67 
6069.58 
5760.00 

W 

52 
H 
S6 
58 

2604.17 
2929.33 
3280.50 
3658.67 
4064.83 

3255.21 
8661.67 
4100.63 
4573.33 
6081.04 

3906.25 
4894.00 
4920.75 
5488.00 
6097.25 

4567.29 
5126.33 
5740.88 
6403.67 
7113.46 

5208.33 
5858.67 
6561.00 
7317.33 
8129.67 

5859.38 
6591.00 
7381.13 
8232.00 
9145.87 

6510.42 
7323.33 
8201.25 
9146.67 
10162.08 

10 

4500.00 

5625. OU 

6760.00 

7875.00 

9000.00 

10125.00 

11250.00 

*/-^.      Section  modulus    S-^-|W>. 

Resistitig  moment  Af'-  —  -  "^  -/5- 1  fb<P,  In  which 

/—the  value  in  above  table: 

/-the  outer  fiber  stress  in  beam,  in  lb«.  per  sq.  m.;     ^^  , 

Af  *  -  moment  in  inch-lbs. ;    M'  -  moment  in  it.-lbs.  (i^ij  JjjI^i^Q  [q 


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30.— PROPERTIES  AND  TABLES  OF  STEEL 
SHAPES. 

List  op  Tables  in  This  Section  (30). 

TaMe   1.— Steel  Rods— Weights  and  Areas Pages  542-643 

"      2. -Steel  Plates— Weights  and  Areas ^  644-547 

"      3.— Properties  of  Angles  (Steel)— Unequal  Legs **  648-661 

*  4.— Properties  of  Angles  (Steel)— Equal  Legs "  682-663 

"      6.— Properties  of  I-Beams  (Steel) **  664-656 

*  6.— Properties  of  Channels  (Steel) **  666 

'      7— Properties  of  Z-Bars  (Steel) **  667 

"      8— Properties  of  T-Shapes  (Steel) **  658-650 

*•      9.— Standard  Rail  Sections— Cambria  and  A.  S.  C.  E. . .      **  560 

List  op  Relevant  Tables  in  Other  Sections. 
Section  2. 

Table   ».— Squares  of  Numbers  1  to  1800 Pages  31-48 

Section  4. 

TaWe    6.— Fractions  of  an  Inch  Reduced  to  Millimeters ^^8^  60 

"      6.— Hundredths  of  an  Inch  Reduced  to  Millimeters. ...  60 

"      7.— Millimeters  Reduced  to  Decimals  of  an  Inch **  70 

*  13.— Square  Inches  and  Square  Millimeters- Equivalents     **  80 
■    28.— Pounds  and  Kilograms— Equivalents **  86 

Section  11. 
Table  11. —Circumferences  of  Circles  for  Given   Diameters- 
Decimals Pages  224-226 

12.— Circumferences  of  Circles  for  Given  Diameters  in 

Inches **  226-229 

13.— Areas  of  Circles  for  Given  Diameters  in  Inches "  230-231 

I    19— Properties  of  Hollow  Cylinders— Dia.  to  Circum..  etc.      **  246-247 

20.— Spheres— Areas  of  Surface  for  Given  Diameters. ...      "  261 

*  21.— Spheres— Volumes  for  Given  Diameters "  262 

Section  27. 

Table  9.— Weights  and  Specific  Gravities  of  Metals Pages  478-482 

"    11— Weight  Equivalent  for  Any  Specific  Gravity "  483 

12.— Weight  of  Sheets.  Bars  ana  Wire — from  the  Specific 

Gravity "  484 

14.— Comparison  of   Various   Weights,  Capacities   and 

Volumes **  486 

Section  29. 
Table  1.— Properties  and  Tables  of  Geometrical  Figures Pages  624-529 

*  2.— Properties  and  Tables  of  Skeleton  Figures ^  629-532 

3.— Properties  and  Tables  of  Block  Shapes : -  53»-534 

"     4.— Properties  and  Tables  of  Rolled  Shapes "  635-538 

"      6.— Moments  of  Inertia  of  Rectangles **  639-640 

Section  31. 

Table  8.— Bethlehem  Girder  I-Beams Page  683 

"     9.— -Bethlehem  Special  I-Beams **  684 

Section  32. 

Table  14.— RoUed  Steel  H-Columns Page  808 

Section  50. 
Table  43.--Standard  Dimensions  of  Rails Pages  1060-1062 


641  Digitized  by  Google 


JzeM^t^Ogte^^ 


v.uuuu  I   I  iroov  I,  V  .-.piULAfij'OiDQmiit  '     w.uw  i  ^ 


STEEL  RODS— SQUARE  AND  ROUND. 


543 


1. — Stbbl  Rods — ^Weights  and  Arbas. — Concluded. 
Weights  at  489 . 6  lbs.  per  cu.  ft.,  or  2%  more  than  Iron  at  480  lbs. 


h5 

Weight 

9^ 
rToot 

Long. 

LbS: 

Weight 

9^ 

1  Foot 
Long. 
Lbs. 

Area 

of 
DBar 

in 

Square 

Ins. 

Area 

of 
OBar 

in 

Square 

Ins. 

k 

! 

Weight 

■l^ar 
IFoot 
Long. 
Lbs. 

Weight 

•  Bar 
1  Foot 
Long. 
Lbs 

Area 

of 
DBar 

in 
Square 

Area 

of 
OBar 

in 

Square 

Ins. 

( 

122.4 
125.0 
127.6 
130.2 

96.14 
96.14 
100.2 
102.2 

36.000 
36.754 
37.516 
38.285 

28.274 
28.866 
29.465 
30.060 

9 

275.4 
279.3 
283.2 
287.0 

216.3 
219.3 
222.4 
225.4 

81.000 
82.129 
83.266 
84.410 

63.617 
64.504 
65.397 
66.296 

1 

132.8 
135.5 
138.2 
140.9 

104.3 
106.4 
108.5 
110.7 

39.063 
39.848 
40.641 
41.441 

30.680 
31.296 
31.919 
32.548 

I 

290.9 
294.9 
298.9 
302.8 

228.5 
231.5 
234.7 
237.9 

85.563 
86.723 
87.891 
89.066 

67.201 
68.112 
69.029 
00.953 

1 

143.6 
146.5 
149.2 
152.1 

112.8 
114.9 
117.2 
119.4 

42.250 
43.066 
43.891 
44.723 

33.183 
33.824 
34.472 
35.125 

I 

306.8 
310.9 
315.0 
319.1 

241.0 
244.2 
247.4 
250.6 

90.250 
91.441 
92.641 
93.848 

70.882 
71.818 
72.760 
73.708 

I 

154.9 
157.8 
160.8 
163.6 

121.7 
123.9 
126.2 
128.5 

45.563 
46.410 
47.266 
48.129 

36.785 
36.450 
37.122 
37.800 

I 

323.2 
327.4 
331.6 
335.8 

253.9 
257.1 
260.4 
263.7 

95.063 
96.285 
97.516 
98.754 

74.662 
75.622 
76.589 
77.561 

7 

166.6 
169.6 
172.6 
175.6 

130.9 
133.2 
135.6 
137.9 

49.000 
49.879 
50.766 
51.660 

38.485 
39.175 
39.871 
40.574 

10 

340.0 
344.3 
348.5 
352.9 

267.0 
270.4 
273.8 
277.1 

100.00 
101.25 
102.52 
103.79 

78.540 
79.525 
80.516 
81.513 

1 

178.7 
181.8 
184.9 
188.1 

140.4 
142.8 
145.3 
147.7 

52.563 
53.473 
54.891 
55.316 

41.282 
41.997 
42.718 
43.445 

A 

367.2 
361.6 
366.0 
370.4 

280.6 
284.0 

287.4 
290.9 

105.06 
106.35 
107.64 
108.94 

82.516 
83.525 
84.541 
85.562 

1 

191.3 
191.4 
197.7 
200.9 

150.2 
162.7 
155.2 
157.8 

56.250 
57.191 
58.141 
59.008 

44.179 
44.918 
45.664 
46.415 

i 

374.9 
379.4 
383.8 
388.3 

294.4 
297.9 
301.4 
305.0 

110.25 
111.57 
112.89 
114.22 

86.590 
87.624 
88.664 
89.710 

1 

204.2 
207.6 
210.8 
214.2 

160.3 
163.0 
165.6 
168.2 

60.063 
61.035 
62.016 
68.004 

47.173 
47.937 
48.707 
49.483 

1 

392.9 
397.5 
402.1 
406.8 

308.6 
312.2 
315.8 
319.5 

115.56 
116.91 
118.27 
119.63 

90.763 
91.821 
92.886 
93.956 

8 

217.6 
221.0 
224.5 
228.0 

171.0 
173.6 
176.3 
179.0 

64.000 
65.004 
66.016 
67.035 

60.265 
51.054 
51.849 
52.649 

11 

411.4 
416.1 
420.9 
425.5 

323.1 
326.8 
330.5 
334.3 

121.00 
122.38 
123.77 
125.16 

95.033 
96.116 
97.205 
98.301 

1 

231.4 
234.9 
238.5 
242.0 

181.8 
184.5 
187.3 
190.1 

68.063 
60.098 
70.141 
71.191 

53.466 
54.260 
56.088 
55.914 

1 

430.3 
435.1 
439.9 
444.8 

337.9 
341.7 
345.5 
349.4 

126.56 
127.97 
129.39 
130.82 

99.402 
100.61 
101.62 
102.74 

1 

2456 
249.3 
252.9 
256.6 

193.0 
196.7 
198.7 
201.6 

72.250 
73.316 
74.301 
75.473 

56.745 
57.583 
58.426 
59.276 

ii 

449.6 
454  5 
459.5 
464.4 

353.1 
357.0 
360.9 
364.8 

132.25 
133.69 
135.14 
136.60 

103.87 
105.00 
106.14 
107.28 

1 

200.3 
264.1 
267.9 
271.6 

204.4 
207.4 
210.3 
213.3 

76.363 
77.660 
78.766 
79.879 

60.132 
60.994 
61.862 
62.737 

1 

469.4 
474.4 
479.6 
484.5 

388.6 
372.6 
376.6 
380.6 

138.06 
139  54 
141.02 
142.50 

106.43 
109.59 
110.75 
111.92 

9 

275.4 

216.3 

81.000 

63.617 '1 12    !    489.6  1 

384.6 

144  00 

113.10 

F  STEEL  SHAPES. 


AND  Areas. 
cubic  foot.) 


aches. 


ZH'    3H' 


lin.  ft. 


.68 

.64 

.69 

.74 

1.17 

1.28 

1.38 

1.49 

1.75 

1.91 

2.07 

2.23 

2.34 

2.56 

2.76 

2.08 

2.92 

3.19 

3.45 

3.72 

3.51 

3.83 

4.15 

4.47 

4.09 

4.46 

4.83 

6.20 

4.67 

5.10 

5.63 

6.96 

5.26 

5.74 

6.22 

6.70 

5.84 

6.38 

6.91 

7.44 

6.43 

7.02 

7.60 

8.18 

7.02 

7.65 

8.29 

8.03 

7.60 

8.29 

8.98 

9.67 

8.18 

8.93 

9.67 

10.41 

8.77 

9.57 

10.36 

11.16 

9.35 

10.20 

11.05 

11.90 

9.93 

10.84 

11.74 

12.66 

0.52 

11.48 

12.43 

13.30 

111 

12.12 

13.12 

14.13 

1.69 

12.75 

13.81 

14.87 

2.27 

13.30 

14.50 

15.62 

2.86 

14.03 

15.20 

16.36 

344 

14.66 

16.88 

17.10 

1.03 

15.30 

16.68 

17.85 

.172 
.344 
.616 
.688 

.188 
.375 
.663 
.750 

.203     .219 
.406     .438 
.609     .656 
.813     .875| 

.869 
1.03 
1.20 
1.38 

.938 
1.13 
1.31 
1.50 

1.02 
1.22 
1.42 
1.63 

1.09 
1.31 
1.63 

1.75 

1.55 
1.72 
1.89 
2.06 

1.69 
1.88 
2.06 
2.26 

1.83 
2.03 
2.23 
2.44 

1.97 
2  19 
2.41 
2.63 

2.23 
2.41 
2.68 
2.76 

2.44 
2.63 
2.81 
3.00 

2.64 
2.84 
3.05 
3.25 

2.84 
3.06 
3.28 
3.50 

2.92 
3.09 
3.27 
3.44 

3.19 
3.38 
3.56 
3.76 

3.46 
3.66 
8.86 
4.06 

3.72 
3.94 
4.16 
4.38 

3.61 

3.78 

^3.96 

Digitized  by  VjOO 

3.94 
4.13 
4.31 
4.60 

4.27 
4.47 
4.67 
4.88 

4.69 
4.81 
6.03 
6.25 

STEEL  PLATES— WEIGHTS  AND  AREAS. 


645 


2. — Stbbl  PlXtbs — Wbiohts  and  Arbas. — Continued. 
(Weights  at  489.6  lbs.  per  cubic  foot.) 


Width  of  Plate  in  inches. 

u 

4" 

4M' 

4H' 

4?r 

5' 

5H' 

5H' 

s^' 

6' 

HH' 

«H' 

W 

3  ^ 

d  by  Google 


d  by  Google 


STEEL  PLATES—WEIGHTS  AND  AREAS. 


647 


2. — Stbbl  Platbs — Wbiohts  and  Abbas. — Concluded. 
(Weights  at  489 . 0  lbs.  per  cubic  foot.) 


g 

Width  of  Plate  in  Inches. 

b 

IC 

KW' 

lOH* 

mi" 

ir 

wye  nhT  IIH' 

12* 

12H'  12H' 

12H' 

i"c 

WEIGHT  lbs.  per  lin.  ft. 

&" 

1 

HBI^^B 

H 

\ 

2.13 
4.25 

6.38 
8.30 

2.18 
4.36 
6.64 
8.71 

2.23 
4.46 
6.70 
8.92 

228 
4.57 
6.86 
9.14 

234 
4.68 
7.02 
9.34 

2.39 
4.78 
7.17 
9.57 

2.44 
4.89 
7.32 
9.78 

2.50 
4.99 
7.49 
10.00 

2.55 
6.10 
7.65 
10.20 

2.60 
6.21 
7.82 
10.42 

2.66 
5.31 
7.96 
10.63 

2.71 
5.42 
8.13 
10.84 

1 

10.62 
12.75 
14.88 
17.00 

10.80 
13.07 
15  25 
17.42 

11.16 
13.39 
15.62 
17.85 

11.42 
13.71 
15.99 
18.28 

11.68 
14.03 
16.36 
18.70 

11.96 
14.35 
16.74 
19.18 

12.22 
14  68 
17  12 
19.65 

12.49 
14  99 
17.49 
19.97 

12  75 
15.30 
17.85 
20.40 

13.01 
15.62 
18.23 
20.82 

13.28 
15.94 
18.60 
21.25 

13.65 
16.26 
18.97 
21.67 

§ 
I 

10.14 
2125 

19.61 
21.78 
23  96 
26.V4 

^.08 
22.82 
^.54 
26.78 

20.56 
22.85 
25.13 
fl7.42 

21.02 
23.38 
25.70 
28.06 

21.51 
23.91 
26.30 
28.68 

22  00 
24  44 

26.88 
29.33 

22.48 
24.97 
27.47 
29.97 

22  95 
25.50 
28.05 
30.60 

23.43 
26.03 
28.64 
51.25 

23.90 
26.56 
29.22 
31.88 

24.39 
27.09 
29.80 
32.52 

1 

27.62 
29.75 
21.88 
34.00 

28.32 
30.50 
32.67 
84.86 

^.00 
31.24 
33.48 
36.70 

29.60 
31.96 
34.28 
36.55 

30  40 
32.72 
35.06 
37.40 

31.06 
33.47 
35.86 
38.26 

31.76 
34.21 
36.66 
39.10 

32.46 
34.95 
37.46 
39.95 

33.15 
35.70 
38.25 
40.80 

33.83 
36.44 
39.06 
41.65 

34.53 
37.19 
39.84 
42.50 

35.22 
37.93 
40.64 
43.35 

1 

36.12 
38.25 
^.38 
^.50 

87.03 
39.21 
41.39 
43.56 

87.92 
40.17 
42.40 
^.63 

^.83 
41.12 
43.40 
46.60 

39.74 
42.06 
44.42 
46.76 

40.64 
43.04 
45.42 
47.82 

41.54 
44.00 
46.44 
48.88 

42.46 

44.94 
47.46 
49.94 

43.35 
45.90 
48.45 
51.00 

44.26 

46.86 
49.46 
52.06 

45.16 
47.82 
^.46 
53.12 

46.06 
48.77 
51.48 
54.19 

1 

44.64 
46.76 
48.88 
51.00 

45.76 
47.92 
50.10 
92.28 

46.86 
49.06 
51.32 
53.55 

47.97 
50.25 
52  54 
54.83 

49.06 
51.42 
53.76 

Sa.io 

50.20 
52.50 
54.99 
K7.37 

51.32 
53.76 
56.21 
^.65 

52.44 
54.93 
57.43 
59.93 

53.65 
56.10 
68.65 
^1.20 

54.67 
57.27 
59.87 
62.48 

55.78 
58.44 
61.10 
«3.75 

56.90 
59.60 
62.32 
«5.03 

AREA  of  section. 

c 

1 

.625 
1.26 
1.88 
2.50 

.641 
1.28 
1.92 
2.56 

.656 
1.31 
1.97 
2.63 

.672 
1.34 
2.02 
2.69 

.688 
1.38 
2.06 
2.76 

.70^ 
1.41 
2.11 
2.81 

.n9 

1.44 
2.16 

2.88 

.734 
1.47 
2.20 
2.94 

.750 
1.50 
2.25 
3.00 

.766 
1.53 
2  30 
3.06 

.781 
1.56 
2.34 
3.13 

.797 
1.59 
2.39 
3.19 

1 

3.13 
3.75 
4.38 
5.00 

3.20 

3.84 
4.48 
5.13 

3.28 
3.94 
4.59 
6.25 

3.36 
4.03 
4.70 
5.38 

3.44 
4.13 
4.81 
5.50 

3.62 
4.22 
4.92 
5.63 

3.59 
4.31 
5.03 
5.76 

3.67 
4.41 
5  14 
6.88 

3.75 
4.50 
6.25 
6.00 

3.83 
4.59 
5  36 
6.13 

3.91 
4.69 
5.47 
6.25 

3.98 
4.78 
5.58 
6.38 

1 

5.63 
6.25 
6.88 
7.50 

6.77 
6.41 
7.05 
7.69 

6.91 
6.56 
7.22 
7.88 

6.06 
6.72 
739 
8.06 

6.19 
6.88 
7.56 
8.25 

6.33 
7.03 
7.73 
8.44 

6.47 
7.19 
7.91 
8.63 

6.61 
7.34 
8.08 
8.81 

6.75 
7.50 
8.25 
9.00 

6.89 
7.66 
8.42 
9.19 

7.03 

7.81 
8.59 
9.38 

7.17 
7.97 
8.77 
9.56 

.i 

8.13 
8.76 
9.38 
10.00 

8.33 
8.97 
9.61 
10.25 

8.53 
9.19 
9.84 
10.60 

8.73 
9.41 
10.08 
10.76 

8.94 
9.63 
10.31 
11.00 

9.14 
9.84 
10.65 
11.26 

9.34 
10.06 
10.78 
11.50 

9.55 

10  28 

11  02 
11.76 

9.75 
1050 
11.25 
12.00 

9.95 
10.72 
11.48 
12.25 

10.16 
10.94 
11.72 
12.50 

10.36 
11.16 
11.95 
12.76 

1 

10.63 
11.25 
11.88 
12.50 

10.89 
11.53 
12.17 
12.81 

11.16 
11.81 
12.47 
13.13 

11.42 
12.09 
12.77 
13.44 

11.69 
12.38 
13.06 
13.76 

11.95 
12.66 
13.36 
14.06 

12.22 
12.94 
13.66 
14.38 

12.48 
1322 
13.95 
14.60 

12.75  13.02  |13.28 
13.60  13.78  14.06 
14.25  14.65  14.84 
15.00  15.31   15.63 

13.55 
14.34 
15.14 
15.94 

13.13  13.45 
13.75  ^4.09 
14.38  54.73 
115.60  fi5.88 

^3.78 
14.44 
16.09 
16.75 

14.11 
14.78 
16.45 
16.13 

14.44 
15.13 
15.81 
16.50 

14.77 
15.47 
16.17 
16.88 

15.09  !l5.42  115.76  '16.08  |l6.41 
15.81  ilB.ie  16.60  16.84  117.19 
16.53  16.89  17.25  il7.61  'l7.97 
17.25  117.63  llS.OO  ilS  38  118.75 

16.73 
17.63 
18.33 
19.13 

548      ^.—PROPERTIES  AND  TABLES  OF  STEEL  SHAPES. 


3. — Properties  of  Angles  (Steel). 
Unequal  Legs. 


^^ 


I: 


(Weights  at  489.6  lbs.  per 
cubic  .foot.) 


Fig.  2. 


-\^aiTicKie  special  angles. 
tr, 


,"^r: 


minimum  raaius. 


''y+U, 


ote. —  rx*  —  /x  - 


STEEL  ANGLES—UNEQUAL  LEGS, 


540 


«.-^ 


3. — ^Propbrtibs  of  Anolbs  (Stbbl). 
Unbqual  Lbos.  , 

9  — Continued. 

(WdghU  at  489.6  lbs.  per 
cubic  foot.) 


< r, 


L^npigs 


Fig.  2. 


Pig.   3. 


1 

•3 

H 

t 

Ins. 


LL 


Wt. 

W 
Lbs. 


Area 

of 
Sec. 

A 
Sq. 
Ins. 


Dist.  from 
h  of  Angle 

to  c  of  f . 

*Pig.  1 


Moment 
of 

Inertia/. 
(Pig.  1) 
about 


Radius  of  Gyration  r. 


Single  Angle, 

O^ig.l) 
about  axis 


2  Angles 
about  axis 
(Fig.  (Fig. 

2)       8) 


I 


— IB- 

■ft 


H 


17.8 
16.2 
14.5 
12.8 
U.O 

22.7 
21.3 
19.8 
18.3 
16.8 
15.2 
13.6 
12.0 
10.4 
8.7 

19.9 
18.5 
17.1 
15.7 
14.3 
12.8 
11.3 
9.8 
8.2 

18.5 
17.3 
16.0 
14.7 
13.3 
11.9 
10.6 
9.1 
7.7 

13.5 
17.3 
10.0 
14.7 


5.23 
4.75 
4.25 
3.75 
3.23 

6.67 
6.25 
5.81 
5.37 
4.92 
4.47 
4.00 
3.53 
3.05 
2.56 

5.84 
5.44 
5.03 
4.61 
4.18 
3.75 
3.31 
2.86 
2.40 

5.43 
5.06 
4.68 
4.30 
3.90 
3.50 
3.09 
2.67 
2.25 

5.43 
5.06 

4.68 
4.30 


1.62 
1.60 
1.57 
1.55 
1.53 

1.79 
1.77 
1.75 
1.72 
1.70 
1.68 
1.66 
1.63 
1.61 
1.50 

1.86 
1.84 
1.82 
1.80 
1.77 
1.75 
1.78 
1.70 
1.68 

1.66 
1.63 
1.60 
1.58 
1.56 
1.54 
1.51 
1.49 
1.47 

1.36 
1.34 
1.32 
1.29 


1.12 
1.10 
1.07 
1.05 
1.08 

1.04 
1.02 
1.00 
0.97 
0.95 
0.93 
0.91 
0.88 
0.86 
0.84 

0.86 
0.84 
0.82 
0.80 
0.77 
0.75 
0.73 
0.70 
0.68 

0.90 
0.88 
0.85 
0.83 
0.81 
0.79 
0.76 
0.74 
0.72 

l.U 
1.09 
1.07 
1.04 


7.14 
6.56 
5.96 
5.32 
4.67 

6.21 
5.89 
5.55 
5.20 
4.83 
4.45 
4.06 
8.63 
3.18 
2.72 

3.71 
3.51 
3.29 
3.06 
283 
2.58 
2.32 
2.04 
1.75 

3.60 
8.40 
8.19 
2.98 
2.75 
2.51 
2.25 
1.08 
1.73 

5.49 

5.18 
4.86 
4.52 


12.61 
11.55 
10.46 
9.32 
8.14 

15.67 
14.81 
13.92 
12.99 
12.03 
11.03 
9.99 
8.90 
7.78 
6.60 

13.98 
13.15 
12.28 
11.37 
10.43 
9.45 
8.43 
7.37 
6.26 

10.33 
9.73 
9.10 
8.44 
7.75 
7.04 
6.29 
5.50 
4.69 

7.77 
7.32 
6.86 
6.37 


1.17 

1.55 

0.84 

1.80 

1.18 

1.56 

0.85 

1.79 

1.18 

1.57 

0.85 

1.78 

1.19 

1.58 

0.85 

1.76 

1.20 

1.50 

0.86 

1.75 

0.96 

1.53 

0.75 

1.61 

0.97 

1.54 

0.75 

1.60 

0.98 

1.55 

0.75 

1.60 

0.98 

1.56 

0.75 

1.57 

0.09 

1.56 

0.75 

1.56 

1.00 

1.57 

0.75 

1.55 

1.01 

1.58 

0.75 

1.54 

1.01 

1.59 

0.76 

1.52 

1.02 

1.60 

0.76 

1.51 

1.03 

1.61 

0.76 

1.50 

0.80 

1.55 

0.64 

1.37 

0.80 

1.55 

0.64 

1.36 

0.81 

1.56 

0.64 

1.34 

0.82 

1.57 

0.64 

1.33 

0.82 

1.58 

0.65 

1.32 

0.83 

1.59 

0.65 

1.30 

0.84 

1.60 

0.66 

1.29 

0.84 

1.61 

0.65 

1.27 

0.85 

1.61 

0.66 

1.26 

0.81 

1.38 

0.64 

1.46 

0.82 

1.39 

0.64 

1.44 

0.83 

1.39 

0.64 

1.42 

0.83 

1.40 

0.64 

1.40 

0.85 

1.41 

0.64 

1.38 

0.85 

1.42 

0.65 

1.37 

0.85 

1.43 

0.65 

1.35 

0.86 

1.44 

0.66 

1.33 

0.88 

1.44 

0.66 

1.31 

1.01 

1.19 

0.72 

1.69 

1.01 

1.20 

0.72 

1.68 

1.02 

1.21 

0.72 

1.67 

1.03 

1.22 

0.72 

1.66 

2.43 
2.42 
2.41 
2.39 
2.38 

2.55 
2.54 
2.53 
2.51 
2.50 
2.49 
2.48 
2.46 
2.45 
2.44 

2.62 
2.61 
2.50 
2.58 
2.57 
2.55 
2.54 
2.52 
2.51 

2.35 
2.34 
2.32 
2.31 
2.30 
2.28 
2.27 
2.25 
2.24 

2.01 
2.00 
1.99 
1.97 


*Camegie  special  angles,    fra  —  minimum  radius. 


..-V^T^T^  ,.-^...(..|)'  ^-^^t 


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STEEL  I-BEAMS. 


555 


5 

. — Properties  op  I-Bbams  (Steel).-— Concluded. 

(WeighU  at  48».6  lbs.  per  cubic  foot.) 

\ 

|fl 

i 

1 
H 

eg 

r 

|2 

III 

I 

V 

Ij. 
Iff 

li 

r 

til 
11 

ft 

51 

30.00 

8.82   0.455 

4.805 

134.2 

7.65 

3.90 

0.93 

7.67 

35.00 

7.37 

0.310 

4.660 

122.1 

6.89 

4.07 

0.97 

7.91 

85.00 

10.29 

0.732 

4.772 

111.8 

7.31 

3.29 

0.84 

6.36 

30.00 

8.82 

0.569 

4.609 

101.9 

6.42 

3.40 

0.85 

7.58 

25.00 

7.85 

0.406 

4.446 

91.9 

6.65 

3.64 

0.88 

6.86 

21.00 

6.31 

0.290 

4.330 

84.9 

5.16 

3.67 

0.90 

7.12 

35.50 

7.50 

0.541 

4.271 

68.4 

4.75 

3.02 

0.80 

5.82 

23.00 

6.76 

0.449 

4.179 

64.5 

4.39 

3.09 

0.81 

5.96 

20.50 

6.03 

0.357 

4.087 

60.6 

4.07 

3.17 

0.82 

6.12 

18.00 

5.33 

0.270 

4.000 

56.9 

3.78 

3.27 

0.84 

6.32 

20.00 

5.88 

0.458 

3.868 

42.2 

3.24 

2.68 

0.74 

5.15 

17.50 

5.15 

0.353 

3.763 

39.2 

2.94 

2.76 

0.76 

5.31 

15.00 

4.42 

0.250 

3.660 

36.2 

2.67 

2.86 

0.78 

5.50 

17.25 

5.07 

0.475 

3.576 

26.2 

2.36 

2.27 

0.68 

4.33 

14.75 

4.34 

0.352 

3  452 

24.0 

2.09 

2.35 

0.69 

4.49 

12.35 

3.61 

0.230 

3.330 

21.8 

1.85 

2.46 

0.72 

4.70 

14.75 

4.34 

0.504 

3.294 

15.2 

1.70 

1.87 

0.63 

12.25 

3.60 

0.367 

3.147 

13.6 

1.45 

1.94 

0.63 

9.75 

2.87 

0.210 

3.000 

12.1 

1.23 

2.05 

0.65 

10.50 

3.09 

0.410 

2.880 

7.1 

1.01 

1.52 

0.57 

9.50 

2.79 

0.337 

2.807 

6.7 

0.93 

1.55 

0.58 

8.50 

2.50 

0.263 

2.733 

6.4 

0.85 

1.59 

0  58 

7.50 

3.21 

0.190 

2.660 

6.0 

0.77 

1.64 

0.59 

7.60 

2.21 

0.361 

2.521 

2.9 

0.60 

1.15 

0.52 

5.50 

1.91 

0.263 

2.423 

2.7 

0.53 

1.19 
1.23 

0.52 

5.50 

1.63 

0.170 

2.330 

2.5 

0.46 

0.53 

Note. — ^Weights  in  heavy  type  are  standard;  others  are  special. 
For  Bethlehem  jrirder  (single  I)  beams  and  Bethlehem  special  I-beams, 
see  Tables  8  and  9,  Sec.  31.  pages  583  and  584. 


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CHANNELS.    Z-BARS, 


667 


7. — Propbrtibs  of  Z-Bars  (Stbbl). 
(Weights  at  489.6  Ibe.  per  cubic  foot.) 


00 


M 

1 

%f- 

Z  c 

&I 

r§ 

ss 

'o  3 

■gi 

8« 

^ 

< 

Moment  of 

Inertia. 

I 


J3      U3 

III 

111 


15.6 
18.3 
21.0 

4.69 
5.39 
6.19 

22.7 
26.4 
28.0 

6.68 
7.46 
8.26 

29.3 
81.9 
34.6 

8.63 

9.40 

10.17 

11.6 
13.9 
16.4 

3.40 
4.10 
4.81 

17.9 
20.2 
22.6 

6.26 
6.94 
6.64 

23.7 
26.0 
28.3 

6.96 
7.64 
8.33 

8.2 
10.3 
12.4 

2.41 
3.03 
3.66 

13.8 
16.8 
17.9 

4.06 
4.66 
6.27 

18.9 
20.9 
23.0 

6.65 
6.14 
6.76 

6.7 
8.4 

1.97 
2.48 

9.7 
11. 4 

2.86 
3.36 

12.5 
14.2 

3.69 
4.18 

25.32 
29.80 
34.36 

34.64 
38.86 
43.18 

42.12 
46.13 
60.22 

13.36 
16.18 
19.07 

19.19 
21.83 
24.63 

23.68 
26.16 
28.70 

6.28 
7.94 
9.63 

9.66 
11.18 
12.74 

12.11 
13.62 
14.97 

2.87 
3.64 

3.85 
4.67 

4.50 
6.26 


Zoo 


9.11 
10.96 
12.87 

12.60 
14.42 
16.34 

15.44 
17.27 
19.18 

6.18 
7.65 
9.20 

9.05 
10.61 
12.06 

11.37 
12.83 
14.36 

4.23 
5.46 
6.77 

6.73 
7.96 
9.26 

8.73 

9.95 

11.24 

2.81 
3.64 

3.92 
4.75 

4.85 
5.70 


Radii  of  Gyration. 

r 


^;ocu 


2.35 
2.36 
2.36 

2.28 
2.28 
2.29 

2.21 
2.22 
2.22 

1.98 
1.99 
1.99 

1.91 
1.91 
1.92 

1.84 
1.85 

1.86 

1.62 
1.62 
1.62 

1.55 
1.55 
1.55 

1.48 

1.48 
1.49 

1.21 
1.21 

1.16 
1.17 

1.12 
1.12 


P 

HO** 
3C.S 

!§J<S 


1.41 
1.43 
1.44 

1.37 
1.39 
1.41 

1.34 
1.36 
1.37 

r.35 
1.37 
1.38 

1.31 
1.33 
1.35 

1.28 
1.30 
1.31 

1.33 
1.34 
1.36 

1.29 
1.31 
1.33 

1.25 
1.27 
1.29 

1.19 
1.21 

1.17 
1.19 

1.15 
1.17 


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DEFLECTION.    LONGITUDINAL  SHEAR.  665 

Furthermore,  if  the  allowable  outer  fiber  stress  /  for  timber  is  1000  lbs. 
per  sq.  in.,  and  /  for  steel  is  15000,  we  have,  from  II  and  IV: — 


Loading. 
V.    Uniform  load  IV 

VL    Center  load  W 


Woodtn  B9ams.* 
L^jd-^LSb-'bd 

L-?|<i-1.94^4d 


Si09l  Girders, 
L-^y-S.STOtv 


which  are  the  limiting  spans  for  plastered  ceiling,  and  which  enable  us  to 
deagn  these  spans  economically. 

LoAsitadinal  Shear  in  Beams. — While  long  beams,  even  of  sufficient 
strength  to  resist  bending,  are  often  limited  by  the  deflection,  asprcviously 
noted,  short  beams  may  fail  by  horizontal  (longitudinal)  shear.  The  general 
formula  for  longitudinal  shear  is 

In  which  //  —  the  longitudinal  shearing  force  in  lbs.  per  unit  (lin.  in.)  length 
of  becun; 
V  — the  total  vertical  shear  in  lbs.  at  section  considered; 
0  — the  statical  moment  in  in.-Ibs.  of  the  area  Ai  above  the  plane 
of  shear  — i4tyi,  in  which  yi  — distance  from  neutral  axis  to 
cen.  of  grav.  ot  At; 
/—the  moment  of  inertia  of  beam  section. 
For  a  rectangular  beam,  the  longitudinal  shear  at  the  neutral  axis 
would  be,  if  fr  —  breadth  and  d  —  depth  in  inches: 

«-f-f*^-M C2) 

and  the  intensity  of  shear  per  square  inch  would  be 

6      2     bd ^^ 

Note  that  the  vertical  shear  V  at  any  point  of  a  beam  is  equal  to  the 
differential  coefficient  of  the  bending  moment  at  that  point;  thus, 

y-'-i <« 

X  bexns  the  distance  from  left-hand  end  of  beam  to  section  considered. 

Problem: — A  wooden  beam  12  x  12  ins. .  weighing  600  lbs.  (— tt;) ,  supports 
a  uniform  load  of  W  lbs.  What  will  be  the  maximum  value  of  W,  so  that 
the  maximum  intensity  of  shear,  H  -t-  b,  (at  the  neutral  axis.)  shall  not 
exceed  50  Iba.  per  sq.  in.  ? 

Solution: — ^The  maximum  vertical  shear  (at  the  end  of  the  beam)  equals 

V  ■■  — 5 — .      Substituting  this  value  of  V  in  equation  (3),  we  have. 

Intensity  of  *°«*'*""r""Y  *  "o^^—^O 

Hence,  by  substitution,  IV—  9600-600-9000  lbs.     Ans.     (See  also.  Example 
1,  bottom  of  page  567.) 

Note  that  the  length  of  span,  in  the  above  problem,  is  not  a  factor  in 
longitudinal  shear. 


•  Note  that  W  and  /  are  directly  proportional  to  the  modulus  of  elastic- 
ity, £,  of  the  material,  which,  in  the  present  instance,  is  assumed  at 
1  OiiW  000.     For  any  other  modulus,    as   Ei,  multiply   above    values   by 

— ^ See  Sec.  28.  Strength  of  Materials.  Table  7,  page  496.         . 

tized  by  Google 


1000  000' 


6M  n— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRl 


2. — Uniformlt  Distributbd  Loads  W  in  Pounds 
On  Rbctanoular  Bbams  1  Inch  Widb 
Producing  Extrsmb  Fibbr  Strbss  /« 1000  Las.  prr  Sg, 

(By  Formula,  Case  Dd  (2):  ^^-^-^^9^- 

For  any  other  fiber  stress,  as  fu  multiply  values  in  table  by  •= 
[Total  load  in  Pounds,  including  weight  of  beam.] 


cob 


Depth  of  Beam. 


r 


r    r 


lif 


111 

56 
37 


444 

222 
148 
111 


1000 
fiOO 
333 
250 

200 
167 
143 
125 
111 

100 
91 
83 
77 
71 

67 
62 
59 
56 
53 

50 
48 
45 
43 
42 


ms 

889 
593 
444 

356 

296 
254 
222 

198 

178 
162 
148 
137 

127 

119 
111 
105 
09 
94 


2778 
1389 
926 
694 

656 
463 
897 
347 
809 

278 
253 
231 
214 
198 

185 
174 
163 
154 
146 

139 
132 
126 
121 
116 


4000 
2000 

1333 
1000 

800 
667 
571 
500 
444 

400 
364 
833 


267 
250 
235 
222 
211 

200 

190 
182 
174 
162 


2722 
1815 
1361 

1069 
907 
778 
681 
605 

544 
495 
454 

419 


363 
340 
320 
302 
287 

272 
259 
247 
237 
227 


3656 
2370 
1778 

1422 
1185 
1016 
8S9 
790 

711 
646 
503 
647 
506 

474 
444 
418 
395 
874 

356 
339 
323 
309 
296 


3000 


1800 
1500 
1286 
1125 
1000 

900 
818 
750 
692 
643 

600 
663 
629 
500 
474 

450 

429 
409 
391 
875 


3704 
2778 

9999 
1852 
1587 
1389 
1235 

1111 
1010 
926 
855 
794 

741 
094 
654 
617 


656 

629 
506 
483 
463 


13*   14' 


15* 


16'   17* 


Depth  of  Beam. 


18' 


lO'   20'   21 


22^ 


8 
9 

10 
11 
12 
13 
14 

15 
16 
17 
18 
19 


2347 


1878 
1707 
1565 
1444 
1341 

1252 
1174 
1105 
1043 


2722 
2420 

2178 
1980 
1815 
1675 
1556 

1452 
1361 
1281 
1210 
1146 


3125 
2778 

2500 
2273 
2083 
1923 
1786 

1667 
1563 
1471 
1389 
1316 


3556 
3160 

2844 
2586 
2370 
2188 
2032 


1778 
1673 
1580 
1497 


4014 


3211 

2919 
2676 
2470 
2294 

2141 
2007 
1889 
1789 
1690 


4500 
4000 

3600 
3273 
3000 

2769 
2571 

2400 
2250 
2118 
2000 
1895 


5014 
4457 

4011 
3646 
3343 
3085 
2865 

2674 
2507 
2359 
2228 
2111 


5556 


4444 

4040 
3704 
3410 
3175 


2778 
2614 
2469 


6125 
6444 

4900 
4455 
4063 
3769 
3500 


6722 
5976 

6378 
4880 

4481 
4137 
3841 


3267 
3062 


2722 
2579 


3861 
3163 


Note.— For  allowable  fiber  stresses  in  Wooden  Beams,  so 
btrentrth  of  Materials.  Table  7,  column  ^.  page  496.  For  bridge 
use  safety  factor  6;   for  floorbeams.  5.     jOOQIC 


LOADS  ON  RECTANGULAR  BEAMS. 


667 


2. — ^Uniformly  Distributed  Loads  W  in  Pounds 

On  Rectangular  Beams  1  Inch  Wide. 

— Concluded. 

[Total  load  in  Pounds,  including  weight  of  beam.] 


u 

Depth  of  Be^ 

m. 

ir 

14' 

isr 

16' 

'''^ 

18' 

19* 

20* 

21' 

22* 

23* 

24' 

» 

939 

1089 

1260 

1422 

1606 

1800 

2006 

2222 

2460 

2689 

2939 

3200 

21 

S04 

1037 

1190 

1354 

1629 

1714 

1910 

2116 

2333 

2661 

2799 

3048 

22 

854 

990 

1136 

1298 

1460 

1636 

1823 

2227 

2444 

2672 

2909 

23 

816 

947 

1067 

1237 

1396 

1565 

1744 

1932 

2130 

2338 

2556 

2783 

M 

7B2 

907 

1042 

1185 

1338 

1600 

1671 

1862 

2042 

2241 

2449 

2667 

25 

751 

m 

1000 

1138 

1284 

1440 

1604 

1778 

1960 

2181 

2351 

2660 

26 

722 

838 

962 

1094 

1235 

1385 

1643 

1709 

1886 

2068 

2261 

2462 

27 

605 

807 

926 

1053 

1189 

1333 

1486 

1646 

1816 

1992 

2177 

2370 

28 

6n 

778 

893 

1016 

1147 

1286 

1433 

1687 

1750 

1921 

2090 

2286 

29 

648 

761 

862 

981 

1107 

1241 

1383 

1633 

1690 

1864 

2027 

2207 

ao 

626 

726 

833 

948 

1070 

1200 

1337 

1481 

1633 

1793 

1960 

2133 

31 

606 

703 

806 

918 

1036 

1161 

1294 

1434 

1681 

1735 

1896 

2066 

32 

667 

681 

781 

889 

1003 

1125 

1253 

1389 

1631 

1681 

1837 

2000 

33 

669 

660 

768 

862 

973 

1091 

1216 

1347 

1485 

1630 

1781 

1939 

M 

562 

641 

736 

837 

944 

1059 

1180 

1307 

1441 

1682 

1728 

1882 

35 

637 

622 

714 

813 

917 

1029 

1146 

1270 

1400 

1537 

1677 

1829 

36 

622 

605 

694 

790 

894 

1000 

1114 

1235 

1361 

1494 

1633 

1778 

37 

607 

689 

676 

760 

868 

973 

1084 

1201 

1324 

1463 

1589 

1730 

38 

494 

673 

668 

749 

846 

947 

1066 

1169 

1289 

1416 

1547 

1684 

39 

481 

558 

641 

729 

823 

923 

1028 

1140 

1266 

1379 

1507 

1641 

40 

460 

m 

626 

711 

803 

900 

1003 

nil 

1226 

1344 

1460 

1600 

Note. — For  allowable  fiber  stresses  in  Wooden  Beams^  see  Sec.  28, 
Strength  of  Materials,  Table  7.  column  8,  page  406.  For  bridge  stringers 
nse  safety  factor  6;  for  floor  beams,  6. 

Remember  that  W  is  proportional  to  d*  and  inversely  proportional  to  L; 
thus  the  range  of  the  table  may  be  extended  greatly. 

Examples  in  Use  of  Table  2. 

Example  1. — In  the  problem  at  bottom  of  page  666,  longitudinal  shear,  we 
find  that  a  12  x  12-in.  wooden  beam  will  support  a  total  load  (including 
weight  of  beam  —  600  lbs.)  of  9600  lbs.  Find  the  maximum  length  of  span 
•o  that  the  outer  fiber  stress  /  shall  not  exceed  1000  lbs.  per  square  inch. 

Solution. — From  the  data  given,  abeam  12  ins.  wide  and  12  ins.  deep 
will  support  a  total  load  of  9600  lbs.;  hence,  for  the  same  depth  of  beam, 
each  one  inch  in  width  will  support  0600-1-12-800  lbs.  Now,  in  the  last 
column  (the  12' column)  on  precedmg  page  we  find  that  the  load  800  corre- 
sponds to  a  span  of  20  ft.     Ans. 

Example  2. — In  the  preceding  Example,  find  the  maximum  length  of 
span  so  that  the  outer  fiber  stress  /  shall  not  exceed  600  lbs.  per  square  inch. 

Solution. — Corresponding  length  of  span, 

1,-20^-20^-12  ft.   Ans. 

Example  3. — A  beam  supports  a  load  W=  9600  lbs.,  producing  an  outer 
fiber  stress/— 1000.  What  load  Wt  will  it  support  if  the  allowable  fiber 
stress  /i  is  increased  to  1200  lbs.  per  square  inch  ? 

Solution. — W  is  proportional  to  /;  hence 


IV,-  H^A-9e0(^='11620  lbs. 


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BEAM  BOX  GIRDERS. 


569 


8. — Bbam  Box  Girobrs  (Stbbl) — Concluded. 
(Adapted  from  Carnegie  and  Cambria.) 


Section. 


Sec- 
tion 
modu- 
lus 

y 

Ins. 


♦Safe  , 

total 
loadivl 

Unif. 

Dis- 
trib'fdl 
forlO-ft 

span. 

Lbs. 


Section. 


Two 
I-Beams 


Two 
Plates 


Fin- 
ished 
weight 

per 
foot. 


Lbs. 


Sec- 
tion 
modu- 
lus 


Ins. 


♦Safe 

total 
loadJV 

Unif. 

Dis- 
trib'fd 
forlO-ft 

span. 

Lbs. 


195.5 
202.2 
209.0 
215.8 
222.6 
299.4 
238.2 
248.1 
249.8 
256.7 
263.4 

2155 
222.2 
229.0 
235.8 
242.6 
249.4 
256.2 
263.1 


299.7 
311.0 
822.4 
333.7 
345.1 
356.6 
368.1 
379.6 
301.2 
402.8 
414.4 

340.5 
355.8 
371.2 
386.6 
402.0 
417.5 
433.0 
448.6 
464.2 
479.8 
495.4 

411.8 
428.7 
445.7 
462.7 
479.7 
496.7 
513.8 
531.2 


;s^ 


299.700ifa0^-65# 
311,00m 
822.40a 
333.700 
345.100 

856.600  20'-80# 
368.100 
379.6001.-    - 
391.200|j±    " 
402.80a;S     «    1 
414.400|^     •    •< 

340.50(^'l:^    I    S 
356.800,'r  I 

371.200^"     -     J. 

386.60ar    -   i 

402.0001 
417.500! 
433 .000;! 
448.600|i  24'-80# 

464.200^ 
479.8001^        -    ^ 

m.i^ :  ? 

411.800,7    . 
428. 700*  J>     « 
445 .700  00     . 
462.700  R 
479.700  a     - 
496.700! 
518.800* 
531.200j 


18x  H 


xl 

xlK 
xlA 

xlK 
xlA 

x\H 
xlA 


269.8 
276.7 
283.4 


245.5 
252.2 
259.0 
265.8 

272.6 
279.4 
286.2 
293.1 

299.8 
306.7 
313.4 


265.7 
263.3 
271.0 
278.6 

286.2 
293.9 
301.5 
309.2 

316.8 
324.5 
332.1 
339.8 


548.1 
565.3 
582.5 


463.8 
480.4 
497.1 
513.8 

530.6 
547.3 
564.1 
581.2 

597.8 
614.7 
631.7 


593.7 
616.9 
640.1 
663.4 

686.7 

no.o 

733.3 
757.1 

780.2 
803.6 
827.1 
850.5 


548.100 
566.300 
582.500 


468.800 
480.400 
497,100 
513.800 

530.600 
547,300 
564.100 
581.200 

507.800 
614.700 
631,700 


598,700 
616.900 
640.100 
636,400 

686.700 
710.000 
733.300 
757.100 

780.200 
803.600 
827.100 
850.500 


♦Based  on  allowable  fiber  stress  of  15000  lbs.  per  sq.  in.  For  16-ft.  span, 
divide  total  load  by  1.6;  20-ft.  span,  divide  by  2;  30-ft.  span,  divide  by  3;  etc. 

Note  that  total  load  W  includes  weight  of  girder,  which  must  be  de- 
ducted to  obtain  superimposed  load. 

Probkm. — Required  to  design  a  beam  box  girder  of  16-ft.  clear  span, 
for  a  superimposed  load  which  produces  a  maximum  bending  moment  M"" 
8,150.000  in. -lbs.;  with  a  total  allowable  fiberstress/»  14400  lbs.  per  square  inch. 

Solution. — (See  Table  1,  page  562,  for  formulas.)  From  the  general 
formtilas  (3)  we  nave. 

(1.)  For  the  superimposed  load:   Sec.  mod.  5 --- ^  -  ?J^? -  218.75 

From  the  above  table  this  value  of  S  calls  for  16*— 42#  beams  with 
plates. 

(2.)  For  the  weight  of  the  girder:  Sec.  mod.  5  —  —  -7—  —  -oT  —  -5-r* 

y        T         of       Of 
in  wbich  w  —  the  weight  in  lbs.  per  lin.  ft.  of  girder.    From  tne  above 
,  ,  .                                             -o,    ,-        -      183X266X12X12  „  ._ 

table,  we  may  assume  w  - 183;  then  S  — 8x14400 " 

(1  and  2.)   Ans. — ^Use  two  16*  -  42/  beams  and  two  14  X 1'  plates:  For 
required  5 -  ^g,,.^^, .^ GoOgl^'^ 


570  3i— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS. 

4. — Platb-Girdbr  Tables*  (Stbel). 

Propbrties  op  Platb  Girdbrs  Complbtb. 

(Compiled  from  Tables  6.  6  and  7,  following.) 

[Resisting  moment  (  —  bending  moment)  in  1000  Ft. -Lbs.] 


f  ^Z  ^¥^®  *  ^^^  cover  most  cases  in  practice;  but  Tables  5,  6  and  7 
turtherbe  combined  to  meet  almost  any  requirement. 
T  One  top  and  one  bottom.  f^r^r^^]^ 

Digitized  by  VjOOv  IVL 


d  by  Google 


672  Zi— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS. 


5. — ^Plate  Girders  (Stbbl). 
Properties  op  Flange  Angles  Only. 


Fig.  2. 


8 


4  Flange 
Angles. 


Sise. 
Ins. 


£§ 


w 

Lbs. 


D 
Ins. 


o6 

Ins. 


NetArea 
Each 
Flange 

(2 
Angles) 

A 
Sq.  Ins. 


Ins. 


g-gq 

iw's 


Resist- 
ing 
Moment 

12j. 
for 

Hio.ooo 

Ft.-Lbs 


1^3 


(a)  Use  with  or  without  Cover  Plates.   Rivets  H'- 

One  Ji*  rivet-hole  < 

leduc 

from  Each  Angle  for  A. 

2Jx2ixA 

12.4 

12>^ 

10  87 

1.47 

16.98 

17.64 

13  320 

14 

"  ^H 

16.4 

10.81 

1.94 

20.97 

23.28 
28.66 

17  480 

19 

*    3cA 

20.0 

m 

10.77 

2.39 

25.74 

21  450 

23 

"   xH 

23.6 

•* 

10.73 

2.80 

30  04 

33.60 

26  040 

28 

-\% 

27.2 

" 

10.69 

3.23 

34.53 

38.76 

28  770 

33 

30.8 

** 

10.63 

3.63 

38.69 

43.66 

32  160 

W 

3  x2JxK 

18.0 

12K 

10.93 

2.18 

23.83 

26.16 
32.28 

19  860 

21 

22.4 

« 

10.89 

2.69 

29.29 

24  410 

96 

•    x^ 

26.4 

« 

10.83 

3.18 

34.44 

38.16 

28  700 

31 

•   V4 

30.4 

• 

10.79 

3.67 

39.60 

44.04 

83  000 

as 

34.0 

• 

10.76 

4.13 

44.40 

49.66 

37  000 

41 

3  x3  x)i 

19.6 

18M 

16.67 

2.44 

40.43 

29.28 

83  090 

34 

"     3tA 

24.4 

** 

16.61 

3.01 

49.70 

36.12 

41410 

30 

*     *^ 

28.8 

m 

16.47 

3.56 

68.63 

42.72 

48  860 

86 

-    xtj 

33.2 

» 

16.43 

4.09 

67.20 

49.06 

66  000 

40 

37.6 

m 

16.39 

4.63 

75.89 

65.66 

63  240 

46 

'-ih 

41.6 

» 

16.35 

5.14 

84.04 

61.68 

70  030 

51 

60.0 

M 

16.29 

6.63 

91,71 

67.66 

76  430 

66 

3ix2JxK 

19.6 

18K 

17.03 

2.44 

41.55 

29.28 

34  630 

24 

"     3tA 

24.4 

• 

16.97 

3.01 

61.08 

36.12 

42  670 

3D 

■  4i 

28.8 

m 

16.93 

3.56 

60.27 

42.72 

60  230 

85 

33-2 

m 

16.89 

4.09 

69.08 

49.08 

67  570 

40 

37.6 

» 

16.86 

4.63 

78.02 

66.56 

65  010 

46 

-    xii 

41.6 

* 

16.79 

6.14 

86.30 

61.68 

71  920 

61 

60.0 

M 

16.76 

6.63 

94.30 

67.66 

78  600 

66 

3ix3xA 

26.4 

18^ 

16.63 

3.31 

65.05 

39.72 

46  870 

SS 

31.6 

H 

16.69 

3.94 

65.36 

47.28 

64  470 

30 

36.4 

• 

16.65 

4.53 

74.97 

64.36 

62  480 

4S 

40.8 

m 

16.49 

5.13 

84.59 

61.66 

70  490 

61 

*    xA 

45.6 

* 

16.46 

6.70 

93.77 

68.40 

78  140 

57 

*    xj4 

50.0 

a 

16.41 

6.25 

102.66 

76.00 

85  470 

a 

•    xH 

64.4 

« 

16.37 

6.80 

111.32 

81.60 

02  760 

68 

-    x^ 

68.8 

• 

16.33 

7.31 

119.37 

87.72 

99  480 

73 

dbyGoogk 


d  by  Google 


674  Si— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS. 


6. — Platb  Girders  (Stbbl) — Concluded. 
Propbrtzbs  op  Flanob  Anglbb  Only.* 


4  Flange 
Angles. 


Size. 
Ins. 


1* 

« 

Po 
D 
Ins. 


I 

si 

d 
Ins. 


NetArea 
Each 
Flange 

(2 
Angles) 

A 
Sq.Ins. 


•8 


^  3 


Ins. 


2^ 
ga»s 


III 


Resist- 
ing 
moment 

\2y 
for 
f-10.000. 

Ft.-Lbs. 


1-2  i 

iJ  ^M   Vi 

S^Wo 


(b)  Use  with  or  without  Cover  Plates.  Rivets  Ji*.  Two  J^  rivet-holes  deducted 
from  Each  Angle  for  A. 


6x3ixH 

-    xK 
6x4xH 


•  xS 

•  xj^ 


46.8 

80^ 

28.67 

5.53 

158.55 

64.0 

28.63 

6.41 

188.52 

61.2 

• 

28.50 

7.25 

207.28 

68.4 

• 

28.58 

8.09 

230.81 

75.6 

M 

28.49 

8.91 

253.85 

82.4 

• 

28.45 

9.71 

276.25 

89.6 

« 

28.39 

10.50 

296.10 

96.0 

• 

28.35 

11.28 

319.79 

102.8 

• 

28.31 

12.04 

340.85 

49.2 

80Vi 

28.37 

5.91 

167.67 

57.2 

a 

28.33 

6.83 

193.49 

64.8 

• 

28.27 

7.75 

219.10 

72.4 

a 

28  23 

8.65 

244.19 

80.0 

« 

28.19 

9.53 

268.65 

87.2 

» 

28.13 

10.41 

292.83 

94.4 

* 

28  09 

11.26 

316.29 

101.6 

■ 

28  05 

12.10 

339.41 

108.8 

28.01 

12.92 

361.89 

86 
92 
00 
08 
92 
52 
00 
36 
48 

70.82 
81.96 
93.00 
103.80 
114.36 
124.92 
135.12 
145.20 
155.04 


132  120 

153  930 

172  730 

193  340 

311  540 

230  210 

248  410 

366  600 

284  040 

139  720 

161  240 

182  580 
303  490 

223  880 

244  030 

263  580 

282  840 

301  570 

55  800 
64  100 
73  800 
80  900 
89  100 
97  lOD 
105  000 

112  800 
130  400 

59  100 

68  aoo 

77  800 
86  800 
96  800 
104  100 

113  000 
121  OOO 
129  800 


(c)  Use  with  or  w 

ithout  Cover  Plates.  Rivets^.  Two  1*  rivet-holes  dedxicted 

from  Each  Angle  for  A. 

6x6xiV 

68.8 

dOH 

26.93 

8.37 

225.40 
255.46 

H 

100.44     187  840 

83  700 

78.4 

26.89 

9.60 

114.00     312  880 

05  000 

"    xAf 

"    xH 

87.6 

*• 

26.83 

10.61 

284.67 

127.32     237  220 

106  100 

96.8 

" 

26.79 

11.72 

313.98 

140.64     361  660 

117  300 

:in 

106.0 

" 

26.75 

12.81 

342.67 

153.72     285  560 

188  100 

114.8 

• 

26.69 

13.88 

370.46 

166.56     306  710 

138  800 

-   xH 

124.0 

" 

26.65 

14.93 

397.88 

179.16     831  570 

149  800 

-   xj« 

132.4 

« 

26.61 

15.96 

425.23 

191.76     354  380 

180  800 

8x8xH 

105.6 

36V^ 

31.87 

13.50 

430.25 

162.00     358  540 

185  000 

-    x/. 

118.4 

31.83 

15.11 

480.95 

181.32 

400  790 

151  100 

-  xk 

130.8 

" 

31.79 

16.72 

531.53 

200.64 

442  940 

107  200 

143.2 

31.75 

18.31 

;    581  34 

219.72 

484  460 

183  100 

155.6 

" 

31.60 

19.88 

630.00 

238.56 

625  000 

196  800 

168.0 

31.65 

21.43 

678.26 

257.16 

565  230 

214  900 

180.0 

31.61 

22.96 

725.77 

275.52 

604  800 

329  600 

*Sce  t  ig.  2,  page  572. 


d  by  Google 


\ 
Fig. 


PLATE  GIRDERS— WEB  PLATES  ONLY, 

6. — Plate  Girdbrs  (Stbbl) 

Properties  of  Web  Plates  Only. 

(If  — moment  in  ft.-lbs.;  M'  — moment  in  in.-lbs.) 


576 


1 

2 

3 

4 

5 

6        1      7 

8               9 

i 
I 
\ 

o 

I 

Pull  Efficiency  of 
Web;HAreadon- 

75%  Efficiency  of  60%  Efficiency  of 
Web;  >4AreaCon-  Web;  AArea  Con- 

sidered at  Upper 
and  Lower  Eoges; 

sidered  at  Upper 
and  Lower  Edges; 

sidered  at  Upper 
and  Lower  Edses: 

g 

NoDeduction  for 

25%  Dcducfn  for  40%  Deduct 'n  for 

Web 

1 

Rivet  Holes,  etc. 

Rivet  Holes,  etc. 

Rivet  Holes,  etc. 

Plate. 

\ 

Moment 

Moment 

Moment 

Sj 

of  Re- 

of Re- 

of Re- 

a 

O 

sistance 

sistance 

sistance 

*i 

"o 
t 

Section 

^12 

Section 

M'-i 

Section 

^12 

Modulus 

Modulus 

Modulus 

Q   ^ 

^ 

^ 

s-\' 

1(X)00) 

-     Ad 

KWOO) 

■^       10 

IMOO) 

d     h 

W 

A 

In*. 

Lbs. 

Sq.Ins 

Ft.-Lbs. 

Ft.-Lbs. 

Ft.-Lbs. 

nt 

.212 

.062 

.010 

9 

.006 

7 

.006 

5 

.85 

.25 

.042 

35 

.031 

26 

.025 

21 

•xl 

3.40 

1.00 

.167 

ISO 

.125 

104 

.100 

83 

nti 

.425 

425 

.042 

35 

.031 

26 

.025 

21 

1.70 

.60 

.167 

139 

.125 

104 

.100 

83 

•  xl 

6.80 

2.00 

.667 

556 

.600 

417 

.400 

333 

Note.— Columns  4  and  5  are  useful 

l^ti 

.63t 

.187 

.094 

78 

also  in  the  calculation  of  wooden 

•  X  K 

2.55 

.76 

.375 

312 

-xl 

10.20 

3.00 

1.500 

1250 

Problem. — What  bending 
moment  in  ft.-lbs.  will  a  beam 

•xl 

.85 

.25 

.167 

139 

STxS*  sustain  safely  at  an  allow- 
able fibre  stress  of  1100  lbs.  per 
8^*"'.               ,„       11005 

8.40 
13.60 

1.00 
4.00 

.667 
2.667 

556 
2222 

Solution  1  —  Af'  —  — ^-^  » 

6xiV 

1.062 

.312 

.260 

217 

llM             A.       iw             ^ 

•x  Ji 

4.25 

1.25 

1.042 

868 

i^  X  3  X  10.667  -  2933  ft.  lbs. 

-xl^ 

17.00 

5.00 

4.167 

3472 

^J  ,  ..      «      ...    3X8889X1100 
Solution  2.    Af'-        ^^^ 

-  3  X  8889  X  .11  -  2933  ft.-lbs. 

!:,« 

1.275 

.376 

.375 

312 

5.10 
20.40 

1.487 

1.50 
6.00 

.437 

1.500 
6.000 

.510 

1250 
5000 

425 

Hence,  the  problem  can  be  solved 
by  the  use  of  either  S  or  M'. 

!:iS 

.383 

319 

.306 

255 

5.95 

1.75 

2.042 

1701 

1.531 

1276 

1.225 

1021 

•xl* 

23.80 

7.00 

8.167 

6806 

6.125 

5104 

4.900 

4063 

2;:j^ 

1.70 

50 

.667 

556 

.500 

417 

.400 

333 

6.80 

2.00 

2.667 

2.000 

1067 

1.600 

1333 

-Xl* 

27.20 

8.00 

10.667 

8889 

8.000 

6667 

6.400 

5333 

9x  ^ 

1.912 

.562 

.844 
3.375 

703 

.633 

527 

.506 

422 

•x3 

7.85 

2.25 

2812 

2.531 

2109 

2.025 

1687 

•  xl 

30.00 

9.00 

13.600 

11250!    10  125 

8437 

8.100 

6750 

Note  that  properties  in  table  are  directly  proportional  to  width  fc;  and 
that  the  Sectional  Moduli  and  Moments  of  Resistance  are  proportional  to 
the  sqware  of  depth  d.  Hence  the  range  of  the  table  may  be  increased 
indcfinitety.    Seefirst  column  on  following  page. 


676  SI— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS, 


6. — Platb  Girobrs  (Steel) — Continued. 

Properties  of  Web  Platbs  Only.* 

(M'  —  moment  in  ft.-lbs.;  M"  —  moment  in  in.-lbs.) 


1 

2 

3 

c 

.S 

^ 

Web 

1 

Plate. 

^ 

£ 

S 

h 

g 

s. 

o 

«^ 

1 

0 

1 

d   b 

W 

.4 

Ins. 

Lbs. 

Sq.Ins 

10  X  A 

Six  A 

•^  OX  A 

12  X  A 

a  ~*^  TTi 

g«xH 

OCX    ,'$ 

Sj^-xl 
14  X  K 


2.125 

.625 

1.042 

868 

.781 

651 

-26 

4.25 

1.25 

2.063 

1736 

1.562 

1802 

5 

6.375 

1.875 

3.125 

2604 

2.344 

106S 

76 

8.50 

2.50 

4.167 

3472 

3.125 

2604 

0 

10.625 

3.125 

5.206 

4340 

3.906 

'^TSS 

25 

12.75 

3.75 

6.250 

5206 

4.687 

100 

5 

14.875 

4.375 

7.292 

6076 

5.460 

167 

75 

17.00 

5.00 

8.333 

0944 

6.250 

06 

0 

19.125 

5.625 

9375 

7812 

7.031 

;5o 

26 

21.25 

6.25 

10.417 

8681 

7.812 

>10 

5 

23.375 

6.875 

11.458 

9549 

8.504 

61 

76 

25.50 

7.60 

12.500 

10417 

9.875 

112 

0 

27.625 

8.125 

13.542 

11285 

10.166 

^ 

26 

29.75 

8.75 

14.583 

12153 

10.937 

16 

5 

31.875 

9.375 

15.625 

13021 

11.719 

'66 

75 

34.00 

10.00 

16.667 

13889 

12.600 

il7 

0 

2.55 

.750 

1.500 

1250 

1.125 

087 

.9 

5.10 

1.50 

3000 

2500 

2.250 

1876 

1.8 

7.65 

2.25 

4500 

3750 

3.375 

2813 

27 

10.20 

3.00 

6.000 

5000 

4.500 

3760 

3.6 

12.75 

3.75 

7.500 

6250 

5.625 

4687 

4.6 

15.30 

4.50 

9.000 

7500 

6.760 

5626 

6.4 

17.85 

5.25 

10  500 

8760 

7.875 

6662 

6.3 

20.40 

6.00 

12.000 

10000 

9.000 

7600 

7.2 

22.95 

6.75 

13.600 

11260 

10.125 

8437 

8.1 

25.50 

7.60 

15.000 

12500 

11.250 

9375 

9.0 

28.05 

8.25 

16.500 

13750 

12.875 

10312 

9.0 

30  60 

9.00 

18.000 

15000 

13.600 

11260 

10.8 

33.15 

9.76 

19.600 

16250 

14.625 

12187 

11.7 

35.70 

10.60 

21  000 

17500 

15  760 

18126 

12.6 

38.25 

11.25 

22.600 

18750 

16.875 

14062 

13.6 

40.80 

12.00 

24.000 

20000 

18.000 

16000 

14.4 

11.90 

3.50 

8.167 

6806 

6.125 

5104 

4.90 

14.88 

4.38 

10.208 

8507 

7.656 

6380 

6.126 

17.85 

5.25 

12.250 

10208 

9.187 

7656 

7.35 

20.83 

6.13 

14.292 

11910 

10.719 

8932 

8.575 

23.80 

7.00 

16.333 

13611 

12.260 

10208 

9.80 

47  GO  14  00 

32.667 

27222 

24.500 

20417 

10.600 

►per 
jes; 

for 

etc 


ice 
12 

i) 

b& 


621 
1012 
15«2 
2063 
2604 
3126 
8646 
4167 
4687 
6808 
6729 
62S0 
6771 
7291 
7812 


750 
1600 
2250 
8000 
3750 
4600 


6750 
7600 


9730 
10000 
11280 


4063 
6104 
6125 
7146 
8167 
16338 


PLATE  GIRDERS— WEB  PLATES  ONLY, 


677 


6. — Plate  Girders  (Steel) — Continued. 

Properties  of  Web  Plates  Only.* 

(Af'  —  moment  in  ft  .-lbs.;  Af*  —  moment  in  in.-lbs.) 


2 


c 

.2 

1 

1 

O 

Web 

Plate. 

I 

P^ 

u 

K 

■tj 

U3   03 

J2 

a  "S 

.» 

1 

d     b 

W 

Ins. 

Lbs. 

12.75 

3.75 

9.375 

7812 

7.081 

5850 

15.94 

4.687 

11.719 

9766 

8.789 

7324 

19.13 

5.625 

14.062 

11719 

10.547 

8789 

22.31 

6.562 

16.406 

13672 

12.306 

10254 

25.50 

7.500 

18.75 

15625 

14.002 

11719 

51.00 

15.000 

87.50 

31250 

28.125 

23438 

i3.eo 

4.00 

10.667 

8889 

8000 

6667 

17.00 

5.00 

13.833 

11111 

10.000 

8333 

30.40 

6.00 

16.000 

13333 

12.000 

10000 

23. SO 

7.00 

18.667 

15556 

14.000 

11667 

27.20 

8.00 

21.333 

17778 

16.000 

13333 

54.40 

16.00 

42.667 

35556 

32.000 

26667 

15.30 

4.50 

13.500 

11250 

10.125 

8437 

19.13 

5.625 

16.875 

14062 

12.656 

10547 

22.96 

6.75 

20.250 

16875 

15.187 

12666 

26.78 

7.875 

23.625 

19687 

17.719 

14766 

30.60 

9.00 

27.000 

22500 

20.250 

16875 

61.20 

18.00 

54.000 

45000 

40.500 

33750 

17.00 

500 

16.667 

13889 

12.500 

10417 

21.25 

6.25 

20.833 

17361 

15.625 

13021 

25.50 

7.50 

25.000 

20833 

18.750 

16625 

29.75 

8.76 

29.167 

24306 

21.875 

18229 

34.00 

10.00 

33.333 

27778 

25.000 

20833 

68.00 

20.00 

66.667 

55556 

50.000 

41667 

18.70 

5.50 

20.167 

16806 

15.125 

12604 

23.38 

6.875 

25.208 

21007 

18.906 

16755 

28.05 

8.25 

30.250 

25208 

22.688 

18906 

32.73 

9.625 

35.291 

29410 

26.469 

22057 

37.40 

11.000 

40.333 

33611 

30.250 

26208 

74.80 

22.000 

80.667 

67222 

60.500 

50417 

20.40 

6.00 

24.000 

20000 

18.000 

16000 

25.50 

7.50 

30.000 

25000 

22  600 

18760 

30.60 

9.00 

36.000 

27  000 

22500 

36.70 

10.50 

42.000 

35000 

31.500 

26250 

40.80 

12.00 

48.000 

40000 

36  000 

30000 

81.60 

24.00 

96.000 

80000 

72  000 

60000 

ficiency  of 
AreaCon- 
at  Upper 
ver  Edges: 
duct'n  for 
ioles.  etc. 


Moment 

of  Re- 

sistance 

\ 

LS 

-'-% 

f 

(/- 

' 

10000) 

Ft.-Lbs. 

6.625 

4687 

7.031 

5859 

8.437 

7031 

9.844 

8203 

11.250 

9375 

22.500 

18750 

6.400 

5333 

8.000 

6667 

9.600 

8000 

11.200 

9333 

12.800 

10667 

25.600 

21333 

8.100 

6750 

10.125 

8437 

12.150 

10125 

14.175 

11812 

16.200 

13500 

32.400 

27000 

10.000 

8333 

12.600 

10417 

16.000 

12600 

17.600 

14583 

20.000 

16667 

40.000 

12.100 

10833 

16.125 

13542 

18.150 

16260 

21.175 

18958 

24.200 
48.400 

21667 

43333 

14.400 

12000 

18.000 

16000 

21.600 

18000 

26.200 

21000 

28.800 

24000 

67.600 

48000 

*SeGFi«.3.  pa«e575. 


d  by  Google 


PLATE  GIRDERS— WEB  PLATES  ONLY, 


679 


8. — Platb  Girdsrs  (Stbbl) — Concluded. 

Properties  of  Web  Plates  Only.* 

(Af'  —  moment  in  ft. -lbs.;  M"  •=»  moment  in  in.-lbs.) 


8 


.9 


I 

O 

8 


I 

w 

Lbs. 


JPull  Eflficiencyofp6% 
IWeb ;  H  Area  Con- 
isidered  at  Ui 

land  Lower  Ed 

jNo  Deduction  for|25% 
iRivet- Holes,  etc    ~  * 


O 
"3 


A 
Sq.In 


.  ^  Efficiency  of  |60% 
web ;  H  Area  Con- 
sidered at  UpF 
and  Lower  Edgi  .      ^ 
25%  Deduct'nfor|40% 
Rivet  Holes,  etc.  *" ' 


iwyo  Efficiency  of 

Web:AAreaCon- 

■  "er«3  at  Upper 

1  Lower  Edges: 

/o  Deduct 'n  for 

Rivet  Holes,  etc. 


Ppersid 
;es;and 


Section 
Modulus 

^     Ad 


Moment 
of  Re- 
sistance 

-"% 

IMOO) 
Pt.-Lbs 


Section 
Modulus 

^     Ad 

^~  8 


Moment 
of  Re- 
sistance 


Pt.-Lbs 


M'- 


12 


Section 
Modulus 

^      10 


Moment 
of  Re- 
sistance 

IMW) 
Pt.-Lbs. 


46.75 
66.10 
65.46 
74.80 

51.00 
61.20 
71.40 
81.60 

63.13 
63.76 
74.38 
85.00 

57.38 
68.85 
80.33 
01.80 

76.60 
89.25 
102.00 

80.25 
104.13 
119.00 

119.00 
136.00 

133.88 
163.00 

148.75 
170.00 

204.00 


13.75  I  100.83 
16.50  121.00 
19.25  141.17 
22.00  I  161.33 

15.00  I  120.00 
18.00  144.00 
21.00  168.00 
24.00  I  192.00 


15 
18.75 
21.875 
25.00 


39.375^ 
45.OOI 

43.75 
60.00 

60.00 


225.00 

262.60 
300.00 


466.67 
533.33 


500.62 
675.01 


729.17 
833.33 


84028 
100633 
117639 
184444 

100000 
120000 
140000 
160000 

106607 
130208 
151910 
173611 

126562 
151875 
177187 
202500 

187500 
218750 
250000 

255208 
297743 
340278 


1.00 


liiill 


492187 
562500 


607639 
694444 


1000000 


75.62 
90.75 
105.87 
121.00 

90.00 
106.00 
126.00 
144.00 

97.53 
117.04 
136.54 
156.05 

113.91 
136.69 
159.47 
182.25 

168.75 
196.87 
225.00 

229.69 
267.97 
306.25 

350.00 
400.00 

442.97 
506.25 

546.87 
625.00 

900.00 


63021 
75625 


100633 

75000 
90000 
105000 
120000 

81276 
97531 
113786 
130042 

94922 
113906 


151875 

140625 
164062 
187500 

191406 
223307 
2S2O8 

291667 
333333 

360141 
421875 

455729 
520833 

750000 


60.50 
72.60 
84.70 
96.80 

72.00 
86.40 
100.80 
115.20 

78.12 
93.75 
109.37 
125.00 

91.12 
109.35 
127.57 
145.80 

135.00 
157.50 
180.00 

183.76 
214.37 
245.00 

280.00 
320.00 

354.37 
405.00 

437.50 
500.00 

720.00 


50417 
60500 
70583 
80667 

60000 

72000 
84000 
96000 

65104 
78125 
91146 
104167 

75937 
91125 
106312 
121500 

112500 
131250 
150000 

153125 
178646 
204167 


266667 

295312 
337500 

364583 
416667 

600000 


yLjOogle 


*SeeFig.  3.page576. 


580  Zi^PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS, 


t.ex= 


1 


Fig.  4. 


7. — Platb  Oirdbrs  (Stbbl). 
Propbrtibs  of  Planob  Platbs  only. 

Af' "-moment  in  ft.-lbs.; 
Af"— moment  in  in.-lbs. 


(a)  Uae  with  smaller  Flange  Angles.    Rivets,  fi".    Two  H"  rivet-hoks  de- 
ducted from  Each  Plate  tor  A. 


6x1 


x^a 


i2yi 


"  12H 
12?* 
12>i 


18Ji 


UM 


2iH 


,24K 


12}4  1.06 

im  i-fio 

12»||  2.13 

I2h  2.66 


4 


18H 
18A 

18H 
18i4 
18"^ 

18^^ 

181 

10 

19A 

19»" 

19>i 
24^ 

mi 

243r 

24- 
25 


'i 


24 
24* 
24%^ 

24  J  H 
25 


24^^ 
24H^ 

2434 
24' J 
25    I 


1.31 
1.97 
2.63 
3.28 

1.56 
1.95 
2.34 
2.73 
8.13 
3.52 
8.91 
4.30 
4.69 
5.08 
5.47 
5.86 
6.25 

1.81 
2.72 
3.63 
4.53 
5.44 

I 
2.06  , 
3.09 
4.13 
5.16 
6.19 

2.31 
3.47 
4.63 

5.78 
6.94 


13.25 

8.12 

20.07 

4.73 

27.16 

6.87 

34.25 

8.05 

16.37 

3.12 

24.87 

4.73 

83.53 

6.37 

42.23 

8.05 

28.80 

4.62 

36.20 

5.80 

43.58 

6.98 

51.02 

8.18 

58.69 

9.37 

66.22 

10.58 

73.80 

11.80 

81.43 

13.02 

89.11 

14.25 

96.84 

15.49 

104.61 

16.73 

112.44 

17.99 

120.31 

19.25 

44.35 

6.12 

66.98 

9.23 

89.84 

12.37 

112.68 

15.55 

136.00 

18.75 

50.47 

6.12 

76.09 

9.23 

102.22 

12.37 

128.36 

15.55 

154.75 

18.75 

56.60 

6.12 

85.45 

9.23 

114.59 

12.37 

143.78 

15.65 

173.60 

18.75 

12.72 
19.08 
25.56 
31.92 

15.72 
23.64 
81.56 
89.36 

18.72 
23.40 
28.06 
32.76 
87.56 
42.24 
46.92 
51.60 
56.28 
60.96 
05.64 
70.32 
75.00 

21.72 
32.64 
43.56 
54.36 
65.28 

24.72 
37.08 
49.56 
61.92 
74.28 


11040 
16  730 
22  630 
28  540 

13  650 
20  730 
27  940 

35  190 

24  050 
30  160 

36  820 
42  520 
48  910 
55  180 
61500 
67  860 
74  £60 
80  700 
87  180 
93  700 

100  260 

36  950 
55  820 
74  870 
93  900 
113  330 

42  060 
63  410 
85  180 
106  960 
129  000 


27.72  47  160 
41.64  ,  71  210 
55.56  95  490 
69.36  I  119  810 
83.28  ii  144  580 


2600 
3950 

5  810 

6  710 

2600 
8950 

5  310 

6  710 

3850 
4830 
5820 

6  810 

7  810 
8820 
9^0 

10  850 

11  870 

12  910 

13  950 

14  990 
16  040 

5  100 
7700 
10  310 
12  960 

15  620 

5  100 
7700 
10  310 
12  960 
15  620 

5  100 
7  700 
10  310 
12  900 
15  620 


96.0^ 

95.0  • 

94.1  • 
93.2* 

96.04 
95.0' 

94.1  • 

93.2  • 

64.94 
64  6* 
64  4  • 
64  2 - 
64  0- 
63.8' 

8.6  • 
.4  • 

63.2  • 

es.o- 

62.7' 
62.5- 

62.3  • 

49.04 
48.7- 
48.5- 
4S.2  • 
4S.0  ' 

49.04 
48.7' 
48.5' 
48.2- 
48.0' 

49.04 
48.7* 
48-5- 
48  2  • 
48  0- 


*  Percent  of  increase  is  same  as  for  column  11. 

t  Actual  increase  in  ft.-lbs.  -=  10  000  A  (col.  5).     n^^r^n]^ 

Digitized  by  V^OOQlC 


PLATE  GIRDERS^FLANGB  PLATES  ONLY. 


681 


7. — Plat*  Girdbrs  (Stbbl) — Continued. 
Propbrtibs  op  Plangb  Platbs  only. 


moment  in  ft  .-lbs.; 
■moment  in  in. -lbs. 

I 

2 

3 

4 

5            0 

7 

8 

0 

10 

U 

1 

S«e. 
Ins. 

IJ 

w 

Lbs. 

o 
D 

B 

II 

d 
Ins. 

Net 

Area 

Each 

Flange 

Plate) 

i4 

Sq.Ins 

if 

Ins. 

Increase  of 
S  for  Each 
Additional 

Resist- 
ing 
Moment 

-^ 

Ft.-Lbi. 

Increase  of 
Af' for  Each 
Additional 

lin. 
Width 

of 
Plate. 

12  in. 

of 
Depth 

lin. 
Width 

of 
Plate. 

12  ins. 

of 
Depth 

(a)  Use  with  smaller  Flange  Angles.     Rivets,  %".    Two  H'  rivet-holes  de- 
ducted from  Each  Plate  for  A. 


12xH 

20.40 

24H 

iJ^ 

2.56 

62.72 

0.12 

30.72      52  270 

5  100 

40.0$t 

•x^ 

ao.60 

3.84 

94.56 

9.23 

46.06      78  800 

7700 

48.7- 

40.80 

« 

24?^ 

5.13 

126.97 

12.37 

61.56     106  810 

•lO  310 

48.5* 

51.00 

« 

24?i, 

0.41 

160.45 

16.55 

76.92     132  870 

12  960 

48.2- 

*xH 

61.20 

« 

25 

7.69 

192.25 

18.75 

92.28     160  210 

15  620 

48.0- 

(b)  Use  with  6x3i  and  6x4  Angles. 

Rivets.  Ji". 

TwoJ^' 

rivet-holes  de- 

ducted  from  Each  Plate  for  A. 

Itx^ 

33.15 

30^ 

30f^ 

4.22     129.24 

11.48 

50.64 
67.66 

107  700 

9  570 

39.2^ 

'x^ 

44.20 

30^ 

5.63     173.12 

15.37 

144  270 

12  810 

39.0* 

56.25 

m 

30K 

7.03     217.05 

19.30 

84.36 

180  880 

16  080 

38.9* 

"xT? 

66.30 

• 

31 

8.44     261.64 

23.26 

101.28 

218  030 

19  370 

38.7  • 

77.35 

a 

31 K 

9.84     306.27 

27.23 

118.06 

255  230 

22  700 

38.6- 

•xl 

88.40 

m 

31M 

11.25     351.56 

31.25 

135.00 

292  970 

26  040 

38.4- 

14x^ 

35.70 

30^ 

30H 

4.59     140.67 

11.48 

56.06 

117  140 

9570 

39.2^ 

•xli 

47.60 

30»^ 

6.18     188.50 

16.37 

73.66 

157  080 

12  810 

39.0- 

50.49 

• 

307^ 

7.66 

236.50 

19.30 

91.92 

197  090 

16  060 

38.9- 

•x»^ 

71.40 

« 

31 

9.19 

284.89 

23.26 

110.28 

237  410 

19  370 

38.7  - 

•x  H 

83.30 

• 

31 V^ 

10.72 

333.66 

27.23 

128.64 

278  050 

22  700 

38.6- 

•xl 

95.20 

< 

31M 

12.25 

382.81 

31.26 

147.00     319  010 

26  040 

38.4- 

(c)  Use  with  6x6  and 

8x8  Angles. 

Rivets.  H". 

Twol' 

rivet-holes  de- 

ducted  from  Each  Plate  for  A. 

nn 

47.60 

30^ 

2fH 

6.00     184.50 

16.37 

72.00 

163  750 

12  810 

30.0<^ 

50.50 

» 

^Vn 

7.50 

231.66 

19.30 

90.00 

192  970 

16  080 

38.9  - 

•x  *A 

71.42 

m 

31 

9.00 

279.00 

23.26 

108.00 

232  500 

19  370 

38.7" 

-X  H 

83.30 

* 

zi}4 

10.50 

326.81 

27.23 

126.00 

272  340 

22  700 

38.6  • 

•xl 

06.20 

» 

SiH 

12.00 

375.00 

31.25 

144.00 

312  500 

26  040 

38.4- 

15z  H 

•  X  H 

51.00 

30W 

210^^ 

6.50 

199.88 

15.37 

78.00 

166  560 

12  810 

39.0^ 

63.76 

30?1» 

8.13 

251.01 

19.30 

97.56 

209  180 

16  080 

38.9  - 

*  X  « 

76.50 

• 

31 

9.75 

302.26 

23.25 

117.00 

251  870 

19  370 

38.7  - 

•  X  ^ 

80.25 

« 

31H 

11.38 

851.20 

27.23 

136.56 

295  170 

22  700 

38.6  - 

•  xl 

102.00 

« 

31K 
31*^ 

13.00 

406.26 

31.25 

156.00 

338  540 

26  040 

38.4- 

•  xlH 

114.76 

» 

14.63 

459.02 

35.30 

176.56 

382  510 

29  410 

38.2- 

•xIH 

127.50 

m 

31^ 

16.25 

611.88 

39.37 

196.00 

426  560 

32  810 

38.1  • 

♦Percent  of  increase  is  same  as  for  column  11. 

t  Actual  increase  in  ft.-lbs.  —  10  000  A  (col.  5).     Digitized 


by  Google 


582   Zi— PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS. 

7. — Plate  Girdbrs  (Stbbl) — Concluded. 

Propbrtibs  of  Planob  Platbs  only. 

(See  Pig.  4.  page  £80.) 

Af' —moment  in  ft.-lbs. : 

Af'— moment  in  in  -lbs. 


1 

2 

8 

4 

5 

6 

7           8 

9 

10           U 

8 

II 

Size. 
Ins. 

|l 

a 

w 

Lbs. 

2  . 

D 
Ins. 

5 
P'o 

d 

Ins. 

Net 
Area 
Each 

Plate) 

A 
Sq.Ins 

n 

Ins. 

Increase  of 
S  for  Each 
Additional 

Resist- 
ing 
Moment 

Ft. -Lbs. 

Increase  of 
Af'forEadi 
Additional 

lin. 
Width 

of 
Plate. 

12  ins. 

of 
Depth 

*{D). 

lin. 
Width 

of 
Plate. 

12  ins, 

of 
Depth 

HD). 

(c)  Use  with  6x6  and  8x8  Angles.      Rivets.  %'.    Two  T  rivet-holes  de- 
ducted from  Each  Plate  for  A. 


16xH 

•xH 

54.40* 

30Vi 

^^ 

7.00 

215.25 

15.87 

84.00 

179  870 

12  810 

30.04 

68.00 

dOH 

8.75 

270.16 

19.30 

105.00 

1225  130 

16  080 

38.9" 

"  x% 

81.60 

31 

10.50 

325.50 

23.25 

126.00 

271  250 

19  870 

88.7" 

'xh 

95.20 

31 V^ 

12.25 

381.28 

27.23 

147.00 

317  730 

22  700 

88.6- 

-xl 

106.80 

31 'i 

14.00 

437.50 

81.25 

168.00 

364  580 

26  040 

38.4  • 

•xU^ 

122.40 

31^^ 

15.75 

494.16 

35.30 

189.00 

411  800 

29  410 

88.2* 

•xl^ 

136.00 

31H*  17.50 

551.25 

39.87 

210.00 

459  380 

82  810 

38.1- 

"xlH 

149.60 

31*8  19.25 

608.78 

43.48 

231  00 

507  320 

36  240 

87.9- 

163.20 

315i  21.00 

666.75 

47.62 

252.00 

555  630 

30  600 

37.8- 

ISxH 

•  xH 

61.20 

36K 

38^ 

8.00 

294.00 

18.37 

96.00 

245  000 

15  310 

32.7^ 

76.50 

36V« 

10.00 

368.75 

23.05 

120.00 

307  290 

19  210 

32.6- 

*  X  «4' 

91.80 

87 

12.00 

444.00 

27.75 

144.00 

370  000 

23  120 

52.4- 

•x7/„ 

107.10 

37H 

14.00 

519.75 

32.48 

168.00 

433  120 

27  070 

323- 

•^1     J 

122.40 

37^ 

16.00 

596.00 

37.25 

192.00 

496  670 

81040 

32.2- 

•xm 

137.70 

37^ 

18.00 

672.75 

42.05 

216.00  j 

560  620 

35  040 

32.1  - 

•  xl>i 

153.00 

37H 

20.00 

760.00 

46.87 

240.00 

625  000 

39  060 

82.0- 

•  xlH 

168.80 

* 

37»< 

22.00 

827.75 

51.73 

264.00 

689  790 

43  110 

31.9- 

-xl>^ 

183.60 

37>4 

24.00 

906.00 

56.62 

288.00 

755  000 

47  190 

31.8- 

*  Percent  of  increase  is  same  as  for  column  11. 
t  Actual  increase  in  ft.-lbs.  —  10000  A  (col.  5). 


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REINFORCED  CONCRETE  BEAMS.  585 

Reinlorcad  Concrato  Beams.— The  following  Working  Stresses  for  Static 
Loads  are  recommended  by  the  Special  Committee  of  the  Am.  Soc.  C.  B., 
on  Concrete  and  Reinforced  Concrete.  (See  Trans.  A.  S  C.  E.,  Vol.  LXVII., 
page  452. )  For  Notation  and  Formulas,  see  Sec.  25.  Masonry,  page  446.  For 
worldng  stresses  for  columns,  see  Sec.  32,  Columns,  page  909. 

Compressive  Strength  of  Stone  Concrete. — ^Average,  2000  lbs.  per  sq.  in. 
at  28  days,  when  tested  in  cylinders  8  ins  in  dia.  and  16  ins.  long,  under 
laboratory  conditions  of  manufacture  and  storage. 

Bearing. — 650  lbs.  per  sq.  in.  on  2000-lb.  concrete. 

Bending. — Compression  on  extreme  fiber  of  beam.  650  lbs.  per  sq.  in.  for 
aOOO-lb.  concrete;  adjacent  to  support  of  continuous  beiams,  750  lbs.  per  sq.  in. 

Pure  Shear. — When  uncombined  with  compression  normal  to  the  shear- 
ing surface,  and  with  all  tension  normal  to  the  shearing  plane  provided  for 
by  metal  reinforcement,  120 lbs.  per  sq.  in.  on  2000-lb.  concrete. 

Shear  with  Diagonal  Tension.— In  beams  without  diagonal  reinforcement, 
40  lbs.  per  sq.  in.  for  2000-lb.  concrete. 

Bond. — Between  concrete  and  plain  reinforcing  bars.  80  lbs.  per  sq.  in. 
for  2000-lb.  concrete;  between  concrete  and  drawn  wire.  40  lbs.  per  sq.  in. 

Reinforcement. — Tensile  stress  in  steel  shall  not  exceed  16000  lbs.  per 
sq.  in. 

EXCERPTS  AND  REFERENCES. 

Tests  off  Reinforced  Concrete  Beams  (By  W.  K.  Hatt.  Proc.  A.  S. 
T.  M.,  1002;  Eng.  News,  July  17,  1902).— This  is  a  very  complete  Paper 
and  contains  numerous  diagrams  and  tables  of  the  tests,  with  discussion 
of  same:  also  includes  Hatt  s  formula  for  reinforced  concrete  beams. 

Compiitiag  the  Strength  of  Reinforced  Concrete  B^ms  (By  Edwin 
Thacher.  Eng.  News,  Feb.  12,  1903). — Discussion  of  above.  "It  is  the 
practice  of  the  writer  to  give  the  concrete  a  certain  factor  of  safety  at  the 
end  Qf  one  month,  and  to  give  the  steel  the  same  factor  of  safety  as  the 
concrete  at  the  end  of  six  months,  as  it  is  evident  that  if  there  was  not  an 
excess  of  steel  in  one  month,  there  would  be  a  deficiency  after  the  concrete 
gained  its  full  strength.  For  example,  to  design  a  slab  of  length  /— 0  ft.. 
using  60000-lb.  steel,  for  a  total  load  w  of  400  lbs.  per  sq.  ft.,  that  shall 
have  a  factor  of  safety  of  4  in  one  month,  but  in  which  the  tensile  strength 
of  the  steel  shall  be  equal  to  the  compressive  strength  of  the  concrete  alter 
6  months: — ^Then,  the  distance  from  top  of  beam  to  center  of  reinforcement 

-J-  VAiz-s-SSS-  Vox 6X400-i- 883-  3.92  ins.;  or,  if  the  center  of  bars  is 
1.08  ins,  from  bottom  of  concrete,  the  total  height  /»— 3.92+ 1.08  —  5  ins., 
and  the  area  of  metal  for  I'  width  of  beam  — A— d-»-90-3.92-*-90— .0435 
sq.  in.  Using  Thacher  bars,  having  original  diam.  of  |  in.,  area  — .276, 
weight  per  ft. -.94  lb.,  dist.  c.  to  c.  bars-. 276 +.0435- 6.36  ins."  Gives 
tabtilated  formulas  for  calcxdating  rein.  cone,  beams  (£,—  30,000,000). 

Table  of  Tests  on  the  Union  Between  Concrete  and  Steel  (At  Mass. 
Inst.  Tech.  Eng.  News,  May  5.  1904). — ^Types  of  rods  used  in  the  tests 
were:  Thacher,  Ransome,  Johnson,  and  plain  rotmd  and  square  rods. 

Teste  of  Reinforced  Concrete  Beams  (By  Arthur  N.  Talbot.  Proc. 
A.  S.  T.  M.,  1904.  Eng.  News.  Aug.  11,  1904).— Tvpes  of  rods  used  in  the 
tests  were:  Thacher,  Ransome,  Johnson,  Kahn,  and  plain  rotmd  and  square 
rods.    Table  and  Diagrams. 

Teste  of  Reinforced  Concrete  Beams  and  IHoors  (At  St.  Louis  Expo- 
sition. By  R.  L.  Humphrey.  Eng.  News,  Sept.  21,  1905).— -Illustrated 
diagrams  of  beams  tested. 

The  Design  of  Reinforced  Concrete  Structures  (By  F.  W.  Keyser  and 
E  L.  Heidcnrcich;  and  C.  A.  P.  Turner). — Discussion. 

Notes  on  the  Stress-Deformation  Curve  in  Concrete  Beams  (By 
N.  Werenddold.    Eng.  News,  April  6,  1906.) — Diagrams  and  formulas. 

Economic  Desifn  off  Reinforced  Concrete  (By  F.  W.  Hanna.  Eng. 
News,  Feb.  21,  1907).— Gives  a  table  of  the  economical  working  stresses 
and  percentages  of  steel  reinforcement  for  varying  relative  costs  of  steel 
and  concrete — calculated  for  imit  compressive  working  stress  in  outer  fiber 
of  concrete -600  lbs.  per  sq.  in.,  and  forf-E.-i-£,-10.  ^-fSee.  also,  Eng. 
News,  June  20.  1907.)  DgtizedbyV^OOglC 


586  Zl—PROPERTIES  AND  TABLES  OF  BEAMS  AND  GIRDERS, 

Dlacnm   for   Proportioniof   Reinforced   Coocrete   Beami  (By  A.  H. 

Perkins.  Eng.  News,  April  26,  1007). — It  is  a  compound  diagram,  com- 
prising (1)  a  set  of  lines  giving  the  bending  moment  in  a  simple  beam  for 
any  span  and  any  load  per  foot  of  length  and  per  inch  of  width;  ^2)  a  set 
of  lines  giving  the  corresponding  values  of  breadth  and  depth  of  remforced 
concrete  beam  to  resist  this  moment.  This  latter  part  oi  the  diagram  is 
based  on  the  following  imit  values: — Max.  comp.  in  concrete  c  — oOO  lbs. 
per  sq.  in.;  tension  in  steel  5  —  12,000  lbs.  per  sq.  in.;  Es-t-Ecn^  10; 
percentage  of  steel  ^"•0.95%:  moment  capacity  of  beam  b  inches  wide 
and  d  inches  deep  — M  — 100  bd*.  The  stress-strain  curve  of  concrete  is 
assimied  to  be  between  the  straight  line  and  the  parabola.  (See,  alao.Tiech- 
man's  formula  and  diagrams  in  Eng.  News,  July  11,  1007.) 

Reinforced  Concrete  T-Beam  and  Cdomn  Teste  (At  Univ.  of  HL 
By  A.  N.  Talbot.  Bulletins  Nos.  10  and  12  of  the  Eng.  Exper.  Station, 
Univ.  of  111.;  Eng.  News,  July  11, 1907). — ^Diagrams  of  beams  and  columns 
tested,  and  tablet  of  tests. 

Teste  of  Adhesion  of  Steel  to  G>ncrete  in  Beanu  (By  L.  J.  Johnson. 
Jl.  of  Assn.  of  Eng.  Soc.  for  June,  1007;  Eng.  News.  Aug.  15, 1007) .—Tables 
and  distgrams. 

Effect  of  Time  Element  in  Loading    Reinforced    Concrete    Beams  (By 

W.  K.  Hatt.  Proc.  A.  S.  T.  M.,  1007;  Eng.  News,  Oct.  24.  1007).— Tables 
and  diagrams. 

Section  Modulus  Diagram  for  Plate    and    Lattice    Qirders   (By  L.  R. 

Shellenbergcr.  Eng.  News,  Nov.  26,  1908). — ^The  diagram  is  for  flange 
angles  6'x  6';  and  for  section  moduli  up  to  3400  ins.,  and  depth  of  web  up 
to  85  ins. 

Teste  of  Standard  I  Beams  jindSptclal  I  Beams  and  Qirder  Beams  (Br 


Edgar  Marbui«.     Proc.  A.  S.  T.  M.,  Vol.  IX..  1000;  Eng.  News,  Aug.  1 
1009). — Illustrations,  diagrams  and  tables.    (Generally  speaking,  the  modu- 
lus of  rupttire  in  lbs.  per  so.  in.  decreases  as  the  depth  of  the  giroer  increases. 
In  actual  practice,  however,  the  beams  would  be  supported  laterally,  at 
intervals,  which  might  affect  the  comparative  results  of  the  experiments. 


Momente  in  Continuous  Concrete  Beams  Under  Uniform  Loading  (By 

R.  E.  Spaulding.     Eng.  News,  Sept.  30,  1900). — Numerous  formulas  and 
diagrams. 

Slide-Rule  for  Reinforced-Concrete  Slabs  (By  A.  W.  French.  Eng. 
News,  Feb.  3,  1910).— Illustrated. 

Table  of  Momente  of  Inertia  of  Flat  Rectangles  (By  H.  Loewenhem- 
Enc.  News.  Feb.  24.  1010). — For  widths  6  (advancing  by  one  inch  from  6  to 
40  ins.)  and  depths  d  (advancing  by  sixteenths  of  an  inch  from  ^  to  3  inches). 

Some  Deductions  from  Warburg's  I-Beam  Teste  (By  C.  J.  Tilden.  Eng. 
News,  Feb.  24,  1910). — With  discussion  by  Edgar  Marburg. 

ComiMirison  of  Methods  of  Computing  the  Strength  of  Flat  Reinforced 
Concrete  Plates  (By  A.  B.  MacMillan.  Paper.  Natl.  Assn.  Cement  Uaen, 
Feb.  21-25,  1910;  Eng.  News,  Mar.  31.  1910).— Illustrated.  Discussions: 
Cantilever  method;  Tumeatire  and  Maurer  method;  Grashof's  Analysis; 
Mensch's  method;  Turner's  method;  Macmillan  method;  Mushroom  floor. 

Interesting  Illustrations. 

Description.  Eng.  Rec 

Diagrams  for  reinforccd-concrete  beams. — Schermerhom  Mar.    6,  "09 

Diagrams  for  disigning  reinforced-concrete  beams — Carter  June  18,  '10 

Instruction  sheet  for  placing  floor  reinforcement  June  25,  '  10 


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32.— PROPERTIES   AND    TABLES    OF 
COLUMNS. 

Qencral  Streatef. — A  column  is  a  pillar  or  strut  acting  mainly  in  com- 
pression; but  in  addition  to  the  direct  compressive  stress,  it  has  also  to 
resist,  to  a  greater  or  less  extent,  shearing  and  bending.  To  what  degree 
the  shearing  stresses  enter  into  and  afiFect  a  column  we  are  unable  to 
say.  and  no  coltimn  formula  has  yet  been  devised  which  includes  the  shear- 
ing effect  of  the  stresses.  Indeed,  omitting  the  effect  of  shear  altogether, 
it  18  a  mooted  question  whether  we  are  able  even  to  combine  rationaUy  in  a 
tingle  formula  the  effects  of  direct  compression  and  bending. 

SlwarifiK  Effect. — Although  the  effect  of  shear  is  seldom  noticeable  in  an 
ordinary  commn,  yet  it  becomes  quite  apparent  in  a  short  block  or  cube  of 
itone.  cement,  or  other  granular  material  when  tested  in  compression. 
The  sides  of  the  block  flake  away,  often  leaving  the  broken  specimen  like  a 
blattered  pyramid  or  cone.  The  same  shearing  stresses  which  rupture  the 
block  of  stone  are  undoubtedly  present  in  complex  form  in  any  column, 
but  otxr  means  of  analjrsis  are  hmited.  If,  insteaiid  of  the  stone,  we  select  a 
short  block  of  wood,  with  the  grain  in  the  direction  of  the  pressure,  the 
shearing  will  be  along  the  grain,  or  planes  of  least  resistance,  although  the 
tendency  to  shear  will  be  along  sloping,  pyramidal  planes. 

If,  now,  a  sheet  of  lead  is  interposed  between  the     f^M^j^^^^y^^^^^^y/^y/^^^^ 
stone  cube  and  one  of  the  platforms  of  the  testing  t«77/7W7rl  *-*^ 

madiine  the  flaking  of  the  stone  will  be  more  pro- 
nounced, due  to  the  spreading  or  lateral  expansion 
of  the  lead  as  it  is  flattened  against  the  stone.*  This 
illustrates  in  an  exaggerated  way  how  the  material  in 
any  coltimn  tends  to  spread  out  under  pressure,  and 
wMken  the  resistance  to  shear. 

Notation  for  Colmnn  Formulas: 

A  ->area  of  column  section,  in  sq.  ins.; 

/"  moment  of  inertia  of  section  in  ins.  —  i4r^[^ 

f— radius  of  gyration  of  section  in  ins.  =-  v7"+i4 ; 

tif*- least  diam.  of  rectangular  section,  in  ins.; 

(^"•diameter  of  round  column,  in  ins.; 

P» total  load  on  coltunn,  in  lbs.: 

^»load  per  sq.  in.  on  column  — P+A* 

y* distance,  in  ins.,  of  most  strained  nber,  from  neutral  axis; 

p  — lateral  deflection  of  column  in  ins.,  tmder  load  P; 

e  — eccentricity  of  loading  on  columns,  in  ins.; 

/c —compressive  stress  in  lbs.  per  sq.  in.  —  P-^A  —  p\ 

/b— bending  stress,  outer  fiber,  in  lbs.  per  sq.  in.  —  Pto'+/— /try +'"': 

/  —  max.  outer  fiber  stress,  comp.  + bending,  in  lbs.  per  sq.  m.  -/c+Zb; 

/e  — /  at  the  elastic  limit  of  the  material; 

fu  — /  at  the  ultimate  strength  of  the  material; 

P  — /  at  any  assignable  value,  for  distinction; 

£  — modulus  of  elasticity  of  material,  in  lbs.  per  sq.  in.; 

/—effective  length  of  column,  in  inches 

/.  —  effective  length  of  column,  in  feet; 

-.„,,,           1    r     ,             t                ««*  ^  *'*      ^^  ^  »■* 
a — value  of  p  in  Buler  s  formula  for  long  columns  — ^ —  —    .^  ,,  : 

In  which  «  —  1   for  2  pivot  ends  —  established  by  Eulcr, 

M— Vifor  2  pin  ends     —  established  by  Johnson, 
M  — V  for  I  pivot,  1  fixed  —  established  by  Euler, 
«  — If  for  1  pin,  1  flat        —  established  by  Johnson. 
>!—»/,  for  2  flat  ends  —  established  by  Johnson, 

»  — 4  for  2  fi*ed  ends       —  established  by  Euler. 

*  For  this  reason  sheets  of  lead  or  other  soft  material  are  now  considered 
objectionable  in  testing  machines;  and,  by  some,  on  masonry  abutments 
unider  bridge  shoes  or  pedestals.  Digitized  by  vjOOQLC 


588 


Zi.^PROPERTIES  AND  TABLES  OF  COLUM 


Short  Scrot— Direct  Conprestioa  Only.— By  a  short  strut 
irhoae  length  is  not  over,  say,  12  or  15  times  its  diameter  or  lo 
For  siicb  a  colunm  we  have  the  formula: 

'-^ 


Whence  P'^fA  and  A'^-r. 


.Short  Stnrt — Ecccotric  Loadiaf — ^The  usual  formula  for  t 
stress  /  in  a  short  column  eccentrically  loaded,  is 


A^     I        AV^  f*) 


it  being  assumed  that  the  column  is  braced  laterally,  as  ii 
building,  against  falling  over;  and  furthermore  that  there  is 
appreciable  lateral  deflection  v.  If  lateral  deflection  were  a 
taken  into  account  we  would  have 


Long  Columns — Bendinf  Only. — ^The  following  formulas 
end  conditions  of  long   columns,    bending   only,    are   adapt 
from  Euler  and  T.  H.  Johnson. 

EuUt's  Formulas: 

P     "l44L« 


3  Pivot  Ends 


1  Pivot, 
1  Fixed 


2  Fixed  Ends 


2  Pin  Ends 
O  O 

1  Pin,  1  Flat 

O  O 

2  Flat  Ends 

D  Q 


P- 

P" 
P 


P 

l^fEI 
9P 

l^fEr* 
9P 

P 
4x*£r« 


-(T)-G-iT)*- 


n*EI 
'  81  L» 


-m'^-i^y^ 


T*EI 
36L» 


Johnson's  Formulas: 
5r*El     5i^El 
ZP  "432L« 


-Hiy^-MtY' 


p  -- 


3/3 

2bri^EI    25r*EI 
12P    "l728L« 

25s*Er2     25/>rf\« 


12P 


25/»rf\«  25    />rr\» 

i2\l)  ^^im\L)  ^ 


2P    "288L« 


.       5^Er*     5  /7tr\*-       5    /irr\  « 


O    4 


It;  iv 


•    1 

Fig. 


O 


O 
Pig 


COLUMN  FORMULAS. 


589 


There  is  one  peculiar  feature  about  the  preceding  formulas,  namely,  that 
they  do  not  taice  into  consideration  the  compressive  (nor  the  shearing) 
r»istance  of  the  material,  but  simply  the  bending  resistance  or  stiffness  of 
the  column.  Hence  they  give  excessive  values  for  the  loads  P  or  p.  Euler 
attempted  to  remedy  this  defect  by  placing  an  upper  limit  to  the  value  of  f , 
eqtial  to  the  compressive  resistance  ;.  of  the  material.  This  is  illustrated  in 
Pig.  5,  a  diagram  showing  the  (elastic)  strength  of  steel  columns  with 
pivoted  ends. 


Values  of  f . 

Pig.  5. 

Ritter's  Formula  for  Colmnns. — ^The  following  formula  was  proposed  by 
Rioter  in  1878  and  has  been  worked  out  by  others  later.  Although  very 
^^igenious  and  possessing  considerable  merit  the  reasoning  by  which  it  is 
'^uced  is  not  considered  strictly  rational  and  it  takes  its  place  with  all 
other  formulas  in  this  respect.  The  equation  of  the  elastic  strength  of 
cohuDns  is      • 


^-J- 


fe 


fe 


1  + 


na 


.(11) 


^  curve  of  this  formula,  for  pivoted  ends,   is  platted  in  Pig.   5.    The 
°Kthod  of  applying  a  factor  of  safety  to  formula  (11)  is 

P ^7 (12) 

na 
^  which  /  is  considered  to  be  the  working  stress  of  the  material,  and  f  any 
value  between  the  working  stress  and  the  ultimate  stress.  It  is  to  be  noted 
^  with  /  constant,  the  factor  of  safety  increases  as  f^  increases,  but  not 
proportionately.  Strictly  speaking,  the  formula  applies  only  Vithin  the 
«la^  Hmit  of  the  material,  i.  e.,  when  f  (and  /)  do  not  exceed  fe.  The 
^'ahie  of  f  should  be  above  any  possible  value  of  /,  and  should  always  be 
Plater  than  2/  for  maximum  static  loading,  or  its  equivalent.  Again,  with 
'  ^/  the  factor  of  safety  is  greater  for  long  columns  than  for  short. 


500  dZ.—PROPERTIES  AND  TABLES  OF  COLUMNS. 

P     Pw 
Author's  Formula  forColuinns. — From  mechanics,  f— /c  +/*>="  T"*"/" 


p(l+^)  ,  whenco 


'"^"Tfe "' 

Again,  the  bending  moment  at  center  o£  column  is 

Af-Pto (14) 

But  according  to  Euler.  P  —  — ^ — ,  whence  (14)  reduces  to 

M       MP  ,,_ 

'^-p-^T^TE/ (^« 

Substituting  this  value  of  v  in  equation  (13)  we  have 

From  the  theory  of  flexure,  we  have, 

M  =  j;fl,'^(f-h)-j{f-^)'j;U-P) (17) 

Whence,  by  substitution,  equation  (16)  reduces  to 

na       \       naf      na 

So  far,  our  reasoning:  seems  to  be  correct,  but  when  we  attempt  to 

solve  equation   (18)  we  nnd  that  p^j  or  na.     Prom  an  examination  of  the 

last  form  of  equation  (18)  it  will  be  seen  that  the  first  term  p,  equal  to  the 

load  per  sq.  in.  on  column,  would  be  decreased  by  substituting  unity  for 

the  quantity  (  1  —  — )  in  the  denominator,  and  hence  would  be  on  the  side  of 

safety.  Moreover,  it  would  reduce  to  Fitter's  formula  (12),  by  making  f—/; 

thus,  p  —  — —r" '    ^^*  irom  the  above  discussion,  we  are  certain  that,  for  any 

na 

column  of  given  length  I,  p<  na,  and  (l~-^)  <  unity.    Assuming  tents- 

tively  the  value  of  Rittcr,  p— j-,  in  order  to  arrive  at  an  approximate 

na 


value  of  (  1 — —\  in  the  second  form  of  equation   (18),  we  have  p  +  —  «/; 

whence,  by  transpos 
equation  (18)  gives 


fPPP 
whence,  by  transposition,  p— / ,  or  1 ="t5  *^*^  ^^^  substituted  in 

na  na     j  \ 

"-jfr <»» 

/      na 
This  reduces  still  further  to 

p=-/  (sec  5-tan  6) (20) 

the  desired  formula;  in  which  tan  <?•■  o — ' 

In  using  formula  (20).  find 
Ist.     The  value  of  \/tan  6,  from  Table  1,  on  the  following  page, 
2nd.   The  corresponding  value  of  sec  tf— tan  6,  from  Table  2. 
3rd.    Mviltiply  this  last  value  by  /  to  obtain  the  allowable  load  pperaq. . 

on  column;   /  being  the  allowable  working  stress  per  8q\iarein< 

for  a  short  column. 

g^.^""8-;by  the  use  of  Tables  1  and  2,  the  value  (sec.  tf-tan  B)  in  equati 
u;  call  be  transformed  into  a  numerical  quantity,  orvdecimal  factor.  S 
xamples.  page  «B.  ^         ized  byCoOglC 


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592 


Si.— PROPERTIES  AND  TABLES  OF  COLUMNS. 


2. — Values  op  (Sec  5-tan  0)  in  Column  Formula,  Equation(20) 
For  Successivb  Values  op  Vtan  d.  Table  1. 
[Values  of  Vtan  d  may  be  derived  from  Table  1.] 


> 


0.50 


1.000 
.990 
.961 
.914 
.853 
.781 


*c2 


.010 
.029 
.047 
.061 
.072 


0.50 
0.60 
0.70 
0.80 
0.90 
1.00 


.781 
.703 
.624 
.547 
.477 
.414 


1.00 
1.10 
1.20 
1.30 
1.40 
1.50 


f 


.414 
.360 
.313 
.274 
.240 
.212 


^1 


.054 
.047 
OSO 
.034 
.028 


1.50 
1.60 
1.70 
1.80 
1.90 
2.00 


.212 

.18^ 

.16 

.1511 

.130 

.123 


.024 
.090 
.017 
.015 
.013 


Examples  in  the  Use  op  Tables    1  and  2. 
[From  Column  Ponnula,  p=-f  {sec  d-tam  6),  equation  (20).] 

Ex.  1. — Find  the  safe  load,  factor  4,  of  a  medium-steel  z-bar  column 
with  fiat  ends,  whose  length  is  26  ft.,  sectional  area  24.8  sq.  ins.,  and  radius 
of  gyration  2.6. 

Solution.— From  Table  1,  Vtan  ^-.058  — -.58;   and  from  Table  2,  the 
,  f 

corresponding  value  of  (sec  0— tan  9)«.72:    hence  the  safe  woridng  load 

f-.72x  15  000»  10.800  lbs.  per  sq.  in.,  and  the  total  safe  load- 10  800  X 
4.8-267  840  lbs. 

Ex.  2. — Find  the  safe  load,  factor  5,  of  a  vertical  post  of  Douglas  spruce 
in  a  Pratt  steel  combination  highway  bridge,  said  post  being  12  X  14  ins., 
28  ft.  long,  and  with  pin  end  bearings. 

Solution. — ^The  value  of  /  for  Douglas  spruce  (col.  4,  Table  7,  page  495) 
is  1400.  From  Table  1.  Vtan  <?- A  •  f?  =.933;  and  from  Table  2.  the  cor- 
resix>nding  value  of  (sec  <7— tan  0)  is  .456;  hence  total  allowable  load 
P-.456X  1400X12X14- 107  251  lbs.    (See  also  Table  3.) 

Ex.  3. — What  load  would  be  carried  by  a  column  similar  to  that  in 
Ex.  2,  but  with  flat  ends? 

Solution.— Table  1:  t^  •  If  -.747;  Table -2  equivalent -.588;  hence 
P-.588X  1400X  12X  14-  138  298  lbs. 


Gordon's  Formula  for  Columns. — Probably  no  other  formula  has  been 
so  universallv  accepted  as  that  of  Gordon — sometimes  called  Ranldne's 
formula.  Adopting  the  previous  notation,  it  is  deduced  as  follows:  The 
maximum  outer  fiber  stress  due  to  both  compression  and^nding  is 


whence 


'-^^M^-^) ••••<"' 


j'P- 


1+ 


vy 


(22) 


Now  the  deflection  v  of  the  column  is  an  unknown  quantity,  but  Gordon 

assumed  it  to  be  proportional  to  — ,  which  assumption  would  be  allowable 

if  the  total  fiber  stress  f  were  due  to  bending  only.  Substituting  this  iMt)por- 
tional  equiA^ent  of  i;  in  equation  (21)  and  supplying  the  coefficient  c  whose 
value  IS  to  be  determined  by  experiment,  we  have  the  general  form: 

p — ^- (»» 


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CORDON'S  FORMULA.   STRAIGHT-UNE  FORMULA.       603 

For  the  working  formula,  the  value  aasigned  to  f  is  usually  the  ultimate 
strength  per  sq.  in.  of  a  short  column  of  the  material,  divided  bv  factor  of 
safet^r,  as  4,  6,  6,  etc.  The  coefficient  c  is  an  arbitrary  constant  determined 
bv  trials  in  fitting  the  curves  of  the  formula  to  plattings  from  actual  tests 
of  strengths  of  columns  up  to  the  points  of  failure,  and  making  /  ■■  ult. 
strength -(-factor  of  safety.  (See  Sees-  on  Bridges  and  Buiidings  tot  special 
application  of  Gordon's  formula;  also  the  tables  following  under  this 
•ection.) 

C.  Shaler  Smith's  Pormula  for  Wooden  Columns. — This  formula  gives 
values  much  too  low  for  long  colucms.  It  is  reproduced  here  more  for  its 
historical,  than  for  iU  actual  working  value.     The  formula  is  as  foUows: 


P" 


f 


i+.oo4^; 


(24) 


the  ultimate  strength  of  white  pine  being  assumed  at  /,—  5000.    The  ends 
of  the  column  are  to  be  fiat  and  firmly  fixed;  with  concentric  loading. 

Straight-Line  FormnUs. — Curved-line  formulas,  previously  explained, 
may  be  reduced  to  straight-line  formulas  by  finding  the  equation  of  the 
tangent  to  the  ctu^e  at  the  point  of  contra-flexure.  Thus,  in  Pig.  5,  page  589, 
c  is  the  point  of  contra-fiexure  of  the  curve,  and  its  tangent  at  that  point  cuts 
the  coordinate  axes  of  the  diagram  at  T  and  t;  the  resulting  stiaight-line 
formula  for  the  elastic  strength  of  the  steel  coltunn  with  pivot  ends  thus 
reducing  to 


#'-85  400-169-^ 


(25) 

in  which  35  400-1.18 /e- 1.18X30  000;  £  being  assumed  at  80  000  000  in 
the  present  instance.  If  now  this  tangent  is  swimg  slightly  on  the  point  c 
so  that  the  point  T  is  lowered  to  34  000.  it  will  practically  fit  the  curve  for 
a  long  distance,  with  the  resulting  equation 


p- 34  000- 150-^ 


(26) 


Straioht-Linb  Formulas  for  Stbbl  and  Wrought  Iron  Ck>LUicNS. 
(Reduced  from  data  in  Tables  1  and  2.) 


Material. 

Ulti. 

mate 

Stren'th 

Elastic 

Limit. 

/e 

Elastic  Strength  of  Column. 
Pounds  per  sq.  in. 

Pm  Ends. 

Pin  &  Flat. 

Flat  Ends. 

Wrought  iron — 

Soft  steel 

Medium  steel.. . . 
Hard  steel 

AdOOO 
50000 
60000 
70000 

25000 
30000 
35000 
40000 

28500-  05y 
35000-130- 
41000-160^ 
46500- 185y 

28500-  85-^ 
35000-115-^ 
41000-145^ 
46500-170^ 

28500-  75^ 
35000- 100^ 
41000-130^ 
46500-155-^ 

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M« 


22.— PROPERTIES  AND  TABLES  OF  COLUMNS. 


Stcd  Cdiioinfl. — Prom  the  pracediog  discuMion  of  Column  Pon 
might  readily  conclude  that,  tor  a  column  of  given  sectional  are 
length  /,  that  column  is  the  strongest  which  has  the  greatest  r 
fl[yration  r.  But  this  is  not  always  true.  To  illustrate:  On  p 
Fig.  20,  we  find  the  properties  of  the  Hollow  Circle,  of  outside  dii 

and  inside  diameter  </»,  giving  r  ■• -g — ^  and  A  ■•0.7834  {jP'^dt 

if  we  let  A  remain  constant  and  gradually  increase  <^from  sere 
until  it  approach  d,  which  must  also  gradually  increase,  out  less  ra 
then  r  likewise  increases  in  value  from  r  —0.25  d  (when  the  column  i 
circular  cylinder)  up  to  its  maximum  limit  r»0.3535  d  (when  tlu 
becomes  a  cylindrical  shell  whose  thickness  approaches  zero), 
quite  apparent  that  before  the  maximum  limit  of  r  is  reached,  tt 
column  will  fail  through  auxiliary  OT  stcondary  stT€ss«St  sitt  up  in 
metal  shell,  causing  it  to  buckle  and  collapse. 

The  Secondary  Stresses,  above  described,  may  be  provided  ag 
either  (1)  Making  the  metal  thick  enough,  tnroughout,  to  withstai 

(2)  Providing  longitudinal  ribs,  as  in  the  case  with  the  Phoenix  col 
Table  11.   page  004)  and    other    standard  built-up   columns,    in 

(3)  Inserting  (transverse)  diaphrams  at  intervals  along  the  colu 
aone  with  very  large  sections. 

Where  Columns  are  Latticed,  or  where  stay-plates  are  simply 
independent  (unsupported)  portion  should  be  calculated  as  a 
column  with  its  own  radius  of  gyration. 

Column  Sections  may  be  made  up  as  follows: — 
(A).  — ^Two  angles  riveted  back  to  back,  forming  a  T-«ection, 
(Aa). — Same  as  (A),  but  with  round  fillers  or  a  plate  riveted  bet 

angles,  giving  a  greater  radius  of  gyration. 
(B).  — Pour  anKies  and  a  web  plate,  forming  an  H-section,  simil 

rolled  H -Column  of  Table  14.  page  606.    The  distance  bac 

of  angles  should  be  in  whole  or  half  inches,  and  from 

greater  than  width  of  web  plate. 
(Ba). — Same  as  (B).  but  with  the  addition  of  two  channels  rivet 

backs  of  the  angles,  with  flanges  of  channels  projecting  in 
(Bb). — Same  as  (B).  but  with  lattice  bars  instead  of  web  plate. 
(C).  — ^Two  channels  and  two  plates,  as  per  Fig.  6,  below.    See  al 

8.  9,  and  10.  pages  661,  etc. 
(Ca). — Same  as  (C).  but  with  latticing  instead  of  plates — one  or  bol 
(Cb). — Same  as  (C).  but  with  flanges  of  channels  projecting  in\i 

latticing  or  stay  plates  instead  of  cover  plates. 
(D).  — Same  as  (C).  (Ca)  and  (Cb),  but  with  plate  and  two  azigl< 

of  channel. 
(E).  — Z-bar  column.    See  Tables  6  and  7,  pages  898.  etc 
Also  other  sections  made  up  of  a  combination  of  these  shapes. 

To  find  the  movement  of  inertia,  /,  and  the  radius  of  gyration, 
column  section,  see  Example,  page  627,  in  connection  with  Tables  2 
pages  639,  etc. 

The  Channel  Column,  Pig.  6,  is  standard  for  all  classes  of  con: 
The  following  table  gives  the  standard  dimensions: 

4. — Channel  Columns — Standard  Dimensions  in  Inchbj 


Depth  of 

Width  of 

Channel 
C 

Plate 
P 

W 

R 

W-\-R 

E 

,ff*-r 

15 

18 

5H 

\H 

7H 

IH 

•^ 

1 

15 

16 

4>4 

l?i 

6>i 

^H 

1 

12 

16 

6 

IH 

t^ 

^^ 

1 

12 

14 

4 

IH 

IH 

^ 

10 

14 

4Vi 

\\i 

5^ 

IvH 

1 

10 

12 
12 
10 

1^ 

M 

i 

0 
0 

i^......p. 

8 
8 

^ 

2l^ 

1^ 

1^ 

Fig. 

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STEEL  Z-BAR  COLUMNS. 


699 


— ^ToTAL  Sapb  Load  in  Thousand  Pounds  fob  Z-Bar  i^LUMNs 
(Without  Sidb  Platbs.) 
/» thickness  of  metal; 
4 -area  of  cross-section  of  column; 

v<- weight  of  column  in  lbs.  per  lin.  ft.,  not  including  weight  of  rivets; 
r- least  radius  of  gyration. 

Allowable  stresses  i 
sq.  in.:  safety  factor  4 


on. 

I  p^  (- 12.000  lbs.  for  lengths  of  90  radii  or  under: 

or  4: 1 17.100-  67— for  lengths  over  90  radii. 


(See  opposite  page  for  Dimennons.) 


*   A 

fi;* 

r 

Length  of  Columns  in  Feet. 

'^t. 

Lbs. 

rMin'. 

12 

14 

18 

22 

26 

30 

34 

38 

42 

46 

50 

K|9.31 
A  11.7 

81.7 

1.86 

111 

111 

98 

84 

70 

67 

6 -in.  Col. 
For  columns 
leas  than  12 
ft.  long  use 

gven    loads 
rl2ft. 

nal  metal    from 
imns  tends  to  In- 
i  of  gyration  of 
ce  the  resulting 
nal  area  by  add- 
etal  will  allow  a 
rease  In  the  tab- 
u   But  see  next 
with  side  plates. 

99.^ 

1.90 

141 

141 

125 

103 

91 

74 

H  I3.e 

40.2 

1.88 

168 

163 

143 

124 

104 

84 

A  16C 

54. S 

1.98 

192 

192 

171 

149 

128 

103 

H  n.t 

50.t 

1.90 

211 

211 

187 

162 

136 

111 

A  20.0 

67.9 

1.95 

240 

240 

216 

188 

160 

132 

H  "3 

38.2 

2.47 

i|fl 

135 

124 

111 

99 

86 

74 

A  14.1 

48.1 

2.52 

170 

167 

142 

127 

111 

96 

B.~Addltlo 
%teB  on  ooli 
the  radlui 
ctlon;  hen 
se  In  secUo 
e-plate  m 
tlonatelnc 
safe  loadf 
)r  columns 

H  17.1 

58.0 

2.67 

205 

192 

174 

165 

137 

119 

A39.C 

64.7 

2.40 

■^fc-l^ 

228 

211 

190 

169 

148 

127 

H  21  fl 

74.4 

2.55 

262 

245 

221 

198 

174 

151 

S248 

84.1 

2.60 

297 

280 

254 

228 

202 

176 

f5?«-3 

89.2 

2.62 

315 

292 

264 

235 

207 

179 

III 

H^O 
H  31.9 

98.fi 

2.58 

349 

327 

296 

265 

235 

204 

106.4 

2.68 

382 

363 

329 

296 

263 

230 

A  15  8 

H$9.Q 

63.7 

3.06 

«l   ! 

189 

179 

165 

151 

137 

123 

108 

94 

^i 

3.13 

228 

217 

200 

184 

167 

161 

134 

117 

A  22  2 

76.8 

3.18 

|8     ' 

268 

267 

237 

218 

199 

180 

161 

141 

H  24. £ 

83.S 

3.10 

294 

278 

257 

236 

214 

192 

170 

149 

A  27  1 

94.2 
105  2 

3.16 
8.21 

832 
871 

317 
357 

293 
881 

269 
805 

246 

278 

221 
262 

197 
225 

173 

H  39.S 

199 

H^.7 

lll.C 

3.13 

392 

373 

344 

316 

287 

269 

230 

202 

121. « 

3.18 

430 

412 

382 

a5i 

320 

289 

258 

228 

132.6 

3.25 

^i    la 

468 

453 

420 

388 

365 

322 

289 

266 

nkj 

72.7 
85.2 
97.8 
106.2 
118.6 
130.9 
137.8 
149.9 
162.1 

3.67 
3.72 

r?s 

3.75 
3.73 
3.68 
3.66 
3.64 

257 
301 
345 
375 
418 
462 
486 
529 

m 

246 
290 
335 
360 
405 
447 
466 
506 
646 

230 
272 
314 
337 
380 
418 
436 
473 
610 

214 
263 
294 
314 
354 
390 
406 
440 
476 

198 
236 
273 
291 
829 
362 
376 
407 
489 

182 
217 
252 
268 
303 
334 
346 
374 
403 

166 

198 

{5  ^   Q 

281 

A  m  2 

?46 

n  ni'e 

?78 

U  m'fi 

806 

n  Fja  e 

816 

ipi 

841 

867 

*Add  weight  of  rivet  heads. 


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600 


Si.—PROPERTIES  AND  TABLES  OF  COLUMNS. 


Fig.  8. 


7. — Carnboib  14-inch  Z-Bar  Columns. 
With  Side  Platbs. 
Note. — Diameter  of  Bolt  in  Rivet.  K  in. 
For  notation,  A,w,r, safety  factor,  working  formula, 
etc.,  see  top  of  page  1044. 

For  increase  of  safe  load  over  tabulated  values,  the 
area  A  may  be  increased  proportionately  by  increasiiig 
metal  in  side  plates.       ^ 


Dimensions  and  Properties 

1 

Safe  Load  in  Thousand  Pounds. 

Two 
Side 
Pl'ts 

Dim'n's    A 

w* 

w3 

Length  of  Column  in  Feet. 

A 

B    Ins. 

Lbs. 

B 

26t 

28 

80 

34 

88 

42 

46 

60 

14xH 

.S.S 

19A 

6|i49.0 

166.6 

8.80 

688 

688 

578 

638 

608 

467 

4JB 

897 

14x,V 

14xH 

19tt 

6IS50.8 
0|i52.6 

172.6 

3.81 

609 

609 

604 

568 

621 

486 

449 

412 

?? 

19^ 

178.6 

3.82 

030 

630 

616 

678 

640 

603 

465 

427 

14xA 

^. 

{Kl 

7^54.3 

184.5 

3.82 

661 

651 

637 

698 

660 

620 

481 

443 

14xii 

7A66.0 

190.4 

3.83 

672 

672 

658 

618 

678 

638 

498 

468 

14xH 

II 

20tV 

20H 

7A57.8 

196.4 

3.84 

608 

603 

679 

638 

607 

666 

614 

473 

14xfdL 

7i^,l69.5 

202.3 

3.86 

714 

714 

700 

658 

616 

673 

630 

48S 

14x4 

^1 

20^ 

7^*61.3 

2X»A 

3.85 

735 

735 

721 

677 

634 

600 

647 

603 

14xJ^ 

•^r-4 

7i|63.0 

214.2 

3.86 

766 

756 

742 

697 

662 

608 

668 

51S 

14xH 

i»A 

65^*51 .0 
6452.8 

6kS4.5 

173.4 

3.76 

612 

612 

603 

1b6 

619 

482 

446 

W 

u 

.ss 

19k 

179.4 

3.76 

633 

633 

614 

676 

638 

490 

461 

423 

186.3 

3.77 

664 

654 

636 

596 

667 

617 

477 

438 

14xA 

SJ 

195i 

o4 

56.3 

191.4 

3.78 

676 

675 

657 

616 

675 

635 

404 

45S 

14x& 

194 

7 

68.0 

197.2 

3.79 

696 

606 

678 

686 

604 

552 

610 

466 

14xH 

19^ 

?)^. 

59.8 

203.2 

3.80 

717 

717 

699 

656 

613 

670 

627 

4S4 

14xC 

14x4 
14x^ 

20 

61.5 

209.1 

3.80 

738 

738 

720 

676 

681 

687 

643 

499 

^ 

7A 

63.3 

216.1 

3.81 

750 

769 

741 

696 

650 

606 

660 

614 

"••-H 

7>4 

65.0 

221.0 

3.82 

780 

780 

762 

716 

609 

622 

576 

629 

14xH 

.si 

1! 

\t^ 

6|i 

54.6 

185.6 

3.78 

656 

653 

633 

503 

658 

618 

473 

li 

14xi^ 

618 

56.8 

191.5 

3.74 

676 

676 

654 

613 

672 

631 

490 

449 

14xH 

mi'  m 

58.1 

197.5 

3.76 

697 

697 

675 

633 

601 

649 

606 

4« 

14xA 

14xH 

19^  ni 

59.8 

203.4 

3.76 

718 

718 

697 

653 

610 

666 

623 

479 

19ll 

7A 

61.6 

209.4 

3.n 

739 

739 

718 

673 

628 

684 

689 

494 

14x« 
14xk 
14x4 

14x^« 

II 

7*4 

63.3 

215.3 

3.78 

760 

760 

789 

603 

647 

601 

665 

510 

20H 

65.1 

221.3 

3.78 

781 

781 

760 

718 

666 

619 

672 

62S 

20A 

7_» 

66.8 

227.2 

3.79 

802 

802 

781 

733 

686 

636 

568 

6iO 

20M,  7ii 

68.6 

233.2 

3.80 

823 

823 

802 

763 

708 

664 

606 

555 

14x^g 

.5.2 

194 

6H 

58.2 

197.8 

3.71 

698 

696 

673 

681 

688 

646 

602 

460 

u 

7 

59.9 

203.8 

3.72 

719 

717 

694 

650 

606 

662 

618 

474 

T^ 

19>8 

7A 

61.7 

209:7 

3.73 

740 

738 

716 

670 

626 

680 

636 

490 

u 

^* 

20 

7K63.4 

215.7 

3.74 

761 

760 

737 

090 

644 

696 

661 

60S 

1-a 

^k 

7iV^.2 

221.6 

3.75 

782 

782 

758 

710 

663 

615 

668 

520 

14xH 

II 

7K66.9 

227.6 

3.76 

808 

803 

779 

730 

682 

638 

684 

53S 

id 

20H 

7k  70.4 

233.6 

3.77 

824 

824 

800 

760 

700 

650 

6or 

561 

t^^ 

20A 

239.6 

3.77 

846 

845 

821 

770 

719 

668 

617 

666 

■*»H 

7A72.2 

246.4 

3.78 

866 

866 

842 

790 

788 

686 

688 

5fil 

*  Add  weight  of  rivet  heads. 


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Z-BAR  COLUMNS.     CHANNEL  COLUMNS.  Ml 

LjB_  r^  0*         8  — Carnboib  Channel  Columns — Flat  Ends.  7* 

J  .Q.  L  Safe  Loads*  and  Properties. 

(Safe  Loads  are  in  Thotisand  Pounds.) 


Fig.  9. 


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002  22.— PROPERTIES  AND  TABLES  OF  COLUMNS. 


Pig.  9. 


9. — Carnbgib  Channbl  Columns — ^Flat  Ends. 
Safe  Loads  and  Properties. 
^1  ^  ^^  (Safe  Loads  are  in  Thousand  Pounds.) 


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Ma 


FIg.g. 


CHANNEL  COLUMNS.  603 

10*      10. — Carnboib  Channbl  Columns — Flat  Ends.      12* 
Safe  Loads  and  Properties. 
(Safe  Loads  are  in  Thousand  Pounds.) 


d  by  Google 


604 


d^.—PROPERTIES  AND  TABLES  OF  COLUMNS, 


11. — *  Pr<bniz  Stbbl  Columns. 
Dimensions,   Properties  and   Loads. 

'The  dimensions  given  in  the  following  table  are  subject  to  such  slight 
variations  as  are  unavoidable  in  the  manufacture  of  these  shapes. 

The  weights  given  are  those  of  the  segments  composing  the  columns, 
and  from  2  to  6  per  cent  must  be  added  for  weight  of  the  rivet  heads. 

The  safe  loads  specified  are  computed  as  being  one-fourth  of  the  tilti* 
mate,  or  breaking  loads,  and  as  producing  a  strain,  or  pressure,  in  an  axial 
direction  on  square-end  columns,  of  not  more  than  12,000  lbs.  per  square 
inch  for  lengths  of  90  radii  and  under. 

The  A,  Bl,  B2,  and  C  columns  have  each  4  segments,  the  £  have  6. 
and  the  G  have  8  segments. 

Any  desired  thickness  between  the  minimum  and  mayimum  can  be 
furnished. 
Least  Radius  of  Gyration  ^  Dp  X 0.8636. 


One  Segment. 


Diameters,  in  Ins. 


One  Column. 


Section. 


D 
Inside 


Out- 
side. 


Over 
Flan- 
ges. 


Area 

of 

Cross 

Sec- 

tion. 

Sq.In. 


Wt. 

Frot 

in 

Lbs. 


Least 

Rad. 

of 

Gyra- 
tion 

in  Ins 


3di 
1^^ 


A 

m 


4 

4H 

4M 
4J« 


3.8 
4.8 
6.8 
6.8 


12.9 
16.3 
19.7 
23.1 


1.45 
1.60 
1.55 
1.59 


10 
47 


Bl 


h% 

6 

6>i 


IS 


6.4 
7.8 
9.2 
10.6 
12.0 
13.4 
14.8 


21.8 
26.5 
81.3 
86.0 
40.8 
45.6 
50.3 


1.95 
2.00 
2.04 
2.09 
2.13 
2.18 
2.23 


74 
90 
106 
126 
144 
161 
178 


B2 
6A 


9K 
9H 

9?i 


7.4 
9.0 
10.6 
12.2 
13.8 
15.4 
17.0 


25.2 
30.6 
36.0 
41.5 
46.9 
52.4 
57.8 


2.39 
2.43 
2.48 
2.52 
2.57 
2.61 
2.66 


80 
106 
127 
146 
166 
185 
204 


C 

7A 


10.0 
12.1 
14.1 
16.0 
18.0 
20.0 
21.9 
24.3 
26.6 
28.6 
30.6 
34.9 
38.8 
42.7 


34.0 
41.3 
48.0 
54.6 
61.3 
68.0 
74.6 
82.6 
90.6 
97.3 
104.0 
118.6 
132.0 
145.3 


2.84 
2.88 
2.93 
2.97 
3.01 
8.06 
3.11 
8.16 
320 
3.24 
3.29 
3.94 
3.48 
3.67 


120 
145 
109 
1» 
216 
280 
263 
291 
319 
8U 
167 
418 
466 
£13 


*By  permission  of  Mr.D.  W.  Bowman.  Chief  Engineer  Phoenix  lionWoriks. 


PHCENIX  COLUMNS. 
11. — Pb(xnix  Stbbl  Columns. — Concluded. 


006 


One  Segment. 

Diameters,  in  Ins. 

One  Column. 

gs 

Wt. 

^0 

Out- 
side 

Di 

Area 
of 

Wt. 

Least 
Rad. 

!§:§ 

Section. 

§.s 

in 
Lbs. 

D 
Inside 

Over 
Flan- 
ges. 

Cross 
Sec- 
tion. 
Sq.In. 

pS)t 

in 

Lbs. 

of 
Gyra- 
tion 
in  Ins. 

1^5 

^ 

9.3 

"iV 

\^i 

16.5 

560 

4.20 

196 

/S>/ 

•£ 

10.8 

11  1 

19.1 

65.0 

4.25 

229 

Vs:^ 

M 

12.3 

111 

15«^ 

21.7 

74.0 

4.29 

260 

ul   ^ 

^ 

14.0 

nil 

15ii 

24.7 

84.0 

4.34 

296 

16.7 

12iV 

27.6 

940 

4.38 

331 

St  1  u           t; 

■X 

17.3 

12tV 

16,V 

30.6 

IM.O 

4.43 

367 

^ 

10.0 

E 

12A 
12^ 

16A 

83.6 

114.0 

4.48 

402 

u 

20.7 

lliV 

lOS 

36.4 

124.0 

4.52 

437 

i 

22.7 

12A 

16A 

40.0 

136.0 

4.56 

480 

5  3a     1 

24.3 

12H 

leS 

43.0 

146.0 

4.61 

516 

20.0 

12i{ 

16H 

45.9 

156.0 

4.66 

551 

I 

29.3 

13tt 

16H 

51.7 

176.0 

4.73 

020 

Pig.  14. 

IH 

32.7 

13A 

17iV 

67.6 

196.0 

4.84 

691 

IH 

36.0 

13A 

17A 

63.5 

216.0 

4.93 

762 

ti 

"ToT 

15^i 

19H 

24.3 

82.6 

5.54 

290 

12.0 

16»^ 

19H 

28.2 

96.0 

5.50 

337 

(^ 

tV 

13.7 

15^ 
155| 

im 

821 

109.3 

5.64 

384 

^^^^ 

^ 

15.3 

19H 

mi 

36.0 

122.6 

5.68 

432 

5  /  ;7 

tV 

17.0 

Wi 

40.0 

136.0 

5.73 

479 

^ 

18.7 

15H 

im 

43.9 

149.3 

5.77 

526 

4^ 

20.3 

G 

16 

20 

47.8 

162.6 

5.82 

572 

8 

22.0 

14H 

16^^ 

20H 

51.7 

176.0 

5.88 

620 

23.7 

iwl 

20M 

65.7 

189.3 

5.91 

667 

®  J3\      » 

25.3 

2XA 

50.6 

202.6 

5.95 

715 

r^::^ 

1 

28.7 

im 

20?i 

67.4 

229.3 

6.04 

809 

Ui?» 

32.0 

WA 

20J8 

75.3 

256.0 

6.13 

904 

1^ 

35.3 

IIH 

21 

83.1 

282.6 

6.27 

997 

Pi«.  15. 

38.7 

i7H 

21H 

90.9 

309.3 

6.32 

1091 

d  by  Google 


6(M 


Zi.—PROPERTIES  AND  TABLES  OF  COLUMNS, 


12. — Ultimate  and  Sapb  Oi)  Strbnoths  op  Hollow  Round  and 
Hollow  Rectangular  Cast  Iron  Columns. 
In  the  following  formulas,  C/  —  80  000  and  5-  10  000  lbs.  per  sq.  in.: 

Round  Columns.                             Rbctangular  Columns. 
Square         Square             Pin             Square  Square  Pin 

Ends.          &  Pin.            Ends.           Ends.  &  Fin.  Ends. 

UorS  _     UorS    _    UorS    _    UorS UorS  U  or  S 


(12L)«     ,  ■  8(12L)« 
^'^'mcP      "^  iaood» 


i4.<i2L)i     ,  .8(12L)_«     ,  .  0(12L)«    ,  .3(12L)« 
*'^400d»  aaOOii*        "^  6400d«       "^  160(W> 


L— length  of  column  in  feet;  d  —  (least)  outside  diameter  in  inches; 
p— load  in  lbs.  per  sqtuuv  inch  on  column  to  produce  U  or  5. 


Round  Columns. 

1 

Rectangular  Columns. 

L 
d 

Loads  In  1000  lbs. 

per  square 

Inch. 

Loads  In  1000  lbs.  per  square  Indt 

Square  Ends 

sq.  and  Pin 

Pin  Ends 

Square  Endslsq.  and  Pln|  Pin  Ends 

TJlt. 

Bate 

TTlt. 

Sate 

Ult. 

Sate 

Ult. 

Safe 

Ult. 

Safe 

Ult. 

Saff 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

Load. 

1.0 

67.80 

8.47 

62. .99 

7.87 

58.82 

7.35 

70.48 

8.81 

66.62 

8.31 

62.99 

7.87 

1.1 

65. 6{ 

8.21 

60. 3( 

7.54 

55.72 

6.97 

68. 7{ 

8.6C 

64.2( 

8.03 

60.. 1( 

7M 

1.2 

63.5S 

7.94 

57. 6( 

7.2C 

62. 6< 

6.59 

67. OC 

8.37 

61.94 

7.74'  67.6C 

7.20 

1.3 

61.34 

7.67 

54.93 

6.87 

49.7^ 

6.22 

65.14 

8.14 

59. 6C 

7.4! 

54.96 

6.?7 

1.4 

59.14 

7.39 

52.31 

6.54 

46.90 

6.86 

63.26 

7.91 

67.27 

7.16 

52.32 

6.54 

1.5 

68.94 

7.12 

49.77 

6.22 

44.20 

5.52 

61.35 

7.67 

54.96 

6.87 

49.76 

6.22 

1.6 

54. 7« 

6.84 

47. 3C 

6.91 

41.63 

5.20 

59.45 

7.43 

52.61 

6.5i 

47.SC 

5.91 

1.7 

62.62 

6.5i 

44.94 

5.62 

39.21 

4.90 

57.5! 

7. IS 

50. 4( 

6.31 

44.96 

5.63 

1.8 

50.63 

6.32 

42.67 

6.33 

36.93 

4.62 

55.67 

6.M 

48. 3C 

6.04 

42.67 

«.» 

1.9 

48.49 

6.06 

40.51 

5.06 

34.79 

4.35 

53.80 

6.72 

46.23 

6. 7  J 

40.61 

S.K 

2.0 

46.61 

6.81 

38.46 

4.81 

82.79 

4.10 

51.94 

6.49 

44.20 

5.52 

28.46 

4.81 

2.1 

44. 6C 

5.57 

36.52 

4.66 

30.92 

3.86 

50.16 

6.27 

42. 2< 

6.2{ 

36.52 

4.66 

2.2 

42.75 

6.34 

34. 6i 

4.33 

29.  le 

3.65 

48.40 

6.05 

40. 4( 

5.0! 

34. 6f 

4.33 

2.3 

40.98 

6.12 

32.94 

4.12 

27.64 

3.44 

46.67 

5.83 

38.63 

4.83 

32.99 

4.12 

2.4 

39.28 

4.91 

31.31 

8.91 

26.03 

3.25 

44.99 

5.62 

36.93 

4.62 

31.31 

3.91 

2.5 

37.65 

4.71 

29.77 

8.72 

24.62 

3.08 

43.39 

5.42 

35.31 

4.41 

29.76 

S.7J 

2.6 

36.  OS 

4.51 

28.32 

8.54 

23.3( 

2.91 

41.82 

6.23 

33.77 

4.22 

28.32 

3.64 

2.7 

34. 6( 

4.32 

26.91 

3.37 

22.07 

2.76 

40.32 

6.04 

32.31 

4.04 

26.9a 

3.37 

2.8 

33.  If 

4.19 

25.67 

3.21 

20.93 

2.62 

38.87 

4.8C 

30.92 

3.86 

25.67 

S.21 

2.9 

31.82 

3.9f 

24.46 

3.06 

19.86 

2.48 

37.47 

4.6£ 

29.60 

8.70 

24.46 

8.M 

3.0 

30.53 

3.82 

23.32 

2.91 

18.87 

2.36 

36.12 

4.51 

28.34 

8.54 

23.32 

2.91 

3.1 

29.31 

3.6« 

22.25 

2.7C 

17.94 

2.24 

34.83 

4.35 

27.15 

3.39 

22.2! 

2.:ii 

3.2 

28.14 

3.52 

21.25 

2.66 

17.07 

2.13 

33. 6J 

4.2( 

26.03 

3.2! 

21.2! 

2.16 

3.3 

27.03 

3.3f 

20. 3C 

2.54 

16.26 

2.03 

32.39 

4.0! 

24.96 

3.12 

20.3( 

2.M 

3.4 

25.97 

3.25 

19.41 

2.43 

15.50 

1.94 

31.26 

3.91 

23.94 

2.99 

19.41 

2.43 

3  5 

24.96 
24.00 
23.09 
22.23 
21.40 

3.12 
3.00 
2.89 
2.78 
2.67 

18.5fi 
17.71 

2.32 
2.21 

30.15 
29.10 
28.09 
27.13 
26.21 

3.77 
3.64 
8.51 
3.39 
3.28 

22.97 
22.05 

2.87 
2.76 

3  6 

3  7 

3  8 

3  9 

Safe  loads  given  in  the  table  are  equal  to  one-eighth  the  ultimate  loads, 
that  is,  using  safety  factor  8.  If  the  safety  factor  10  is  preferred  the  wn 
safe  load  may  be  found  from  the  uUimatt  load  by  moving  the  decimal  point 
one  place  to  the  left. 


d  by  Google 


CAST  IRON  COLUMNS. 


607 


13.- 

Sapb  (H)  Loads 

ON  Hollow  Round  Cast  Iron  Columns  with  Plat  Ends 

10  AAA>I 

f  P- 

-total  load 

on  column 

in  1000  lbs. 

By  Formula  P-  — 



^•.Jnwhirh    A' 

»  sectional  area  of  column  in  sq.in. 

14 

{\2L)' 

^■ 

-length  of  column  in  feet. 

800d> 

[d^ 

-outside  diam.  of  column  in  ins. 

ll 

it 

IM. 

Ina. 

Lbe. 

Length  of  Column  In  Feet. 

6 

8 

10 

12 

14 

16 

18 

20 

22 

24 

Ins. 

Total  •Sate  Load  on 

Column  m  1000  lb& 

< 

H 

8.6 

27.0 

73 

65 

67 

60 

44 

38 

33 

29 

25 

22 

10. « 

83.0 

90 

80 

71 

62 

54 

46 

40 

35 

31 

27 

^ 

12.4 

38.7 

105 

94 

82 

72 

.  «2 

54 

47 

41 

86 

32 

14.1 

44.0 

119 

107 

94 

82 

71 

62 

54 

47 

41 

36 

1 

15.7 

49.1 

133 

119 

105 

91 

79 

69 

60 

52 

46 

40 

7 

^ 

12.5 

39.1 

111 

101 

91 

82 

73 

64 

57 

51 

45 

40 

14.7 

46.0 

130 

119 

108 

96 

86 

76 

67 

60 

63 

47 

yi 

18.8 

52.6 

149 

136 

123 

110 

98 

87 

77 

68 

61 

54 

1 

18.9 

58.9 

167 

153 

138 

123 

109 

97 

86 

76 

68 

60 

IM 

20.8 

64.9 

184 

168 

152 

136 

121 

107 

95 

84 

75 

67 

8 

^ 

17.1 

53.4 

155 

145 

133 

122 

110 

99 

89 

80 

72 

65 

11.6 

61.2 

178 

166 

153 

139 

126 

114 

104 

93 

83 

75 

1 

22.0 

68.7 

200 

186 

172 

158 

142 

128 

115 

103 

93 

84 

m 

24.3 

75.9 

220 

206 

190 

173 

157 

142 

127 

114 

103 

93 

IM 

26.6 

82.8 

239 

225 

207 

189 

171 

154 

139 

125 

112 

101 

f 

M 

22.3 

69.8 

207 

196 

183 

169 

159 

142 

130 

118 

108 

98 

1 

26.1 

78.5 

233 

220 

206 

190 

179 

160 

146 

133 

121 

110 

iH 

27.8 

87.0 

258 

244 

228 

211 

198 

177 

163 

147 

134 

122 

1^ 

30.4 

95.1 

281 

m 

249 

230 

212 

194 

177 

161 

147 

133 

I9(i 

32.9 

102.9 

304 

288 

269 

249 

229 

210 

191 

174 

159 

145 

10 

?« 

26.1 

78.4 

235 

225 

212 

199 

185 

172 

158 

146 

134 

123 

1 

28.3 

88.4 

265 

254 

240 

224 

209 

194 

178 

164 

151 

139 

IM 

34.4 

107.4 

323 

308 

291 

273 

254 

235 

217 

200 

184 

169 

1^ 

41.1 

125.2 

376 

359 

339 

318 

296 

274 

253 

233 

214 

197 

m 

45.4 

141.7 

426 

407 

884 

360 

335 

310 

286 

264 

242 

223 

11 

I 

31.4 

98.2 

298 

287 

273 

259 

243 

227 

212 

197 

183 

169 

38.3 

119.7 

363 

850 

333 

315 

296 

277 

258 

240 

223 

206 

1^ 

44.8 

139.9 

425 

409 

390 

369 

346 

322 

302 

286 

260 

241 

i9i 

50.9 

158.9 

483 

464 

443 

419 

394 

368 

343 

324 

296 

274 

2 

56.6 

176.7 

537 

516 

492 

466 

438 

409 

381 

354 

329 

306 

12 

1 

34.6 

108.0 

831 

320 

307 

293 

277 

262 

246 

230 

215 

201 

IM 

42.2 

131.9 

404 

891 

375 

358 

339 

320 

300 

281 

263 

245 

iS 

49.5 

154.6 

473 

458 

440 

419 

397 

375 

352 

330 

308 

288 

iS 

56.4 

176.1 

540 

622 

601 

477 

453 

427 

401 

376 

351 

328 

2 

62.8 

196.4 

603 

682 

558 

532 

505 

476 

447 

419 

391 

365 

13 

1 

37.7 

117.8 

363 

353 

341 

327 

312 

296 

280 

264 

249 

234 

13 

46.1 

144.2 

444 

432 

417 

400 

382 

363 

343 

323 

304 

286 

54.2 

169.4 

522 

507 

490 

470 

448 

426 

403 

380 

358 

336 

\H 

61.9 

193.3 

596 

579 

559 

636 

512 

486 

460 

434 

408 

383 

2 

69.1 

216.0 

665 

647 

625 

599 

572 

543 

514 

485 

456 

428 

14 

1    J 

40.8 

127.6 

395 

886 

374 

361 

346 

331 

315 

299 

283 

267 

IH 

50.1 

156.5 

485 

473 

459 

442 

424 

405 

886 

366 

847 

327 

iH 

58.9 

184.1 

570 

556 

540 

520 

499 

477 

454 

431 

408 

385 

m 

67.4 

210.5 

652 

636 

617 

595 

571 

545 

519 

492 

466 

440 

2 

76.4 

235.6 

730 

712 

690 

666 

639 

610 

581 

551 

522 

493 

15 

1 

44.0 

137.4 

427 

418 

407 

394 

380 

866 

349 

333 

317 

301 

ii< 

54.0 

168.7 

525 

514 

500 

484 

467 

448 

429 

409 

389 

370 

IH 

63.6 

203.4 

618 

605 

589 

570 

550 

628 

505 

482 

459 

439 

\H 

72.9 

227.6 

708 

694 

676 

653 

630 

605 

577 

552 

525  1    502 

2 

81.7 

356. 2 

795 

777 

756 

732 

706 

678 

649 

619 

589  1    569 

*  This  table  is  for  safety  factor  8; 
lar  safe  loads  by  A< 


for  safety  factor  10  multiply  the  tabu- 


22,-'PROPERTlES  AND  TABLES  OF  COLUMNS, 


14. — RoLLBD  Stbbl  H  Columns. 
(Bethlehem  Steel  Co.) 


For  all  sections. 


K— -B— H 
Fig.  16. 
W«=wt.  of  section  in  lbs.  per  lin.  ft. 
A  —area  of  section  in  sq.  ins. 
r'  "» least  radius  of  gyration. 
5*  H  Columns. 
(Section  Number  -  H8.) 


Dimen.  In  Ins.i  | 

w 

A 



D 

t 

to 

31.5 

9.17 

m 

A 

.31 

10.17 

8 

.31 

11.50 

m 

X 

.35 

12.83 

SH 

«| 

.39 

14.18 

m 

'tr 

.43 

15.53 

SH 

'A 

.47 

16.90 

■  1 

.51 

18.27 

Ig 

'  1 

.55 

19.66 

1 

.59 

21.05 

9 

1 

.63 

22.46 

iT^ 

.67 

23.78 

gi^ 

lU 

.70 

85.5 

25.20 

996 

lA 

.74 

90.5 

26.64 

9H 

iM 

.78 

1.98 
2.01 
2.03 
2.04 
2.05 
2.07 
2.08 
2.09 
2.11 
2.12 
2.13 
2.14 
2.16 
2.17 


»/ =  6.14=  tang.  dist.  bet.  fillets:  r^ 
0.40  =  rad.  of  fillets;  B-7.69+w:  w-= 
i-0.038;n=-/+0.038. 

icr  H  Columtis. 
(Section  Number -HIO.) 


DImen.  In  Ins.* 

w 

A 

r 

t 

D 

' 

w 

49.0 

14.37 

m 

A 

49 

54.0 

15.91 

10 

^ 

51 

59.5 

17.57 

lo^ 

u 

53 

65.5 

19.23 

IS^ 

zi 

54 

71.0 

20.91 

tt 

56 

77.0 

22.59 

lOH 

n 

57 

82.6 

24.29 

im 

58 

88.5 

25.99 

\i^ 

60 

94.0 

27.71 

lA 

61 

S9.6 

29.32 

J  J 

m 

62 

105.6 

31.06 

UH 

jS 

64 

111.5 

32.80 

UM 

iH 

65 

117.6 

34.55 

n% 

lA 

.82 

66 

123.5 

36.32 

iiH 

m 

.86 

2 

67 

«  ;~7.«7-tang.  dist.  bet.  filleU; 


i^*  H  Columns. 
(Section  Number -H12.) 


64.5 
71.5 
78.0 
84.6 
91.5 
98.5 
105.0 
112.0 
118.6 
125.5 
132.6 
139.5 
146.5 
153.6 
161.0 


19.00 
20.96 
22.94 
24.92 
26.92 
28.92 
30.94 
32.96 
34.87 
36.91 
88.97 
41.03 
43.10 
45.19 
47.28 


DImen.  in  Ins.* 
D 


S 


.39 
.43 
.47 
.51 
.55 
.59 
.63 
.67 
.70 
.74 
.78 
.83 
.86 
.90 
.94 


2.91 

3.00 
3.01 
3.03 
3  04 
3.06 
3.07 
3.08 
3.10 
3.11 
3.13 
3.14 
3.15 
3.16 
3.18 


»  /-9.21  «.tang.  dist.  bet.  fillets:  r- 
0.80 -rad.  of  fillets:  B'-ll.SS+wxm" 
l/-0.068:i«=-/-»-0.058. 

14'  H  Columns. 
(Section  Number -H 14.) 


w 

A 

DImen.  In  Ins.* 

f 

D 

( 

v> 

83.5 
91.0 

24.46 

26.76 

13H 

^ 

.43 

.47 

3.47 
3.49 

99.0 
106.5 
114.5 
122.6 

29.06 
31.38 
33.70 
36.04 

14 

} 

.51 
.55 
.59 
.63 

3.50 
3.52 
3.53 
3.55 

130.5 
138.0 
146.0 
154.0 

38.38 
40.59 
42.95 
45.33 

14H 

i 

.67 
.70 
.74 
.78 

3.56 
3.58 
3.59 
3.61 

162.0 
170.5 
178.5 
186.5 

47.71 
50.11 
52.51 
54.92 

15 

i 

.82 
.86 
.90 
.94 

3.63 
3.64 
3.65 
3.66 

195.0 
208.5 
211.0 
219.5 

67.35 
59.78 
62.07 
64.62 

i 

i 

.98 
1.02 
1.05 
1.0» 

3.6$ 
3.69 
3.70 
3.71 

227.5 
236.0 
244.5 
253.0 

66.98 
69.45 
71.94 
74.43 

16 

16M 

ji 

1.13 
1.17 
1.21 
1.25 

3.72 
8.74 
3.75 
3.71 

261.5 
270.0 
278.5 
287.5 

76.93 
79.44 
81.97 
84.50 

1 

1.29 
1.33 
1.87 
1.41 

3.77 
3.79 

3.80 
3.81 

I  */- 11.06  =  tang.  dist.  bet.  fillets: r» 
0.60 -rad.  of  fiUets;  B- 13.49+ w;  m- 
,v<-0.067;n-«+0.067. 


STEEL  H-COLUMNS.   REIN. -CONC.  COLUMNS,  609 

Reinforced  Concrete  Colomns.— The  following  working  stresses  for  static 
loads  are  recommended  by  the  Special  Committee  of  the  Am.  8oc.  C.  E.,  on 
Concrete  and  Reinforced  Concrete.  See  Trans.  A.  S.  C.  E.,  Vol.  LXVI., 
page  462.  For  Notation  and  Pormtilas,  see  Sec.  25,  Masonry,  page  44ft.  For 
working  stresses  for  Beams,  see  Sec.  31.  page  585. 

Average  compressive  strenfi[th  of  concrete — ^2000  lbs.  per  so.  in.  at  28  days, 
when  tested  in  cylinders  8  ins.  m  dia.  and  16  ins.  long,  under  laboratory  con- 
ditions of  manufacture  and  storage. 

Bearing. — See  page  586. 

Axial  Compressions. — (A).  For  concentric  compression  on  a  plain  con- 
crete column  orpier,  when  the  length  does  not  exceed  12  diameters,  460  lbs. 
per  sq.in.  on2000-lb.  concrete  may  be  allowed.  (B).  Columns  with  longi- 
tudinal reinforcement  only,  460 lbs.  per  sq.  in.  on  2000-lb.  concrete.  (C).  Col- 
umns with  reinforcement  of  bands  or  hoops,  540  lbs.  per  sq.  in.  on  2000-lb. 
concrete  may  be  allowed.  (D).  Columns  reinforced  with  not  less  than  1% 
and  not  more  than  4%  of  longitudinal  bars  and  with  bands  or  hoops,  660  lbs. 
per  sq.  in.  for  2000-lb.  concrete.  (E).  Columns  reinforced  with  structural 
steel  column  units  which  thoroughly  encase  th9  concrete  core.  660  lbs.  per 
sq.  in.  for  2000-lb.  concrete. 

Reinforcement. — In  all  cases,  lon^tudinal  steel  is  assumed  to  carry  its 
proportion  of  stress;  and  the  compressive  stress  shall  not  exceed  16000  lbs.  per 
K).  in.  or  15  times  the  working  compressive  stress  in  the  concrete.  Hoops  or 
bands  are  not  to  be  counted  upon  directl>r  as  adding  to  the  strength  of  the 
column.  Bars  composing  longitudinal  reinforcement  shall  be  straight,  and 
shall  have  sufficent  lateral  mpport  to  be  securely  held  in  place  until  the  con- 
crete has  set.  When  bands  or  hoops  are  used,  the  total  amount  of  reinforce- 
ment shall  not  be  less  than  1%  of  the  volume  of  the  colimin  enclosed.  The 
clear  spacing  of  such  bands  or  hoops  shall  not  be  greater  than  one-fourth  the 
diameter  of  the  enclosed  column.  Adequate  means  must  be  provided  to 
hdd  buids  or  hoops  in  place  so  as  to  form  a  column  with  a  straight  and  well- 
centered  core.  Bending  stresses  due  to  eccentric  loads  must  be  provided  for 
by  increasing  the  section  until  the  maximum  stress  does  not  exceed  the 
values  above  ^>ecified. 

EXCERPTS  AND  REFERENCES. 

Retaforcement  of  Concrete  Colomnt  (By  E.  P.  Goodrich.  Bng.  News, 
July  19j  1906). — "Considere  reports  that  S|nral  steel  is  2.4  times  as  effective 
as  longitudinal  reinforcement  of  equal  weight,  and  this  figure  was  closely 
checked  by  v.  Bach,  of  Stuttgart." 

Table  of  Wights  of  Lacing  for  Sted  Compression  Memben  (By 
C.  T.  Lewis.  Eng.  News,  Aug.  2, 1006). — Weights  are  in  lbs.  per  lin.  ft.  of 
Jingle-  or  double-utced  member  on  on*  aide;  the  depths  of  member  ranging 
from  5*  to  23*.  and  the  sise  of  lacing  bars  from  If'x^"  to  S'xf*'.    Rivets, 

rtor 

Table  of  the  Various  Column  Formulas  in  Use  (Eng.  News.  Jan.  3, 
1007). — (Comprises  formulas  of  the  Rankin  type  for  steel  and  cast  iron;  of 
the  straight-lme  type  for  steel,  cast  iron  and  timber;  and  of  miscellaneous 
type  for  timber:  with  an  equivalent  reduction,  for  all  formulas,  to  a  formula 
having  a  factor  of  eccentricity  e.    Interesting  as  a  study. 

Detachable  Form  for  Concrete  Columns  (By  W.  S.  Coulter.  Eng. 
Mews,  Mar.  28,  1907). — Illustration  and  description.  When  building 
reinforced  concrete  columns,  having  flexure  rods  xmited  at  intervals  by  ties, 
forms  are  often  used  having  one  side  open,  which  is  built  up  in  sections  as 
the  concrete  is  deposited.  These  forms  usually  consist  of  four  or  more 
t2pri|[ht8  enclosed  on  three  sides,  the  fourth  being  open  to  allow  access  to 
tnc  mterior,  and  closed  as  the  work  proceeds  by  horizontal  boards  nailed 
to  the  uprights.  Through  the  open  side  all  the  operations  of  depositing, 
spading  and  tying  are  conducted.  The  present  device  is  intended  to  facili- 
tate the  work  of  erection  and  expedite  the  placing  of  the  concrete. 

Table  of  TeeU  of  Carbon-Steel  and  Nickel-Steel  Columns,  and  Com- 
IMriton  wHh  Formulas  (By  C.  P.  Buchanan.  Eng.  News.  Feb.  13,  1908).— 
Table  gives  actual  strength  and  computed  strength  of  columns.  The  com- 
puted strengths  are  from  the  following  formiilas: 

(1)  DagroiTs  teste  (steel  cols.)  compared  with P-  61000-  263  Ijr 

(2)  WaddelVs  tests  (nickel-steel)  compared  with P  =  47000  -  178  IJr 

(3)  Buchanan's  teste  (steel)  compared  with P  =  79000  -  388  //r 

In  which  P— computed  strength  in  lbs.  per  sq.  in.;    and  /  and  r  the 

length  and  radius  of  gjrration.  in  ins.   (See,  also,  Eng.  News  of  April  9,  1908.) 


etO  82.— P/?OPE/?r/£S  AND  TABLES  OF  COLUMNS. 

Sftfc  StreuM  In  SUd  Cdnmiis  (By  J.  R.  Worcester.  Trans  A. 
Vol.  LXI). 

TmU   of   Reinforced   Concrete   Columns   at    MinneapolU,  Mi] 

J.  G.  Houghton  and  W.  P.  Cowlcs.    Eng.  News,  Dec.  8,  IMS). — The 
tested   had   the   following  kinds  of  reinforcement:    Spiral   wire 
circular  flat-bar  bands;  wire  bands,  square;  wire  bands,  circxilar. 
columns  were  made  of  1:2: 3}  concrete,  using  bank  sand  and  blue  lii 
one-half  of  the  stone  beinff  of  i-in.  size  and  one-half  of  p>ea  size, 
inforced  columns  averaged  about  26%  stronger  than  the  plain  < 
though  5  of  the  17  failed  at  lower  loads  than  the  plain  columns. 

Preliminery  Proffram  of  Tests  of  Sted  Cdumns  (Proc.  A.  S.  T. 
VIII..  1908). — ^Tjrpcs  of  sections  selected  for  testing,  at  Watertown 
(a)  Annular  section  (welded  tubesV,  (b)  New  wide  flange  H  sectioi 
section  of  four  angles  and  central  weo-plate;  (d)  Double-channel 
latticed  in  two  planes.  Alao  other  shapes.  Illustrated.  "Some  r 
the  tests,"  by  J.  £.  Howard,  may  be  foimd  on  pages  336  to  344,  si 
of  Proc.;  also  Vol.  DC..  1000.  page  413. 

Tests  of  Plain  and  Reinforced  Concrete  Cdnmns  (By  M.  O. 
Proc.  A.  S.  T.  M.,  Vol.  IX..  1909).— Tables  and  diagrams. 

TesU  of  PUIn  and  Reinforced  Concrete  Cdnmns  (Bv  M.  O. 
Paper  A.  S.  T.  M..  July  1.  1909:  Eng.  Rec.,  July  10,  1909).— Cot 
derived  from  the  tests:  1.  A  small  amount,  i  to  1%,  of  closely  space 
reinforcement,  such  as  the  spirals  used,  will  greatly  increase  the  tt 
and  ultimate  strength  of  a  concrete  column,  but  does  not  material 
the  yield  point.  More  than  1%  of  lateral  reinforcement  does  not  a 
be  necessary.  The  use  of  lateral  reinforcement  alone  does  not  sec 
aV)le.  2.  Vertical  steel  in  combination  with  such  a  lateral  reinfc 
raises  the  yield  point  and  ultimate  strength  of  the  column  and  inct 
stilTncss,  Columns  reinforced  with  vertical  steel  only  are  brittle 
suddenly  when  the  yield  point  of  the  steel  is  reached,  but  are  con« 
stronger  than  plain  columns  made  from  the  same  grade  of  cone 
Increasing  the  amount  of  cement  in  a  spirally  reinforced  column  i 
the  strength  and  stillness  of  the  column.  A  column  made  of  rich  co 
mortar  and  containing  small  percentages  of  longitudinal  and  late 
fo'ccment  is  without  doubt  fully  as  stiff  and  strong  and  more  eo 
than  one  made  from  a  leaner  mix  reinforced  with  considerably  vnt 
In  these  tests  doubling  the  amount  of  cement  increased  the  yield  p 
ultimate  strength  of  the  columns  without  vertical  steel  about  100%  ai 
al)out  50%  to  the  strength  of  those  with  6.1%  vertical  steel.  4.  I 
beha^nor  of  the  columns  reinforced  with  spirals  and  vertical  steel,  lu 
and  the  results  computed,  it  would  seem  that  a  static  load  equal  to  3. 
of  the  yield  point  would  be  a  safe  working  load.  As  the  Tiltimate 
of  the  concrete  and  the  yield  point  of  the  steel  are  generally  knor^nn 
be  assumed  with  fair  accuracy,  formula  (A)  can  be  readily  used  to  di 
the  working  load.  In  Fig.  7  the  dotted  lines  represent  working  -^ 
P+A  equal  to  40%  of  the  yield  point  load.  (Sec  original  article  for 
A  and  Fig.  7).  6.  The  results  obtained  from  tests  of  columns  re 
with  structural  steel  indicate  that  such  columns  have  considerable 
and  toughness  and  that  the  stael  and  concrete  core  act  in  tmison  t 
yield  point  of  the  former.  The  shell  concrete  will  remain  intact  i 
yield  point  of  the  steel  is  reached,  but  no  allowance  should  be  mac 
strength  or  stillness.  6.  As  many  of  the  blotters  on  the  tops  and 
of  columns  bore  imprints  of  the  vertical  steel  after  failure,  it  wouli 
safe  precaution  to  use  bed  plates  at  the  foundations  for  such  colu 
thus  prevent  any  possibility  of  the  steel  punching  through  the  concn 
an  excessive  load. 

Tests  of  Nickd-Steel  Models  of  Compresskni  Members  in  the 
Design  of  the  New  Quebec  Bridge  (Eng.  Rec..  Nov.  19,  1910).— II] 
description  with  table  of  results  of  tests. 

Illustrations  and  Diagrams. 

Description.  E 

Rein.-terra-cotta  col.  tested  to  4 109  lbs.  per  sq.  in.,  uninjured  Pel 

Economy  diagrams  of  plain  and  reinforced  concrete  columns  Jai 

Repeated  and  eccentric  load  tests  on  rein.TConc.  wlumxui  Jul 

Digitized  by  VjOOQ  IC 


33.— STRUCTURAL  DETAILS. 


The  handbooks  published  by  the  various  steel  manufacturers  are  now 
pretty  well  standaroized,  and  are  indispensable  to  constant  designers  and 
detaiicrs  of  structural  work.  The  writer  aims  to  keep  this  volume  abreast 
of  the  most  approved  practice  in  the  design  of  ordinary  structures. 

Rivets. — In  the  'SCs,  iron  rivets  began  to  give  way  to  steel  rivets  in 
engineering  structures,  and  now  the  latter  are  universally  employed.  The 
best  rivet  steel  is  a  aott  steel  whose  tensile  strength  varies  not  more  than  a 
few  thousmd  potmds  from  53  000  lbs.  per  sq.  in.;  the  manuf act  tuber's  stan- 
dard vpedtying  48  000  and  58  000  as  the  lower  and  upper  limits.  Higher 
grades  of  steel  are  more  liable  to  fracture  both  in  driving  and  afterward 
when  subjected  to  repeated  stresses  in  the  structure. 


Shop. 


CoNyBNTIONAL  RiVBT   SlONS. 

(Osbom  Code.) 


Field. 


Pull  Heads 


I  Both  Sides. 
Figs.  1. 


El 


( 

Q 

) 

SI 

Countersunk  and 
Chipped.  ,  When 
,  No  Chipping  is 
Requirea     Mark 


"Not  Chipped" 
(Or  See  Below). 


This  Side  (Outside). 
Other  Side  (Inside). 
Both  Sides. 


Figs.  2. 


» 

1 

« 

a 

UJ 

Head  Flattened 
To  H'  High,  or 
Countersunk  and 
Not  Chipped. 


This  Side  (Outside). 
Other  Side  (Inside). 
Both-Sides. 
Pigs.  8. 


5  e 


fi 


Shop. 


0 


Head 
Flattened. 


This  Side  (Outside). 
Other  Side  (Inside). 
Both  Sides. 
Figs.  4. 


ToV 

m 


Digitized 


All 


shear. 

Problem  in  Rivbtbd  Joints. 
(Reference  to  Tables  1,  2,  6;  and  to  Figs.  5,  6,  29.) 

ExampU. — Let  it  be  required  to  design  a  flat  steel  bar,  spliced  at  r 
with  a  chain-riveted  joint  (Fig.  29.  page  617),  to  resist  a  tensile  str 
69600  lbs. ;  as  per  following  data. 

Data. — Assume  rivets  in  single  shear  at  10000  lbs.  per  sq.  in.  and  bi 
value  for  plates  at  20000  lbs.  per  sq.  in.  (see  Table  1,  above).  Assume  i 
able  tension  on  net  area  of  splice  plates  and  bars,  at  17JS00  lbs.  per ! 
(see  Figs.  5  and  6,  in  Table  2,  for  pitch,  etc.,  of  rivets.) 

Solution. — 
Allowable  total  stress  on  bar  and  joint  ">600( 

Rivets  in  shear  (Table  1) :  Eight  ^-in.  rivets  in  doable  shear 

-8X2X4430 -TOTS 
Rivets  xn  bearing  on  splice  plates  (Table  1) :  Two  A-in.  plates 

—8X2x4690  —  7504 
Rivets  in  bearing  on  main  bar  (Table  1):  One  H-in.  bar  -8X9380-75W 
Tension  on  mam  bar:  HX17500X6H  (net  width  of  bar  in  ins.)  -6971 
iransverse  width  m  bar  occupied  by  holes  (see  Note  to  Table  6): 

Digitized  by  8(H+H)  —2*^1 


RIVETS  AND  RIVETING, 


618 


Total  width  of  bar  (or  splice  plate)  required  for  stress 

-(^(net)+2H(holcs)  -0  ins. 
Natural  spacing  of  rivets  on  transverse  section  of  bar  and  splice 

-9-i-8-3ins. 
(This  pitch  is  allowable,  from  Table  2,  second  column.) 
Distance  from  center  of  rivet  to  e<%e  of  plate  «■  (0+2) — 3  —  IH  ins. 

(This  is  allowable,  from  Table  2.  and  Pig.  6.) 
wstance  between  centers  of  rows  of  rivets  (Table  2) :       8X  cos  30*»  -  2H  ins. 
Distance  from  centers  of  rivets  to  ends  of  bars  or  plates: 

not<Hpltch  J  -IHins. 

Length  of  spUce  plates:  lM+2f<+2H+lH+lH+2^+2H+lH  -WH  ins. 


2. — Gbnbral  Rivbt  Spacing.  Clbarancbs,  btc. 
(All  dimensions  in  Inches.) 


i    * 

"S 

e 

II 

S 

5. 

It 

Min.l 

Oist.  €  to  Edge  tgo  o( 
of  Plate.             ^* ' 

Min.  Clear. 

From  Center 

of  Rivet. 

rig.  o. 

1 

1 

Plates  Over 
W  Thick. 

Plates  Not 

Over 
H'  Thick. 

^ 

0 

u 

o 

J 

Fig.  6. 

Min. 
Pitch. 

p 

1^ 

jl 

1 

Fii 

a. 

J.  7. 
>1 

vet 
Pig.  8. 

H 

Best 
Hi 

Not  including  Fillers 
or  Lattice  Bars. 

A  (min 

H 

^ 

1 

\\Z 

4 

4 

4 
4 

r 

SH 

6 

¥ 

...... 

ivl 

f 

1^ 

IS 

IH 
IM 

iS 

d  by  Google 


d  by  Google 


RIVETS  AND  RIVETING.  616 

4. — Standard  Connbction  Akolrs   for   I-Bbams   and  Channels. 

For  I2f  Beams  and  Channels. 

e'x4'xH'xO'7H' 


For  24'  Beams. 


Fig, 


For  2fr  Beams. 

ui'xi'x^'xvr  UA'xi'T^'xvr 


5 
1 

I 


Pig.  15. 


L5  4'x4'x^'xl'l' 


For  18*  Beams. 
The  Carnegie  Steel 
Company  usessame 
connections  as  for 
ar  Beams. 


For  15*  Beams  and  Channels. 

u^xi'x^'Tdyitr  Ls&'xi'T^'xxnor 


Pig.  17. 


U^xVx^xfflW 
Xj6 


Fig.  18. 


For  10.'  9*.  8'  and  7"  Beams  and 
Channels. 

Uerxi'x^'xO'S'  Li  6'x4'x^''x0' 6' 
Rivet  Spacing  21^. 


^^^ 


-Miff 


Pig.  10. 


For  6'  and  5'  Beams  and  Channels. 

6in.: 

Ls  6'x4'x  A'xC  3*  Ls  e'x4'xH'xO'  2H' 

6  in.:     do.   xO'2H'' 


Pig.  20.' 

For  4'  and  8*  Beams  and  Channels. 
L56'x4'xA'x0'2'  Ls  8'x4'xH'xO'15i» 


Fig.  21. 


Note. — In  the  above  illustra- 
tions, two  systems  of  connection 
angles  are  shown,  that  of  the  Car- 
negie Steel  Co.  being  on  the  left, 
and  Cambria  on  the  right,  in  each 
case.  Legs  showing  shop  rivets 
are  riveted  directly  to  ends  of 
I-beam  or  channel,  while  those  show- 
ing field  rivets  are  for  field  connec- 
tion. Angles  are  riveted  on  in 
pairs.  A  play  of  A  of  an  inch 
IS  allowed  at  each  end  of  the  built 
member  between  the  back  of  angles 
and  the  girder  to  which  it  is  to  be 
connected  in  the  field. 


d  by  Google 


RIVETS  AND  RIVETING. 


Lap  Joints. 


6. — RiVBTBD    JOIKTS. 

Kinds  of  Riveted  Joints. 


Butt  Joints. 


Single  Riveted. 


o  jo 
ojo 
ojo 


Fig.  24. 


Fig.  25. 


Double  Riveted. 


o  o 

o  jo 
O      J      o 
0!0   " 


Fig.  26. 


Pig.  27. 


o\  Ol 

O^O 





Chain  Riveted. 


Fig.  28. 


Fig.  20. 


Table  for  Finding  Net  Areas  of  Riveted  Joints. 

Areas  in  square  inchesto  be  deducted  for  rivet  holes  in  plates  of  various 
thicknesses  to  obtain  net  area  of  joint  for  tension. 


*  Note  that  diam.  of  hole  is  greater  than  diam.  of  rivet;  usually  assumed 
at  ^  to  >^  in.  greater.  ^  . 

For  Problem  in  Riveted  Jomte  see  page  ei^jOOglC 


618 


Zi,— STRUCTURAL  DETAILS, 


7. — Standard  Bolts  for  PAsrsNiifos. 


Drift  Bolts  for  Timber. 


Headed 

and 
Pointed. 


II 

Fig.  30.    Fig.  31. 


Screw  Bolts  for  Timber  and  Metal. 


Hexagonal 

Head 
and  Nut. 


Figs.  34.  36. 


Expans'n  Bolts  for  Timber  and  Stone. 


Before 
Expansion. 


In  Place. 


Figs.  32.  33. 


Hook  Bolt  for  Bridge  Work. 

Fastening 

Guard  Rail  and  Tie 

to  Girder. 


Fig.  36. 


Stone  Bolts  for  Bridge  Work. 


Diam.  of  hole  ■»  diam. 
of  bolt  +  H". 

Length  of  wedge  for 
split  bolt  =  3(f;  width  =  (i; 
thickness  at  head  —  H^; 
point  rounded. 


Swedge 

Bolts. 

(Fig.  37.) 


«i'x  9'.Wt.-2^. 

Vxl2'.Wt.-3#. 
1  'xir.  Wt. -4*. 
lM'xl6'.Wt.-7#. 


-^_  ^.^    e J^^^^?'     35)  with  flat  wSEcre: 

S.M<i9«l  SpM.   Sor«»A  Bolts  for  {  middle  of  bolt  de- 
Concrete    fleeted  1  dla.  before 
Figs.  37,  38.  39.  '^  seiUnij. 


8. — Standard  Scrbw  Thrbads. 
(Sellers;  Franklin  Institute.  Dec..  1864;  United  States,  1868.) 


Diam. 


^t 


•sS.1   s 


.185 
.240 
.294 
.344 
.400 
.464 
.607 
.620 
.731 


Diam. 


El 

O  ft 


.837 

.940 

1.066 

.160 

IHI.284 

1?K 1.389 

I  1»4 1.490 

rHl.616 


2^'  >    Diam. 


^^ 


2  1.712 
2K1  962 
2>|t2.176 
2*4^2  425 

3  12.629 
3KI2.879 

3M.317 


•r 


Note.— The  Pitch  is   jj-;  and  the  flat  /,  at  top  and  bottom,  is  g^. 


«f  «fe.*}v  ^lirtworth  or  EngHsh  standard  the  angle  of  thread  is  65*»  ioaUmd 
«;>S«;;i?*Kf*?P  ^^  bottom  of  threads  are  rounded;  and  iV  is  J 2  for  D-H. 
othen^ise  AT  IS  the  same  as  above  for  jD  up  to  3  inches.^ ^- 


aOOgfe 


BOLTS  AND  NUTS. 


dlO 


0. — DiifBNSioifs  AND  Wbiobts  op«Hot  Prkssbd  Nut8. 

The  sizes  are  the  usual  manufacturers',  not  the   Franklin    Institute 
Standard.    Both  weights  and  sizes  are  for  the  unfinished  nut. 
(Dimensions  in  ins.;  weights  in  lbs.) 


*  Square  Nuts. 


Di 


(lag- 
nal. 


Wt.of 

100 
Nuts. 


No.  of 
Nuts 
in       Cc  e 
100  Ibs.'iH  """Z 


t  Hexagon  Nuts. 


li^ 


Short 
Diam. 


Long 
Diam. 


Wt.of 

100 
Nuts. 


No.  of 

Nuts 

in 

100  lbs. 


.71 

.88 

1.00 

1.24 

1.24 
1.41 

1.60 

1.60 
1.77 


1.6 
2.9 
4.9 
7.7 

8.6 
11.8 
16.7 

17.7 
22.8 


1.04 
2.12 
2.30 
2.47 

2.47 
2.83 
2.83 
8.18 

3.18 
3.54 
3.89 

4.24 
4.60 
4.05 
5.30 

5.66 
5.66 
6.01 

6.01 
6.36 
6.72 

7.07 
7.78 
8.49 


82.3 
39.8 
63. 
63. 


04. 
103. 
137. 

145. 
186. 
247. 

319. 
400. 
500. 
620. 

750. 
780. 
930. 

960. 
1130. 
1370. 

1610. 
2110. 
2750. 


3480 
2060 
1290 

1170 
850 
600 

670 
440 


310 
251 
190 
159 

146 
106 

97 

73 

60 
54 
41 

31.3 
24.8 
19.9 
16.2 

13.4 
12.8 
10.7 

10.4 
8.9 
7.3 

6.2 
4.7 
3.6 


m 

1^ 

m 

IH 
2 

2 

2H 

2H 
2H 

3 
3H 


^ 


1 
IH 

\n 

m 


2H 
2H 

3 

3M 


in 


4 


.72 

.87 

1.01 

1.01 
1  15 
1.30 

1.30 
1.44 
1.44 

1.59 
1.78 
1.88 

1.88 

2.02 
2.02 
2.31 


1.3 
2.4 
4.1 

6.8 

7.1 
9.8 
14.0 

14.7 

19.1 
22.9 

27.2 
39. 
44. 
50. 

57. 
64. 
96. 


2.60 
2.89 

3.18 
3.46 
3.75 
4.04 

4.04 
4.33 
4.33 

4.62 
4.91 
5.20 

5.48 
5.T7 
6.06 


134. 
180. 

235. 
300. 

370. 
460. 

450. 


810. 
980. 

1160. 
1340. 
1580. 


8000 

4170 
2410 
1460 

1410 
1020 
710 

680 
620 
440 

870 
256 
226 
196 

176 
156 
104 


75 
56 

42 
33.4 
26.7 
21.5 

22.4 
18.0 
17.7 

14.7 
12.3 
10.2 

8.7 
7.5 
6.3 


Thickness  of  sqiiort  nut  is  equal  to  diameter  of  bolt. 
tThickneas  of  kixagon  nut  not  always  equal  to  diameter  of  boH. 


d  by  Google 


d  by  Google 


BOLTS  AND  NUTS. 


021 


11. — Wbiqht  of  100  Bolts  with  Square  Heads  and  Nuts. 


Length 
unaer 

Diameter  of  Bolts. 

head 
to  point. 

Kin. 

A  in. 

Hin. 

A  in. 

Hin. 

Hin. 

Hin. 

Kin. 

lin. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

lbs. 

IH 

4.0 
4.4 

4.8 

7.0 
7.6 
8.0 

10.5 
11.3 
12.0 

15.2 
16.3 
17.4 

22.5 
23.8 
25.2 

39.5 
41.6 
43.8 

63.0 
66.0 
69.0 

IH 

2^ 

109.0 

163 

2^ 

6.2 

8.5 

12.8 

18.5 

26.5 

45.8 

72.0 

113.3 

169 

2^ 

5.5 

0.0 

13.6 

19.6 

27.8 

48.0 

75.0 

117.5 

174 

2^ 

5.8 

9.5 

14.3 

20.7 

29.1 

50.1 

78.0 

121.8 

180 

3 

6.3 

10.0 

15.0 

21.8 

30.5 

52.3 

81.0 

126.0 

185 

f^ 

7.0 

11.0 

16.5 

24.0 

33.1 

56.5 

87.0 

134.3 

196 

7.8 

12.0 

18.0 

26.2 

35.8 

60.8 

93.1 

142.6 

207 

4H 

8.5 

13.0 

19.5 

28.4 

38.4 

65.0 

99.1 

151.0 

218 

5 

9.3 

14.0 

21.0 

30.6 

41.1 

69.3 

105.2 

169.6 

229 

6H 

10  0 

15.0 

22.6 

32.8 

43.7 

73.5 

111.3 

168.0 

240 

0 

10.8 

16.0 

24.0 

35.0 

46.4 

77.8 

117.3 

176.6 

251 

Q^ 

25.5 
27.0 
28.5 
30.0 

37.2 
39.4 
41.6 
43.8 
46.0 
48.2 
50.4 
52.6 

49.0 

51.7 

54.3 

50.6 

64.9 

70.2 

75  5 

80.8 

86.1 

91.4 

96.7 

102.0 

107.3 

112.6 

117.9 

123.2 

82.0 
86.3 
90.5 
94.8 
103.3 
111.8 
120.3 
128.8 
137.3 
145.8 
154.3 
162.8 
171.0 
179.5 
188.0 
206.5 

123.4 
129.4 
135.0 
141.5 
153.6 
165.7 
177.8 
189.9 
202.0 
214.1 
226.2 
238.3 
250.4 
262.6 
274.7 
286.8 

185.0 
193.7 
202.0 
210.7 
227.8 
244.8 
261.9 
278.9 
296.0 
313.0 
330.1 
347.1 
364.2 
381.2 
398.3 
415.3 

262 

Tf 

273 

7H 

284 

8 

295 

9 

317 

10 

339 

11 

360 

12 

382 

13 

404 

14 

426 

15 

448 

16 

470 

17 

492 

18 

514 

19 

536 

20 

558 

Per  Inch 

1.4 

2.1 

3.1 

4.2 

5.5 

8.5 

12.3 

16.7 

21.8 

additional. 

Weights  op  Nuts  akd  Bolt-Hbads  in  Pounds. 
For  calculating  the  weight  of  longer  Bolts.    , 


Diameter  of  Bolt 
in  Inches. 

H 

H 

H 

Vs 

H 

H 

Weight  of  Hexagon  Nut 
and  Head 

.017 
.021 

.057 
.069 

.128 
.164 

.267 
.320 

.43 
.55 

.73 

Weight  of  Square  Nut 
and  Head 

.88 

Diameter  of  Bolt 
in  Inches. 

1 

IH 

IH 

IH 

2 

2H 

3 

Weight  of  Hexagon  Nut 
and  Head 

1.10 
1.31 

2.14 
2.56 

3.78 
4.42 

5.6 
7.0 

8.75 
10.5 

17.0 
21.0 

28.8 

Weight  of  Square  Nut 
and  Head 

36.4 

d  by  Google 


622 


SL^STRUCTURAL  DETAILS. 


12. — Lao  Screws — ^Wbioht  in  Lbs.  of  100. 


Fig.  44. 


The  Use  of  Lao  Screws. 

The  principal  use  of  las  screws  is  for  bridge  work — in  fastening  ooe 
timber  down  on  another.  Thev  are  better  than  spikes,  Ixit  not  as  good  as 
screw  bolts  (with  nut  and  head. ) 

The  lag  screw  has  a  square  head  and  is  screwed  in  place  with  a  wrench. 
A  plate  washer  is  used  under  the  head  to  distribute  the  bearing  stress  on 
the  timber. 

A  hole  is  first  bored  in  the  timber,  somewhat  smaller  in  dJxuneter  than 
the  screw,  the  lag  screw  is  inserted  in  the  hole  and  tapped  on  the  head  a  few 
times  with  a  sledge  hammer,  and  then  screwed  to  a  nrm  bectfing  with  the 
wrench. 

CaM/«(7n.The  writer  has  used  lag  screws  for  fastening  small  wooden  guard 
rails  (4* xO*)  to  wooden  ties.  When  such  work  is  being  done,  especially  by 
contract,  there  should  be  an  inspector  on  the  work  to  see  that  the  lag  screws 
are  not  hammered  into  the  timber  too  far  with  the  sledge  hammer  before 
the  wrench  is  used.  To  the  contractor,  hammering  is  much  the  cheaper  uad 
is  a  great  temptation. 


13. — ^WooD  Screws — Sizes. 
(Diameter  in  Inches- Number  x  0 . 01826+ 0 .066.) 


d 

i 

6 

E  1 
(A 

6 

i\ 

d 

% 

d 

% 

6 

1 

6 

i 

d 

1 

"^ 

O 

2 

Z 

p 

:z; 

P 

2 

P 

^ 

P 

^: 

P 

25 

P 

0 

066 

4 

.109 

8 

.162 

12 

.216 

16 

.268 

20 

.321 

24 

.374 

28 

.427 

1 

060 

6 

.122 

9 

.175 

13 

.228 

17 

.281 

21 

.334 

26 

.887 

20 

.440 

2 

(K2 

6 

.136 

10 

.188 

14 

.241 

18 

.293 

22 

.347 

26 

.401 

80 

.458 

3 

.096 

7 

.140 

11 

.201 

16 

.266 

19 

.308 

23 

.361 

27 

.414 

d  by  Google 


LAG  SCREWS.    CAST  IRON  SEPARATORS. 


623 


/^    ^\             14, — Standard  Cast  Iron  Separators              /    ^    \ 
V /  FOR  I-Bbams.  V ' 

Pig.  45.  Fig.  46. 


Separators  With  Two  Bolts.    (Fig.  45.) 

24 

80 

UH 

T*i 

H 

12 

9H 

3.41 

.250 

32 

5.50 

20 

80 

13^ 

7h 

H 

12 

9H 

3.41 

.250 

28 

3.10 

20 

65 

7 

H 

12 

8H 

3.23 

.250 

25 

3.10 

18 

56 

125^ 

^i 

H 

9 

»H 

3.16 

.250 

16 

2.75 

15 

80 

13H 

7M 

H 

7H 

9 

3.55 

.250 

15 

1.75 

15 

60 

im 

6J^ 

U 

SH 

3.23 

.250 

15 

1.75 

15 

42 

iifi 

6^ 

H 

7Vi 

7H 

2.98 

.250 

15 

1.75 

12 

40 

11^ 

6 

H 

5 

7H 

2.98 

.250 

11 

1.50 

12 

31.5 

imi 

5'/4 

H 

5 

7M 

2.92 

.250 

11 

1.50 

Separators  With  One  Bolt.    (Fig.  46.) 


40.0 
31.5 
25.0 
21.0 
18.0 

15.0 
12.25 
9.75 
7.50 
5.50 


10«i 
lOH 

It!, 


6 

5H 

5 

4H 

J" 


^ 


1  49 
1.46 
1.40 
1.34 
1.28 

1.25 
1.22 
1.16 
1.13 
0.70 


.125 
.125 
.125 
.125 
.125 

.125 
.125 
.125 
.125 
.09 


1.50 
1.50 
1.25 
1.20 
1.00 

.75 
.60 
.50 
.40 
.25 


Separators  for  18,  20  and  24  in.  beams  are  made  of  H  in.  metal. 

Separators  for  6  to   15  in.  beams  are  made  of  H  in.  metal. 

Separators  for  5  in.  beams  and  under  are  made  of  f^  in.  metal. 
Remarks  on  Cast  Iron  Separators. 

The  use  of  cast  iron  separators  and  bolts  for  fastening  two  or  more 
I-beams  together,  side  by  side,  is  gradually  giving  place  to  steel  diaphiams, 
composed  of  angles  riveted  to  a  connecting  web  plate.  The  latter  is  much 
the  better,  and  is  now  preferred  in  important  steel  building  construction. 
Ctat  iron  separators,  however,  are  still  used  in  connecting  steel  I-beams  in 
grillage  foundations,  where  spaces  between  the  beams  are  fuled  with  concrete. 

Cast  separators  for  timber  work  are  round,  of  cylindrical  or  spool  shape, 
with  a  hole  through  which  the  screw  bolt  passes.  They  are  tised  principally 
for  packing,  between  lines  of  wooden  bndge-stringers,  spacing  the  wooden 
rtringers  ^Kjut  one  inch  apart.  This  spacing  provides  for  the  circulation  of 
air,  which  dries  the  moisture  from  rain  and  retards  rotting  of  the  wood.  Cast 
spool  separators  are  shaped  like  a  spool,  while  the  cylindrical  separators  are 
perfectly  cylindrical  on  the  outside.  In  order  to  save  metal,  in  the  separator, 
the  hole  expands  towards  the  ends,  being  a  little  larger  than^he  bolt.  only, 
at  middle  of  separator.  Digitized  by  LjOOg IC 


624 


23.— STRUCTURAL  DETAILS. 


16. — Dimensions  and  Wbights  of  Cast  Iron  Washbrs. 
(Dimensions  in  inches;  weight  in  lbs.  each.) 


H 


hw 


Fi^.  47. — Diametric  sec- 
tion of  round  washer. 


o 

W 

w 

n 

r 

1^ 

H 

3V$ 

1^ 

H 

3?4 

1'^ 

4^ 

2»^^ 

4Ji 

2H 

rj 

2H 

2?i 

m 

«H 

3 

l?K 

6»i 

3U 

IH 

714 

3H 

IH 

7H 

3?i 

m 

4 

2H 

«^4 

4^ 

9H 

4^ 

9»^ 

A% 

2h 

m 

5 

H 


Wt. 


032 
0.61 
0.78 
0^ 
1.75 
2.30 
300 
4.20 
520 
7.00 
8.30 
1040 
12.40 
13.40 
16.80 
17.50 

ao.oo 


16. — Platb  (Plat)  Washbrs. 
Dimensions,  and  nimiber  per  pound. 


,2  o  c 


Diam. 

Washer 
in  Inches. 


4j    V 

O  « 


'i 

1 

.1^ 
1^ 
IH 


Thickness 
of  Washer. 


.05 
.062 
.062 

.^8 


450     I 


110 
76 
43 
26 
23 


!   i> 


Diam. 

Washer 

in  Inches. 


^3 


IH 

3H 


Thickness 
of  Washer. 


.126 
H 
.141 
.156 

.^2 


OSS 


23. 
15. 
11 

8.5 
6.3 
4  7 
3.6 


Remarks  on  Cast  and  Plate  Washers. 

Cast  iron  washers  are  used  principally  with  screw  bolts  in  connecton  with 
timber  work.  They  are  round  and  have  a  diametric  section  as  shown  in 
Pig.  47.  These  washers  are  sometimes  called  O.  G.  washers,  or  S  washers, 
because  the  outline  ctirve  has  an  O.  G.  (architectiutd  term)  or  5,  shape,  being 
a  reversed  curve. 

Lar^e,  square,  cast  iron  washers  are  often  used  for  anchorage  at  the  ends 
of  rods  m  concrete. 

,  1  ?'**?•  ^  fl*^'  washers  are  stamped  from  sheet  metal,  being  round  with  a 
no  e  1  n  the  center  for  the  bolt.  Large  bolts  require  the  thicker  washers,  that 
win  not  bend  w1i«»t>  flio  Vi^u  :»  *\^u*^^.^.^  C^ r^,^r^\r> 

Digitized  by  VjOOv  IVL 


will  not  bend  when  the  bolt  is  tightened. 


d  by  Google 


636 


n.'^^TRUCT^RAL  DETAILS. 


18. — Standard  Stbbl  Wirb  Nails. 
Sizes,  Lengths  and  Approximate  Number  per  Pound. 


*  Fine,     t  Common. 


19. — Standard  Stbbl  Wirb  Spikbs. 


Length,  Inches.   .  . . 
No.  per  Pound 


6        5 
.203.220 
3      3H 
37     29 

4 
.238 

4 
23 

3 
.259 

18 

2 

.284 

5 

13 

1 

.300 

5H 

10 

1 

.300 

6 

9 

7}^6H 

^1 

Remarks  on  Spikbs  and  Nails. 

Steel  wire  spikes  and  nails  are  made  from  steel  wire,  being  cut. 
and  pointed  by  machine.  They  may  be  either  plain  (smooth)  or  bar 
added  holding  power). 

Cut  spikes  and  nails  have  greater  holding  power  than  the  smoo 
wire,  because  they  have  a  rougher  surface  to  give  the  greater  friction. 

Tests  on  the  holding  power  of  railway  spikes  were  made  by  Mr 
Webber,  Instructor  of  Civ.  Eng.,  Univ.  of  111.,  and  the  results  are  f 
Bulletin  No.  6.  issued  by  the  Experiment  Station.  The  tests  were  o 
spikes  and  plain  spikes:  direct  pull  and  lateral  displacement. 

It  i*to  be  noted  that  the  variation  in  weight  ot  spikes  and  nails 
siderablc,  even  for  the  same  sizes.  r^  ^  ^  ^  T  ^ 

Digitized  by  VjOO^  Lc 


SPIKES,    NAILS.    TACKS. 
20. — Spikbs  and  Nails. 


627 


21. — ^Tacks. 


5* 

Number 

per 
Pound. 

Title 
Ounce. 

II 

si 

Ii 

Number 

per 
Pound. 

«8 

Li 

1 

1 

16000        3 
10666        4 
8000        6 

6400        8 

1 

5333 
4000 
2666 
2000 

10 
12 
14 
16 

1 

1600 
1333 
1143 
1000 

18 
20 
22 
24 

888 
800 

727 
666 

22. — Miscellaneous  Spikes. 
Railroad  Spikes. 


Size  Measured 

Average 

Quantity  of  Spikes  per 
Mile  of  Single  Track. 

Rail  Used. 

Under  Head. 

Number  per 

Kegof  abo 

Pounds. 

Ties  2  Feet  c.  to  c. 

Weight  per  Yard. 

Inches. 

4  Spikes  per  Tie. 

• 
Pounds. 

Pounds. 

Kegs. 

SHxfi 

300 

7040 

35Va 
29H 

75  to  100 

^A 

875 

5870 

45  -    75 

5    xA 

5    xH 

400 

5170 

26 

40  -    56 

450 

4660 

23H 

35  '    40 

4HxH 

530 

3960 

20 

30  •    35 

4xg 

600 

3520 

17H 

25  -    35 

4HxA 

680 

3110 

15H 

20  -    30 

4    xX 

720 

2910 

UH 

20  -    30 

900 

2350 

11 

16  -    26 

4    xi^ 

1000 

2090 

10>^ 

16  -    25 

^Zjjiz 

1190 

1780 

9 

16  -    20 

3   x^ 

1240 

1710 

8H 

16  -    20 

»S^ 

1342 
1600 

1575 
1292 

71  s 

5   Digitize 

^    8  •    16 

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d  by  Google 


2Z,-^TRUCTURAL  DETAILS, 


35.— PiN»— Bbndzno  M0MBNT8 ;  and  Bbarino  Valubs  on  Platbs  1  In.  Thkx. 
(Bending  moment  -  .0082 X fiber  stre88X(dia.)*-HXfiber  stressXareaXdia.) 


■a 
II 

Area  Of 
Bq.  Ins. 

Moments  In  Inch-Pounds  tor  Fiber  Stroses  of 

Plate  "&.  Uilck!at 

16.000  lbs. 
persq.ln. 

18.000  lbs. 
persQ.ln. 

20.000  lbs. 
persq.ln. 

22.600  ibs. 
persq-ln. 

25.000  lbs. 
persq.ln. 

12.000  lbs. 
persq.ln. 

16.000  lbs. 
per8q.ln. 

% 

0.786 
0.994 
1.227 
1.486 

1  470 

2  100 
a  880 
8  830 

1  770 

2  530 

3  450 

4  590 

1  960 

2  800 

3  830 
5  100 

2  210 

3  140 

4  810 

5  740 

a  450 

8  500 
4  790 
6  380 

12  000 

13  600 

15  000 

16  500 

16  000 
16  900 
18  800 

20  600 

1 

1.767 
2.074 

auo& 

a.  761 

4  070 

6  820 

7  890 
0  710 

5960 
7580 
9  470 
11  600 

6  630 
8  430 
10  500 
12  900 

7  460 
9  480 
11  800 
14  600 

8  280 
10  600 
13  200 
16  200 

18  000 

19  500 

21  000 

22  500 

22  500 

24  400 
26  300 

28  100 

% 

8.142 
3.647 
8.976 
4.430 

11  800 
14  100 
16  800 
19  700 

14  100 
17  000 
20  100 
23  700 

15  700 
18  800 
22  400 
26  300 

17  700 
21  200 
26  200 
29  600 

19  600 
23  600 
88  000 
83  900 

24  000 

25  500 

27  000 

28  500 

30  000 

31  900 
83  800 

35  600 

i 

4.909 
6.412 
6.940 
6.492 

23  000 
26  600 
30  600 
85  000 

27  600 
32  000 
36  800 
42  000 

30  700 
35  500 
40  800 
46  700 

34  500 
40  000 
45  900 
62  500 

38  400 
44  400 
61  000 
58  300 

80  000 
31  500 

33  000 

34  500 

37  500 

39  400 
41  300 
43  100 

i 

7.069 
7.670 
8.296 
8.946 

39  800 
44  900 

60  600 
66  600 

47  700 
63  900 
60  700 
67  900 

63  000 
69  900 
67  400 
75  500 

59  600 
67  400 
75  800 
84  900 

66  300 
74  900 
84  800 
94  400 

36  000 
87  500 

39  000 

40  600 

45  000 

46  900 
48  800 
50  606 

i 

9.621 
10.321 
11.045 
11.793 

63  100 
70  100 
77  700 
86  700 

75  800 
84  200 
93  200 
102  800 

84  200 
93  600 
103  500 
114  200 

94  700 
105  200 
116  500 
128  500 

105  200 
116  900 
129  400 
142  800 

42  000 

43  500 

45  000 

46  600 

62  800 

54  400 
56  300 
58  100 

1 

12.566 
13.364 
14.186 
15.033 

94  300 
103  400 
113  000 
123  800 

113  100 
124  000 
135  700 
148  000 

125  700 
137  800 
150  700 
164  400 

141  400 
155  000 
169  600 
185  000 

167  100 
172  300 
188  400 
205  500 

48  000 

49  500 

61  000 

62  500 

60  000 

61  900 

63  800 
65  600 

4% 

16.904 
16.800 
17.721 
18.665 

134  200 
145  700 
157  800 
170  600 

161  000 
174  800 
189  400 
204  700 

178  900 
194  800 
210  400 
227  500 

201  300 
218  500 
236  700 
255  900 

223  700 
242  800 
263  000 
284  400 

64  000 
55  500 

57  000 

58  500 

67  500 

69  400 
71  300 
73  100 

5 

19.635 
20.629 
21.648 
22.691 

184  100 
198  200 
213  100 
228  700 

220  900 
237  900 
255  700 
274  400 

245  400 
264  300 
284  100 
304  900 

276  100 
297  300 
319  600 
343  000 

306  800 
330  400 
355  200 
381  100 

60  000 

61  600 

63  000 

64  500 

75  000 

76  900 

78  800 
80  600 

m 

23.758 
24.850 
25.967 
27.109 

245  000 
262  100 
280  000 
298  600 

294  000 
814  500 
335  900 
358  300 

326  700 
349  500 
373  300 
398  200 

367  500 
393  100 
419  900 
447  900 

408  300 
436  800 
466  600 
497  700 

66  000 

67  600 

69  000 

70  500 

83  500 

84  400 
86  300 
88  100 

6 

SI 

28.274 
29.465 
30.680 
31.919 

318  100 
338  400 
359  500 
881  500 

381  700 
406  100 
431  400 
457  800 

424  100 
451  200 
479  400 
508  700 

477  100 
507  600 
639  800 
572  300 

530  200 
564  000 

599  200 
635  900 

72  000 
78  500 

75  000 

76  500 

90  000 

91  900 
93  880 
95  600 

1 

38.183 
34.472 
35.786 
87.123 

404  400 
428  200 
452  900 
478  500 

485  300 
513  800 
643  500 
574  200 

539  200 
570  900 
603  900 
638  000 

606  600 
642  300 
679  400 
717  800 

674  000 
713  700 
754  800 
797  500 

78  000 

79  500 

81  000 

82  500 

97  800 
99  400 
101360 
103  100 

7 
8 

38.486 
44.179 
60.265 

505  100 
621  300 
.754  000 

606  100 
745  500 
904  800 

673  500 

828  400 

1  005  300 

757  700 

931  900 

1  131  000 

841  900 
1  035  400 
1  256  600 

84  000 
90  000 
96  000 

106  066 
112  500 
120  000 

d  by  Google 


633 


2&,-~STRUCTURAL  DETAILS. 


27. — Clbvisbs. 
American  Bridge  Company's  Standards. 


All  dimensions  in 
inches. 


D(g>0=> 


Grip  G  can  be  made 
to  suit  connections. 


Diameter 

Max. 

Pin  P. 

aevis 

of  aevlB 

D. 

ForkF 

Nut  N 

Width  W 

ThlckDeasT 

A 

B 

ApTx.Wl. 

IH 

m 

m 

IH 

H 

6 

5 

5 

2M 

\H 

1^4 

1»4 

^ 

9 

8 

9 

2H 

2k 

2H 

H 

9 

8 

14 

3H 

2H 

2^4' 

2H 

H 

9 

8 

25 

3K 

3>i 

3H 

Vs 

9 

8 

38 

Table  giving  Diameter  of  Clevis  for  given  Rod  and 

Pin. 

Rod. 

Pins. 

Rod 

1 

1 

\ 

1  m  M  m 

2  2H  2H  2H 

3  ZH  3H  SH 

4 

i 

1 

1 

OJ 

di 

D 

p 

li 

0: 

h 

1 
\M 

\H 

iH 
\% 

2 

1 

IH 

IH 
IH 

m 

\H 

VA 

2 

2H 

214 

2H 

2M 

2% 

2H 

2H 

i 

ah    3 

3     3l    3 

4 

5      5 
5      5 

5 
5 
6 
5 

nr 

6 

6      6 
6      6 

7 
7 

1 
w 

IH 
IH 
IH 

\H 
2 

H 
H 
H 

1 
IH 

IH 
IH 

H 

4      4 
4      4 

4 

4 

4 

4, 

H 
1 
IH 

5      5 

5      5 

5 

5 

5    5      6      5 

5    5      5      6 

TlS      5      5 

515      5  16 

IH 

in 

2 

6  T     6      6 
6    6      6      6    f 

6  617 
-17      7 

7  7      7 

7 
7 
7^ 

2yH 

7      7    1 

7    7      7 
7    7      7 

2H 

M 

1 

c? 

1  IH  m  IH 

2  2H  2H  2^i 

3  3H  SH  S^i 

4 

Rod. 

Pins. 

Rod. 

Clevises  above  and  to  right  of  heavy  zigzag  line  may  be  used  with  forks 

have  forks  cl( 

by  Google 


Btraigrht 

.    Clevises  below  and  to  left  of  same  line  should  have  forks  closed  in  until 
pm  IS  not  overstrained. 


d  by  Google 


634 


Zi,— STRUCTURAL  DETAILS. 


20. — Upset  ^crbw  Ends  for  Round  and  Square  Bars. 
Screw  threads  are  the  Franklin  Institute  Standard. 
Allow  6  inches  additional  length  of  rod  for  5  in.  length  of  thread. 


U 


lis 


If 


Length  of 
Upset. 
Inches. 


hi 


|5S^ 


Length  of 
Upset. 
Inches. 


in 

IS 


1-4 


in 


I 

18 

1^ 

151. 

m 

VA 
VA 
2 
2 

ill 
i^ 

2H 

2i^ 
2H 


.731 
.837 


.940 
1.065 
1.066 

1.160 
1.160 
1.284 
1.284 

1.389 
1.389 
1.490 
1.490 

1.616 
1.615 
1.712 
1.712 

1.837 
1.837 
1.962 
1.962 

2.087 
2.087 
2.175 


6H 

6 
5 

5 
5 

4H 
4>4 

4^ 

4H 
44 
4>4 

4H 
4>s 
4 


2H 
2^ 

2K 
3 

3}i 
3M 

4 

4 

4^4 

45i 

5 
6  , 

5Ji^ 
6^i 

6H 
5k 

5?4 

6^ 

6>4 

6H 


4>i 
4>i 
4H 
4>i 

4H 

4^ 

4*4 

4^4 

6 
5 
6 
6 


6^2A 
6H   2H 

5H 


2A 
2K 

"2A' 


6^4 

6 
6 
6 


I 

6J^2K 


3H 


^ 


2H 


2ii 


2.175 
2.30O 
2.300 
2.425 

2  550 
2.550 
2.629 
2.754 

2.764 
2.879 
2.879 
3.004 

3.0O4 
3.100 
3.225 
3.225 

3.317 
3.442 
3.442 
3.667 

3.692 
3.692 
3.798 
3.923 


6H     6 
6^4     - 

6?-4 


7H 


6^ 


4  7H1  6W 

4  7H  ok 

3H  7>4  6^ 

3H  8  m 


I. 

3H 

3 
3 
3 
3 

3 
8 

2H 
2H 


^?4 

2H 


8 

8Vi 
8M 
8H 


10 
10 
10 
10 

lOH 
lOH 
lOH 
lOH 


6»i 


7 
7 
7K 

7K 

7a 

7H 
7H 

8 


lOH    8 

11  1   $H 


*  Phoenix  Iron  Company. 

t  Cambria  Steel  Company  upset  lengths  for  use  with  Standard  tum- 
buckles  (6  inches  between  heads)  and  with  clevises.  Make  upset  one  inch 
shorter  for  use  with  ordinary  right  and  left  nuts.  For  other  uses  length  of 
upset  will  vary  to  suit  the  particular  case. 

Right  and  Left  Nuts. 
(Sleeve  Nuts.) 


Fig.  57. 


Counter  and  Lateral  Rods. 
Solid  or  Upset  Eyes. 


Counter  and  Lateral  Rods. 
Loop  Welded  Eyes. 


>  n' K >A-. 

nour^Bni*.  Sc(uar«Bar». 
Fig.  68. 


Digitized  by  CjC^^'L 


d  by  Google 


686 


Z^-^TRUCTURAL  DETAILS. 


and  if  p  is  leas  than  h. 


,.*_y  (*)•_.„-,>. 


.(« 


Combining  the  equation  of  the  circle  (1)  and  of  the  equilateral  hyper- 
bola (2)  analytically  IS  a  complex 
process  and  unnecessary  in  solv-    Tt: 
mg  the  values  of  x  and  y. 

By  inspection.  Fig.  61,  it  will 
be  seen  that  as  the  point  s  ap- 
proaches the  origin  o  (as  tne 
width  of  brace  decreases)  the 
angles  a  and  Oi  increase,  and 
when   5  reaches  o  tan   a  »  tan 

tion  of  a  straight  line  tangent  to 
the  hyperbola  at  the  origin  o  is 


That  is  to  say,  the  equa- 


.(3) 


H X- 

Pig.  62. 
,  we  know  very  nearly  where  the  point  s 


Plotting  this  line  (see  Fig.  62). __  ^ 

is  on  the  circle  (1).  It  will  be  just  below  and  close  to  it.  Then  solving 
equation  (3)  for  two  values  of  x,  on  either  side  of  and  near  s  will  give,  without 
appreciable  error,  the  tangent  to  the  hyperbola  at  5,  and  the  intersection  erf 
this  tangent  with  the  circle  will  be  the  point  s. 

Example:  Let  height  of  truss  <-  20  ft.  clear  between  chords;  panet 
length  —  12  ft.;  width  of  brace  *-  14  ins.;  then,  reducing  to  inches,  k  » 
120.  p  -  72.  d  -  7.  With  o  as  origin  plot  circle  (1)  with  d  as  radius,  fuD 
sire;  also  lay  off  tangent,  equation  (3),  intersecting  the  circle  at  T.  The 
point  s  will  he  a  little  below  T  on  the  circle.  Assume  Xx  —  6,  then,  equation 
(2),  yi  -  60  -  \/3. 600  -  396  ->  3.40.  Assume  Xi  -  6>i.  then  equation  (2). 
yj  -  60  -vTeOO  -  410.94  -  3.62. 

Plot  Xt  Vi  and  X2  yal  connect  with  line  intersecting  circle  at  s.  Then, 
by  scale,  x  »>  6.09  ins.,  y  »  3.45  ins.     A  s  B  is  face  of  angle  block.     Length 

of  brace  is       

2  \/(A  -  y)»  +  (p  -  «)»  -  22  ft.  3W  ins.  +  .     Ans. 

*Table8  of  Cubes  and  Squares. — ^The  subjoined  tables  of  cubes  and  sqtsares 
are  very  useful  in  designing  and  detailing.  For  convenient  reference  they 
are  listed  as  follows: 

Table  31.  —Cubes  of  Inches,    0*  to      V,  advancing  by  64ths  and  S^ds. 

••      31a.—    "       "        ••         9*  to    29'.         "  **     16ths. 

"      81b.—    "       ••        "       29*  to  lOO*.         *'  "       8ths. 

"      32.  —Squares of  Inches,     O'to  12*  (0' to  1').  advancing  by  64ths. 

••      32a.— 12*  to  120*  (1'  to  lO')      "  '^  Sinds. 

"      32b.—     "        "        "     120*  to  624*  (lO'to  6^)    "  "  leths. 

Note  that  the  last  coliimn  of  Table  82b.  (  + A),  is  the  average  amovmt 
(the  amount  at  the  center  of  the  respective  line — the  half-inch  column)  to 
be  added  for  each  32nd  of  an  inch.  Thus,  the  square  for  13*  OA  « 
24472.69;  and  for  13' OH'  is  24472.69+9.78-24482.47.  The  same  iesu:t 
can  also  be  obtained  by  adding  the  squares  of  13^  OiV'  and  13^  OW 
together,  and  dividing  the  sum  by  2;  thus,  ( 24 4 72. 69 -f  24492.25) -4-2 « 
24482.47.  Remember  that  this  difference  for  (j^)  is  for  the  H^'-column,  in 
middle  of  line;  and  that  for  the  beginning  of  the  line  the  tabular  difference 
in  the  last  column  should  be  decreased  by  0.03,  and  increased  by  O.OS  for 
end  of  same  line.  This  refinement,  however,  of  modifying  the  amounu 
given  in  the  last  column,  to  conform  to  different  parts  of  the  line,  may 
generally  be  neglected. 

«    ,^*P^»^*on  of  Uses  of  Tables  31  to  32  6.— These  tables  may  be  used  ic 

J:V^  bending  moments,  moments  of  resistance,  moments  oi  inertia  and 

radu  of  gyration;  and  in  the  solution  of  right  angle  triangles  when  two  sides 


PROBS,  IN  CUBES  AND  SQUARES^MOMENTS. 


637 


are  gi'ren,  and  of  any  triangle  when  three  sides  are  given.    The  following 
examples  will  illustrate. 

PiKDiNo  Bbkdino  Moments.    (Table  32b.) 
Example. — A  girder  having  a  span  (L)  of  14'  6A'  supports  a  uniform 
load  (IV)  of  400  lbs.  per  lin.  ft.    What  is  the  bending  moment  (Af ')  in  tn.-lbs.  ? 

12  WL* 
Solution. — ^Prom  the  well-known  formula  M'  —  — s *  ^e  have,  if  /  — 


span  in  ins.  —  12L,Af'*- 


WP         400  X  30080.6 


8 
-  126336  in.-lbs.    Ans. 


12X8  12X8 

PiNDiNO  Rbsistino  Mombnts.     (Table  32a.) 
Example. — What  is  the  resisting  moment  in  inch4bs.  (Af')  of  a  rect- 


angular beam  (f  wide  (b}  and  12^'  deep  (i).  assuming  the  allowable  fiber 
■CSS  per  sq.  '       ^ 
Solution  .- 


stress  per  sq.  in.  (/)  —  1000  lbs.? 

lution. — From  the  well-known  formula  Af *  ■■  H  /  ^  <^i  we  have,  by 


substitution.  M'  -  >000X  6X  165.766   _  ^^^^^^  j^  j^     ^^ 
o 
Finding  Radii  op  Gyration. 
The  square  of  the  radius  of  gyration  (r*)  —  the  moment  of  inertia  (/) 
divided  by  the  area  (A)  of  the  section.     Thus  r  -  Vl+A. 

Finding  Mombnts  op  Inbrtia. 

Example.  —  Fig.  63 
represents  the  section  of 
a  steel  column  latticed  on 
two  of  its  sides.  Find  the 
moments  of  inertia  about 
the  axes  X  and  Y, 

Solution. — ^The  mom- 
ent of  inertia  (/)  of  a  rect- 
angle about  its  base,  is  /  — 
W*  +  3;  in  which  6  — width 
and  li»  height  of  rectangle. 
Hence.  3/-W.  Now 
Pig.  63  is  symmetrical 
about  each  of  its  axes, 
hence  if  we  find  the  value 
of  3/  for  one-quarter  of  the 
section  and  then  increase 
this  value  by  one-third,  we 
obtain  the  value  4/  for  one- 
fourth  of  the  section  —  / 
for  the  whole  section.  The 
calculation  is  tabulated 
below;  the  values  of  6/r* 
being  made  up  from  the 
various  rectangles  in  one- 
quarter  of  the  section. 


frfc*  about  axis  X. 


bf^  about  axis  Y. 


30 


)»  -  -f 


plate.       ttX(16 
173^  plate.      «X(^)»  -  + 


2320.31      15 

-  16 
418.70        8«4^X 

-  8?^X 


X(10A)»  -  +16450.65 
X(  »*8)»  -  -13375.00 


angle.  6  X(16H)»  -  +20760.48  6  X( 
'^  -^X(14M)»  -  -16386.36  -  5«h'X( 
"      -  HX(  9H)»  -    -      474.88  -     HX( 


9h)»  -  + 

7802.08 

9  )« 

6378.75 

9H)>  -  + 

5350.00 

9  )« 

3918.38 

m)*  — 

29.77 

Add  one-third — 

For    the  whole  section.  Ix 


6638.25 
2212.75 


8851.00 


+  5900.83 

^  1966.94 

Digitized  by  VjOC 

ly  -  7867.77 


638  nSTRUCTURAL  DETAILS. 

Another  Method. — Inttead  of  using  the"rectanfl1e  method*' (moedbg 
case),  we  may  use  the  method  of  "transferrence  of  neutral  azis.  Thns. 
to  find  the  moment  of  inertia  of  the  17H'  X  H*  plate  about  the  axis  Y  iw 
proceed  as  follows:  Find  lo  about  its  own  neutral  axis  (/o  —  W»»  -«-  12  - 
17H  X  (H)*  ■•-  12  -  0.366)  and  then  use  the  formula  ly  »  lo  •¥■  Ac^,  in 
which  A  —  area  of  plate  —  ITVi  X  H.  and  a  —  distance  between  the  two 
axes  (see  Pig.  68).  Hence,  tne  moment  of  inertia  of  the  plate  about  the 
axis  y  -  /y  -  /o  +  ila»  -  0.366  +  17H  X  H  X  (»A)«  -  M8.88.  Proceed 
in  like  manner  with  the  other  plates,  and  the  angles,  etc.  The  sum  of  the 
several  moments  of  inertia  will  oe  the  total  moment  of  inertia  of  the  sectioiL 

Corollary. — In  the  last  method,  above,  we  have  the  equation,  ly  •■ 
lo  +  Acfi.  When  the  section  of  the  column  is  unsymmetrical,  it  is  often 
necessary  to  assume  an  axis  Y  and  find  the  value  of  Jy  about  this  axis,  and 
then,  from  the  said  equation,  to  find  the  vaulea  of  a  and  lo, 

SoLViNo  Right  Anolb  Trianolbs.     (Tables  83,  83a.  83b.) 

Example. — ^What  is  the  hypothenuse  of  a  right  angle  triangle  whose 
base  is  21'  741"  and  perpendicular  Sr  9A'?     (tf-6»-f?.) 

Solution. — ^Prom  Table  32b  we  have: 

Por  square  corresponding  to        21'  TH*  -"    67340.26 

+  *'  -  l«-22 

38*  W  -216616.70 

-383872.17 
Ans.     44'  411'  -  283866.0 

Corollary. — Prom  the  above  equation,  li*  —  6*  +  ^,  it  is  evident  that 
(S  -/i«-//andp«  -  A«-6«. 

Solving  Any  Trianolb — 3  Sidbs  Givbn. 

Example. — In  Fig.  64  let  there  be  given  the  sides  H,  h  and  B  +h. 
Solve  the  triangle. 

Solution. — Drop  the  perpen- 
dicular p  upon  the  base  B  +  6. 
Then,  />«  -  //a  -  B«  -  A»  -  6»; 
therefore.  H«-  A«-  B«-6«. 

Whence,    B  -  6  -  ^^-^. 

ProbUm. — Given  the  three  sides  of  a  triangle  (Pig.  64)  J  fc  —  14'  8ft'. 
H  -  28^  IH",  and  B  +  6  -  36'  6^'.  Solve  for  the  left-hand  angle  at  the  base 
(which  call  ^)? 

Solution. — Using  the  formulas  in  the  solution  to  the  above  Example, 
we  have, 

H-28'  7H':  H«  (ins.) -118078.1 
A-14'3A':   fcMins.)-  29433.7 

.-.  H«  -  A«  (ins.)  -  88644.4;     log  -  4.0476618 
B  +6  (ins.)-      426.60;  log  -  2.6280100 

diff.  -  2.3177328 

.-.  B  -6  (ins.)-      207J4;  log  -  2.3177301 

2)634.34 

.-.  B  (ins.)-      317.17;   log  -  2.6013021 

H  (ins.)  -      343.626;  log  -  2.6800848 

diff. -0.9653073 
Ans.— 5«22°  37'  46'.  from  log  cos  »-  0.06SS076 


C  (-(K  O*)— CI;B£S— 9*  (-(K  9*). 


639 


■CnbM  of  Inches,  0*  to  9*,  Advancino  bt  d4TB8  and  SSnds. 


No. 


8 147  •11  1/32 
0518  i  1/16 
0300  i  3/32 
4414  y  1/8 
7684  i  5/32 
2397  U  3/16 
"  7/32 

»/*^ 
9/32 

5/16 
11/32 
3/8 
13/32 
4675  B  7/16 
B746  315/32 
S250  i  1/2 
7416  !l7/32 
2473  H  9/16 
1650  yi9/32 
S176  i  5/8 
1279  i21/32 
1189  ill/16 
1134  123/32 
r344  I  3/4 
S046  125/32 
)471  gl3/16 
)847  027/32 
r402  i  7/8 
)367  |29/32 
►968  315/16 
1436  |31/32 
»000  [2 

1/32 

1/16 

3/32 

1/8 

5/32 

3/16 

7/32 

1/4 

9/32 

5/16 

11/32 

512  i   3/8 

148  13/32 

7/161 

15/32  1 

1/2  ' 

17/32 

9/16 

9/32 

6/8 

2l/32j 

1/16 

23/32 

25/32 
13/16 
27/32 

29/32^ 
15/16 


Cube. 


.OUOOOOl'i 

09671 

19946 

3084411 
.423821 

5458071 

674561 

810272 

953121 

1033021 
.260981 
.426361 
.599601 

78091 

970451   . 

168427|l5/32 

375000|  1/2 


1/32 

1/16 

3/32 

1/8 

6/32 

3/16 

7/32 

1/4 
9/32 
5/16 
1/32 
3/8 
13/33 
7/16 


.590363 


.814697  9/16 


048187 
291016 
543365 
805420 
077362 
359375 
651642 
954346 
267670 
591797 
926910 
273193 
630829' 
000000 


17/32 


9/32 

6/8 
21/82 
11/16 
23/32 

3/4 
25/32 
13/16 
27/32 

7/8 
29/32 
15/16 
31/32 


380890  1/32 


773682 


178558  3/32 


595703 
025299 
467529 
922577 
390625 
871857 
366455 
874603 
396484 
932281 
482178 
046356 
625000 
218292 
826416 
449554 
087891 
741608, 


1/16 


/8 

6/32 

3/16 

7/32 

1/4 

9/32 

5/16 

11/32 

3/8 

13/32 

7/16 

15/32 

1/2 
17/32 
9/16 
19/32 
5/8 
21/32 
410889  11/16 
095917  23/32 
7968751  3/4 
513947!25/3^ 
2473l4|l3/16 
997162127/32 
7636721  7/8 
547028i  29/32 
34741215/16 


Cube. 


31/32  36. 165009y31/S2il22 


9J31/82|i: 


.00000 
.85257 
,72290 


61118  3/32 


1/32 
\0A 


.51758 
44229 
38550 
347361 
3281 
3279 
34692 
38535 
44336 
52115 
61890 
73679 
87500 
03372 
21313 
41342 
63477 
87735 
14136 
42697 
73438 
06375 
41628 
78915 
18555 
60464 
04663 
51169 
00000 
51175 
04712 
60629 
18945 
79678 
42847 
08469 
76563 


1/8 

6/32 

3/16 

7/32 

1/4 

9/32 

6/16 

11/32 

3/8 

13/32 

7/16 

15/32 

1/2 
17/32 
9/16 
19/32 
6/8 
21/32 
11/16 
23/32 

3/4 
25/32 
13/16 
27/32 

7/8 
29/32 
15/16 
31/32 

1/32 
1/16 
3/32 

1/8 
5/32 
3/16 
7/32 


20239 
95859 
74023 
54752 
38062 
23972 
12500 
03665 
97485 
93979 
93164 
95059 
99683 
07053 
1718a 
30106i 
468251 
643651 
857421 
099761 


47147  9/32 


5/16 
11/32 

3/8 
13/32 

7/16 
15/32 

1/2 
17/32 

9/16 
19/32 

5/8 
21/32 
11/16 
23/32 

3/4 
25/32 
13/16 
27/32 

7/8 
29/32 


Cube. 


37085i'15/16 
67087il31/32, 


125 
127 
129 
132 
134 
137 
139 
142 
144 
147 
49 
52 
56 
58 
60 
163 
166 
169 
172, 
75, 
177 
180 
183 
187, 
190, 
93 
196, 
199 
202, 
206, 
209. 
212. 
216 
219 
222. 
226 
229. 
233. 
236. 
240. 
244 
247. 
251 
256. 
259 
262. 
266. 
270. 
274. 
278 
282. 
286. 
290 
294. 
299 
303. 
307 
311 
316 
320. 
324 
329. 
333 
338 


000001 
35843 
74634 
16391 
61133 
08878 
59644 
13449 
70313 
30252 
93286 
59433 
2871 
01138 
76733 
55515 
37500 
22708 
11157 
02866 
97852 
96133 
97729 
02658 
10938 
22586 
37622 
56064 
77980 
03238 
32007 
64255 
00000 
39261 
82056 
28403 
78320 
31827 
88940 
49680 
4063 
82108 
53833 
29257 
08398 
91275 
77906 
68307 
62500 
60501 
623291 
68002 
77639 
90958 
082761 
29514; 
54688^ 
83817 


No, 


/32 

1/16 

3/32 

1/8 

6/32 

3/16 

7/32 

1/4 

9/32 

6/16 

11/32 

3/8 

13/32 

7/16 

15/32 

1/2 
17/32 
9/16 
19/32 
6/8 
21/32 
11/16 
23/32 

3/4 

26/32 

13/16 

27/32 

7/8 

29/32 

15/16 

31/32 

8 

1/32 

1/16 

3/32 

1/8 

5/32 

3/16 

7/32 

1/4 

9/32 

6/16 

11/32 

3/8 

13/32 

7/16 


Cube. 


343 
347 
352 
366 
361 
366 
371 
376 
381 
386 
391 
396 
401 
406 
411 
416 
421 
427 
432 
437 
443 
448 
454 
459 
465 
471 
476 
482, 
488 
494 
500, 
506 
512, 
518 
524 
530, 
536, 
542, 
548. 
555. 
561. 
567. 
574. 
580 
687 
594 
600. 


16919 
54013. 
951171 
402501 
89429| 
42673 


15/321607 

1/2  614. 
17/32620. 

9/16'627. 
19/321634. 

5/8  641. 
21/32648 
11/16655 
23/32  662. 

3/4  669. 
25/32  677. 
13/16684. 
27/32  691. 

7/8  699. 
29/321706. 
15/16>713 
31/32721 


.00000 
.61429 
26978 
.96664 
70608 
.48526 
30737 
17160 
.07813 
.02713 
.01880 
.05331 
.13086 
.25162 
.41577 
.62350 
.87500 
.17044 
.51001 
.89389 
.32227 
79532 
31323 
87619 
48438 
13797 
83716 
58212 
37305 
21011 
09351 
02341 
00000 
02347 
09399 
21176 
37695 
58975 
85034 
15891 
51563 
92068 
37427 
87656 
42773 
02798 
67749 
37643 
2500 
92337 
77173 
67026 
61914 
61856 
66870 
76974 
92188 
12527 
38013 
68661 
04492 
45523 
91772 
43269 


t 
t 


ft 


r 


f^ 

*.'» 


t: 


47^.0000038147. 


d  by  Google 


640  83.— STRUCTURAL  DETAILS, 

31a. — Cubes  of  Inches,  9*  to  29*.  Advancing  by  IOtbs. 


d  by  Google 


d  by  Google 


842 


S&.— STRUCTURAL  DETAILS, 


31b.- 


of  Inches,  69*  to  109*,  Advancing  by  8ths. — Concluded. 


Cube. 


No. 


Cube. 


No. 


Cube. 


Cube. 


«9 


1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 


70 


73 


76 


1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 
I 
1/8 

M^ 
3/8 

1/2 

5/8 

3/4 

7/8 

1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 

3 
1/8 
1/4 
3/8 
1/2 
6/8 
3/4 
7/8 

4 
1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 

5 
1/8 
1/4 
3/8 
1/2 
5/8 
3/4' 
7/8 

1/8 
1/4 
3/8 
1/2 
6/8 
3/4 
7/8 


828509. 
330297. 
332092. 
333894. 
335702. 
337567. 
339338. 
341165. 
343000. 
344840. 
346688. 
348542. 
350402. 
352269. 
354143. 
356024. 
357911. 
359804. 
361705. 
363612. 
365525. 
367446. 
369373. 
371307. 
373248. 
375195. 
377149. 
379110 
381078. 
383052. 
385033. 
387022. 
389017. 
391018> 
393027. 
395043. 
397065. 
399094. 
401130. 
403174. 
405224. 
407281. 
409344. 
411415. 
413493. 
415578. 
417670. 
419769. 
421875. 
423987. 
426107. 
428234. 
430368. 
432510. 
434658. 
436813. 
438976. 
441145. 
443322. 
446506. 
447697, 
449895 
452100 
454313 


77 


/8 
1/4 
3/8 
1/2 
6/8 
3/4 
7/8 
78 
1/8 
1/4 
3/8 
1/2 
6/8 
3/4 
7/8 


5 

0 

0  79 

7   1/8^ 

1  -  " 
V 
9 


5 
0 
4 

7 
9 
0 
0 
0 
9 
8 
6 
5 
3 
1 
083 


U 


1/4 
3/8 
1/2 
5/8 
3/4 
7/8 

0 
1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 

1 
1/8 
1/4 
3/8 
1/2 
5/8 
3/4 

//« 

\^A 

3/8 
1/2 
5/8 
3/4 
7/8 

1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 

1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 


456533 
458760 
460994 
463235 
465484 
467740 
470003 
472274 
474552 
476837 
479129 
481429 
483736 
486051 
488373 
490702 
493039 
495383 
497734 
500093 
502459 
504833 
507215 
509603 
512000 
514403 
616815 
519233 
521660 
524094 
526535 
528984 
531441 
533905 
536377 
538856 
541343 
543838 
546340 
548850 
651368 
553893 
556426 
558967 
561515 
564071, 
566635, 
569207 
671787 
574374, 
576969, 
579572 
582182 
584801 
587427 
590061 
592704 
595353 
598011 
600677 
603351 
606032 
608722 
611419 


85 


1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 

6 
1/8 
1/4 
3/8" 
1/2 
6/8 
3/4 
7/8 

7 
1/8 
1/4 
3/8 
1/2 
5/8 
3/4 

1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 
89 
1/8 
1/4 
3/8 
1/2 
0  6/8 
■  3/4 
7/8 
90 
1/8 
1/4 
3/8 
1/2 
6/8 
3/4 
7/8 


0  91 

31  1/8 
3    ' 
2, 


1/4 
3/8 
1/2 
5/8 
3/4 
7/8 
3 
1/8 
1/4 
3/8 
1/2 
5/8 
3/4 
7/8 


614125. 
616838, 
619559. 
622289. 
625026. 
627771. 
630625. 
633286. 
636056, 
638833. 
641619. 
644412. 
647214. 
650024, 
652842. 
655668. 
658503, 
661345. 
664196. 
667054. 
669921. 
672797. 
675680. 
678672. 
681472. 
684380. 
687296. 
690221. 
693154. 
696095. 
699044. 
702002. 
704969. 
707943. 
710926. 
713917. 
716917. 
719925. 
722941. 
725966. 
729000. 
732041. 
735091. 
738150. 
741217. 
744293. 
747377. 
750469, 
753571. 
756680. 
759798. 
762925. 
766060. 
769204. 
772367. 
775518. 
778688, 
781866. 
785063 
788248, 
791453 
794666 
797887 
801118 


93 

1/8 

*// 
3/8 

1/2 

5/8 

8/4 

7/8 
94 

1/8 

1/4 

3/8 

1/2 

5/8 

3/4 

7/8 
95 

1/8 

1/4 

3/8 

1/2 

5/8 

3/4 

7/8 
96 

1/8 

1/4 

8/8 

1/2 

6/8 

3/4 

7/8 
97 

1/8 

1/4 

3/8 

1/2 

6/8 

3/4 

7/8 
98 

1/8 

1/4 

8/8 

1/2 

5/8 

3/4 

3/8 
1/2 
6/8 
3/4 
7/8 
100 
1/8 
1/4 

8/8101 
1/2  " 
5/8 


804357 
807604 
810861 
814126 
817400 
820683 
823974 
827274 
830584 
833901 
837228 
840564 
843908, 
647261, 
850624 
853995, 
857375 
860768 
864161, 
867568 
670988 
874408 
877842 
881284, 
884736, 
888196 
891666 
895144, 
898632, 
902128, 
905634 
909149. 
912673, 
916205, 
919748, 
923299 
926859, 
930428, 
934007, 
937595, 
941192, 
944798 
948418. 
952037, 
955671, 
959314 
962966, 
966628, 
970299, 
973979 
977668 
981367, 
985074. 
988792 
992618 
996254 

1000000 
003754, 

1007518 
1292 

1015075 
018867 

1028669 
7/8^1026480 


/2 


'A 

3/8 

'A\ 
'A' 

/8 

/2 

5/8 


P05 


106 


030301.6 
034131.1 
037970.7 
/8^104]819.8 
~ 1045178.4 
L5 
1053424.1 
I0573U.3 
.1081208.0 
7^1065114.8 
106M30.1 
1072955.6 
,^1071890.6 
/8  1080885.8 
3/4  1084789.5 
~/8  1088753.5 
1092727.0 
1096710.2 
1100703.1 
1104705.6 
1108717.9 
112739.8 
1116771.5 
120818.9 
1124864.0 
128924.9 
132905.5 
1137075.9 
1141166.1 
1145266.1 
1149375.9 
53495.5 
1157625.0 
161764.3 
165913.5 
1170672.5 
1174241.4 
1178420.2 
1182608.9 
186807.5 
1191016.6 
196834.5 
1190463.9 
1203701.8 
207949.6 
312208.6 
316476.3 
1320754.6 
1225042.0 
I22924I.4 
1232649. S 
1237968.3 
242296.9 
^.246625.5 
3/^12509M.2 
'    1266242.1 
1259712,0 
1264092.1 
.    .12684M.S 
/8 1272279.6 
/21277289,I 
'^1281798.5 
._  1286128. T 
/8  1290978.7 


69*  (-5'  9')-CUBES-~lWl^%^\^og\e 


0»  (-0'  irh-SQUARES-^'  (-C  6^. 


643 


32.'-S4iMres  of  InchM,  if  to  ^  (0"  if  to  V  tT),  Advancino 
BY  64ths. 


Ilk 

0 

1 

2 

3 

4 

S 

la. 

1.0000000 
1.0314941 

4.0000000 
4.0627441 

9.000000 
9.093994 

16.000000 
16.125244 

25.000000 
25.156494 



1/64 

■';66e244i4 

i/64 

1/32 

.00097656 

1.0634766 

4.1259766 

9.188477 

16.250977 

25.313477 

1/32 

3/64 

.00219727 

1.0959473 

4.1896973 

9.283447 

16.377197 

25.470947 

8/64 

1/16 

.00390625 

1.1289063 

4.2539063 

9.378906 

16.503906 

25.628906 

1/18 

5/64 

.00610352 

1.1623535 

4.3186035 

9.474854 

16.631104 

25.787364 

5/64 

3/32 

.00878906 

1.1962891 

4.3837891 

9.571289 

16.758789 

25.946289 

3/32 

T/64 

.01196289 

1.2307129 

4.4494629 

9.668213 

16.886963 

26.105713 

7/64 

1/8 

.01562500 

1.2656250 

4.5156250 

9.765625 

17.015625 

26.265625 

1/8 

f/64 

.01977539 

1.3010254 

4.5822754 

9.863552 

17.144775 

26.426025 

9/64 

5/32 

.02441406 

1.3369141 

4.6494141 

9.961914 

17.274414 

26.586914 

5/32 

11/64 

.02954102 

1.8732910 

4.7170410 

10.060791 

17.404541 

26.748291 

11/64 

3/16 

.03515625 

1.4101563 

4.7851563 

10.160156 

17.535156 

26.910156 

3/16 

13/64 

.04125977 

1.4475098 

4.8537698 

10.260010 

17.666260 

27.072510 

13/64 

7/32 

.04785156 

1.4853516 

4.9228516 

10.360352 

17.797852 

27.235352 

7/32 

15/64 

.05493164 

1.52S6816 

4.9924316 

10.461182 

17.929932 

27.898682 

16/64 

1/4 

.06250000 

1.5625000 

5.0625000 

10.562500 

18.062500 

27.562500 

1/4 

17/64 

.07055664 

1.6018066 

6.1330566 

10.664307 

18.195657 

27.726807 

17/64 

9/32 

.07910156 

1.6416016 

5.2041016 

10.766602 

18.329102 

27.891602 

9/32 

lt/64 

.08813477 

1.6818848 

6.2756348 

10.869385 

18.463135 

28.056885 

19/64 

6/16 

.09765625 

1.7226563 

5.3476563 

10.972656 

18.597656 

28.222656 

.6/16 

21/64 

.10766602 

1.7639160 

5.4201660 

11.076416 

18.732666 

28.388916 

21/64 

11/32 

.11816406 

1.8056641 

5.4931641 

11.180664 

18.868164 

28.555664 

11/32 

23/64 

.12915039 

1.8479004 

5.6666504 

U. 285400 

19.004150 

28.722900 

23/64 

8/8 

.14062500 

1.8906250 

5.6406250 

11.390625 

19.140625 

28.890625 

3/8 

23/64 

.15258789 

1.9338379 

6.7150879 

11.496338 

19.277588 

29.058838 

25/64 

13/32 

.16503906 

1.9775391 

5.7900391 

11.602539 

19.415039 

29.227539 

13/32 

27/64 

.17797852 

2.0217285 

5.8654785 

11.709229 

19.552979 

29.396729 

27/64 

7/16 

.19140625 

2.0664063 

5.9414063 

11.816406 

19.691406 

29.566406 

7/18 

29/64 

.20532227 

2.1115723 

6.0178223 

11.924072 

19.830322 

29.736572 

29/64 

15/32 

.21972656 

2.1572266 

6  0947266 

12.032227 

19.969727 

29.907227 

15/32 

31/64 

.23461914 

2.2033691 

6.1721191 

12.140869 

20.109619 

30.078369 

31/64 

1/2 

.25000000 

2.2500000 

6.2500000 

12.250000 

20.250000 

30.250000 

1/2 

33/64 

.26586914 

2.2971191 

6.3283691 

12.359619 

20.390869 

30.422119 

38/64 

17/32 

.28222656 

2.3447266 

6.4072266 

12.469727 

20.532227 

30.594727 

17/32 

35/64 

.29907227 

2.3928223 

6.4865723 

12.580322 
-fS. 691406 

20.674072 

30.767822 

35/64 

9/16 

.31640625 

2.4414063 

6.5664063 

20.816406 

30.941406 

9/16 

37/64 

.33422852 

2.4904785 

6.6467285 

12.802979 

20.959229 

31.115479 

37/64 

19/3^ 

.35253906 

2.5400391 

6.7275391 

12.915039 

21.102539 

31.290039 

19/32 

39/64 

.37133789 

2.5900879 

6.8088379 

13.027588 

21.246338 

31.465088 

39/64 

5/8 

.39062500 

2.6406250 

6.8906250 

13.140625 

21.390625 

31.640625 

5/8 

41/64 

.41040039 

2.6916504 

6.9729004 

13.254150 

21.535400 

31.816650 

41/64 

21/32 

.43066406 

2.7431641 

7.0556641 

13.368164 

21.680664 

31.993164 

21/33 

48/64 

.45141602 

2.7951660 

7.1389160 

13.482666 

31.826416 

82.170166 

43/64 

11/16 

.47265625 

2.8476563 

7.2226563 

13.597656 

21.972636 

32.347656 

11/16 

45/64 

.49438477 

2.9006348 

7.3068848 

13.713135 

22.119385 

32.525635 

45/64 

38/32 

.51660156 

2.9541016 

7.3916016 

13.829102 

22.266602 

32.704102 

23/32 

«?/»4 

.53930664 

3.0080566 

7.4768066 

13.945557 

22.414307 

32  883057 

47/64 

3/4 

.66250000 

3.0625000 

7.5625000 

14.062500 

22.562500 

33.062500 

3/4 

49/64 

.58618164 

3.1174316 

7.6486816 

14.179932 

22.711182 

33.242432 

49/64 

25/32 

.61035156 

3.1728516 

7.7353516 

14.297852 

22.860352 

33.422852 

25/32 

51/64 

.63500977 

3.2287598 

7.8225098 

14.416260 

23.010010 

33.603760 

51/64 

13/16 

.66015625 

3.2851563 

7.9101563 

14.535156 

23.160156 

33.785156 

13/16 

53/64 

.68579102 

3.3420410 

7.9982910 

14.654541 

23.310791 

33.967041 

63/64 

27/32 

.71191406 

3.3994141 

8.0869141 

14.774414 

23.461914 

34.149414 

27/32 

55/64 

.73852539 

3.4572754 

8.1760254 

14.894775 

23.613525 

34.332275 

65/64 

7/8 

.76562500 

3.5156250 

8.2656250 

15.015625 

23.76.1625 

34.515625 

7/8 

S7/64 

.79321289 

3.6744629 

8.3557129 

15.136963 

23.918213 

34.699463 

67/64 

29/32 

.82128906 

3.6337891 

8.4462891 

15.258789 

24.071289 

34.883789 

29/33 

59/64 

.84985352 

3.6936035 

8.5373535 

15.381104 

24.224854 

35.068604 

69/64 

15/16 

.87890625 

8.7539063 

8.6289063 

16.503906 

24.378906 

35.253906 

15/16 

61/64 

.90844727 

3.8146973 

8.7209473 

15.627197 

24.533447 

35.439697 

61/64 

81/32 

.93847656 

3.8759766 

8.8134766 

15.750977 

24.688477 

35.625977 

31/32 

63/64 

.96899414 

8.9377441 

8.9064941 

15.876244 

24.843994 

35.812744 
r^ 

63/64 

Digitized  by 


Google 


644 


9B.— STRUCTURAL  DETAILS, 


32.— Squares  of  InchM,  6"  to  ir  (Cd*  to  I'O*),  Advamcino 
BY  64ths. — Concluded. 


la. 

6 

7 

8 

9 

10 

n 

la. 

36.000000 
36.187744 

49.000000 
49.218994 

64.000000 
64.250244 

81.000000 
81.281494 

100.00000 
100.31274 

121.00000 
121.84399 

'i'/u 

i/ii 

1/32 

36.875977 

49.438477 

64.500977 

81.563477 

100.62598 

121.68848 

1/32 

S/64 

36.564697 

49.658447 

64.752197 

81.845947 

100.93970 

122.03345 

3/64 

1/16 

36.753906 

49.878906 

65.003906 

82.128906 

101.25391 

122.37891 

1/1« 

6/64 

36.943604 

50.099854 

65.256104 

83.412354 

101.56860 

122.72485 

5/64 

3/32 

87.133789 

50.321289 

66.608789 

82.696289 

101.88379 

123.07129 

8/32 

7/64 

37.324463 

30.543213 

65.761963 

82.980713 

102.19946 

123.41821 

7/64 

1/8 

37.515625 

60.765625 

66.015625 

83.265635 

102.51563 

123.76663 

1/8 

«/64 

37.707275 

50.988525 

66.269775 

83.551025 

102.83228 

124.11353 

9/64 

5/32 

37.899414 

51.211914 

66.524414 

83.836914 

103.14941 

124.46191 

S/32 

11/64 

38.092041 

51.435791 

66.779541 

84.123291 

103.46704 

124.81079 

11/64 

8/16 

38.285156 

61.660156 

67.035156 

84.410156 

103.78516 

125.16016 

3/16 

13/64 

88.478760 

51.885010 

67.291260 

84.697510 

104.10376 

125.51001 

13/64 

7/32 

38.672852 

62.110352 

67.547852 

84.985352 

104.42285 

125.86035 

7/32 

15/64 

38.867432 

52.3361821  67.804932 

85.273682 

104.74243 

126.21118 

15/64 

1/4 

39.062500 

52.562500 

68.062500 

85.662500 

105.06250 

126.56250 

1/4 

17/64 

39.258057 

52.789307 

68.820557 

85.851807 

105.38306 

126.91431 

17/64 

9/32 

39.454102 

53.016602 

68.579102 

86.141602 

105.70410 

127.26660 

9/32 

19/64 

39.650635 

53.244385 

68.838135 

86.431885 

106.02563 

127.61938 

lf/«4 

6/16 

39.847666 

63.472656 

69.097656 

86.722656 

106.34766 

127.97266 

5/16 

21/64 

40.045166 

53.701416 

69.357666 

87.013916 

106.67017 

128.32642 

21/64 

11/32 

40.243164 

63.930664 

69.618164 

87.305664 

106.99316 

128.68066 

11/82 

23/64 

40.441650 

54.160400 

69.879150 

87.597900 

107.31665 

129.03540 

23/64 

3/8 

40.640625 

64.390625 

70.140625 

87.890625 

107.64063 

129.39063 

3/8 

26/64 

40.840088 

54.621338 

70.402588 

88.183838 

107.96509 

129.74634 

25/64 

13/32 

41.040039 

54.853539 

70.665039 

88.477539 

108.29004 

130.10254 

18/32 

27/64 

41.240479 

55.084229 

70.927979 

88.771729 

108.61548 

130.45923 

27/M 

7/16 

41.441406 

55.316406 

71.191406 

89.066406 

108.94141 

130.81641 

7/16 

39/64 

41.642822 

55.549072 

71.455322 

89.361572 

109.26782 

131.17407 

29/64 

15/64 

41.844727 

55.782227 

71.719727 

89.657227 

109.59473 

131.53223 

15/33 

31/64 

42.047119 

56.015869 

71.984619 

89.953369 

109.92212 

131.89087 

31/64 

1/2 

42.250000 

56.250000 

72.250000 

90.250000 

110.25000 

132.25000 

1/2 

33/64 

42.453369 

66.484619 

72.515869 

90.547119 

110.57837 

132.60962 

33/64 

17/32 

42.657227 

56.719727 

72.782227 

90.844727 

110.90723 

132.96973 

17/32 

35/64 

42.861572 

56.955322 

73.049072 

91.142822 

111.23657 

133.33032 

85/64 

9/16 

43.066406 

67.191406 

73.316406 

91.441406 

111.56641 

133.69141 

9/16 

37/64 

43.271729 

57.427979 

73.584229 

91.740479 

111.89673 

134.05296 

37/64 

19/32 

43.477539 

57.665039 

73.852539 

92.040039 

112.22754 

134.41504 

19/33 

39/64 

43.683838 

57.902588 

74.121338 

93.340088 

112.55884 

134.77759 

39/64 

5/8 

43.890625 

58.140625 

74.390625 

92.640625 

112.89063 

135.14063 

5/8 

41/64 

44.097900 

58.379150 

74.660400 

92.941650 

113.22290 

135.50415 

41/64 

21/32 

44.305664 

58.618164 

74.930664 

93.243164 

113.55566 

135.86816 

21/32 

43/64 

44.513916 

58.857666 

75.201416 

93.545166 

113.88892 

136.23267 

43/64 

11/16 

44.722656 

59.097656 

75.472656 

93.847656 

114.22266 

136.59766 

11/16 

45/64 

44.931885 

59.338135 

75.744385 

94.150635 

114.55688 

136.96313 

45/64 

23/32 

45.141602 

59.579102 

76.016602 

94.454102 

114.89160 

137.32910 

23/32 

47/64 

45.351807 

69.820557 

76.289307 

94.758057 

115.22681 

137.69556 

47/64 

3/4 

45.562500 

60.062500 

76.662500 

05.062500 

115.56250 

138.06250 

3/4 

49/64 

45.773682 

60.304932 

76.836182 

95.367432 

115.89868 

138.42993 

49/64 

25/32 

45.985362 

60.547852 

77.110352 

95.672852 

116.23535 

138.79786 

25/33 

51/64 

46.197510 

60.791260 

77.385010 

95.978760 

116.57251 

139.16626 

51/64 

13/16 

46.410156 

61.053156 

77.660156 

96.285156 

116.91016 

139.53516 

13/lS 

53/64 

46.623291 

61.279541 

77.936791 

96.592041 

117.24829 

139.90454 

53/64 

27/32 

46.836914 

61.624414 

78.211914 

96.899414 

117.58691 

140.27441 

27/33 

55/64 

47.051025 

61.769775 

78.488525 

97.207275 

117.92603 

140.64478 

55/44 

7/8 

47.265625 

62.015625 

78.765626 

97.515626 

118.26563 

141.01563 

7/8 

67/64 

47.480713 

62.261963 

79.043213 

97.824463 

118.60571 

141.38696 

67/64 

29/32 

47.696289 

62.508789 

79.321289 

98.133789 

118.94629 

141.75879 

29/38 

69/64 

47.912354 

62.756104 

79.599854 

98.443604 

119.28735 

142.13110 

59/«4 

15/16 

48.128906 

63.003906 

79.878906 

98.753906 

119.62891 

142.50301 

16/16 

61/64 

48.345947 

63.252197 

80.158447 

99.064697 

119.97095 

142.87720 

61/64 

31/32 

48.563477 

63.500977 

80.438477 

99.375977 

120.31348 

143.20098 

31/32 

63/64 

48.781494 

63.750244 

80.718994 

99.687744 

120.65649 

143.62524 

63/64 

of  Inchet,  IT  to  JO*  (I'O*  to  2'0.  Adtancino 

BT  32NDS. 


d  by  Google 


646  ZS.STRUCTURAL  DETAILS, 

a2a.— Squares  of  Inches,  3<r  to  4^*  (2' 6'  to  4'0'),  Advancino 
BY  32nds. — Continued. 


t 

I 
I 
I 
I 

d  by  Google  I 


30*  (-2'  ^')— SQUARES— 6ib'  (-5'  O. 


647 


32a.— SqMTW  of  InchM,  48*  to  M'  (4'  0*  to  5'  6'),  Adtancino 
BT  32NDS. — Continued. 


83 


88 


1/32 
1/16 
8/32 
1/8 
5/32 
8/16 
7/32 
1/4 
8/32 
5/16 

n/32 
8/8 

18/38 
7/16 

15/32 
1/8 

17/32 

18/32 

5/8 

21/32 

11/16 

28/32 

8/4 

35/33 

18/16 

27/32 

7/8 

88/32 

15/16 

31/38 


2304.000 
307.001 
310.004 
313 

2316.016 
311.024 
322.035 
826.048 

2328.063 
331 .07t 
334.098 
337.118 

2340.141 
343.156 
346.191 
849.220 

2352.250 
355.282 
358.316 
361.358 

2364.391 
367.431 
370.473 
373.517 

2376.563 
379.610 
382.660 
385.712 

3888.766 
391.821 
394.879 
397.938 


2500.000 
503.136 
506.254 
600.384 

2512.516 
515.649 
518.785 
521.933 

8525.063 
528.204 
531.348 
534.493 

2537.641 
540.790 
543.941 
547.095 

2550.250 
553.407 
566.566 
559.728 

2562.891 
566.056 
569.223 
572.392 

2575.563 
578.786 
581.910 
585.087 

2588.266 
591.446 
594.629 
597.813 


2704.000 
707.251 
710.504 
713.759 

2717.016 
720.274 
723.535 
726.798 

3730.063 
733.329 
736.598 
739.868 

2743.141 
746.416 
749.691 
752.970 

2756.260 
759.532 
762.816 
766.103 

2769.391 
772.681 
775.973 
779.267 

2782.563 
785.860 
789.160 
792.462 

2795.766 
799.071 
802.379 
805.688 


2916. 
919.876 
922.754 
926.134 

2929.516 
982.899 
936.285 
939.673 

2943.063 
946.454 
949.848 
953.243 

2956.641 
960.040 
963.441 
966.845 

2970.250 
973.667 
977.066 
980.478 

2983.891 
987; 306 
990.723 
994.142 

2997.563 

3000.985 
004.410 
007.837 

3011.266 
014.696 
018.129 
021.563 


3136.000 
139.501 
143.004 
146.509 

8150.016 
153.524 
157.035 
160.548 

3164.063 
167.579 
171.098 
174.618 

3178.141 
181.665 
185.191 
188.720 

3192.250 
195.782 
199.316 
202.853 

3206.391 
209.931 
213.473 
217.017 

3220.563 
224.110 
227.660 
231.212 

3234.766 
238.321 
241.879 
245.438 


3364 
367, 
371, 


396 
400 
403 

3407 
411 
414 
418 

3422 
425 
429 
433 

3436 
440 
444 
447 

3451 
455, 
458. 
462 

3466 
469, 
473 
477, 


3600 

603 

607 

611 
3615 

618 

622 

626. 
3630 

633 

637 

641 
3645. 

648. 

652. 

656. 
3660. 

664. 

667. 

671. 
3675. 

679. 

682. 

686. 
3690. 

691. 

698. 

701. 
3705. 

709. 

713. 

717. 


3844, 
847, 
504]  851 


865, 
3859. 

863, 

867. 

871. 
3875. 

878. 


3890 
894 
898 
902 

3906 
910 
914 
917. 

3921 
925. 
929 
933, 

3937. 
941 
945 
949. 

3953 
957 
961 
965 


4096.000 

.876    100.001 

754]  104.004 

108.009 

4112.016 
116.024 
120.035 
124.048 

4128.063 
132.079 
136.098 
140.118 

4144.141 
148.165 
152.191 
156.220 

4160.250 
164.282 
168.316 
172.353 

4176.391 
180.431 
184.473 
188.517 

4192.565 
196.610 
200.660 
204.712 

4208.766 
212.821 
216.879 
220.938 


la. 


49 


81 


87 


89 


61 


63 


65 


1/32 

l/l« 

8/82 

1/8 

5/32 

8/16 

7/33 

1/4 

9/33 

5/18 

11/32 
3/8 

18/82 

yi% 

15/33 

1/2 
17/38 

9/18 
18/33 

6/8 
81/33 
11/18 
83/32 

3/4 
7&ptt 
13/18 
27/32 

7/8 
29/33 
15/18 
31/33 


3401.000 
404.063 
407.129 
410.196 

2413.266 
416.337 
419.410 
432.485 

2425.563 
428.642 
431.723 
434.806 

2437.891 
440.978 
444.066 
447.157 

2450.250 
453.345 
458.441 
459.540 

2463.641 
465.743 
468.848 
471.954 

2475.063 
478.173 
481.285 
484.399 

2487.516 
490.634 
493.764 
496.876 


2601.000 
604.188 
607.379 
610.571 

2618.766 
616.962 
620.160 
623.360 

2626.563 
629.767 
632.973 
636.181 

2639.391 
643.608 
645.816 
649.032 

2653.250 
655.470 
658.691 
661.915 

2665.141 
668.368 
671.598 
674.829 

2678.068 
681.298 
684.535 
687.774 

3691.016 
694.359 
697.504 
700.751 


3809 
812 
815 
818 

8822 
825 


2835 

888 
842 
845 

2848 
852 
855 
858 

2862 
865 
868 
872 

2875 
878 
882 
885 

2889 
892 
895 
899. 

2902. 
906. 
909. 
912. 


818 
639 
946 
266 

,587 

.910 
235 

.563 
892 

.223 
556 
891 
328 
566 

.907 
250 

.505 

.941 
290 

.641 
993 
348 
704 
063 

.423 
785 
149 
516 
884 
254 
626 


3025.000 
028.438 
031.879 
035.321 

8038.766 
042.212 
045.660 
049.110 

3052.563 
056.017 
059.473 
062.931 

8066.391 
069.853 
073.316 
076.782 

3080.250 
083.720 
087.191 
090.665 

9094.141 
097.618 
101.098 
104.579 

3108.063 
111.548 
115.035 
118.524 

3122.016 
125.509 
129.004 
132.501 


3249.000 

252.563 

256.129 

269.696 
3263.266 

266.837 

270.410 

273.985 
3277.563 

281.142 

284.723 

288.306 
3291.891 

295.478 

299.066 

302.657 
3306.250 

309.845 

313.441 

317.040 
3320.641 

324.243 

327.848 

331.454 
3335.063  3570 

338.6731  573 

342.285    577 

345.899    581 
3349.5I6'3ri85 

353.1341  588 

356.754|  592 

360.376   596 


3481. 
484 

488. 

492 
3495, 

499 

503, 

506, 
3510. 

514. 

517. 

621. 
3525. 

529. 

532. 

536. 
3540. 

543. 

547. 

551. 
3555, 

558, 

562. 

566, 


3721 
724 
728 
732 

3736 
740 
743 
747, 

3751, 
755 
759, 
763 

3766, 
770, 
774, 
778 

3782, 
786 
789 
793. 

3797 
801 
805 
329  809 
063,3813 
798  816 
5351  820, 


824 
3828. 
832. 
836 
840 


3969 
972 
976 
980 

3984 
988. 
992 
996 

4000 
004 
008 
012 

4016 
020 
024 
028 

4032 
036 
040 
044 

4048 
052 
056 
060 

4064 
U68 
072 
076 

4080 
084 
088 
092 


4225.000 
229.063 
233.129 
237.196 

4241.266 
245.337 
249.410 
253.485 

4257.563 
261.642 
266.723 
269.806 

4273.891 
277.978 
282.066 
286.157 

4290.250 
294.345 
298.441 
302.540 

4306.641 
310.742 
314.848 
318.954 

4323.063 
327.173 
331.285 
336.399 

4339.516 
343.634 
347.754 
351.876 


648  iS.— STRUCTURAL  DETAILS. 

22a. — Squares  of  Inches,  66'  to  84'  (5'  6"  to  7'  0*),  Advancing 
BY  32NOS. — Continued. 


d  by  Google 


W  (-y  ^—SQVARES^X^fr  (-«'  V). 


549 


3ia.— Sqwuct  of  InchM,  84'  to  102*  (JV  XoV  d').  Advancing 
BY  SSnds. — Continued. 


84 


84 


92 


94 


100 


1/32 
1/16 
3/32 
1/8 
5/32 
8/16 
7/32 
1/4 
9/32 
5/16 

11/32 
2/8 

13/32 
7/16 

15/32 
1/2 

17/32 
9/16 

19/32 
5/8 

21/32 

11/16 

23/32 

25/32 
13/16 
27/32 
7/8 
2S/32 
15/14 
31/32 


7056.000 
061.251 
066.504 
071.759 

7077.016 
082.374 
087.535 
092.798 

7096.063 
103.329 
108.598 
113.868 

7119.141 
124.415 
129.691 
134.970 

7140.250 
145.532 
150.816 
156.103 

7161.391 
166.681 
171.973 
177.267 

7182.563 
187.860 
193.160 
198.462 

7203.766 
209.071 
214.379 
219.688 


7396.000 
401.376 
406.754 
412.134 

7417.516 
422.899 
428.285 
433.673 

7439.063 
444.454 
449.848 
455.243 

7460.641 
466.040 
471.441 
476.845 

7482.250 
487.657 
493.066 
498.478 

7503.891 
509.306 
514.723 
520.142 

7525.563 
530. 
536.410 
541.837 

7547.266 
552.696 
558.129 
563.563 


7744.000 
749.501 
765.004 
760.509 

7766.016 
771.524 
777.035 
782.548 

7788.063 
793.579 
799.098 
804.618 

7810.141 
815.665 
821.191 
826.720 

7832.250 
837.782 
843.316 
848.853 

7854.391 
859.931 
865.473 
871.017 

7876.563 
882.110 
887.660 
893.212 

7898.766 
904.321 
909.879 
915.438 


8100.000 
105.626 
111.254 
116.884 

8122.516 
128.149 
133.785 
139.423 

8145.063 
150.704 
156.348 
161.993 

8167.641 
173.290 
178.941 
184.595 

8190.250 
195.907 
201.666 
207.228 

8212.891 
218.556 
224.223 
229.892 

8235.563 
241.235 
246.910 
252.687 

8258.266 
263.946 
269.629 
275.313 


8836. ( 
841.1 


8464.000 
469.751 
475.504   847 
481.259   853 

8487.016 


8859.516 


754   228 
634   234 


492.774   865.399   246 


498.535 

504.298 
8510.063 

515.829  888 

521.598  894 

527.368  900 
8533.141 

638.915 

544.691 

550.470 
8556.250 

562.032 

567.816 

573, 
8579.391 

585.181 

590.973 

596.767 
8602.563 

608.360 

614.160 

619.962 
8625.766 

631.571 

637.379 

643.188 


8906 
913 
918 
924 
(930 
936 
942 
947 

8953 
959 
965. 
971. 

8977. 
983 
989 
995 

9001. 
007. 
013 
019. 


9240 


252 
258 

9264 
270 
276 
282 

9288 
294 
300 
306 
250  9312 


LOOO 
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.004 
,009 
,016 
,024 
035 
048 
063 
079 
098 
118, 
141 
165 
191 
220 


610 
616 
622 

9628 
634 
640 
646 

9653 
659, 
665 
671. 

9677. 
683. 
689. 
696. 


9336 
806  342 


25019702 


348 
354 
9360. 
366, 

372. 
378. 
9384. 
390 
396. 
402. 


708 
714 
720 

9726 
733 
739 
745. 

9751, 
757 
763 
770 

9776 
782, 
788. 
794 


000 
126 
.254 
384 
.616 
.649 
.786 
.923 
.063 
.204 
.848 
.493 
,641 
790 
941 
,095 
.250 
407 
566 
,728 
891 
056 
223 
392 
563 
735 
910 
087 
266 
446 
629 
813 


10000.00 
0006.25 
0012.50 
0018.76 

10025.02 
0031.27 
0037.54 
0043.80 

10050  06 
0056.83 
0062.60 
0068.87 

10075.14 
0081.42 
0087.69 
0093.97 

10100.25 
0106.53 
0112.83 
0119.10 

10125.39 
0131.68 
0137.97 
0144.27 

10150.56 
0156.88 
0163.16 
0169.46 

10175.77 
0182.07 
0188.88 
0194.69 


87 


91 


93 


97 


101 


1/32 

1/10 

3/32 

3/f 

5/32 

3/10 

7/32 

1/4 

9/33 

5/16 

11/32 
8/8 

U/32 
7/10 

15/32 
1/2 

3/4 


U/1 

27/3: 


7225.000 
230.313 
235.629 
240.946 
7246.266 
251.587 
256.910 
262.235 
7267.563 
272.893 
278.223 
283.556 
7288.891 
294.228 
299.666 
304.907 
7310.250 
315.595 
320.941 
326.290 
7331.641 
336.993 
342.348 
347.704 
7353.063 
358.423 
363.785 
369.149 
7374.516 
379.884 
385.254 
390.626 


7569.000 
574.438 
579.879 
585.321 

7590.766 
596.212 
601.660 
607.110 

7612.563 
618.017 
623.473 
628.931 

7634.391 
639.853 
645.316 
650.782 

7656.250 
661.720 
667.191 
672.665 

7678.141 
683.618 
689.098 
694.579 

7700.063 
705.548 
711. 
716.524 

7722.016 
727.509 
733.004 
738.601 


7921.000 
926.563 
932.129 
937.696 

7943.266 
948.837 
954.410 
959.985 

7966.663 
971.142 
976.723 
982.306 

7987.891 
993.478 
999.066 

8004.657 

8010.250 
015.845 
021.441 
027.040 

8032.641 
038.243 
043.848 
049.454 

8055.063 
060.673 
066.285 
071.899 

8077.516 
083.134 
088.754 
094.376 


8281.000 
286.688 
292.379 
298.071 

8303.766 
309.462 
315.160 
320.860 

8326.663 
332.267 
337.973 
343.681 

8349.391 
355.103 
360.816 
366.532 

8372.260 
377.970 
383.691 
389.415 

8395.141 
400.868 
406.598 
412.329 

8418.063; 
423.79a 
429.535! 
435.274, 

8441.016' 
446.759 
452.5041 
458.251 


8645.000  9025.000 


654.813 
660.629 
666.446 

8672.266 
678.08: 
683.910 
689.735 

8695.563 
701.392 
707.223 
713.056 

8718.891 
724.728 
730.566 
736.407 

8742.250 
748.095 
753.941 
759.790 

8765.641 
771.493' 


030 
036 
042 
9048 
054 
060 
066 
9072 
078 
084 
090 
9096 
102, 
108 
114, 
9120. 
126, 
132. 
138, 
9144. 
150. 
777.3481  156. 
783.204  162. 
8789  0639168. 
794.9231  174. 
800.785!  180. 
806.649  186. 
8812.51619192. 
818.384,  198. 
824  2541  204. 
830.126  210. 


938 
879 
821 
766 
712 
660 
.610 
563 
517 
473 
431 
391 
353 
316 
282 


9409. 
415. 
421. 

427. 
9433. 

439. 

445. 

451. 
9457. 

463. 

469. 

475. 
9481. 

487 

494 

500 


0009801 
063,  807 
1291  813 
196i  819 


9825, 
831 


250  9506 
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,165  524, 
1419530, 
118  536. 
098'  542. 
079  548, 
063  9555 
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035  567. 
024,  573. 
01619579. 
009|  585. 
004  591. 
001    597. 


844 
163  9850 
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806  869. 
891  9875 
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066  887 
157|  894 
25019900 
345j  906 
441  912 
5401  918 
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743,  931 
848,  937 
954  943 
063  9950 
173  956 
285,  962. 
399!  968, 
5I6'9975, 
634  981, 
754;  987. 
876    993. 


.000  10201.00 
0207.31 
0213.63 
0219.95 

10226.27 
0233.59 
0238.91 
0245.24 

10251.66 
0257.89 
0264.22 
0270.56 

10276.89 
0283.23 
0289.57 
0295.91 


250110302.25 


0308.59 
0314.94 
0321.29 
10327.64 
3681  0333.99 
598j  0340.35 
8291  0346.70 
063  10353.06 
298|  0359.42 
535  0365.79 
7741  C372.15 
01610378.52 
259  0384.88 
504  0391.25 
751   0397.63 


•so 


n.— STRUCTURAL  DETAILS, 


of  InchM,  lOr  to  l2Qr  (y  6'  to  IV  «0,  ADVA 
BT  8nds. — Concluded. 


d  by  Google 


^^  ^—STRUCTURAL  DETAILS, 


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d  by  Google 


662  Zi.— STRUCTURAL  DETAILS. 


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S9S'  (-49'  Of)— SQUARES— ^24'  (-Sr  V).  665 

EXCERPTS  AND  REFERENCES. 

Direct  Method  of  SfMcinc  Rivets  and  Findinf  Positioa.  etc»  of  Stiff- 
rs  in  Plate  Qirden  (By  E.  Schmitt.    Trans.  A.  S.  C.  E..  Vol.  XLV). 


Diagnuns  for  Determiaiiif  Miaimain  Altemate  Spadoc  of  Rivets  (By 

P.  L.  Batchelder.  Eng.  News,  Oct.  31,  1901). — ^This  diagram  is  very  simple 
to  construct  for  any  diameter  of  rivets,  and  is  based  on  the  general  equation, 

A  Table  for  Pitcii  and  Efficiency  of  Riveted  Joints  (By  P.  B.  Hill. 
Bn^.  News,  July  16,  1003). — For  various  thicknesses  of  plates  and  diameters 
of  nvets. 

Standard  tfeads  for  Machine  Screws  (By  H.  G.  Reist.  Eng.  News. 
Tune  29.  ISOI^. — Illustrations  and  table  of  dimensions  of  screws  with  round 
oead,  fillister  head,  flat  head  and  hexagon  head.  (Also  see  Eng.  News.  Dec. 
28,  1905,  for  table  of  standard  threads  for  machine  screws  and  taps,  for  ^' 
diameter  and  less;  also,  Eng.  News.  Jtme  20,  1007.  for  A.  S.  M.  E.  stand- 
ards.) 

Tension-Tests  of  Steel  Angles  with  Various  Types  of  End-Connection 

(By  P.  P.  McKibbcn.    Proc.  A.  S.  T.  M..  1006;  Eng.  News,  July  6,  1006).— 
Table  shows  percent  strength  of  material  developed:    usually  from  76  to 
80%.    (See,  also.  Eng.  News.  Aug.  22.  1007.) 

Cost  of  Shop  Drawings  for  Structural  Iron  and  Steel  (By  R.  H.  Gage. 
•The  Technograph."  Univ.  of  HI.,  No.  21,  1006-7;  Eng.  News,  Aug.  8, 
100^. — Condensed  as  follows: 

Av.  Cost 
Type.  Character  of  Building.  per  Ton. 

A.  Entire  skel.  cons.;  loads  all  carried  to  found'n  by  steel  columns    $1 .45 

B.  Exterior  support^  on  steel  cols. ;  floor  loads  earned  by  exter.  walls  1 .  22 

C.  Inter,  portion  sup.  by  cast  iron  cols.;  li.  Ids.  by  exter.  walls  .70 

D.  No  cols.;  floor  beams  resting  on  masonry  walls  throughout  .  85 

E.  Structure  consisting  mostly  of  roof  trusses  resting  on  columns  2 .47 
P.  Structtare  consisting  mostly  of  roof  trusses  resting  on  mas.  walls  1 .25 
G.  MHlbuUdings  2.56 
H.  Flat  one-story  shop  or  manufacturing  buildings  .  74 
L  Tipples,  mining-  or  other  complicated  structures  4 .  88 
J.  Malt  or  grain  bins  and  hoppers  2.47 
K.     Remodeling  and  additions  where  measurements  are  necessary  before 

details  can  be  made  1 .  87 

The  Detailing  of  Skew  Portals  (By  T.  P.  Davies.  Eng.  News,  Feb. 
11.  1000). — Pormtdas,  diagrams  and  shop  detail  drawings. 

Diagrams  for  Rivet  Pitch  in  Loaded  Girder  Flanges  (By  P.  L.  Pratley. 
Eng.  News,  Feb.  18,  1000). — Formulas  and  diagrams. 

Testa  of  Nickel  Steel  Riveted  Joints  (By  A.  N.  Talbot.  Eng.  Rec.,  Aug. 
20,  1010) . — Gives  details  and  results  of  tests  made  for  the  Board  of  Engineers 
of  the  Quebec  Bridge.  Ulustrations  of  the  joints  tested,  and  tables  of  the 
results  of  the  tests.  Table  3  (not  reproduced  here)  gives  the  tiltimate 
strength  of  the  nickel  steel  joints,  and  of  the  carbon  steel  joints  (tested  in 
1006  by  Am.  Ry.  Eng.  &  M.  W.  Assn.)  reported  in  lbs.  per  sq.  in.  of  the 
shearing  area  of  the  rivets.  The  average  for  the  nickel  steel  joints  is  seen  to 
be  about  16%  greater  than  for  the  carbon  steel  joints.  It  ^ould  be  noted 
that  the  rivets  of  the  nickel  steel  joints  are  considerably  weaker  than  the 
plates  and  that  the  failure  of  these  joints  was  due  in  all  cases  to  shear  of 
rivets,  while  in  the  carbon  steel  joints  there  was  evidentljr  less  inequality 
between  the  strength  of  rivets  and  of  plates,  a  number  of  joints  failing  by 
tgftri"8  the  plate. 

Fonnnlas  for  Use  in  Detailing  Steel  Structures  (By  H.  Vance.  Eng. 
News,  Sept.  1,  1010). — Examples:  Hoppers,  towers  and  oblique  bends  in 
riveted  pipe. 


d  by  Google 


34.— METAL  GAGES. 

1. — Standard  Gagbs.* 


& 

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0 

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.32486 

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.324 

.3066 

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1 

.300 

.2893 

.28125 

.300 

.2830 

.285 

.237 

2 

.284 

.25763 

.265625 

.276 

.2625 

.265 

.219 

8 

.259 

.22942 

.25 

.252 

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.245 

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4 

.238 

.20431 

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6 

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.2070 

.206 

.204 

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.203125 

.192 

.1920 

.190 

.201 

7 

.180 

.14428 

.1876 

.176 

.1770 

.175 

.199 

8 

.165 

.12849 

.171875 

.160 

.1620 

.160 

.197 

9 

.148 

.11443 

.15625 

.144 

.1483 

.145 

.194 

10 

.134 

.10189 

.140625 

.128 

.1350 

.130 

.191 

11 

.120 

.090743 

.125 

.116 

.1205 

.1175 

.IM 

12 

.109 

.0»U808 

.109376 

.104 

.1055 

.1050 

.185 

13 

.095 

.071961 

.09375 

.092 

.0915 

.0925 

.182 

14 

.083 

.064084 

.078125 

.080 

.0800 

.0800 

.180 

15 

.U72 

.057068 

.0703125 

.072 

.0720 

.0700 

.178 

16 

.065 

.05082 

.0625 

.064 

.0625 

.0610 

.175 

17 

.058 

.045257 

.05625 

.056 

.0540 

.0525 

.172 

18 

.049 

.040303 

.05 

.048 

.0475 

.0450 

.168 

19 

.042 

.03589 

.04375 

.040 

.0410 

.0400 

.164 

20 

.035 

.031961 

.0376 

.036 

.0348 

.0360 

.161 

21 

.032 

.028462 

.034375 

.032 

.03175 

.0810 

.157 

22 

.028 

.025347 

.03126 

.028 

.0286 

.0280 

.155 

23 

.025 

.022571 

.028125 

.024 

.0258 

.0250 

.153 

24 

.022 

.0201 

.025 

.022 

.0230 

.0225 

.151 

25 

.020 

.0179 

.021875 

.020 

.0204 

.0200 

AiS 

26 

.018 

.01594 

.01875 

.018 

.0181 

.0180 

.146 

27 

.016 

.014195 

.0171875 

.0164 

.0178 

.0170 

.143 

28 

.014 

.012641 

.015625 

.0148 

.0162 

.0160 

.139 

29 

.013 

.011257 

.0140625 

.0136 

.0150 

.0150 

.134 

30 

.012 

.010025 

.0125 

.0124 

.0140 

.0140 

.127 

31 

.010 

.008928 

.0109375 

.0116 

.0132 

.0130 

.130 

32 

.009 

.00795 

.01015625 

.0108 

.0128 

.0120 

.115 

33 

.008 

.00708 

.009376 

.0100 

.0118 

.0110 

.113 

34 

.007 

.006304 

.00859375 

.0092 

.0104 

.0100 

.119 

35 

.005 

.005614 

.0078125 

.0084 

.0095 

.0095 

.108 

36 

.004 

.005 

.00703125 

.0076 

.0090 

.0090 

.106 

87 

.0044.53 

.006640625 

.0068 

.0085 

.0085 

.103 

38 

.003965 

.00625 

.0060 

.008 

.0080 

.101 

39 

.003531 

.0052 

.0075 

.0075 

.099 

40 

..003144  . 

.0048 

.007 
RoebllDg. 

.0070 

!097 

Stubs' 

Iron 
Wire 

American 

Waah- 
bum  A 
Moen 

mritt^^^S^^'E?^'^  I-  S*^-  35.  Cordage.  Wire  and  Cables,  page 
includes  the  Edison  Gage.  t  T>  means  0000000,  Pi£«Si 

660 


d  by  Google 


El 

:2| 


35.— CORDAGE,  WIRE  AND  CABLES. 

Technical  Cordofe  Temu. 
Makb  Up  (ik  Manupacturb): 
Marlins. — ^Two  yarns  twisted  together. 
Thrtad.— Two     or  i 
more   small    yams  >  Cord. — Several  threads  twisted  toftether. 
twisted  together.       ) 
String. — ^Two  or  more  slightly  larger  yams  twisted  together. 


Strand.— -Three  (by 
some  authorities 
two)  or  more  large 
yams  twisted  to- 
gether. 


Ropf.  —  Several 
strands  twisted  to- 
gether. 

Hawser. — Large  rope 
of  three  strands. 


Shroud  laid. — ^Rope 
of  four  strands 
(with  a  heart). 

Cable.— Thrte  haw- 
sers twisted  to- 
gether  (left 
handed). 


A  Rope  Is: 
Laid — By  twistiiig  strands  together  in  making  the  rope. 
Spliced — By  joining  to  another  rope  by  interweaving  the  strands. 
whipped — ^By  winding  yam  or  small  stuff  arotmd  the  end  to  prevent  tin- 
stranding. 
Served — When  wound  tightly  or  continuously  with  yam  or  small  stuff. 
Parceled — When  served  or  wrapped  tightly  with  canvas. 
Seized — ^When  two  parts  are  bound  tightly  together  by  yam  or  small  stuff. 
Payed — When  painted,  tarred  or  greased  to  resist  wet. 

Practical  Operation: 


Haul. — ^To  pull  on  a  rope. 
Taut. — Drawn  tight  or  strained. 
Bight. — A  loop  in  the  rope. 
Fall. — ^The  rope  in  a  hoisting  tackle. 
Tackle.— An  assemblage  of  ropes  and 
blocks. 


Hitch. — ^Attaching  a  rope  to  an 
object. 

Bend. — ^Attaching  two  ropes  to- 
gether or  to  an  object. 

Knot. — A  loop  or  fastening  with  a 
rope. 


Knots,  Hitches,  etc. — (See  Manila  Rope,  next  page.) 

(Note  that  Ends  are  whipped  to  prevent  unstranding.) 


Fig.  1,  Bight. 


Fig.  2,  Simple  Knot.  Fig.  3,  Figure  8  Knot. 


Fig.  7,  Square  Knot. 


Fig.  8,  Weaver's  Knot. 

Digitized 

668 


.vCf^o^F^"" 


CORDAGE—ROPE, 


669 


Fig.  10.  Carrick  Bend.     Fig.  11.  Stevedore  Knot.      Fig.  12,  Slip  Knot. 

^  ^  -8- 

Fig.  18.  Half  Hitch.       Fig.  14,  Timber  Hitch.     Fig.  16.  Clove  HHch 


Fig.  16.  Timber  Hitch  and  Half 
Hitch. 


Fig.  17,  Round  Turn  and  Half 
Hitch. 


Pig.  18,  Blackwall  Hitch.  Fig.  19.  Fisherman's  Bend. 

Splices. — To  splice  an  ordinary  transmission  rope,  wind  twine  around 
the  rope  the  length  of  the  proposed  splice,  say  6  ft.  or  more,  from  each  end, 
and  unlay  the  strands  back  to  the  twine.  Then  butt  the  ropes  together  so 
that  the  untwisted  strands  will  meet  opposite  each  other  in  pairs.  Next, 
cut  the  twine  and  unlay  one  strand  from  one  rope  end,  following  it  up  with 
a  strand  from  the  other  rope  end.  and  leaving  about  18  or  20  ins.  loose  end 
on  each  strand  at  the  meeting  point,  for  sub-splicing.  Make  the  points  of 
meeting  of  other  pairs  of  strands  sta^sered  regularly  so  no  two  points  will 
be  opposite.  For  sub-splicing  of  each  pair  ot  strands,  split  each  strand, 
unlay  and  interweave,  passing  the  ends  through  the  rope,  or  tie  with  ordi- 
nary knots.    Hammer  smooth. 

Manila  Rope. — (Adapted  from  C.  W.  Hunt.*)  Manila  rope  is  made 
from  Manila  hemp  fibers  (inferior  in  strength  to  the  Italian  hemp).  In 
manufacturing  rope,  the  fibers  are  first  spun  into  a  yam  about  i  in.  in  diam. 
this  yam  being  twisted  in  a  "right-hand  '  direction.  From  20  to  80  of  these 
yams,  depending  on  size  of  rope,  are  then  put  together  and  twisted  in  a 
left-hand"  direction,  into  a  strand.  In  a  3-strand  rope  three,  and  in  a 
4-strand  rope  four,  of  these  strands  are  then  twisted  together,  again  in  a 
'*right-hana"  direction.  Note  that  when  each  strand  is  twisted  it  tends  to 
untwist  the  threads,  but  later  when  the  strands  are  twisted  together  into  a 
rope,  each  strand  tends  to  untwist,  but  to  twist  up  the  threads.  It  is  this 
opposite  twist  of  the  threads  and  strands  that  keeps  the  rope  in  its  proper  form . 

The  durabilitv  of  Manila  rope  is  quite  variable  under  different  uses. 
Experience  has  shown  that  4-strand  rope  is  more  serviceable  than  3-8trand; 
it  is  stronger  for  the  same  diameter,  wears  rounder  and  smoother,  and  the 
section  is  much  nearer  a  circle. 

The  Strenglti  and  Weight  of  Manila  Rope  are  given  by  Mr.  Hunt  in  the 
following  formulas: 

Breaking  strength,  in  pounds  —     7160  X  (diam  in  inches)' (1) 

—       726  X  (circum  in  inches)*  ....  (la) 

Weight  per  lineal  foot,  in  potmds     —     0. 34  X  (diam  in  inches)' (2) 

« 0.0344  X  (circum  in  inches)* (2o) 

♦Sec  Manila  Rope  by  C.  W.  Hunt;  also  Trans.  An>.  Sqc-tM.  E.. 
Vol.  xH.  p.  280.  and  Vol.  xxiii  (1901).  d g tized  byT~,OOgie^ 


670 


U.-^ORDAGE,  WIRE  AND  CABLES. 


Hence,  from  (1)  and  (2)  we  have: 
Breaking  strength  (lbs.)  -  21060  X  weight  per  lineal  foot  Obs.) (S) 

It  is  to  be  noted  from  formula  (3)  that  pound  for  pound,  manila  rope  is 
as  strong  as  steel  which  has  an  ultimate  tensile  strength  of  71600  lbs.  per 
square  inch:  as  a  square  inch  bar  of  steel  weighs  3 . 4  lbs.  per  lineal  foot,  aad 
21060X3.4-71600  lbs. 


1 

. — Weight  akd 

Strbngth  op 

Mani 

LA  RopB.   (By  SLn 

DB  RULB.) 

8 
c 

1 
tStrength  of 

gthof 

R 

Rope. 

>pe. 

§ 

ft) 

♦Weight  ot 
100  ft.  of 

Q 

1 

fi 

Rope. 

;. 

Safe 

. 

Safe 

^ 

g 

h. 

Stren- 

1                                                a. 

Strn- 

o 

gth. 

gth. 

Ins. 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Ins. 

Ins. 

Lbs. 

Lbs. 

/Jrs. 

t 

1.1  +  1.0 

230 

11 

m 

4V, 

69.6-   4.5 

14600 

730 

y£ 

1.9+0.8 

410 

20 

lA 

*H 

77.6-   6.0 

16300 

815 

j^ 

1 

8.4  +  0.6 

730 

36 

5 

85.9-   5.5 

18200 

010 

7^ 

IH 

4.4+0.4 

920 

46 

lU 

5H 

104.0-   6.5 

21800 

1090 

X 

6.4  +  0.2 

1130 

57 

2 

6 

124. OJ-  8.0 

26100 

1300 

\i 

7.7±0.0 

1630 

81 

2^ 

6H 

145.0-   9.0 

30600 

1530 

% 

l^i 

10.5±0.0 

2220 

111 

2Vi 

7 

168.0-10.0 

35500 

1780 

2 

13.8-0.3 

2900 

145 

2H 

7H 

193.0-11.0 

4080O 

2040 

u 

17.4-0.6 

3660 

183 

2^ 

8 

220.0-12.0 

46400 

2330 

2V^ 

21.6-0.9 

4530 

226 

2% 

8H 

247.0-13.0 

52200 

2610 

>8 

2*^ 

26.9-1.2 

5480 

274 

3 

9 

278.0-14.0 

5860O 

2930 

1 

3 

30.9-1.6 

6520 

326 

3^ 

9H 

310.0-16.0 

65400 

3270 

lA 

36.3-2.0 

7630 

382 

3V4 

10 

344.0-16.0 

72600 

3630 

IH 

3H 

42.1-2.5 

8880 

444 

^h 

11 

416.0-18.0 

87800 

4390 

m 

334^ 

48.4-3.0 

10200 

610 

3^^^ 

12 

495.0-20.0 

104300 

5210 

4 

56.0-3.6 

11600 

580 

4V« 

13 

580.0-22.0 

122400 

6120 

IH 

i>i 

60.4-4.0 

13100 

655 

4H 

14 

670.0-24.0 

142000 

7100 

*  The  left-hand  figures  in  the  colimin  are  the  weights  according  to  Mr. 
Hunt's  formula  (2),  and  the  right-hand  figures  are  corrections  which  give 
resulting  weights  in  accordance  with  some  of  the  manufacturers'  tables. 
The  true  weights  are  somewhat  approximate  and  probably  lie  within  the 
two  limits. 

t  Calculated  from  Mr.  Hunt's  formula.  See  also  table  of  Breaking 
Strength  of  Manila  Rope  by  Spencer  Miller  in  Eng.  News,  Dec  6,  1890. 

The  safe  strenph  of  manila  rope  given  in  the  above  table  is  based  on  a 
safety  factor  of  20,  which  Mr.  Hunt  recommends  for  rope  driving.  The 
following  working  loads  are  recommended  for  rapid  (400  to  800  feet  per 
minute),  medium  (wharf  and  cargo,  hoisting  150  to  300  feet  per  minute), 
and  slow  (derrick,  crane  and  quarry,  speed  at  50  to  100  feet  per  minute) 
work: 

2. — WoRKi.vo  Load  por  Manila  Ropb. 


Diameter 

Ultimate 

Working  Load  in 

Pounds. 

Minimum  Diameter  of 
Sheaves  in  Inches. 

of  Rope. 

Strength, 

Inches. 

Poimds. 

Rapid. 

Medium. 

Slow. 

Rapid. 

Med'm. 

Slow. 

1 

7.100 

200 

400 

1.000 

40 

12 

8 

IV^ 

9.000 

250 

500 

1,250 

45 

13 

Ik  1 

11.000 

300 

600 

1.500 

50 

14 

ly  [ 

13.400 

380 

750 

1,900 

55 

15 

iVa 

15.800 

450 

900 

2.200 

60 

16 

1^ 

18.800 

530 

1.100 

2.600 

66 

17 

1^ 

21.800 

620 

1,250 

3.000 

^70 

I     18 

AiOO<^ 

He 

d  by  Google 


672  ^.^CORDAGE,  WIRE  AND  CABLES. 

4. — Properties  or  Roebling  Steel  Wire. 


*T1>l8table  was  calculated  on  a  basis  of  483.84  lbs.  per  cubic  foot  tor  steel  wire. 
Iron  wire  Is  a  trifle  llKhtcr. 

The  breaking  strains  were  calculated  for  100.000  lbs.  per  sq.In.  tbrougbout*  ■tni' 

S yf or  oonvenience.  so  that  the  breaking  strains  of  wires  of  any  strength  persquarp 
ch  may  be  quickly  determined  by  multiplying  the  values  given  In  the  table  by  the 
ratio  between  the  strength  per  square  Inch  and  100.000.   Thus,  a  No.  15  wire,  with  a 

strength  per  square  Inch  of  1  SO.OOO  lbs.,  has  a  breaking  strain  of  407  X  [^^- 610.S  Its. 

« .Hi  ^""^  °o^  ^  thought  from  this  table  that  steel  wire  invarlabl/  has  a  stmMrth 
oflpo.ooo  lbs.  per  sq.  In.    As  a  matter  of  fact  It  ranges  from  45.000  lbs.  for  soft  t 
"®**f4?wV*  <*y?'  400.000  lbs.  per  sq.  In.  for  hard  wire. 

Tni»t!?- !fi!f  ^*?  Jf*^^*  ^^^  strength  of  wire  at  the  mte  of  70,8  knograma  per  square  mBII- 
atm^i^  T^^^  '■  eoulvalent  to  100.000  lbs,  per  sq.  In.  and  was  caleulatMl  on  this  baalfl  , 
KTOm7»Sr£?«  ^^"'^Ilf^-    ^****  ^''"*  "^y  ^«ve  a  tensile  strength  from  SO  to  300  kilo*  J 
Krama  per  square  millimeter,  according  to  treatment,  composition,  etc 


d  by  Google 


674 


25.— CORDAGE,  WIRE  AND  CABLES, 


6. — RoBBLiNo  Round  Wirb-Ropb. 

(Swedish  Iron,  Cast  Steel.  Extra  Strong  Crucible  Cast  Steel,  and 

Plough  Steel.) 

Table  of  dimensions,  weight,  breaking  strength,  safe  O/s)  strength. 

Also  minimum  diameter  of  dnim  or  sheave. 


r 


Breaking  Strength 
in  iJOO  lbs. 


O  V  V 


Safe  (Vft)  Strength 
in  1,000  Pounds. 


A 


C0   3  4-> 

Si- 


Min.  Diam.  of  Drxun 
or  Sheaves  in  Ft .  for 


A 


His 

c 


I 

D 


Rope  Composed  of  6  Strands  and  a  Hemp  Center.  19  Wires  to  the  Strand. 

^Js'm.M 

228. 

456. 

532. 

610. 

45.6 

91.2. 

106.4 

122.0 

16. 

10. 

10. 

11. 

2»^7'sl  9.81 

189. 

379. 

444. 

508. 

37.9 

75.8 

88.8 

101.6 

17. 

9.6 

9.5 

10. 

2H1H  8.0C 

m. 

312. 

364. 

416. 

31.2 

62.4 

72.8 

83.2 

13. 

8.6 

8.6 

9. 

2    av/ 

fl.3C 

124. 

248. 

288. 

330. 

24.8 

49.6 

67.6 

66.0 

h. 

8. 

8. 

8. 

l»i5''i 

4.8,' 

96. 

192. 

224. 

256. 

19.2 

38.4 

44.8 

61.2 

10. 

7.M 

T.2& 

7.5 

1^h5 

4.U 

84. 

168. 

194. 

222. 

16.8 

33.6 

38.8 

444 

85 

6.2s 

6.25',  6. 

lfv4»^ 

35i 

72. 

144. 

168. 

192. 

14.4 

28.8 

33.6 

38.4 

7.5 

6.7S 

5.76  5.5 

158  4>4 

3.0( 

62. 

124. 

144. 

164. 

12.4 

24.8 

28.8 

32.8 

7. 

5.6 

65 

5.25 

l';r4 

2.4f 

fiO. 

100. 

116. 

134. 

10.0 

20.0 

23.2 

26.8 

6.5 

6. 

6. 

5. 

lKi3H 

2.a 

42. 

84. 

98. 

112. 

8.4 

16.8 

19.6 

22.4 

6. 

4  5 

45 

4  5 

1     3 

l.M 

34. 

68. 

78. 

88. 

6.8 

13.6 

15.6 

17.6 

6.25 

4. 

4. 

4.25 

78  23< 

1.2( 

26. 

62. 

60. 

68. 

5.2 

10.4 

12  0 

13.6 

4.6 

8.6- 

8.5 

3.75 

?42«^ 

0.8! 

19.4 

38. f 

44. 

50. 

3.8f 

7.76 

8.8 

10.0 

4. 

3. 

3. 

3.5 

M 

O.ftS 

13  C 

27.2 

31.6 

30. 

2.72 

6.44 

6.32 

7.2 

3.6 

2.23 

2.2^ 

3. 

Al'4 

0» 

11  0  22. C 

254 

29. 

2.2C 

4.4C 

60S 

68 

2.75 

1.7( 

1.75 

Z.h 

hl'i^O.31 

8  8  17.6;  20  2 

22. « 

1.76  3.52 

4.04 

4.5< 

2.2S 

15 

1.5 

2. 

AUii  o.a 

6  8   13.6  15.6 

17.7 

1  36  2.72 
1.00  2.00 

3.12 

3.& 

2. 

l.« 

1.2£ 

1.5 

fsir^s  0.2J 

6  0  10  C 

11  5 

13.1 

2.31 

2.61 

1.6 

1. 

1. 

1. 

Al 

O.lf 

3.4    6.S 

8.1 

9.( 

.68,  1.3(1 

1.62 

1.8( 

1. 

.61 

.67 

.88 

>i|^ 

0.10 

2.4    4.8 

6.4 

6.C 

.48     .96 

1.08 

i.« 

.76 

.60 

.60 

.67 

Rope  Composed  of  6  Strands  and  a 

Hemp  Center.  7  Wires  to  the  Stnmd. 

VMH 

3.M 

68. 

136. 

158. 

182. 

13.6 

27.2 

31.6 

36.4 

13. 

8.5 

8.5 

8.5 

lH'4Vi 

30( 

58. 

116. 

136. 

156. 

11.6 

23.2 

27.2 

31.2 

12. 

8. 

8. 

8. 

IK  4 

2M 

48. 

96. 

112. 

128. 

9.6 

19.2 

22.4 

25.6 

10.7i 

7.M 

7.25^ 

725 

n' 

2.0( 

40. 

80. 

92. 

106. 

8.0 

16.0 

18.4 

21.2 

^9.6 

6.21 

6.25f6.25 

1.5J 

32. 

64. 

74. 

84. 

64 

12.8 

14.8 

16.8 

8.6 

6.7i 

5.75 

^.5 

n2-r,' 

1.2( 

24. 

48. 

56. 

64. 

4.8 

9.6 

11.2 

12.8 

7.6 

6. 

5. 

5. 

i|2V,' 

0.8( 

08. C 

37.2 

42. 

48. 

3.72 

7.44 

8.4 

9.6 

6.7S 

4.5 

4.6 

4. 

m 

0.7/ 

158 

31.6 

36.8 

42. 

3.16 

6.32 

7.36 

8.4 

6. 

4. 

4. 

3.5 

0.6: 

13.2 

26  4 

30.2 

34. 

2.64 

5.2* 

6.04 

6.8 

6.21 

3.5 

3.5 

8. 

0.5( 

10.6 

21  2 

24.6 

28. 

2.12 

4.24 

4.92 

6.6 

4.5 

3. 

3. 

2.75 

u\\Vr 

0.3J 

8.4 

16.8 

19.4 

22. 

1.6« 

3.36 

3.8ii 

4.4 

4. 

2.5 

2.6 

2.6 

i^\H 

03( 

6.6 

13.2 

15.0 

17.1 

1.32 

2.64 

3.0c 

3.45 

3.25 

2.2i 

2.25 

2. 

k\'%  0.2i 

4.8 

9.6 

11  1 

12."; 

.96 
.68 

1.92 

2.22 

2.5^ 

2.75 

2. 

2. 

15 

M      0.1/ 

34 

6.8 

7.7 

8.7 

1.36 

1.64 

1.7^ 

2.6 

1.75 

1.75 

1.25 

^  7 80  125 

2.8 

5.6 

6.4 

7.i 

.56'  1.12 

1.28 

1.4€ 

2.26 

1.6 

1.3 1,. 

,  Note. — ^Thc  above  rope  is  furnished  either  galvanized  or  tinned ;  also  with 
Wire  center — at  an  extra  cost  of  10  per  cent  for  each.  For  standard  hoisting 
rope  the  Swedish  iron  (A)  and  cast  steel  (B)with  19  wires  to  the  strand,  are 
^d;  while  for  transmission  or  haulage,  the  same,  but  with  7  wires  to  the 
strand,  are  used.  Before  ordering,  consult  the  manufacttirers  in  r^ard  to 
tne  best  size  of  rope,  grade  of  steel,  etc.,  to  use.  if  not  familiar  wIt&JHMr 


WIRE  ROPE  AND  FASTENINGS. 


676 


WlKB  ROPB  PA8TBNIN08. 

(Best  Poiged  SteeL) 


Fig.aa   Ooaed  Socket. 


Pig.  22.    Socket  and  Swivel  Hook.        Pig.  23.    Open  Socket  and  Hook. 


24.    Special  Swivel  Hook  and  Pig.  25.    Hook  and  Thimble. 

"     .  (Double  Swivel).. 


Pig.  27.  Closed  Cast-iron  Socket  for     Pig.  28.  Open  Ca.«rt;-Iron  Socket  for 
Suspension  Bridge  and  Cableway.         Suspension  Bridge  and  Cableway. 


M    #  ^    # 


Pig.  30.    Crosby  Wire-Rope  Clip.  Pig.  31.    Jupiter  Wire-Rope  Clip. 


Pig.  32.    Roebling's  Extra  Heavy  Wire-Rope  Clamp  with  Three  Bolts. 


Pig.  33.    Tumbuckle. 


tizedbyVjOC 


676  2S.^C0RDAGE.  WIRE  AND  CABLES. 

EXCERPTS  AND  REFERENCES. 

Telephone  Cable  in  the  St.  Oottbard  Tunnel  ("Blektrotedm  Zest- 
schrift"  for  June  27.  1901;  Eng.  News.  Dec.  5.  lOOl).— Illustrated.  A 
paper-ftnd-air-insulatcd  cable.  It  includes  7  two-wire  circuits,  each  wire 
1.8  m  m.  in  dia..  each  set  being  covered  with  paper  tape  to  a  dia.  of  7  m  m.: 
stranded  together  and  covered  with  a  triple  envelope  of  cotton  and  a 
double  tin-lead  sheath;  outside  is  a  layer  of  waterproof  compoimd,  a  strong 
armor  of  interlocking  steel  wires  and  an  outer  coating  of  jute  yam  soaked 
in  a  protecting  compound.  The  finished  external  diameter  is  44  m  m.,  or 
1.7  ins. 

READER'S  MEMORANDA. 

The  following  skeleton  outline  is  for  the  use  of  the  reader  in  maldiis 
reference  to  tables  and  general  items  of  interest  which  may  be  found  in  this 
book  or  in  other  works. 

Cordage. 


1.  See 

2.  See 

3.  See 

• 

Page 
Page 
Page 

4.  See 

5.  See 

6.  See 

Steel  Wire. 

Page 
Page 
Page 

7.  See 

8.  See 

9.  See 

Copper  Wire. 
Table  1,  Section  70.  Electric  Power  and  Lighting 

Page 
Page 
Page 

10.  See 

11.  See 

12.  See 

Aluminum  Wire. 

Page 
Page 
Page 

13.  See 

14.  See 
16.    See 

Cables. 

Page 
Page 
Page 

16.  See 

17.  See 

Laying  Cables. 

Page 
Page 

18.    See 
10.    See 
20.    See 

Miscellaneous. 
Table  1.  Section  34.  Metal  Gages 

Page 
Page 
Page 

d  by  Google 


36.— PIPES  AND  TUBES. 

(See  also  various  pipes,  fittings  and  specials  in  Sec.  64,  Water  Worics,  page 
U07.  etc.) 


1. — ^^Standard  Wrought  Iron  Wbldbd  Stbam,  Gas  and  Water  Pipe. 
(National  Tube  Works.) 

[Per  Weight  of  Seamless  Brass  tubing,  iron  pipe  size    (1).  following  page, 
multiply  tabulated  weight  by  1 .  07.  j 


(a)  External  Diameters  and  Properties. 

External. 

L'thpcr 

Couplings  for  (1).  next  page. 

Nom. 
Dlam. 

Thre'dB 

per 

Inch. 

8q.  Ft. 
Extcr'l 
Heafg 

Surf. 

Dtam. 

Caicum. 

Area. 

Inside 
Dlam. 

Outside 
Dlam. 

Length 

^TgS 

Ins. 

Ins. 

Ins. 

8q.  Ins. 

No. 

Ft. 

Ins. 

Ins. 

Ins. 

Lbs. 

y^ 

.406 

1.272 

.1288 

27 

9.44 

11/32 

19/32 

13/16 

.031 

u 

.540 

1.696 

.2290 

18 

7.07 

15/32 

23/32 

15/16 

.046 

:  2 

.675 

2.121 

.3578 

18 

5.66 

37/64 

27/32 

1     1/16 

.078 

:  2 

.840 

2.639 

.5542 

14 

4.55 

23/32 

1 

I    5/16 

.124 

i  U 

1.050 

3.299 

.8659 

14 

3.64 

63/64 

1  21/64 

1    9/16 

.250 

1 

1.M5 

4.131 

1.3581 

11^ 

2.90 

1  n/64 

1    9/16 

1  13/16 

.455 

iH 

1.660 

5.215 

2.1642 

ll2 

2.30 

1    1/2 

1  61/64 

2^ 

.562 

iS 

1.900 

5.969 

2.8353 

nH 

2.01 

1    3/4 

2    7/32 

29^ 

.800 

2 

2.375 

7.461 

4.4301 

WH 

1.61 

2    7/32 

2    3/4 

m 

1.250 

a» 

2.875 

9.032 

6.4918 

8 

1.33 

2  21/32 

3    9/32 

t% 

1.757 

8 

3.500 

10.996 

9.6211 

8 

1.09 

3     1/4 

3  15/16 

2.625 

3^ 

4.000 

12.566 

12.566 

8 

.955 

3  25/32 

4    7/16 

4.000 

4 

4.500 

14.137 

15.904 

8 

.849 

4  17/64 

5 

3^ 

4.125 

*H 

5.000 

15.708 

19.635 

8 

.764 

4    3/4 

5    1/2 

3H 

4.875 

5 

5.563 

17.477 

24.306 

8 

.687 

5    9/32 

6    7/32 

4^ 

8.437 

6 

6.625 

20.813 

34.472 

8 

.677 

6  11/32 

7    5/16 

AM 

10.625 

7 

7.625 

23.955 

45.664 

8 

.601 

7    3/8 

8    5/16 

m 

11.270 

8 

8.625 

27.096 

58.426 

8 

.443 

8    3/8 

9    5/16 

AH 

15.150 

9. 

9.625 

30.238 

72.760 

8 

.397 

9    7/16 

10    3/8 

6H 

17.820 

10 

10.760 

33.772 

90.763 

8 

.355 

10    7/16 

11  21/32 

6W 

27.700 

11 

11.760 

36.913 

108.43 

8 

.325 

11  15/32  12  21/32 

6^ 

33.250 

12 

12.750 

40.055 

127.68 

8 

.299 

12    7/1613    7/8 

6Vi 

43.187 

*  Allow  variation  of  5  per  cent,  above  and  5  per  cent,  below  standard  in 
weight  per  foot.    Cannot  cut  to  length  closer  than  A  inch. 

t  Shipped   threads  and   couplings   (above)    imless  otherwise  ordered. 

t  Shipped  plain  ends  tmless  otherwise  ordered.  Where  Extra  Strong 
Pipe  is  orderea  with  threads  and  couplings,  regular  line  pipe  couplings  (not 
shown  above)  will  be  furnished,  unless  otherwise  spedned. 

II  Shippea  plain  ends  unless  otherwise  ordered. 


677 


d  by  Google 


678 


m.—PIPES  AND  TUBES. 


1. — Standard  Wrought  Iron  Welded  Pipe. — Concluded, 
(b)  Internal  Diameters  and  Properties. 


Internal. 

Metal. 

Nom. 

Weight 

per 

Foot. 

L'th  per 
Sq.Ft. 
Intern'l 
Heat'g 
Surf. 

Lth  of 

Pipe 

Con-tg 

1  Cubic 

Foot. 

U.S. 
GsUoos 

Nom. 
Dlam. 

Dlam. 

Circum. 

Area. 

Thick- 
ness. 

Area. 

Pipe. 

Ina. 

Ins. 

Ids. 

Sq.  Ins. 

In. 

Sq.  Ins. 

Lbs. 

Ft. 

Ft. 

Gala 

(1)  Black  or  Galvanized  Standard  Weight  Pipe.f 


\^ 

2 

2^ 

3 

3« 

4 

6 

6 

7 

8 

9 
10 
11 
12 


2 
3 

m 

A 

AH 
5 

7 

8 

9 
10 
12 


.269 

.845 

.0568 

.068 

.0720 

.241 

14.2 

2535. 

.864 

1.144 

.1041 

.088 

.1249 

.42 

10.5 

1383. 

.493 

1.549 

.1909 

.091 

.1669 

.659 

7.76 

754.8 

.622 

1.964 

.3039 

.109 

.2503 

.837 

6.15 

473.8 

.824 

2.589 

.6333 

.113 

.3326 

1.115 

4.64 

270.0 

1.047 

3.289 

.8609 

.134 

.4972 

1.668 

3.66 

167.3 

1.380 

4.335 

1.4957 

.140 

.6685 

2.244 

2.77 

96.3 

1.610 

6.058 

2.0358 

.145 

.7995 

2.678 

2.38 

70.8 

2.067 

6.494 

3.3556 

.154 

1.074 

3.609 

1.85 

42.9 

2.467 

7.750 

4.7800 

.204 

1.712 

5.739 

1.55 

30.1 

3.066 

9.632 

7.3827 

.217 

2.238 

7.536 

1.25 

19.5 

3.548 

11.146 

9.886 

.226 

2.680 

9.001 

1.08 

14.56 

4.026 

12.648 

12.730 

.237 

3.174 

10  665 

.949 

11.31 

4.508 

14.162 

15.960 

.246 

3.676 

12.34 

.848 

9.02 

5.045 

15.849 

19.985 

.259 

4.321 

14.502 

.757 

7.20 

6.065 

19.054 

28.886 

.280 

6.586 

18.762 

.630 

4.98 

7.023 

22.063 

38.743 

.301 

6.921 

23.271 

.544 

3.72 

7.981 

26.073 

60.021 

.322 

8.405 

28.177 

.478 

2.88 

8.937 

28.076 

62.722 

.344 

10.04 

33.701 

.427 

2.29 

10.018 

31.472 

78.822 

.366  ;u.94 

40.065 

.381 

1.82 

11.000 

34.558 

95.034 

.375   13.40 

46.95 

.348 

1.62 

12.000 

37.699 

113.09 

.376 

14.59 

48.985 

.319 

1.27 

(2 

Standard  Extra  Strong  Pipe.t 

.206 

.644 

.033 

.100  1    .096 

.29 

18.63 

4364. 

.294 

.924 

.068 

.123       .161 

.64 

12.99 

2118. 

.421 

1.323 

.139 

.127 

.219 

.74 

9.07 

1036. 

.642 

1.703 

.231 

.149 

.323 

1.09 

7.05 

623. 

.736 

2.312 

.425 

157 

.441 

1.39 

5.11 

339. 

.951 

2.988 

.710 

.182 

.648 

2.17 

4.02 

202.8 

1.272 

3.996 

1.271 

.194 

.893 

3.00 

3.00 

113.1 

1.494 

4.694 

1.753 

.203 

1.082 

3.63 

2.56 

82.2 

1.933 

6.073 

2.936 

.221 

1.495 

5.02 

1.97 

49.1 

2.315 

7.273 

4.209 

.280 

2.283 

7.67 

1.65 

84.2 

2.892 

9.086 

6.569 

.304 

3.052 

10.26 

1.33 

21.95 

3.358 

10.549 

8.858 

.321 

3.710 

12.47 

1.14 

16.25 

3.818 

11.995 

11.449 

.341 

4.455 

14.97 

1  00 

12.57 

4.280 

13.446 

14.387 

.360 

5.248 

18.22 

.893 

10.01 

4.813 

15.120 

18.193 

.375 

6.113 

20.54 

.793 

7.92 

6.751 

18.067 

25.976 

.437 

8.496 

28.58 

.664 

5.54 

6.625 

20.813 

34.472 

.500 

11.192 

37.67 

.598 

4.18 

7.625 

23.955 

45.664 

.500 

12.763 

43.00 

.502 

3.15 

8.625 

27.096 

58.426 

.500 

14.334 

48.25 

.443 

2.46 

9.750 

30.631 

74.662 

.600 

16.101 

54.25 

.399 

1.93 

11.760 

36.914 

108.43 

.500 

19.25 

65.00 

.325 

1.33 

(3)  Standard  Double  Extra  Strong  Pipejl 

^ 

.244 

2.639 

.654 

.298 

.507 

1.7 

15.67 

260.0 

.029 

.422 

3.299 

.866 

.314 

.726 

2.44 

9.05 

166.3 

.046 

1 

.587 

4.131 

1.358 

.364 

1.087 

3.65 

6.61 

106.0 

.071 

iH 

'  .885 

6.215 

2.164 

.388 

1.549 

6.2 

4.32 

66.6 

.113 

iH 

1.088 

6.969 

2.835 

.406 

1.905 

6.4 

3.61 

50.8 

.148 

2 

1.491 

7.461 

4.430 

.442 

2.686 

9.03 

2.66 

32.5 

.231 

2H 

1.755 

9.032 

6.492 

.660 

4.078 

13.68 

2.18 

22.20 

.339 

3 

2.284 

10.996 

9.621 

.608 

5.524 

18.56 

1.67 

14.97 

.502 

3H 

2.716 

12.566 

12.566 

.642 

6.772 

22.75 

1.41 

11.46 

.656 

4 

3.136 

14.137 

15.904 

.682 

8.180 

27.48 

1.22 

9.06 

.830 

4« 

3.564 

16.708 

19.635 

.718 

9.659 

32.53 

1.07 

7.33 

Iffi 

6 

4.063 

17.477 

24.306 

.750 

11.341 

38.12 

.94 

6.93 

1.270 

6 

4.875 

20.813 

34.472 

.875 

15.807 

53.11 

.78 

4.18 

1.80 

7 

5.875 

23.955 

45.664 

.875 

18.555 

62.38 

.66 

3.15 

9.S8 

8 

6.875 

27.096 

58.426 

.875  ;21.304 

71.62 

.65 

2.47 

3.08 

t  1 1 1  Foot-notes,  preceding  page, 


by  Google 


WROUGHT  IRON  PIPE,    LEAD  PIPE. 


679 


2.^Lbad  and  Tin  Linbd  Lbad  Pipb. 
(Tatham  and  Brothers,  New  York.) 


§•25 

k 

Weight 
per  Ft. 

u 

^Q 

^8 

Weight 
per  Ft. 

si 

Is 

Weight 
per  Ft. 

si 

Weight 
per  Ft. 

Ins. 

Ins, 

Lbs. 

Ins. 

Ins. 

Lbs. 

Ins. 

Ins. 

Lbs. 

Ins. 

Ins. 

Lbs 

H 

.06 

0.42^2 

;g 

.26 

3. 

'    1 

.11 

2. 

IH 

.23 

6.6 

.06 

0.625 

.08 

0.72-72 

.14 

2.6 

.26 

7.6 

.08 

0.75 

.09 

1. 

.17 

3.26 

•  • 

.27 

8. 

.12 

1. 

.13 

1.6 

.21 

4. 

.28 

8.6 

.16 

1.26 

.16 

2. 

.24 

4.76 

IH 

.13 

4. 

.19 

1.60 

.20 

2.6 

.30 

6. 

.17 

6. 

.27 

1.76 

.22 

2.75 

I  ^i^ 

.10 

2. 

.19 

6. 

*  I 

0.8126 

.26 

3.6 

.12 

2  6 

♦  " 

.21 

6.6 

1. 

1  ^ 

.08 

1. 

.14 

3. 

.23 

7. 

H 

".07 

0.64''64 

.10 

1.26 

.16 

3.76 

.27 

8.6 

.09 

0.76 

.121.76 

.19 

4.76 

.30 

10. 

.11 

I. 

.142. 

.26 

6.75 

2^ 

.15 

4.76 

.13 

1.26 

.162.26 

.28 

6.76 

.18 

6. 

.14 

1.60 

.20,3. 

IH 

.12 

3. 

.22 

7. 

.16 

1.75 

.23:3.6 

.14 

3.5 

.25 

8. 

.19 

2. 

.3014.76 
.101.6 

.17 

4.26 

.27 

9. 

.23 

2.6 

1 

.19 

6. 

.30 

11.76 

V 

Repeating  decimal: 

0.42^42  lb.  per  ft. -7  lbs.  per  rod:  0.64''64   lb. 
L  72-72  lb.  per  ft. -12  lbs.  per  rod. 

per  ft 

=  9  lbs.  per  rod;  ( 

*J 

Special. 

IRea 

omroended  for  pressi 

ire  of  16  lbs  per  sq.  in. ,  or  hydrostatic  head  of  30  ft. 

•               •   "^      • 

•  26     " 

«••«                         •                              «                .^Qi. 

•               •           • 

•  38     - 

-     .  .     .           •             •       -    76  * 

•               «      ^   « 

•  60     - 

-     -  -     -                        -       -100  - 

«                        m                 » 

-  76     • 

•     -  -     -           -             -       -160  - 

m 

m 

• 

« 

100    • 

•     1 

t           • 

• 

•200  • 

Wbioht  op  Lbad  Pipb  pbr 
Lin.  Ft.* 


Thickness. 

Inner 

Diam. 

A* 

H' 

A' 

H' 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

W 

8. 

11. 

14. 

17. 

3 

0. 

12. 

16. 

20. 

8H 

9.6 

16. 

18. 

22. 

4 

12.6 

16. 

21. 

26. 

4H 

14. 
16. 

18. 
20. 

6^ 

26. 

31. 

6 

18. 

24.6 

30. 

37. 

Lbad  and  Tin  Tubing. 
H  inch.  Ji  inch. 

Shbbt  Lbad. 
Weight  per  square  foot.  2^.  3,  3H, 
4,  4H,  6,  6.  8.  9.  10  lbs.  and  upwards. 
Lighter  weights  rolled  to  order  at 
si>ecial  prices. 

Block  Tin  Pipe. 


*  Manufactured  in  lengths  of 
10  ft. 


Lbad  Wastb  Pipb. 


^  in.,  4. 6. 6 and  8 

oz.  per  ft. 
Hin.,6.7HandlO 

oz.  per  ft. 
?^in.,8andl0oz. 

per  ft. 
H  in..  10  and  12 

oz.  per  ft. 


1  in.,  16andl8oz: 
per  ft. 

lKin..l>iandlH 

lbs.  per  ft. 
IH  in..  2 and  2H 

lbs.  per  ft. 

2  in..  2i  and  3 lbs. 
per  ft. 


lHin..2and3]bs 

per  ft. 
2  m.,  8  and  4  lbs. 

per  ft. 
3ni..^  6and6 

lbs.  per  ft. 
8Hin.,41b8.pcrft. 


4  in..  6.  6  and  8 

Ibe.  per  ft. 
4Hin..6and81bs. 

per  ft. 
6  in..  8.  10  and  12 

lbs.  per  ft. 
6  in.,  12  lbs.  per  ft. 


Special  sizes  made  to  order. 
Lead:  Wt.  per  cu.  ft.,  about  710  lbs.; 

{)er  sq.  ft.  1  in.  thick,  about  69 . 2 
bs.;  bar  1  in.  square  and  1  ft.  long, 
about  4 . 93  lbs.;  per  cu.  in.,  about 
0.4111b. 
Cast  Tin:  Wt.  per  cu.  ft.,  about  459 
lbs.;  per  sq.  it.  1  in.  thick,  about 
38 .  25  lbs. ;  bar  1  in.  square  and  1 
ft.  'ong,  about  3.19  lbs.;  pcrcu.  in. 
about  0 .  266  lbs. 


680 


3^.— PIPES  AND  TUBES. 


3. — Spiral  Rivbtbd  Stbbl  Pipb  as  Manufacturbd  by  Ambrican  Spiral 
PiPB  Works,  Chicago. 


Standard  Weight  Pipe. 

Extra  Heavy  Weight  Pipe. 

UseGalvanteed 
Pipe  tor: 

Use  Galvanized  or 
Asphalted  Pipe  tor. 

Asphalted  tor: 

Galvanised  and 
Flangedfor: 

Exhaust  Steam. 

Paper  and  Pulp 

Intake  Mains. 

Oompreesed  Air. 

Diam- 

Pump Suction 

Pump  Suction. 

eter. 
Indies. 

Brine  Circulation. 
Refrigerating 

00fl8.£tC 

Pump  Discharge. 
Water  Pipe 
Lines.  Etc 

Hydraulle  Mto- 
WaterSup-Llnes. 

Condenser  Pipes. 
Vacuum  Pipes. 
Etc 

h 

Ifl 

III 

IP 

III 

5a5 

1 

|| 

1 

5  -^ 

III 

No.  20 

fO.60 

10.35 

2.25 

1500 

No.  18 

10.55 

10.40 

2.60     laoo 

•• 

.70 

.45 

3.00 

1125 

•• 

.80 

.55 

3.45 

ISBO 

" 

1.00 

.55 

4.00 

900 

•• 

1.10 

.65 

4.60 

1210 

No.  18 

1.20 

.75 

5.00 

1000 

No.  16 

1.30 

.90 

6.40 

12S0 

•• 

1.40 

.80 

6.00 

860 

*• 

1.50 

.95 

7.50 

1070 

•• 

1.70 

.95 

7.00 

750 

** 

1.85 

1.15 

8.90 

935 

" 

2.00 

1.10 

8.00 

665 

** 

2.20 

1.30 

10.25 

S35 

No.  16 

2.60 

1.45 

11.00 

750 

No.  14 

2.80 

1.65 

13.25 

985 

2.85 

1.55 

12.00 

680 

•« 

3.05 

1.80 

14.75 

850 

•• 

8.15 

1.80 

14  00 

625 

•* 

3.40 

2.15 

17.00 

781 

" 

3.60 

1.96 

15.00 

675 

•* 

8.80 

2.35 

18.25 

730 

No.  14 

4.00 

2.50 

20.00 

670 

No.  12 

6.00 

3.30 

24.50 

135 

4.40 

2.75 

22.00 

625 

6.26 

3.60 

26.85 

875 

!      *• 

6.00 

3.05 

24.00 

685 

•  • 

6.00 

3.80 

29.20 

620 

1      •• 

6.00 

3.50 

29.00 

520 

•• 

7.00 

4.20 

34.70 

«7S 

20 

" 

7.00 

3.90 

34.00 

470 

•* 

8.00 

4.80 

40.30 

655 

22 

No.   12 

9.00 

5.55 

40.00 

695 

No.  10 

10.00 

6.20 

50.10 

7(5 

24 

10.50 

6.00 

50  00 

540 

12.00 

7.00 

60.20 

705 

26 

" 

11.80 

8.50 

68.00 

606 

** 

18.00 

9.55 

66.00 

est 

28 

No.  10 

14.60 

10.25 

27.00 

605 

No.  8 

16.60 

11.65 

83.00 

735 

30 

•  • 

15.70 

11.25 

79.00 

660 

•  • 

17.66 

12.60 

90.00 

685 

32 

•• 

16.70 

12.00 

85.00 

625 

*• 

19.25 

13.80 

97.00 

675 

36 

•• 

18.45 

13.20 

94.00 

469 

«« 

21.00 

16.00 

112.00 

571 

40 

20.80 

14.90 

106.00 

420 

26.00 

17.80 

128.00 

515 

^_-^TJ»e  above  list  is  for  pipe  in  standard  lengths,  with  flanges  attached  or 
w  J*^'"^  connection. 

Y^  recommend  the  use  of  bolted  joints  with  asphalted  oipc  for  all  higfc 

pressure  water  works.  ,,^,,3,  by^Oglc 


d  by  Google 


683 


».— PIPES  AND  TUBES, 
Spiral  Rivbtbd  Stbbl  Pipb  Dbtails. 


fH 

^         I 

r^ ]i 

H.-. 

P^g^ij 

Fig.  5.  Riveted  Lap. 


Fig.  6.  Flange  Connection. 


Fig.  7.    Bolted  Joint  Connection.         Fig.  8.  Slip  Joint  Connection. 


Pig.  9.   Bolts. 


Fig.   11.  Fig.  12. 

Threaded  Disc.     Clamp  Band. 


Fig.  10.    Gaskets. 


Fig.  18.    Reducer. 


EXCERPTS  AND  REFERENCES. 

Making    Tight    Joints    in    Vitrified    Pipe   at  AUantk:  City,  N.J.  (By 

Kenneth  Allen.    Eng,  News.  Oct.  8,  1903.) 

Experiments  on  Reinforced-Concrete  Pipes  Made  for  the  U.  S.  Rec- 
lamation Service  (By  J.  H.  Quinton.  Eng.  News.  Mar.  9,  1906).— Illus- 
trated 

Reinforced-Concrete  Pipe  with  Reinforced  Joint  (By  Lock  Joint  Pipe 
Co..  N.  Y.;   Eng.  News,  Dec.  10.  1908).— lUustrated. 

SUndard  Specifications  for  Hard-Drawo  Copper  Wire  (Proc.  A.  S.  T.  M.. 
Vol.  IX..  1909).--Adopted  Aug.  16.  1909. 

Illustrations. 
Description.  Eng.  Rec. 

Tests  of  lock-bar  pipe  42*  dia.,  Springfield.  Ms^f^edbyGoOglcApril  17.  '09 


37.— BRIDGES. 

Econooiic  Lensthfl  of  Spans. — If  a  bridge  consisting  of  any  number  of 
spans  (to  be  determined)  is  to  be  built  over  a  stream  or  other  crossing  of 
len^^th  L,  it  can  be  shown  that,  aside  from  the  (end)  abutments.*  the  rnoa 
economic  layout  of  spans  and  piers  will  obtain  when  the  cost  of  each  pier  is 
about  equal  to  the  cost  of  that  portion  of  the  structure  which  it  supports 
when  stripped  of  about  one-half  the  floor  system ;  that  is.  equal  to  the  cost 
of  the  supported  trusses  and  laterals  and  about  one-half  the  floor,  the  cost 
per  Hn.  ft.  of  same  being  assumed  as  proportional  to  length  of  span. 
Let  L  — total  length  of  crossing,  in  ft.; 

P  — cost  in  dollars  of  one  pier  at  any  given  point  of  profile; 
/—length  of  economic  spans,  in  ft.,  based  on  P; 
x—number  of  spans  /  in  the  crossing  L\ 

C  — cost  in  dollars  per  lin.  ft.  of  trusses,  laterals,  etc.,  for  span  L; 
c  —  cost  in  dollars  per  lin.  ft.  of  trusses,  laterals,  etc..  for  sf>an  /; 
>" total  cost  of  trusses,  lafisrals,  etc..  piers,  and  a  proportionate  cost  of 
fotmdations  in  abutments. 


Then,  since 
we  have. 


c  —  — ,  and  /  —  — 

X  X 

y  —  —  +  Px, 


(1) 


Differentiating,  and  equating  with  zero,  for  minimum. 


whence.  p  ^  £^  ^  d  (2) 

Now  the  value  of  c  for  span  /  may  be  obtained  from  any  known  value  <f 
for  span  t  as  follows: 

c-f  (3) 

it  being  assumed  of  course  that  the  same  types  of  bridges  are  used  and  the 
same  specifications;  also  that  the  lengths  of  spans  /  and  f  do  not  vary 
greatly. 

Eauation  (2)  may  be  applied  without  serious  error  to  a  crossing  with 
irregular  profile  as  in  Pig.  i.  In  such  a  case  we  would  have,  numbermg  the 
piers  and  spans  consecutively. 


Pi- 


Cih  +  C7I2, 


^2  -  5 .    P3  =  «■ 


^4^.. 


2         •  '  ^  2         •      *  2 

which  is  the  proportion  stated  in  the  opening  paragraph. 


etc.. 


(4) 


Fig.  1. 
Referring  to  Fig.  1  and  to  equation  (4)   it  will  be  noted  that  for   the 
deeper,  or  rather  more  expensive,  foundations    the    longer   spans   are   re- 
quired.    The  principles  evolved  above  will  apply  to  spans  of  plate  girders, 
beams,  etc.,  and  also  to  many  other  economic  problems. 

*  Abutments  usually  perform,  in  part,  certain  "constant"  functions,  as 
retaining  walls,  etc.,  not  connected  with  "supporting"  the  spans,  and,  if 
included  in  the  problem,  these  fimctions  should  be  considered  canefuUy. 

683  '"'"^^^  ^ 


684  Zl.-^BRIDGES. 

Equation  (2)  may  be  transformed  into 

an  economic  fonn  for  general  use,  in  which  —  —  ratio  of  length  of  span  to 

weight  in  lbs.  per  tin.  ft.  of  trusses,  laterals,  etc.,  and  will  be  found  to  be 
fairly  constant  within  quite  wide  limits  of  /;  and 
p  «  price  in  dollars  per  lb.  of  w. 

Economic  Depth  of  Plate  Girders.— Equation  (7)  will  usually  give  a 
greater  depth  of  girder  than  practice  warrants,  but  it  will  be  \isef\il  in 
finding  out  how  much  material  is  sacrificed  in  any  practical  limitation  of 
depth. 
Let  Af  "total  max.  bending  moment  in  ft.-lbs.  on  girder; 

A  —area  of  top  flange  — area  of  bottom  flange,  in  89.  ins. 

/  —  allowable  compressive  stress  in  lbs.  per  sq.  in.  m  top  flange; 

X— effective  depth  of  girder— depth  of  web,  in  ins.; 

<— thickness  of  web  in  ins.; 

a  — total  horizontal  section  of  vertical  stiffeners  and  fillers,  in  sq.  ins.; 

L  — length  of  span,  in  ft.; 

>'— total  weight  of  girder,  in  lbs. 
Then,  for  a  steel  girder,  assuming  no  part  of  web  to  resist  bending,  we  have. 

12Af 
smce  A  —  — 1 — , 
/* 

y  — ^ +  8.4    Ltx  +  -75-  ax.  (6) 


Differentiating  and  equating  with  zero,  for  minimum 

'4n 


dy  3.4    X   24  AfL  3.4 

Tx T^^ +  3.4    L<  +  ^o  -  0. 


whence  .    -    ,«.»7^  ^-^j^^^^  (7) 

the  economic  depth  of  girder. 

Ex. — A  track  stringer,  20-ft.  span,  is  designed  to  support  a  total  imiform 
load,  including  its  own  weight,  of  2600  lbs.  per  lin.  ft.  Assuming  /— 10  000. 
I—  I,  and  a—  30,  find  the  economic  depth. 

2600  L* 
Solution. — Prom  equation  (7)  we  have,  since  M  — ■= — , 


W< 


16.97  X  60   X    »H/ 8X10  000  (240X1  +  80)-  "*  ™-  *~- 

Economk:  Depth  of  Trasses. — In  the  preceding  case,  of  the  plate  girder, 
it  is  to  be  noted  that  the  weight  of  each  part  of  the  girder  is  given  in  tenns 
of  the  variable  depth  x  in  order  that  the  value  of  x  may  be  found  for  the 
minimum  value  oi  y.  This  will  be  done  also  in  the  present  case,  of  the 
truss,  but  in  order  to  introduce  the  working  stresses  per  sq.  in.  in  the  com- 
pression members  as  "constants"  into  the  fundamental  formula  (8)  for  total 
weight  of  truss  it  is  convenient  to  assume  that  the  bridge  has  been  designed 
using  a  certain  depth  of  truss  (parallel  chords)  and  find  whether  this  depth 
is  the  most  economic  one,  which  will  be  the  case  when  the  value  of  x  in 
equation  (10)  is  equal  to  the  asstuned  depth.  If  less,  the  depth  will  be  de- 
creased; if  greater,  increased.  If  the  difference  is  slight  the  economic 
depth  may  be  assumed  equal  to  the  value  of  x  found.  One  or  two  triab 
will  be  sufficient  in  most  cases.  The  general  equation  for  total  weight  of 
steel  truss  members  is 


(8) 


Wt.             Wt. 

Wt.              Wt. 

Wt. 

Wt. 

bottom            top 
chord.          chord. 

end              int. 
posts.          posts. 

vert, 
stifp. 

diag- 

y-     B      +       r      + 

E        ^         P        A 

\....Yac^ 

Y^o\P 

ECONOMIC  DESIGN.   ESTIMATING  WEIGHTS.  085 


Natation: 
(May  vary  for  each  member.) 
Jf -"bending  moment.  ft.-lbiB.; 
/  —  allowable  stress  per  sq.  in.; 
jC"- depth  of  truss,  in  ft.; 
p  — panel  length,  in  ft.; 
f#  — added  length  for  two  heads; 
%  a  percentage  added  for  details; 
5  -°  vertical  shear,  in  lbs. 


InwhichB-3.4J~(p+#) 

P-  ZAI  J  (1  +  %) 

V-    3.4Jy  (1  +  %) 

Now,  substituting  the  above  values  in  equation  (8)  and  using  summated 
constants  for  simplicity,  we  have  the  following  form: 

Differentiating  and  equating  with  zero,  for  minimum. 

whence.  *  -  ^    ^  ^  p.  ^  {^,  ^  jy  (10) 

M 

In  which  B*  "  I  -r-  (p  +  g),  for  each  bottom  chord  member; 

r-J^(l  +  %)  "  top 

fi'-Jj(l  +  %),  ••  end  post; 

P*  -  JT  J  (1  +  %),  "  intermediate  post; 

V  —  JT-T-  (1  +  %),  "  vertical  suspender; 

ly  -  J-r  (1  +  %),  *•  diag.  (incl.  counters). 

Estimating  Welglits  off  Bridges. — The  correct  weight  of  a  proposed 
structure  can  be  estimated  only  from  a  complete  bill  of  material  of  the 
finished  design,  and  young  engineers  should  use  this  method  on  all  possible 
occasions.  After  he  has  become  expert  in  bridge  designing  he  may  resort 
to  quicker  methods,  more  or  less  approximate,  depending  on  the  purpose 
for  which  the  estimate  is  to  be  used. 

In  designing  a  structure  the  live  loads,  snow  load  and  wind  loads  mtist 
of  course  be  known  or  assumed.  The  lengths  of  spans,  if  indefinite,  may 
be  fixed  by  the  use  of  formulas  (2)  and  (5);  the  depths  of  steel  stringers, 
floorbeams  and  plate-girders,  by  equation  (7);  and  the  depth  of  trusses,  by 
equation  (10);  bearing  in  mind,  of  course,  that  these  values  are  often  fixed 
arbitrarily  and  that  any  moderate  variation  from  the  economic  depth  will 
not  add  greatlv  to  the  weight  or  cost.  For  instance,  the  depth  of  plate- 
girders  is  usually  assumed  at  about  i^  the  span,  and  the  depth  of  trusses 
at  about  i  to  ^  the  span,  the  larger  ratio  applying  to  the  shorter  spans. 

The  steps  m  calculating  the  design  ana  weights  of  an  ordinary  span  are 
as  follows:  (1)  That  part  of  the  roadway  which  directly  supports  the  live 
load,  as  the  paving,  planking  and  street-car  tracks  of  highway  bridges; 
and  the  "track"  (including  rails,  guard  rails,  ties  and  fastenings)  of  railroad 
(steam  and  electric)  bridges,  usually  assumed  at  400  to  450  lbs.  per  lin.  ft. 
per  track.  (2)  The  baBast  and  corrugated  flooring,  if  used.  (3)  The 
stringers  or  loists.  (4)  The  floorbeams.  (6)  The  top  and  bottom  lateral 
systems.    (0)  The  portal  and  vertical  sway  bracing.    (7)  The  trusses. 

*  (l  +  %)ia  used  instead  of  (p  +  4)to  simplify  equation^ 9).     j 
t  See  formula  (11)  for  value  of  #.  Digitized  by  LjOOglC 


686  ZJ.—BRIDGES, 


Bach  of  the  above  operations,  excepting  (5)  and  (6),  is  dependent  on 
the  weights  obtained  from  the  preceding  operations.  Although  no  "backing 
up"  is  required  we  have  to  assume  in  some  of  the  operations,  as  (3),  (4)  and 
(7),  the  weights  of  the  members  we  are  calculating,  and  sometimes  two  or 
three  "assimiptions"  are  necessary  before  the  correct  one  is  made. 

In  estimating  the  weights  of  details  it  is  the  practice  with  many  engi- 
neers to  add  certain  percentages  to  the  weights  of  the  main  ribs  of  such 
members,  or  to  add  to  their  lengths,  or  both.  The  method  of  percentages  it 
always  tmcertain.  and  may  vary  from  a  few  %,  for  rivet  heads,  up  to50  or 
60  %  or  more  for  latticing  both  sides  of  light  channels.  For  instance,  lacing 
■  may  be  used  instead  of  latticing,  or,  what  is  still  cheaper,  occasional  tie 
plates  may  be  used.  Again,  a  top  chord  may  or  may  not  have  a  cover 
plate,  and  with  this  uncertainty  note  what  a  variation  in  percentage  for 
details  this  would  implv.  Very  close  estimates  have  been  made  on  the 
total  weights  of  bridges  by  adding  a  certain  percentage,  say  25%,  to  the 
weights  of  all  the  main  members  stripped  of  their  details.  As  the  per- 
centage varies  with  the  type  of  structure  and  the  specification  such  a  prac- 
tice would  be  dangerous  tor  any  but  the  most  careful  expert. 

A  ^ood  formula  for  estimating  the  added  length  of  eye  bars  to  form  the 
heads  is  the  following:    For  formmg  two  heads, 

The  added  length  in  ft.  « —  f  diam  of  pin  in  ins (11) 

this  to  be  added  to  length  c.  to  c.  of  pins  and  estimated  as  a  plain  bar. 

EXCERPTS  AND  REFERENCES. 

Diasrams  and   Formulas   for   Weights   of  Steel  Bridges  and  Trestles 

(By  H.  G.  Tyrrell.  Eng.  News,  May  and  June,  1»01). — ^The  following 
excerpts  are  noted  from  the  formulas: 

Unit  stresses  in  all  cases  are  10.000  and  12,000  lbs.  per  sq.  in.  L— length 
of  span  in  ft.,  c.  to  c.  bearings. 

Railway  Bridges. — ^Weights  are  per  lin.  ft.  of  single  track  bridge  for 
steel  only;  1. 1.,  2  100-ton  engines  followed  by  4,0(K)  lbs.  per  lin.  ft.  of  track: 
Deck  plate  girder  bridge,  100  + 9L:  deck  lattice  girder  brid^,  100+ 8L: 
half  through  pi.  gird.  br.  with  floor.  300+ 12L;  same  with  ties  on  shelf 
angle,  200  +  8iL;  same  with  trough  floor.  600+  lOL;  riveted  through  truss 
br.,  400+ 6L;  riveted  deck  truss  bridge  (ties  on  top  chord),  200+ 7L:  pin 
through  truss  bridge,  400+  6iL;  pin  deck  truss  bridge  with  stringers, 
400+ 6L;   pin  deck  truss  bridge  (ties  on  top  chord),  800+  6L. 

Railway  Trestles. — Assumed  loads  same  as  above;  weight  of  spans  as 
above.  Weight  of  bents  and  bracing  is  9  lbs.  per  sq.  ft.  of  side  profile  from 
ground  to  base  of  rail. 

Electric  Railway  Bridges. — Live  load  assumed  25-ton  cars,  or  2,000  lbs, 
per  lin.  ft.  of  track:  Beam  bridges,  SO+fi^L;  deck  plate  girder  bridges. 
30+ 6L;  Pony  truss  bridges,  200+1.8  L;  through  truss  bridges,  200+  1.6L. 

Highway  Bridges  with  Wooden  Floors. — Assumed  dead  weight  of  floor 
is  40  lbs.  per  sq.  ft.;  assumed  live  load  is  100  lbs.  per  sq.  ftj  the  weights 
are  per  sq.  ft.  of  floor,  and  include  that  only  with  joists:  Girder  bridges 
and  sidewalks,  3  +  L-I-4.4;  same  without  sidewalks.  3  +  L^-3.4;  Tniss 
bridges  with  sidewalks.  3  +  L+8;  same  without  sidewalks,  6+L-4-7. 

Highway  Bridges  with  Solid  Floors. — Assumed  dead  weight  of  floor  is 
160  lbs.  per  sq.ft.:  Deck  plate  girder  bridges,  3+L-I-2.6;  Half-through 
girder  bridges,  3  +  L-4-2.4;   Truss  bridges,  3  +  L+4. 

Graphical  Method  for  Finding  Bending  Stresses  In  Eyebars  (By  W.  B. 

Belcher.    Eng.  News,  July  17,  1902). — From  the  formula. 
^  4  900  000^ 

Pt+23  333  000^ 

Where  P  — stress  in  lbs.  per  sq.  inl  due  to  bending; 
P«-»  working  tensile  stress  in  lbs.  per  sq.  in.; 
A— depth  of  bar  in  inches; 
/•==  length  of  bar  in  inches. 


MISCELLANEOUS  DATA.  687 

Wind   Pressure  to   be  Assumed   in  tiie  Design  of  Lonf  Bridge  Span 

(By  Theodore  Cooper.    Eng.  News,  Jan.  6.  1»06). 

Nickel  Steel  for  Bridges   (By  J.  A.  L.  Waddell.    Trans.  A.  S.  C.  B.. 
Vol.LXIII). 

Concrete  Floors  for  Railway  Bridges   (Eng.  News.  Feb.  16.  1906).— 
Dlustrated. 

Tables   and   Diagrams   of   the    31    Bridges  Over  the  Missouri  River 

(Eng.  News.  April  29,  1909). 

Standard  Specifications  for  Structural  Steel  for  Bridges  (Proc.  A.  S.  T.  M.. 
VoL  IX..  1909).— Adopted  Aug.  16,  1909. 

Diagrams  and  Illustrations. 

Description.  Eng.  Rec. 

Diagram  of  compression  formulas  in  long-span  bridges  Sept.  3» '  10 


d  by  Google 


38.— RAILROAD  BRIDGES. 

I.—  MOMENTS  AND  SHEARS— BEAMS  OR  GIRDERS. 
(a)  Uniformly  Distributed  Loads. 

If— load  in  lbs.  per  lin.  foot;  /—span  in  feet. 

Pull  Loading — Moments  and  Shears — Pios.  1  and  8. 
At  any  point  distant  x  from  left  end: 

Moment  Mx  —J  wx,  (/—*),  in  ft.-lbs. 

—  6  wx  (/—«),  in  in.-lbs. 
Maximum  moment  (at  center), 

-  J  u/P,  in  ft.-lbs. 
*i  «;/>,  in  in.-lbs. 


.>^r 


V- 


Full. 
f  Loading 


Pig.  2.  Shears. 


I  in  lbs.. 


Fig.  L  Moments. 
Shear  5^  -w  ("2  ~*)  ' 

(left  end  positive;  right  end  negative). 
Maximum  shear  (at  ends), 
—  I  u//,  in  lbs. 
Minimum  shear  (at  center)  —0. 
Note  that  maximum  moment  occurs  at  point  of  minimum  shear;  and 
minimum  moment  occiu^  at  point  of  maximum  shear. 

To  Draw  a  Moment  Parabola,  divide  the  span  into  any  nMwhtr  di 
eqtial  parts,  odd  or  even;  number  the  points  from  one  end,  b^inning  with 
zero;  and  for  ordinates,  multiply  together  the  numbers  equidistant  from 
center.  Afterward,  all  ordinates  so  obtained  may  be  mxxltiplied  by  a  con- 
stant (one  that  will  give  the  required  middle  ordinate).    See  Figs.  3  and  i 

Pig.  3.  Even.  Fig.  4.  Odd. 

Partial  Loading — Moments  and  Shears — Pigs.  5  and  8. 
At  any  point  distant  x  {>d)  from  left  end: 

Moment  M.-y  f  j(/-a)»-(i;-a)«l,  in  ft.-lbs. 

-fta;  [^  (/-a)«-(«-a)«l  ,in  in.-lbs. 


Maximum  moment  is  at  Ji;  — 


;»+a« 


Fig.  5.  Moments. 


d  by  Google 


600 


Z&.—RAILROAD  BRIDGES. 


the  "curve  of  moments"  comprises  the  parabola  Ti  —  Tj  and  the  adjacent 
tangents,  their  intersection  at  /  being  vertically  above  the  center  of  gravity 
of  the  tmiform  load. 

(b)  Concentrated  (Encine,  Car,  Axle,  Wheel,  etc.)  Loads.— Dunne  the  past 
76  years  the  weight  of  the  locomotive  has  increased  from  about  7  to  over 
200  tons.  In  approachinj?  the  latter  mark  many  engineers  predicted  that 
we  were  reaching  the  limit,  but  similar  prophesies  may  be  recalled  for  the 
100-ton  engine  which  appeared  and  disappeared  as  a  standard  for  bridge 
calculations  during  the  short  period  of  about  ten  years.  The  following 
may  be  considered  as  typical  for  our  heaviest  loading — present  and  pros- 
pective— ^for  bridge  calculations: 

Two  engines  coupled  and  followed  by  uniform  load  of  w  pounds  per  lin.  ft 


Axle  concentrations:   Bogie  axle  load  —   6  w 

Driving  "    '*       — 10  a;,  each 
Tender  "     "       —6  to  7 a;  *' 

Or.  for  floor  loads,  jjjrg^}"    "       -14w       " 

as  per  the  following  diagrams: 


laxle. 

4,  spaced  5  ft. 

4,  spaced  5  and  6  ft. 

2,  spaced  7  ft. 


Type  R — Engine  Diagrams — Axle  Loads. 

Note. — Wheel*  or  rail  loads  Wi  are  one-half  of  axle  or  track  ksads  w.) 
Diagram  No.  1.  No.  2. 


IIJI 


[< it,-^ 5,- w •I'Tt. 


Pigs.0. 


-.#i 


1.  Types  "R"  Enoinb  Diaoraus — ^Axlb  Loads. 
[From  Figs.  9.) 


Driver 

Tender 

Pi 

Special  Pair 

1 

Bogie 

Loads. 

Loads. 

of  Axles. 

Loads. 

m 

7'  Centres. 

^ 

Each. 

Total. 

Each. 

Total. 

Each. 

Both. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

Tons 

Lbs. 

Lbs.     Lbs. 

R 

6  w 

10  If 

40  w 

6  w 

24  10 

.0345  a/ 

w 

14t»  1  38» 

R30 

15.000 

30.000 

120.000 

18 .000 

72,000 

103.5 

3.000 

42.000i  84.000 

R35 

17.500 

35,000 

140,000 

21 .000 

84,000 

120.75 

3.500 

49.00a  96.000 
56.000112.000 

R40 

20,000 

40,000 

160.000 

24.00(1 

96,000 

138. 

4.000 

R45 

22.500 

45.000 

180.000 

27.000 

108.000 

155.2S 

4.500 

63.000126,000 

R50 

25.000 

50.000 

200,000 

30.000 

120.000 

172.6 

5.000 

70.00ai40.000 

R56 

27.500 

55.000 

220.000 

33.000 

132.000 

189.75 

5.500 

77.000454.000 

R60 

30.000 

60.000 

240.000 

36.000 

144.000 

207. 

6.000 

84 .0001108 .000 

.  ^  ^y  substituting  w,  for  w  the  diagrams  will  represent  "wheel-load" 
instead  of  "axle-load"  diagrams.  Wheel  load  diagrapas  are  often  used  in 
calculations,  but  axle  load  diagrams  are  safer.       ized  byVjOOglc 


d  by  Google 


693  K.'-RAILROAD  BRIDGES. 

Table  2,  {ollomiig,  shows  the  positions  of  axle  loads.  R  60.*  givifi? 
maximum  bending  moments  on  spans  up  to  55  feet;  the  maxim tmi  bendinjz 
momenu  in  ft.-lbe.  from  these  positions:  and  the  maximum  shears.  UsehD 
to  the  design  of  girders,  stringers,  and  lloorbeams. 

2. — Bbnding  Moments  and  Shears  for  "R  50"  Loading. 


*  The  "positions"  and  bending  moments  arc  for  "R  50".     The  positions 
will  remain  the  same  for  any  engine  of  Type  R,  Table  1;  and  the  bending 
moments  and  shears  will  be  directly  proportional  to  the  loading.     Thus,  j 
for  "R  40"  mult,  above  tabular  values  by  0.8;  for  "R  60,"  by  1.2;  etc. 

i  t  The  position  of  the  loading  which  gives  the  maximum  bending  momef^t 

at  center  of  any  span  /  will  give  also  the  max.  floor-beam  reaction,  or  max. 

I  loading  on  a  floor-beam  joining  two  panels  each  -srin^JCTglth. 


MOMENTS  AND  SHEARS— SPANS.  6»a 

2.— Bending  Moments  and  Shears  for  "R  50"  Loading.— Concluded. 


II.— MOMENTS  AND  SHEARS— SPANS  WITH  FLOOR  BEAMS. 
(a)  Uniformly  Distributed  Loads. — ^The  maximum  moment  at  any  panel 
point  obtains  with  the  span  fully  loaded  from  end  to  end.  The  maximum 
shear  in  any  panel  obtains  with  the  head  of  the  moving  load  at  or  in  that 
panel:  specifically,  when  the  length  of  moving  load  in  the  panel -i- panel 
length  <->  (the  number  of  the  panel  from  the  right  end  of  span,  minus  1)  ■*■ 
(total  niunber  of  panels  in  the  span,  minus  1).  Thtis: 
Let  p  — panel  length  in  feet, 

n  — total  number  of  panels  in  span. 

jt  —  thc  number  of  the  panel  from  right  end  of  span;  then  for  maxi- 
mum shear  in  panel  x,  the  length  of  load  in  "panel  *""^^3j-  Thus  for 
a  six-panel  span  the  head  of  load  for  maximum  shear  in  the  5th  panel  is 
•-=-  across  the  panel;   for  the   4th 


1  "fiHT"'  T*  ""^"^^  ^^^  panel;   lor  tne   4tn        yrr — k-     a      a — -pK 
icl.  4-.  for  the  3rd  panel. -|;  etc.   The  maxi-  /     1 1  M^  V  j/^^j^'l'''^   I    3 


panel,  -r'.  for  the  3rd  panel.  -=- 

0  0 

mum  shear  in  the  0th  panel  obtains  with  the  Pig.   IL 

full  panel  (and  bridge)  loaded. 

In  practice,  however,  the  above  refinement  is  eliminated,  the  panel 
loads  being  considered  as  concentrated  at  the  panel  points  or  joints — upper 
for  "deck*  and  lower  for  "through"  bridges.  This  applies  also  to  dead 
bads,  for  short  spans.  For  long,  through  spans  a  certain  portion,  say  }  to  i, 
of  the  dead  load  per  panel  is  often  assumed  to  be  carried  at  the  top  chord  joints. 

In  calculating  live  load  stresses,  engineers  as  a  rule  prefer  to  use  specified 
engine  diagrams,  somewhat  heavier  and  more  severe,  for  the  structure. 
than  the  actual  engines  in  use  or  immediately  contemplated.  This  is  by 
far  the  safer,  more  scientific  and  more  economical  when  we  consider  the 
strength  of  a  structure  to  be  measured  by  its  weakest  part.  An  approxi- 
mation to  actual  engine  diagrams  is  the  use  of  equivalent  uniform  loads 
which  may  be  used  with  or  without  "engine  excess." 


694 


».^RAILROAD  BRIDGES. 


(b)  Concentrated  Loads — Maximum  Floor-Beam  Reactions. — The  loading 
which  gives  the  greatest  bending  moment  at  the  center  of  a  span  two  pantls 
in  length,  will  give  alao  the  greatest  loading  at  that  point  when  supported 
by  a  floor-beam,  and  this  loading  or  its  equivalent  is  called  the  floor-bean: 
reaction^ — a  necessary  factor  in  the  design  of  the  floor-beam  itself. 

Table  No.  3  gives  the  floor-beam  reactions  due  to  "R  60"  axle  loads, 
and  the  positions  of  the  loads,  over  two  panel  lengths,  which  produce  these 
reactions.  For  any  other  loading  of  Type  R  the  floor-beam  reaction  will 
be  directly  proportional  to  the  weights  on  the  drivers. 
3.— Maximum  Floorbeam  Reactions  and  Positions  of  Loading  foe 
Same.     Type  "R  50." 


Position  of  Loading  for 

Maximum  Floor-beam 

Reaction. 


70000 
Change  at  p-6.25 — 


5Q000  5Q0OD  SaOOO 
♦  *g  P  ^ 

K"p~;-p-»r 


Change  at  /> » 10.00 

soooo  ayw  soooD  saw 

— i^  tws; 
jt — p.— ^ — p  — ^ 

Change  at  p  =»  13.00 


SKnOSipoo  9)000  5«l»syiQ0 

is    iSjSXSX 


Change  at  ^-18.17 

7^000  SQQOOS^Stm  9)000  30000 
1  8    |5|5X5;   9  I 

k p k p M 

Change  at  p  - 19.00 


cfe 


6.5^ 
7 

7.6| 
8 

8.5 
0 

9.5| 
10 


10.5 

11 

11.6 

12 

12.5 

13 


;  |19 


§^1  l^lrl 


[se^ 


J^ 


70,000 
70,000 
70.000 
70.000 
70.000 
70.000 


73,080 
78.670 
83,330 
87.500 
91.180 
94.440 
97 .370 
100,000 


104,760 
109,090 
113.040 
116.670 
120.000 
123,080 


126,850 
130.360 
133.620 
136.670 
139.520 
142,190 
144.700 
147.060 
149.290 
151.390 


37  18.5  153.920 


156.580 


tifn  94000  sqpoo  sqpNSQDOO  3qooD3Qflpo, 

i    8   iSiSJSi    9    151     ! 


39  119.5 

40  ,20 

41  ,20.5 

42  21     I 

43  21  5 

44  22    I 
46  22.5 

46  23 

47  |23.5 

48  124    I 

49  124.5^ 

50  25    I 


.2   H^ 


,Floor-beam  Moments 
for  Single  and 
Double  Track. 


159.870 
163.000 
165,960 
168.810 
171 .510i 
174.090 
176 ,560| 
178.910 
181 .170 
183 .33(^ 
185,410, 
187.400 


36.000 
36,000 
35.000 
36,000 
35,000 
36,000 


36.540 
39,285 
41.666 
43.760 
45.590 
47.220 
48.685 
60.000 


62.380 
64.646 
66.620 
68.336 
60.000 
61.640 


63.426 
66.180 
66.810 
68.336 
69.760 
71.096 
72.350 
73,530 
.74,645 
76.696 


76.960 
78.290 


79.935 
81.600 
82.980 
84,406 
85.756 
87.046 
88.280 
89.465 
90.685 
91.666 
92.706 
93 .700  > 


3i 


o 


-04(u 


I 


E 


oo^Ie 


FLOORBEAM  REACTIONS.    CHORD  STRESSES. 


696 


(c)  Concentrated  Loads — Posltlonfl  for  Maximum  Moment. — In  order  to 
find  the  stresses  in  the  top  and  bottom  chords  of  bridge  trusses  and  girders 
with  floor-beams,  it  is  necessary  to  know  the  maxim imi  bending  moments 
at  the  floor-beam  or  panel  points.  The  main  problem  consists  in  finding 
the  "position"  of  the  loading  at  each  panel  point,  the  bending  moment 
being  then  found  by  taking  moments  about  that  point.  The  chord  stresses 
are  obtained  by  dividing  the  bending  moments  in  ft. -lbs.  by  the  respective 
moment  arms  of  the  chord  pieces,  in  feet.  For  tnasses  with  parallel  chords 
the  moment  arm  is  constant,  being  the  height  of  truss. 

The  position  of  loading  for  maximum  bending  moment  at  any  panel 
point*  usually  obtains:  , 

?!)  When  the  heaviest  loads  are  nearest  the  point. 

(2)  When  one  of  these  loads  is  ai  the  point. 

(3)  When  the  average  loading  per  lineal  foot  to  the  left  of  the  point  "the 
average  loadinj;  per  lineal  foot  on  the  whole  span  (the  load  at  the  point 
to  be  applied  m  whole  or  in  part  to  either  portion  of  the  span). 

Chord  Stresses  in  Pratt  Truss. 
Problem. — ^Find  the  live-load  stresses  in  the  top  chord  member  T  and 
in  the  bottom  chord  member  B  of  Prattt  truss.  Fig.  12,  of  a  single  track 
railroad  bridge,  144  ft.  span;  using  loading  *'R  60"    (page  691).     Note  that 
in  all  cases  the  moving  load  comes  on  at  the  right  hand  end  ol  span. 


/1%M)^^/KI 


M        ApiB    B' 

Fig.  12. 

Solution. — By  "cutting"  sections  a-a  and  b-b  it  is  evident  that  the 
bending  moment  for  maximum  stress  in  T  will  be  at  the  point  P*,  and  for 
B,  at  the  point  P,  directly  above.  Hence  the  same  bending  moment  will 
do  for  both  stresses.  Applying  the  moment  diagram  and  the  rules  just 
given,  we  place  one  of  the  heavy  loads  at  P*  so  that  the  loads  to  the 
kft  of  P*  will  equal  8  (or  i)  the  total  loads  on  the  bridge.  Hence,  if  load 
(5)  is  placed  at  P*  the  load  to  the  left  is  175  to  225  thousand  lbs.,  while  the 
whole  load  on  the  span  is  690+  5 X  22-  800  thousand  lbs.  As  }  of  800,  or 
200,  is  between  175  and  225  we  adopt  this  position  as  the  probable  one  for 
majcimum  moment  at  P*.  By  trial  we  find  this  to  be  true  and  that  the 
moment  at  P'  — 12.045,000  ft. -lbs.  As  there  are  two  trusses  each  resisting 
one-half  the  moment,  and  further,  as  the  moment  arms  are  26  ft.  the  stresses 
in  T  and  B  are  each  equal  to  12,045,000-»- 52=*  231.600  lbs. -compression 
in  T  and  tension  in  B.  If  the  engine  loading  is  "R  40"  instead  of  "R  50" 
the  stresses  will  be  |  the  above  or  185.300  lbs.,  etc. 

The  following  are  methods  of  calculation  with  various  loads  at  P*. 
udng  the  engine  diagram: 
Load  (3)  at  >.  Load  (4)  at  P'. 

12  ft.  of  uniform  load.  17  ft.  of  uniform  load. 

Mom.  at  H  » 40.090.  Mom.  at  //  =  40.090. 

Add  690X12-  8.280.  Add  690X17=11,730. 

"5X12X6-      360.  "6X17X8*-       722.6 


Load  (6)  at  P*. 
22  ft.  of  uniform  load. 
Mom.  at  H«  40.090. 
Add  690X22-15.180. 
6X22X11-    1.210. 


48,730. 
-12,182.5 
576. 


52.542.5 


X~|- 13.135.6 
1.200. 


56.480. 


X-J-- 14.120. 
2,075. 


48.730X36 
144 
Deduct 

11,607.5  11.935.6  Max. -12.045. 

Hence  the  maximum  moment  is  12.045.000  ft. -lbs.,  as  above  noted.     With 
toad  6  at  P'  the  moment  is  only  11,870,600  ft.-lbs. 


♦  The  moment  at  any  floor-beam  panel  point  for  any  system  of  loading 
is  the  same  as  if  there  were  no  floor-beams. 

t  In  this  case  the  chord  stresses  will  be  the  san^e  n^J^^tl©(5^^^dge  is 
**dcck"  or  "through."  ^  '^^    ^  o 


896 


^L—RAILROAD  BRIDGES. 


Chord  Stresses  in  Wamn  Truss. 
Triangular  Web  System. — For  practical  reasons  the  Post  truss  and  the 
throiigh  triangular  or  Warren  trfiss  types  have  nearly  disappeared.  The 
Warren  truss  remains  principally  for  deck  spans  and  swing  bridges;  and 
for  short,  fixed,  through  spans.  For  deck  spans  it  is  economical  to  erect 
verticals  at  the  lower  chord  panel  joints  to  support  intermediate  floor-beams 
as  in  Fig.  13. 


T    TV 


A 

7 

^ 

A 

»-/8J<a^-' 

|4 

fi     \ 

t  * 

i 

I 

Pig.  18. 

Using  the  same  live  load,  "R  50,"  as  in  the  preceding  case^  note  that 
the  stress  in  the  top  chord  members  TT  is  equal  to  the  stress  in  T  of  the 
Pratt  truss,  Fi^.  12,  namely,  231,600  lbs.  It  is  obtained  by  placing  load 
(6)  of  the  engine  diagram  at/,  a  fioor-beam  pointy  and  taking  momenu 
about  f.* 

Consider,  now,  the  stress  in  the  upper  chord  a  b.  Pig.  13,  assuming  no 
floor-beam  at  *,  in  a  vertical  line  xvith  the  center  of  moments ^  f.  For  this 
case  the  loading  for  maximum  will  be  somewhat  modified,  and  the  following 
rule  will  usxially  apply:  The  average  loading  per  lineal  foot  to  the  left  of  the 
center  of  moments,  r,  {including  one-half  \  the  load  in  the  panel  under  con- 
sideration, ab)'^the  average  loading  per  lineal  foot  on  the  whole  span.  Aha 
the  position  of  loading  for  maximum  has  been  fixed  take  moments  about  f, 
using  the  reaction  at  a  due  to  loading  in  panel  ab,  in  deducting  the  negative 
moment. 

(d)  Concentrated  Loads — Positions  for  Maximum  Shear. — On  page  601. 
under  uniformly  distributed  loads,  we  find  that  for  maximum  shear  in  any 

panel  the  length  of  the  moving  load  in  that  panel  will  be  P'^Zi'  *°  ^Wch 

^»  panel  length,  x— number  of  the  panel  from  right  hand  end  of  m^ 
and  K  —  the  total  number  of  panels.  Thus,  the  head  of  the  mqving-4oadt  m 
any  panel  is  such  that  the  average  load  per  lineal  foot  in  'iM^panel  equals  the 
average  load  per  lineal  foot  on  the  whole  span.  This  principle  may  be  applied 
tentatively  in  fixing  the  position  of  concentrated  loads  for  maximum  shear. 
The  positiod'  ofloading  for  maximum  shear  in  any  panel  of  a  truss 
with  simple  web  system ||  usually  obtains: 

(1)  When  the  heaviest  loads  are  nearest  to  and  just  to  the  right  of  the  panel. 

(2)  When  oneof  these  loads  is  at  the  panel  point  at  the  right  hand  end  of 
the  ptTnatln  question. 

(3)  When  thf  average  loading  per  lineal  foot  in  the  panel— the  average 
loading  per  lineal  foot  on  the  whole  span  (the  load  at  the  panel  point  at 
the  right  hand  end  of  the  panel  may  be  applied  in  whole  or  in  part  to  the 
panel  loading). 

Problem. — ^Find  the  live-load  shear  in  panel  /  6,  Pig.  13.  of  a  two-truss 
double  track  deck  railroad  bridge,  144  ft.  span;  using  loading  "R  60.*' 

*  The  stress  in  B  of  the  Warren  truss  is  greater  than  B  of  the  Pratt, 
and  is  obtained  by  taking  moments  about  b,  as  would  naturallv  be  indicated 
by  the  cutting  section  c-c,  with  load  (8)  at  the  panel  point.  This  produces  a 
moment  of  14,698,750  ft.-lbs.  and  a  corresponding  stress  in  B,  for  one 
triangular  truss,  of  282.670  lbs.,  equivalent  to  stress  in  B*  of  the  Pratt  truss. 

tAccuratelv.  at-t-ah,  whether  it  is  one-half  or  any  other  fraction. 

tThe  head  of  the  moving  load  for  maximum  shear  is  at  the  "neutral 
•  ^  point"  because  any  concentrated  load  at  that  {>oint  produces  zero  shear 
in  the  panel.  A  load  to  the  right  of  the  neutral  point  will  produce  positive 
■'^^^f'.^hile  a  load  to  the  left  will  produce  negative  shear. 

11  jex>T  special  case  with  sub-panel  sj^tem,  see  Sec.  40,  Highway  Bridges, 


MAXIMUM  SHEAR.    LATERAL  BRACING.  697 

Solution. — ^The  three  conditions  above  named  for  masdmum  shear  are 
fulfilled  by  placing  load  (3)  at  b,  whence  the  total  load  in  the  panel.  75  to  125. 
equals  the  total  load  on  the  bridge,  660.  divided  by  the  number  of  panels, 
8:  thus.  660-4-8— 82.5.  Inspection,  however,  reveals  to  us  the  possibiHty 
at  a  maadmtmi  with  load  (2)  at  b,  hence  we  tolve  for  these  two  positions. 
I  moment  <" 


Load(2)  at  b.  Load  (8)  at  b. 

Ril~  29,560  Rtl"  88.340 

+  680X5-   8,150  +660X4-   2.640 


-82.710  85.980 
Dividing  hyURt-      227. 1 53  lbs.  Dividing  by  /,  Ri  -      249.86 1  lbs. 
Deduct  reac-      1  Deduct  reac- 
tion at  t  due  to  I             1 1  1 1 1  •«  tion  at  t  due 
load  (1)  in  pan-               **'"*  loads  (1)    an 
el.  25  XA            j     (2)  in  panel 

Shear-      216,042  "  Shear- 217,917         " 

Therefore,  maximum  shear.  217,917  lbs.,  b  obtained  with  load  (3)  at  b.  With 
load  (4)  at  b  the  shear  is  206,944  lbs.    The  compressive  stress  in  the  diagonal 

fb  U  217,917  X  j^  -  217.917  X  U16  -  264.990  Ibe. 

III.— LATERAL  BRACINa— WIND  AND  CURVE  PRESSURE. 

Horizontal  or  lateral  bracing  is  designed  to  resist  the  lateral  forces  due 
to  wind  pressure,  and  the  centrifugal  pressure  of  moving  trains  on 
curves;  to  shorten  the  unsupported  " column  length  "  of  upper  chord,  for 
economy  of  design;  and  to  give  general  rigidity  to  the  structure.  Stiff 
bracing  is  preferable  to  rods. 

Wind  Pressure. — ^The  direct  wind  pressure  on  any  exposed  surface  is 
about  proportional  to  the  sauarc  of  the  velocity.*  A  velocity  of  100  miles 
per  hour  produces  a  normal  pressure  of  about  50  lbs.  per  sq.  ft. ;  90  miles 
per  hour,  about  40  lbs. ;  and  80  miles  per  hour,  about  30  lbs.  As  rigidity 
IS  a  very  essential  feature  it  is  advisable  to  use  the  higher  figure,  50  lbs., 
as  the  pressure  per  sq.  ft.  on  the  exposed  surface  of  all  trusses  and  the  floor 
system  when  the  bridge  is  unloaded.  An  alternative  wind  load  of  30  lbs. 
per  sq.  ft.  on  the  same  surface  and  also  on  a  moving  train  between  elevations 
2.5  and  10  ft.  above  base  of  rail  is  also  prescribed.  Sometimes  the  wind 
kmd  per  lin.  ft.  is  stated  in  actual  amotmts  for  each  chord.  Thus,  a  load 
(either  fixed  or  moving)  of  sav  150  lbs.  per  lin.  ft.  for  the  unloaded  chord 
and  a  moving  load  or  say  600  lbs.  per  fin.  ft.  for  the  loaded  chord.  See 
Wind  Pressure  tmder  General  Specifications  for  Steel  Railroad  Bridges, 
following. 

Problem. — Find  the  stresses  in  top  lateral  system  of  single  track  through 
Pratt  truss  span  of  144  ft.,  as  per  following  sketch;  loading  75  lbs.  per  lineal 
foot  for  each  chord  (18  X  75- 1,350  lbs.  per  joint.) 


Lii^ixKixi^: 


Fig.  14. 

Solution. — Let  the  diagonals  and  struts  be  stiff  members  and  let  either 
single  member  in  each  panel  be  capable  of  "taking"  all  the  shear,  in  tension 
or  compression.  Then  with  a  moving  load  from  A  to  B  of  1350  lbs.  per 
single  joint  or  2700  lbs.  per  double  joint  (both  chords)  the  shears  in  panels 
a.  6  and  c,  due  to  the  top  lateral  span  of  108  ft.,  are  6750  lbs.,  4500  lbs.  and 
2700  lbs.,  respectively.      Hence    the  stresses  in  the  diagonals   (f|  X  the 

«  p,«.«««.  ;«  n^   n^  .«    ff  ^(Velocity  in  miles  per  hour)»    „„„^  . 

"  Fressure  m  lbs.  per  sq.  it.— neA »  approxi- 
mately. (Recent  experiments  by  M.  Eiffel,  and  also  by  Dr.  Stanton,  indi- 
cate that  for  velocities  of  40  to  90  miles  per  hour  the  denominator  of  the 
fraction  may  safely  be  increased  from  250  to  300  or  333. — See  Engineering 
Digest,  March.  1908.)     See  also.  Section  46.  Roofs,  pages  794.  etc. 


SS.^RAILROAD  BRIDGES. 


shears)  are  10.100  lbs..  6.800  lbs.  and  4.100  lbs.  In  practice,  minimum 
sections  of  material  are  specified,  eithei^direct  or  by  formula,  below  which 
the  design  would  be  considered  weak  no  matter  how  small  the  stresses.* 

IV.— PORTAL  AND  INTERMEDIATE  VERTICAL  BRACINa 

Portals  should  be  designed  to  transmit  all  lateral-bracing  stresses  at 
the  unloaded  or  far  chords,  directly  to  the  abutments  through  the  end 
posts.  For  long  spans,  vertical  bracing  is  inserted  at  the  intermediate 
posts  rather  for  stiffness  than  to  transmit  any  wind  pressure  from  one 
lateral  bracing  system  to  another,  although  it  is  usually  designed  suffi- 
ciently strong  to  meet  the  "local '  wind  pressure.  The  same  principles 
which  apply  to  portal-  also  apply  to  intermediate  bracing,  hence  our  re- 
marks will  be  confined  to  the  former,  and  for  brevity  of  explanation,  to 
"through"  bridges. 

The  calculations  of  portal  stresses  are  much  simplified  by  making  certain 
assumptions  which  render  the  framework  quite  statically  determinate. 
These  assumptions  are  that  the  bottoms  of  the  end  posts  are  hinged  laterally: 
that  all  stiff-riveted  pdftal  connections  are  also  hinged;  and  that  for  a  double 
or  multiple  system  of  portal  bracing  only  one  simple  statically  determinate 
system  acts  at  a  time.    These  assumptions  are  on  the  side  of  safety. 

The  following  simple  illustrations  are  typical.  They  are  tipped  to  a 
horizontal  position  so  that  the  acting  forces  P  may  be  vertical  and  perhaps 
better  illustrate  the  cantilever  principle.  Note  that  the  horizontal  and 
vertical  reactions  at  the  bottom  of  the  two  end  posts  are  ntunerically  the 
same  for  each  post  and,  consequently,  the  shears  and  the  bending  moments 
in  the  latter  are  respectively  similar.f 

Diagonal  d  in  tension.  Diagonal  d  in  compression. 


'i 


v^ 


b|Vt| 


V 


Fig.  16. 


Pig.  16. 


Fig.  15  or  16.  with  either  P  or  P*  acting:  H^^H'^j  or  -y;  V- V'-^^or 

PI         PI 

-  or— *" 


PI  PI  PI 

— ;  stress  in  ac—H orH ;  stress  in  x' = 


w  w 

Fig.  15,  with  either  P  or  P  acting: 
Stress  m  6=»  —-^_  or— -g— 


w 


w 


••  d--l- 


/=-  iP+ 

7    d 


Px(         Px 


PI    d 


The  following  are  some  of  the  usual  types  of  po: 


Fig.  16,  with  either  P  or  P'  acting 

PI  PI 

Stress  in  6-  -f--^  ^^'^'l^T* 

..     ...         PI    d  PI    d 

—  y     w 


rtais. 


a  b 


p^ 


Pigs.  17. 


*  VoT  highway  bridges  adjustable  rods  are  often  used  instead  of  stiff  mem-> 
bcrs  and  it  is  customary  to  specify  an  initial  stress  of,  say,  10,000  lbs.  to  be 
added  to  the  calculated  stress  in  proportioning  the  dimensions  of  the  laterals. 

tjp  the  design  of  the  posts  tnese  wind  stresses  have  to  be  "considered" 

in  aadltion  to  the  recmlar  strMua«>.«  as  f  rns«  mAmKnm      r~>  i 


ddition  to  the  regular  stresses  as  truss  members. 


W  Google 


PORTAL  BRACING.    SPECIFICATIONS. 


699 


Pig.  a  is  the  simplest  and  the  one  just  analyzed  bv  calculation.  By 
similar  methods  and  with  reasonable  assumptions  the  others  may  be  calcu- 
lated readily. 

v.— OENERAL  SPECIFICATIONS  FOR  STEEL  RAILROAD  BRIDGES. 

The  main  specifications  below  are  adapted  from  those  of  the  American 
Bridge  Company  ^Am,  Br  Co.).  1900.  C.  C.  Schneider,  Vice  President. 
The  foot-notes  are  inserted  by  the  writer  as  showing  the  practice  (in  devia- 
tion or  otherwise)  of  a  few  of  our  leading  railroad  companies,  as  follows: 
Chicago.  R.  I.  and  Pacific  (C.  R.  I.  &  P.),  1906;  J,  B.  Berry,  Chief  Engineer. 
DclTLack.  and  Western  (D.  L.  &  W.),  1903;  A.  E.  Deal,  Bridge  Engineer. 
Lake  Shore  and  Mich.  Sou.  (L.  S.&Af.  S^,  1904;  Sam'l  Rockwell.  Chief  Eng. 
•Lehigh  Valley  (L.  V.),  1906;  Walter  G.  Berg.  Chief  Engineer. 
Philadelphia  and  Reading  (P.  &  R),  1906;  William  Hunter.  Chief  Engineer. 
Southern  Pacific  (S.  P.).    1906;  William  Hood.  Chief  Engineer. 

(a.)    Qeneral  Description. 
Material. — 1.  To  be  of  rolled  steclt  as  specified  below.     tCast  iron  or  cast 
steel  permitted  only  in  machinery  of  movable  bridges  and  in  special  cases 
for  shoes  and  beanngs. 
Types  of  Bridges  Recommended. — 2.  Limiting  spans,  in  ft.  to  be:  || 
CiMrance. — 3.  On  straight  line  a  clear  section  shall  be  provided  to  con- 
form to  given  requirements.lf     The  width  must  be  increased  so  as  to 
allow  the  same  minimimi  clearance  on  curvesS  and  on  double  track. 


*  "All  Railroad  Bridges  on  the  Lehigh  Valley  Railroad  System  are  to 
be  built  in  accordance  with  the  'General  Specifications  for  Steel  Railroad 
Bridges  and  Viaducts;  New  and  Revised  Edition,  1901;  by  Theodore  Cooper, 
Coasting  Engineer,'  modified  as  follows:"  [Some  of  the  modifications  are 
incorporated  in  these  foot-notes.] — F.  E.  Schall,  Bridge  Engineer. 

t  P.  &  R.  allows  use  of  wrought  iron  for  laterals  and  unimportant 
members. 

tL.S.&  M.  S.  specifies  all  castings  to  be  cast  steel.  5.  P.  specifies 
rollers  for  swing  bridges  to  be  cast  steel;  expansion  rollers  to  be  bar  steel, 
or  cast  steel  of  equal  strength. 


II  Type. 

Am.   B. 
Co. 

C.  R.  I. 
&  P. 

D.L.  & 
W. 

L.  S.  & 

M.S. 

L.  V, 

S.  P. 

Trough  floors  (long'l)  . . . 

Rolled  beams 

Plate  girders  (riv.) 

Lattice  girders  (riv.)  .... 

0-20 

0-20 

20-100 

100-140 

0-20 

0-20 

20-120 

0-19 
19-110 

0-20 
16-100 
90-160 

0-23 
23-100 

0-19 
19-100 

Riveted  trusses 

100-180 

120-160 

'uiy-'" 

166-200 
266^' * 

100-150 

Pin  con   trusses ........  . 

150- 

180- 

160- 

with  inclined  end  posts 

150- 

H' 

H 

m 

i 

h 

d 

h 

— 

tRoad. 

1 

CR.I.SC  P..... 

D.L.8cW 

L.  SSc  M.S... 
L  V 

23'-6' 
22'-0' 

22'-0* 

r-er 
r-o* 

7'-6' 

3'-6' 
3'-6' 
4'-0' 
2'-9' 

y-o* 

6'-6' 
6'-3^ 

5' -6' 

y-o* 

6'-0' 

e'-o* 

4'-3' 
5'-0' 
S'-O* 

4'-0' 
4'-0' 
S'-O* 
6'-6' 
2'-0' 
4^-0* 

P.&R. 

S.  P 

h 

//'=-    to    Top    of    Rail. 

//  -  to  Base  of  Rail. 
I  Increase  width  for  curvature  and  super-elevation  for  car  80^  Ig.,  14' 
higb  and  60'  c.-c.  trucks — C.  R.  I.  &  P.  Increase  m  1  in.  per  de^.  of  curva- 
ttirc,  and  increase  m  on  inside  of  curve  2i  ins.  additional  per  each  inch  super- 
elevation of  track.  Width  to  be  increased  proportionately  for  2  or  more 
tradw.-L.  S.  &  M.  S.  ,,.,,^,  ,^  GoOglc 


Digitized  b 


700  9^— RAILROAD  BRIDGES. 

SfMdnf  of  Truftes. — 4.  Width  between  centers  of  truases  to  be  not  less  than 
A*  of  the  span. 

Spadng  of  Deck  Plate  Qirden. — 6.  Generally  6it  ft.  centers. 

Floor  Beams. — 6.  Shall  be  riveted  between  the  posts,  above  or  below  the 

pin,  in  through  bridges. 
Sfiacinc  of  Stringers. — 7.  Generally  6U  ft.  centers,  the  tracks  being  IS  ft 

centers,  standard. 
Wooden  Roor.|| — 8.  Cross-ties  8^x8*  for  stringers  spaced  6i  ft.  cenUn 


For  spacing  over  6i  ft.,  ties  to  be  proportional  for  fiber  strain  not  to 
exceed  lOOO  lbs.  per  sq.  in.  on  timber,  asstiming  max.  wheel  load  do- 
tributed  over  three  tics.  Ties  to  be  spaced  6*  or  less  in  the  clear,  notched 
down  i'.  and  have  full  bearing  on  stringers.  9.  Every  fifth  tie  to  be 
tastened  to  stringer  by  a  }'  bolt. 

Guard  Rails.<^ — 10.  Timbers  6'x8'  on  each  side  of  each  track,  with  inner 
faces  not  less  than  3^-3*  from  cen.  of  track.  To  be  notched  1'  over 
every  tie  and  fastened  to  every  third  tie  and  at  each  splice  by  a  f-ii^  boH. 
Splices  to  be  over  floor  timbers,  with  half -lap  joints  O'  long.  1 1.  Floor 
timbers  and  guards  to  be  continuous  over  piers  and  abutments.  12. 
On  curves,  outer  rails  to  be  elevated  as  may  be  required. 


(b) 

Dead  Load.f — 13.  In  estimating  the  weight  of  the  structure  for  the 
purpose  or  calculating  stresses,  timber  is  assumed  at  4i  lbs.  per  ft.  B.M.; 
and  rails,  spikes  and  joints  at  100  lbs.  per  lin.  ft.  of  traick. 

Live  Load.lf — 14.  A  moving  load  for  each  track,  consisting  of  two 
engines  coupled  at  the  head  of  a  uniformly  distributed  train  load,  placed 
so  as  to  give  the  greatest  stress  in  each  part  of  the  structure.  The  load 
will  be  as  specified  by  the  railroad  company.  Cooper's  standard  loading, 
however,  is  recommended.     (See  Tables  4  and  5,  pages  707, 708.) 


*  And  preferably  not  less  than  ^  of  the  span. — L.  5.  &  M.  S. 

t  7  ft.  for  spans  up  to  60  ft.;  8  ft.  for  spans  60  to  110  ft.— C.  R,  I.  &  P. 

X  7  ft.— C.  R.  I.  &  P.  and  S.  P.  6  ft.  for  double  track  through,  and 
deck  plate:  8  ft.  for  single  track  through.— P.  &  R,  t\  ft.— Z>.  L. &W.  and 
L.  S.  &  Ai.  S. 

\\  S'xS*  by  10  ft.,  framed  to  7i',  for  stringers  spaced  6i  ft.  centers; 
deptn  of  tie  to  be  increased  1'  per  each  6'  increase  in  stringer  spacing. 
Ties  spaced  12^  centers,  every  fourth  tie  fastened  to  each  stringer  by  a  4' 
hook  bolt — L.  S.  &  M.  S.  Ties  (yellow  pine  or  white  oak)  to  be  propor- 
tioned to  an  extreme  fibre  stress  of  800  lbs.  per  sq.  in.  from  the  loading; 
spaced  not  over  6'  in  clear,  notched  down  J  ,  and  secured  to  supporting 
girders  by  1*  bolts  not  over  6  ft.  apart. — L.  V. 

**  Guards  to  be  8*  wide  and  0"  deep,  framed  to  4'  over  ties,  with  inner 
edges  4^-2'  from  cen.  of  track.  They  shall  be  fastened  to  the  ties  by  a 
V  bolt  through  every  fourth  tie,  these  bolts  to  be  through  the  ties  which  i 
are  connected  to  the  stringers  by  hook  bolts. — L.  S.  &  m.  S.  Guards  to  I 
be  ffx^  southern  yellow  pine,  notched  \^  over  every  tie,  bolted  by  a  {' 
bolt  to  every  third  tie  and  spliced  over  a  tie  by  half  and  half  joint  8^  wide* 
bolted  at  splice;  the  inner  lace  of  guard  to  be  4'-li*  from  cen.  of  track; 
and  all  heads  or  nuts  on  upper  faces  of  guard  timber  to  be  ooontcxsunk 
below  surface  of  wood. — L.  V. 

#  Timber  at  4)  lbs.  per  ft.  B.  M.;  ballast,  100  lbs.  per  cu.  ft.- raik  and 
fastenings,  160  lbs.  per  lin.  ft.  of  track.— C  R.  I.  &  P.  The  floor,  con- 
sisting of  the  ties,  rails,  guard  rails,  and  all  spikes  and  bolts  necessary  to 
fasten  same,  assumed  at  400  lbs.  per  lin.  ft.  of  track. — D.  L.  &  W.  Ordinary 
floor  at  400  lbs.  per  lin.  ft.  of  track.  Make  due  allowance  when  plank-  or 
ballast  floor  is  used. — L.  S.  &  M.  S.  Ordinary  floor  assumed  at  600  lbs. 
per  lin.  ft.  of  track.  For  ballast  floors  allow  following  weight  per  cu.  ft.: 
Ballast.  120  lbs.,  C^oncrete,  140  lbs..  Asphalt,  90  lbs.,  Ltunber  64  lbs.— 
P.  &  R.  Ordinary  floor  assumed  at  5(K)  lbs.  per  lin.  ft.  per  track.  Apply 
three-fourths  of  total  dtad  load  at  panel  points  of  loaded  chord,  and  one- 
fourth  at  unloaded  chord.— S.  P 

HThe  following  are  Railroad  0>.  Standards.  Diagrams  1  and  2  are 
anown,  and  that  one  which  will  produce  the  greatest-stress  in  any  member 


d  by  Google 


702  3^.— RAILROAD  BRIDGES, 

Wind  Pressure.* — 16.  Shall   be   assumed    acting  

horizontally:  First.  At  30  lbs.  per  sq.  ft.  on  exposed  surface  of  al!  trusses 
and  the  floor  as  seen  in  elevation,  in  addition  to  a  train  of  10  ft.  average 
height,  beginning  2^-6'  above  base  of  rail,  moving  across  the  brit^ 
Second.  At  50  lbs.  per  square  foot  on  the  exposed  surface  of  all  trusses  and  the 
floor  system.  The  greatest  result  to  be  asstimed  in  proportioning  the  ports. 
17.  For  determining  the  requisite  anchorage  for  the  loaded  structure,  the 
train  shall  be  assumed  to  wagh  800  lbs.  per  lin.  ft. 

Momentum  of  Train. — 18.  Coefficient  of  sliding  frictioD  of  wheels  oc 
rails,  in  stopping  train,  to  be  assumed  at  0.3;  this  to  apply  to  longitodtnsi 
braong  of  trestle  towers  and  similar  structures. 

Ceatrifugal  Force  of  Train. — 10.  On  curves,  asstime  the  centrifuge 
force  C,  in  lbs.,  due  to  each  train,  to  be:  C-  0 .  03  ( Wt.  of  train  in  lbs.  X  degnr* 
of  curvature,  up  to  6^;  the  coefficient  (0.08)  to  be  reduced  0.001  for  ever>* 
degree  of  curvature  above  6  degrees. 

(c.) —Proportion  of  Parts. 
Least  Thickness  of  Material. t — 20.    Except  for  lining  or  filling  vacant 
spaces,  I*  thick  for  main  members  and  their  connections,  and  A'  thick  for 
laterals  and  their  connections. 

Permissible  Tensile  Stresses.^ — 21.  On  all  parts  of  structure,  sum  of 
maxim imi  loads,  together  with  impact:  Soft  steel,  15000;  Meditmi  ste«l. 
17000  lbs.  per  sq.  in.  22.  Same  limiting  stresses  for  wind  pressure,  centrif- 
ugal force,  or  momentum  of  train.  23.  For  net  section,  deduct  size  of 
rivet  hole  K  larger  than  diam.  of  rivet.     24.  For  pin  connected  riveted 


•"Lateral  Load:"  760  lbs.  per  ft.  of  loaded  chord;  200,  fortmloaded; 
both  considered  as  moving.  "Wind  load"  on  viaduct  towers:  50  lbs.  per 
sq.  ft.  on  li  times  the  vertical  projection  of  structure  unloaded;  or  30  lbs. 
per  sq.  ft.  on  same  surface  plus  400  lbs.  per  lin.  ft.  of  structure  applied  7  ft- 
above  the  rail  for  assumed  wind  on  train  when  the  structure  is  either  folly 
loaded  or  loaded  on  either  track  with  empty  cars  assumed  to  weigh  1304 
lbs.  per  lin.  ft.,  whichever  ^ves  the  greater  stress. — C,  R.  I.  &  P. 

For  spans,  300  lbs.  per  lin.  ft.  of  bridge,  acting  on  moving  train  of  locKtod 
or  tmloaaed  cars,  for  lateral  system  attached  to  the  loaded  chord,  and  300 
lbs.  per  lin.  ft.  acting  on  trusses  and  divided  equally  between  top  and 
bottom  lateral  systems.  Trestle  towers  shall  be  proportioned  for  abov^e 
wind  forces  for  spans,  and  in  addition  thereto  a  wmd  pressure  of  100  lbs. 
per  vertical  ft.  ot  tower. — D.  L.  &  W. 

For  single  track  bridges,  300  lbs.  live  load  and  150  lbs.  dead  load  per 
lin.  ft.  of  loaded  chord,  and  150  lbs.  dead  load  per  lin.  ft.  of  unk>aded  chord. 
For  double  track  bridges,  increase  the  above  loads  50%.  Where  30  n» 
per  sq.  ft.  of  exposed  surface  produces  larger  dead  loads  than  the  above  tn 
plate  girder  bridges  or  special  structures,  these  shall  be  taken  instead. — 

For  girder  bridges,  200  lbs.  per  lin.  ft.  for  each  chord.  Also,  for  loaded 
chord,  a  moving  load  of  400  lbs.  per  lin.  ft.,  with  point  of  appliottion  7 J  ft. 
above  the  rail.  For  viaducts  and  trestle  towers,  50  lbs,  per  sq.  ft.  of  the 
projected  surface  of  two  trusses  and  two  sides  of  towers  on  the  vertical 
plane  through  the  axis  of  the  structure  when  same  is  imloaded;  with  struc- 
ture loaded,  take  30  lbs.  per  sq.  ft.  of  this  same  surface,  and  in  addition, 
the  moving  wind  load  specified  for  girder  bridges.  For  determining  the 
requisite  anchorage  for  the  loaded  structxire,  assume  the  train  to  weigh 
600  lbs.  per  it.— P.  &  R. 

Lateral  wind  pressure  same  as  Am.  Br.  Co.  specifications  with  the 
following  minimum  values;  Bracing  of  loaded  chord,  500  Iba.  per  lin.  ft.. 
300  of  which  is  moving-  and  200  dead  load;  unloaded  chord,  150  lbs.  per 
lin.  ft.,  uniformly  distributed.  On  viaduct  towers,  as  seen  in  elevatwo, 
use  60  lbs.  per  sq.  ft.  on  the  loaded,  and  100  lbs.  per  aq.  ft.  on  the  ualoaded. 
structure. — ^S.  P. 


.tr  except  for  fillers. — C.  R.  I.  &  P.     f  except  for  fillers;  1  sq.  in.  m  i 
1 J  sq.  ins.  for  counters. — D,  L.  &  W.     f*^  except  i 


section  for  rods  or  bare 


--^•.w.»  »„i  4uu»  or  oars;  ij  sq.  ins.  lor  couniers. — i/.  i«.  <7  rr.      f    except  i 

^ViS12?,^<*  fi"ere;  3X3X1  angles.—L.  S.  &  M.  S. 

%}S^^?^  structural  steel  at  60000  ult.— C.  R.  I.&P,  J 

I4n^?w  •?<'*f:--Bottom  chords  and  main  diagonals:  Eye  bars,  0000  I  I A 
MWO  d.  /.;  built  sections.  8500  /.  /..  12500  d/T;  counters.  8500.     Hip  soil 


d  by  Google 


704  ».^RAILR0AD  BRIDGES. 

Alternate  Stresses. — 38.  Make  total  area  in  member  equal  to  sum  ci 
areas  required  for  each  stress. 

Combined  Stresses. — 29.  Maximum  stresses  due  to  wind  and  centrifussl 
force,  added  to  those  due  to  vertical  loading  (including  impact),  shall  not  ex- 
ceed: 19000  lbs.  for  soft  steel,  or  210001bs.  for  meditmi  steel,  properly  reduced 
for  compression.     30.  Reversal  of  stresses,  if  any.  must  be  centered. 

Transverse  Loading  of  Tension  or  Compression  Members.* — 31.  When 
the  floor  system  rests  directly  on  the  chord,  the  chord  member  must  be  oro-  ' 
portioned  so  that  the  algebraic  stmi  of  the  stresses  p>er  sq.  in.  on  outer  fibre, 
resulting  from  the  direct  compression  or  tension,  and  H'of  the  max.  bending 
moment  (considering  the  chord  as  a  beam  of  one  pa.nel  length,  supported 
at  ends),  shall  not  exceed  the  before-mentioned  limiting  stresses  in  tensioo 
or  compression,  the  proper  amount  of  impact  being  added  to  each  kind  of 
loading.  32.  Bending  moment  at  panel  points  shall  be  assumed  equal  to 
that  at  center,  but  m  opposite  direction.  33.  Other  members  similarly 
affected  are  to  be  treated  likewise. 

Shearing  and  Bearing  Stresses  f. — 34.  For  rivets,  bolts  and  pins,  the 
shearing  stress  per  sq.  in.  wall  not  exceed  11000  for  soft  steel,  and  120CK)  for 
medium  steel;  and  tne  pressure  upon  the  bearing  surface  of  the  projected 
semi-intrados  (diam.  X  thickness)  shall  not  exceed  22000  for  soft  steel,  and 
24000  for  medium  steel.  (See  Table  1.  page  612.)  35.  Increase  number  of 
rivets  thus  found  if  field  driven:  by  hand.  26%;  by  power.  10%. 

Bending  Stresses  on  Pins.t— 36.  Extreme  fibre  stress:  Soft  steel.  22000;  , 
medium  steel.  25000  lbs.  per  sq.  in.  Use  centers  of  bearings  of  strained  j 
members.     (See  Table  25.  page  680.) 

Plate  Qirder8.|| — 37.  Assume  M  gross  area  of  web  as  available  flange 
area.     Compression  flange  to  have  same  sectional  area  as  tension  flange; 

*  Should  the  pins  be  out  of  the  neutral  axis,  the  additional  stress  thus 
produced  shall  be  provided  for. — P.  &  R. 

t  Shearing:  Shop  rivets  and  pins,  12000;  field  rivets  and  turned  bolts, 
lOOCfO:  plate  girder  webs  (gross  section)  10000.  Bearing:  Shop  rivets  and 
pins,  24000;  field  rivets  and  turned  bolts,  20000;  granite  masonry  and  Port- 
land cement  concrete,  600;  sandstone  and  limestone,  400  lbs.  per  sq.  in.— 
C.  R.  I.  &  P. 

Shearing:  Pins  and  rivets,  7500;  web  plate.  5000  in  direction  of  roUing. 
and  6000  across  fibre.  Bearing:  Pins  ana  rivets,  12000;  bed  plates  on  ma- 
sonry. 250.  Decrease  25%  for  hand  and  field  rivets;  increase  26%  for  lateral 
and  vibration  riveted  connections. — D.  L.  &  W. 

Shearing:  Rivets,  bolts  and  pins,  11000;  web  plates  of  stringers,  floor 
beams,  and  plate  girders  (net  section),  llOCK).  Bearing:  Rivets,  bolts  and 
pins,  22000;  masonry,  400.  Deduct  20%  for  field  rivets. — L.  S.  &  M.  5. 
Same  as  preceding  excepting,  use  10000  lor  "shear  in  webs  of  plate  girders." 
—P.  &  R. 

Shearing:  Pins  and  rivets.  7500;  webs  of  plate  girders.  6000.  Bearing: 
Pins  and  rivets,  15000.  Increase  stresses  50%  for  knee  bracing;  decrease 
20%  for  hand  rivets.— S.  P. 

t  24000.— C.  R.  I.  &  P.  and  L.  S.  &  M.  S.  15000.— D.  L.  &  W. 
22000— P.  &  R.     1800.— S.  P. 

II  Proportioned  either  by  moment  of  inertia  of  net  section:  or  by  assuming 
3^s  of  gross  web  section  to  be  added  to  flange  area.  Gross  section  of  comp 
flange  shall  not  be  less  than  that  of  tens,  flimge;  nor  shall  working  stress  m 

comp.  flange  of  any  beam  or  girder  exceed  16000— 200^-.  where  /—unsup- 
ported distance,  and  6— width  of  flange. — C.  R.  /.  &  P. 

Girders  and  beams  must  have  top  or  comp.  flange  braced  at  intervals 
of  at  least  20  times  the  width  of  flange.  No  part  of  web  of  plate  girder 
considered  as  flange  area. — D.  L.  &  W. 

Depth  of  girder  generally  H  to  A  of  span  up  to  75  ft.  span,  and  propor- 
Uonately  less  up  to  a  minimum  of  t\  for  the  largest  practicable  plate  girder. 
No  part  of  web  to  be  considered  as  flange  area.  No  cover  plate  ^alT  have 
a  thickness  greater  than  the  angles;  ?i  m.  to  be  about  the  max.  thickness. 
*^»^  covCT  plate  to  extend  full  length;  other  plates.  12*  beyond  theoretical 
cut-off.  For  spans  over  70  ft.,  flange  members  may  be  spliced,  only  one 
J™*  **  ^^Y^^:^^  Poi"*  o^  flange.  Stiff ener  angles  to  be:  3Hx^3^  for 
spans  up  to  So  ft.;  4x3i^xH.  60  to  70  ft.  spans;  5x3HxH.  70  to  90  ft.  spans; 
6x3HxH.  above  90  ft.— L.  S.  &  M.  S.  ^^ 


SPECIFICATIONS  FOR  STEEL  R.  R,  BRIDGES.  706 

but  unsupported  length  shall  not  exceed  16  times  its  width.  38.  In  design- 
ing web  nvets  of  plate  girders,  assume  total  shear  at  abutment  as  transferred 
into  flange  angles  in  a  distance  equal  to  depth  of  girder.  30.  Minimum 
web,H'-  Shear.  9000  for  soft  steel;  10000  for  med.  steel.  40.  Stiff eners, 
both  sides,  close  flange  bearings,  at  points  of  concentrated  load;  also,  when  • 
t  of  web  is  less  than  ^  of  unsupported  distance  between  flange  angles,  stiff- 
eners  to  be  spaced  generally  not  farther  apart  than  depth  of  lull  web  plate, 
with  max.  Umit  of  o  ft. 

Provision  for  Future  Increase  of  Live  Load.* — 41.  When  live  and 
dead  load  stresses  are  of  opposite  character,  only  70%  of  the  dead  k>ad 
stress  shall  be  considered  as  effective  in  coxmteracting  the  live  load  stress. 

(d.)    Details  of  Conttmctlon. 

Camiyer.t— 42.  For  truss  bridges,  increase  length  of  top  chord  H'  to 
evety  10  ft.    [Best:  Shorten  diagonals,   without  increasing  the  chord. — 

Adjastal>le  Members.— 44.  Preferably  avoided. 

Trass  Bridges. — 45.  Stiff  end  vertical  suspenders  for  through  spans. 
For  end  panels  of  lower  chord,  preferably  stiff  members  for  single  track 
spans. 

Lateral  and  Sway  Bracing.— 48.  To  be  compression  shapes. 

Diacooal  Bracing .t— 50.  Deck  bridges  shall  have  diagonal  braces  at  each 
panel,  of  sufficient  strength  to  carry  half  the  maximum  strain  increment 
due  to  wind  and  centrifugal  force. 

Qnsset  Plates.— 51.  At  each  end  of  pony  trusses  and  through  plate 
girders,  and  at  floorbeam  cf  same. 

Tenperatnre.ii — 52.  Provision  for  150**  F.  variation. 

Bolsters  and  Expansion  Rollers.l — 53.  For  bridges  exceeding  80  ft. 
span,  hinged  bolsters  at  both  ends,  with  nests  of  turned  friction  rollers  at 
one  end.  Rollers  not  less  than  i'  dia.;  and  pressure  p,  in  lbs.  per  Jin.  in. 
of  roller,  not  to  exceed  1200  y/d  for  steel  rollers  between  steel  surfaces 
(J— diam.  of  roller  in  ins.). 

Bed  PUtes.i  — 55.  Pressure  on  masonry,  including  impact.  400  lbs.  per 
sq.  in. 

Rivets. — 56.  In  direction  of  strain,  max.  pitch  to  be  0*  or  1ft  X  thickness 
of  thinnest  outside  plate,  at  right  angles  to  strain,  max.  pitch  to  be  402" X 
that  thickness.  At  ends  of  compression  members,  pitch  not  to  exceed  4 
diameters  of  rivet  for  a  length  equal  to  2#  times  width  of  member. 

Tie  Plates. — 60.  All  s^fments  of  compression  members  connected  by 
latticitig  only,  shall  have  tie  plates  placed  as  near  the  ends  as  practicable, 
with  length  not  less  than  greatest  depth  or  width  of  member,  and  thickness 
not  less  than  Jt  of  the  distance  bet.  the  rivets  connecting  them  to  the  com- 
pressed members. 

*  If  live  load  be  increased  70%  the  stress  per  sq.  in.  in  any  member  shall 
not  exceed  1 . 7  X  the  allowed  unit  stress,  and  in  case  of  reversal  of  stress 
proper  provision  shall  be  made  for  same. — C.  R.  I.  &  P. 

•  t  Camber  for  plate  girders  over  50  ft.  span  to  be  A*  per  10  ft.  of  length. — 
C.  R.  /.  <y  P.  Camber  for  all  spans,  about  W  in  1 00  f t.— £>.  L.&W.  Cam- 
ber for  movable  bridges,  such  that  when  end  supports  are  raised  to  their 
exact  position  the  base  of  rail  will  be  at  the  same  level  on  ends  of  bridge  as 
at  center. — L,  S.  &  M.  5.  Arc  of  circle;  and  at  least  t<\hi  of  the  span. — 
S.P. 

t  Overhead  diag.  bracing  at  each  panel  point  when  height  of  truss 
exceeds  25  ft— P.  d*  R. 

II  Expansion  and  contraction,  1'  in  every  100  ft. — D.  L,  &  W.  and 
L  S.  6r  At.  5.    150*  F.— P.  &  R.  and  S.  P.    J^/for  each  10  ft.— C.  R.  I.  &  P. 

I  Rollers  not  less  than  6*  diam. — C.  R.  I.  &  P.  Rollers  not  less  than 
Vi^  diam.;  or  f- 300  d.—D.  L.  &  W.  Rollers:  1200  y/d.—P.&R.  For 
bndgea  over  7o  ft.  span,  segmental  steel  friction  rollers  not  less  than  6' 
diam;  but  cylindrical  rollers  4*  diam.  may  be  used. — S.  P.  i 

J  See,  also,  foot-notes  to  34,  preceding,  for  bearing  on  masonfidC 

I  aa— P.  irR,0  m.-c.  k,  i.&  p,  ^ 


706 


iB.^RAtLROAD  BRIDOBS. 


Lacing.* — 61.  Single  lattice  bars  shall  have  a  thickness  of  not  less  than 
and  double  bars  connected  by  rivet  at  intersection,  not  less  than  ^. 
[  dist.  bet.  rivets  connecting  them  to  the  member;  and  their  width  shall  be: 
■"  riv.)  for  16'  chans.,  or  built  sections  with  Si^and  4' angles: 

*•  12'andl(r r  ^^ 

"    rand    r  "        "    • 2** 

Pin  Plates. — 62.  Mtist  contain  enough  rivets  to  transfer  the  proportion 
of  pressure  upon  them,  and  at  least  one  plate  on  each  side  shall  extend  not 
less  than  6*  beyond  edge  of  tie  plate. 

(e.)    Workmanship. 

Riveted  Work. — 66.  Hole  «=  rivet  +  A";  enlargement,  by  reaming. 

Planing  and  Reaming. — 67.  In  medium  steel  over  H  .  sheared  edges 
to  be  planed,  and  holes  to  be  drilled  or  reamed  to  diam.  of  rivet +H''. 

Eye-Bars. — 76.  Heads  of  eye-bars  to  be  made  by  upsetting,  rolliog. 
or  forging.     Welds  not  allowed.     78.  All  eye-bars  shall  be  annealed. 

Machine  Work. — 79.  Abutting  surfaces  in  compression  members  shall 
be  truly  faced  to  even  bearin^p.  80.  Ends  of  floor  sirders  shall  be  faced 
true  and  square.  81.  No  variation  of  more  than  A  for  every  20  ft.  will 
be  allowed  in  length  between  centers  of  pin  holes.  84.  Clearance  between 
pin  and  pin  hole  ^lall  be  A'  for  lateral  pins;  and  for  truss  pins,  ^'  for  pins 
3K  diam.,  gradually  increased  to  ;^'  for  pins  0*  diam.  and  over. 

(f.)   Steel. 
Process  of  Manufacture. — 87.  Open  hearth.     If  by  acid  process,  not 
over  .08%  phosphorous;  if  by  basic  process,  not  over  .06%  phosphorous. 
Physical  Properties.t  —92.  Three  grades: 

Rivet  Steel,  Soft  Steel.  Medium  Steel 
Ultimate  strength,  lbs.   pcrs9.  in.,       48-68000.    62762OOO.      00-70000. 


|ult. 
Flat 


iult. 
26%. 
Flat 


iult. 
22-" 


on 

itself. 


22%. 

To    diam. 

-thick. 

of  piece. 


Elastic  limit, 
Elongation, 

Bending  test — ^without  fracture  on 
outside  bent  portion.     180** J     itself. 

Pins. — 100.  Up  to  T  diam.,  rolled.     101.  Above  7*  diam.,  forged. 

Steel  Castings.! — 103.  Open  hearth,  containing  from  0.25  to  0.40% 
carbon,  and  not  over  .08%  phosphorous. 

tSame  as  Am.  Br.  Co.,  61,  above.— <7.  R.  I.  &  P. 

Lacing  bars  shall  not  be  less  than  2ix|,  and  shall  fonn  an  angle  of  not 
less  than  60^  with  axis  of  member  in  single  lacing,  and  46^  in  double  lacing. 
Double  lacing  mtist  be  riveted  at  intersections. — D.  L.  &  W. 

Latticing  shall  be  double,  and  shall  preferably  cross  at  right  angles, 
and  be  riveted  at  intersections.  Lacing  shall  be  single,  and  be  at  angle  of 
about  60**  with  axis  of  member.  Minimum  size  of  lattice  bars  shall  be  as 
follows:  2txA  for  8*  and  9*  chans.;  2ix#  for  10*  and  12'  chans.  and  2* 
angles;  2}xrt  for  16'  chans.  and  3i*  and  4'  angles;  connected  by  one  rivet 
at  each  end.  4xA  for  built  sections  over  16'  wide;  connected  by  two  rivets 
at  each  end. — L.  S.  &  M.  S.  For  chords  and  posts  the  lattice  bars  sha!l 
generally  be  3xtV;  the  width  may  be:  2*  for  lattice  imder  10*  Llong.  21' 
under  15'  long,  and  2J'  under  20'  long.— P.  (S*/?. 


fRoad. 

Properties. 

Steel. 

Medium. 

R*yBr. 

Struct!. 

Soft. 

Rivet. 

OMttofSL 

C.R.I.&P. 

Ult.  tens.  str.. 

56-64000 

54-62666 

.Suit. 

26 

46-64000 

48-56000 

.Suit. 

28 

48-56000 

.6  ult. 

28 

CSOM 

r  Ult.  tens.  str.. 

Elas.  limit.... 

Elong.,  %.  8*. 

Ult.  tens.  str.. 

Elas.  limit.... 

Elong.,  %.... 

For  bed  plates 
,  '''or  genrlng;. , . 

62-70000 

.Suit. 

22 

62-70000 

.6  Ult. 

35 

D  L.  &  W 

.5idt 

L.  8.  4  M. 

8. 

P.  4R. 
8.  P. 

56-64000 

.6  Ult. 

28 

55-65H0 

65-76N0 

UlL  tens  str.. 

66-64000 

46-54000 

46-54000 

26000 

C50H1 

Ult.  tens.  str.. 

§Uis.llmlt...j 

I  Eloag..  %,  v: 

60-68000 
33000 

^ 

22 

26 



d  by  Google 


SR.—RAILROAD  BRIDGES. 


AXIMUM  MOMBNTS  Af .  EnD  ShBARS  5,  AND  PlOORBBAII  RBACTIONS  R, 

*ER  Track,  Producbd  by  Coopbr's  Loadings*  E  60  and  E  40. 
[Mult.  Values  in  Table  by  1000.] 


Loading  E  50. 

Loading  B  40. 

Ih 

ill 

Equlv.  Unlf.  Load 

ni 

III 

i«3 

Eqtilv.Unir.Lowl 

In  1000  Lbs, 

m  1000  LiM. 

M 

S 

R 

M 

a 

R 

141 

76 

100 

11.25 

15.00 

10.00 

113 

60 

80 

9.00 

12.00 

Toi 

1«4 

82 

109 

10.86 

14.88 

9.92 

131 

66 

87 

8.69 

11.91 

7.94 

200 

88 

117 

11.11 

14.58 

9.72 

160 

70 

93 

8.89 

11.67 

7.77 

238 

92 

123 

11.24 

14.21 

9.47 

190 

74 

99 

9.00 

11.85 

7.58 

275 

96 

130 

11.22 

13.78 

9.31 

220 

77 

104 

8.98 

11.03 

7.45 

313 

100 

137 

11.11 

13.33 

9.11 

250 

80 

109 

8.89 

10.67 

7.39 

350 

106 

142 

10.94 

13.28 

8.89 

280 

86 

'  114 

8.75 

10.63 

7.11 

388 

112 

147 

10.73 

13.15 

8.66 

310 

90 

118 

8.58 

10.53 

6.92 

425 

117 

152 

10.49 

12.96 

8.43 

340 

93 

121 

8.40 

10.38 

6.74 

466 

121 

157 

10.34 

12.74 

8.28 

373 

97 

126 

8.27 

10.19 

6.63 

516 

125 

164 

10.31 

12.60 

8.19 

413 

100 

131 

8.25 

10.00 

6.51 

565 

129 

170 

10.25 

12.24 

8.09 

452 

103 

136 

8.20 

9.79 

6.48 

614 

133 

175 

10.15 

11  98 

7.97 

491 

10« 

140 

8.12 

9.59 

6.38 

664 

135 

180 

10.04 

11.72 

7.84 

631 

108 

144 

8.03 

9.38 

6.r 

713 

139 

185 

9.90 

11.55 

7.70 

670 

111 

148 

7.92 

9.23 

6.17 

763 

142 

189 

9.76 

11.36 

7.6« 

610 

114 

161 

7.81 

9.09 

6.0S 

812 

145 

194 

9.61  111.18 

7.47 

650 

116 

166 

7.69 

8.93 

5.97 

862 

148 

200 

9.46   10.97 

7.41 

689 

119 

160 

7.56 

8.78 

5.93 

914 

151 

206 

9.32    10.79 

7.35 

731 

121 

165 

7.46 

8.63 

5.8S 

970 

154 

211 

9.23    10.61 

7.27 

776 

123 

169 

7.37 

8.49 

5.83 

1026 

158 

216 

9.12  'lO.Sl 

7.19 

821 

126 

173 

7.30 

8.41 

1.75 

10S2 

161 

221 

9.01 

10.39 

7.14 

866 

129 

177 

7.21 

8.31 

5.71 

1139 

164 

227 

8.90 

10.27 

7.11 

911 

132 

182 

7.12 

8.22 

5.69 

1195 

167 

233 

8.78 

10.14 

7.07 

956 

134 

187 

7.02 

8.11 

566 

1251 

170 

239 

8.66 

10.01 

7.02 

1001 

136 

191 

6.92 

8.01 

5.63 

1307 

173 

244 

8.54 

9.88 

6.97 

1046 

138 

195 

6.84 

7.tl 

5.57 

1372 

176 

249 

8.47 

9.80 

6.91 

1097 

141 

199 

6.77 

7.84 

5.  a 

U36 

180 

253 

8.39 

9.71 

6.86 

1149 

144 

203 

6.71 

7.77 

5.50 

1500 

183 

259 

8.31 

9.62 

6.82 

1200 

146 

208 

6.65 

7.70 

5.46 

1567 

186 

265 

8.24 

9.52 

6.79 

1254 

149 

212 

6.59 

7.62 

5.43 

1639 

189 

270 

8.20 

9.43 

6.75 

1311 

161 

216 

6.56 

7.54 

5.40 

17^4 

195 

280 

8.09 

9.30 

6.67 

1427 

156 

224 

6.48 

7.46 

534 

1929 

201 

291 

7.97 

9.15 

6.62 

1543 

161 

233 

6.37 

7.32 

5.30 

2074 

207 

302 

7.84 

9.00 

6.56 

1659 

166 

241 

6.28 

7.30 

5.24 

2219 

212 

312 

7.71 

8.84 

6.49 

1776 

170 

250 

6.17 

7.07 

5.30 

2377 

218 

322 

7.61 

8.71 

6.44 

1902 

174 

257 

6.09 

6.97 

5.14 

2J33 

223 

333 

7.51 

8.58 

6.40 

2030 

179 

267 

6.01 

6.87 

5.13 

2703 

228 

345 

7.42 

8.44 

6.39 

2162 

182 

276 

5.93 

6.76 

5.12 

2v>*0 

233 

357 

7.35 

8.30 

6.38 

2304 

186 

286 

5.88 

6.64 

511 

3058 

238 

370 

7.27 

8.22 

6.38 

2446 

191 

295 

5.82 

6.58 

5.09 

3247 

244 

383 

7.22 

8.13 

6.38 

2599 

195 

305 

5.78 

6.51 

5.08 

3441 

250 

395 

7.16 

8.07 

6.37 

2753 

200 

315 

5.73 

6.46 

6.08 

3639 

256 

407 

7.11 

8.01 

6.36 

2911 

205 

326 

5.69 

6.41 

6.07 

3^49 

262 

419 

7.07 

7.95 

6.35 

3079 

210 

334 

6.66 

6.36 

5.07 

4059 

270 

431 

7.02 

7.93 

6.34 

3247 

216 

344 

5.61 

6.84 

5.06 

4269 

276 

443 

6.97 

7.89 

6.32 

3416 

221 

364 

6.6S 

6.31 

5.06 

4479 

283 

454 

6.91 

7.87 

6.30 

3584 

227 

362 

6.64 

e.30 

5.03 

4699 

291 

465 

6.86     7.86 

6.28 

3758 

233 

371 

5.49 

6.29 

5.01 

4925 

298 

476 

6.82  1  7.83 

6.26 

3942 

238 

379 

5.46 

6,27 

4.99 

5160 

304 

487 

6.79  1  7.80 

6.24 

4129 

243 

388 

6.43 

6.34 

4.97 

5399 

311 

497 

6.75 

h\76 

6.21 

4321 

248 

396 

5.40 

6.21 

4.96 

*  Note  that  values  for  all  classes  are  proportional; 
es  for  E  60  by  1 . 1;  for  E  46.  by  0.9;  etc. 


thxis,  for  E  &5,  mah. 

tizedbyGOOgFe 


MAX.  M.  S  AND  R  FOR  ENGINE  LOADS.    IMPACT. 


709 


5. — ^Maximum  Moiibnts  Af .  End  Shbars  5.  and  Floorbbaii  Rbactions  R, 

Pbr  Track,  Producbd  by  Coopbr's  Loadings*  E  60  and  E  40. — Cond'd 

[Mult.  Values  in  Table  by  1000.] 


Loading  j;  50. 

Loading  B  40. 

i 

I 

III 

Hi 

III 

Ml 

Equlv.  Unlf.  Load 
InlOOOLba. 

ill 

EQulv.Unlt.Load 
InlOOOLba. 

i« 

ii^ 

m 

ii 

1   s 

R 

m\   8     \b 

82 

5638 

317 

507 

6.71 

7.74 

6.19 

4513 

254 

404 

5.37 

6.19 

4.93 

84 

5891 

324 

517 

6.68 

7.71 

6.16 

4713 

259 

412 

6.34 

6.17 

4.91 

» 

1145 

330 

527 

6.65 

7.68 

6.13 

4919 

364 

421 

5.32 

6.15 

4.89 

S8 

6406 

337 

637 

6.62 

7.65 

6.10 

5128 

269 

429 

5.30 

6.12 

4.87 

90 

0074 

343 

546 

6.59 

7.62 

6.07 

5341 

275 

437 

5.28 

6.10 

4.86 

93 

0941 

849 

556 

6.56 

7.60 

6.04 

5552 

280 

444 

5.25 

6.08 

4.83 

»4 

7309 

356 

566 

6.53 

7.57 

6.02 

5771 

285 

452 

5.23 

6  06 

4.81 

96 

7470 

362 

575 

6.49 

7.54 

5.99 

5988 

290 

459 

5.20 

6.03 

4.78 

n 

7756 

369 

584 

6.46 

7.62 

5.96 

6213 

295 

467 

5.18 

6.02 

4.76 

100 

8048 

375 

003 

6.44 

7.50 

5.93 

6440 

300 

474 

5.15 

6.00 

4.74 

125 

IS491 

449 

6.40 

7.18 

9993 

359 

5.12 

5.74 

ISO 

17025 

522 

6.26 

6.96 

14100 

418 

5.01 

5.67 

175 

S3400 

585 

6.11 

6.69 

18720 

468 

4.89 

5.36 

200 

29625 

656 

5.92 

6.55 

23700 

624 

4.74 

5.24  1 

250 

44025 

787 

5  64 

6.29 



35220 

629 

4.51 

5.03 



*  Note  that  values  for  all  classes  are  proportional;  thus,  for  £  65.  mult. 
values  f or  E  60  by  1.1 ;  for  E  46.  by  0.9 ;  etc. 

0. — COBPPICIBNTS  OF  ImPACT  (/). 

(See  page  701.) 


L. 

aoo 

L+300 

L. 

300 

L. 

300    1 

L. 

1 

83 

300     I 

L. 

300 

L4-300 

L+300 

L+300| 
0.783 

L+300 

5 

0.984 

31 

0.906 

57 

0  840 

145 

0.674 

6 

0.960 

82 

0.904 

58 

0  R38  , 

84 

0.781 

150 

0.667 

7 

0.977 

83 

0.901 

69 

0.836 

85 

o.ng 

155 

0659 

8 

0.974 

84 

0.888 

60 

0833  1 

86 

0.777 

1    160 

0652 

9 

0971 

36 

0.896 

61 

0  831   1 

87 

0.775 

^    165 

0645 

10 

0.968 

36 

0.983 

62 

0.829  1 

88 

0.773 

170 

0.638 

11 

0.966 

87 

0.890 

63 

0  826  1 

89 

0.771 

175       0.632 

12 

0.962 

88 

0888 

64 

0824 

90 

0.769 

180    '  0.625 

13 

0.968 

39 

0886 

65 

0.822 

91 

0  767  1 

185     '  0  619 

14 

0.966 

40 

0882 

66 

0  820 

92 

0.765  ' 

190    1  0  612 

IS 

0.952 

41 

0880 

67 

0817 

93 

0.763  , 

195 

0606 

16 

0.949 

42 

0877 

68 

0  815 

94 

0.761 

200 

0600 

17 

0.946 

43 

0875 

69 

0  813 

95 

0  759 

210 

0  588 

18 

0.943 

44 

0.872 

70 

0811 

96 

0.758 

220 

0.577 

19 

0.940 

45 

0.870 

71 

0809  ' 

97 

0.756  1 

230 

0  566 

» 

0937 

46 

0.867 

72 

0  806  1 

98 

0.764  1 

240 

0556 

21 

0.936 

47 

0.865 

73 

0  804 

99 

0.752  ' 

250       0  546 

22 

0.932 

48 

0.862 

74 

0.802 

100 

0  750 

260 

0536 

23 

0929 

49 

0.860 

75 

0  ^K)  1 

105 

0.741   1 

,    270 

0  526 

24 

0.926 

60 

0.857 

76 

0.798   ' 

110 

0.732  ' 

1     280 

0517 

26 

0.92S 

61 

0.856 

77 

0.796   1 

I     115 

0  725 

290 

0.508 

26 

0.920 

62 

0852 

78 

0.794 

120 

0.714  1 
0.706 

1    300 

0500 

27 

0.917 

63 

0.850 

79 

0.792 

125 

400 

0  429 

28 

0916 

64 

0.847 

80 

0.789 

130 

0.698 

500 

0.375 

29 

0.912 

66 

0.845 

81 

0.787 

135 

0.690 

600 

0.333 

30 

0.900 

66 

0.843 

82 

0.785 

140 

0.682 

1 

No 

te.— Fo 

rnotati 

on  and  l 

ormula 

.seepaf 

je701.  t 

digitized  by  V 

.oog 

le 

d  by  Google 


WEIGHT  OF  STEEL  BRIDGES,   HOWE  TRUSS. 


711 


9. — ^Valum  op  VLoadi}»o,  in  prbcbdino  Pormxtla. 


Loading  (Class):— 

E60 

E65 

£50 

E45 

£40 

£85 

£30 

7.76 

7.42 

7.07 

6.71 

6.32 

5.92 

VLoading: — 

5.48 

Relative    Values   of 

1.00 

1.05 
1.10 
1.15 
1.23 
1.31 
1.41 

0.96 
1.00 
1.05 
1.10 
1.17 
1.25 
1.85 

0.91 
0.95 
1.00 

1.05 
1.12 
1.19 
1.29 

0.86 
0.90 
0.95 
1.00 
1.06 
1.13 
1.22 

0.81 
0.85 
0.89 
0.94 
1.00 
1.07 
1.15 

0.76 
0.80 
0.84 
0.88 
0.94 
1.00 
1.08 

0.71 
0.74 
0.78 

VLoading.  for  Classes 
E  30  to  E  60. 

0.82 
0.87 
0.93 
1.00 

Example. — Find  the  approx.  weight  of  steel  in  a  Through  Plate  Girder 
Bridge  with  floor  beams  and  stringers,  span  100  ft.,  loading  £40? 
Solution.— /Xtw- 100  (180+  70)  6 .  32- 158000  lbs. 

VIll.-PLANS  AND  DETAILS  OF  RAILROAD  SPANS. 
Howe  Truss  Bridges  are  being  rapidly  replaced  by  steel  and  concrete 
structures  on  all  of  our  American  roads,  but  the  following  typical  plans  will 
be  of  interest. 

N.  P.  R'y  Standard  Plan  op  Howb  Truss  and  Dbtails. 
90  Ft.  Through  Span. 
Loads. — Dead  Load,  1300  lbs.  per  lin.  ft.    Live  Load,  consolidation 
engine  and  tender,  225.000  lbs.,  followed  by  3000  lbs.  per  lin.  ft. 


Top  Cniord.- Pack- 
ing bolts  H*  dia.  C.-I. 
Sep.  for  bolts,  5'  and 
^dia. 


^"fid^ 


OB 


iiil  in^iiiil  ly^iihl  iiliiiJ  nJf^iii.l  III! 

Rft  ^iiniisi'ri  /iiiinrTriii  iiiiininTii  ,^i:niirfr!i  iin 


y^iMAtA^iMi\  '/^iA|U|iu^  VJjjx  IUIU.V  V^mjUlllA;  MUU|^aiAf 


Bottom  Chord.  — 
Iron  packing  keys. 
Packing  bolts,  %"  dia. 


Figs.  25. — General  Plan  and  Elevation. 
Timber  Specifications. — Must  be  sound,  live,  straight  and  close  grained 
red  or  yellow  fir,  cut  free  from  wanes,  shakes,  pitch  scams  and  clear  of 


7ia 


m.'-RAlLROAD  BRIDGES. 


knots  larger  than  I'dia.,  nor  cloier  than  4  ft.  on  any  side  ol 
must  be  sound  and  clear  of  pitch.  All  timber  must  be  cut  1 
loffs  free  from  heart  and  sap.  and  sawed  true  to  sizes  ordered 
f .  o.  b.  cars,  subject  to  inspection  before  delivery. 

Notts. — Use  red  fir  cross-ties  west  of  Helena.  Frame  < 
siting  stringers  into  floor-beams.  In  framing,  carpenters 
panels  full  size,  make  templates  of  angle  blocks  from  the  c 
braces  to  correct  1  ength  and  shape  so  determined.  Cast  iro: 
packing  bolts  in  top  chord  are  6  dia.  except  for  bolts  in  cc 
and  at  ends  of  chords,  which  have  separators  ZH'  dia.  All  c 
for  packing  bolts  are  3H'  dia.  Guard  rails  bolted  to  ties  i 
middle  and  spiked  to  all  other  ties  with  H'xW  bridge 
fifth  tie  spiked  to  stringers  with  H'  x  14'  bridge  spikes. 


K— iw~-  >^ 

k — m- — »l; 

1     o     o     o    j  •§ 

Steel  Ch 

o  o  o 

\  1 

Holes  spaced 
Make  8  chans.  wit 

Sfttf  Chenvwi* 

..      g       ..        .* 
..      8       ..        .. 
..      4 

Top  Vitw.    I    Botf.View. 


Top  View.    I   Bott.  View. 


BHU  of  I 
iron.  16.908 
iron.  17.948  1 
126  ft.  B.M. 


Top  Viev*      Bottom  Y«w. 


w 


.Side.  Eleva+ton», 


Figs.  26. — Howe  Truss  Details. 
Reinforced  Concrete  Bridges. — ^The  principal  use  of  rcii 
in  railroad  bridges  is  in  the  form  of  trestles  and  arches.  \< 
tain  conditions,  it  is  found  most  economical.  Many  usef^ 
Class  of  construction  will  be  found  in  the  three  following  paj 
«S2  S  o*^"*^®s''  For  formulas  and  working  stresses,  sec 
and  38.    See.  also,  other  Sections  and  Index. 


HOWE  TRUSS  DETAILS.    MISCELLANEOUS. 


713 


EXCERPTS  AND  REFERENCES. 

A  Qraphioa  Method  of  Finding  Floor^Beam  Concentrations  Under 
Wheel-Loads  (By  R.  H.  Bulloch.    Eng.  News,  May  21.  1903). 

SUndard  Plans  for  Bridges  on  the  Atchison,  Topeka  ft  Santa  Fe  Ry. 

(By  J.  Dun.    Eng.  News.  May  28,  1803).— Illustrated. 

A  ComiNtfison  of  the  Requirements  of  Recent  Railway  Bridge  Sped- 
fications  (By  A.  H.  Heller.  Eng.  News,  Nov.  19.  1903).— Tabulated  data, 
from  29  spmfications. 

A  New  Tmss  Design  (By  J.  W.Schaub.  Eng.  News,  Mar.  24, 1904).— 
Warren  type,  with  a  combination  of  pin  and  riveted  connections.  Adopted 
by  some  m.  the  railroads. 

A  Moment  Table  for  Wheel  Loads  (By  R.  B.  Ketchum.  Eng.  News. 
May  12,  1904).    Table  and  diagrams. 

New  Westminster  Bridge  over  Fraser  River.  B.  C.  (By  Waddell  and 
Herrick.  Eng.  News,  June  15  and  22,  1905). — Foundations,  superstructure 
and  erection;   iU\istrated. 

Recent  Railway  Viaducts  of  Reinforced  Concrete  (Eng.  News.  May 
31.  1906).— Ilhistrated. 

Diaptun  Table  for  Cooper's  E-50  Loading  (By  J.  Gibson.  Eng. 
News.  June  21,  1906). — Double  inset  sheet.    Very  elaborate  Uble. 

Wheel  Loadings  of  Mallet  Duplex  Compound  Locomotive  for  Qreat 
Northern  Ry.  (Eng.  News,  Nov.  22,  1906). — Corrected  diagram. 

Rail  Expansion  Joints  on  the  Thebes  Bridge  (By  Ralph  Modjeski. 
Eng.  News,  Aug.  22,  1907).— Illustrated. 

Proportioning  Steel  RaUway  Bridge  Members  (By  H.  S.  Pritchard. 
Eng.  News.  Sept.  19.  1907). 

Erection  of  Long  Span  Trusses  by  End  Launching  (C^an.  Soc.  Civ. 
Engrs.  April  16,  1908;  Eng.  News,  July  23.  1908).— Blustrated. 

Safe  Unit  Stresses  hi  Structural  Timber  (Eng.  Rec.,  Apr.  24,  1909).— 
The  safe  unit  stresses  in  structural  timber  recommended  by  the  committee 
on  wooden  bridges  and  trestles  of  the  Am.  Ry.  Eng.  and  M.  of  W.  Assn.,  for 
^reen  condition  of  timbers  and  without  increasing  the  live-load  stresses  for 
impact,  are  as  follows: — 


Bending, 

Shearing. 

compression. 

Extreme 
fiber 
stress. 

Parallel 

to 
grain. 

Long'l 

in 
beams. 

Perp. 

to 
grain. 

Parallel 

to 
grain. 

C^ols. 

under 

ISdia's. 

pottgUs  fir 

Loagleaf  pine  .... 

S}w>rtleaf  pine 

White  pine 

Spj^cc   

1  200 

1  300 

1  100 

900 

1000 

800 

900 

1  100 

900 

900 

800 

1  100 

170 
180 
170 
100 
150 
130 
170 
160 
80 
120 

'2i6 

110 
120 
130 
70 
70 
100 
100 
100 

iio 

310 
260 
170 
150 
180 
150 
220 
220 
150 
170 
230 
450 

1  200 
1  300 
1  100 
1  000 
1  100 

800 
1  000 
1  200 

900 
1  100 

900 
1  300 

900 
980 
830 
750 
830 

Norway  pine 

Tamarack 

Western  hemlock  . 
Red-wood 

600 
750 
900 
680 

Bald  cypress 

Red  Cedar 

White  oak 

830 
680 
980 

For  kmg  columns  exceeding  15  diameters  in  length  the  safe  stress  given 
for  compression  parallel  to  grain  are  taken  and  decreased  by  QOL-*-D. 
frbere  £-— length  in  ins.,  and  D—least  side  in  ins. 

Measurement  of  Impact  Stresses  (By  B.  W.  Dunn.tizePt^(^^I?.  M., 
Vol-  IX..  1909).  "^ 


714  2S,— RAILROAD  BRIDGES. 

Rdnforced-Concrete  Brldfet  for  Track  Elevation  on  III.  Cent  R.R.; 
Failure  Test  of  Very  Large  Concrete  Slabs  (Eng.  News,  Axig.  6,  1908). — HJus- 

trated. 

Application  of  Spiral  Hooping  to  a  French  Concrete  Bridge  (Eng. 
News,  April  22,  1909).— Dlustrated. 

Erection  of  New  River  Bridge  by  the  CantHever  Method  (By  L.  L.  Jewel. 
Eng.  News.  July  8.  1909).— Single-track  deck  structxirc.  2166  ft.  kmg.  112 
.  ft.  above  low  water;  spans.  125  to  140  ft.;  all  trusses  are  riveted  Waireo 
trusses.  26  ft.  deep  c.-c.  chords  and  spaced  12  ft.  apart;  no  floor  svstem 
provided ;  the  deck  of  extra  heavy  ties  being  carried  directly  on  the  topcnofxls. 
Erected  by  cantilever  traveler;  11  illustrations. 

Guard  Rail  and  Deck  Construction  for  Railway  Bridges  (Eng.  News. 
Sept.  9.  1909). 

Illustrations: 

Typical  arrangement  of  bridge  guards;  Lehigh  Valley  R.  R.  Dedc  and 
guarcf  rail  construction  (with  two  and  three  inside  guards);  Can.  Pac.  R-  R. 
Bridge  deck  with  sidewalk;  Carolina,  Clinchfield  and  Ohio  R.  R.  Bridge 
deck  construction  on  curves;  Carolina,  Clinchfield  and  Ohio  R.  R.  Details 
of  bridge  deck  and  guards;  Lehigh  Valley  R.  R.  Bridge  deck  with  timber 
guards;  Louisville  and  Nashville  R.  R.  Bridge  deck  and  guards  (with 
tangents  and  curves);  Pcnn.  Lines.  Bridge  gtiards  with  re-railing  devices; 
Southern  Pacific  R.  R.  Details  of  re-railing  devices:  Southern  Pacific  R.  R 
Re-railing  devices  at  approaches  to  jack-knife  draws;  B.  &  M.  R.  R 
Bridge  guards  on  concrete  bridge  on  a  French  railway.  Deck  and  guanl 
rail  construction;  So.  Side  Elev.  Ry.,  Chicago.  Deck  and  guard  rail  con- 
struction for  curves;  So.  Side  Elev.  Ry.,  Chicago.  Examples  of  bridge 
guards  on  English  railway  bridgea 

LethbHdge  Viaduct  over  the  Belly  River,  Canadian  Pac.  Ry.  (By  J.  E. 

Schwitzer.     Eng.  News,  Sept.  23,  1909). — Plans  of  floor  and  tower.  • 

Four-Track  Truss  Bridge  with  Solid  Floor;  Chicago  ft  Oak  Park  Elev. 

Ry.  (Eng.  News,  Dec.  9,  1909). — Numerous  plans  and  details*  including 
falsework. 

Long  Span  Reinforced-Concrete  Qirder  Bridf^  (By  F.  W.  Scheidenhelir. 
Eng.  News,  Jan.  27,  1910). — Illustrations:  Girders,  abutment  and  piers; 
with  details  of  centering  and  forms  used  on  the  76-ft.  girder;  also,  splice 
clamp  for  reinforced-concrete  bars. 

Reinforced-Concrete  vs.  Steel  for  Short  Span  Railway  Bridges  (Eng. 
News,  Mar.  24,  1910). — Reinforced-concrete  flat  slabs  or  girders  not  gener- 
ally advisable  for  railway  loads  in  spans  exceeding  40  feet. 

450-Ft.  Steel  R.  R.  Span  of  the  MHes  Glacier  Bridge,  Alaska  (Eng.  Rec  . 
Aug.  6,  1910). — Illustrations:  Elevation  of  bridge  (one  460'  span,  two  4BQ' 
spans,  one  300'  span);  truss  details  of  460'  span;  nxed  and  expansion  end 
shoes,  with  segmental  rollers  and  nest  and  grillage,  460'  span;  erection  filler 
between  shoes  on  pier;  erection  adjustment  devices  for  top  and  bottom 
chords. 

The  St.  Louis  Municipal  Bridge  Superstructure  (Eng.  Rec.  Dec.  3.  1910) 

— Bridge  comnoscd  of  three  668-ft.  steel  spans  carr>'ing  two  railroad  tracks 
on  the  lower  floor  at  bottom  chord  level,  and  two  electric  car  tracks,  a  drii-e- 
way,  and  two  cantilever  sidewalks  one  on  second  floor  22  ft.  in  the  clear 
above  the  lower  floor.  The  two  pin -connected  trusses  36  ft.  ai^art  on  centers 
are  110  ft.  deep,  66  ft.  in  the  clear  above  high  water  and  will  be  made  ci 
nickel  steel,  while  the  floor  system  and  bracing  will  be  made  of  carbon  steel 
(See  Eog.  Rec.  of  Oct.  30,  1909,  for  diagrams,  stress  sheets,  spccificatior-s. 
etc.;  also  Eng.  Rec.  of  Oct.  16,  1910,  for  description  of  design  and  coc- 
struction  of  the  substructure.)  The  main  span  trusses  are  longer  than  those 
of  any  other  span  with  independent  trusses;  the  panel  lengths  vtay  with  the 
depths  of  the  trusses  in  accordance  with  economical  inclinations  of  the 
diagonal  members :  the  top  chord  has  a  special  type  of  cross-section ;  the  nppcr 
*u^  **.n^ade  with  intermediate  floorbeams  carried  on  longitudinal  sitoers. 
the  main  truss  shoes  and  pedestals  are  heavy  steel  castings;  many  of  iV 
compression    members  have   half -hole   pin-bearings   without   interlocking 


REFERENCES.  7U 

ma  plates;  and  the  members  and  details  are  of  standard  construction. 
Illustrations: — Regular  cro^-section;  general  diagram  of  668-ft.  span. 
giving  heights  of  truss;  upper  and  lower  portal  bearing;  roadway  bent  over 
pier;  sections  of  upper  and  lower  decks;  expansion  uioe  and  pedestal  for 
b;  pedestal  for  fixed  shoe;  top  chord  details  of  sidewalk  and  curb  girder. 


Important  lUuftratioiis  of  Railroad  Bridgcf  and  Details. 

Description.  '  Eng.  News 

Large  rein.-conc.  railway  viaduct,  Rotterdam,  Holland Time  16,' 10 

Through-truss,  517J-ft.  river  spans.  St.  Louis July  28.*  10 

Part  details  420-ft.  truss  span  and  floor Aug.  26,'  10 

Stringer  connection  allowing  flexibility Aug.  26.'  10 

Erie  R.  R.  ^daduct,  Penhom  Creek Oct.  13,  '10 

Eng.  Rec. 

Details  of  steel  viaduct.  B.  &  M.  R.  R Feb.  27,  '09 

Ballasted-floor  details  and  steel  construction.  Erie  R.  R Feb.  27,  '09 

110-ft.  railroad  span Mar.  27. '09 

Erection  of  long  span  bridges  across  the  Susquehanna Apr.  3.  '09 

Falsework  for  replacing  the  Cuyahoga  Val.  viaduct June  6.  '09 

5-track,  short  span,  solid-floor  bridge,  N.  Y..  N.  H.  &  H.  R.  R.  .July  24,  '09 

Strain-fihect  668-ft.  span — St.  Louis  Municipal  Bridge Oct.  30,  '09 

Typical  falsework  for  Poughkcepsie  Bridge  reinforcement Oct.  30,  '09 

Heavy  steel  floor  for  double-track  bridge,  D.  L.  &  W Jan.  16, '  10 

100-ft.  span  plate-girder  bridge,  N.  Y.,  N.  H.  &  H.  R.  R Mar.  12, '10 

C.  M.  &  St.  P.  R.  R.  bridge  across  Missouri  River,  Mobridge, 

S.  Dak June  U.'IO 

Standard  160-ft.  Howe  truss  R.  R,  span  and  details Sept.  3.  '10 

Standard  I-beam  R.  R.  bridges  over  streets.  N.  Y.  Cent Sept.  17.'  10 

Elcv.  and  section  of  8-track  K.  R.  bridge  over  streets Oct.   1,  '10 

Structural  details,  Providence,  R.  I.,  station  viaduct,  N.  Y.,  N. 

H.  &  H.  R.  R Oct.  22,  '10 

*  Construction  and  reconstruction  of  the  Coteau  steel  bridge Dec.  3.  '10 


d  by  Google 


39.— ELECTRIC   RAILWAY   BRIDGES. 

See.  also,«Sec.  40,  Highway  Bridges,  page  727. 

Typical  "L**  Loading  as  follows,  for  electric  railway  bridges  may  be 
used  for  any  structure,  heavy  or  light,  by  assigning  proper  values  to  w.* 

(a)  For  calculation  of  floor  system,   use  two    axle  concen-     ic,^       p;^ 
trations  of  16  a;  each,  spaced  10  ft.  centers.     (See  Fig.  1.)         ^  i#\»  J 

(b)  For  calculation  of  trusses,  use  for  each  track  a  uniform     JlT'^'tjL 
moving  load  of  te/lbs.  per  lin.  ft.  for  spans  up  to   100  ft.:    MJ      Qj 

and  0.8  «;  for  spans  200  ft.  and  over;  with   a   reduction  of  -^"^^ ^i^ 

loading  for  intermediate  spans  of  0.01  w   for  every  5-ft.        Pig.  1. 
increase  over  100  ft.     The  uniform  load  w  per  track  is  assumed  to  cover 
a  surface  12  ft.  wide  for  single  track;  22  ft.  wide  for  double  track. 
Tables  1  and  2  are  based  on  the  above  typical  "L"  loading. 

1. — Special  Type  "L"  op  Electric-Car  LoADiNcf — Axlb  and  Unipomi. 


Typical  "K"  Loading,  Fig.  2,  consists  of  a  train  of  electric  cars  with 
axle  spacing.  5'-16'-5'-16',  etc..  continuous  The  loading  shown  in  the  sub- 
joined diagram  is  for  100,000-lb.  cars,  each  covering  a  length  of  40  feci. 
Tables  3,  4  and  5,  following,  arc  calculated  from  this  diagram. 

i  i         i  i         i  i         i  i 

oo  oo  oo  SS 

8     §.   50-Ton     o^     S     Ax/e        8     ^   SO-Torr     8.     8 
^     ^      Car        }G     JS    Loac/s      t(J    iS      Cor        '^     '^ 


,K5'>!<- /5'  — — >i<5'>< J5'  — -->}<5'H<- /5'  —->i<^'*! 

Fig.  2. 


♦  For  the  Manhattan  suspension  bridge  across  the  East  River,  New 
York,  the  value  of  w  was  originally  assumed  at  1700  lbs.  per  lin.  ft.  for 
each  of  four  rapid  transit  trains;  and  1000  lbs.  per  lin.  ft.  for  each  of  four 
lines  of  trolley  cars.    The  revised  loading  is  given  on  page  766. 

tThe  concentrated  loading  gives  maximum  moments  for  spans  under 
48  2  feet,  and  the  uniform  loading  for  spans  over  48 . 2  feet.  For  maximum 
noorbeam  reactions  use  concentrated  loading  for  panels  up  to  23.66  feet 
in  length  (2  panel  span  of  47 .  32  feet).  Beyond  this  length  imiform  loading 
gives  maximum  floorbeam  reaction.  For  maximum  end  shear  use  con- 
centrated loading  up  to  64.6  ft.  span,  and  xmiform  loading  beyond. 

71ft 


MOMENTS  AND  SHEARS  FOR  BRIDGE  SPANS 


717 


S. — MAXiifuif  MoiiBNTS.  Bkd  Shbaiis,  and  Ploorbbam  Rbactionb   R 
P€f  track  for  concentrated  "L  24"  loading — 24,000  lbs.  on  each  of  two  axles 
spaced  10  feet  apart. 
Vahxes  for  any  other  "L"  loading  are  directly  proportional  to  the  axle  loads. 


B 

Eauivalent 

^r 

M. 

1 

Uniform 

Pt.-Ibs. 

U 

[yoad  w  for 

3»  M 

] 

Floorbcam 

pft 

Reaction. 

Lbs.  per 
lin.  ft. 

s  >^ 

From 

I  ®r 

« 

equation 
R^wl 

/ 

J 

we  have 
R 

U*     : 

w^-r 

»- 

» 

< 

10 

60.000 

4.800 

24.000 

4.800 

24  .000 

2.400 

11 

66,000 

4.364 

26.180 

4.760 

26.180 

2.380 

12 

72,000 

4.000 

28.000 

4.667 

28  .000 

2.383 

13 

78.000 

3.692 

29  .540 

4.545 

29  .540 

2.272 

14 

84.000 

3.429 

30.860 

4.409 

80.860 

2.204 

15 

90.000 

3.200 

32.000 

4,267 

82  .000 

2.133 

10 

96.000 

3.000 

33.000 

4.125 

83  .000 

2.062 

17 

102 ,000 

2.824 

33  .880 

3.986 

83  .880 

1.993 

18 

112.670 

2.782 

34  .670 

8.852 

84  .670 

1.926 

10 

123,790 

2,743 

35.370 

3.723 

35.370 

1.861 

20 

135.000 

2.700 

36  .000 

3.600 

86  .000 

1.800 

24 

146.290 

2,654 

36.570 

8.483 

36  .570 

1.741 

22 

157,640 

2,606 

37 .090 

8.372 

37  .090 

1.686 

23 

169  ,040 
180.500 

2.556 
2.507 

87.570 
38 .000 

8.267 
8.167 

37.570 

1.633 

24 

25 

192  .000 

2.458 

88  .400 

8.072 

20 
27 

208  .540 
215.110 

2.409 
2,361 

88 .770 
89.110 

2.982 
2.897 

Single  Track. 

28 

226,710 

2,313 

89  .430 

2.816 

^...A  *-- 4k 

29 
80 

238.340 
250.000 

2  267 

89.720 
40  ,000 

2.740 
2.667 

^"  •       ^ 

2;220 

1  ui 

31 

261 .680 

2.178 

40.260 

2.598 

4         % 

32 

273.380 

2.136 

40.600 

2.531 

T             T 

33 

285  .090 

?'2«* 

40.730 

2.468 

Floorbcam    Moment  — 

34 

296  .820 

2.054 

40.940 

2,408 

R  is-c)    ,     .. 

35 

308  .670 

2.015 

41.140 

2.351 

Y-^i       ^^^'^^' 

30 

320.330 

1.977 

41.330 

2.296 

37 

332.110 

1.941 

41 .510 

2.244 

38 

342  .900 

1.905 

41.680 

2.194 

39 

355.700 

1.871 

41 .850 

2,146 

40 

367 .600 

1.838 

42  .000 

2.100 

41 

379.820 

1.806 

42.150 

2.056 

42 
43 

391 .140 
402  .980 

1.774 
1.744 

42.290 
42  .420 

2.014 
1.973 

Double  Track. 

44 

414.820 
426  .670 

1.714 
1.686 

42  .550 
42.670 

1.934 
1.896 

!^     1 

45 

^   ojV 

46 

438  .520 

1 ,658 

42  .780 

1.860 

t  l7  Ui  1 

47 

450.380 

1.631 

42.890 

1.825 

48 

402.250 

1.605 

43.000 

1.792 

R                         R 

49 

48  100 

1  769 

Floorbcam  Moment: 
ata-i^^^-^'^^ft-lba. 

60 

43.200 

1.728 

51 

43.290 
43.380 
43.470 
43,560 

1.698 
1.668 
1.640 
1.613 

52 

53 

atb-/?^'^-^^   ft.lbs. 

54 





D 

gitized  by  VjOt 

jijie 

Zfi.—ELECTRIC  RAILWAY  BRIDGES. 


Iaximum  Moments  M  pbr  Track  for  Concbntratbd  **K  26"  Load- 
ing (Fig.  2) — A  Train  of  50-Ton  Elbctric  Cars.* 


Dy03.1%. 

Iaximum  Floorbeam  Reactions  R,  per  Track,  for  Concbntratbd 
"K25"  Loading  (Fig.  2). — A  Train  of  50-Ton  Elbctric  Cars. 

(Span  =  Panel  length.) 
;s  for  any  other  "K"  loading  arc  directly  proportional  to  the  axle  toads. 


Floor- 

Equival't 
Umf.Load 

■J 

Floor- 

Equival't 
Umf.Load 

8 

Floor- 

Equival't 
Umf.Lo«d 

beam 

tt'  for 

beam 

a;  for 

beam 

IV  for 

■leaction 

Floorbe'm 

•H 

Reaction 

Floorbe'm 

Reaction 

Floorbe'm 

R. 

Reaction. 

a 

R. 

Reaction. 

c 

R. 

Reaction. 

Lbs. 

Lbs.  per 
lin.  ft. 

Lbs. 

Lbs.  per 
lin.  ft. 

Lbs. 

Lbs.  per 

37.600 

3.750 

15 

41,700 

2.780 

20 

60.000 

2.500 

g.eoo 

3.510 

16 

42.200 

2.636 

21 

62.400 

3.4ft5 

39,600 

3.300 

17 

43.100 

2.540 

22 

66.700 

2.631 

40,400 

3.110 

18 

44.900 

2.495 

23 

6B.700 

2.6SB 

41.100  1        2.936 

10 

47.400 

2.490 

24 

02,800 

3.616 

d  by  Google 


40.— HIGHWAY  BRIDGES. 

I.— UNIVERSAL  STRESS^HEETS. 
ExpUnation. 

The  followiog  are  types  of  trusses  suitable  for  bridge  spans  up  to  aboat 
200  ft.  in  length.  They  are  designated  by  a  figure,  indicating  the  number  oi 
panels  in  the  truss,  and  also  by  a  distinguishing  letter  when  more  than  cne 
type  of  the  same  number  of  panels  are  used.  Thus.  Types  iA,  4B  and  4C 
each  have  4  panels,  but  their  truss  systems  are  different. 

The  Diagrams  are  proportioned  by  scale  and  show  height  of  truss  in 
terms  of  panel  length  p— 1.  The  members  of  the  truss  are  ntunbered  in 
each  case  to  correspond  with  the  niunbcrs  in  the  adjoining  tables.  The 
practical  upper  and  lower  limiting  spans,  with  resxilting  panel  length,  are 
given  for  each  type.  The  fractions  at  lower  chord  joints  express  the  bve- 
load  reactions,  at  left  abutment,  in  terms  of  a  panel  load  — unitv.  of  panel 
loads  from  the  right-hand  end  up  to  and  including  that  joint;  and  are  useful 
for  finding  the  shears. 

The  Tables  accompanying  the  diagrams  give  the  unit  Ungth  of  each  truss 
member  for  a  panel  length  of  unity  (actual  length*- unit  length X panel 
length) ;  also  the  dead-  and  live-load  unit  stressts  in  each  truss  member  for 
imit  panel  loads  (actual  stress  — unit  stress  X  panel  load  per  truss). 

Ex.  1. — What  type  of  truss  would  be  suitable  for  a  l68-ft.  span?  Find 
the  lengths  of  the  members?    Find  maximum  stresses  in  members  11  and  18? 

Solution  —Type  8;  8  panels  @  21  -  168.  Height  -  21 X  li  -  28.  Diago- 
nals =21  X  li='35  ft.  Assuming  dead-load  at  1000.  and  live-load  at  1200 
lbs.  per  lin.  ft.  of  bridge,  the  respective  panel  loads  per  truss  are:  d.  1. «  10.5 
and  1.  1.  — 12.6  thousand  lbs.;  whence  the  max  compressive  stress  in  11" 
1.5X10.5+  1.876X  12.6- 39.376  lbs.,  and  the  max  tensile  stress  in  16- -.625 
X  10.6  +  .938X  12.6- 6,266  lbs. 

Types  of  Trusses,  and  Unit  Stress  Sheets. 

[See  Explanation,  preceding], 
c  — compression;  <<=  tension. 


Type  2A. 
For  spans  36^  to  40*. 

2  (?^  18*  -  36'. 

2  (iu  2(y  =  40^. 
Live  reaction  siunmations: 


Table  2A. 


Name  of  member. 


Unit  length  of  member. 
Dead  load  unit  stress,  D 
Live  load  unit  stress,  L. . 


.500  t 
.600  t 


1.414 
.707  c 
.707  c 


1.000  t 
1.000  < 


Type  2B. 
For  spans  26'  to   32'. 

2(0,  12'.5=26'. 

2^16'-   32'. 
Live  reaction  summations: 


Table  2B. 


Name  of  member. 


Unit  length  of  member.  . 
Dead  load  unit  stress.  D. 
Live  load  unit  stress.  L.  . 


1. 

.800  / 
.800  / 


1.179 
.043  c 
.043  c 


.625 
1.000  i 
1.000  t 


720 


UNIVERSAL  STRESS^HEETS, 


721 


Type  2C. 
For  spans  25"  to  82^. 

2  @  12'.5  -  25'. 

2  §  lO'      -  32^. 
Live  reaction  summations: 


/^ 


Tablb  2C. 

Name  of  member 

1           2 

3 

4 

6 

Unit  length  of  member.  . 
Dead  load  unit  stress.  D  . 
Live  load  unit  stress,  L. . 

1.            .5 
.400  t\  .800  c 
.400  ^  .800  c 

.8 

.640  c 
.640  c 

.8 

.640/ 
.640  t 

.625 
0 
0 

Type  aA. 
For  spans  48^  to  63'. 

3  @  16'  -  48'. 

8  @  21'  -  63'. 
Live  reaction  summations: 


/M\ 


Tablb  3A. 


Name  of  member. 


Unit  length  of  member. 
Dead  load  unit  stress,  D 
Live  load  unit  stress,  L. , 


1.2 


.889  I 
.889  t 


.880? 
.889  c 


1.505 
1.338 
1.338  c 


1.125 

1. 

1. 


0 
.446  c 


Tjrpe  3B. 
For  spans  37'.  5  to  48'. 

3@  12'.5-37'.5 

3  §16'    -48'. 
Live  reaction  summations: 


Tablb  3B. 

Name  of  member 

1.2 

3 

4 

5 

6 

Unit  length  of  member.  . 
Dead  load  unit  stress,  D . 
Live  load  tmit  stress,  L. . 

1. 

1.600  1 
1.600  / 

1. 

1.600  c 
1.600  c 

1.179 
1.887  c 
1.887  c 

.625 
1.        / 
1.        t 

1.179 
0 
.629/ 

Type  3C. 

For  spans  37'. 6  to  48'. 
8  @  12'.5  -  37'.5 
3  @  16'      -  48'. 

Live  reaction  summations: 


Tablb  8C. 


1.179 
0 
.629  t 


Name  of  member. 


Unit  length  of  member.  . 
Dead  load  unit  stress,  D  . 
Live  load  unit  stress,  L. . 


.800  / 
.800  I 


1.600  t 
1.600  t 


1. 

1.600  c 
1.600  c 


.5 
1.600  c 
1.600  c 


.8 

1.281  c 
1.281c 


.8 
1.281  / 
1.281 


Google 


.625 
0 
.333  c 


722 


40.— HIGHWAY  BRIDGES. 


Type  4A. 
For  spans  64'  to  SC. 
4  @  16'  «  64'. 
4  §  2(y  =  8(y. 

Live  reaction  summations: 


/#fL 


Tablb  4A. 


Name  of  member. 


1.  2 


Unit  length  of  member. 
Dead  load  unit  stress.  D 
Live  load  unit  stress,  L. . 


I. 

1.3125/^1 

L3125n 


750  c 
.760  c 


.519 

1.904  c 
1.094  c 


1.143 

I. 

1. 


1.510 
.666  t 
.997  / 


1.143 
0 
.260  c 


.519 
.665  c 
.332X 


Type  4B. 
For  spans  50*  to  60^. 

4@  12'.6  =60'. 

4  @  16'     -  60'. 
Live  reaction  summations: 


-"^^^ 


Table  4B. 


Name  of  member. 


1.2 


Unit  length  of  member.  . 
Dead  load  unit  stress,  D . 
Live  load  unit  stress,  L. . 


1. 

2.400  / 
2.400  / 


3.200 
3.200  c 


1.179 
1.831 
2.831  c 


c2. 


.625 
1. 000 
1.000  A 


1.179 
.943  t 
1.414  / 


.625 
0 
.250  c 


1.179 
.943  c 
.471  I 


Type  4C. 
For  spans  5^  to  60'. 

4@12'.5  =  60'.  „. 

4  @  15'     =60'.  ^J. 

Live  reaction  summations: 


/^ 


Tablb  4C. 


><-i 

^ 


1.179 
.943 
1.414 


.625 
0 
.250  c 


10 


1.179 
.943  c 
.471  / 


Name  of  member. 


Unit  length  of  member.  . 
Dead  load  unit  stress,  D . 
Live  load  unit  stress.  L.  . 


1. 

1.200 
1.200  / 


1. 

400 
2.400 


t2. 


.200  c 
1.200  c 


5 
2.400  c 
2.400  c 


.8 
1.920 
1.920 


.8 
.020  t 
920  / 


.625 
.500c 
.760  c 


Type  6A. 
For  spans  80*  to  106'. 
6@  16'-   80'. 

5@  2r=ioy. 

Live  reaction  summations: 


Tablb  6A. 


10 


1.637 
0 
.790/ 


Name  of  member. 


1.2 


4.6 


Unit  length  of  member.  . 
Dead  load  unit  stress.  D. 
Live  load  unit  stress.  L. . 


1. 

1.714 

1.714 


.571  /} 
571  t 


2.571  c 
2.571  c 


1.537 
2  634  c 
2.634  c 


.167 


1.637 
dl.Zll  t 
n.680  t 


1.167 
0 
.600  c 


OOglf 


d  by  Google 


724 


4/^— HIGHWAY  BRIDGES. 


Type  8. 
For  spans  144'  to  IT^. 

8®  18'    -144'. 

8@  21'.6-172'. 
Live  reaction  summations: 


7       6        S 


Name  of  member. 


1.2 


Unit  length  of  member. 
Dead  load  unit  stress,  D 
Live  load  unit  stress.  L. . 


I. 

2.625 

2.625. 


.600 
.500 


.625 
.626 


000 
000 


.625 
.625 


600 
600 


IH 

4.375  c 

875  c 


d4 


10 


11 


12 


13 


14 


15 


16 


IH 


1.125  t 
3.281  t 


tZ. 


1.600  c 
1.875  c 


1  875 

2!344  <|l.260c 


.600  ( 


.626 
1.663  l( 


.750  ci 


IH 
.625  c 
.988  f 


Type  9A. 
For  spans  162'  to  19  J'.  6 

9@  18'    -162'. 

9  &  21'.6-193'.5 
Live  reaction  simimations: 


Name  of  member. 


1.2 


Unit  length  of  member. . 
Dead  load  tmit  stress,  D. 
Live  load  unit  stress.  L. . 


1. 

2.667 
2.667  t 


1. 

.667 
4.667 


M. 


000/^ 
000 


1 

6.667  t 
667  t 


m- 


1. 

6.667 
6.667  cj 


c6. 


667 
667 


000  c 
000  c 


10 


11        12 


13 


14 


16 


16 


17 


18 


19 


1 

4.667d4. 
4.667cl4 


1.803 
.808  c 
.808  c 


1.803 
3.606 
3.740 


L5 
2.000  c 
2.333  c 


1.803 
2.404  t 
2.805  t 


1.5 
1.000  c 

1.667  c 


1.803 
1.202  / 
2.003 


dl 


1.6 
0 

lllcl 


808 
0 
336  4 


1.808 
.202  c 
.801  t 


Type  9B. 
ans  162^ 


M' 


For  spans  162' to  19  3'.  6 
9  ©18'    =162'. 
9  @  2l'.5-193.'6 

Live  reaction  summations; 


Table  9B. 


Name  of  member. 


1.2 


Unit  length  of  member. . 
Dead  load  unit  stress.  D . 
Live  load  unit  stress.  L. . 


1. 

2.667  i 
2.667 


1. 

4.391 
.391 


M 


L 

5.333  /^5.926  /^5. 
333  /}5.926  ^5. 


^5. 


926  c 
926  c 


1. 

5.926 
6.926  ci 


1.004 
..357  c 
6.357  c 


c6. 


10 


11 


12 


13 


14 


15 


16 


17 


18 


19 


1.004 
4.410 
4.410  c 


1.803 
4.808 
4.808 


1.803 
111  t 
299  t 


<3, 


/1 3. 


1.594  il.882 
1.588  dl. 771 
2.059  d2.296 


1.688 
.500  c 
1.389  c 


1.962 
1.163 
1.938  / 


1.688 

0 
1.111 


1.962 

0 
1.292 


1.962 
1.163  c 
.775  t 


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726 


¥L— HIGHWAY  BRIDGES. 


V 


5^-. 


HanMofbad       K     P«    »l    P.    P,    »l    »i    R    R    f»    P 


^*:j^ 

'^.x 


/ 


12,'  12     12     12    R    R     12    12    12    12    H 
X    li    5     Pt    P7    P.    P5    ?    ^3    ^2    ? 

Pig.  22.    Type  12. 


Type  12. 


For  spans  ai^to  268'. 
12  @  18'.  -  216'. 
12  @  21'.6-258'. 


Table  12. 


Name  of  member 

Unit  length  of  member. 
Dead  load  tmit  stress,  D 
Live  load  unit  stress.  L. 


1.  2 


3.4 


5.  6       7.  8 


9.10 


1. 

3.667  i 
3.667  / 


1. 

6.333  t 
5.338 


7.111  i%Aiic 

111  ?8.444  ? 


tl 


1.017 

7.687  c 

7.687  c 


I 


11 


12 


13 


14 


16 


16 


17.22 


18 


19 


80c 


1.068 

6.096c 
6.696c 


1.803 

6.611c 

6.611c 


1.6 
1.     / 
1.     / 


1.803 
3.005 
3.306  / 


1.876 


1.876 


1.600  c  1.600  c 
2.250  d  .600  / 


1.371 
3.046 
3.666 


1.126 
0 
0 


.088 


1.871 
1.332  t 
.042 


2.25 
.795c 
.667c 


n. 


20    / 


21 


23 


24 


25 


26 


27 


28 


2.25 
.796c 
.583/ 


1.606 
2.007 
3.122 


261 


1.1 
1.      / 
1.      I 


.605 

1.338  / 

2.453  / 


2.26 
1.        d 
1.833  c 


1.506 
.669  i 
.669  / 


1.505 

669 

1.672 


1.606 
0 


Notes. — Using  "balanced  loads,"  the  tension  of  0.6  in  member  16  is  ob- 
tained from  live  loads  Pj,  Pg.  Pio  and  Pjt.  Tension  of  0.683  in  member  20  s 
obtained  from  live  loads  Pi,  Pj,  P,.  P%,  Pio  and  Pji.  Compression  of  1.567 
in  member  20  is  obtained  from  live  loads  Pi  to  P9  inclusive,  omitting  P?. 
In  the  last  calculation  note  that  the  cutting  plane  will  cut  four  active 
members,  9,  28,  20  (27  inactive)  and  6,  with  the  center  of  moments  at  C. 
But  the  stress  in  member  28  is  one-half  the  panel  load  P«  multiplied  by  the 
secant  of  its  angle  of  inclination  — .6X1. 267 -"0.628,  and  the  moment  ot  thit 
stress  about  0'  is  6. 138.  This  enables  us  to  solve  the  stress  in  member  20  by 
cutting  the  four  active  members.  Thus,  stress  in  member  20  ->  A  ( —  /?i  X  8 
6.138+P9X11)  =  -1.667. 


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d  by  Google 


728 


4li,'-HIGHWAY  BRIDGES. 


14. — ^LiVB-LoAD  Data  for  Dbsionino  Floor  Ststbms  and  Spans 

Undbr  60  Ft. 

Maximum  Moments  M  and  End  Shears  5  per  Track  for  "L"  Loadings. 

Note. — For  maximum  floor-beam  reactions  use  the  end  shears  5  down  to  the 

(*),  and  below  the  {*)  use  the  uniform  load,  covering  the  two  panels. 


aassA 

aassB 

aaasC 

ClassD 

aasB  E 

"L  30" 

Load- 

"L  2-  4-  Load- 

"L 18"  Load- 

"L 12* 

Load- 

"L  6" 

Load- 

ing. 

ing. 

ing. 

ing. 

ing. 

30  Tons— 2 

24  Tons— 2 

18  Tons— 2 

12  Tons— 2 

6Tons-2 

Span. 

Axles— lO'c.-o. 

Axle»-lO'c-o. 

Axles— lO'c-c 

Axles— lO'o-c. 

Axles— lO'c-c 

12'  Wide— y 

12' Wide— 5* 

13' Wide— 6' 

12'  Wide— 5* 

12' Wide— 6' 

Ga«c. 

Qage. 

Gage. 

Gage. 

Gage. 

M 

S 

M 

8 

M 

S 

M 

8 

M 

8 

Thou- 

Thou- 

Thou- 

Thou- 

Thou- 

Thou- 

Thou- 

Thou-1 

Tliou- 

Thott- 

sand 

sand 

sand 

sand 

sand 

sand 

sand 

sand 

sand 

sand 

Ft.-Lb. 

Lb. 

Ft.-Lb. 

Lb. 

Ft.-Lb. 

Lb. 

Ft.-Lb. 

Lb. 

Ft.-Lb. 

Lb. 

Ft. 

Unite. 

Unite. 

Units. 

Unite. 

Units, 

Unite. 

Unite. 

Unite. 

Unite. 

Units. 

76.0 

30.0 

60.0 

24.0 

46.0 

18.0 

30.0 

12.0 

15.0 

82.5 

32.7 

66.0 

26.2 

49.5 

19.6 

33.0 

13.1 

16.6 

90.0 

35.0 

72.0 

28.0 

54.0 

21.0 

36.0 

14.0 

18.0 

97.5 

36.9 

78.0 

29.5 

68.6 

22.2 

39.0 

14.8 

19.6 

106.0 

38.6 

84.0 

30.9 

63.0 

23.1 

42.0 

15.4 

112.6 

40.0 

90.0 

32.0 

67.5 

24.0 

45.0 

,16.0 

120.0 

41.3 

96.0 

33.0 

72.0 

24.8 

48.0 

•16.6 

127.5 

42.4 

102.0 

33.9 

76.5 

25.4 

61.0 

16.9 

140.8 

43.3 

112.7 

34.7 

84.5 

26.0 

56.3 

17.3 

«s 

184.7 

44.2 

123.8 

35.4 

92.9 

26.5 

61.9 

17.7 

168.8 

45.0 

135.0 

36.0 

10  r.  3 

27.0 

67.5 

18.0 

§ 

182.9 

45.7 

146.3 

36.6 

109.7 

27.4 

78.1 

18.3 

g 

197.1 

46.4 

157.6 

37.1 

118.2 

27.8 

78.8 

18.5 

g 

1 

211.3 

47.0 

169.0 

37.6 

126.8 

«28.2 
•28.5 

84.5 

18.8 

. 

225.6 

47.6 

180.6 

38.0 

135.4 

90.3 

19.0 

1 

240.0 

48.0 

192.0 

38.4 

144.0 

28.8 

96.0 

19.2 

254.4 

48.6 

203.6 

38.8 

152.7 

29.1 

101.8 

19.4 

b 

M 

268.9 

48.9 

215.1 

39.1 

161.3 

29.3 

107.6 

19.6 

S 

g 

283.4 

49.3 

226.7 

39.4 

170.0 

29.6 

113.4 

19.7 

« 

** 

297.9 

49.7 

238.3 

^39.7 
40.0 

178.8 

29.8 

119.2 

19.9 

a 

312.5 

60.0 

260.0 

187.6 

30.0 

125.0 

20.0 

B 

J 

327.1 

50.3 

261.7 

40.3 

196.3 

30.2 

130.8 

20.1 

i 

w 

341.7 

60.6 

373.4 

40.6 

205.0 

30.4 

136.7 

20.3 

i 

356.4 

60.9 

286.1 

40.7 

213.8 

30.5 

20.4 

371.0 

^51.2 

296.8 

40.9 

223.6 

30.7 

20.5 

i 

I 

385.7 

*51.4 

308.6 

41.1 

231.4 

30.9 

20.6 

400.4 

51.7 

820.3 

41.3 

240.2 

31.0 

20.7 

% 

i 

415.3 

51.9 

332.1 

41.6 

249.1 

31.1 

20.8 

Ok 

429.9 

52.1 

343.9 

41.7 

257.9 

31.3 

0 

20.8 

0 

i 

444.6 

62.3 

356.7 

41.9 

266.8 

31-.  4 

Id 

20.9 

1 

459.4 
474.2 

62.6 
52.7 

367.5 
879.3 

42.0 
42.2 

276.6 
284.5 

31.6 
31.6 

21.0 

0 

i- 

1 

488.9 

52.9 

391.2 

42.3 

293.4 

31.7 

l<^ 

1 

603.7 

63.0 

403.0 

42.4 

302.2 

31.8 

1 

618.5 

53.2 

414.8 

42.6 

311.1 

31.9 

2  c 

i 

«.: 

533.3 

53.3 

426.7 

42.7 

320.0 

32.0 

B^ 

1 
i 

548.2 

63.5 

438.5 

42.8 

328.9 

32.1 

y 

563.0 

53.6 

450.4 

42.9 

337.8 

32.2 

S 

577.8 

63.8 

462.3 

43.0 

346.7 

32.3 

=  S 

S3 

592.7 

53.9 

474.1 

43.1 

ilU 

32.3 

^2 

1 

1 

60 

607.5 

54.0 

486.0 

43.3 

32.4 

1 

=s 

Unlf. 

oad. 

UnlMoad. 

Below  1 
useunIM 
of  1200 
per  lln. 

>2 

s 
s 

1 

12x 
-1 

125 
500 

12x1 12i 
-1350 

1^ 

*  See  note  at  head  of  table. 


d  by  Google 


UNIVERSAL  LOADINGS. 


729 


15. — Uniform  Livb  Loads  por  Trusses  op  Spans  over  60  Ft. 

(Bach  street  car  track  loading  occupies  width  of  12  feet  for  single  track, 

and  11  feet  for  double  track.) 


aaa 

lA 

OaasB 

aassC 

OassD 

aanE 

Vehic- 

Each 

Vehic- 

Each 

Vehic- 

Each 

Vehic- 

Each 

Vehle- 

Each 

ular 

Street 

ular 

Street 

ular 

Street 

ular 

Street 

ular 

Street 

Road- 

oar 

Road- 

car 

Road- 

car 

Road- 

car 

Road- 

car 

Bpan. 

way, 

Track, 

way. 

Track. 

way, 

Track. 

way. 

Track. 

way, 

Track. 

and 

Lbs. 

and 

Lbs. 

and 

Lbs. 

and 

Lbs. 

and 

Lbs. 

Walks. 

per 

Walks. 

ffi 

Walks. 

per 

Walks. 

per 

Walks. 

per 

Lbs.  per 

Lin. 

Lbs.  per 

Lbs.  per 

Lin., 

Lbs.  per 

Lin. 

Lbs.  per 

Lin. 

Ft 

8q.  Ft. 

Ft. 

Sq.  Ft. 

Ft. 

8q.  Ft. 

Ft.' 

8q.  Ft. 

Ft. 

8q.  Ft. 

Ft. 

Wto 

m 

100 

2000 

90 

1600 

80 

1200 

60 

lOS 

99 

1980 

89 

1684 

79 

1188 

^ 

59 

d 

110 

98 

1960 

88 

1568 

78 

1176 

69 

lis 

97 

1940 

87 

1552 

78 

1164 

7 

58 

t 

120 

96 

1920 

86 

1536 

77 

1152 

68 

12S 

95 

1900 

86 

1520 

76 

1140 

|J4 

ll 

67 

1-^ 

130 

94 

1880 

85 

1504 

76 

1138 

56 

135 

93 

1860 

84 

1488 

74 

1116 

56 

^1 

140 

92 

1840 

83 

1472 

74 

1104 

55 

U6 

91 

1820 

82 

1456 

78 

1002 

q  V 

55 

ll 

150 

90 

1800 

81 

1440 

72 

1080 

h 

54 

155 

89 

1780 

80 

1424 

71 

1068 

53 

100 

88 

1760 

79 

1408 

70 

1056 

It 

53 

II 

105 

87 

1740 

78 

1392 

70 

1044 

52 

170 

86 

1720 

77 

1376 

69 

1032 

52 

175 

85 

1700 

77 

1360 

68 

1020 

51 

180 

84 

1680 

76 

1344 

67 

1008 

50 

18S 

83 

1660 

76 

1328 

66 

996 

.§ 

50 

^g 

190 

82 

1640 

74 

1312 

66 

984 

49 

105 

81 

1620 

73 

1296 

65 

972 

B 

49 

p 

200 

80 

1600 

72 

1280 

64 

960 

^ 

48 

^ 

and 

OQ 

00 

over 

III.— DETAILS  OP  COMBINATION  BRIDOE,  230  FT.  SPAN. 
TYPE  12. 


Dioqram  of  Truss  sHowing  Capib«'  and  Heights 


of  Chonls. 


""«:      rfordencts 


Figs.  24.    Truss  Diagram.  Bottom  Chord  fiiifi&tt^9g'^ 


730 


Timber  Details. 
Chord  Uj-Lo. 

Cast  Details. 
End  shoe.  12B. 
Post  shoe,  12G, 
Bed  plate.  12A. 
Lateral  struts,  12 J. 
Lateral  struts,  12K. 
Washers. 
Separators, 


40.— HIGHWAY  BRIDGES. 


,."♦ 


gj^ygf     ZSficHs7i'y.lSi'xV'lO'k3ng  "» 


Fig.  26, 


J5.    Elevation. 

Steel  Details. 

Figs. 

Stone  bolt. 

S3 

Lateral  rods. 

36,40.41 

Eye-bars, 

37 

Counters. 

as 

Suspenders, 

88 

Pin  fillers. 

99 

Portal  rods 

41 

Nominal  rods. 

42 

Sway  rods. 

43 

Cotter  pins. 
Wing  plates. 

44.49 

45 

Lateral  plates. 

46 

Chord  pins. 

47,51 

Hangers. 

SO 

Bolts. 

53 

Washers, 

M 

Pig.  26.    Section. 


d  by  Google      ^ 


d  by  Google 


733 


4a.'-HIGHWAY  BRIDGES. 


-«•— ii 


^i- 


-in 


^.^i^ 


@ 


Stdtt  VIcwtr. 


.»•>*" 


^^ 

BonomVlvw. 

Pig.  aO.    End  Shoe. 


Note. — For 
tails  see  pages 


K~f-H 


Pig.  31.    Posi 


"^^h 


cy-tj-hoi,       ^  6    1'^ 


forSMnffin^ 


Pig.  32.    Bed  Plate. 


H 


Pig.  83. 


o 

o— |i*  I 


4*v 
Pig.  34. 


^k 


K 


-B "a — *!v-s-? 


Pig.  36.    Lower  Lateral  Rods  and  Table. 


Number 
Required. 

Mark. 

Dia. 
d 

B 

A 

Ends 

Upset 

to 

Nom- 
inal 
D 

7 

4 

u-u 

U'D 

23'  61' 

24' 4 

1  'O 

2" 

Li -La 

1  'D 

23' 7  ' 

24' 5 

1  'O 

2' 

f2-L3 

"a 

23' 6' 

24' 4 

1  "O 

I' 

u-u 

"D 

23' 6' 

24' 4 

I'O 

I  ' 

u-u 

'O 

23' 6  " 

23' sr 

24' 4 

I'O 

I  ' 

u-u 

ro 

24' 3j 

I'O 

& 

d  by  Google 


734 


40.— HIGHWAY  BRIDGES. 


Top  Lateral  and  Portal  Rods. — Concluded. 

f„^ 


=#^ 


.'^/U- 


Fig.  41. 


Number 

Mark. 

d 

L 

A 

B 

T 

u 

H 

Required. 

Portal 

Ij 

\'o 

21'2' 

4' 

20' 10' 

ir 

IKO 

21 

U2-U2 

'O 

26' ft' 
26' S' 

r 

26'   3f' 

26'  2r 

1  'O 

11 

v\-v. 

"n 

y 

1   m 

I'O 

11 

u,-u. 

"O 

26' 3  • 

r 

26'  0  ' 

1   # 

I  'O 

11 

U,-Ut, 

'O 

26' 2r 

r 

26' Hi' 

t   m 

I'O 

11 

Nominal  Rods. 


v±. . 


>*i» 


Pig.  42 

►. 

Number 
Required. 

Mark. 

d 

L 

U 

( 

8 
8 

Ma-Ma 

ro 

I'O 

22' 04' 
22' Of' 
19' 9i' 

VO 
i'O 

ro 

1- 

r 

V 

Sway  Rods. 


Fig.  43. 


...K5^4 


?5^i' 


Number 
Required. 

Mark. 

Dia. 

Length 

4 
6 

V2 
1/4  and  Ut 

t'o 

VO 

IJiF 

Cotter  Pins  for  Lower  Lateral  Rods. 


s 


5^ 


Pig.  44. 


Number 
Required. 

Mark. 

D 

L 

G 

P 

Remarks. 

8 

8     ' 
16 
16 

LoandLi 
Lx and  La 
La  La  &  L4 
L4  U&Lt 

If '0 
IH'O 
lA'O 

0'41' 
0'3' 
0'3' 
0'3' 

2\' 
2}' 
2' 

ir 

1  • 

Turned 

d  by  Google 


780 


iSi.— HIGHWAY  BRIDGES. 


Cotter  Pins  for  Mid  Truss 
Connections. 


■^^s^y 


Fig.  49. 


Number 
Required. 

Mark. 

G 

4 
4 

A/3 
Af5 

11  ' 
\2\' 

Bottom  Chord  Pins. 


6  - -H 

Fig.  61. 


Number 

Mark. 

D 

(7 

P 

Required. 

U 

2fro 

17  ' 

r 

U 

2S'0 

11  ' 

V 

l\ 

2t}'0 

14  ' 

2" 

U 

2^*0 

12  ' 

r 

U 

2lro 

16' 

r 

U 

2Vo 

13J* 

2' 

2 

U 

2H''0 

17i' 

r 

Hanobrs  and  Platbs. 
PfnUamS.1 


«v-e<0 


K It'"" 

Pig.  60. 

.->1 

Number 
Required. 

Mark. 

D 

10 
12 

Li-Lt-Ls 

8» 
2i' 

Cast  Separator  Spools  for  Floor 
Beams. 


Fig.  62. 


Number 
Required. 

Mark. 

90 

Floor  Beam 

Bolts  with  Nut  and  2  Washers 
Each. 


Fig.  68. 

Number 
Required. 

Mark. 

d 

L 

.Si 

Floor  Beam 

Chords 

Posts 

Railing 

ro 

15i' 
17" 
18' 
8' 

Wrought  Packing  Washers  for 
Chords. 

Fig.  64. 


Number 
Required. 


150 


Mark. 


Chords 

by 


Remarks. 


Standard  a  and  JD 


d  by  Google 


788  .  i/H.—HIGHWAY  BRIDGES. 

Notation. 
/  and  f  — length  and  radius  of  gyration  of  member,  in  ins. 
P  — percentage  of  impact  tor  live-load  stress, 
In  formula,  P=-  1 0000 -f-  (1 50+  length  of  span,  in  feet,  or  portion  of  span  cov- 
ered by  live  load  when  the  member  considered  is  subject  to  maximum  stress.) 

36. — Coif  PARisoN  OP  Carbon-Stbbl  and  Nickbl-Stbbl  Spans.  40-200  Ft 
Roadway,  20  Fbbt  Widb. 


v.— REINFORCED  CONCRETE  BRIDGES. 

Desig;!!    and    Cost  of  Reinforced-Concrete  Highway  Bridges  (By  A.N. 

Johnson.     Paper,  111.  Soc.  Eng'rs  and  Survejrors,  Jan.  26,  28,  1910;  Eng. 
News,  Feb.  10,  1910). — Summary  of  cost  per  cu.  yd.  of  concrete  is  as  follows: 

Cement $2 .  85  to  $1 .25 

Stone : 8.23  ;;      1.30 

Sand  (excluding  gravel  concrete) 1.47  "        .32 

Gravel 2.43"        .70 

Forms 8.96"        .88 

Steel  in  phice 8. 10  "        .80 

Mixing  and  placing  concrete 3.72  "        .72 

Excavation 8.91"        .21 

Total $17.61  "  $e.54 

Spans  range  from  7  ft.  to  60  ft.,  roadways  mostly  16  ft.,  abutments 
mostly  10  to  13  ft.  high.     Extensive  cost  table  not  reproduced  here. 


NICKEL',  CARBON',  CONCRETE-STEEL  SPANS.  739 


EXCERPTS  AND  REFERENCES. 

Bascule  Bridge  at  Orand  Ave.,  Milwaukee,  Wis.  (Eng.  News,  July  8. 
1902).— Illustrated. 

Pace  Bascule'  Bridge  Over  Chicago  River  at  Ashland  Ave.  (Eng.  News. 
Jan.  1.  lfM>3.— Illustrated. 

The  Wabash  River  Bri^e  at  Terra  Haute,  Ind.  (By  M.  A.  Howe. 
Eng.  News.  Mar.  8.  1906). — Dlustrated. 

Retaforced-Coocrete  Viaduct  with  sone  Structural  Steel  Reinforcemeut 
(Eng.  News,  July  1,  1909). — Illustrated:  lon^tudinal  section,  tower  bent, 
detail  of  floor  sjrstem,  detail  of  expansion  joint,  (consists  of  three  24-ft., 
five  30-ft.  and  two  24-ft.  spans.  Floor,  3-in.  tar-macadam  roadway  16-ft. 
wide,  carried  on  a  slab  crowned  to  9  ins.  Designed  for  1.  1.  of  100  lbs.  per 
sq.  ft.,  with  a  concentrated  load  on  the  floor  system  of  a '15-ton  wagon* 
future  provision  for  dO-ton  car.  Cost  of  viaduct,  about  12.30  per  sq.  ft.  of 
roadway. 

Reinforced-Concrete  aod  Steel  Sfwns,  Sparkman  St.  Bridge,  Nashville 
(By  Howard  M.  Jones.  Eng.  News.  Nov.  25,  1909). — Illustrations:  Half 
section  of  roadway  (macadam);  reinforced -concrete  retaining  walls;  floor 
system;  typical  bent  of  trestle  approach;  reinforced-concrete  staircase; 
details  of  reinforced-concrete  hand  railing;  details  of  reinforced-concrete 
trusses:  typical  channel  pier;  stress  sheet  of  318-ft.  truss;  details  of  318-ft. 
truss. 

lllustrattons  and  Diagrams. 

Description.  Eng.  News. 

Truss  and  floor  details  of  194-ft.  span,  Waterford,  N.  Y July  14,  '10 

Eng.  Rec 
Steel  highway  bridge  with  concrete  stringers  and  floor  slabs. . .  .Mar.  20.  '09 
Short  span  bridges,  N.  Y..  N.  H.  &  H.  R.  R.,  N.  Y.  City  cross- 
ings  July  10,  '09 

Short  span  bridges,  N,  Y.,  N.  H.  &  H.  R.  R.,  N.  Y.  City  Cross- 
ings   July  17,  "09 

Umbrella-column  for  supporting  foot-bridge  over  street Aug.  14. '09 

Strain-sheet  668-ft.  span — St.  Louis  Municipal  Bridge Oct.  30.  '09 

Pier  type  of  abutment  for  highway  bridges Feb.  5,  *  10 

2-5pan  (each  30  ft.}  rein.-conc.  bridge;  cost  table Feb.  19, '  10 

Overiiead  street  bridge  details;  concrete-protected  floorbcams.  .Mar.  6,  '10 
Rein.-conc.  girder  bridge  (80  ft.  span),  arched  bottom  chord...  .Apr.  9,  '10 

109-ft.  concrete-floor  plate  girder  bridge May  21.  *  10 

Floor  construction.  Kensington  Ave.  bridge,  Buffalo Oct.  22,  '10 


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41.— CANTILEVER  BRIDGES. 

In  Trae  CiotUever  Bridges  the  stresses  are  statically  detenninate,  and  to 
American  engineers  this  tvpe  offers  weighty  advantages  over  the  continttous- 
girder*  types  generally  adopted  by  Eiiropean  engineers.  Let  us  assume  an 
ordinary  form  of  cantilever  as  per  Pig.  1.  with  a  free  central  span  /  suspended 


Pig.  1. 

at  the  points  b  and  f,  introducing  in  the  cantilever  at  those  points  the 

p  7 

downward  forces  /?i  and  Ri*.    Ri  produces  a  downward  reaction  R9  ■=  — r^  t 

and  an  upward  reaction  j?a"    '    ? — —',  and  similarly  with  Rt'  and  Rt'- 

h 
Reaction  Rz  is  upward  when  /s  is  loaded  direct,  and  likewise  with  R^'  when 
the  loading  is  on  la.    Hence  to  resist  both  kinds  of  reaction,  upward  and 
downward,  at  the  ends  of  the  bridge,  anchorages  as  well  as  piers  or  supferts 
are  required  (see  Pig.  2) ;  while  at  R^  and  R2,  supports  only  are  needed. 

In  erection,  the  spans  are  built  outward  from  the  abutments  in  canti- 
lever fashion  to  the  central  point  o;  hence  the  lower  chords  out  to  the 
points  a  and  of  must  be  stiff  members  to  resist  compression,  while  be  and 
o'c'  are  introduced  as  tension  members.  Por  any  load  P  on  span  1%  the 
reactions  Rp  and  R^  may  be  obtained  as  above,  but  by  using  Px  instead  of 
Rifi.  Any  loading:  on  h  can  affect  only  that  si^an.  The  usual  problem  is  to 
(I)  find  the  loading  which  will  give  the  maximum  f+and  — )  stresses  for 
each  member;  (2)  find  the  required  reaction;  and  (3)  solve  as  in  ordinaiy 
trusses.  For  instance,  the  maximum  compressive  stress  in  the  end  post  £ 
obtains  with  /a  full  loaded  (/j  and  /  unloaded) ;  but  for  maximum  tensile 
stress  in  that  member  the  reverse  loading  obtains,  k  and  /  loaded  (/a  unloaded). 

The  position  of  loading  for  reactions  at  supports,  and  also  for  maximum 
stresses  m  members,  may  sometimes  be  studied  conveniently  by  the  use  of 
influence  diagrams.     Pig.  2  is  such  an  influence  diagram,  and  shows  the 


Pig.  2.    Reactions  R3  for  Left  Support, 
reaction  R3  for  a  load  moving  from  the  right-hand  end  of  the  central  span  I 

*  The  writer  knows  of  but  one  steel  truss  bridge  in  America  built  on  the 
coigmuous  girder  principle,  exceptingof  course  draw  bridges.  This  is  the 
u.  R.  &  N.  R'y  Co. 'a  bridge  across  the  William ette  river  at  Portland,  Oregon, 
un  tHe  other  hand,  the  statically  indeterminate  types  prevail  in  Europe. 


THROUGH  AND  DECK  SPANS. 


741 


toward  the  left-hand  anchorage,  over  /,  A  and  k-  The  reactions  Rg,  for 
successive  positions  of  the  concentrated  load,  are  shown  by  the  ordinates 
at  the  point  where  the  load  is  applied  on  the  structure  (see  Pig.  1);  down- 
ward when  load  is  on  /  and  1%,  and  upward  when  load  is  on  ^ 

Carbon-steel  cantilever  spans  are  economical,  generally,  up  to 
about  1600  to  1700  feet;  nickel-steel  spans,  up  to  about  1900  or  3000  feet. 
Bejrond  these  spans,  suspension  bridges  become  more  economical.  Much 
depends  on  local  conditions. 

The  limiting  length  of  carbon-steel  cantilever  spans  is  practically 
about  aOOO  feet;  and  of  nickel-steel  cantilever  spans,  about  2500  feet. 

Deck  Cantilever  Bridges  are  economical  in  certain  localities  where  there 
is^  sufficient  head-room  over  the  street,  valley  or  stream  to  be  bridged. 
Fig.  3  is  typical.   The  general  outline  is  practically  an  invert  of  Pig.  1. 


The  stresses  in  the  truss  shown  in  Fig.  3  are  rendered  statically  deter- 
minate by  making  slotted  pin-holes  at  5.  inserting  pins  at  all  lettered 
pointt,  and  providing  a  roller  end  at  R.    F  is  the  fixed  end. 


-In  providing  for  camber  the  simplest  method,  and  the  best 
for  erection,  is  to  raise  the  panel  points  by  shortening  the  diagonals,  main- 
taining aU  vertical  posts  mathematically  parallel. 


EXCERPTS  AND  REFERENCES. 

Tb0  MIssisslppJl  River  CantUever  Bridge  at  Thebes,  111.  (Eng.  News, 
May  11,  1905).— Illustrated.    Railway. 

Quebec    Cantilever    Bridge    Disaster    and    Discnssions    (Eng.  News, 
Sept..  1907.  to  Aug.,  1908). 

Information   about  Qreat   Cantilever   Bridges   (Eng.  News.  April  30. 
1908).— Tables. 

Stresses  in  the  Blackwell's   Island  Cantilever  Bridge  (By  Boiler  and 
Hodge.    Eng.  News.  Nov.  19.  1908).— Table  of  calculated  stresses. 

lUostrations. 

Description.  Eng.  News. 

P.  &  L.  E.  cant,  bridge  (769-ft.  span}  and  foundations May  5.  '10 

Outline  of  trusses  for  new  (^ebec  bndge Sept.  8,  '10 

Eng.  Rec. 
Board  of  Engineers'  design  for  new  Quebec  bridge Sept.  lO.'lO 


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42.— MOVABLE   BRIDGES. 

Movable  Bridges  are  designed  to  provide  temporary  openings  for  one 
.line  of  traffic  (usually  a  waterway)  which  is  crossed  by  another  (usually  a 
street  or  railway).    There  are  five  distinct  types,  as  follows: 

(1).  Swing  Bridge  or  "Drawbridge" — balanced  and  swinging  horixon- 
tally  round  an  arc  (usually  a  quadrant)  of  a  circle:  (a)  Bqual  spans  or 
arms,  supported  by  pivot  pier;  (b)  One  span,  counterpoised;  (c)  Two  spans 
counterpoised. 

Type  (la)  is  discussed  below. 

(2).  Traversing  Bridge — counterpoised  tail-end  raised  from  its  sup- 
ports and  span  drawn  back  on  rollers  along  one  of  its  approaches.  Used 
principally  for  narrow  openings. 

(3) .  Bascule  Bridge — tail-end  ballasted  with  cast  iron  and  lead  and  span 
swinging  vertically:  (a)  One  arm;  (b)  Two  arms,  either  with  tail-ends  to- 
gether, or  like  a  jack-knife  with  two  blades  hinged  at  either  end.  The 
bascules  are  raised  and  lowered  by  pinions  (operated  by  hydraulic,  electric. 
steam,  gasoline  or  other  power)  working  in  segmental  racks. 

(4).  Lift  Bridge — whole  span  raised  vertically  by  chains,  at  the  four 
comers,  suspended  from  towers.  O)unterpoised  weights  are  used  in  order 
to  reduce  the  required  power  for  operating. 

(5).  Floating  or  Pontoon  Bridge — iron  pontoons  (usually  rectangular) 
coupled  in  pairs  for  stability  and  moored  at  all  comers.  Bndge  is  open»i 
to  river  traffic  by  the  use  of  running  back  drawbridges.  This  type  of  bridge 
is  used  where  foundations  for  piers  would  be  difficult  and  excessively 
expensive. 

SWING  BRIDGES. 

Drawbridges  may  be  either  rim-bearing  or  center-bearing. 

The  rim-bearing  draw,  with  each  truss  supported  at  two  points  on  the 
center  pier,  is  the  more  common  type  of  the  two.  This  is  shown  in  Fig.  1, 
the  center  points  of  support  for  the  trusses 
being  &t  a  o  c  d,  irrespective  of  the  diam- 
eter of  circular  drum  or  turntable.  Usxially 
the  circular  drxim  is  of  such  diameter  as  to 
give  support  to  the  center  panel  of  draw  at 
8  equi-distant  or  nearly  equi-distant  points, 
as  shown  in  the  figure.  In  such  a  case  heavy 
girders,  acting  as  cantilevers,  are  introduced 
m  the  chords  ab  and  cd  and  in  the  floor- 
beams  ad  and  be  in  order  to  distribute  the 
loads  more  tmiformly  on  the    table.     These  „.     , 

cantilevers    may    be    designed     sufficiently  x'lg.  i. 

strong  to  carry  the  live  and  dead  loads,  or  only  sxifficient  to  carry  the  dead 
load,  in  which  latter  case  adjustable  supports  may  be  introduced  at  points 
a  b  c  d  to  transmit  the  live  loads  directly  from  trusses  to  center'  pier 
when  draw  is  closed.  In  either  event  the  center  pier  supports  are  aX 
a  b  c  d  60  far  as  the  calculation  of  trusses  is  concerned,  and  when  the  draw 
is  closed  each  truss  becomes  a  continuous  girder  of  3  spans  over  4  supports, 
for  any  moving  load  on  the  draw. 

The  center-hearing  draw  differs  from  the  rim  bearing  in  that  the  weiQ^t 
is  supported  at  the  center  either  (1)  on  a  vertical,  steel  pivot  pin,  or  (2)  on 
a  nest  of  conical  rollers.  The  weight  is  transferred  to  the  center  from  the 
trusses  by  means  of  transverse  superimposed  girders  between  the  chords, 
a  light  turntable  being  used  to  "steady"  the  span  in  revolving,  but  tkA 
calculated  to  give  material  support.  When  the  draw  is  closed  each  truss 
becomes  a  continuous  girder  or  two  spans  over  3  supports,  for  any  moving 
load  on  the  draw ;  and  such  live  load  may  be  supported,  if  desirable,  by  adjust- 
able  wedges  placed  at  the  middle  of  draw  under  the  trusses, 

742 


CONTINUOUS  GIRDER— FOUR  SUPPORTS.  743 

For  the  cakuiation  of  swing  bridges  three  cases*  or  conditions  are  usually 
employed  in  determining  the  stresses,  as  follows: 
L  Bach  ann  treated  as  a  simple  span  resting  on  two  supports,  with  live-. 

dead-  and  wind  loads  acting. 
Ua.  Bridge  swinging  and  treated  as  a  cantilever,  with  dead-  and  wind 

loads  acting,  and  with  reactions  at  center  supi>orts  only. 
Ilh.  Bridge  closed  and  treated  as  a  continuous  girder  over  all  supports, 
with  live  load  acting.     It  is  assumed  in  this  case  that  the  vertic^  re- 
actions at  ends  of  draw  are  ±0  when  no  live  load  is  acting.     The  live 
load  is  considered  as  "  balanced,"  that  is.  it  advances  symmetrically 
on  both  anns  from  the  ends  towaid  center  of  span. 
For  maximum  stresses  in  the  truss  members  use  Case  I.  or  Cases  Ila 
and  lib  combined,  whichever  gives  the  maximum.     For  maximum  stresses 
in  the  lateral  systems  use  each  of  the  cases  separately  and  select  that  stress 
which  is  a  maximum  for  each  member.     In  case  there   is   a  reversal  of 
■tress  in  an^  member,  two  maxima  will  be  required,  one  in  tension  and  one 
in  compression.     Some  specifications  make  it  necessary  to  determine  raini- 
mtim  as  well  as  maximum  stresses,  in  which  case  it  is  evident  that,  for  the 
trusses.  Case  lib  cannot  be  used  alone. 

Rfan-bearfaiK  Draw — 4  Supports. — For  Case  I  with  the  draw  considered 
as  two  simple  spans,  and  Case  Ila  as  a  cantilever,  the  reactions  at  the  sup- 
ports are  obtained  easily  and  the  stresses  in  the  members  are  statically 
determinate.  For  Case  lib,  however,  it  is  treated  as  a  continuous  girder 
which  takes  the  form  of  an  elastic  curve  when  loaded.  The  girder  is  as- 
siamd  to  be  of  homofi^eneous  material  with  constant  modulus  of  elasticity. 
E;  constant  cross-section  or  rather  moment  of  inertia,  /;  and  resting  on  level 
supports.  As  a  matter  of  fact  none  of  these  exact  conditions  actually 
obtain  in  practice.  The  necessary  reactions 
at  the  supports  due  to  any  loading  on  the 

continuous   girder  are  deduced   from   the  i*-- a-«f       u.       u         K--   -*i 
"theorem  of  three  moments."  i * !!p ^ *- 1 

Rtactions  at  the  Supports — Continuous^ 1 T"*^"T ^ 3 

Girdtr. — Let  P  be  any  concentrated  load,  »i  n^       w*  fU 

Pig.  2.  on  the  left  arm,  distant  a  from  the  ' 

end;  then  will  Fig.  2. 

..-p(i-^)[.-(i.^)f-^j-i— ^] ,„ 


1 

tr 
/ 

(2) 


.(8) 


Rt'      [k.-/?4-p(i  -j)]j-R4 

Ra-'P- {Ri  +  Ra) -R*  (algebraically) (4) 

Of  course  it  is  clearly  evident  that  if  the  load  P  is  on  the  right  arm  instead 
of  the  left,  and  distant  a  from  the  right  hand  end.  the  resulting  reactions 
will  be  interchanged — Rt  with  R4,  and  R2  with  R^.  Hence,  for  balanced 
loads,  that  is,  the  same  loading  in  position  and  amount  on  both  arms,  each 
end-support  reaction  will  equal  R1  +  R4,  and  each  center-support  reaction 
will  equal  (algebraically)  R2+R3  for  we  specified  load  on  either  arm.  In 
drawbridge  calculations  P  is  the  panel  load  and  a  the  distance  from  end  of 
draw  to  each  consecutive  panel  point  where  the  load  acts.  When  the 
reactions  are  known  the  stresses  in  the  structure  may  be  solved  by  the  or- 
dinary methods. 

^Assumptions  for  cheap  highway  drawbridges, — Various  assumptions 
an  made  for  cheap  swing  bridges  as  follows:  Case  A.  Draw  swinging  and 
treated  as  a  cantilever,  as  in  Case  Ila  above.  Case  B.  Draw  closed  and  end 
nised  to  support  say  H  the  dead  load  of  one  panel;  and  acting  as  a  continu- 
oos  girder  for  the  live  load. 


744 


42.— MOVABLE  BRIDGES. 


It  is  to  be  noted  that  the  length  c  of  the  center  panel  (over  the  pier) 
affects  the  values  of  the  reactions.  Preferably,  c  is  made  equal  to  the  dis- 
tance between  the  trusses  unless  this  is  so  great  as  to  reqviire  too  laige  a 
turntable.  It  is  also  usually  equal  to  about  one  panel  length  of  trusL 
The  following  Table  of  reactions  is  based  on  c«-one  panel  length  of  trass, 
and  will  be  useful  for  general  reference. 

1. — ^Rbactions  Rt,  Rt,  Ra  and  Ra  for  Drawbridge  Spans  op  2  to  10  Pakbu 

IN  BACH  Arm;  with  Central  Panel  c  bqual  to  One  Panbl  Length  of 

Truss;  and  Load  P  equal  to  Unity. 

See  Fig.  1.  and  Formulas  (1).  (2).  (3).  and  (4). 

^— One  Panel  Length  — Unity. 


No.  of 

Panels 

in  Each 

Arm  /of 

Draw. 


I 
I 

0 


I 


I 
I 


» 


B 


I 


I 

5* 


10 


+0.865 
+0.002 
-0.473 
+0.616 


+0.713 
+0.004 
-0.919 
+  1.202 


+0.676 
+0.006 
-1.307 
+  1.726 


+0.447 
+  0.007 
-1.607 
+  2.163 


+0.329 
+0.006 
-1.794 
+  2.46? 


+0.226^ 
+0 

-1.836 
+  2.603 


+0.137 
007 

1.707 
+2.663 


006+0 


+0.t 
+0.006 
-1.378 
+  2.303 


+0.0B 
+0.001 

-0.818 
+  1.792 


I: 


+  0.839  +0.682  +0.633  +0.395  +0.271  +0.166  +0.064 
+0.002  +0.005  +0.007  +0.008  +0.009  +0.008  +0.007 
-0.470  -0.905  -1.270-1.531  -1.646-1.688  -1.816 
+0.629|  +  1.218|  +  1.730|  +  2. 1281+2. 366|  +  2.414|  +  2.226 


+  0.027 
+0.004 
-0-799 

+  1.788 


+0.646 


+  0.820 

+0.003+0.006^+0 
-0.466 
+  0.643 


-0.888 
+  1.236 


+  0.481  +0.333  +0.205  +0.104  +0.034 

008  +0.010  +0.009  +0.008  +0.005 

-1.222-1.426-1.444-1.248-0.777 

+  1.733+2.082+2.230+2.181+1.738 


I; 


+0.796 
+0.004 
-0.460 
+0.660 


+0.599 
+0.007 
-0.864 

+  1.258 


+0.418+0 
+  0.010 
-1.152 
+  1.724 


260 
+0.011 
-1. 
+  1.997^+2 


+  0.132+0.049 

+0.010+0.006 

-1.152-0.740 

.0101  +  1,70(1 


+0.764 
+0.005 
-0.464 
+0.685 


+0.639+0 
+0.009 
-0.830 
+  1.282 


.388 
+  0.012 
-1.050 
+  1.700 


+  0.174 
+0.011 
-1.037 
+  1.852 


+0057 
+0.006 
-0.713 

+  1.648 


[R2  = 


+  0.719+0 
+  0.007 
-0.443 
+  0.717 


+  0.239 

0121+0.013 

-0.886 

+  1.634 


459 
+  0 

0.775 
+  1.304 


+0.079 
+0.010 
-0.665 
+  1.676 


+  0.656+0.349^ 
+  0.009+0 
-0.426 

+  0.762 


.015 
-0.682 
-1.318 


+0.118 

+0.013 

0.593 

+  1.462 


3 


+0.654 
+  0.014 
-0.395 
+0.827 


+  0.192 
+0.018 
-0.494 
+  1.284 


\rI: 


+  0.371 
+0.021 
-0.321 
+0.929 


Note — ^The  reactions  given  in  the  tablfe  are  for  loads  P— 1  at  panel  points.. 
Hence,  to  find  the  actual  reactions,  multiply  values  inriable  by  actual  lowis 
P  at  panel  points.  Digitized  byXjOOgl^ 


DRAWBRIDGE  REACTIONS  AND  MOMENTS. 


746 


2. — Practical  Data  for  Drawbridob  Calculation,  4  Supports. 

Casb  lib. 

Reactions  and  Moments  for  Balanced  Loads. 

Reactions  are  in  tenns  of  unit  panel  load.     Moments  are  at  foot  of  Tower 

Poets,  and  are  for  Unit  Panel  loads  and  Unit  Panel  Len^hs.     The  Loads 

are  considered  as  extending  from  the  ends  toward  the  center. 


No.  of  Panels 

in  Each    Arm 

/  of  Draw. 


A 
0) 


A  B 
(2) 


AB 
(3) 


CA 


tcD 
(4) 


A  to  E\A  toF\Ato  G 
(6) 


(6) 


(7) 


AtoH 
(8) 


A  to  I. 


I.; 


+0.867 

+0.14a^+0.426H-0 

-0.43 


+1 
+0 
-1.26 


674^+2. lfi«^+2.M0^+2.947 
2.05J 
6.63 


844 
-2.44 


+1. 
-3.90 


+3.180+3.324 

3901+2.053  +2.820  +3.676 

-7.20  -8.76 


+  3.399 
+4.601 
-10.01 


+3.426 
+6.676 
-10.76 


+0.841+1.528+2.068+2.471+2.761+2.925+3.016 
+0.169+0.472+0.932+1.629+2.249+3.075+3.984 
-0.43  -1.25  -2.39  -3.76  -6.24  -6.68  -7.86 


+3.047 
+4.953 
-8.58 


+0.823+1.476+1.964+2.307+2.521 
+0.177+0.625  +  1.036+1.693+2.479+3.3671+4.328 
-0.42  -1.20  -2.29  -3.54  -4.83  -6.94  -6.r 


+2.633^+2.672 

+3.36: 

-6.94 


+0.800+1.406^+1 

+0.200^ 

-0.40 


+0. 
1.16 


.296 
6941+1. 1661+1. 8061+2.7531+3.704 


834 

m 

-2.16 


+2.106+2.2471+2.J 

+1.805 

-3.27 


L27 


Ja/jIa/s" 


+0.769 
+0.231 
-0.39 


.667  + 


+1.317+1 
+0.683+1.333^+2 
-1.10  -2.00 


1.852 

148 

2.89 


+1.917 
+  3.083 
-3.50 


+0.726 

+0.274+0.803^+1 

-0.37 


-1.197^+1 

-0.80i 

-1.02 


449* 
551 
1.76 


+1 
+2.462 
2.31 


A    b   CEtc 


Etc.C    B   k 


{Rx  ' 


+0 
+0 
0.34 


664  +  1.028  +  1.159 

336^+0.972+1.841 

-1.36 


-1 
-0 
-0.89 


{Ri- 


■jI*: 


+0.668+0  _ 
+0.432^+1.222 
-0.30 


.778^ 
.22J 
-0.67 


+0.608^ 
0.22 


,     1    1    1     ..*^M» ill 

IRi  R2  R5  R4 

Fig.  3. 
Example. —  For  /— 9  (^panels),   and  with 
Loads  at  A,  B    and  C  on    each  arm, 
the  end    reactions    are   2.068  times  a 

Eanel  load;  and  center  reactions,  0 .  932. 
[oments  Af  2  and  Mi  are  —  2 .  39   times 
a  panel  load  times  a  panel  length. 


Calculation  of  815-Pt.  Draw.    (Fio.  4,  pagb  746.) 

Figs.  6,  6.  7  and  8  are  stress  diagrams. 

Fig.  5  (Case  I)  shows  one  arm  treated  as  a  simple  span,  fullv  loaded. 
Similar  diagrams  must  be  drawn  for  live  load  retreating,  panel  by  panel, 
from  end  oTspan  toward  center. 

Fig.  6  (Case  Ila)  is  a  dead-load  stress-diagram  of  one  arm  when  both 
arms  are  swinging  clear  of  end  supports. 

Fig.  7  (Case  lib)  is  a  stress-diagram  for  full  live  load  when  draw  is 
dosed;  the  condition  being  that  ends  of  arms  are  simply  touching  supports 
under  the  dead  load  only.  Similar  diagrams  must  be  drawn  for  live  load 
symmetrically  retreating,  panel  by  panel,  from  the  pier  ends  of  arms. 

Fig.  8  (Case  lib)  is  a  stress-diagram  of  a  retreatingload  last  mentioned — 
witli  symmetrical  loads  at  panel  points  A,  B,  C  and  D,  for  maximum  stress 
in  member  17.  .    ..     ,    ^     ,  ^^1 

"Wind-load  stress  diagram  can  similarly  be  drawgi-^.^^^  bvCjOOQlC 

Sec.  also,  page  742.  o 


746 


42.— AfOV^BLE   BRIDGES. 


Tbp  Chord  fbMS'4  fbroboh 


iis  zi 


(*!aad9  at  6  for  &jb9inKfun) 
FiR.  4.    315-Ft.  Draw. 


Fig.  6. 
Cash  I — Simple  Span — 
Pull  Loaded — Live  or  Dead. 


2*-25- 


Fig.  6. 
Cash  Ila — Draw  Swinging— 
Cantilever — Dead  Load  only. 

(Stress    in    24-26-^=  V  +  2J- U.) 
n 

Load  at  end.  a.  is  }  of  Panel  Load. 


Fig.  7. 
Case  lib — Continuous  Span — 
Full  Loaded — Live  Load, 
i?.- 2.296:  /?9« 3.704; 
Af2-4.93  .*.  Stress  in  24-25  = 


-2.11 


4.93  +  24 

(See  Table  2.) 


Fig.  8. 

Case  lib — Continuous  Span — 

Loaded   (A,  B^  C,  D.  both  anns)  for 

Max. Live  Load  in  17. 

/?i»2.105  (See  Table  2). 


Center-bearing  Draw — 3  Supports. — ^This  differs  from  the  rim-bearizijr 
draw  in  having  one  support  at  the  center  pier  in- 
stead of  two.     Hence.  Case  lib  (the  only  variation 
from  the  preceding  illustrations)  will  be  treated  as  a  j^-a— ^  „    fw.<i~j 

continuous  girder  of  two  equal  spans  over  three  sup-  J- * — A—* ^ 

ports.  ,     „  ^      .  .  ^  k V— S" — >■ — i 

Reactions  at  the  Supports— Continuous  gtrder. —  «i  Rt  «» 

Let  P  be  any  concentrated  load.  Fig.  9,  on  the  left 
arm,  distant  a  from  the  end;  then  will 


M  ''"  ft        "'  1 

''»  -  —Ji  V  ~  IP. 


Fig.  9. 

l-/?a/.] f5) 

^=^] (6) 

=^  -  2Rs  (algebraically)  1  . .  (7) 
[-  P  (l  -jj  +i?3  (algeb'y)]  (S) 


CONTINUOUS  GIRDER— THREE  SUPPORTS. 


747 


The  right  hand  half  of  the  following  table  is  all  that  is  necessary  in  Case 
lib  of  drawbridge  calculations,  the  first  half  being  interesting  as  a  study  of 
the  continuous  girder  of  two  equal  spans  for  any  concentrated  loading.  It 
is  to  be  noted  that  for  loading  on  right-hand  arm,  Ri  and  R3  will  be 
interchanged. 


3. — ^Practical   Data    for    Drawbridge   Calculation,    3   Supports. 
Case  lib. 
Reactions  and  Moments  for  Balanced  Loads. 
Reactions  are  in  Terms  of  Unit  Panel  Load.     Moments  are  at  Center  Sup- 
port and  are  for  Unit  Panel  Loads  and  a  (Respective  Distance  from  End 
Support).     Balanced  loads  are  Symmetrical  Loads,  Both  Arms. 


Concentrated 

Loads    on  Left  Arm 
a  From  End. 

,  Distant 

Balanced   Concentrated 
Loads  on  Both  Arms.  Dis- 
tant a  From   Ends. 

J 

a 

Double 

^ 

Ma 

Rz 

Ri 

Rt 

T 

Ma 

RfRi 

Shear. 
R2 

.04 

-0.2496  a 

-€ 

0.950016 

.04 

-0.499  a 

0.940 

0.120 

.08 

-0.2484  a 

-0 

0.900128 

.08 

-0.497  a 

0.880 

0.239 

.12 

-0.2464  a 

-« 

0.860432 

.12 

-0.493  a 

0.821 

0.358 

.16 

-0.2436  a 

-0 

0.801024 

.16 

-0.487  a 

0.762 

0.476 

.20 

-0.2400  a 

-0 

0.752000 

.20 

-0.480  a 

0.704 

0.592 

.24 

-0.2356  a 

-0 

0.703456 

.24 

-0.471  a 

0.647 

0.706 

.28 

-0.2304  a 

-0 

0.655488 

.28 

-0.461  a 

0.591 

u0.818 

.32 

-0.2244  a 

-0 

0.608192 

.32 

-0.449  a 

0.536 

20.927 

.X 

-0.2176  a 

-0 

0.561664 

.36 

-0.435  0 

0.483 

.cl.033 

.40 

-0.2100  a 

-0 

0. 516000 

.40 

-0.420  a 

0.432 

*'1.136 

.44 

-0.2016  a 

-d 

0.471296 

.44 

-0.403  a 

0.383 

^1.235 

.48 

-0-1924  a 

-0 

0.427648 

.48 

-0.385  a 

0.335 

gl.329 

.52 

-0.1S24  a 

-0 

0.385152 

.52 

-0.365  a 

0.290 

-^1.419 

.56 

-0.1716  a 

-0 

0.343904 

.56 

-0.343  a 

0.248 

vjl.504 

.60 

-0.1600  a 

-0 

0.304000 

.60 

-0.320  a 

0.208 

^1.584 

.64 

-0.1470  a 

-C.w.,-^ 

v.«.ww-^ 

0.265536 

.64 

-0.295  a 

0.171 

-».1.658 

.68 

-0.1344  a 

-0.091392 

0.862784 

0.228608 

.68 

-0.269  a 

0.137 

XI.  726 

.72 

-0.1204  a 

-0.086688 

0.893376 

0.193312 

.72 

-0.241  a 

0.107 

1.787 

.76 

-0.1056  a 

-0.080256 

0.920512 

0.159744 

.76 

-0.211  a 

0.079 

1.841 

.80 

-0.0900  a 

-0.072000 

0.944000 

0.128000 

.80 

-0.180  0 

0056 

1.888 

.84 

-0.0736  a 

-0.061824 

0.963648 

0.098176 

.84 

-0.147  a 

0.036 

1.927 

.88 

-0.0564  a 

-0.049632 

0.979264 

0.070368 

.88 

-0.113  a 

0.021 

1.959 

.93 

-0.0384  a 

-0.035328 

0.990656 

0.044672 

.92 

-0.077  a 

0.009 

1.981 

.96 

-0.0196  a 

-0.018816 

0.997632 

0.021184 

.96 

-0.039  a 

0.002 

1.995 

^^^P^    g 


Mi_ 


Fig.  10. 
Example. — Solve  for  one  load 
P-  16000  lbs.  on  left  arm ;  /-  45  ft. ; 
a  - 17  ft. 

Solution.— J-  Jl-  .378;  Ma- 

-.214XaXP     --.214X17X 

16.000-  -58,200  ft.-lbs.-  /?i-  .642 
X  16,000-8.672  lbs.;  K2-.639X 
X  16.000- 8,624  lbs.;  i?s=-  -  .081 X 
16.000- -1.290  lbs.  {R3  acting 
downward.) 


R» 


a 


Fig.  11. 

Example. —  Solve  for  load  P=» 
16,000  lbs.  on  each  arm;  /«45  ft.; 
a=17ft. 

Solution.—  Ma-  -  .428  X  17  X 
16,000=  -  116  .400  ft.-lbs.;  /?,  -i?, 
=  .46Xl6.000=7,3601bs.;/?2=1.08 
X  16,000=  17.280  lbs.  (All  reac- 
tions acting  upward.) 

Note. — A  minus  bending  mo- 
ment (  — M2)  means  tension  in  top 
flange  or  chord,  and  ^mpression  in 

bottom.  Digitized  by  VjOOQ  IC 


748 


41.—MOVABLE  BRIDGES. 


Dbck  Drawbridge — Cbntbr  Bearing. 


(*loatlate  far  mibtlnKHm} 


Fig.  12. 

Hints  for  Calculation  of  Trusses. — In  Fig.  12,  let  P— panel  load  per  trass 
at  A,  B,  C,  D  and  E;  and  let  H  P»dead  load  at  a  when  draw  is  swinging. 

Case  I — Simple  Span. — Ends  at  a  are  raised  so  there  is  no  stress  in 
DE.  For  dead  load  and  full  live  load  the  shear  in  panels  a— A  and  D—E 
are  equal.  Maximum  compressive  stress  in  10  occmrs  with  live  loads  at 
B,  C  and  D. 

Case  II — Cantilever. — Draw  swinging,  assuming  H  panel  load  at  a  and 
full  panel  load  at  other  points.     Shear  at  P  —  £  which  is  used  for  R^  in  this 

casc-4KP.     Stressmi?-J£-13HPXj-13>i  P. 

Case  III — Continuous  Girder. — Draw  closed  and  just  touching  supports, 
with  no  live  load.  Balanced  live  loads  are  now  applied  on  both  arms, 
extending  from  ends  toward  center  of  draw.  The  reactions  and  moments 
for  this  loading  may  be  obtained  from  the  preceding  table,  as  it  now  becomes 
a  continuous  girder  of  two  equal  spans  over  three  "level"  supports. 


For  loads  at  A, 
For  loads  at  B, 


f-.20: 


/?i-.704:Hi?2-.296:  Ms- -0.48a<- -0.48/>. 


/ 


.40;   /e,-.432;M/?a-.568;  Ma- -0.42a- -0.84  ^ 


For  loads  at  C.  -j"  .60;  i?i- .208;  H -Rj- .792;  M,--0.32o- -0.9e^ 
For  loads  at  P,  —--SO;   /?!- .066;  H /?2- .944;  Afa- -0.18a- -0.72  ^ 


For  loads  at  A,B,C,D,Rt^l. 400;  H /?»- 2.600;  *Af ,-  -  -  3 .00 ^ 

Note  that  all  calculations  can  be  made  for  any  loading  when  Rt  is 
known,  for  we  have  only  to  apply  the  methods  of  moments  and  shears  from 
the  outgr  forces  acting  to  the  leit  of  the  section  oonadered*  to  obtalo  the 
stress  in  any  member. 

WEIGHT  OF  STEEL  IN  MOVABLE  BRIDQBS. 

Steel  Swing  Bridges. — The  following  formula  is  for  single  track  standard 
R.  R.  bridges  calculated  for  live  load  of  two  180- ton  engines  followed  by  a 
uniform  load  of  4800 lbs.  per  lineal  foot:  Total  weight  of  steel  in  lbs.  — 
7.8L«4-12(LXvT)+100L+20000;  in  which  L- extreme  length  of  draw  in 
feet.  For  double  track  bridges,  multiply  results  obtained  in  above  fomaola 
by  1.86. 

Counterweight  Jack-knife  Draw.— In  Fig.  13,  let  /-the  span  HE^ 
hinged  at  H  and  connected  at  Di  (distant 


/.  from  H)  by  the  chain  C  +  Ct  running  over 
the  pulley  P,  with  the  cylindrical  coimter- 
weipht  Vki,  suspended  at  the  other  end  and 
rolling  along  the  modified  cycloidal  plane 
AP.  Assume  the  total  weight  of  the  mova- 
ble leaf  to  be  IV  acting  at  the  point  ^ 
Then  we  have  the  following;  

Wly/2 
Weight  of  counterweight  Wi  — — jr-j ;     a 

Length  of  chain  C,  -ZiVT  (l+sin|  -cos|)  .  ^^'  ^^ 

*Hence.  for  full  loading,  both  arms,  stress  ifflgferi^^^l^-  -  »  4  H 
-3X1- -8    (panel  loads).  ^  * 


d  by  Google 


43.— SUSPENSION    BRIDGES. 


THEORETICAL  CONSIDERATIONS. 

Curve  of  Main  Cables. — The  curve  assumed  by  the  main  cables  of  a 
suspension  bridge  when  the  latter  is  imiformly  loaded,  is  called  a  mod^itd 
or  transformed  catenary.  This  curve  lies  somewhere  between  the  catenary 
and  the  parabola.  When  the  cables  are  first  suspended  between  the  bridge 
towers  (before  they  support  any  extraneous  load)  they  form  a  true  catenary, 
due  to  the  weight  of  the  cables  alone,  assuming  of  course  that  they  have  i 
uniform  weight  ^r  lineal  foot  of  cable.  But  later,  when  the  floor  of  the 
bridge  is  in  position,  that  is,  suspended  from  the  main  cables,  the  curve  of 
the  cables  is  "modified"  and  tends  to  approach  the  parabola  in  form.  The 
true  parabola,  however,  is  hardly  ever  realized,  the  ideal  condition  for  this 
curve  obtaining  only  when  the  horizontal  combined  loading  per  lineal  foot 
on  the  cables  (including  weight  of  cables  themselves)  is  uniform. 

For  Short  Spans,  where  weight  of  cables  is  small  compared  with  weight 
of  floor,  we  may  assume  for  all  practical  purposes  that  the  main  cables 
take  the  form  ot  a  parabola:  also  bearing  in  mmd  that  on  this  assumpt ion 
the  error  decreases  as  the  ratio  of  central  deflection  to  length  o£  span  de- 
creases. Indeed,  even  the  arc  of  a  circle  may  be  used  in  the  drafting  Toom 
and  also  for  the  purpose  of  making  estimates,  when  the  central  denicction 
is  only  ^  or  even  i^  the  span.    See  also  Tables  1  and  2. 

In  the  above  discussion  of  the  modified  catenary  and  the  parabola  H  is 
assumed  that  the  suspenders  transmitting  the  loads  to  the  cables  are  verti- 
cal, uniformly  spaced  horizontally,  and  very  close  together,  so  that  the 
cables  form  true  and  continuous  curves  throughout,  between  points  of 
supports.  But  in  actual  practice  the  suspenders  are  not  always  vertical 
and  are  usually  spaced  quite  far  apart,  tending  to  further  modify  tliese 
curves. 

Force  Polygons. — ^The  following  force  polygons  assume  that  the  cables 
or  chords  of  the  equilibrium  polsrgon  have  no  weight,  being  acted  upon  by 
outside  forces  only. 


itfuUibrfom  Potygon. 


Pigs.  2. 


The  Parabolic  Cable. — Horizontal  Uni- 
form Load. — Let  w  =  uniform  load,  in  lbs.,  per 
lineal  foot  of  bridge;  /^span,  in  feet;  c— half 
span;  s  =  len^h  of  cable  between  towers; 
6  »  angle  of  inclination  of  tangent  at  any 
point  p  whose  coordinates  are  x  and  y\  d^ 
center  deflection  of  cable;  constant  //=»  hori- 
zontal component  of  tension  (lbs.)  of  cable  at 
any  point  p.  Then  with  vertical  suspenders, 
we  have: 


^=^^P^^ 


wx^    Ad^ 
"2^"   P    ' 


Pig.  3. 


General  equation. 


CURVE  OF  MAIN  CABLES.  751 

At  any  point  p,  tan  ^-^-^ (^ 

At  top  of  towers.  tan  0%  -~ (4) 

Length  of  cable.  *-i.\/S?+7»+2.3026Mm*log  /cH-v/m^+?\ (5) 

•»  V  m        / 

inwbichm---.|j;  c--;  --7- -tan  e^. 

wP 
Tension  In  cables  at  any  pointy— H  sec  tf  —  jj- sec  6 (6) 

Tension  in  cables  at  top  of  towers— gjVi«+  16d> (7) 

Tension  in  cables  at  top  of  towers  is  sreater  than  at  points  between, 
being  the  least  at  point  of  greatest  deflection.  Hence  bv  the  use  ot 
equation  (7)  we  may  determine  the  size  of  cables  required;  and  their  weight 
per  lineal  foot  multiplied  by  the  value  of  «  in  equation  (5)  will  give  tha 
weight  of  suspended  cable  between  towers. 

Pormid'Span.  equation  (6)  reduces  to  /f  —  gj (8) 


JUrwcfnx. 
Fig.  4. 

The  Catenarian  Cable— Load   Uniform  Along  Cable. — In  Pig.  4  let 
/-span,  in  feet; 
c-half  span: 
J— center  deflection: 

f — ksigth  of  suspended  cable  between  towers; 
Wi  -weight  of  cables  per  lin.  ft.  of  5; 
9— angle  of  inclination  of  tangent  at  point  ^  whose  coordinates  are  a;  and  y; 
//—constant  horizontal  component  of  tension  (lbs.)  in  cable  at  any  point  p: 

A— majdmum  value  of  ordinate  jr—d  +  m;    m— —  —  — ; 

Wi       s 
As  -area  of  shaded  portion  of  length  x,  above  directrix. 
A  —  m  5  — total  area  for  length  /.  between  catenary  and  directrix; 
ftf  — 2. 7 182818 -base  of  Naperiah  system  of  logarithms. 
Then  for  equation  of  the  catenary,  we  have: 

General  equation.  3"— «(»»+*    •) (1) 

.  'AH       horizontal  tension     ,     - ,  ... 

where  m—  —  —  —  —  — r-rr r. — 77-  of  cable (la) 

5      Wt       weight  per  hn.  ft. 
But  as  A ,  5  and  H  are  functions  of  m  itself  we  have  to  resort  to  other  methods 
to  find  the  value  of  m.    Thus: 

The  approximate  value  of  m-  2(y^m)''2d''8d ^^^^ 

which  may  be  substituted  for  value  of  m  in  the  second  member  of  equa- 
tion (Ic)  to  obtain  its  more  nearly  correct  value. 

„      _      ,        ,  0.4342945  c ,,  , 

Exact  value  of  m—         7—; p^^-^==- — r-  (Ic) 


^pisr(%^)'-') 


•Common    logarithm.    2.302585  -  , ;  in  which  g  is  the  Neparian  base  — 

2.7182818.     Log  2.302585  is  0.3622157. 
t  Log* -0.4842945;      log  (log*)  -  9.6377843- 10.       Also    note    that 

#-•=:-  ^.  in  the  general  equation  of  the  «it«»a^-3,,yGoOgIe 


762 


4S,— SUSPENSION  BRIDGES, 


when  the  exact  value  of  m  is  substituted  in  the  second  member;  but  when  m 
from  equation  (lb)  is  substituted,  the  result  from  (Ic)  is  too  small  by  about 
its  excess  over  that  obtained  from  equation  (lb)  alone.  In  the  following 
table,  column  Ct  is  obtained  by  adding  this  excess,  i.  e..  the  differenoe4>etweeo 
values  in  columns  6  and  c,  to  the  values  in  column  c.  Column  "difT."  b  a 
difference  column,  omitting  the  decimal  point,  between  Ci  and  e.  the  latter 
containing  exact  values  of  m;  and  is  useful  in  making  corrections  to  valiies 
in  column  Ci  obtained  by  the  approximate  method  as  above  described*  for 


any  values  of  4- 


1. — Values  op  Parambter  m  for  the  Catbnart.  based  on  /— umitt. 
For  successive  values  of  -j-. 


(Multiply  tabular  values  of  m.  below,  by  length  of  span 

L) 

a 

b 

c 

Cl 

DifTl     r 

a 

b 

c 

Cl 

DiflF 

# 

+ 

U 

it? 

^i« 

+ 

=?? 

lis 

C 

'o 
S 

8 

K 

%U 

1 

B+o. 

hi 

I 

&1^ 

1 

6+  c. 

£|"S 

.01 

12.5 

12.50064 

12.50168 

1 

12.50167 

11 

1.13636 

1.14541 

1.16446 

22 

1.15424 

.02 

6.26 

6.26166 

6.26333 

0 

6.26333 

12 

1.04167 

1.05161 

1.06135 

27 

1.06108 

.0^ 

4.16667 

4.16917 

4.17167 

1 

4.17166 

.18 

.96154 

.96217 

.98280 

83 

.98347 

.04 

3.126 

3.12832 

3.13166 

1 

3.13165 

.14 

.89286 

.90427 

.91509 

41 

.91528 

.66 

2.6 

2.50416 

2.5O830 

2 

2.50828 

.16 

.83332 

.84553 

.85773 

50 

.86723 

2.6633S 

2.06832 

4 

2.09326 

.16 

.78125 

.79422 

.80719 

60 

.80658 

.07 

1.78671 

1.79162 

1.79732 

6 

1.79726 

.17 

.73629 

.74902 

.76276 

70 

.76106 

1.5626 

1.66912 

1.57574 

9 

1.575651.18 

.69444 

.70694 

.72344 

82 

.72961 

.06 

1.38886 

1.39632 

1.40375 

11 

1.40364  .19 

.6578S 

.67812 

.68836 

94 

.66741 

.10 

1.26 

1.26824 

1.26648 

16 

1.266321.20 

.626 

.64097 

.65604 

107 

.66567 

Remarks. — ^To  find  values  of  m  (coltmin  #)  for  values  of-y  intermediate 

to  those  in  the  table:    Calculate  for  column  c^  and  subtract  the  interpo- 
lated difference  in  column  "diff." 

.  (2) 


Length  of  arc  fc—'o'  (  '  »   —  #"  »  j     — m  tan  0  . 


Substituting  c  for  x  in  above  equation,  we  have,  when  towers  are  of  equal 
height. 


Total  length  of  cable  s 


-«(.:-. ;)- 


2mtan0i. 


.(3) 


2. — Lengths  s  of  Cable  in  the  Catenary,  based  on  /—unity. 

For  successive  values  of  -r . 

(Multiply  tabular  values  of  5,  below,  by  length  of  span  /.) 


.01 
.03 
.08 
.04 
.06 


1.000267 
1.001066 
1.002396 
1.004264 
1.006636 


.06 
.07 
.08 
.09 
.10 


1.009537 
1.012949 
1.016868 
1.021283 
1.026187 


.11 
.13 
.13 
.14 
.15 


1.031600 
1.037431 
1.043739 
1.060464 
1.067674 


*Sec  foot-note,  following  page. 


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764  43.— SUSPENSION  BRIDGES. 

Comparing  equations  (1)  and  (2)  we  note  that  any  ordinate  y  of  the  trans* 

formed  catenary — —times  y  of  the  true  catenary,  for  constant  values  of  «and 

m.  In  fact  the  catenary  is  a  special  case  of  the  trans- 
formed catenary  where  a^m,  just  as  the  circle  is  a  special 
case  of  the  ellipse  where  the  semi  axes  a  and  6  become 
equal  to  each  other  and  are  called  r,  the  radius  of  circle. 
In  Fig.  6,  let  A  B  C  £>  be  the  diagram  of  a  catenary, 
similar  to  one-half  of  Fig.  4.  The  curve  A  B  is  that  due 
to  the  weight  Wg  per  lineal  foot  of  the  cable  itself.  Now 
if  there  is  an  additional  weight  n/  per  horiMonuU  lineal 
foot  imposed  upon  the  cable  the  latter  will  assume 
the  exaggeratca  form  AB',  the  middle  ordinate  will 
become  a,  and  the  directrix,  FE.  Let  Sx  be  the  length  1 
of  curve  from  A  to  any  point  ^,  whose  coordinates  are  x 
and  y.  Then  will  the  load  on  Sx  he  proportional  to  the 
area  Af/GF,  in  the  same  way  that  the  load  on  the  arc 
A  pot  tne  true  catenary  is  proportional  to  the  area  ApkD.  Fig.  6. 

'  PRACTICAL   HINTS. 

Cables  or  Chains. — These  may  be  composed  of  wire  cables  or  of  steel 
eye-bars,  as  follows:  (1)  For  short  spans,  twisted  wire  ropes  are  generally 
preferred  as  they  can  be  manufactured  and  handled  conveniently.  (2)  For 
spans  of  moderate  lengths,  strands  composed  of  parallel  wires,  laid  together 
near  the  bridge  site  and  then  hoisted  into  position,  possess  an  advantage  in 
economy  of  material  over  twisted  strands,  which  latter  develop  only  about 
90%  of  the  strength  of  straight  wires.  (8)  For  very  long  spans,  the  cables 
are  made  up  of  parallel  wires  as  in  the  second  case,  but  they  are  built  ts 
plac4  as  it  woula  be  impossible  to  raise  them  bodily  on  accotmt  of  their 

great  weight.  (4)  Steel  eye-bars  may  be  used  instead  of  wire  cables,  as  at 
rst  proposed*  for  the  Manhattan  suspension  bridge  over  the  East  River, 
New  York.  This  bridge  to  be  composed  of  a  centml  span  of  1.470  ft.,  and 
two  end  spans  of  725  ft.  each.  The  four  main  chains  to  lie  in  vertical  places 
20  and  48  ft.  distant  from  the  axis  of  the  bridge.  The  eye-bars  to  be  of 
nickel  steel,  Z\  to  3i%  nickel;  not  over  0.05%  sulphur:  not  over  0.06% 
phosphorus  if  made  by  acid  O-H  process,  and  not  over  0.04%  phospboms 
if  made  by  basic  O-H  process.  The  reauired  ultimate  strength  was  85000 
lbs.  per  sq.  in.;  actual  elastic  limit,  48000;  percentage  of  elongation  in  18  ft. 
0;  percentage  of  reduction  at  fracture,  40.  Among  the  advantages  claimed 
for  the  eye-bar  cables  are:  They  offer  better  connections  for  the  vertical 
suspenders;  they  are  better  adapted  to  form  integral  parts  of  the  stiffening 
trusses  to  equalize  moving  loads  on  the  bridge;  and  they  can  be  propor- 
tioned economically  with  varying  cross-section  to  the  exact  stresses  in 
various  parts  of  the  cables,  whereas  wire  cables  mtist  have  a  uniform  cross- 
section.     (For  revised  plans  and  specifications,  see  pag^  766,  etc.) 

The  parabolic  curve  may  be  used  in  making  up  preliminary  estimates, 
and  also  for  designing  small  suspension  spans  m  generaL  See  Pig.  3  and 
equations  (1)  to  (8). 

Example. — What  will  be  the  tension  in  each  cable  at  top  of  tower,  at 
mid  span,  and  at  quarter  span,  for  a  clear  span  of  600  ft.,  and  a  center  de- 
flection of  50  ft.;  assuming  total  load  at  8000  lbs.  per  lin.  ft.  of  bridge,  and 
supported  by  two  cables? 

Solution. — From  the  preceding  equations: 

At  towers,  each  cable,  eqtiation  (7).<  —  J  .srVP+lO^-"  8,795,000  Ib«. 
At  mid  span,  each  cable,  equation  (8),  <-  J  .  If  -  J  .  ^  -  3.600,000  lbs. 

At  quarter  span,  each  cable,  equa's  (6)(3).  f  —  }.HvT+tiu?0—  8.660.000  Ihs 

Towers  and  Backstays. — Provision  for  expansion  and  contraction  of  the 
cables  may  be  made  at  the  towers  in  several  ways: 

,  ( 1 )  One  of  the  most  common  methods  is  to  sling  the  cables  over  the 
main  piers  on  Saddles  resting  on  a  nest  of  rollers  as  in  Fig.  7.    Note  in  this 

*  Eye-bars  not  adopted;  wire  cable  used  in  plans  finally  approved. 


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756 


4^.— SUSPENSION  BRIDGES. 


DETAILS  OF  MANHATTAN  SUSPENSION  BRIDGE. 

Description. — Wire  cable  bridge  of  three  spans:  central  span,  1470  ft.; 
two  side  spans,  725  ft.  each.    Foxir  cables. 

Cables. — About  20^4"  in  dia.^  each  consisting  of  37  strands  and  contain- 
ing 0472  parallel  wires  of  0.192  m.  dia.  before  galvanizing,  and  not  mat 
than  0.107  in.  dia.  after  galvanizing. 


I 


/     / 


0 

c 
.2 


^C//7    J94U9J 


Live  Loads. — (1)  For  the  cables,  trusses  and  towers:    (a)  a  load  of  8000 

lbs.  per  lin.  ft.  of  bridge  as  "regular,"  or  (b)  16000  lbs.  per  lin.  ft.  of  bridge 

as  "congested"  traffic.     (2)  For  the  hangers,  floor  beams  and  floor  system: 

v<=>  on  each  elevated  track  a  load  of  52  tons  on  four  axles,  6'-10'-6',  the  motor 

I        ®f,9*  o^  cara  of  the  Interborough  R.  T.  Co.;   (d)  on  each  street  car  track 

I        either  a  load  of  26  tons  on  2  a^es  10  ft.  apart  or  a  load  of  1800  lbiU£«£J|fl^^H 


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758 


4Z,— SUSPENSION  BRIDGES. 


The  suspenders  shall  be  1^  in.  in  dia.  and  wei^h  not  less  than  5.1  lbs. 
per  Hn.  ft.  They  shall  be  composed  of  six  strands  of  19  wires  each,  laid 
arotrnd  an  independent  wire  rope  center  consisting  of  49  wires,  left  hand  lay. 
The  suspenders  shall  be.  preferably  of  long  lay,  but  the  lay  must  not  be 
long  enough  to  caxise  trouble  in  keeping  the  core  in  its  true  position  durins 
any  of  the  operations  before  the  suspenders  are  in  their  final  position  and 
loaded  with  tne  superstructure. 

RsguisBD  Physical  Propbrtibs  of  Finishbd  Material. 
(Manhattan  Bridge.) 


Ultimate 
Material.  *  Strengtb. 

Lbs.  per 
sq.ln. 
Oarbon  Steel. 

Shapes  and  universal  mill  plates 60-68.000 

Eyebars,  pins  and  rollers 64-72.000 

Rivet  rods 60-58.000 

High  carbon  steel  for  trusses 85-95.000 

Sheared  plates 60-68.000 

Nickel  Steel. 

Shapes  and  plates 85-95.000 

Rivet  steel 70-80,000 

Steel  Castings. 
Test  pieces  from  annealed  castings 65.000 


Minimum 
Elastic 
Limit. 

Lbs.  per 
sq.ln. 

33.000 
85.000 
30.000 
45.000 
33.000 

55.000  V 
45.000  / 

35.000 


Minimum  Mlnlmtm 

Elongat'n.  ReducU'n. 

Per  cent     Per  cent 

In  8  Ids.      of  area. 


1.500.000 
divided  by 
ultimate. 


44  pereL 
40      •• 
50      •• 
35      •• 
44      •• 


1.600.000 
ultimate 

In  a  Ins. 

20% 


{« 


perct. 


Allowablb  Maximum  Unit  Strbssbs. 

For  dead  load« 
For  dead  load,  tempcrafreand 
temperature     congested  live 
and  regul'r  lite  load,  or  for  dead 

load,  or  for  load,  regular 
dead  load.tem-  live  load,  tem- 
perature and     peratureand 

wind.  wlDd. 

Lbs.  perSq.  In.  Lbs.  per  Sq.  In. 


Material,  and  Parts  of  Structure. 


Wire: 

Main  cables 

Suspenders 

Nickel  Steel: 

Tension  In  stiffening  trusses 

Compression  In  stiffening  trusses 

Shear  on  rivets  in  stitfenlng  trusses;  field 

Bearing  on  rivets  In  stiffening  trusses;  field. . . . 

Structural  Steel  In  Towers: 

Tension 

Compression n2.00O-90  <-(•  r   n27.000-l00l-i-r 

Shear  on  shop  rivets  and  bolU 13.000  16,000 

Bearing  on  snop  rivets  and  bolts 25.000  30.000 

Structural  Steel  In  Stiffening  Trusses: 

Tension 20.000  24.000 

Compression •SO.OOO-gOI^r    •24.000-100 /-i-r 


60,000 
80.000 


20.000 


73.000 


40.000 

•40.000-1 50  l+r 

20.000 

85.000 


tZSLOOO 


Shear  on  shop  rivets . 

Bearing  on  shop  rivets 

Structural  Steel  In  Floor  System  of  Roadway  and 
Footways: 

Tension  chords 

Shear  on  shop  rivets,  bolts  and  web-idate  net  section 
Bearing  on  shop  rivets  and  bolts 

Structural  Bte^  In  Floor  System  for  Railroad  and 
Trolley  Tracks : 

Tension  chords 

Shear  on  shop  rivets,  bolts  and  web-plate  net  section 
Bearing  on  shop  rivetsand  bolts 

Structural  Steel  in  Anchorages: 

Tension  In  eye-bars 

Bearing  on  diameter  of  pins 

Bending  or  outer  fibre  or  pins 

Shear  on  pins 

„    High  Carbon  Steel : 

T"»"*on  In  atlffenlnc  trusses. 

OompresBlon  In  stiffening  trusses  . 


13.000 
25.000 


15.000 
10.000 
20.000 


10.000 
7.000 
14.000 

16.000 
22.000 
22.000. 
12.000 


20.000 


35.000 
•35.000-135  f^r 


Note. — For  Weights  of  Materials  in  Manhattan  Dridob,  see  page 780- 


!5^!i*«5.'-'<*n8*h  and  r 
tlnduding  secondary  ^ 


least  radius  of  gyration,  both 


'Oigifeed  by  ^Tjt^  l^ 


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760  4»,— SUSPENSION  BRIDGES. 

AppRozniATB  Wbiorts  of  Materials  in  Makhattaic  Bridob. 

AnehorageB.  Towers.   G&bles.   Main  span.  Side  spans.   Totals. 

LbsT         Lbe.         Lba.           Lbe.            Lbs.  Lba 

Nickel  steel 7.849.600     8.897.800  16.247.400 

BtniCtnral  steel 1.335.600    21.333.800         80.200  10.602.600  10.447.200  43.749.400 

Wire 12,176.200 12.176.200 

Suspenders,  etc 1.163.600 1.153,«0I 

Eye-bars 3,731.900 8.781.90I 

CasUngs.  steel 1.500     8.385.200     1.744.600         13.700         28.200  5.173.a0i 

Castings.  Iron 18.500         189.100         54,500          7.600         24.600  294.J0O 

Pins,  bolts,  nuts.  etc.       307.500        119.100       883.000         10.000         22.600  842JtO 

Totalsof  Sted. . .     5.395.000    25.027.200  15.542.000   17.983.500   19.420.400  83.368.200 

Ooncrete  (cu.  yds.) 930 9S0 

Bronze 400    12.000          2.100           4.200  18.700 

Zinc 26.200 25.200 

Lead 20.600          7.400 28.000 

Economic  Considerations. — ^The  approximate  costs  of  materials,  erected, 
in  a  suspension  bridge  of  about  1200  to  1600-ft.  spans  designed  for  combined 
railway  and  highway  traflBc.  are  as  follows:  Steel  in  wire  cables,  6  to  ^JU 
cents  per  lb.  (add  about  4%  to  this  for  copper  covering) :  riveted  steel  in 
center  span.  4.25  to  4.5  cents  per  lb.  (nickel  steel,  6  to  d.26  cents) ;  steel  in 
towers,  side  spans  and  anchorage,  3.4  to  3.6  cents  per  lb.  •  steel  in  viaduct 
spans,  about  3  cents  per  lb. ;  anchorage  masonry,  lo.SO  to  16.50  per  cu.  yd. 

Steel  in  cantilever  spans,  erected,  about  4.5  cents  per  lb.  (nickel  steel, 
about  6  cents  per  lb.). 

EXCERPTS  AND  REFERENCES. 
Waterproof  Wnippinf  for  the  Cables  of  the  New  East  River  Svfpco- 
sion  Bridge  (By  WilhelmHilden brand.    Eng.  News.  Nov.  13.  1M2). — Illus- 
trated.   Discussed  by  A.  H.  Sabin,  in  Eng.  News,  Nov.  20,  1902. 

The  Wniiamsburg   Bridge   Across  the   Ea8t  River  at  New  Yoik  City 

(Eng.  News,  Nov.  17,  1903). — Illustrations  of  anchorages  and  details. 

A  Rational  Form  of  Stiffened  Suspension  Bridge  (ByGustav  Linden- 
thai.  Trans.  A.  S.  C.  E^Vol.  LV).— Discussions  by  W.  Hildenbrand. 
Joseph  Mayer,  R.  S.  Buck.  W.  W.  Crehore,  Theodore  Cooper,  C.  C.  Schnieder. 
Owsald  Erlinghagen,  H.  W.  Hodge,  F.  Schule,  J.  Melan,  L.  S.  Mnimriff. 
A.  Rieppel. 

The  Monongahela  River  Sjispension  Bridge    at  Mofgantown,  W.  Va. 

(By  W.  H.  Boughton.    Eng.  News,  April  18,  1907).— Illustration  of  saddle 
and  top  of  tower. 

The  Towers  of  the  Manhattan  Bridge  Over  the  East  Rfvcr  at  New 
York  City  (Eng.  News,  April  16,  1908).— Illustrated. 

Report  on  the  Manhattan  Suspension  Bridge  at  New  Yoric  City  (By  Ralph 
Modjeski.  Eng.  News.  Oct.  14,  1909).— C^culatlons.  (a)  Extract  from 
specifications  for  superstructxire,  with  table  of  unit  stresses;  (b)  Derivataoo 
of  formulas  used  in  the  calculation  of  stresses  in  the  stiffening  trusses,  witl& 
moment  and  shear  diagrams:  (c)  Method  used  in  the  calculation  of  stresses 
in  the  tower  and  cable,  with  formulas  and  diagrams;  (d)  Method  used  in  the 
calculation  of  stresses  in  the  lower  iloorbeams  and  lateral  system,  with  formu- 
las and  diagrams.  Illustrated:  Fig.  1  (not  reproduced  here)  is  a  diagram  of 
dead-loads  and  cable  ordinates;  showing  (1)  Panel  load  of  susp.  strticture, 
(2)  Total  panel  load,  (3)  Actual  ordinates,  in  feet,  (4)  Ordinates  to  para- 
bolas, in  feet.  For  discussions  of  calculations,  see  Eng.  News,  Mar.  3, 1910. 
Illustrations. 
Description.  Eng.  Rec 

Machine   for  winding  wire   around    main   cables — ^Manhattan 

bridge July  31,  •<>» 


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44.— ARCHES. 

Qeoeral  Dlaciuskm. — An  arch  is  a  structtare  so  designed  that  the  loading, 
includixi^  the  weight  of  the  structure  itself,  produces  a  thnist  at  the  abut- 
ments, ia  such  a  manner  that  the  resultant  horizontal  reactions  at  those 
points  tend  to  relieve,  wholly  or  in  part,  the  bending-moment  eflfect  on 
the  span. 

The  Idea]  Arch  would  naturally  take  the  (inverted)  form  which  the 
cables  of  a  suspeiunon  bridge  assume  for  the  particular  conditions  of  load- 
ing impoe«l;  for  then  the  horizontal  reactions  at  the  abutments  will  relieve 
the  arch  ring  of  any  bending  moment  whatsoever,  the  stresses  throughout 
being  purely  of  axial  compression.  Either  of  the  curves  described  in  Sec.  43, 
Suspension  Bridges,  if  inverted,  will  become  ideal  archra  for  the  givfn  load- 
ings. Such  arches  are  called  linear  arches.  The  circttlar  arch  also  is  a  linear 
arch  when  the  resulting  forces  are  radial,  as  in  the  case  of  a  circular  dam 
where  the  hydrostatic  pressure  is  normal  to  the  up-stream  face. 

Tbe  Circnlar  Arch  as  a  Dam. — Let  r,  Pig.  1.  be 
the  radius  in  feet  of  the  up-stream  face  of  the  dam; 
Jk.  the  depth  in  feet  below  the  surface  of  the  water 
to  the  level  at  which  the  pressure  is  to  be  considered; 
p,  the  ^ressxire  in  lbs.  per  sq.  ft.  at  depth  h:  W,  the 
we^t  in  lbs.  of  a  cu.  ft.  of  water.  Then  p — Wk ;  and 
the  tangential  compressive  stress  at  any  point  of  the 
circle  for  one  foot  vertical,  and  at  depth  h,  is  T— ^■- Wfcr  —  62.5  hr  lbs.  =»/?. 
If  I  is  the  thiclmess  of  the  masonry  in  feet  at  depth  h,  the  compressive  stress 

in  Iba.  per  sq.  ft.  on  the  masonry  is  —  —62.6  --.    For  overturning  eflfect  see 

Sec  49.  Dams. 

The  Catenary. — ^Let  Pig.  1  represent  a  vertical  arch  of  uniform  thick- 
ness t  and  suppcnrting  its  own  weight  only;  then  in  order  to  be  a  true  linear 
axch  its  curvature  should  be  that  of  a  catenary  instead  of  a  circle. 

Tbe  Parabola.— Let  Pijj.  1  represent  a  vertical  arch  supporting,  including 
weight  of  arch  itself,  a  uniform  korisontal  load ;  then  in  order  to  be  a  true 
lixiear  arch  its  curvature  should  bethat  of  a  parabola. 

The  Tranflformed-Catenary  Arch. — Let  it  be  re- 
quired to  design  a  masonry  arch  of  40  ft.  span,  2  ft.    .  ^     .    -^ 
in  depth  at  the  crown  and  8  ft.  at  the  springing  line ;  ^— Wsi 
and   supporting  a  line  load  of   140  lbs.  per  sq.  ft.  ^^  ^^  _    _ 
Assuming  the  weight  w  of  masonry  at  140  lbs.  per  cu.  *^  *    p_  «  ' 
ft.,  and  the  spandrel  filling  F  to  be  solid  at  the  same  *^*e-  ^• 

w^ght;  and,  further,  reducing  the  live  load  to  equivalent  depth  of  masonry. 
namely,  one  foot,  we  have  the  outline  diagram  as  shown  m  Fig.  2.  The 
problcxn  is  to  find  the  cturve  of  the  intrados  (a  transformed  catenary)  so 
that  the  line  of  resultant  pressure  shall  trace  the  center  line  of  the  arch 
stones  (practically)  as  shown  by  the  middle  dotted  line.  Note  that  the 
thinner  the  arch  stones  and  the  flatter  the  arch,  the  more  nearly  will  this 
be  true. 

Solution. — First,  find  the  value  of  m  in  the  equation* 

0.4342946c         ..11.34+;  and  substitute  the  values  of  a(- 2+1) 


com  log 


I  of  the  catenary  and  transfi 

yjl  Digitized  by  VjOOQ IC 


*  See  also  the  equation  of  the  catenary  and  transformed  catenary  in 
Sec.  43,  Suspension  Bridges. 


762  a.— ARCHES, 

and  m  in  the  general  eqxjation  ♦>— -5- 1   #-'+#"'- I  — y  (#"^H —j  .Then: 

For  *-  0.  6.  10.  W.  20. 

y^         8.00        3.30        4.24        6.03         9.00 
Depth  of  masonry  *-         2.00-      2.30        3.24        5.03        8.00 
The  above  calculation  is  very  simple,  requiring  only  a  few  minutes' 
time,  remembering  that  log*"^^—  logr,  -0.4342945+11.34-0.03828  for 

this  particular  case;    and  log  fl^*  —  0.03828  x.     Also  note  that  ^"^is  the 
reciprocalof  t'^and  hence  log  #""5  —1  — logo's". 

The  Horizontal  Thrust  H  at  any  point  of  the  arch  for  each  foot  in 
length  (perpendicular  to  face)  is  H  =  tiwf«-140X(11.34)«-18  000  lbs.;  and 
at  crown  ot  arch  —  9000  lbs.  per  sq.  ft.  —  62.5  lbs.  per  sq.  in. 

The  Vertical  Shear  P%,  at  any  point  distant  x  from  the  center  of  arch,  is 

tj     

Pa— — \/>^— a*  — twK  \/y*  —  a*;  and  at  the  abutment  the  shear  is  equal  10 

the  vertical  reaction  P  -  —  V¥^*  -  wm  s/h^'a^  -140X11. 34  XV  81  —  9  - 
13471  lbs.—  per  lin.  ft.  (axial)  of  bridge. 

The  Area  -r-  of  Half  the  catenary,  between  directrix  and  soffit,  is 

^  -  mVh^^*'-"  -?tP  -  96.22  sq.  ft. 
2  ttf        140  ^ 

The  area  of  face  of  masonry-  96.22-  20-  76.22  sq.  ft. 

The  depth  of  arch  stones  is  assumed  to  be  24  inches,  but  with  a  uniform 
live  load  as  above  it  may  safely  be  much  less.  The  tangential  thrust  at  the 
springing  line  is  equal  to  VH*+P*  —  22482  lbs.  or  only  78  Ib^.  per  sq.  in. 
The  tangent  of  the  angle  which  this  thrust  makes  with  the  horizontal  at 

that  point  is  tan  fl,=.i-N/A«-a>- 77-0.7484;  therefore  tfi-36*»— 49^,  the 

in  ti 

thrust  being  tangent  to  the  soffit  of  the  arch.  At  any  point  distant  x  from 

center  of  span,  tan^  — —  v^p'— a*.     With  a  variable  live  load  on  the  arch 

the  resultant  line  of  pressure  through  the  middle  of  the  arch  stones  wiD 
change  its  form  and  deviate  from  a  true  central  position.    The  amount  of 

dtviation  in  the  present  instance  cannot  be  more  than-x-X-g  —  4  inches,  or 

one-half  the  "middle  third,"  without  producing  tension  in  the  maaocuy 
joints,  which  is  not  allowable.    (See  Masonry  Arches,  following.) 

The  live  load  on  the  span  is  assumed  at  140  lbs.  per  sq.  ft.  of  floor. 
equivalent  to  a  depth  of  one  foot  of  masonry.  Now  it  is  plainly  evident 
that  the  curve  of  the  intrados  of  the  arch  (Fig.  2)  win  not  be  anected  by 
any  relative  change  of  live  load  to  dead  load  provided  the  "loading  contour* 
remains  the  same.  Thus,  we  may  increase  the  uniform  live  load  to  380  lbs. 
per  sq.  ft.  by  decreasing  the  depth  of  masonry  one  foot,  making  the  depth 
of  arch  stones  12  ina  instead  of  24  inches.  This,  of  course,  would  dotatde 
the  thrust  on  the  arch  stones  per  sq.  in.,  making  the  horizontal  thrust  at 
crown  125  lbs.  per  sq.  in.,  and  the  tatigential  thrust  at  springing  156  lbs. 
per  sq.  in.  The  line  of  resultant  pressure  would  not  change  its  form  bat 
would  now  conform  more  nearly  with  the  (new)  middle  line  of  the  arch  TtTm« 
They  will  never  exactly  coincide  unless  the  arch  ring  is  reduced  to  a  tkm 
plate. 

The  resultant  line  of  pressure  as  previously  determined  will  evidently 
be  affected  bjr  changes  in  the  loading  contour:  (1)  By  raising  the  loadii^ 
contpiu",  that  is,  increasing  the  imiform  load  per  sq.  ft.;  (2)  by  lowering  thi 
Joadinj^  contour,  that  is.  decreasing  the  unilorm  load;  (8)  by  considenc« 
tne  umform  load  at  middle  of  spem  only;    (4)  by  considering  the  unifom 

*  ^^  '-0.4842945.  OgtizedbyGoOglC 


d  by  Google 


764 


iL'-ARCHES. 


Tudor  arch,  modified  Gothic  with  intrados  pompotinded.  The  **  four- 
centered  "  Tudor  arch  is  shown  in  Pig.  6.  The 
radii  are  i  and  U  of  the  span,  respectively.  ElUp- 
tical  arch,  intrados  is  part  of  an  elh(Mse.  The  major 
axis  may  be  either  hcpzontal  or  vertical.  (Any  arch 
is  said  to  be  surbased  when  the  rise  is  less  than  the 
half-span;  and  surmounUd  when  the  rise  is  greater 
than  the  half -span.)  Oval  or  "  basket-handle  arch, 
intrados  composed  of  arcs  or  circles  approaching  the 
elliptic  arc  in  form.  The  "  three-centered  "  oval  is 
very  common.  Parabolic  arch,  intrados  is  parabolic. 
CaUnarian  arch^  intrados  is  catenarian. 

Farther  Qasslficatioii  of  Arches. — Right  arch^  one 
whose  ends  or  faces  are  perpendicular  to  axis  of 
arch.    Skew  arch,  an  arch  whose  ends  or  faces  are  _  .„    - 

oblique  to  axis  of  arch.  There  are  two  kinds: 
First  (Fig.  6)j  the  skew  arch  proper,  with 
smooth  cylindrical  soffit,  spiral  iomts  and  un- 
broken axis;  Second  (Pig.  7),  the  oblique  arch 
being  made  up  of  a  number  oi  short,  right  arches 
called  ribs,  which  are  oSaeit  transversely  and 
successively  in  one  direction.  Flat  arch,  flat  soffit 
with  wedge  shaped  voussoirs;  used  for  doors  and 
windows.  Vault,  surface  generated  by  the  in- 
trados of  an  arch  moving  m  a  straight  line  <m 
the   springing    lines.     Cloistered   vault,    formed 

when  two  vaults  or   arches   meet;  as  "  vaulted 

Fig.  7.  ceiling."     Groined  vault,  formed  when  two  vaidts 

or  arches  cross  each  other.  Dome,  formed  by  right  section  of  arch  revolving 
around  vertical  axis  through  center  of  keystone.     (Also,  see  Glossary.) 

Brick  Arches. — The  three  principal  methods  of  bonding  brick  arches 
are  illustrated  in  Pig.  8,  and  described  as  follows: 

Rowlock  bond  (R). — All  the  bricks  are  laid  as  stretchers  in  concen- 
tric rings.  The  average  thickness  of 
joint  is  less  imder  this  construction, 
and  hence  more  bricks  and  less  mor- 
tar are  required.  It  is  cheaper  to 
lay.  and  is  employed  largely  in  tunnel 
work,  sewers,  etc.,  where  architec- 
tural effect  is  not  important. 

Header    and   Stretcher   bond    (H.  ^        ^^-  ^' 

&  S.). — Radial  joints  continuous^  and  bricks  laid  as  headers  and  stretchers. 
The  average  thickness  of  joint  is  greater  under  this  method,  and  hence 
more  mortar  and  less  (the  least)  number  of  bricks  are  required.  It  is 
more  pleasing  to  the  eye  than  the  rowlock  bond,  and  is  used  largely  in 
the  fronts  of  buildings. 

Block  in  Course  bond  (B.  in  C). — This  bond  aims  to  attain  with  brick 
the  wedge-shaped  voussoirs  of  the  stone  arch.  That  is,  the  bricks  are 
grouped  in  sections  bounded  by  continuous  radial  joints.  Adjacent  sec- 
tions are  of  different  bond,  any  good  bond  being  permissible.  Bonds  with 
continuous  radial  joint  are  usually  made  narrower  than  those  bonds  where 
radial  joints  are  broken. 

The  Masonry  Arch  Is  s  Statically  Indeterminate  Structure,  and  its  solu- 
tion is  based  on  various  assumptions  more  or  less  approximate.  These  will 
be  considered  in  the  material  order  of  design.  To  begin  with,  we  have  to 
assume  the  finished  arch  and  then  examine  it  for  stability  (resistance  to 
defonnation),  strength  (resistance  to  crushing),  economy,  etc 

Curve  of  Intrados. — ^The  form  of  curve  selected  for  the  intrados  wiH 
naturally  affect  the  thickness  of  the  arch  ring  and  the  economy  of  the 
whole  structure.  We  have  seen  (Fig.  2)  that  the  transformed  catenary  is  the 
ideal  curve  of  soffit  where  the  loading  contour  is  a  horizontal  line,  and  this 
curve  would  undoubtedly  be  used  were  the  conditions  of  loading  constaxit 
*^  f  fl  "'  ^^  ^*^^  ^  noted  that  in  the  transformed  catenary  the  curve  » 
quite  flat  at  the  crown  and  gradually  becomes  sharper  toward  the  springiiu. 
1  ne  eutpse  is  a  curve  that  can  be  made  to  approximate  the  modified  catenary* 


d  by  Google 


766  a.— ARCHES. 

absolute,  simple  rules  can  be  devised,  but  the  writer  presents  the  foUowing 
as  giving  very  close  results  for  first-class  concrete  and  cut  stone  work: 
Thickness  U  at  crown  (all  dimensions  in  feet): 


For  highway  bridges  U  at  crown  -^0.01  span  (^^+3J  +0.15 (1) 

For  high  H.  W.  em- )  /  Tsoan      \" 

bankmenta.or     Vu  at  crown  -^/O.Ol  span  I ~— +  41  +0.20 (2) 

For  railroad  bridges )  \ ^'^       ' 

^""'^^^i^^r  }^  -'  ^^-  -^0.01  span  (^+6)  +0.26 (3) 

Thickness  U  at  springing  (all  dimensions  in  feet) : 
For  all  cases.  U  at  springing  -  (<  [l  +  0.002(span+2Xrise)] (4) 


1. — Crown  Thickness  ^  (Pbet)  for  Masonrt  Archbs. 
[Calculated  from  Formulas  (1).  (2)  and  (3).] 


Remarks. — ^The  above  table  is  for  solid  arch  rin^  Where  arx^  tw  ^ 
arc  ribbed  the  thickness  or  depth  of  ribs  should  be  increased.  For  sp«uas 
under  76  ft.  an  arch  ring  of  uniform  thickness  may  be  used  by  increasing 
SP«  crown  thickness  obtained  from  above  table  by  from  6  to  20%.  See 
iable  2. 


MASONRY  ARCH^THICKNESS  OF  RING. 


767 


2. — Tablb  for  Obtaining  Thicknbss  u  of  Arch  Stonbs  at 
Springing. 
Values  of  [1  +  0.002  (span  +  2  X  rise)]  in  Equation  (4). 
Thickness  at  springing— thickness  at  crown  X  tabular  values  below.) 


Rise -4- 
Span. 


Span,  in  Feet. 


Rise  + 

Span. 


Span,  in  Feet. 


76 


100 


1(0 


200 


260 


800 


76 


100 


160 


200 


260 


300 


1-10.10 
.1251 


1-8 
1-7 
l-ra.l5 


181 
191 


1-6 


142  1 .  19  1 

1.201 

167*1.201 


.241.8fll.48        _, 
.261.881.601.63^1 


.261.89 

.261 

.271 


861 
401 


1  61 


1.6C1.72 

"  "    76' 


1.64^ 
.621. 
621.67^1 


1-6 
1-4 

1.77il-3 
6dl.78:^l-2J 

-2 


80  1 


20 
.25 

3331 

40 

50 


1.21 
1.23 
1.25 
1.27 
1.30 


1.281.42 
1.301. 


451 
601 


1.331..-, 
1.36^1.64 
1.401.60 


1.6611.70 
.60(1.76 
.6611.83 

1.721.90 

1.802. 


00  2 


1.84 
1.00 
2.00 
2.08 
20 


Note  from  Tables  1  and  2  that  for  any  given  span  the  actual  thickness 
of  arch  ring  at  springing  remains  nearly  constant  as  the  rise  approaches  the 
half  span. 

Problem. — In  designing  a  railroad  masonry  arch  of  200  ft.  span  and 
40  ft.  rise,  what  thickness  of  arch  ring  shall  be  assumed,  tentatively,  at 
crown ?    Also  at  springing? 

Solution. — At  crown,  4.44  ft.  (from  Table  1).  At  springing.  4.44X1.66 
(from  Table  2)  — 6.98  ft.    Hence  use  4.6  and  7.  respectively,  for  trial. 

Forces  Acting  on  a  Masonry  Arch. — ^These  may  be  classified  as  the 
"outer"  and  the  "inner"  forces,  the  same  as  in  any  other  structure.  The 
OHtrr  forces  include  (1)  the  moving  loads  due  to  trains,  vehicles,  etc.;  (2)  the 
mixed  loads,  due  to  weight  of  track,  roadway,  embankment,  spandrel  fill- 
ing, etc.*  (3)  the  dead  loads  due  to  weight  of  arch  ring  itself;  (4)  the  reac- 
tions. The  inmr  forces  comprise  the  stresses  in  the  arch  ring,  usually 
calculated  at  points  of  imaginary  joints.  These  stresses  are  examined  for 
compression,  shear,  and  possible  tension.  The  compression  is  determined 
fxnm  the  line  of  resultant  pressure  through  the  arch  ring,  which  also  reveals 
possible  tension.  The  shear  at  any  point  of  the  arch  is  eqiml  to  the  alR:ebraic 
sum  of  the  outer  forces  at  the  left  of  that  point,  taken  in  the  direction  of 
the  cutting  plane.  Furthermore,  we  know  that  the  algebraic  sum  of  the 
outer  forces,  either  of  the  whole  structure  or  of  that  portion  at  the  left  of 
any  given  cutting  plane,  is  equal  to  zero.  The  same  is  true  of  the  inner 
forces:  also  of  the  outer  and  inner  forces  combined.  Hence,  an  inner  force 
in  a  complete  structure  may  be  determined  by  assuming  it  to  be  an  outer 
force  in  maintaining  equilibriimi  in  a  portion  of  the  structure. 

Direction  off  Outer  Forces. — Let  Fig.  10  represent  a  masonry  arch 
with  arch  ring  drawn  to  scale.  Let  MM  represent 
the  mixe^d  static  loading  above  the  arch  ring  due  to 
spandril  filling,  roadway  and  tiack,  and  with* depth 
Traced  to  equivalent  masonry  loading,  so  that  d.  in 
itet,  at  any  point  distant  x  from  left  abutment,  will 
represent  the  intensity  of  the  total  static  loading  at  < 
that   point  in  terms  of  the  weight  of  masonry  per 

cubic  foot.     If,  now,  we  add   the   moving  load   m  _  _„ 

for  any  particular  case  of  loading,  say  on  the  right  half  of  span,  and  re- 
duce the  same  to  equivalent  depth  of  masonry,  we  obtain  the  loading  con- 
tour for  calculating  the  arch  for  that  particular  cast  of  loading. 

Vtrtical  Loading. — In  fixing  the  loading  contour  as  above  we  have 
asstimed  all  loading  to  be  vertical,  which,  although  not  quite  correct,  is  the 
osual  assumption.  Note  that  the  line  of  resultant  pressure  (dotted)  through 
the  arch  ring  approaches  the  upper  edge  on  the  more  heavily  loaded  half, 
and  the  lower  edge  on  the  less  heavily  loaded  half,  indicating  a  tendency  to 
cause  tension  in  joints  at  /,  which  must  be  guarded  against,  as  well  as  undue 
oompresskm  at  c.  The  thrust  T  at  crown  will  not  be  horizontal  but  will 
iacUoe  upward  to  the  right  because  of  the  heavier  loading  on  that  side. 


Fig.  10. 


768  U.—ARCHBS. 

producing  positive  vertical  shear  V  at  crown.  The  horinmtal  component  H  d 
thrust  T  is,  H^s/'H—  V^=»hori«>ntal  component  of  Ri  or  of  R^  also. 

Inclingd  Loading. — ^The  loading  at  the  crown  may  always  be  assumed 
as  vertical;  also  at  the  haunches  if  the  spandril  filling  is  of  rough  masonry, 
or  of  earth  or  clay  well  tamped  and  kept  thoroughlv  drained.  But  if  the 
filling  is  of  loose  earth,  sand  or  gravel,  and  especially  if  liable  to  become 
saturated  with  rain,  from  poor  drainage,  the  material  will  have  a  tendency 
to  slide  along  a  low  angle  of  repose,  with  resultant  inclined  loading  at  the 
haunches,  as  FFF,  Pig.  10.  Such  inclined  loading  will  produce  a  different 
line  of  resultant  pressure  in  the  arch  ring  than  will  vertical  loading. 

Three-tfiofed  Masonry  Arch. — (The  following  theories  are  approximate 
only.)  The  three  hinges,  a  f  k  (Fig.  11),  placed 
at  crown  and  at  springing,  are  necessarilv  pomts  of 
zero  moment  and  hence  the  line  of  resultant  pres- 
sure must  pass  through  those  points.  The  method 
of  procedure  is  as  follows:  Divide  the  arch  ring  into 
imaginary  voussoirs  with  radial  joints.  Prom  the 
upper  extremities  of  these  joints  draw  vertical  lines 
up  to  the  loading  contour  L.  C,  Find  the  area  and  j^ 
the  center  of  gravity  of  each  of  these  figures,  bounded 
by  full  lines,  between  the  L.  C.  and  the  soffit  of  arch.  Fig.  11. 

Then  the  area  multiplied  by  the  weight  of  the  masonry 
per  cu.  ft.  will  give  the  vertical  loads  P|,  P2.  Pa,  etc.,  passing 
through  the  centers  of  gravity  of  the  figures.    The  reactions 
/?i  and /?2iaswell  as  their  horizontal  and  vertical  compo- 
nents, may  be  found  graphically  (see  Pig.  17,  Sec.  16.  page 
315)  by  treating  each  load  separatelv  or  bv  using  one  or 
more  resultant  Toads.    With  H,  V. ,  V2,  and  the  loads  Pi. 
P2.  etc.  J  the  force  polygon  (Fig.  12)  may  be  constructed,  and 
the  tqutlibrium  polygon  shown   in   Fig.  11  may  bo   drawn; 
thus,  draw  Ri  through  a,  parallel  to  Ri  of  the   force   poly- 
gon, to  meet  Pi  produced;   from   this   intersection  draw  1'       Pig.  12. 
parallel  to   1  to  meet  Pa  produced,  etc.    If  the  work  is  done  carefully 
the  equilibrixun  polygon  will  pass  through  the  hinges  /  and  k.     See  alM 
Pig.  14. 

The  Line  of  Resistance  or  line  of  resultant  pressure  (not  shown  in  Pig.  11^ 
may  be  drawn  by  connecting  the  points  a  b  c  d — f — k 
where  the  chords  of  the  equilibrium  polygon,  as  shown,  in- 
tersect the  masonry  joints.  But  it  must  be  remembered 
that  if,  in  the  equilibnum  polygon,  any  point  as  p  due  to  a 
load  as  P'  falls  outside  the  area  from  which  the  loading  is 
derived,  then  the  chords  of  the  equilibrium  polygon  must 
be  produced  to  meet  the  joint  and  ^ive  position  to  points 
on  the  line  of  r&istance.  Thus,  in  Pig.  13  the  line  of  resistance 
will  pass  through  l/c  instead  01  through  be.  Fig.  IS. 

It  is  to  be  noted  that  the  pressure  at  each  of  the  joints  may  be  obtained 
by  scaling  the  rays  of  the  force  polygon^  using  the  proper  scale;  thus,  tW 
pressure  at  c,  intersected  by  2*  (Fig.  11),  is  obtained  by  scaling  ray  2;  a,  bj 
scaling  ray  3;  /,  by  scaling  ray  6.  The  force  polygon  also  gives  the  verticd 
shear  V^  at  crown.  As  the  loading  is  all  vertical  the  value  of  H  (horiiontaJ 
thrust)  is  constant  throughout  the  arch. 

Three-hinged  masonry  arches  are  usually  constructed  of  concrete  of 
reinforced  concrete.  The  hinges,  at  crown  and  springing,  usually  consist  o^ 
steel  shoes  with  pin  bearing;  sometimes  lead  sheets  are  used.  1 

The  Criterion  of  Stability  of  a  masonry  arch  is  whether  the  tme  Une  d 
resistance  for  any  case  of  assumed  loading  lies  wholly  within  the  middU 
third.  If  it  does,  the  arch  is  stable  for  that  loading.  Now,  while- we  can 
draw  practically  a  true  line  of  resistance  for  an  arch  with  three  hinge' 
(Pig.  11),  it  is  impossible  to  draw  a  true  line  of  resistance  for  an  ordinal 
arch  with  no  hinges,  and  in  order  to  determine  its  stability  we  have  to  main 
certain  assumptions. 

Ordinary  Masonry  Arch — ^No  Hinges. — ^Dr.  Winklers'  theory  for  the  Kn^ 
?i  '^^^.'^^oce  of  an  arch  is  as  follows:  "For  an  arch  of  constant  cross-sectioaj 
that  hne  of  resistance  is  approximately  the  true  one  which  lies  nearest  to  tW 


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770 


iA.^ARCHES. 


the  selected  middle  portion  of  the  arch  ring  the  arch  is  considered  stab\ev 
if  not,  select  three  points  again  until,  by  repeated  trial,  it  is  determinea 
whether  or  not  the  arch  is  stable,  as  explained  for  Fig.  14.  Two  methods  will 
be  shown  for  drawing  the  equilbrium  polygon,  from  which  the  line  of  resist- 
ance is  detennined. 

First  Method. — ^Time  will  be  saved  by  a  proper  selection  of  points  to  be 
assumed  for  the  hinges.  In  Fig.  16  where  the  heavier  loading  is  on  the  right 
half  of  span  the  hinge  c  on  that  end  is  assumed  at  the  inner  edge  of  the 
middle  portion;  on  the  left  end,  carr3ring  the  lighter  load, 
the  hinge  a  is  assumed  at  the  Outer  edge  of  the  middle 
portion;  while  at  center  of  span  the  hinge  b  is  assumed  at 
the  middle  of  the  vertical  joint.  Draw  the  equilibrium 
polygon  passing  through  those  points,  a  b  c,  treating  the 
arcn  as  3-hinged,  as  explained  for  Pig.  11.  Examine  for  sta- 
bility. 

Second  Method. — Select  the  hinges  as  above  (Fig.  18). 
Lay  off  the  load  line  in  the  force  polygon.  Pig.  17.  Choose 
any  pole  as  O,  and  draw  the  rays  (dotted)  of  the  force  poly- 
gon. Construct  the  equilibrium  polygon  (dotted)  in  Fig.  lo,  be- 
ginning at  c  and  ending  at  of.  Draw  the  trial  closing  line  a'c. 
Draw  OM  (Pig.  17)  parallel  to  </c  to  meet  the  load  line  at  M. 


Fig.  17. 


From  3/ 

draw  MOi  parallel  to  the  true  closing  line  ca.    Make  the  distance  MOi «  k^  . 

in  which  Ar«»the  horizontal  distance  to  the  load  line.  Tben  will  point  0%  be 
the  true  pole  of  the  force  polygon.  Draw  the  rays  (full)  from  Oi,  and  cor.- 
struct  the  equilibrixun  polygon  (full)  in  Pig.  16,  peginnine  at  c.  It  will  be 
found  that  the  chords  will  pass  through  the  hinges  b  and  a.  Examine  for 
stability.     If  unstable  select  new  points  for  hinges,  and  proceed  as  before. 

The  "middle  third"  of  the  arch  ring  is  usually  selected  as  the  "middle 
portion"  within  which  to  draw  the  line  of  resistance  because,  theoretically, 
when  the  line  of  resistance  passes  within  the  middle  third  there  can  be  no 
tension  in  any  part  of  the  masonry,  nor  opening  of  any  of  the  joints.  If  the 
arch  ring  is  stiffened  greatly  by  solid  spandril  walls  the  criterion  of  stability 
may  not  require  that  the  line  of  resistance  be  confined  within  the  middfe 
third,  but,  say,  within  the  middle  half. 

The  cases  of  loading  for  an  arch  are:  (1)  dead  load  only;  (2)  full  load, 
including  live  load  over  whole  span;  (3)  including  liVe  load  over  one-halt 
of  span;  (4)  including  live  load  in  any  position;  (5)  including  concentrateci 
loads.  It  must  not  be  presumed  however  that  for  all  these  cases  of  loading 
it  is  necessary  to  assume  the  hinges  in  any  one  fixed  position. 

Ceaters  for  Arches. 

Definition. — ^An  arch  center  is  a  framework  for  supportins  an  btA 
during  construction,  and  hence  of  temporary  character,  it  is  so  designra 
that  it  can  be  removed  readily  after  the  completion  of  the  arch;  and  in  the 
removal  it  has  to  be  lowered  somewhat  in  order  to  give  sufficient  cleannct 
at  the  soffit  of  the  arch,  as  the  latter  settles  and  becomes  se]f-supportii%. 

Parts  of  the  Arch  (Center. — Pig.  18  shows  two  half -sections  of  ard] 
centers  with  an  end  view  of  one  of  the  frames.    One  half -section  illustrate; 


Fig.  18. 
the  unbraced  rtbwhich  supports  the  sheeting  or  lagging  on  which  the  arj 
stones  are  laid.   The  other  half-section  is  a  trussed  frame,  sxiitablc  for  lonj 


CENTERS  FOR  MASONRY  ARCHES,  771 

spans.  When  troand,  the  rib  is  called  the  bach  pUc9.  The  truss  shown  in  Pig. 
18  is  the  King  post,  the  inclined  bracts  transmitting  the  stresses  from  the 
haunches  directly  to  the  vertical  post,  and  then  down  the  inclined  struts 
to  ends  of  span.  Various  forms  of  trusses  are  used  for  the  frames,  depend- 
ing upon  length  of  span.  rise.  etc.  The  frames  are  placed  perpendicular  to 
the  axis,  spaced  in  parallel  planes,  and  supported  by  wedgts  which  are 
**  5tnick  "  when  the  center  is  removed.  Instead  of  the  wedges,  jacks  or 
softd  cylinders  can  be  used  for  this  purpose. 

Loads. — ^The  loads  which  an  arch  center  has  to  support  are: 
Live  loads,  including  (1)  The  percentage  of  weight  of  placed  masonry 
supported,  in  different  sections  of  the  arch;  (2)  Same  with  regard  to  un- 
pla<»d  masonry  and  other  materials,  machines,  derricks,  men,  etc.;  (9) 
Impcurt  due  to  handling  material  during  construction  of  arch. 

Dtad  loads,   comprising  weight   of   center  itself,   including   sheeting, 
frames,  trestlinig.  etc. 

Calcolatioa  of  live  loads. — ^Three  cases  will  be  considered,  as  noted  above: 

fl)  Masonry  in  place. — In  Fi^.  19  let  the  ""^ 

ihaaed  portion  show  the  voussoir  V  or  sec-  ^'^^i^              ^  — " 

tion  of  masonry  whose  weight  is  W.    Then:  i^^!^^J^' 

(a)  If  we  assume   V  as  merely  resting  '*J|%'  ^^^I^Sk;^''*'* 
withimi  friction  on  the  joint   J   and  on  the  y^^S^ 
back   of  the  arch    center,  we   have,  letting  /^%sL^3l^  i? 
$  equal  the  angle  of  inclination  of  the  nor-  /     7^^  .\  S 
mal  pressure  Wm  with  the  horizontal,  /    /     ^  ^    \ 
IF.-Wsin^ (1)  //       '5S^ 

"isuid  the  vertical  and  horizontal  components    rW5*         ^'H*'* 
of  W^  are  W^^W  sin«  B,  and  W  «iv  sin  ^   /     L 

cos  i?,  respectively.    H^»(-Wco8  &)   is   the   " — ^- — -V""*ro*" 

tangential  thrust.     It  is  worthy  of  note  that  *^*8.  *»• 

the  normal  pressure  TT,  of  equation  (1)  would  equal  W  for  any  voussoir 
at  the  crown  c,  and  tero  for  any  voussoir  at  the  hor.  springing  s.  Authori- 
ties differ,  however,  as  to  the  value  of  the  equation  for  sections  between 
these  two  points,  on  account  of  the  unknown  effects  of  friction,  which 
latter  would  tend  to  reduce  the  value  of  H^.. 

(b)  If  we  assume  the  voussoir  V  as  hinged  at  o.  then,  by  taking  moments, 

W.k-'W/.d,  or  W.'-W-j (2) 

Now  W/  of  equation  (2J  will  equal  Wm  of  equation  (1)  only  when  the 
voussoir  V  is  extremely  thin,  practically  a  plate,  and  when  its  intrados  is  a 
straight  line  instead  of  a  curve  as  shown  m  Pig.  19.  Otherwise  its  value 
wUl  be  less  than  Wm  of  equation  (1). 

(c)  If  we  assume  friction  at  the  joint  J  we  have,  calling  a  the  angle 
w^hich  the  joint  makes  with  the  horizontal,  and  0  the  angle  of  repose  of  the 
masonry. 

Normal  pressure   W/ "W,  —W  tan  0  cos  a,  nearly (3) 

or  H^.'- W^.'-PV  tan  5  cos  a.  nearly (4) 

in  which  tan  6  may  vary  from  0 .  50  to  0.66;  that  is,  the  angle  of  repose  6 
may  vary  between,  say,  27*  to  33°.  The  problem  becomes  more  difficult 
if  we  attempt  to  include  the  friction  of  the  soffit  of  V  on  the  back  of  the 
ardi  center. 

(2)  Unplaced  ntasonry,  machines,  etc. — ^These  would  tend  to  increase 
the  stresses  and  must  be  allowed  for  liberally,  especially  over  the  haunches 
where  the  stresses  are  particularly  indeterminate. 

(3)  Impact. — ^The  arootmt  of  impact  would  depend  largely  on  the  size 
of  the  stones  used;  it  can  be  taken  into  account  in  a  general  way,  if  small, 
by  the  "  factor  of  safety  *'  adopted. 

Practical  f omnia  for  live  loads. — Let  TV  =»  weight  of  section  or  voussoir 
V  (Pig-  19).  Wm  — normal  pressure  due  to  W;  and  i9  — angle  of  W\n  with  the 
Jiorizontal.     Then  r^^^^T^ 

IVk - H'  sin»  $     .D^iied  by. V?QOg LC . . (5) 


772 


44.— ARCHES. 


3. — ^Valubb  op  Wm  for  Succbssivb  Valubs  op  $. 
From  i9—  90*  (at  crown)  to  ^  «=•()**.  Equation  (6). 


Normal 

Normal 

Normal 

Normal 

Angle 

Pressure 

Angle 

Prcsstire 

Angle 

Pressure 

Angle 

PreGSuiv 

fi. 

Wn. 

fi. 

Wk. 

0. 

Wh. 

0- 

Wn. 

9a» 

1.000  W 

70» 

0.830  W 

60* 

0.460  W 

30* 

0.126  W 

88* 

.998  •• 

68* 

.797  •• 

48* 

.410  " 

28* 

.108  " 

86* 

.993  " 

oe* 

.762  " 

46* 

.372  " 

26* 

.084  " 

84- 

.984  " 

640 

.726  •• 

44* 

.836  " 

24* 

.067  •• 

82* 

.970  " 

62** 

.688  " 

42* 

.300  •• 

22* 

.068  " 

80» 

.966  •• 

60* 

.660  " 

40* 

.266  •• 

20* 

.040  •• 

78« 

.986  " 

68* 

.610  •• 

88* 

.233  •• 

15* 

.017  •• 

76«» 

.914  •• 

66* 

.670  " 

36* 

.203  " 

10* 

.006  " 

740 

.888  " 

64* 

.630  '• 

34* 

.176  •• 

6* 

.001  •• 

7r 

.860  " 

62* 

.489  •• 

32** 

.149  •• 

0* 

.000  " 

Us0  of  Table:  Example. — A  section  of  arch  masonry  weighing  20  tons 
is  supported  radially  by  a  brace  of  the  arch  center  acting  normal  to  the  in- 
trados  and  making  an  angle  fi^5(f*  with  the  horizontal.  Find  the  oom- 
pressive  stress  on  the  brace  due  to  this  load? 

Solution:  Wk  for  ^-60*  is  0.46  H^-9  tons.     Ans. 

Types  of  arch  coitcrs. — Pig.  20  illtistrates  the  most  simple  form  of 
centmng,  that  for  a  flat-soffit  arch.  The  illustration  is  that  of  a  Flat 
Arch  of  the  recessed   type.    They  axe  built  up  to  8  or  10  ft.  in  span. 


^ 


Fig.  20. 


Fig.  21. 


The   caps   supporting   the 
are  in  turn  supported  by 


lagging   rest   on  longitudinal  stringers,  whkh 
y  posts.    Note  the  economy  of  material  in  U 
by  increasing  the  depth  of  strips  at  the  expense  of  width. 


posts.    Note  the  economy  of  material  in  i^^ggmg 
,  strips  at  the  expense  of  width.     The  stxnogtA 

is  proportional  to  width  and  to  (depth)'. 

Fig.  21  is  the  standard  segmental  arch  used  over  doors  and  windows. 
The  '  back  "  of  the  center  consists  of  templates  of  thick  boards  cleated 
together.  The  lagging  is  spaced  closer  together  if  the  arch  is  of  bride. 
Note  that  the  points  0  a  a  form  an  equilateral  triangle  in  both  Figs.  20 
and  21. 

Pig.  22  shows  the  make-up  of  braced  or  unbraced  wooden  rib  as  illus- 
trated in  Fig.  18.  The  segmental  pieces  are 
sawed  from  plank  and  (nailed  or)  bolted  together 
into  two  or  more  leaves  cu:cording  to  the  strength 
desired.  The  ribs  should,  preferably,  be  braced, 
althovigh  unbraced  ribs  have  been   used  up   to  «.       ^ 

60  or  60  ft.  spans.  F«-   22. 

Fig.  23  represents  the  leaves  of  the  rib  laid   llat-wiae  instead   of  vei^ 
tical  as  in  the  preceding  case.     This  type  is  the  same  as  that    used  ia 
chords    of    ordinary    wooden    bowstring     truss 
bndses. 

f    ^3^  ^^  tteel  ribs  are  sometimes  used  instead 
ot  wooden  ribs   in    cases  where   great   strength 
jnd  stiffness    are    required.     I-beams    are    the       r^___i^ 
oest  lor  this  purpose.  Digitized  by  V^OOgtg.    23, 


CENTERING  FOR  MASONRY  ARCHES, 


773 


Pig.  34  iUttstrates  a  supported  trussed  frame,  mainly  of  the  Warren 
type.  The  left  half-section  is  shown  supported  by  vertical  posts.  The 
nc^t  half -section  is  shown  supported  by  inclined  posts,  which  system  is 


Pig.  24. 


Fig.  26. 


sometimes  adopted  for  economy,  as  in  the  case  of  swift  currents  or  ice. 
The  same  type  may  also  be  used  without  interior  supports.  In  fact  the 
end  supports  may  also  be  omitted  by  allowing  the  ends  of  frames  to  rest 
on  projections  or  in  (artificial)  recesses  of  the  abutments. 

Pig.  25  is  a  skeleton  outline  of  center  used  in  the  erection  of  60-ft.  arch 
ol  Washington  bridge.*  New  York  City.  The  sand  cylinders  s,  are  used 
instead  of  wedges  or  jacks  for  lowering  the  center  after  the  arch  is  completed. 
They  consist  of  12-in.  plate-iron  cyhnders  filled  with  sand  on  which  rests 
the  plunger,  which  forms  a  support  to  the  centering  above.  By  manipu- 
lating a  plug  at  the  bottom  of  the  cylinder  the  outfiow  of  sand  is  regulated 
and  consequently  the  lowering  of  the  center.  In  using  sand  cylinders 
under  centers,  care  must  be  used  to  keep  the  sand  perfectly  dry.  They 
have  met  witn  varying  success. 

In  Table  6,  next  to  last  column,  reference  is  made  to  the  files  of  Eng. 
News,  by  date^  of  descriptions  of  some  recently  constructed  arches.  Many 
of  these  descriptions  embody  the  designs  of  the  centers  quite  as  much  as 
of  the  masonry. 

Strikiog  the  center. — ^This  consists  in  lowering  the  center  for  removal 
after  the  masonry  arch  is  completed,  either  by  striking  the  wedges,  operating 
the  ja|ck8  or  mampulating  the  sand-boxes  to  relieve  the  pressure  at  the  soffit. 

The  time  when  this  should  be  done  will  depend  upon  the  length  of  span; 
size  and  kind  of  voussoirs,  whether  bnck  or  stone;  character  of  bond;  char- 
acter and  thidcness  of  joint;  quality  of  mortar,  etc.  For  instance,  there 
could  be  little  objection  to  striking  the  center  almost  immediately  of  a  first- 
class  stone  arch  bridge  of  moderate  span  with  large  voussoirs.  well  bonded, 
with  close-fitting  joints.  On  the  otoer  hand,  it  would  be  unwise  to  do  so 
in  the  case  of  a  brick  arch  of  long  span,  small  rise,  thick  joints,  and  bricks 
poorly  bonded,  as  considerable  unnealthy  deformation  might  take  place. 
Again,  in  the  case  of  arches  in  building  walls,  considerable  time  uiould 
elapse  before  the  centers  are  removed,  at  least  until  the  bricklaying  above 
the  arch  is  beyond  its  sphere  of  influence  in  causing  additional  weight  or 
preastire.  Three  or  four  months  is  the  outer  Kmit  for  any  case,  as  that  gives 
ample  time  for  hardening  of  the  mortar.  The  presence  of  the  centering 
need  in  no  way  interfere  with  the  traffic  over  the  structure. 

Camber  of  center. — In  layini;  out  and  erecting  the  center  of  an  arch,  it 
is  snnetim^  advisable  to  give  the  frames  a  slight  camber,  amounting,  at 
the  crown,  to  about  ^  or  J  per  cent,  of  the  radius  of  the  intrados.  Of 
course  the  object  of  this  camber  is  to  provide  for  all  settlement  so  that  the 
intrados  of  the  finished  masonry  structure  shall  be  the  true  curve  as  de- 
signed, and  on  which  the  calculations  of  the  structure  are  based. 

The  total  camber  to  be  provided  for  will  equal  (1)  the  deflection  of 
frame  due  to  its  own  dead  weight;  (2)  the  deflection  due  to  weight  of  masonry 
of  completed  arch;  (3)  settlement  when  center  is  removed;  (4)  further 
settlement  due  to  superimposed  loads  on  arch. 

If  the  center  is  rijfidly  constructed,  the  arch  stones  well  laid  with  close 
joisxts,  and  the  arch  itself  not  of  the  pronoimced  "  flat  "  tyi>e,  very  little, 
Sany.  camber  is  required. 


*  Wm.  R.  Button,  chief  engineer. 


d  by  Google 


774  U,— ARCHES, 

TabiM  of  ArchM. 

Table  5.  following,  is  a  list  of  some  notable  arches  that  have  been  boih. 
with  principal  dimensions  and  important  remarks. 

Table  6  comprises  some  typical  modem  arches.  Reference  is  giyrcn  tc 
the  files  of  Engineering  News,  where  fuller  descriptions  are  given. 

5. — SoMB  Notable  Archbs  tbat  Havb  Bbbn  Built. 

Note. — ^/?i5  — rise;  i^od  — radius  at  crown;  Cf- thickness  of  ring  at 
crown;  5p<»  thickness  at  springing;  all  dimensions  in  feet  and  decimals. 
Rein.-conc.  "^reintoTced  concrete;  3-c^m. -•  3-ccntcred,  etc. 

No.  Span.   (Dimensions.)  Name  and  "Kind."  [En^neerand        Remarks. 
Location.  Date.] 

1*  296.27  (Ris-60±,  Rad-344.48.  Cr-4.92,  Sp- 11.16).  Platen. 
Saxony.  "  Stone;  3-cen."  [1905.]  Flattest  stone  arch  ever 
built,  and  longest  span.  Solid  arch  (without  hinges).  Arched 
abutments  rise  from  solid  rock  foundation  so  that  static 
(elastic)  arch  proper  has  span  of  213.2  and  rise  of  21.2ft, 
Live  loads:  (1)  A  16-ton  vehicle  9 .84  ft.  bet.  axles  and  a  unif. 
load  of  114.6  lbs.  per  sq.  ft.:  (2)  8  steel  rollers  total  weight 
26.16  tons  and  a  unif.  load  ot  114.6  lbs.  per  sq.  ft.  Cak'd 
prcssyre,  including  temp.,  was  981.4  lbs.  per  sq.  in.  on  top 
edges  of  joints  at  crown,  and  746.1  lbs.  on  lower  edges  of 
joints.  Max.  pres.  on  foundations  366.6  lbs.  per  sq.  in.,  the 
foundation  rock  having  crashing  strength  of  23760  lbs.  per  sq. 
in.  Mortar  for  foundations,  1  Portland  cement  to  4  sand- 
for  main  and  secondary  arch,  1  Port.  cem.  to  3  sand 
Large  spandrel  openings. 

2*  276.6  (Ris=100±.  Rad=  .  Cr=  .  Sp-  ).  Luxemburg. 
••  Stone,       -ccn."     [1901.] 

3       261.  (Ris-88,    Rad-133,    Cr-4).     Trezeo,    over    Adda,    Italy. 

'^Granite;    circ."     [Built,  1380;  destroyed  intentionally,  1420 

4*  233.  (Ris-70.26.  Rad-118.76.  Cr-6.5,  Sp-9.6).  WaJnvt 
Lane,  Phila.  "ODncrete,  3-centered."  [Webster,  1907] 
Twin  arch  rings.  Spandrel  arches;  and  arch  approaches. 
Actual  deflection  on  removing  centers  was  f$  in.  at  crown  and 
1-32  in.  at  quarter  points,  the  calculated  deflection  at  cro^ti 
being  f,  the  difference  being  accounted  for  partly  to  rise  in 
temp. 

6  220.  (Ris-57,  Rad-134,  Cr-4. 2+4,  Sp-6-H6).  Cabin  John, 
Washington,  D.  C,  aqueduct.  "  Stone,  circ."  (Meigs,  1853- 
9.]  The  voussoirs  of  the  arch  ring  are  of  Qumcy  granite 
making  depth  at  crown  4.2  ft.,  and  thickness  at  springmc 
6  ft.  The  spandrel  filling  of  sandstone  is  laid  partly  with 
radial  joints  so  as  to  increase  effective  depth  of  rin^  to  8 . 2  ft. 
at  crown  and  21  ft.  at  springing.  The  arch  carries  a  20-ft. 
roadway  and  a  9-ft.  conduit. 

6  213.  (Ris  =  59.6,  Cr- 6.9.  Sp- 10.2).  Jaremcne,  Axxstiia,.  -Circ." 
[1892.]     Spandrel  openmgs.     Railroad. 

7*  211.6  (Ris-87.6.  Rad-89.26,  Cr-4. 33,  Sp-6.6).  Kempten, 
Bavaria.  "  Concrete;  ba^et-handle."  [1907.]  4-track  rail- 
road.    Twin  arch  rings. 

8*     210.         jrRis-52.5).     Gutach  Riv.,   Bavaria.     "Stone."     [1906?] 
Spandrel  walls.     Railroad. 

9*     209.9       (Cr-3.4).     Bogenhausen,  over  Tsar  JL,  BavBiUi.     "Stone." 
[1902.]     3-hinged  arch,  21.4  ft.  rise.     Highway. 

10     200.         (Ris-42.     Rad  =  140,     Cr-4. 6,     Sp-7).     Grosvenor,    over 
Dee,  Chester,  Eng.     "  Circular."    [Hartley,  1833.] 

*  Described  also  in  Table  6.  Digitized  by  CiOOglc 


MASONRY  ARCHES  ERECTED.  77fi 

&. — SoiCB  NoTABLB  AitCHBs  THAT  Havb  Bbbn  Built. — Continued. 

No.  Span.   (Dimenskmt.)  Name  and  "  Kind.'*  [En^mieer  and       Remarks. 
Location.  Date.] 

11     1M.8      (Ris-52.8.     Cr-5.6.     Sp-13.8).    G<mr     Noir,     France. 

"  Circular."    [Draux.  1888.J     Railroad. 
13*   187.6      (Ris-82.2).     Lauirach,   over   Bier.    Bavaria.     "Concrete." 

[1907.1 
18*  187.         (Ri8-65.8.   Cr-6.68,   Sp-9.18).    SdtwaendtrhoU,   on   N. 

&  D.  Ry      "  Stone.''     Railroad. 

14  181.         (Ris-90.6.  Rad-90.  Cr-4.6.  Sp-«).    BallochmyU,  Ayre. 

Scotland.     "Circular."    [Miller.]     Railroad. 

15  164.         (Ris-16.4,  Cr-3.3.  Sp-3.6).     Mundtrkingtn,  over  Dan- 

ube.    "  Circular."     [Bois.  1893.]     Hinged  arch.     Railroad. 
1«»   164.         fRia-16.76.    Cr-1.77,    Sp-2.98).     ChattelUrauU,   France. 
Reinforced  concrete."     [1902-.]     Four  arched  ribs.     Hen- 
nebique  system.     Highway. 

17  159.         (Ris-28.  Cr-4.6.  Sp-6).     Whtfling,  W.  Vti.    "Circular." 

[Hogue  and  White.  1891] 

18  163.         (Ri8-87.     Rad-162.     Cr-4.9.     Sp-10).     London,     over 

Thames.  Eng.     "EUip."     [Rennie.  1831.]     6  spans. 

19  160.         (Ris-36.    Rad-98.     Cr-4.6).    GlouctsUr^    over    Severn, 

Eng.     "Ellip."    fTelford.l 

20  160.         (Ris-27,  Cr-3.8,  So -4. 6).     Elyria,  Ohio.     "Sandstone; 

circ."    [Kinney.  1886.]     Highway. 

21  148.         (Ris-18,    Rad-160.    Cr-4.92).     Turin,    Italy.    "Circu- 

lar."   [Mosca.] 

22  144.         (Ris-19.3.  Cr-4.2).     P«<mfy.  over  Thames.  Eng.    [Bazal- 

zette.  1886.)     4  other  spans. 
23*   143.87     (Ris- 19.03.     Cr-4.10.     Sp-4.78).     Orisons,     over     the 

Loire.    France.     "  Stone;    catcnoid."     [Rencudier,    1906.] 

Highway.     70  spans. 
24     141.         (Ris-28.     Rad-103.     Cr-4.92).    Alma,    Paris.     "Small. 

cement  rubble;  ellip."     [Darcel.]     Railroad. 

26  140.         (Ris-36.  Rad-88.Cr-l. 5+1,  Sp-2.6  +  ).     Pont-y-Prydd, 

over  TaflF,  So.  Wales.  "Rough  rubble  in  lime  mortar; 
circular."  [Built  bv  a  stone  mason  in  1760.  to  replace  a 
former  bridge  of  the  same  general  design  which  fell  on 
striking  centers:  present  bndf^e.  however,  has  spandrel 
openings  which  former  bridge  did  not.] 
26*  140.  (Ris- 30.  Cr-6+2).  ///.  C€fU,  R.  R„  over  Big  Muddy. 
"  Concrete;  ellip.**     [1903.1 

27  131.2       (Ris-18.2,Cr-3,Sp-3).     Couhuvrtnurt,Fnnce.     'Circ." 

[Bois.  1896.] 

28  128.2       (Ris-32.     Cr-6.1).     Neuilly,     Seine,     France.      'EUip." 

[Perronet.  1773.]     Arch  settled  2  ft.  on  removing  center, 
and  radius  at  crown  increased  from  160  to  about  260  ft. 

29  128.         (Ris-24.2,    Rad-169.    Cr-6.26.    Sp-7.2).     Maidenfuad, 

Eng.     "  Brick  in  cement;  Ellip,"  [Bnmel,  1837.]  Railroad. 

30*  126.  (Ris- 39.  Rad-67.75.  Cr-5.  Sp-7.67).  Piney  Branch. 
Wash..  D.  C.  "  (Concrete;  parabolic."  [Douglas  and 
Darwin.  1906.]     Highway. 

81  124.  (Ris-6.92.  Rad-281.  Cr=2.67,  Sp-3.60).  Experimental 
Arch  at  Souppes,  France — See  No.  32.  Cut  granite  in 
Portland  cement;  circular."  [Vaudrcy,  1866.|  Width, 
12  ft.  Ratio  span  to  rise,  17-83.  Centers  struck  m  4  mos. : 
deflection  1 1  ins.  Tested  without  injury  by  distributed  load 
of  about  600  lbs.  per  sq.  ft.;  also  by  weight  of  about  6  tons 
falling  18  ins.  on  key. 


*  Described  also  in  Table  6. 


d  by  Google 


77«  U.— ARCHES. 

6. — SoMB  NoTABLB  Arcrbs  THAT  Havb  Bbbn  Built. — Cootintied. 

No.  Span.  (Dimensions.)  Name  and  "  Kind."  [Biwineer  and       RemariEs. 
Location.  Date.] 

82  124.  (Ris-6.92.  Rad-281.  Cr-2.67.  Sp-3.60).  Bourbotmais, 
Prance.  "  Cut  granite;  circ."  [Vaudrey.J  Very  boW: 
built  after  experiment  at  Souppes,  preceding.     Railroad. 

33  120.  (Ris-31.  Rad-112,  Cr-4.6.  Sp-8.)  Waterloo,  over 
Thames,  London.  "  Granite;  ellip."  [Rennie.  1816.] 
8  other  spans. 

34*  120.  (Ris=12.  Cr-2.33).  Jacagnas  Riv.,  Porto  Rico.  "Rein- 
concrete."  [Thacher,  1901.J  Highway.  Two  other  spans, 
each  100  ft. 

35  118.         (Ris«>38,   Rad-d5.  Cr-3.6.   Sp-3.6).     Tongmland,   over 

Dee,  Eng.     "  Circular."     [Telford.  1801. J     Highway. 

36  116.         (Ris-21.2,   Cr-3,5.   Sp-4).     Cnsheim,   Fairmount    Park, 

Phila.     ''Sandstone;    circ."     fWebster.     1893.J     Sewer. 

37  110.         (Ris-14.8.   Rad-120,   Cr-4).     Napoleon,   Paris.     "  SmaU 

rough  rubble  in  cement;  circ."     [C^uche.]     Railroad. 
38*   112.         (Ris-17.7,    Cr-2.46,    Sp-.2.79).     Miltonburg,    over    the 
Main,      Germany.       "  Concrete."      [Fleiflchman,       1899.) 
Highway.     6  other  spans. 

39  100.         (Ris-25,  Cr-4,  Sp-4).     Etkerow  Riv.,  Eng.     "Circular." 

[Haskoll.]     Railroad.     3  other  spans. 

40  100.         (Ris-22.     Cr-1.83,     Sp-1.83.)     Bishop'-Aukland,      Eng. 

"  Circular."     [1888.1     Highway. 

41  100.         (Ris-15,    Cr-3,    Sp-7).     Wellington,    over    Aire.    Leeds. 

Eng.     [Rennie,  1819.] 

42  90.         (Ris»30,   Rad-49.  Cr-3).     Dean,  near  Edinburgh.   Soot. 

"  Circular."     [Telford.]     Highway. 

43  90.         (Ris-15,  Rad-75,  Cr-2.83).     Licking  Aqueduct,  Ches.  ft 

O.  Canal.     "  Circular."     [Fisk.J 

44  84.         (Ris-27.9.     Cr-3.     Sp-4).     Elkader,     la.     "Limestone: 

circ."     [Tschirgi,  1888.J     One  other  span. 

45  83 .         (Ris  - 1 1 .  75,  Cr  -  4 . 6) .     Over  the  Ois0,  France.     "  Circular." 

Railroad. 

46  81.         (Ris- 28,  Cr-4, 5).     Tri/^w/.  France.     "Ellip."     Railroad. 

47  80.         (Ris-40.  Rad-40.  Cr-3.  Sp-3.50).     Conemaugk  Viaduct, 

Penn.  R.  R.     "Sandstone  in  lime   without   sand;    circ." 

48  80.         (Ris-40,     Rad-40.     Cr-2  66).     Royal    Border     Viaduct, 

Eng.     "  Brick  in  cement;  circ.  * 
40       80.         (Ris  =16.   Rad-58.  Cr-4. 66).      Posen  Viaduct,  Gemuusy. 

"  Brick  in  cement;  circ." 
50*     80.         (Ris- 12.    Rad-88,   Cr-1.33).     Cliffy  Creek,   Greensbtirg. 

Ind.     "Rein. -con.;    5-cen."     [Luten,     1906.]    Highway. 

(Ris- 26. 3,  Cr-4).     Orleans,  France.     "Ellip."     Railix>ad. 

(Ris- 13.    Cr-3.5,    Sp-4.^.     Hutcheson,    Glasgow.    Scot. 

[Stephenson.] 
(Ris-U,     Rad-88.    Cr-1,5.     Sp-2.5).    Grand    Rapids. 

Mich.     "  Rein.-con.;     3-cen."     [Anderson.]     Highwav. 
(Ris-25,  Rad-43,  Cr-3).     Falls,  P.  St  R.  Ry.     "  Circ" 
(Ris- 38.    Rad  =  38.    Cr-7.6,    Sp-14).     W0Stminsl9r,    over 

Thames,  London.     "Circ."     [Labelye,  1747.J     12-i-2other 

spans. 

(Ris-15.  Cr-2  4.  Sp-2.4).     Albany  St,  New  Brunswick. 
N.  J.     *•  Brick  ring;  circ.''     [1893.J     Small  skew;  6  other 

•Described  also  in  Table  6.  Digitized  by  GoOglc 


51 

79. 

52 

79. 

58* 

79. 

54 

78. 

55 

76. 

60 

76. 

MASONRY  ARCHES  ERECTED.  777 

6. — SoMB  NoTABLB  Archbs  THAT  Have  Bebn  Built. — Concluded. 


i 


67 

76. 

58 

72. 

69* 

70. 

00 

70. 

61 

70 

62 

70 

63 

65. 

64 

65. 

65 

64. 

No.  Span.   (Dimensions.)  Name  and  "  Kind."  [Engineer  and        Remarks. 
Location.  Date.] 

(Ris-11.5.    Cr-2.5.     Sp-3).     AUenUmn,    Eng.     "  Circ." 

[Stephenson.]     Highway. 
(Ria-16.6,    Rad-47.    Cr-2.75.    Sp-2.75).     Black    Rock 

Tuntul  Br.,  P.  &  R.  Ry.     "  Circular."     [Robinson.] 
(Ris- 19.76,   Cr-8,   Sp-3).     Rockvilk   Br.,    Penn.    R.    R 

"Stone;  circ."     [Brown,  1901.]     47  other  spans. 
(Ris-25,   Cr-8.5,   Sp-3. 6).        Swatara,   P.   &   R.   Ry. 

"  Brick;  drc."     [Osbom.] 
(Ris-17.6.  Rad-44,  Cr-3).     Brm/ Viaduct.  Eng.     "Brick 

in  cement;    ellip."     [Bnmel.    1837.]      Railroad.     7    other 

spans. 
(Ris- 17.5.  Cr-2  +  .6).     TFW/riilO'.  Limerick.      "Ellip."     4 

other  spans. 
(Ris- 13.8.    Rad-47.    Cr-2.5).     Bow,    over    Lea.     Eng. 

"  Granite;  ellip."     [Walker.  1887.]     Highway. 
(Ris- 82.5.    Cr-2.75.    Sp-2.75).     Haugkton    Riv.,    Eng. 

"  Circular."     [Haskoll.]     Railroad. 
(Ris- 16.5,  Rad- 39.28.  Cr-3,  Sp-3).     Watcriown,  Wis., 

C.  M.  &  St.  P.  R.  R.     "  Stone;  circular."     [Loweth,  1903.1 

Double  track;  3  other  spans. 
66        60.  (Ris -80,    Cr-2.7,    Sp-2.7).     Cort4maugh    Viaduct.    Penn. 

R.  R.     "Stone;  circ."     [Brown,   1890.J     One  other  span; 

3  tracks,  on  curve. 
(Ris -20.  Rad -33.  Cr-2-2).     Btwdky,  Eng.     "Circular." 

[Telford.]     Highway. 
(Ris- 18.  Rad -84.  Cr-2.5).     Chestnut  St..  Phila.      '  Brick 

in  cement;*  circ."     [Kneass.] 
(Ris-8.5,  Rad-42.33.   Cr-1.75,   Sp-2.5).     Sandy  Hill, 

over  Hudson.     "  Rein.-conc;    circ.*      [Kasson.     1906.] 

Highway  &  Elec.  Ry. 
(Ris -29,    Rad -29,    Cr-2.5.    Sp-2.5).     Carrollton.    near 

Baltimore.     "  (Granite;  circ.       Railroad. 
(Ris- 17.  Rad- 33.  Cr-1.5).     Llanrwast.   Wales.     "Circ." 

[Jones,  1636.]    Highway. 
(Ris-28,  Rad-28,  Cr-3. 17.  Sp  =  3.17).     Raritan  Riv.;    P. 

R.  R-    "  Stone;  circ."     [Bowles.  1903] 
(Ris- 9.   Rad -45.   Cr-2.5).     Monacacy   Viaduct,   Ches.   & 

O.  C:anal.     "  Ellip."    [Fisk.] 
(Ris- 10.3,    Cr-2.75).      Stirling,    over    Fourth.      "Circ." 
(Ris- 3.8,  Cr-3. 16).  Nemours,  FTance.  "Circ."     [Perronet.] 
(Ris- 5.1,  Cr-3).     Abbatoir  St.,  Paris.     "Circ."     Railroad. 
(Ris- 15,  Rad -28. 3.  Cr-2).     Avon  Viaduct,  Eng.     "  Brick 

in  cement;  ellip."     [Vignoles.] 
(Ris -7.  Cr-2).     Filbert  St.,  Phila.;  Penn.  R.  R.     "  Brick  in 

lime  mortar;  circ." 
(Ris - 7,    Rad -47,    Cr-2+.67).     James    Riv.    Aqueduct, 

Va.     "Circ."     [Ellct.] 
(Ris—  3 . 83,  Cr—  3 .  83).  Pesmts,  France.   "  Circ."    [Bertrand.] 
(Ris  -6.1,  Cr  -  3) .     Conturette,  France.     ' '  Cfrc. " 
(Ris- 15,     Rad -21,     Cr-2).     Touoloway     Culvert,     under 

Ches.  &  O.  Canal.     "Rubble  in  cement;  circ."     [Fisk.] 


67 

60. 

68 

60. 

69 

60. 

70 

M. 

71 

68. 

72* 

66. 

73 

64. 

74 

63. 

75 

63. 

76 

63. 

77 

60. 

78 

60. 

79 

60. 

^F* 

46. 

F 

43. 

is 

40. 

•  Described  also  in  Table  6. 


d  by  Google 


778 


i^.— ARCHES. 


6. — Some  Typical — 
Note^ — The  next  to  the  last  column  in  table  makes  reference,  by 


1 

Name  and 
LocaUon. 

Mate- 
rial. 

Bridge 
Ft. 

One 
Arch 
Span. 

H.. 

Rad. 

at 

Crown 

Curve! 

of 
Intra- 

Thickness  at 

FOOB- 

da- 
you. 

d<w. 

Oown 

pp'rg. 

7 

Plauen  Arch  B., 
Plauen.  Saxony. 
Luxemburg  B. 
(VaUey   of   the 
Pretrusse.) 
Walnut  Lane  B.. 
Philadelphia. 

Stone 
Stone 

Oonc. 

492. 
585. 

295. 27:60. ± 
(213.2)  (21.2) 
275.6    i00.± 

233.       70'-3' 

344.48 

i^. 

4.92 

11.15 

(TDDC 

3 

118'-9' 

3-cen. 



5'-6' 

9'.e» 

oonc 

4 

Kempton    B.. 
Bavaria  (Across 
the  lUer  R.) 

Cone. 

2ir-6' 
(166) 

87.6 
(29) 

89.25 

Basket 
-h'ndle 

4'-4' 

6'-6' 
(6.1) 

Cone. 

6 

Outach  Rlv.  B. 
(On  Neustadt  & 
Donaeuschlngen 
Ry). 

Bogcnhausen  B.. 
Bavaria  (Across 
Isar  R.). 
Lantrach    B., 
Bavaria  (Across 
the  Iller  R.). 

B.    (On    Neus- 
tadt &  Donaeu- 
schinpen  Ry.). 
Chatellerault  B.. 
France. 

Orieans  B.. 
France    (Across 
the  Loire  R.). 
Illinois  Cent.  R. 
R.    B.    (Across 
BiR  Muddy  R.). 
PIncy  Branch 
B..  Washington. 
D.  a 

Jacasuas  R.  Br., 
Porto  Rico. 

Stone 

Stone 
Oonc. 
Stone. 

210. 

209.9 

187.5 
J  87. 

164. 

143.87 

(70 
spans) 
140. 

125. 

120. 
(3 
spans) 

52.5 

0 



3.4 

7 

32.2 
55.8 

15.75 

19.03 

30. 

39. 

12. 

CODC 

S 

6.66 

1.77 

4.10 

5.-*-2. 

9.18 

J.Sfi 
4.78 

9 

Reln- 
conc 

Stone 

CJonc. 

Cone 

Rein- 
Cone. 

442.8 

(bet. 

abuts.) 

1088.8 

272. 
404. 

Cone. 

10 
]  ] 

6  7'- 9* 

Cate- 
nold 

EUlp. 
Parab. 

Cooc 
Pile. 

12 
13 

5'-0' 
2'-r 

T'fT 

Coast 
Pile  A 

Oooc 

14 

MUtenburg  B.. 
Germany  (Over 
the  River  Main) 

CX>nc. 

733. 

112. 
(6 
spans) 

17.7 

2.46 

2.79 

15 

Lalbach  B.. 
Austria. 

Reln.- 
Conc. 

Skew. 

102.8 

14.6 

Pile  A 

Qioe. 

16 

Venice.  Cal. 

R.-C. 

200. 

96. 

1 3'- lo- 

Elllp 

2'-2- 

3'-(r 

POO 

17 

Yorktown  B.. 
Indiana. 

Reln.- 
C^onc. 

Rcin- 
Conc 

95. 

ll. 1 

cone. 

18 

Dayton  B..  Ohio 
(Across    Miami 

588. 

88. 

8.8 

132. 

3-oen. 

r-8- 

Oooc 

Digitized 

yGo 

bQle 

d  by  Google 


780  U.^ARCHES. 

6. — SoMB  Typical — 
Note. — The  next  to  the  last  column  in  table  makes  reference,  by 


CJurve 

6 

Name  and 

Bfate- 

Bridge 

One 

Rad. 

of 

Thickness  at 

FOOB- 

V! 

Location. 

Ft. 

Arch 
Span. 

Rise. 

at 
Crown 

da- 
tiooa 

dos. 

Crown 

3pg*g. 

19 

Sanu  Ana  Via- 
duct;   San    Pe- 
dro, Lo8  Ang.  & 
St.  Lake  R.  R. 

Oonc 

984. 

86. 

(8 

spans) 

36.9 

43.5 

care 

3'-6' 

20 

Belvldere  B..  lU. 
(ElecRy.)  (A- 
cro68  Klshwau- 
kee  R.). 

Reln.- 
Oonc. 

81. 

(4 

spans) 

10.5 

83.86 

arc. 

8. 

i'-H' 

Cone. 

21 

aifty  Creek  B.. 

Qreensburg. 

Ind. 

Reln.- 
0)nc 

80. 

12. 

88. 

5-cen. 

l'-4' 

Cone 

22 

Grand  RapldflB. 
Mich.   (AcroM 
Grand  R.). 

Reln.- 
Cono. 

79. 

(5 

spans) 

11. 

88. 

3-cen. 

r-o* 

r-er 

Cooc 

2:1 

KrosDoB..  Gal- 
Ida.  Austria, 

Reln.- 
Ctonc. 

257. 

75. 

I'-O* 

r-v 

24 

RoGkvflle     B., 
Penn.,  Penn.  R 
R. 

Stone 

3820. 

70. 

(48 

spans) 

19.76 

arc 

3. 

3. 

Cone 

25 

Guayo  River  B., 
Porto  Rico. 

Reln.- 
Oonc. 

270. 

70. 

spans) 
64. 

7.50 

^e  A 

Cone 

26 

C.  M.  A  St.  Paul 

Stone 

360. 

16'-6' 

39'-3i- 

arc 

3. 

3. 

POe  * 

R.  R.     Br., 

(4 

CDOC 

Watertown, 

spans) 

Win. 

27 

Sandy   HUl    B.. 
N.  Y.     (Across 
the  Hudson  R.) 

Reln.- 
(»nc. 

1026. 

60. 

(6 

spans) 

8'-6' 

42'-4' 

arc 

l'-9- 

2'-6- 

Cone. 

2R 

Decatur  B..  111. 
(Wabash  R.  R.) 

Rdn.- 
Conc 

Skew 
(4 

59. 

3'-9- 

Cooc 

(Across    San- 

spans) 

gammon  R.) . 

29 

Raritan  R.   Br. 
(Penn.       R.R.) 
New  Bnmswfck 
N.J. 

Stone 

1500. 

66. 

(21 
spans) 

28. 

28. 

arc 

3'-r 

3'-2- 

30 

C:omo  Park  B., 
St.  Paul,  Minn. 

Reln.- 
Conc 

50. 

IB'-e* 

O'-IO* 

2'-6' 

at 

Standard   Over- 
head B's.    (Lo- 
cal)   (N.Y.N.H. 
*HJl.R.) 

Reln.- 
Ctonc 

31. 

e'-s* 

EUlp. 

l'-2' 

Ootic. 

(PI««J 

Ai 

L.S.    if    M.S.R. 
R.     Arch     Bs. 
(Local   Stand- 
ard). 

Rein.- 
Ctonc 

30. 

9. 

26. 

Digitized 

3-oen. 
DyGo 

2'-9- 

6'-6' 

Oooie. 

d  by  Google 


782  a.— ARCHES, 

Concrete  Colverts. 

Pig.  26  is  a  section  of  a  small  railroad  culvert.  8 
ft.  wide  and  3  ft.  high,  which  has  been  tised  consider- 
ably on  the  Penn.  R.  R.  as  a  standard.  The  amount 
of  concrete  reqiiired  is  about  0.41  cu.  yd.  per  lin. 
ft.  of  culvert. 

Fig.  26. 

STEEL  AND  COMBINATION  ARCHES. 

A  few  hints  will  be  given  to  illustrate  the  method  employed  in  the 
calculation  of  some  of  the  forms  of  steel  arches  most  commonly  used  >Q 
practice.  Steel  arches  differ  from  stone  arches  in  that  they  are  designed  to 
resist  bending,  as  well  as  compression  and  shear.  In  other  words,  the  line 
of  resultant  pressure  is  not  confined  within  any  given  limits  but  may  pas> 
anywhere  outside  the  middle  third  or  even  outside  the  rib  of  the  arch 
altogether.  Hence  the  form  of  arch  selected,  and  depth  of  rib  or  tniss,  are 
matters  of  economy,  adaptability  and  appearance,  rather  than  of  mere 
gravitational  stability  of  tne  reai^ective  parts. 

In  the  following  discussion  it  is  asstmied  that  the  forms  of  the  structures 
have  been  determined,  the  problems  being  to  find  the  stresses  in  the  various 
members  or  parts  under  certain  given  loading.  The  first  thing  to  do  in 
each  case  is  to  find  (one  or  more  of)  the  reactions  at<he  points  of  support; 
and  when  these  are  known  the  remaining  solution  reduces  to  the  simple  case 
of  "finding  the  inner  forces  or  stresses  when  the  outer  forces  are  given;" 
that  is,  to  the  case  of  any  simple  structure. 

The  methods  used  in  finding  the  reactions  may  be  wholly  analytical  or 
partly  graphical.  The  latter  is  chosen  here  for  simplicity.  The  first  step  is 
to  draw  the  arch  and  its  "position  line,"  sometimes  called  the  "locus  line" 

Arch  with  No  Hinges. — ^This  arch  (Fig.  27)  is  seldom  used  in  practice,  the 

2-hingcd  and  3-hinged  arches  being  mainly  employed. 
The  position  line  is  laid  off  by  means  of  an  equation 
containing  x  and  y.  From  any  point  p  the  direction 
of  the  reactions  for  any  load  P  may  be  obtained  by 
either  one  of  several  methods;  (1)  by  drawing  lines 
from  any  point  as  p  tangent  to  the  reaction  curves; 
(2)  by  calculating  the  vertical  ordinates  y^  and  y^ 
from  the  points  a  and  6,  to  points  on  the  ime  of  di-  _.      . 

rection  of  the  reactions;  (3)  similarly,  by  calctilating  '«•  *•• 

Xt  and  ^t ;  (4)  b}r  calculating  the  right  angle  offsets  from  a  and  b;  (6)  by  cal- 
culating the  horizontal  thnist  H;  etc.  The  force  polygon,  above,  gives  the 
value  and  direction  of  Rt  and  R^.  The  equation  for  giving  these  values 
vary  with  the  form  of  arch,  direction  of  loading,  etc.,  and  will  not  be  given 
here.    The  temperature  stresses  have  also  to  be  considered.* 

Two-Hinged  Parai>olic  Arched  Rib.~Let  the  ctu^e  ab  (Pig.  28)  be  the 
neutral  axis  of  the  rib  with  end  hinges  at  a  and  b. 
The  "position  line"  may  be  determined  from  the 

formula  y  — -ri — r»  ^o**  any  value  of  x  on  either 

5c^—x^ 
side  of  the  vertical  axis;   c  being  the  half  span,  and  jf 
h  the  rise.    The  reactions  Ri  and /?2  arc  obtained  for 
any  force  P  at  point  p  by  drawing  the  triangle  of  Fig.  28. 


forces  as  above.  These  reactions  must  pass  through  or  act  at  the  hinges 
a  and  b.  Hx  and  Vx  are  the  horizontal  and  vertical  components  of  R\\n\ 
and  V2  of  i?2-    The  bending  moment  at  any  point  m  is  equal  to  R2  multiplier 


by  the  offset  d.  The  axial  thrust  due  to  R2  must  also  be  consideied  in 
designing  the  fiangcs  of  the  girder;  and  the  shear,  in  designing  the  web. 
A  table  may  be  made  showing  the  bending,  compressive  and  shearing  stresses 
at  various  points  m  along  the  girder  due  to  loads  P  at  successive  positions^ 
and  summarized,  being  careful  to  use  the  proper  +  and  —  signs. 

The  above  method  is  exact  only  for  shallow,  solid  ribs  of  constant  cross- 
wction;  but  it  is  used  also  for  plate  girders  and  open  ribs  even  when  the 
nange  plates  do  not  extend  to  the  hinges. 

.     *  See  A  Treatise  on  Arches  by  Malverd  A.  Howe ;    also  Trusses  and 
AKhes.  Part  III  Arches,  by  Charles  E.  Green,   ized  byX_36ogre 


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784  a.— ARCHES. 

intersection  of  the  other  two  active  members  c€  and  ad.    Taking  moments 
about  O,  of  the  forces  acting  at  the  left  of  the  cutting  plane,  we  have,  i 


the  lever  arms  m  and  »,  mS  — nRi,  or  S—  --/?t  (tension).     Similarly,  the 

fH 

Stress  in  any  member  may  be  obtained  for  any  loading. 

COST  OF  REINFORCED  CONCRETE  ARCH  BRIDGES. 

Hif  hway  Bridges. — Cost  per  square  foot  of  floor  forfiO-ft.  spans.  S2.00  to 
t2.fi0:75-ft.  spans.  S2.50  to  13.60:  100-ft.  spans.  13.50  to  14.50;  12&-ft.  spans. 
14.50  to  $6.00;  150-ft.  spans.  $6.00  to  $10.00. 

Electric-Railway  Bridges. — Cost  per  square  foot  of  floor  for  50-f t.  spans, 
•3.60  to  $4.00;  75-ft.  spans.  14.00  to  $4.50;  100-ft.  spans.  $4.60  to  $5.00;  Hwt. 
spans.  $6.00  to  $6.60;  160-ft.  spans.  $7.00  to  $10.00. 

Steam-Railway  Bridges. — Cost  per  lineal  foot,  double  track,  for  fiO-ft. 
spans.  $200  to  $260;  75-ft.  spans.  $250  to  $276;  100-ft.  spans,  $276toO00; 
126-ft.  spans.  $300  to  $325;  150-ft.  spans.  $326  to  $850. 

EXCERPTS  AND  REFERENCES. 

(See,  also,  Tables  of  Masonry  Arches,  pages  774,  etc.) 

The  Design  of  Arch  Culverts  (By  D.  B.  Luten.  Eng.  News,  June  II. 
1901).— Illustrated. 

The  Desicn  of  a  Reinforccd-Concrete  Arch  Bridge  (By  D.  B.  Luten. 
Eng.  News,  May  8,  1»02).— Illustrated. 

Stresses  In  Masonry-  and  Concrete  Arches  (By  D.  B.  Luten.  Bng. 
News,  June  12.  1902). 

Steel  Arch  Bridge,  45(M^t.  Span,  Over  the  Rio  Qraade  on  the  Padfic 
Ry.,  Costa  Rica  (By  Theodore  Cooper  and  Gunwald  Aus.  Eng.  News. 
Oct.  23,  1902). — Illustration  of  steel  shoe. 

Design  and  Construction  of  a  50-Ft.  Brick  Arch  Culvert  (By  W.  J. 
Douglas.    Eng.  News,  Dec.  25.  1902). — Illustrated. 

A  Wooden-Braced  Arched  Highway  Bridge  (By  A.  Munster.  Eng. 
News.  Jan.  8,,  1903). — Illustrated. 

A  Reinforced-Concrete  3-Hinged  Arch  Bridge  (Prof.  J.  Mehm.  Bng. 
News,  July  16,  1903).— Illustrated. 

Stress  Diagram  of  Concrete  Areh  (By  H.  W.  Parkhurst.  Eng.  News, 
Nov.  12.  1903).— Illustrated. 

A  Reinforced-Concrete  Highway  Bridge,  With  Cost  Data  (P.  A.  Court- 
right.    Eng.  News.  May  12,  1904). 

Three-Hinged  Steel  Arch  Trusses  for  a  St.  Louis  Exhibitloii  Bolldiag 
(Eng.  News.  Sept.  29.  1904). — Span,  172  ft.  Actual  and  estimated  yf^dgbu 
are  given. 

A  New  Graphical  Method  for  Stresses  in  3-Hinged  Arches  (By  J.  W. 
Balet.    Eng.  News.  Oct.  20,  1904). 

The  Connecticut  Ave.  Concrete  Arch  Bridge  (By  Geo.  S.  Morisoo. 
Eng.  News.  June  1,  1905). — Illustrated. 

Three-Hinged  Steel  Arch  Bridge  at  Exeter,  England  (Eng.  News. 
July  20,  1905). — Illtistrated  details,  and  detailed  elevation  of  hau-rib. 

Parabolic  Reinforced-Concrete  Arch  Bridge  (Trussed  Concrete  Steel 
C>).    Eng.  News.  Nov.  15,  1906). — Illustrated;    76-ft.  span. 

Arch  Rib  Bridge  of  Reinforced  Concrete  at  Grand  Rapids,  Ullch. 
(L.  W.  Anderson.  Eng.  News,  Mar.  22,  1906).— City  Bridge;  illustrated; 
cost  data. 

Three-Hinged  Concrete  Arch  Bridge,  Brookside  Park,  Qeveluid  (By 
H.  F.  Hackerdom.  Eng.  News,  May  10.  1906). — Illustrated  details  of 
hinges. 

Gnphlcal  Method  of  Layhig.  Out  a  5-Centered  Arch  (By  A.  SwarU. 
Eng.  News.  May  10,  1906).  ^^ 

T^,f5f"'*fe?***xf  **"""**»    ^o'    Reinforced    Concrete  ^rches ,  (By    D.     B. 

LAxUn,    Eng.  News,  June  28.  1906).— IllustratedfeedbyGoOgle 


MISCELLANEOUS  DATA.  785 

Low-Coft  Concrato  Culverts  (By  W.  H.  Whorley.  Ens.  News. 
Jtily  6,  1906).— Tables, 

Special  Ponn  of  Arch  Centering  (By  J.  H.  Milbum.  Eng.  News. 
Aug.  28,  1906). — Illustrated  form  for  60-ft.  arch. 

Reinforced  Concrete  Arch  Bridge  Built  in  Reinforced -Concrete 
Forau  Without  Centering  (Eng.  News.  Aug.  30.  1906).— Illustrated. 

Some  3-Hhiced  Concrete  Arches  in  Qemuny  (Eng.  News,  May  2. 
1907).— Dlustratod. 

The  Oakland  Steel  Arch  Bridge  Without  Hhigee,  at  Pittsburg  (By 
Willis  Whited.    Eng.  News,  May  16.  1907). — Illustrated. 

Itemized  Cost  of  Reinforced  Concrete  Arches  (By  G.  P.  Carver. 
Eng.  News.  Aug.  22.  1907). — ^Table  and  diagram  of  costs.  Dlustration  of 
at  100-ft.  arch. 

The  Elastic  Theory  and  a  Faulty  Arch  (By  H.  S.  Pritchard.  Eng. 
News.  Jan.  9,  1908). 

A  Combination  Arch-Cantilever  Concrete  and  Steel  Bridge  In  France 
(Eng.  News.  Mar.  26.  1908).— Illustrated. 

A  3-Hinged  Masonry  Arch  with  Metal  Joints  and  Concrete  Supers 
structure  ("Annales  des  Ponts  et  Chaussees,"  Vol.  29,  part  6.  1907;  Eng. 
News,  Sept.  10.  1908).— Dlustrated. 

A  New  Arch  Curve,  the  Parabolic  Oval  (By  C.  Worthington.  Eng. 
News,  April  15.  1909). — Formulas  and  illustrations. 

Subdividing  An  Arch  Rhig  for  Stress  Analysis  (By  P.  E.  Tumeaure. 
Eng.  News.  April  22.  1909). 

A  259^4^  Concrete  Arch  Bridge  in  Switzerland  (Eng.  News.  Aug.  5. 1909). 
— Illustrated.     Table  of  load  and  temperature  stresses.     Sand  boxes  used. 

Reinforced  Concrete  Arch  Bridges,  Siwns  281  ft  and  120  ft.  (Eng.  News. 
Sept.  2,  1909). — Illustrated,  with  plans  of  floor  system,  abutment  and  high 
retaining  wall. 

List  of  Masonry  Arch  Bridges  over  175-Ft.  S|Min.  (Eng.  News.  Sept.  2, 
1909).— Stone  and  concrete, 

180-Pt.  Stone  Arch  Bridge  at  Wiesen,  Switzerland  (Eng.  News.  Sept.  16. 
1909). — ^Eleven  illustrations. 

Formulas  for  the  Volume  o*  Material  in  Qroined  Arches  (By  C^has.  B. 
Buerger.     Eng.  News.  Oct.  7.  1909).— Illustrated. 

Novul  a-Hfaieed  Steel  Arch,  hi  Greece  (Eng.  News.  Nov.  4.  1909).— 
Railway  arch.  193.5-ft.spcm.  Illustrations: — Plan  and  elevation  of  viaduct; 
i: -tails  of  half  arch  rib;  Details  of  hinges  at  crown  and  springing;  Scheme 
of  e  «ctkm. 

Walnut  L4uie  Bridge,  Phlla.  (By  G.  S.  Webster  and  H.  H.  Quimby. 
Tians.  A.  S.  C.  E.,  Vol.  LXV.,  Dec,  1909). — Plans,  including  central  con- 
crete arch  of  238-ft.  span.  Total  cost  of  bridge,  including  electrical  conduits 
and  lamp  standi^s.  bush-hammering,  and  all  extra  work,  was  1267.000. 
which  gives  a  rate  of  17.60  per  sq.  ft.  of  floor  surface  and  10.880  per  cu.  it.  oi 
space — area  of  profile  by  width  of  bridge. 

Rehiforccd-Concrete  Viaduct  Harrisburg,  Pa.  (Eng.  News.  Jan.  13. 1910). 
— ^The  viaduct  proper  is  1841  ft.  long,  78  ft.  above  grotmd  at  its  highest  point, 
and  carries  on  19  arches  a  28-ft.  roadway  and  two  8-ft.  sidewalks.  Pull 
deacxiption.  illustrated. 

Tests  of  Model  Concrete  Arches  by  the  New  York  State  Engfaieer's  Office 
("Barge  Canal  Bulletin"  for  February.  1910;  Eng.  News.  Mar.  10  and  July 
7,  1©10)  .—Illustrated. 

Failure  of  Reinforced-Concrete  Arch  Highway  Bridge  (Eng.  News.  Mar. 
17,  1010).— Illustrated.     75  and  90-ft.  spans. 

The  Analytkal  Calculation  of  a  Concrete  Arch  (By  Mal^*erd  A.  Howe. 
Eng  News.  May  12,  1910). — Illustrated.  Discussions:  Horizontal  thrust; 
Balding  moments  at  the  supports;  Vertical  reactions;  Dead  load;  Live  load; 
Temperature;  Effect  of  direct  stress;  Changes  in  dimensions.  There  are 
nine  tables  for  use  in  making  calctilations.  Article  continued  in  Eng. 
News.  June  2  1910. 


78«  a.'^ARCHES. 

The  Meadow  St  Relnforced-Coocrete  Arch  Bridge,  PKtBban;,  Pa.  (By 

N.  S.  Sprague.  Eng.  News,  Dec.  1.  1910). — Description  with  8  iUustratioiis. 
The  length  of  the  main  arch  span  is  209  ft.  with  a  rise  of  46.14  ft.  and  con- 
sists of  three  arch  ribs,  the  two  outside  ribs  being  uniformly  8  ft.  9  ins.  in 
thickness  and  the  central  rib  5  ft.  and  all  three  ribs  having  a  depth  varying 
from  5  ft.  at  the  crown  to  6  ft.  2  ins.  at  the  springing  line. 

The  New  Charles  River  Bridge,  Boston  Elevated  Railway  (Eng.  Rec, 
Dec.  17,  1910). — A  reinforced-concrete  arch  bridge  of  five  arches  of  122-ft. 
4-in.  clear  span,  foiu*  of  98-ft.  4-in.  clear  span,  a  ateel  lift  bridge  at  the  xiver 
lock  and  a  special  span  of  125  ft.  4  ins.  at  the  small  boat  lock.  The  special 
illustrations  of  the  98-ft.  span,  accompanying  this  descriptive  article  are: — 
Details  of  hinge,  including  arch  reinforcement  and  plan  of  skewback;  kmgi- 
tudinal  section  of  half  span,  part  plan  cmd  details;  reinforcement  axx>iaDd 
stringers  and  of  floorbeam. 

Illustrations  of  Recent  Arch  Spans. 

Description.  Bug.  News. 

Steel  A-arch,  3-hinged,  180-ft.  span,  61-ft.  rise Apr.  21,  'lO 

Arch  dam  design  for  the  site  of  Shoshone  dam June  9,   '10 

Wooden  arch  centering  for  144-ft.  masonp^  arch,  Norway July  7,    *10 

8-hinged  rein-cone,  arch,  88-ft.  span,  Paris Sept.  IS.'IO 

Bog. Rec 

Details  of  centering  trusses  for  cathedral  stone  arches Jan.  23,  *09 

Table  of  stresses  in  280-f  t.  span,  concrete  arch  bridge Jan.  28,  '09 

Rein.-conc.  arch  bridge.  Grand  River,  L.  S.  &  M.  S.  Ry Apr.  24,  'O* 

3-hinged  centers  for  building  150-f  t.  concrete  arches Apr.  24.  *09 

A  combination  steel  and  concrete  arch  bridge,  250-ft.  span May  22,  *09 

Reinforcement  and  erection  of  concrete  arch June  12,  '09 

139-ft.  rein.-conc.  arch,  Edmondson  Ave.  bridge,  Bsdtimore June  19.'09 

364-ft.  steel  spandrel-braced  arches  and  details June  26,'09 

Elastic  rein.-conc.  railway  arch  span.  97J  ft.,  rise  361  ft Jime  26.*00 

Engineer's  and  contractor's  falsework,  Edmondson  Ave.  bridge  .Aug.  14, '09 

Short-span  (34  to  44  ft.)  rein.-conc.  R.  R.  bridges Mar.  19,  '10 

Determination  of  wind  stresses  in  3-hinged  arches — ^Eusink May  21,  '10 

Rein.-conc.  R.  R.  viaduct,  five  120-ft.  and  two  100-ft.  spans Tuly  10.  '10 

Details  three  8  7. 5  ft.  rein  .-cone,  arch  highway  spans,  Los  Angeles.  Aug.  13L  '10 
Details  of  plate  girder  and  rein.-conc.  arch  (70-ft.  span)  R.  R. 

bridge Aug.  20,'10 

Highway  viaduct — 28  70-ft.  rein.  cone,  arch  spans Oct.  1^  '  10 

Proposed  864-ft.  arch  across  the  Kentucky  River Nov*  20, '  1 0 

149-ft.  rein.-conc.  arch  for  electric  R.  R.,  Maritime  Alps Dec.  8,  "10 

Centerings  for  80-ft.,  90-ft..  100-ft.  stone  arches,  B.  &  O.  viaduct. 

Brand.  Cr Dec  17,  *10 


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45.— TRESTLES. 

A  Trestle  is  a  bridge  composed  of  a  series  of  relatively  short  beam-  <»" 
girder  spans  resting  on  "bents,"  which  take  the  place  of  ordinary  piers. 

POe  Trestles. — ^Where  the  bents  are  composed  of  piles  it  is  called  a  pile 
trestle  or  pile  bridge.  Bach  bent  may  consist  of  any  number  of  piles  driven 
in  line  transversely  with  the  axis  of  the  bridge,  the  number  required  depend- 
ing; upon  the  kind  of  britdge,  the  width,  loading,  height  of  trestle,  Idnd  of 
Bou.  lateral  stiffness  reqtured.  whether  on  tangent  or  ctirve,  etc.  Generally, 
the  pil^  are  driven  vertically  but  where  great  stiffness  is  required  the  end 
piles  of  each  bent  are  driven  commonly  on  a  batter.  In  fact,  this  latter 
practice  is  usual  with  some  railroads  even  for  low  trestles  on  tangents.  The 
cost  of  driving  such  batter  piles  is  not  excessive,  as  the  gins  of  the  driver 
may  be  arranf^ed  easily  so  as  to  swing  laterally  on  a  pivot  like  a  pendulum. 
Per  a  foot  bridge,  two  or  more  piles  are  used  to  the  bent;  for  a  highway 
bridge,  three  or  more;  and  for  a  railroad  bridge,  four  or  more. 

The  maximum  load  on  a  pile  should  be  limited  to  about  40.000  lbs., 
and  a  load  of  25.000  to  30,000  lbs.  is  preferable,  usually.  If  driven  in  soft 
material  a  less  load  should  be  used.  Again,  tne  loading  on  pile  may  be 
limited  to  the  allowable  compression  "across  prrain"  of  the  wooden  cap 
resting  upon  it.  Piles  should  be  peeled  before  driving  unless  they  are  driven 
in  salt  water. 

Wooden  caps  are  usually  12  x  14  ins.  for  railroad  bridges;  12  x  12,  10  x 
12,  10  X  10,  etc.,  for  highway  bridges — ^with  greater  dimension  vertical. 
The  piles  when  driven  are  sawed  off  on  a  plane,  either  level  or  inclined  (to 

g've  proper  elevation  to  outer  rail  if  on  a  curve),  and  the  caps  are  drift - 
>lted  to  them.  The  usual  size  of  drift  bolt  is  }  to  }  in.  in  diam.,  and  18  to 
22  ins.  long.  Holes  are  first  bored  with  an  auger  about  i  in.  smsiller  in  dia. 
than  the  bolt. 

Diagonal  bracing  for  each  bent  consists  usually  of  two  planks,  one  on 
either  side  of  bent  and  crossing  at  the  middle  line,  with  upper  ends  bolted 
to  caps  near  their  outer  ends,  and  with  lower  ends  bolted  to  the  outer  piles 
— using  1-in.  screw  bolts  and  cast  washers.  At  intersection  with  the  inner 
piles  the  braces  are  fastened  to  same  with  two  wrought  spikes  with  length 
at  least  twice  the  thickness  of  the  planks.  Similarly,  horizontal  "sa^" 
braces  may  be  fastened  to  the  piles  on  both  sides  of  the  bent  at  foot  of 
diagonals.  For  railroad  trestles.  4x10  in.  bracing  is  common;  and  for 
hi^way  bridges,  3  x  10.  3  x  8,  2  x  10,  2  x  8.  etc.  High  trestles  are  double 
braced. 

Standard  Plans  for  Pik  Tr^stUs. 

Bach  railroad  has  its  own  standards,  differing  in  certain  essential  details 
ixoax  those  of  other  roads,  such,  for  instance,  as  spacing  of  stringers  and 
jack  stringers,  arrangement  and  size  of  guard  rails,  and  the  design  of  the 
floor  in  general. 

Fig.  1  is  an  elevation  of  bent  of  single  track  trestle  of  the  Oregon  Short 
Line  K.  R.,  showing  ballast  floor. 

Timber  Trestles.— The  term  "frame  trestles"  is  applied  to  those  trestles 
constructed  of  framed  timbers,  usually  sawed  to  "dimension,"  but  some- 
times consisting  of  straight,  round  poles  or  piling  timbers  denuded  of  the 
bark.  The  latter  construction  has  been  used  considerably  in  the  Pacific- 
Northwest.  Where  such  poles  are  used  the  posts  are  commonly  in  one 
length,  even  for  very  high  trestles. 

Ordinarily,  however,  the  bents  of  high  trestles  are  constructed  in 
sections,  vertically:  A  single-deck  trestle  is  one  in  which  the  bents  are  m 
one  section;  double-deck,  in  two  sections;  3-deck.  in  three  sections;  etc. 
Pig.  2  is  an  illustration  of  a  3-deck  trestle  showing  the  right  half  resting  on 
piling,  and  the  left  half  resting  on  mud-sills,  the  latter  being  used  in  cases 
where  piles  cannot  be  driven  or  where  the  cost  of  driving  is  prohibitive. 
The  mud-«lls  should  be  of  cedar,  about  8  x  12  ins.  by  4  ft.  long,  and  laid 
side  by  side  on  a  well  tamped  foundation  thoroughly  drained  and  fr^  from 

787  '"''''  ^ 


788  i5.'-TRESTLES. 

wash.  Instead  of  drtoing  piles,  "false"  piles,  set  b^r  hand,  are  sometimes 
employed.  Concrete  or  rubble  masonry  piers  are  desirable  where  a  suitable 
sub-foundation  is  presented  cheaply. 


Fig.  1.     (See  page  787.) 

Pig.  2  illustrates  a  more  or  less  typical  railroad  trestle  which  will  be 
described  briefly:  The  main  posts,  12  x  12  ins.,  have  a  continuous  batter  oi 
8:12  and  1:12.  They  are  "dapped"  into  the  caps  and  sills  about  |  in.,  drift- 
bolted  at  tops,  ana  doweled  (with  1-in.  round  iron)  and  toe-xudled  (with 
wrought  spikes)  at  feet.  (Mortise  and  tenon  joints  are  no  longer  xtsed.) 
The  "batter"  posts,  used  below  the  top  deck,  are  likewise  framed,  drtft- 
bolted,  doweled  and  toe-nailed.  They  give  latereil  stifTness  as  wdU  as  vertical 
support.  The  main  caps  and  sills  are  12  x  14  ins.,  while  the  inter- 
mediate caps  and  sills  are  12x12  ins.,  extending  12  ins.  or  mart 
beyond  the  outer  edge  of  posts.  Each  section  of  the  bent  is  sway- 
braced  with  4  X  10  in.  plank,  screw-bottled  at  ends,  and  spiked  at  inter- 
sections. The  bracing  between  the  bents  consists  of  12  x  12  in.  lon^tudiaal 
girts  (r,  framed  into  the  intermediate  caps  and  sills,  with  lap  jomts,  and 
thoroughly  drift -bottled  to  them;  and  the  longitudinal  diagonal  braces  L 
consist  of  4  X  10  in.  plank,  screw-bottled  at  ends.  The  floor  of  the  bridge 
rests  on  two  lines  of  main  stringers  and  the  two  lines  of  jack  stringers,  the 
latter  being  tised  as  safety  stringers  in  case  of  derailment.  Main  stringers 
are  ordered  in  2-span  lengths,  that  is.  for  bents  16  ft.  centers  they  are 
ordered  30  ft.  long,  laid  two.  three  or  tour  to  each  Ime  with  alternate  and 
butt  joints,  dapped  over  the  caps  and  drift-bolted  thereto.  They  are 
separated  about  1  inch  laterally  by  cast  spool  separators  through  which 
tne  screw  toUs  are  inserted  (using  cast  washers),  four  to  each  joint  over 
■SS^^SP?"  Between  the  lines  of  stringers  a  4-in.  plank  of  proper  length  is 
spucj^to  top  of  caps  to  preserve  the  required  stringer  spacing.  The  jack 
l*wr^*¥^*^*'^  o*»c  ^oot  longer  than  the  main  stringers  (or  say  82  ft. 
long)  so  that  the  jomts  can  be  "halved"  and  drift-bolted  to  caps  with  one 


PILE  TRESTLES,    TIMBER  TRESTLES. 


789 


boh.  The  i>racttc4l  sties  of  main  stringers  are  8  x  14,  9  x  16.  10  x  18.  using 
two  or  three  (or  more)  stringers  tmder  each  rail.  The  width  of  jack  stringer 
should  be  not  less  than  6  ins.,  and  it  ^ould  not  be  less  than  about  one-thuti 
the  width  of  one  line  of  main  stringers.  High  trestles  are  provided  usually 
with  outer  guard  rails  or  "bull"  rails,  which  have,  in  certain  cases,  preventea 
trains  from  plunging  over  the  side  ot  the  bridge.  These  bull  rails  are  prefer- 
ably about  12  ins.  high,  and  10  x  12  in.  timbers  are  conunonly  used.  They 
mav  be  ordered  in  any  convenient  lengths,  are  halved  like  the  jack  stringers, 
and  secured  firmly  by  screw  bolts  passing  vertically  through  bull  rail,  tie 
and  jack  stringer.  In  addition  to  the  bull  rails  or  "outer"  guard  rails,  there 
should  be  "inner"  guard  rails.  The  inner  guard  rails  are  usually  common 
rails  placed  inside  the  main  rails,  but  wooden  guard  rails,  say  6x8  ins. 
(5  ins.  vertical),  dapped  over  the  ties  to  preserve  proper  spacing  of  the 


Pig.  2. 

latter,  are  frequently  used.  They  are  secured  to  the  ties  by  wood  or  lag 
screws  (8  or  9  in.)  with  heads  flush  with  top  of  guard  and  bearing  on  flat 
washers.  Sections  of  benU  are  from  20  to  24  ft.  in  height  and  uniform 
from  top  of  bridge  downward  so  that  the  various  decks  are  on  planes  parallel 
with  the  track.  Longitudinal  diagonal  bracing  may  generally  be  omitted 
between  alternate  pairs  of  bents. 

Many  modifi^ttions  may  be  made  of  Pig.  2. 
For  instance,  the  inner  mam  posts  may  be  ver- 
tical; all  the  main  posts  may  be  continuous 
(each  composed  of  one  stick,  or  of  two  sticks 
bolted  together  with  alternate  joints)  and  the 
transverse  diagonal  bracing  divided  by  hori- 
zontal sash  braces  spaced  vertically  about  the 
depth  of  one  deck,  with  longitudinal  girts 
bolted  at  intersections  of  sash  braces  and  posts* 
instead  of  having  separate  intermediate  caps  ana 
sills,  one  piece  may  serve  to  act  as  the  cap  of 
the  section  below  as  weJl  as  the  sill  of  the  sec- 
tion above;  etc 

Grass-hopFwr  bents,  Pig.  3.  are  often  used  with  ^ 
economy  on  side-hill  work;  either  to  save  cost 
of  excavation  or  to  avoid  encroachment  on  ad* 


7W  iL—TRESTLES, 

joining  property.  The  writer  has  u§ed  aa  many  aa  three  broken  sills  to 
the  bent  with  perfect  safety  and  even  without  concrete  backing  to  resist 
thrust.  At  a,  the  upper  broken  sill  is  dapped  into  the  post  one  inch  arc 
sash  braces  are  spiked  and  bolted  on  as  shown  in  Pig.  3.  Careful  at- 
tention should  be  paid  to  drainage. 

The  bents  of  wooden  trestles  are  spaced  usually  from  12  to  16  ft.  centcn. 
the  ordinary  spacinfr  being,  perhaps,  16  ft.,  calling  for  80-ft.  stringers  which 
are  shipped  conveniently  on  the  average  nat  car.  Unlike  steel  trestles  the 
spacinj?  is  constant  or  nearly  so  throughout  the  bridge,  regardless  of  the 
variation  in  height  of  bents.  Where  long  spans  are  introduced  in  a  wooden 
trestle,  as  for  spanning  a  creek,  the  supporting  bents  are  usually  doubled 
or  tripled. 

On  curves,  the  caps  are  inclined  in  order  to  give  proper  elevation  to  the 
outer  rail.  This  method  is  preferable  to  using  level  caps,  with  shins  tmder 
the  stringers  or  on  the  ties,  etc.,  as  is  sometimes  done.  The  writer  generally 
supplies  the  foreman  of  the  framing  crews  with  tables  giving  the  increased 
lengths  of  posts  on  outside  of  curve  and  the  decreased  lengths  on  inside  of 
curve  for  each  bent,  to  provide  for  the  proper  elevation  of  the  outer  rail 
and  a  lUce  depression  of  the  inner  rail,  each  being  one-half  of  the  required 
"elevation." 

Pile  and  Timber  Trestles. — ^A  pile  and  timber  trestle  is  one  in  whicb 
the  piling  of  the  foundation  is  cut  off  high  enough  above  the  ground  to 


Pig.  4. 

,  which  tl 

"^y  *  P.»le  foundation.'" ^^^  *  ^'  ' 

rig.  4  IS  a  section  of  a  pile  and  timber  trestlc^jf  ^jie^AiOgte S.  F.  R.  R. 


constitute  the  lower  deck,  and  on  which  the  timber  trestle  proper  is  erected, 
aomctunes,  however,  the  term  is  applied  to  a  frame  or  tnnbcr  trestle  with 
simply  «  ~'-  ' J-'- 


d  by  Google 


702 


i&.— TRESTLES. 


the  amount  of  material  in  both  the  span  and  bracing  between  bents  fis 
and  B^,  and  a  decrease  in  material  in  spans  S4  and  St.  Conversely,  anv 
decrease  in  1$  will  produce  the  opposite  effect.  Hence,  k  should  be  swi 
that  for  any  small  change  in  its  length  the  increase  in  material  on  the  one 


hand  will  just  equal  the  decrease  on  the  other.  But  note  that  in  the  simi- 
lar adjustment  ol  adjacent  portions  the  above  spans  may  require  re-adjust- 
ment; and  likewise,  all  other  sections.  We  have  also  to  take  into  consid- 
eration the  best  relative  len^rths  of  l^,  l^,  k,  etc. 
Tables  or  diagran^is  showmg  the  weights  of 
spans,  bents,  and  bracing  for  various  lengths 
and  heights  lor  the  partictuar  loading  will  greatly 
facilitate  the  above  adjustments. 

The  floor  system  is  arranged  similar  to  that 
of  an  ordinary  steel  bridge,  that  is,  with  floor 
beams  and  stringers,  the  former  being  supported 
directly  by  the  bents.  For  short  spans,  I-beams 
may  be  used;  for  longer  spans,  plate  girders. 
For  very  long  span»  both  floor  beams  and 
stringers  may  be  trussed,  using  deck  girders  for 
this  purpose. 

The  posts  of  the  bents  (Fig.  6.)  are  battered 
about  1:6  —  considerably  less  than  for  wooden 
trestles.  This  narrowing  of  the  space  between 
posts  tends  to  call  for  less  metal  in  the  transverse 
bracing;  for  more  metal  in  the  posts,  from  wind 
stresses;  but  for  slightly  less  metal  in  the  posts 
from  direct  loads.  The  best  designs  have  stiff 
diagonal  bracing  instead  of  rods,  and  large  mem- 
bers with  few  connections  are  preferable.  The 
feet  of  columns  should  be  anchored.  The  wind 
stresses  may  be  calculated  by  treating  the  bent 
as  a  cantilever  arm,  assuming  all  the  joints  to 
be  hinged;  but  if  the  framework  is  stiffened  by* 
heavy  guraet  plates,  and  riveted  connections  are 
used,  it  becomes  statically  indeterminate. 

Elevated  Railroad  Trestles. — For  a  full  discussion  of  this  subject  the 
reader  is  referred  to  Paper  No.  806,  Trans.  Am.  Soc.  C.  E.,  June,  i897,  by 
Mr.  J.  A.  L.  Waddell. 

Reinforced  Concrete  Trestles. — ^The  outline  shown  in  Pig.  6,  abor^re,  for 
steel  trestles,  is  a  good  design  for  a  high  trestle  bent  of  reinforced  concrete. 
It  can  also  be  modified  as  follows:  Ca)  By  omitting  the  horizontal  braces, 
using  the  diagonal  bracing  only;  Cb)  by  omitting  the  diagonal  braces, 
using  the  horizontal  bracing  only;  (c)  by  omitting  all  bracing.    In  case  (b) 


however,  the  mushroom  connections  of  horizontal  braces^  to  posts  must  be 
of  the  large  gusset  type,  in  order  to  introduce  bending  resistance  at  ends  of 
braces;  and  similarly  at  the  floor-beam  coimections.  Case  (c)  should  be 
used  for  short  bents  only. 

The  posts  and  bracing  should  be  calculated  for  live-,  dead-  and  wind 
loadsjfor  centrifugal  force  due  to  moving  load  if  trestle  ia  on  a  curve  (see 
pa^e  702) ;  and  for  longitudinal  thrust  or  momentum  due  to  stopping  of 
traiTOi  (page  702}. 

For  proportioning  the  members,  see  pages  586  and  609:  also  page  446  for 

p  *i      column  formulas. 
j««  References  to  numerous  designs  and  details  may  be  found  on  the  f ollow- 
»"» page.  /^^  1 

Digitized  by  VjOOQ  IC 


MISCELLANEOUS  DATA,  7»3 

COST  OF  RAILROAD  TRESTLES. 

Timber  Trestles.— (a)  SituU  Track.  Cost  in  dollars  per  lin.  ft.  (approx.) 
-8+0.2//  +0.002//*.  DoubU  Track.  Cost  in  dollars  per  lin.  ft.  (approx.)  - 
16  +0.4/f + 0.003//*.    In  which  H  -  height  of  trestle  bent,  in  feet. 

Steel  Trestles. — ^About  three  to  five  times  the  cost  of  timber  trestles. 

Reinforced  Concrete  Trestles. — Low  trestles  cost  about  the  same  as 
small  arch  spans.    See  page  784. 

EXCERPTS  AND  REFERENCES. 

Woo4eo   Trastles,   Utah  Central   Ry.   (Bng.  News,  Jan.  17.  1901).— 

Dlustrated. 

Steel  Trestle  Viadnct,  C.  ft  N.-W.  Ry.  (Bng.  News  April  32.  1901).— 
Illustrated. 

Railway  Trestle  Bents  of  Reinforced  Concrete  (By  W.  A.  Allen.  Bng. 
News..  Mar.  12.  1903).— lUustrated. 

Reinforced-Concrete  Trestlework  Viadnct  for  a  Spanish  Mineral  Ry. 

(Bog.  News.  May  17.  1906). 

Reinforced-Concrete   Viaduct   on   the   Richmond   ft   Chesapealce  Bay 

Ry.  (Bng.  News.  Dec.  12.  1907).— Illustrated. 

A  Traveler  for  Viadnct  Erection  (By  L.  L.  Jewel.  Bng.  News.  Oct.  8. 
1908).— Illustrated. 

The    BeariJ^iver   Sted    Viaduct,    Cal.    (Bng.   News,  Mar.  11.   1909). 

— lUustrated  details. 

Table  for  Esthnating  Quantities  in  Thnber  Trestles  (By  Bmile  Low. 
Bng.  News,  April  22,  1909). 

Reinforced-Concrete  Viaduct  with  Some  Structural  Steel  Reinforcement 

(Bng.  News,  July  1.  1909). — ^Tower  bents  composed  of  two  posts.  18x18  ins. 
square  at  the  high  bents  and  15  x  16  ins.  at  the  low.  spacea  12  It.  c  to  c.  at 
the  girders  and  extending  on  an  outward  batter  of  1  :  6  to  spread  fotmda- 
tions  on  solid  rock.  Posts  are  concrete  reinforced  at  the  four  comers  by 
straight  round  rods,  encircled  every  12  ins.  with  i-in.  wire.  Longitudinu 
and  transverse  braces  are  9-in.  and  12-in.  I-beams  encased  in  concrete. 
Illustrated. 

Reinforced-Concrete  Trestle,  Pasadena,  CaL  (Bng.  News.  Nov.  18, 
1909J. — Consisu  of  six  girder  speins  resting  on  five  tower  bents;  whole  length 
divided  into  panels  of  17  ft.  3  ins.,  each  bent  being  of  that  length,  and  each 
span  divided  into  three  of  such  spaces  by  the  floor  beams,  making  a  span 
length  for  each  girder  of  61  ft.  9  ins.  Towers  consist  of  four  columns;  each; 
columns  18  x  18  ins.  and  reinforced  with  eight  IHn*  round  steel  bars  ex- 
tending into  the  pier  footings  to  within  one  foot  of  their  base.  Nearly  all 
the  ^lumns  are  over'  60  ft.  lon^  and  have  longitudinal  and  transverse 
struts  framing  into  their  third  points  to  stiffen  them.  Struts  vary  in  size 
from  10x18  ms.  to  12  x  24  ins.  and  are  reinforced  with  four  l-in.  or  four 
l-in.  twisted  steel  bars  laced  as  a  column.  Illustrations  include  details  of 
expansion  joint. 

Important  Illnstrations  of  Trestles  and  Details. 

Description.  Bng.  News. 

A  6-milc  railway  trestle  across  Albemarle  Sound Apr.  21,  '10 

Willow  Cxeck  Viaduct,  Des  Chutes  Railway Aug.  11,'10 

Bng.  Rec 

Stresses  in  tjrpical  tower  of  a  railway  trestle Jan.  9,  '09 

Design,  construction  and  cost  of  a  rein.-conc.  trestle Feb.  20,  '09 

Details  reinforcement,  rein.-conc.  R.  R.  trestle Apr.  8,  '09 

The  Sl^o  reinforccd-concrete  highway  viaduct May  16,  '09 

Typical  tower  bent,  manuf 'rs  railway  steel  viaduct May  16,  '09 

A  substitute  for  drift  bolts  on  wooden  trestles Tunc  6,  '09 

Details  of  steel  trestle,  Norfolk  &  Western  Rv Mar.  19,  '10 

Details  O-post  and  4-post  pile  R.  R.  trestle,  Albemarle  Sound..  .Apr.  30,  '10 
Standard  solid  floor  railroad  trestles Oct.  29,  '10 


46.— ROOFS. 

Wind  Pressttre. — ^The  problem  of  wind  pressure  which  indirectly  presente 
itself  to  the  engineer  consists  in  discovering  the  existing  relation  between 
the  velocity  of  the  wind  and  its  piyssurw  against  any  surface — right,  obliotK. 
plane,  curved,  etc.  Then,  knowing  the  maximum  velocity  of  the  wind  in 
the  particular  locality  in  which  a  structure  is  to  be  erected,  the  probable 

Pressure  on  its  surface  is  deduced  within  a  reasonable  degree  of  acctiracy 
y  this  ratio.  The  subject  never  has  been  treated  satisfactorilv  aa  the 
grounds  of  pure  theory,  while  the  few  practical  experiments  recorded  seem 
to  give  results  not  entirely  in  accord  with  each  other  nor  with  any  theor>' 
yet  advanced. 

Velocities  Attained. — The  velocity  of  a  volimie  of  air  moving  along 
the  surface  of  the  earth  increases  with  its  distance  above  the  average  surface, 
hence  high  structures,  or  those  in  exposed  positions,  shoiild  be  designed  to 
resist  the  greater  wind  pressures  in  any  locality.  Prof.  Henry  claims  that 
on  Mt.  Washington,  N.  H.,  150  miles  per  hour  has  been  recorded.  This 
probably  exceeds  by  over  50%  the  maximtmi  velocity  ever  attained  at  iht 
average  surface  of  the  ground  in  that  State.  The  tornado  which  tore  up 
a  portion  of  the  St.  Louis  Bridge  floor  is  credited  with  but  120  miles  per 
hour.  A  hurricane  such  as  occasionally  visits  the  Atlantic  coast  may  attain 
a  velocity  of  60  miles  per  hour  upward,  depending  upon  exposure.  Prom 
90  to  100  miles  per  hour  is  probably  the  maximum  velocity  ever  attained 
in  New  York  City  in  the  most  exposed  positions.  The  Pacific  coast  is  never 
visited  by  the  violent  hurricanes  incident  to  other  sections  of  the  country. 

Direct  Wind  Pressure. — When  the  atmosphere  is  at  rest  it  exerts  a  pres- 
sure at  sea  level  of  about  14.7  lbs.  per  square  inch;  while  a  cubic  foot  ot  dr>' 
air  under  one  atmospheric  pressure  (760  millimeters  of  mercury)  weighs  about 
0.081  lb.  per  cubic  toot.  Wind  is  air  in  motion  caused  by  a  tendency  to 
restore  equilibrium  in  atmospheric  pressure,  at  about  the  same  level,  by 
air  rushing  in  to  replace  a  heated  and  rising  atmosphere  in  another  locality. 
Hence,  the  directing  force  is  a  tension  or  tendency  to  partial  vacuum  "ahead" 
of  the  wind,  as  well  as  a  compression  from  behind.  It  is  well  to  bear  this 
in  mind,  as  explaining  in  part  at  least  the  uplifting  or  overturning  power 
exerted  on  roots,  due  to  suction.  This  suctional  power  is  not  well  Icnown. 
and  its  effect  should  be  considered  more  in  future  experiments  and  inves- 
tigations. Some  attempts  have  been  made  to  deduce  a  rule  for  pressore. 
based  on  the  weight  of  the  volume  of  air  moving  against  the  exposed  surface, 
taking  into  accotmt  temperature,  humiditv  and  barometric  pressure,  but 
the  results  have  been  more  or  less  unsatisfactory. 

Smeaton,  150  years  ago,  made  some  crude  experiments  on  wind  pressure 
in  connection  witn  the  power  of  windmills,  ana  constructed  a  ta^  from 
the  formula 

P-.005  V (1> 

in  which  P— horizontal  normal  pressure  in  lbs,  per  sq.  ft., 

and  V— velocity  of  wind  in  miles  per  hour. 
This  formula  seems  to  agree  fairly  well  with  many  experiments  on  small 
suriaces.     Another  formula,  of  the  same  form  as  &neaton's,  giving  results 
20%  less,  is  used  considerably:* 

P-.004  V« (J) 

In  both  of  the  above  the  pressure  is  assumed  to  be  proportional  to  ihe 
square  of  the  velocity.  Lieut.  Crosby's  experiments  near  Baltimore.  Md. 
(Engineering,  June  13,  1890}  to  determine  the  resistance  of  the  air  to  fast 
moving  trains  seem  to  indicate  that  the  pressure  P  is  directly  proportional 
to  the  velocity  V,  and  not  to  V*.    But  this  conclusion  is  genenuly  discredited. 

The  conclusion  from  Baker's  experiments  in  connection  with  the  con- 
struction of  the  Forth  Bridge  is  that  the  pressures  given  by  Smeaton 's 
formula  (1)  are  too  great  for  high  velocities.     In  the  light,  or  poiiaps  better 

*  This  formula  is  now  used  by  the  U.  S.  Signal  I 

794 


(nal  S^yice.    | 

tizedbyCOOgk 


WIND  PRESSURE. 


706 


"darkness/*  of  modem  experimental  data,  the  pressure  P  may  be  assumed 
to  He  somewhere  between  the  values  given  by  formulas  ( 1)  and  (2) — near 
the  former  for  low  velocities,  and  near  tne  latter  for  high  velocities.  These 
values  are  deduced  in  the  following  table;  and  two  columns  are  added  giving 
results  from  the  experiments  of  Eiffel  and  Stanton. 

1. — DruBCT  Normal  Wind  Prbssurbs. 


Velocity  V 
of  Wmd 

P-.005V» 

P-.004V« 

P-.003iV« 

P-.003  V^ 

(1) 

(2) 

(sm.  areas) 
Pressure  P 

(Ig.  areas) 
Pressure  P 

in  Miles 

Pressure  P 

Pressure  P 

Remarks. 

per  Hour. 

Lbs.  per 
Sq.  *^. 

Lbs.  per 
Sq.  K 

Lbs.  per 
Sq.  pT* 

Lbs._per 
Sq.  fT* 

10 

.50 

.40 

.83 

.30 

20 

2  00 

1.60 

1.33 

1.20 

Brisk  wind. 

80 

4.50 

8.60 

3.00 

2.70 

40 

8.00 

6.40 

5.33 

4.80 

High  wind. 

50 

12.60 

10.00 

8.33 

7.50 

00 

18.00 

14.40 

12.00 

10.80 

Violent   storm. 

70 

24.50 

19.60 

16.33 

14.70 

80 

32.00 

25.60 

21.33 

19.20 

Hurricane. 

90 

40.50 

32.40 

27.00 

24.30 

100 

50.00 

40.00 

33.33 

30.00 

Violent     hurri- 

110 

60.50 

48.40 

40.33 

36.30 

cane. 

130 

72.00 

57.60 

48.00 

48.20 

Tornado. 

Before  considerin|^  the  resolution  of  a  direct  wind  pressure  into  its  nor- 
mal,  vertical  and  horizontal  components,  as  practically  applied  to  roofs  and 
other  structures,  it  will  be  well  to  emphasize  the  above  hints  regarding 
pressure  and  tension  (suction)  on  any  exposed  body.  If  the  surface  of  a 
thin  flat  sheet  is  exposed  to  the  direct  force  of  the  wind,  there  will  be  tension 
or  suction  on  the  leeward  face,  due  to  partial  vacuum,  thus  producing 
apparently  additional  pressure  on  the  windward  face  and  as  these  forces 
act  in  the  same  direction,  the  resultant  "wind  pressure"  is  thereby  in- 
creased. The  tension  may  be  reduced  by  placing  a  long  tapering  pro- 
jection on  the  leeward  face  of  the  plate,  flush  with  the  edge,  to  i>revent  the 
formation  of  air  eddies.  Further,  if  the  windward  face  is  convex. 
iht  pressure  also  will  decrease,  while  if  it  is  concave  the  pressure  wiH 
in<a«aae.  The  thickness  of  the  plate  within  certain  limits  is  also  a  factor, 
as  well  as  the  density  and  humidity  of  the  atmosphere. 


«^6 

Fig.  1. 

Normal  and  Component  Wind  Pressures. — Let  P.  Fig.  1,  be  the  direct 
horizontal  pressure  per  square  foot  on  any  vertical  surface,  and  Pb  the 
normal  pressure  on  the  same  unit  of  inclined  sxirface,  sloping  at  angle  A 
with  the  horizontal.     Then — 

By  Abstract  theory.  Pn-P  sin«  A (8) 

By  Hutton's  experiments,     Pn-P  (sin/l)'**-**-'    (4) 

By  Duchemin's  formula,       Pn'^P  t-, — •  .  a (5) 

The  following  table  gives  values  of  Pn  deduced  from  these  three  for- 
mulas, a^uming  P  —  50,  40  and  30  lbs.     Use  Hutton  or  Duchemin. 

♦From  experiments  by  M.  Eiffel  and  Dr.  Stanton;  on  velocities  of  40  to 
90  miles  per  nour.  See,  also,  remarks  under  Railroad  Bridges.  Section  38. 
page  687. 


706 


4A.-^ROOFS, 


2. — ^Normal  Wind  Prbssurbs  Pa  on  Inclined  Sukfacbs.* 
For  horizontal  pressures  of  50,  40  and  30  lbs. 


Pitch 

60  Lbs. 

40  Lbs. 

30  Lbs. 

Aagle. 
A. 

st 

d 

i 

s| 

d 

st 

^1 

Q 

6" 

0.4 

6.6 

8.61 

0.3 

6.2 

6.89 

0.2 

3.9 

6.17 

lO*' 
16* 

1.5 
3.3 

12.1 
17.8 

17.00 
24.16 

1.2 
2.7 

9.7 
14.2 

13.50 
19.82 

0.9 
2.0 

7.2 
10.7 

10.19 
14.49 

180-28' 
20* 

1-6 

6.0 

6.8 

21.2 
23.0 

28.76 
30.30 

4.0 
4.7 

17.0 
18.4 

23.00 
24.24 

SO 
3.6 

12.7 
13.8 

17.26 
18.18 

21<'-18' 

1-6 

6.9 
8.9 

24.8 
28.3 

32.66 
36.96 

6.5 
7.1 

19.8 
22.6 

26.13 
28.77 

4.1 
6.4 

14.9 
17.0 

10.00 
21.68 

260-84' 
30° 

1-4 

10.0 
12.6 

29.7 
38.1 

37.27 
40.00 

8.0 
10.0 

23.8 
26.6 

29.82 
32.00 

6.0 
7.6 

17.8 
19.9 

22.36 
24.00 

33«-^l' 
36« 

1-8 

16.4 
16.5 

36.6 
37.6 

42.42 
43.16 

12.3 
13.2 

29.2 
30.1 

33.08 
34.52 

9.2 
9.9 

21.9 
22.6 

25.45 
25.89 

40« 
46«'-00' 

1-2 

20.7 
26.0 

41.6 
46.0 

46.60 
47.16 

16.6 
20.0 

33.8 
36.0 

36.40 
37.73 

12.4 
16.0 

25.0 
27.0 

27.80 
28.30 

29.3 
33.6 

47.6 
49.3 

48.30 
49.01 

23.6 
26.8 

38.1 
39.4 

38.64 
30.21 

17.6 
20.1 

28.6 
29.6 

28.96 
29.41 

60<» 
660 

M 

37.6 
41.1 

50.0 
60.0 

49.08 
49.78 

30.0 
32.9 

40.0 
40.0 

89.74 
39.82 

22.7 
24.6 

80.0 
30.0 

20  .SI 
29  .S7 

TV* 

44.2 
46.7 

50.0 
50.0 

49.89 
49.96 

35.3 
37.6 

40.0 
40.0 

39.91 
39.96 

26.6 
28.0 

80.0 
30.0 

29.03 
».07 

80<» 

48.6 
49.6 

60.0 
50.0 

60.00 
60.00 

38.8 
39.7 

40.0 
40.0 

40.00 
40.00 

29.1 
20.8 

30.0 
30.O 

30.00 
30.00 

90** 

50.0 

50.0 

50.00 

40.0 

40.0 

40.00 

30.0 

80.0 

30.00 

*The  normal  pressures  given  in  the  table  are  in  lbs.  per  square  foot  of 
inclined  surface  of  exposed  roof — from  horizontal  winds  producing  pressures 
of  50. 40  and  30  lbs.  per  square  foot  on  vertical  surfaces. 

Example. — Assuming  direct  wind  pressure  to  be  60  lbs.  per  square  foot 
of  vertical  surface,  and  using  Hutton's  f  ormtila,  find  from  the  above  tstt^ 
the  normal  pressure  in  lbs.  per  square  foot  on  a  roof  with  a  pitch  of  oxte  in 
two. 

Answer— 46  lbs.  per  square  foot. 


d  by  Google 


WIND  PRESSURE.    SNOW  LOADS. 


797 


In  dnagning  roofs  and  buildings  it  is  convenient  to  use  the  noitnal 
presBore  against  the  roof  surface,  and  to  know  also  its  vertical  and  hori- 
zontal components.  The  subjoined  table  gives  these  values  for  the  6  stan- 
dard pitches*  of  roofs,  and  betfed  on  Hutton's  and  Duchemin's  formulas  at 
50,  40  and  30  lbs.  direct  wind  pressure.     See  table  2,  preceding. 


3. — Wind  Prbssurbs  in 

Lbs.  pbr  Squarb 

Foot 

ON  Roofs. 

3 

♦ 

i 

o 

60. 

40. 

SO. 

1 

a» 

Nor- 

Hori- 

Ver- 

Nor- 

HoriJ 

Ver- 

Nor- 

Hori- 

Ver- 

Ct. 

du 

< 

mal. 

2ont'^ 

tical. 

mal. 

zont'l  tical. 

mal. 

zonfl 

tical. 

1-6 

18«-2fl' 

21.2 

6.7 

20.1 

17.0 

5.4 

16.1 

12.7 

4.0 

12.0 

§ 

1-5 

21<»H8' 

24.8 

9.2 

23.0 

10.8 

7.4 

18.4 

14.0 

5.5 

13.8 

1-4 

28*»-34' 

20.7 

13.3 

265 

23.8 

10.6 

21.3 

17.8 

8.0 

15.9 

9 

1-3 

ZS^-4V 

35.0 

203 

305 

29.2 

162 

24.3 

21.9 

12.1 

18.2 

X 

1-2 

46*M»' 

45.0 

81.8 

31.8 

36.0 

25.5 

255 

27.0 

19.1 

19.1 

c 

1-6 

IS^-W 

28.8 

9.1 

27.3 

23.0 

7.3 

21.8 

17.3 

5.5 

16.4 

i 

1-6 

21^-48' 

32.7 

12.1 

30.4 

26.1 

9.7 

24.2 

10.6 

7.3 

18.2 

1^ 

26'»-84' 

37.3 

16.7 

33.4 

29.8 

13.3 

26.7 

22.4 

10.0 

20.0 

1 

1-3 

iy'^v 

42.4 

23.5 

35.3 

33.9 

18.8 

28.2 

25.5 

14.1 

21.2 

1-2 

i5'*-W 

47.2 

33.4 

33.4 

37.7 

26.7 

26.7 

28.3 

20.0 

20.0 

Probably  the  low  direct  pressure  value  of  30  lbs.  p^  square  foot,  reduced 
Iw  Hutton'st  (or  Duchemin's)  formula  will  be  sufficient  for  fifeneral  cases; 
the  next  higher  value,  40  lbs.,  for  particularly  exposed  positions;  and  the 
highest  value,  50  lbs.,  for  special  cases  as  in  the  tornado  belts. 

In  open  sheds  the  maximiun  direct  pressure  may  be  asstuned  as  acting 
normal  to  the  inside  leeward  surface,  and  the  "lifting  "  force  may  be  ob- 
tained bv  multiplying  the  total  direct  pressure  by  cos  A,  the  angle  of  incli- 
nation ot  roof  with  the  horizontal. 

On  a  cylinder  the  theoretical  pressure  is  H  that  on  a  corresponding 
plane  diametrical  section  or  rectangular  plate;  but  BordaJ  by  experiment, 
found  it  to  be  only  0 .  57.  Likewise,  he  loimd  the  pressure  on  a  sphere  to 
be  but  0.41  of  that  on  a  corresponding  circular  plate  of  the  same  diameter, 
while  theory  gives  H-  In  general,  the  pressure  on  a  concavity,  measured 
by  the  diametrical  plane  surface,  is  greater  than  unity;  while  on  a  convexity 
it  is  less  than  unity.  The  intensity  of  pressure  may  be  increased  by  the 
deflection  of  the  wind  from  an  adjacent  structure. 


2.— Roof  "Pitches, 


Snow  Loads. — The  snow  loads  which  may  come  on  a  roof  will  vary  with 
the  latitude  of  the  place;  its  altitude  above  sea  level;  the  general  humidity 
of  the  atmosphere;  the  winter  temperature;  the  location  with  respect  to 
mountain  ranges;  the  pitch  of  the  roof  (Fig.  2) ;  the  character  of  roofing. 
The  writer  is  familiar  with  the  character  of  the  snow  fall  in  nearly 
every  State  in  the  Union  and  in  Canada  For  the  Pacific  slope  west 
of  tl^  Coast  and  Cascade  moimtain  ranges,  there  is  no  need  to  provide  for 
any  snow-load,  but  up  in  these  ranges  and  in  Eastern  Washington,  Eastern 
Oregon,  Northern  California,  and  m  all  sections  eastward  to  the  Atlantic 
provision  must  be  made.    The  heaviest  snow-falls  in  the  United 


*  The  pitch  of  a  roof  is  one-half  the  natural  tangent  of  inclination  with 
the  h<mzontal. 

t  The  writer  believes  Hutton's  formula,  founded  on  practical  experi- 
mental data,  to  be  quite  well  established  and  fairly  reliable.  Duchemin's 
formula  gives  values  about  25%  higher  for  the  ordinary  1-4  pitch. 


798  46.— /?00F5. 

States  are  in  the  Central  Northwest,  New  England  and  the  Rocky  Mountain 
regions.  The  following  diagram,  giving  the  snow  load  per  horiaootal 
square  foot  of  roofs  for  different  localities  and  for  standard  roof  pitches, 
will  be  found  practically  reliable.  The  latitude  of  the  place  is  considered 
as  increased  one  degree  for  each  thousand  feet  in  altitude  above  sea  level 


Latitude  in  Degrees  *  one  Degree  for  each  /OOOff. 
in  elevation  above  Sea  Levet. 
Fig.  3. 

Example. — ^To  find  the  snow  load  in  jxjunds  per  horizontal  square  foot 
at  Denver  for  a  pitch  of  1  in  6?  The  latitude  ot  Denver,  40,  plus  leVs  oi 
its  altitude  in  feet  above  sea  level,  6,  gives  46.  Using,  line  (b)  of  abK»T 
diagram  this  is  equivalent  to  a  snow  load  of  28.2  lbs.  per  horizontal  squjuv 
foot  for  a  pitch  ot  1-6. 

Investigations  by  S.  de  Perrot,  in  Switzerland,  according  to  the  "Engi- 
neer" (London),  show  that  where  a  heavy  fall  of  snow  is  followed  by  thawini^ 
and  freezing  and  then  more  snow,  in  repeated  cycles,  the  laminar  mara  ot 
snow  and  ice  will  have  a  weight  of  36  to  38  lbs.  per  cu.  ft. ;  and  the  thic^ess 
of  the  mass  on  the  roof,  from  24  to  32  ins.,  will  produce  a  load  of  70  to  100 
lbs.  per  sq.  ft.,  about  2  to  4  times  the  weight  ordinarily  assxmied  in  calcu- 
lations. 

Roof  Coverinss. — Materials  for  roof  covering  are  selected  for  protection 
against  rain,  snow  and  other  natural  agencies.  They  should  be  light, 
durable,  economical  and  more  or  less  artistic;  and  their  selection  will  be 
dependent  on  the  character  of  the  building,  its  location  with  respect  to 
climate,  the  amount  of  acids  and  injurious  gases  in  the  atmosphere,  and 
the  pitch  of  the  roof.     Among  the  most  commonly  used  materials  fc* 

Sitch"  roofs  are  shingles,  slate  and  tile  for  residences;  slate,  ^avel  and 
s  for  railway  structures;  corrugated  steel  for  warehouses.  For  tem- 
porary structures,  as  exposition  buildings,  the  patented  roofings  are  senerany 
"s«d.  and  then  relaid  elsewhere.  For  "flat  roofs,  tin,  tar  and  gravel 
asphalt,  and  other  compositions  are  preferred. 

♦West  of  the  Coast  and  Cascade  Mt.  ranges,    flngener^k 


ROOF  COVERINGS—SHINGLE,  SLATE. 


799 


,  Shi$igU  Roofing. — Shingles  are  made  of  white  cedar,  red  cedar,  spruce, 
pme,  fir  and  cypress.*  In  the  United  States  the  life,  in  years,  of  cedar 
ihtngles  will  correspond  to  about  the  latitude  of  the  place  in  degrees;  pine 
will  last  about  one-third  to  one-half  as  long  as  cedar,  depending  upon  the 
climate.  The  following  table  is  based  on  shingles  4'  wide,  and  with  an 
average  thickness  of  Vs^.  The  weight  of  cedar  is  assumed  at  36  lbs.  and 
pme  at  40  lbs.  per  cubic  foot.  The  length  of  shingle  is  a  little  over  8  times 
the  'Veather.'^ 

4. — Wbight  of  Shinglbs  0.2  Inch  Thick,  Laid  cm  Roofs. 
(Weight  is  proportional  to  thickness  of  shingles.) 


Assumed 

Weather 

Shingles 
per 

Weight  per 
Square  ot  100 

Nails 

Weight 
of  Nails 

Length. 

Width. 

or 

Square 
of  100 
Sq.  Ft. 

Sq.  Ft. 

per 

per 

Ins. 

IBS. 

Gage. 
Ins. 

Sqtiare. 
Number. 

Square. 
Lbs. 

Cedar. 

Pine. 

Number. 

Lbs. 

Lbs. 

14 

4 

900 

210 

233 

1800 

4.50 

15 

4i 

800 

200 

222 

1600 

4.00 

16 

6 

720 

192 

213 

1440 

3.60 

18 

6i 

655 

197 

218 

1310 

3.28 

20 

6 

600 

200 

222 

1200 

3.00 

22 

6i 

554 

203 

226 

1108 

2.77 

24 

7 

515 

206 

229 

1030 

2.58 

Shingles  are  nailed  directly  on  shingle  laths  or  on  solid  V  sheathing 
covered  with  tarred  paper,  using  two  1  \'  nails  to  each  shingle.  The  laths  are 
from  two  inches  wide  upward,  spaced  a  few  inches  apart,  and  nailed  hori- 
zontally to  the  jack -rafters. 

StaU  Roofing. — Slates  are  laid  shingle  fashion.  The  length  of  slate  is 
usually  2  times  the  "weather"  +  3  inches.  The  following  table  is  based  on 
the  above.  The  number  of  slates  per  square  of  100  sq.  ft.  — 14,400-*-  (width 
X  weather). 

6. — ^NuMBBR  OF  Slatbs  pbr  Squarb,  Laid  on  Roof. 
(See  below  for  weight  per  sq.  ft.  of  slate  unlaid.) 


Slates 

Slates 

Slates 

Wea- 

per  100 
Sq.    Ft. 

Wea- 

per  100 

Wea- 

per  100 
Sq.    Ft. 

Stse. 

ther  or 

Sise. 

ther  or 

Sq.    Ft. 

Size. 

ther  or 

Gauge. 

Gauge. 

Gauge. 

Ins. 

Ins. 

Num- 
ber. 

Ins. 

Ins. 

Num- 
ber. 

Ins. 

Ins. 

Num- 
ber. 

6x12 

4i 

533 

8x16 

6i 

277 

10x20 

8i 

170 

7   12 

» 

467 

9  16 

246 

12  20 

• 

141 

8   12 

m 

400 

10  16 

■ 

222 

14  20 

« 

121 

9   12 

m 

356 

11   16 

202 

12x22 

9} 

126 

10   12 

320 

12  16 

185 

14  22 

• 

108 

7x14 

5i 

374 

9x18 

♦ 

213 

12x24 

10) 

114 

8   14 

• 

327 

10  18 

192 

14  24 

• 

98 

9   14 

m 

291 

12   18 

160 

16  24 

« 

86 

10   14 

m 

262 

14   18 

137 

14x26 

lU 

89 

Note. — Sizes  range  up  to  24*'x44'. 

At  174  lbs.  per  cubic  foot  the  weight  of  one  square  foot  of  slate  at  various 
thicknesses  is  as  follows: 

Thickness,  in  inches     K       A'        K         I'         T         T  K  1' 

Weight,  in  pounds.   1.81     2.72     3.62     5.44     7.25     9.06  ^10.88     14.50 

*  Good  heart-cypress  shingles  are  now  almost  unprocurable,    o 


800 


ia.— ROOFS. 


-Total  Wiioht  of  Slatb  pbr  Squarb  of  Roof. 
(Weather  or  gage  as  per  Table  5.) 


Length 

of  Slate. 

Ins. 

Weight  1 

n  Lbs. 

per  Thickness. 

i' 

A" 

V 

r 

r 

K 

f 

!• 

12 

483 

726 

967 

1450 

1934 

2417 

2900 

3867 

14 

461 

602 

923 

1884 

1845 

2807 

2768 

8691 

16 

446 

669 

892 

1388 

1785 

2231 

2677 

3609 

18 

436 

662 

870 

1305 

1740 

2175 

2610 

3480 

20 

427 

640 

858 

1279 

1706 

2133 

2559 

3412 

22 

420 

680 

840 

1259 

1679 

2090 

2518 

3368 

24 

414 

621 

828 

1242 

1657 

2071 

2485 

3313 

26 

410 

616 

820 

1230 

1639 

2048 

2459 

3278 

Note.- 


'  slates  are  the  most  common. 


Slate  may  be  nailed  on  wooden  sheathing,  laths,  porous  terra  cotta, 
reinforced  concrete  sheathing,  etc.,  with  or  without  lelt  between.  The 
nails  may  be  of  malleable  iron,  copper,  zinc,  or  composition  metal.  Iron 
or  steel  nails  should  be  tinned  or  galvanized.  The  slates  are  often  fastened 
directly  to  the  sub-purlins  bv  copper  wire.  Slater's  cement  makes  a  good 
tight  bond  and  is  recommended  for  flat  pitch,  which  should  not  be  leas  than 
1-4  for  slate  roof. 

TiU  Roofing. — ^Tiles  are  made  of  terra  cotta  GMked  clay),  glass,  and 
metal. 

Clay  tiles  come  in  various  shapes  and  tmder  different  names,  as  plain  or 
flat,  groove-and-fillet,  pan,  Spanish,  etc.  The  plain  clay  tiles,  say  Ot'xlOJ* 
xH  thick,  will  weigh  from  15  to  18  lbs.  per  sq.  ft.  of  roof  when  uud  5^'  to 
weather.  The  weight  of  porous  terra  cotta  roofing  in  lbs.  per  square  foot 
o  4  (thickness  in  inches  + 1). 

The  M.  W.  Powell  (^.'s*  Specifications  for  a  Tile  Roof  are:  First  cover 
the  roof  foundation  with  6  thicknesses  of  No.  1  wool  roofing  felt,  weighing 
not  less  than  15  lbs.  (single  thickness)  per  100  sq.  ft.;  the  felt  to  be  laid 
smoothly  and  evenly,  and  well  cemented  tocether,  not  less  than  0  ins, 
between  each  layer,  with  roofing  cement.  All  joinings  along  the  walls 
and  around  the  openings  to  be  made  carefully.  The  roof  then  to  be  covered 
with  actinolite  cement,  and  vitrified  tile  to  be  laid  on  this  surface,  the  joints 
of  the  tile  to  be  made  with  marmolite  cement.  The  tile  to  be  6*'x9'x|' 
thick.  All  walls  and  openings  should  be  flashed  with  copper.  The  surface 
of  the  roof  foundation  should  be  perfectly  smooth  before  the  felt  is  laid. 

Glass  tiles  are  used  principally  for  skylights. 

Metallic  tiles,  of  copper,  zinc,  iron.  tin.  etc..  are  made  up  in  artistic 
forms  and  laid  as  shingles. 

Tin  Roofing. — ^Tin  plate  proper  consists  of  thin  sheets  of  iron  or  steel 
coated  with  tin  by  dipping  and  rolling.  When  the  molten  tin  is  adulter- 
ated with  lead  the  procfuct  is  terne  plate,  which  is  much  cheaper.  For  the 
base,  "charcoal"  plates  are  better  toan  "coke." 

Roofing  tin  comes  commonly  in  sheets  of  two  sizee.t  14^x20'  and  Vfs. 
28*.  As  manufactured  by  the  American  Sheet  and  Tin  Plate  Co.  of  Pitts- 
burg, there  are  112  14x20  sheets,  or  56  20x28  sheets^  in  a  box.  The  sheets 
are  graded  as  "Primes"  and  "Wasters."  The  Prmies  or  perfect  sheets 
are  branded  according  to  thickness  or  weight  of  iron  body,  as  IC  (4  lb.  pet 
sq.  ft.)  and  IX  (I  lb.  per  sq.  ft).  The  IC  20x28  plates  manufactured 
by  Merchant  and  Evans,  of  Philadelphia,  weigh  about  215  lbs.  net  per  box 
of  112  sheets,  and  the  IX  20x28  plates  weigh  about  270  lbs.  net.  The  IC 
and  DC  plates  are  supposed  to  have  the  same  thickness  of  coating. 

c»    V^.anufacturers  of  patent  roofing  materials,  cements,  etc.,  204  Dearborn 
^»^-  C^cago.  111. 

T  Sheeu  may  be  obtained  in  sizes  10x14  andi«Jaltiples  thereof. 


TILE',  TIN',  CORRUGATED-STEEL  ROOFING. 


801 


The  tin  sheets  are  laid  on  the  roof  in  two  wa3rs,  viz..  with  /lolaeam  (Pig. 
4),  or  with  standing  seara  (Fig.  6).  The  flat  seam  is  preferred  for  roofs  of 
small  pitch,  tisixig  14x20 
plates;  the  standing  seam 
tor  steep  roofs,  using  2(hc28 
plates,  generally.  When 
laid  with  flat  seam,  a  box 
of  112  sheets  20x28,  con- 
taining 436  sq.  ft.  of  plate, 
will  cover  about  884  sq. 
ft.  of  roof,  about  12%  be- 
in^  used  in  seams;  and 
laid  with  standing  seam  it 
will  cover  about  370sq.  ft., 
with  a  loss  of  about  16%. 
If  14x20  sheets  are  used.  Pig.  6. 

the  percentage  of  loss  is  slightly  greater.  Inversely,  to  cover  1000  sq.  ft. 
of  roof  will  require  683  sheets  of  14x20  if  laid  with  flat  seam,  or  803  sheets 
of  20x28  if  laid  with  standing  seam. 

Por  fastening  flat-seam  roofing,  use  1'  barbed  and  tinned  rooflxig  nails 
about  V  apftit  and  well  under  edges  of  seams.  In  soldering  use  rosin  (not 
acid)  as  a  nux.  In  laying  standing-seam  roofing  the  sheets  are  locked  and 
soldered  tocether  in  long  rolls  ixom  ridge  to  eaves.  The  standing  seams 
are  not  soldered,  but  are  locked  together  and  held  in  place  with  tin  cleats 
spaced  16  to  18  ins.  apart,  through  which  nails  are  dnven. 

Sh99i  Stml  Roofing.— ^ttX  steel,  ''black"  or  galvanised,  and  of  Noa. 
26,  27  and  28  gauge,  is  used  for  roofing.  It  comes  in  sheets,  or  in  rolls  up 
to  60  ft.  in  len^h.  The  sheets  are  laid  with  horizontal  flat  seams,  or  by 
lapping,  and  with  vertical  standing  seams,  crimped,  with  tin  fastenings. 

CorrugaUd  SU^l  Roofing. — 0>rrugated  steel,  "black"  or  galvanized, 
and  of  Nos.  16.  18,  20,  22,  24,  26  and  27  gage  is  usually  laid  directly  on  the 
purlins.  To  these  sheets  are  fastened  clips  of  various  kinds  by  means  of 
clinch  rivets  or  bolts.  The  clips  may 
hook  under  some  edge  of  the  purlin  or 
pass  completely  around  it,  as  m  Fig.  0. 
They  are  usually  spaced  12  inches  apart. 
Corrugated  sheets  are  rolled  from  plain 
sheets  30^  wide  and  in  lengths  up  to  10 
feet.  The  standard  corrugation  is  about 
21*  wide  and  K  deep,  which  narrows  the 
3ir  sheet  down  to  27^.  Allowing  for 
side  lap,  the  net  'Veather"  width  is  re- 
duced to  about  24'.  Lengthwise,  the 
sheets  should  preferably  rest  on  three 
purlins  to  give  continuotis-girder  strength, 
althotigh  the  strength  is  calculated  for  a  ^         da 

simple  span.     The  horizontal  or   "end"  F*-  6. 

lap  should  be  from  4'  to  8*,  the  latter  for  the  flaUer  pitches  and  where 
the  use  of  slater's  cement  is  desirable.  The  autragt  end  lap  is  say  0*. 
hence  for  sheeU  4-ft.  long  the  "weather"  area  is  but  70%  of  the  onginal 
flat  sheet;  6-ft.  kmg,  72%;  6-ft.  kwig.  73.3%;  7-ft.  long,  74.3%;  8-ft.Tong, 
76%;  »-ft.  kmg,  76.6%;  10-ft.  tong  76%.  In  other  words  the  weight 
of  cominited  sheeU  per  square  foot  of  roof,  laid,  is  respectively  43, 
30,  8d(.  86,  331^  82|  and  8H  per  cent,  grtater  than  that  of  the  plain  sheet 
metal.  Galvanizing  adds  about  one-third  of  a  pound  per  square  foot  to 
flat  metal,  or,  say,  three-eighths  of  a  pound  per  square  foot  to  corrugated. 
The  strength  of  corrugated  steel  roofing  may  be  obtained  from  the 
formula. 

In  whkh   Af— bending  moment  or  resisting  moment,  in  fl.-lbs.; 

/  —  allowable  stress  in  lbs.  per  sq.  in.  in  the  metal; 

a —depth  of  corrugations,  in  ins.; 

6 —breadth  in  ins.  of  loaded  sheet  b^for*  corrMgaring. 
Tar-Gravtl  Roofing. — Gravel  roofing  is  usually  laid  on  wooden  sheathing 
oovered  with  roofing  felt.    The  felt  is  laid  in  several  thicknesses,  with  lap 


804 


46.— iaX>F5. 


(O- — ^The  only   correct 
method  is  to  make  the  as-      | 
sumptions  as  near  the  true 
conditions  as  possible.  Thus:      I 

For  short  spans  with  both  «« 
ends   fixed,  the  wind   load 
and  reactions  will   be   con- 
sidered normal   to  one  face 
of  the  roof  as  shown  in  truss  ^ 
and  stress  diagrams  (A).  • ' 

For  long  spans  where  one  .   | 
end  of  truss  is  fixed  and  the 
other  end  is  a  roller  or  Blid-nt»M'6'3i 
ing  end,  it  should   be   cal- 
culated for  that   condition;  ^^r> 
namely,  for  wind    pressure    "" 
on  the  fixed  side,  and,  again, 
for   wind    pressure    on    the 
roller  side.     See  truss-  and 


SlmimS^jpO 


stress  diagrams  (j)  and  (o). 
Generally,  in  all  cases,  it  is 
good  practice  to  design  both 
halves  of  the  truss  symmet- 
rically, using  the  maximum 
stresses  obtainable  by  con- 
sidering the  wind  pressure 
on  either  side  of  the  roof, 
and  either  end  of  truss  roller 
or  fixed. 


^,^^  r-  BothEndsHwi,   ^ 
^/dComplmtfim  W'^W 


fixedSidb 


PlM.8.— 

5Stre98 
Diagrwns. 


8. — ^Ukit  ^trbssbs  in  Pratt  Roof  Trussbs  for  Unit  Loads  P. 

(See  Figs.  9,  Next  Page.) 

[+  "tension;  —  —compression.     For  character  of  stress  see  1  to  4  pitch.] 


A 

B 

C 

D 

1 

10- Panel  Pratt. 

8-Panel  Pratt. 

6-Panel  Pratt. 

4- Panel  Pratt. 

j3« 

A^ 

ti 

Ac6 

.C'* 

A*6 
iJo 

,r:c6 

•fi^ 

X{*6 

A<4 

ja** 

.c« 

»jd 

♦i  o 

^0 

^0 

^0 

i^o 

^S 

"5 

^O 

5o 

iio 

s:: 

'^Z 

sr 

s:: 

s:; 

'^Z 

s:: 

s:: 

Si 

s:; 

s:: 

sr 

1 

6.76 

+9.00 

11.26 

6.26 

+  7.00 

8.76 

8.76 

+6.00 

6.25 

2.26 

hTsToo 

3.75 

2 

6.00 

+8.00 

10.00 

4.60 

+6.00 

7.60 

3.00 

+4.00 

6.00 

1.50 

+  2.00 

3.50 

3 

6.26 

+  7.00 

8.76 

3.76 

+6.00 

6.25 

2.25 

+  3.00 

3.75 

2.70 

-8.35 

4.01 

4 

4.60 

+  6.00 

7.60 

3.00 

+  4.00 

5.00 

3.61 

-4.47 

6.99 

2.70 

-3.35 

4.01 

6 

3.75 

+  5.00 

6.25 

4.61 

-6.69 

6.73 

4.61 

-6.60 

6.78 

1.00 

-1.00 

1.00 

6 

6.41 

-6.71 

8.08 

6.41 

-6.71 

8.08 

4.61 

-6.69 

6.78 

1.26 

+  1.41 

1.00 

7 

6.31 

-7.83 

9.42 

6.31 

-7.8S 

9.42 

1.00 

-1.00 

1.00 

8 

7.21 

-8.94 

10.77 

6.31 

-7.83 

9.42 

1.26 

+  1.41 

1.60 

9 

8.11 

-10.06 

12.12 

1.00 

-1.00 

1.00 

1.50 

-1.60 

1.60 

10 

8.11 

-10.06 

12.12 

1.26 

+  1.41 

1.60 

1.68 

+  1.80 

1.96 

11 

1.00 

-1.00 

1.00 

1.50 

-1.60 

1.60 

12 

1.26 

+  1.41 

1.60 

1.68 

+  1.80 

1.96 

13 

1.60 

-1.60 

1.60 

2.00 

-2.00 

2.00 

14 

1.68 

+  1.80 

1.96 

2.14 

+  2.24 

2.36 

16 

2.00 

-2.00 

2.00 

16 

2.14 

+2.24 

2.36 

17 

2.50 

-2.60 

2.60 

18 

2.61 

+2.69 

2.80 

:tized  by 

Zoi 

Igle 

UNIT  STRESSES  IN  ROOF  TRUSSES, 


806 


Note.— Noe.  A,  B,  C  and 
D  corr^pond  with  aimilar 
Nos.  in  Tables  8  and  0. 


"  f\0i9i  Ptatt 


Pigs.  9. 

9. — Unit  Deductions  for  Onb-Half  Truss  (Lban-to). 
Supplementary  to  Table  8. 
(No  deductions  for  web  members.) 
For  unit  stresses  in  aw-half  of  each  of  the  above  trusses,  considered  as 
supported  at  points  a  and  fr.  or  a  and  c,  make  the  following  deductions: 
JSottom  chord  members. — Deduct  from  the  tmit  stress  in  each  bottom  chord 
member,  as  shown  in  Table  8,  preceding,  the  unit  stress  in  the  center 
panel  member  of  truss  (as  shown  in  black  face  type).    The  remainders 
are  the  unit  stresses  to  be  used. 
Top  ck&rd  members. — Deduction  for  each  top  chord  member  will  be  the 
bottom  chord  deduction  multiplied  by  secant  of  angle  of  inclination  of 
roof  with  the  horizontal.     For  1  to  8  pitch,  secant  —  1 .  202;  1  to  4  pitch, 
sec.  —  1.118;  1  to  5  pitch,  sec.  - 1 .077.    The  following  data  in  connec- 
tkm  with  Table  8  will  be  found  useful: 

A.  B.  C.  D. 

ruA„^  (Pitch  1-3:  1.202X8.76-4.51;  X3.00-3.61;  X2.26-2.T0;  Xl.50-1.80. 

^^^S^  i      "     I-*'.  1.118x6.00-6.50;  X4.00-4.47;  X3.00-3.36-.  X2.00-2.24. 

^       (      "     1-6:  1.077x6.26-6.73;  X6.00-6.30;  X3.76-4.04;  X2.80-2.ao. 

10.— Unit  Strbssbs  in  Fan  and  Fink  Roof  Trussbs  for  Unit  Loads  P. 

(See  Figs.  10,  next  page.) 
C+  —tension;  —  —compression.     For  character  of  stress  see  1  to  4  pitch.] 


E 

F 

G             1              H 

i 

Compound  Fan. 

Compound  Fink. 

Simple  Fan. 

Simple  Fink. 

1 

•9  0 

P 

ft 

a  o 

P 

|o 

^  0 

tt 

ti 

£  ** 

£:: 

s:: 

£  ** 

s::: 

sr 

2*  ♦* 

sr 

s:: 

'&:: 

8.26 

+  11.00 

13.76 

6.25 

+  7.00 

8.76 

3.75 

+6.00 

6.25 

2.26 

+  3.00 

3.75 

6.75 

+9.00 

11.26 

4.50 

+6.00 

7.50 

2.25 

+  3.00 

3.75 

1.50 

+  2.00 

2.50 

4.S0 

+6.00 

7.50 

3.00 

+4.00 

5.00 

3.80 

-4.70 

6.98 

2.15 

-2.91 

3.66 

7.14 

-10.06 

12.96 

4.65 

-6.48 

8.31 

3.53 

-4.65 

6.58 

2.71 

-3.36 

4.04 

7.28 

-9.93 

12.64 

6.20 

-6.93 

8.68 

4.50 

-6.50 

6.73 

0.83 

-0.89 

0.93 

8.25 

-10.96 

18.60 

6.76 

-7.88 

9.05 

0.93 

-1.08 

1.21 

0.75 

+1.00 

1.26 

8.8( 

-11.40 

14.07 

6.31 

-7.83 

9.42 

0.93 

-i.oB 

1.21 

8.94 

-11.26 

13.66 

0.83 

-0.89 

0.93 

1.50 

+2.00 

2.50 

9.01 

-12.30 

14.80 

0.75 

+  1.00 

1  25 

10 

0.9a 

-1.08 

1.21 

1.66 

-1.79 

1.86 

11 

0.9a 

-1.08 

1.21 

1.50 

+  2.0(» 

2.50 

12 

1.5( 

+  2.00 

2.50 

0.76 

+  1.00 

125 

13 

3.6( 

-2.00 

2.79 

0.83 

-0.89 

003 

14 

3.21 

+  8.00 

3.76 

2.25 

+3.00 

3.75 

16 

1.61 

+2.00 

2.50 

n 

0.93 

-1.08 

1.31 

17 
tt 

0.9! 
3.71 

;il 

ii 

Di 

jitized  b 

Go 

Ogle 

806 


4«.— iJOOFS. 


Note.— Nos.  E.  F,  G  and  H 
correspond  with  similar  Nos. 
in  Tables  10  and  " 


p  r.i-/^ 


7  Lk/      lA 


f:.  Compound  fan 


6.  Si/nph  Fan 

Pigs.  10. 


11. — Unit  Dbductions  for  Onb-Hal»  Truss  (Lban-to). 

Supplementary  to  Table  10. 

(No  deductions  for  web  members.) 

Bottom  chord  members. — Deduct  from  the  unit  stress  in  each  bottom 

chord  member  as  shown  in  Table  10.  preceding,  the  imit  stress  in  the  center 

panel  member  of  truss  (as  shown  in  black  face  type).     The  ren:iainders  are 

the  tmit  stresses  to  be  used. 

Top  chord  members. — Deduction  for  each  top  chord  member  will  be  the 
bottom  chord  deduction  multiplied  by  secant  ot  angle  of  inclination  of  roof 
with  the  horizontal.     Following  are  tmit  deductions  for  top  chords: 
Pitch  E  F  G  H 

1-3  5.41  3.61  2.70  1.80 

1-4  6.71  4.47  3.85  2.24 

1-5  8.08  5.39  4.04  2.60 

DESIGN  OF  COMBINATION  ROOF  TRUSSES. 

ProUem. — ^Trusses.  8  panels  ^  9  ft.-* 72  ft.,  spaced  14  ft.  centers; 
pitch  1  to  4:  height,  72  +  4-  18  ft.  Covering,  slate  laid  on  felt  and  1-inch 
spruce  sheattiing.  Loads: — Spruce  sheathing.  3  lbs.  per  ft.  B.  M.;  slate  and 
felt,  9  lbs.  per  sq.  ft.;  snow.  20  lbs.  per  horisontal  sq.  ft.;  wind,  30  lbs.  per 
sq.  ft.  against  vertical  surface. 

Solauon. — ^For  lack  of  space,  hints  only  can  be  given.  In  this  calcu- 
lation it  is  assumed  that  the  wind  load  and  snow  load  do  not  act  <m  the  samt 
face  of  roof  at  the  same  time;  but  may  act  separately  on  either  side,  or  simul- 
taneously on  opposite  sides;  For  maximtun  stresses  in  sheathing,  jack- 
rafters  and  purlins,  assume  the  wind  load  or  snow  load  to  act  with  the 
dead  loads;  for  maxim imi  stresses  in  the  trusses,  the  wind  load  is  assumed 
to  act  on  one  side  of  the  roof  and  the  snow  load  on  the  other  at  the  same 
time,  the  wind  load  being  con- 
sidered as  acting  (1)  on  the  fixed 
side,  and  (2)  on  the  roller  side; 
also  (3)  the  snow  load  may  be 
considered  as  acting  on  the 
whole  roof  without  any  wind 
load.  The  trusses  are  then 
designed  symmetrically,  using 
the  maximtun  dimensions  oi 
twin  members  in  either  half  of 
truss.  The  solution  in  detail  is 
as  follows: 

Spacing  of  Jack-Rafiers. — 
The  horizontal  sheathing  is 
nailed  to  the  vertically  inclined 
jack-tafters.  and  these  are  laid 

5****ctly.on  the  horizontal  pur-  - -o-   -- 

tms,  which  m  turn  rest  on  the  top  chord  joisU  of  the  roof 


d  by  Google 


808  4».^R00FS. 

Purlins  (white  pine).— The  span  of  the  purlins  i«  14  feet,  the  distana 
center  to  center  of  trusses.    They  are  laid  horizontally,  resting  on  the  top 
chord  joints,  and  hence  spaced  10  ft.  apart,  centers.    There  are  two  con- 
centrated loads  on  each  purlin,  namely,  where  the  jack  rafters  rest,  at 
points  4' -8'  apart  (Fig.  14).     Let  P  and  P,  Fig.  6. 
represent  respectively  the  normal  and  tangential 
components  of  each  of  these  loads  on  the  purlin.       i^-^'-y-^'y^^ 
Neglecting  the  weight  of  the  purlin  itself,  the  acting      f- — '  .^         + 

forces  are:  H- ^^       n 

Wind  acting.      Snow  acting. 

P F    T ?  "^'^ 

Wind 831         t      >      / 

Snow 747         373  •.    >k     x 

Slate 373         187         373         187 

Sheathing....       126  68         126  68  lO€ 

Jack-rafters..         64  27  64  27  ^-ij^ 

Total,  lbs. .     1384        277       1300        660  Fig.  16.— Purlin. 

Assuming  the  allowable  outer  fiber  stress  /—  1200  lbs.  per  sq.  in.  at  a  and  6. 
and  the  condition  "snow-acting"  for  maxmium,  we  have: 
Fnr    7»,irv    f     1300X14X12X6,  660X14X12X6    ,„-„  «  ^  .  .u^^/^ 
For    7  xlO'.  /-     7X3X10-XI0— *■    10X3X7X7    "^^^O  lbs.,  therefore 

use  purlins  7*'x  10*,  which  allows  liberally  for  weight  of  purlins  themselves. 
At  8  lbs.  per  ft.  B.  M.  these  will  weigh  17i  lbs.  per  lin.  ft. 

Trusses. — ^The  trusses  are  designed  for  the  following  Cases,  considtrim 
only  the  members  in  the  left  hand  half  of  the  symmetrical  truss: 
Case        I. — Dead  load  over  all. 
Case       II. — Snow  load  over  ail. 
Case     III. — Snow  load  on  right  half  only. 
Case     IV. — Snow  load  on  left  half  only. 
Case       V. — Wind  on  left;  left  end  "fixed." 
Case     VI. — Wind  on  left;  left  end  "roller." 
Case    VII.— Wind  on  right;  left  end  "fixed." 
Case  VIII.— Wind  on  right;  left  end  "roller." 

For  maximum  stresses — 
Combine  I  with  II. 

I  with  VI  or  VII. 

I  and  III  with  V  or  VI. 

I  and  IV  with  VII  or  VIII. 

Assuming  the  weight  of  the  truss  at  60  lbs.  per  Un.  ft.,  the  loads  per 
joint  of  truss,  for  calculating  stresses,  are  as  follows: 
Dead  load  per  joint. — Slate,  felt  and  sheathing,   12x14X10—1680  lbs.; 

jack-rafters.  3X 6 X  10"  180  lbs.;  purlins,  14 X  171-246  lbs.;  truss  HO 

lbs. ;  total,  2645  lbs. 
Snow  load  per  joint  (vertical).— 20 X 14 X  9-  2620  lbs. 
Wind  load  per  joint  (normal).— 17.8 X 14 X  10-2492  lbs. 

Table  12,  following  page,  gives  a  summary  of  the  stresses. 

Remarks. — The  preceding  principles  used  in  the  design  of  jack-raften. 
purlins,  trusses,  etc.,  of  the  combination  truss,  can  readily  be  applied  to 
the  design  of  steel  roofs. 

For  weight  of  steel  trusses  and  purlins,  see  pages  810  and  811. 


d  by  Google 


DESIGN  OF  COMBINATION  ROOF  TRUSS. 


800 


tized  by  Google' 


810 


46.^ROOFS. 


Details  of  Desiin.^Beiore  leaving  the  subject  of  the  design  for  com- 
bination root  truss,  three  points  in  the  details  of  design  will  be  considered, 
namely,  (a)  the  center  lower  chord  splice,  (b)  the  end  corbel,  and  (c)  the 
center  lower  chord  block. 

(a). — ^The  writer  can  conceive  of  no  case  in  practice  where  the  tensile 
strength  of  a  full  main  wooden  member  is  used  in  proportioning  that  mem- 
ber in  tension.     But  in  the  case  of  a  splice,  as  shown  m  Pig.  17,  the  tensile 


strength  of  the  rut  sec- 
tions of  main  member  , 
and  of  splice  have  to  beg 

considered,  as  well  as< 

the     shearing      values 
alongthe  grain,  and  the 
end  nber  bearing  values. 
Fig.  17  is  the  splice  de-  ^~' 
signed  for  center  of  low-  ^ 
er  chord  of  roof  truss  ^— 
shown  in  Pig.  16. 


rOak^hoe 


^ 


^F=^ 


k  -a.ir-^k-  k'lT  -•V-- -  ir — 


=f3!=q 


?i 


■9i* — jy--9t 


truss 


Sde 


View 


Fig.  17.— Bottom  Chord  Splice.  (Tension  26.000  lbs.) 
Yellow  pine.       Oak. 

Data. — Shearing  along  grain,  lbs.  per  sq.  in 100  1  SO 

Bearing 1500  1600 

Tension 1500  1500 


For  shear:       Oak  keys,   a  — 
For  bearing: 


26600 

2X8X130 
26600 


-13*;  Yellow  pine,  6- 


26600 
2X8X100 


-17». 


2X8X1500 
T>      .       .  /^  ,   ,  26600 

For  tension:    Oak  keys,   o- 2x8x1600 

(6.) — Fig.  18  shows  the  detail  at  end 
of  truss.  When  a  corbel  is  used  it  has 
to  be  long  enough  to  give  proper  shear- 
ing surface  at  the  right  of  each  key, 
while  the  shear  on  the  bottom  chord 
itself  is  at  the  left  of  each  key.  Vari- 
ous devices  are  used  to  resist  the 
thnist  of  the  rafter.  In  addition  to 
the  XV  notch  at  its  toe,  there  may 
be  a  bolt  or  strap  a  b  used  in  connec- 
tion with  a  corbel:  or  a  shorter  bolt 
a  p  without  the  corbel;  or  (still  without 
the  corbel)  straps  a  p  and  p  s  may  be 
joined  by  a  common  pin  p. 

(c.) — Detail    of  lower  chord  block  *-— 
(cast  iron)  is  shown  in  Fig.   19.     Where 
the  block  is  not  used  the  lower  chord  is 
simply  notched  as  shown  in  Fig.  20. 


-U'.call  ir 


«!*';  Yellow  pine.  y-2r. 


20. 


Framing  TaWc  or  TaMc  of  Squares.         ^«    ^^-  P«- 

— For  calculating  lengths  of  roof-truss  members,  use  Tables  of  Squares, 
Sec.  83.  pages  643  to  064.  (See  problems  on  page  638.)  For  calculating 
Howe  truss  braces  and  blocks  see  page  636. 

Weight   of  Steel  Construction  in  Roofs. — Where  trusses,  purlins,  etc 
are  of  steel  the  following  formulas  may  be  used  in  obtaining  the  approxi- 
mate weights  prior  to  actual  calculation: 
Weight  in  lbs.  of  metal  in  Trusses, )  ^  J_  (.y^,  ^  n) 

per  hor.  sq.  ft.  of  roof J      5  V  10/ 

Weight  in  lbs.  of  metal  in  Trusses.  )      j       (  With  minimum  ) 

Pxu-lins  and  Bracing,  per    hor.  f  =77;  S-{  value  of  about  V (*) 

sq.ft.  of  roof )     *«      M  or  5.  ) 

In  which  S  —  span  of  trusses,  in  feet. 

Weight  of  Sted  Trusses  and  Purlins.—The  above  formulas.  (1)  and  (2). 
are.  of  coitfsc,  only  approximate. 

f  iu  *^.'  ^o^^owi"g.  gives  more  exact  weights  of  trusses  and  of  porUns 
lor  the  specified  horizontal  load  of  60  lbs.  per  square  foot  of  building. 


WEIGHT  OF  STEEL  TRUSSES  AND  PURLINS. 


811 


13. — Stbbl  Roops — ^Approximatb  Wbioht  of  Trusses  and  Purlins. 
(Based  on  Uniform  Load  of  50  Lbs.  per  sq.  ft.  of  Building.) 


Span 

Distance  Center  to  Center  of  Trusses 

in  Feet. 

"      " 

Feet. 

6 

8 

10 

12 

14 

16    I     18 

20 

1  ^ 

24 

Weight  of  Trusses  in 

Lbs.  per  sq.  ft.  of  Bmlding. 

16 

1.61 
1.77 
1.02 
2.07 

1.61 
1.66 
1.81 
1.06 

1.42 
1.57 
1.70 
1.84 

1.84 
1.48 
1.61 
1.74 

1.27 
1.40 
1.53 
1.65 

1.21 
1.33 
1.46 
1.58 

18 

1.27 
1.39 
1.50 

ao 

1.33 
1.44 

22 

1.38 

24 

2.21 

2.08 

1.96 

1.86 

1.77 

1.69 

1.61 

1.54 

1.48 

i'42' 

2« 

2.34 

2.21 

2.09 

1.98 

1.89 

1.80 

1.72 

1.65 

1.58 

1.52 

28 

2.46 

2.38 

2.20 

2.10 

2.00 

1.90 

1.82 

1.75 

1.68 

1.61 

ao 

2  50 

2.45 

2.32 

2.21 

2.10 

2.01 

1.92 

1.85 

1.77 

1.70 

3S 

2.87 

2.72 

2.58 

2.46 

2.35 

2.25 

2.16 

2.08 

2.00 

1.92 

40 

3.13 

2.97 

2.83 

2.70 

2.50 

2.48 

2.38 

2.29 

2.21 

2.13 

46 

3  36 

3.20 

3.05 

2.92 

2.80 

2.69 

2.59 

2.49 

2.40 

2.32 

50 

3.57 

3.41 

3.25 

3.13 

3.00 

2.88 

2.78 

2.68 

2.59 

2.50 

55 

3.77 

3.60 

3.45 

3.30 

3.19 

3.07 

2.96 

2.86 

2.76 

2.67 

00 

305 

3.78 

3.63 

3.49 

3.36 

3.24 

3.13 

3.02 

292 

2.88 

65 

4.11 

3.95 

3.70 

3.66 

3.52 

3.40 

3.28 

3.18 

3.08 

2.96 

70 

4  26 

4.10 

3.95 

3.80 

3.67 

3.55 

3.43 

3.32 

3.22 

3.13 

75 

4.41 

4.25 

4.09 

3.95 

3.81 

8.69 

3.57 

346 

3.36 

3.26 

80 

4.55 

4.38 

4.22 

4.08 

3.95 

3.82 

3.70 

3.59 

3  40 

3.30 

85 

4.61 

4.35 

4.21 

4.07 

3.95 

3.83 

3.72 

3.61 

3.51 

90 

4.62 

4.47 

4.33 

4.19 

4.07 

3.95 

3.84 

3.73 

3.63 

100 

4.84 

4.69 

4.55 

4.41 

4.28 

4.17 

4.06 

3.95 

3.85 

110 

4.88 

5.05 

tofPu 

4.74 

4.92 

irlinsin 

4.61 

4.79 

Lbe.  p 

4.48 
4.66 

4.37 
4.55 

4.25 
4  43 

4.14 

4.33 

4.04 

120 

4.28 

Weigh 

er  sq.  ft.  of  Building. 

1 

0.15  1 

0.20  1 

0.25 

0.30 

0.35 

0.40  1   0.45 

0.50  1   0.55 

0.60 

KcferMice. — See,  also.  Sec.  47,  Buildings. 

EXCERPTS  AND  REFERENCES. 
Concrete  Platform  and  Umbrella  Roof  of  Union  Station,  at  Dayton,  O. 

(Bng.  News,  Aug.  8.  1901).— Illustrated. 

Howe  Truss  Roofs  for  TransfMrtation  Building,  at  St.  Louis  Expo- 
sition (Bng.  News.  May  19.  1904). — Illustrated.  Also  cost  data  of  the  prin- 
cipal buildings. 

Timber  Roof  Trussec  (By  J.  F.  Jackson.  Eng.  News.  June  2, 1904).— 
Ilhistrated. 

Method  of  Erectinff  the  Roof  Trusses  of  the  71  st  Regiment  Armory, 
N.  Y.  City  (By  W.  T.  McCarthy.    Eng.  News,  Tune  16.  1904).— Illustrated. 

Wind  Stneses  in  Knee-Braced  MiU  Buildings  (By  W.  H.  Dunham. 
Eng.  News,  Oct.  6,  1904). — Graphically  illustrated.  Discxissions:  Eng. 
News.  Nov.  10.  1904;   Jan.  25.  1905. 

Reinforced-Concrete  Slab  Roof  for  a  Small  Warehouse  (Eng.  News. 
June  22    1906).— Illustrated. 

Modified  Saw-Tooth  Roof  (By  M.  S.  Ketchum.  Eng.  News.  Nov.  23, 
1906).— Illustrated. 

Rehiforced-Concrete  Shingles  for  Roofing  (Eng.  News,  Aug.  30, 1906). 
— Illustration  of  hand  molding  machine  for  concrete  shingles. 

Saw-Tooth  Roofs  for  Factories  (By  K.  C.  Richmond.  Eng.  News. 
Dec.  13.  1906).— Illustrated. 

Steel  Dome  for  Emporium  Building,  San  Francisco  (Eng.  News, 
May  14.  1908).— Illustrated. 

An.  Improved  Method  of  Saw-Tooth  Roof  Construction  (By  S.  M. 
Green.  Eng.  News.  Sept.  3,  1908). — Illustrations  of  gutter  construction 
and  ventilator  design  for  use  on  weave  sheds. 

Illustrations, 

Description.  ^       Eng.  Rec. 

Roof  of  the  Standard  Steel  Car  Co.,  Butler,  Pa ?.9li.^dby,V?i^§Jov.  26.'10 


47.— BUILDINGS. 

Plastering. — Plastering  usually  consists  of  three  coats,  viz..  (1)  the 
rough  or  "scratch"  coat  which  is  applied  directly  to  the  wood-  or  metal 
laths;  (2)  the  "brown"  coat  which  is  floated  either  on  the  scratch  coat  (the 
latter  having  previously  been  scratched  with  a  comb  in  order  to  rou^en  it 
so  the  brown  coat  will  adhere  better),  or  sometimes  directly  on  the  wall; 
and  (3)  the  finishing  or  "skim"  coat  which  is  applied  to  tne  brown  coat 
after  it  has  been  finely  scratched  or  rou^ened.  The  skim  coat  may  be 
either  "stucco"  or  "hard  finish"  (gage  stuff)* 

(1.) — ^The  scratch  coat  is  composed  of  a  mixture  of  slaked  lime,  clear 
river  or  pit  sand  (essentially  free  from  salt)  and  cattle  hair* 
(preferably  goat  or  cow).  These  arc  mixed  in  the  proportion 
of  one  part  Time  paste  to  two  parts  sand,  with  li  bushels  of 
hair  to  each  barrel  of  unslaked  lime.  Less  hair  is  required 
for  walls  than  for  ceilings.  A  barrel  of  Rockland,  Me.,  lime 
weighs  220  lbs.  net,  contains  about  3i  cubic  feet,  and  will 
make  about  2.6  barrels  or  9  cubic  feet  of  paste.  A  barrel  of 
200  lbs.  will  make  about  8  cubic  feet  of  paste.  Approxi- 
mately. 9  cubic  feet  of  lime  paste.  18  cubic  feet  of  sand  and 
4  bushels  of  hair  will  cover  40  square  yards  about  f  thick 
on  wooden  laths  (Fig.  1).  and  about  30  square  yards  on  metal 
laths.  Fig.  1. 

(2.) — ^The  brown  coat  is  sometimes  leaner  in  cement  than  the  scratch 
coat  and  contains  usually  but  half  the  quantity  of  hair.  It  is  genendly 
I'  thick,  sometimes  |*.  Plaster  prepared  in  sheets  and  shipped  ready  fonr 
nailing  is  a  common  substitute  for  the  scratch  and  brown  coats. 

(3.) — ^The  skim  coat,  usually  f,  contains  no  hair.  Stucco  is  composed 
of  one  part  pure  lime  and  two  parts  clear  sand  of  the  purest  kind,  white 
preferred.  Hard  finish  is  made  from  any  of  the  patent  plasters  on  the 
market.  They  are  composed  principally  of  plaster  of  Paris  or  gypsum. 
which  gives  the  hard  finish,  and  are  recommended  for  general  use.  being 
more  satisfactory  in  many  ways  than  the  ordinary  lime  mixture.  A  mixture 
of  2 1  cubic  feet  each  of  lime,  plaster  of  Paris  and  white  sand  or  marble  dust 
will  skim -coat  about  100  square  yards  from  iV*  to  i"  thick. 

Lathing  and  plastering  is  commonly  estimated  to  weigh  about  10  lbs.  per 
square  foot. 

Lathing. — ^These  may  be  of  wood  or  metal.    Wooden  laths  are  usually 
li'  wide,  r  thick  and  4  ft.  long.    They  are  made  of  pine.  Spruce  or  hem- 
lock.   The  straight-grained  split  lath  is  preferable  to  toe  sawed.    A  bundle 
of  100  laths  (50  sq.  ft.,  solid— 12*  ft.  B.  M.— 37i  lbs.), 
spaced   }  inch,  will  cover  6.48  sq.  yds. :  equal  to  1 543  laths  per  100  sq.  yds. 
f    "        "       "     6.94       ''  ^'      ••  1441     "         "  '^ 

I    "        "       "      7.41       "  ••      "  1350 

About  10  lbs.  of  nails  are  required  per  100  so.  yds.  of  lathing.  From  the 
above  it  is  to  be  noted  that  lathing  weighs  about  f  lb.  per  square  foot  in 
place. 

Metal  lathing,  either  wire  or  expanded  metal  (see  Figs.  7  to  10),  is  now 
universally  used  m  fire-proof  buildings.  .The  weight  ranges  from  2}  to  4i 
lbs.  per  sq.  yd.,  or  i  to  i  lbs.  per  sq.  ft.  Generally,  the  weight  of  the  ex- 
panded metal  per  unit  of  area  is  about  one-half  or  less  than  the  weight  of  the 
original  sheet,  or,  in  other  words,  a  sheet  is  expanded  so  as  to  cover  twice 
or  more  its  original  area,  depending  upon  the  mesh.     Thus.   Diamond 

5 age  24  covers  2.2;  gage  26  covers  2.4;    "A"  gage  24  covers  1.9;    "B"  gage 
7  covers  2.06,  etc.     10  lbs.  of  staples  will  fasten  100  sq.  yds.  of  expanded 
metal  lathing. 

Partitions  are  either  permanent  (fixed)  or  temporary  (movabk).  In 
addition  to  the  ordinary  wooden  partition,  hollow  tiie  and  expanded  metal 
are  very  largely  used. 

*  Wood  fiber  is  often  used  instead  of  hair,  for  chea]^  work. 

gl2  Digitized  by  VjOOQIC 


PLASTERING.    LATHING.    PARTITIONS. 


813 


Wooden  Pariitions.'-^Ti^.  2  represents  the  average  partition  used  in  a 
frame  dwelling.  The  studding  is  spaced  16  ins.  on  centers.  It  will  be  noted 
that  thoee  pieces  marked  with  a  cross  ( X )  would  be  superfluous  if  the  door 
opening  were  omitted:    a,  c,  c  would  complete  the  studding,  and  b  the 


Pig.  2. — Stud  Partition;  dimension  stuff  either  all  Tfx  0* 
or  all  rx  V, 

bridging,  across  the  door  opening.  In  the  above  illustration,  about  26| 
lineal  feet  of  extra  scantling  is  required  for  each  door  opening,  over  that  for 
a  plain  partition.  A  partition  of  this  kind  will  weigh  3  or  4  lbs.  per  square 
foot,  exclusive  of  laths  and  plaster. 

HoUow-Tile  Porlitums.—SoM  terra  cotta  weighs  from  120  to  125  lbs. 
per  cubic  foot.  122|  lbs.  being  a  good  average;  but  the  hollow  blocks  for 
partitions  will  usually  not  exceed  two-thirds  that  amotmt,  and  may  weigh 
somewhat  less.    The  following  types  of  blocks  are  used: 


Fig.  3.— Plain  HoUow      Fig.  4.— Webbed  Block. 
Block. 

Figs.  3  and  4  are  ordinary  blocks 
such  as  are  used  in  a  partition  with 
I-beam  studdina  (sec  Fipj.  6^.  The 
patent  blocks  illustrated  in  Fig.  5  are 
sustained  laterally  by  means  of  hori- 
zontal metal  strips  or  bands  of  steel 
between  vertical  studding. 

Other  Partitions  than  the  hollow 
tile  which  may  be  used  in  connection 
with  I-beam  studding  (Fig.  6)  are 
(a)  plaster  boards,  which  are  laid  in 
between  the  beams  and  flushed  for 
plastering;  (b)  wire  lathing  strung 
between  the  beams  flush  with  the 
flanges  and  fastened  to  them,  and  also 
supported  intermediately  with  angles 
about  2-ft.  centers;  (c)  expanded  metal 
lathing. 


Fig.   6.— Patent   Block 
for  plastering. 


t 


Do 


jTit  rodb       _ _     , 


Fig.  6. — Ordinary    Hollow-tile  wall 
with  steel  I-beam  studs. 


814  Al.—BUILDiNGS. 

These  three  classes  of  materutl  may  also  be  used  wHb  other  skeletoo 
designs,  provided  the  principle  of  rigidity  is  maintained.  Pigs.  7  and  8  are 
examples  of  hollow  and  oi  solid  partition  construction  by  the  expanded 
metal  system,  and  Figs.  9  and  10  are  cuts  of  the  metal  lath  used.  The 
lathing  can  be  plastered  with  ordinary  lime  plaster,  but  cement  plaster  is 
better. 


Fig.  7. — F'kn  of  Expanded  Metal  Hollow  Partition 
Fig.  8. — Plan  of  Expanded  Metal  Solid  Partition. 


Fig.  9.— "Diamond"  Lath  (Expanded  Metal). 
24  Gage.'  Sheets.  18  ins.  x  96  ins.    20  sq.  yds.  per  bundle. 
26  Gage.    Sheets,  24  ins.  x  96  ins.    16  Sq.  yds.  per  bundle. 


Fig.  10.— "A"  Lath  (Expanded  Metal). 
24  Gage.    Sheets,  18  ins.  x  96  ins.     12  sq.  yds.  per  bundle. 

"B"  Lath. 
27  Gage.    Sheets,  18  ins.  x  96  ins.    20  sq.  yds.  per  bimdle. 

Floors,  Ceilings,  etc. — ^The  following  loads  are  considered  in  designing 
the  floors  of  buildings: 
(1.)  Live  loads,  due  to — 

(a)  People; 

(b)  Safes,  merchandise,  furniture,  machinery,  etc.; 

(c)  Partitions  which  are  subject  to  change  of  position. 
(2.)  Dead  loads,  due  to — 

id)  Flooring  or  tiling; 
(•)   Fireproof  arches  between  the  beams; 
(/)    Ceiling,  under  the  floor; 
(«)   Beams  directly  supporting  the  above; 

(»)  Girders,  supporting  the  beams  and  in  turn  directly  supported  by 
the  columns  or  walls* 


FLOORS.    CEIUNGS.    LIVE  LOADS,  815 

XMwt  LmmU. — ^There  is  great  diversity  of  opinion  among  engineers  re- 
garding the  live  loads  to  be  assumed  for  each  class  of  btaiMings,  and  this  is 
aggravated  by  the  decided  lack  of  harmony  of  the  various  city  building 
codes.  For  instance,  the  reqturements  of  the  ten  leading  cities  of  the  United 
States  are  shown  in  the  following  table: 

1. — ^Minimum  Livb  Loads  for  Floors  and  Roofs — ^Tbn  Lbadino 

CiTIBS. 


*  The  lower  supports  to  carry  two-thirds  of  the  total  weight. 
t  Pitch  less  than  20  d^rees. 
1  Pitch  more  than  20  degrees. 
1  For  flat  roofs. 

It  has  been  found  by  actual  test  that  forty  selected  men  with  an  average 
weight  of  163.2  lbs.  may  be  packed  into  a  floor  area  of  6-ft.  square,  when 
each  man  tries  to  occupv  as  little  space  as  possible.  This  is  equivalent  to 
an  occupied  area  of  A  of  a  sq.  ft.  per  man,  an  average  load  of  181.3  lbs.  per 
BQ.  ft.  ot  floor,  and  a  total  load  of  6628  lbs.  Perhaps  the  passenger  elevator 
"vrould  instance  a  locul  approaching  the  above  ideal  more  closely  than  would 
any  other  case  in  practice,  but  even  there  a  load  of  120  lbs.  per  sq,  ft.  makes 
a  very  compact  and  uncomfortable  mass,  and  is  probably  very  rarely  ob- 
tained. For  a  "mixed"  crowd  covering  a  considerable  area  as  in  public 
balls  or  corridors,  100  lbs.  per  sq.  ft.  may  be  taken  as  the  extreme  loading, 
even  when  the  ordinary  crowding  takes  place.  People  in  a  crowd  do  not 
stand  perfectly  erect  and  allow  themselves  to  be  packed  together  as  in  the 
ideal  case  above  cited.  Occasionally  during  a  panic  the  people  in  the  center 
of  a  crowd  may  be  packed  so  as  to  produce  a  concentrated  loading  nearly 
cQuivalent  to  Uie  ideal  load  of  180  lbs.  per  sq.  ft.  over  a  limited  area,  but  by 


816 


4!!. —BUILDINGS. 


no  means  over  the  whole  floor  space  or  even  over  any  oonsidenible  portion 
of  it.  Hence  in  designing  floors  where  people  congregate  it  is  good  practice 
to  adopt  heavier  loadings  for  small  floor  areas  in  a  building  than  tor  large 
ones.  In  other  wcnrds  the  hve  load  per  sq.  ft.  of  floor  area  may  be  allowed 
to  decrease,  in  tall  buildings,  from  the  maximitm  loading  for  floor  beams 
and  arches^  down  to  the  minimum  for  columns  and  foundations — main 
girders  takmg  an  intermediate  position. 

Loads  from  Safes. — One  of  the  most  important  factors  to  be  considered 
in  the  design  of  floors  for  office  buildings  and  offices  in  general  is  the  effect 
due  to  the  weight  of  safes.  Hence  the  following  table  is  inserted  as  com- 
prising the  heaviest  safes  in  use  (the  900's  and  800's)  and  also  thoae  com- 
monly used  for  upper  floor  offices  (the  500's).  Nxunbers  **A",  "B"  and"C" 
are  very  heavy  compared  with  their  dimensions  and  are  liable  to  be  placed 
in  any  office.  The  600's  and  700's,  omitted  in  this  table,  range  in  weight 
between  the  500's  and  800's.  The  2600-lb.  safe.  No.  513,  is  the  lightest  one 
considered.  For  any  desired  calculation  columns  6  and  7.  showing  the 
distance  apart  of  the  supporting  wheels,  may  be  used  in  connection  with 
either  column  8.  or  with  column  2  in  connection  with  10.  11  or  any  other 
assumed  weight  of  the  contents  of  the  safe.  In  general,  the  use  of  column 
8  is  considered  good  practice. 


2. — ^Tablb  of  Wbiohtb  and  Dimensions  of  Heavy  Safes. 
(Hall's  Safe  Company  of  Cincinnati,  Ohio.) 


Outside  Dimen- 

Wheel  Base 

Wt-lnLbs. 

Weight 

stons  In  Inches. 

InFt. 

Dead 

1-40 

of 

of  Safe 

(Approx.) 

Weight 

Contents  at  1 

No. 

(Emp- 
ty.) 

on  Each 
Wheel. 

Kind  of  Rftfr. 

100 

35 

i»iiMi  ui  duiv. 

+  10%. 

Lbs. 

Lbs. 

H-ht 

Wth 

D'th 

Wth 

D'th 

Cu. 

per 
Co. 

per 
Cn- 

Lbs. 

Lbs. 

Ft. 

Ft. 

Ft. 

(1) 

(2) 

(3) 

liT 

(6) 

(6) 

"(tT 

(8) 

(9) 

(10) 

(11) 

(13) 

921 

16080 

86.5 

68.5 

36 

4.7 

2.7 

4422 

29.2 

2920 

730 

Doable- 

920 

12530 

77.5 

59.5 

38 

4.0 

2.6 

3445 

20.2 

2020 

605 

923 

11100 

79 

51 

3.4 

2.5 

3052 

16.0 

1600 

400 

proot  lined 
with    sud. 

918 

9650  69.251 

51 

3.4 

2.5 

2653 

13.2 

1320 

330 

922 

8000 

73.5 

45.5 

2.8 

2.6 

2200 

12.2 

1220 

305 

and  steel  In- 

916 

7270 

61 

44 

2.7 

2.5 

2000 

970 

343 

side    doors. 

916 

6200 

57 

40 

2.6 

2.5 

1705 

760 

190 

For    BsB- 

914 

6380 

53 

38 

2.4 

3.5 

1480 

630 

158 

keis.: 

831 

11000 

86.6 

68.5 

4.7 

2.3 

3025 

28.4 

2840 

710 

820 

8900 

77.5 

69.6 

4.0 

2.8 

244f 

21.8 

8180 

530 

DonUe- 
door.     fire- 
proot  lined 
with    sted: 
no  tnslde 
doors.    For 
Jewelei& 

823 

7900 

79 

51 

3.4 

2.3 

2173 

18.3 

1830 

468 

818 

6400 

69 

51 

3.4 

2.3 

1760 

15.1 

1610 

37{ 

822 

6300 

73.6 

45.6 

2.8 

2.3 

1733 

14.1 

1410 

353 

819 

6250 

69 

38 

2.4 

2.3 

1443 

11.0 

1100 

375 

816 

4900 

61 

44 

2.7 

2.3 

1348 

11.3 

1130 

283 

815 

4200 

56.6 

39.5 

2.5 

2.3 

1165 

860 

213 

817 

4025 

61 

34 

2.0 

2.3 

1107 

800 

300 

814 

3700 

53 

38 

3C 

2.4 

2.3 

1018 

740 

185 

621 

8000 

86.5 

68.5 

34 

4.7 

2.5 

3200 

38!2 

3820 

95B 

' 

620 

6000 

77.6 

69  6 

32 

4.0 

2.4 

1650 

27.0 

3700 

675 

Douhlo- 

623 

5350 

79 

61 

32 

3.4 

2.4 

1471 

23.2 

2320 

580 

door.     Itee- 

518 

6150 

69 

51 

30 

3.4 

2.3 

1416 

17.0 

1700 

436 

prooC  wttb 

632 

4700 

73.5 

45.5 

30 

2.8 

2.3 

1292 

15.9 

1500 

398 

Inside 

516 

3650 

61 

44 

30 

2.7 

2.3 

1003 

12.7 

1270 

3n 

doors;  con- 

619 

3550 

69 

38 

30 

3.4 

2.3 

97« 

12.2 

122c 

305 

taining 

617 

3200 

61 

34 

30 

2.0 

2.3 

880 

89C 

233 

Bank«;s 

515 

3150 

57 

40 

29 

2.5 

2.i 

866 

040 

335 

steel   dieit 

514 

2850 

53 

38 

29 

2.2 

783 

78S 

195 

For    gew*^ 

512 

2800 

55.5 

34.75 

29 

20 

2.2 

770 

720 

180j 

aloAoeaK. 

513 

2500 

49 

36 

28 

2.2 

2.1 

686 

600 

160 

"B" 
"A" 

6760 

52 

30 

26 

1.9 

1.9 

1682 

92S 

330 

Square  _^ 

4600 

45 

28 

25 

1.8 

\.i 

1238 

640 

160 

door.      Foe 

3600141 

25 

24 

1.7 

1.7 

963 

450 

11^ 

Banlwis._ 

WADS  FROM  SAFES.    FLOOR  CONSTRUCTION, 


817 


BoamA      ^ 

6' — I- — «■-- f 


Fixed  Vaults  with  their  contents  may  be  considered  as  static  loads  and 
must  be  specially  considered,  but  Movable  Safes  are  liable  to  be  placed  in 
almost  any  position  on  the  floor. 

Problem  1. — On  the  first  floor  of  a  building  find  what  single  concentrated 
load  will  give  the  same  bending  motnent  as  safe  No.  921,  Table  2,  to  one  of 
a  system  of  parallel  beams  spaced  6  ft.  centers  and  16  ft.  long? 

Solution. — Let  A,  B  and  C,  Fig.  11,  repre- 
sent the  beams  of  which  B  is  the  one  under 
consideration;  D  and  £  the  supporting  girders; 
and  1,  2,  3  and  4  the  four  wheels  supporting 
the  safe,  of  which  c  is  the  center.  From  the 
principle  of  the  maximum  floor-beam  reaction, 
page  (N2.  B  will  sapport  the  greatest  load  when 
It  bisects  the  normal  distance  between  the 
center  of  gravity  c  and  the  line  1-2;  that 
is,  with  maximum  resultant  at  r.  Likewise,  the 
maximum  moment  on  B  will  obtain  at  m.  equi-  ' 

distant  with  r  from  the  line  K-K  which  bisects  Fig.  11. 

the  beams.    If  each  of  the  comer  weights  of  the  safe  is  4422  lbs.,  we  have, 
for  resultant  at  r ,  on  beam  B. 


~wr 


ir- 


eTrTT 


-J^.-^ 


r-8844(^^^^^  -  12912  lbs.. 


and  maadmiun  moment,  at  m,  —  r^  (8- 
10 


1.175)«. 


The  moment  due  to  a  load  P  at  the  center  of  the  beam  » -^  X  8;  whence, 
equating  with  the  above, 

jX8-^(6.825)«  or  P-.7278f- 9400  lbs. 

Hence,  in  the  above  case  it  will  be  noted  that  a  concentrated  load  of  9400 
lbs.  applied  at  the  center  of  the  beam  B  will  produce  a  bending  moment 
equal  to  that  of  the  safe  weighing  17,688  lbs.,  placed  r»ctonf««/ar/y  in  the 
most  critical  position.  Furthermore,  this  is  equivalent  to  a  runnmg  load 
of  1175  lbs.  per  lineal  foot  of  beam,  or  to  a  distributed  load  of  235  lbs. 
per  square  foot  of  floor.  If  safe  is  placed  diagonally  on  beam,  the  bend- 
ing moment  will  be  increased  about  5  per  cent. 

Examples  op  Floor  and  Cbilino  Construction. 


Fig.  12. — Floor  Framing. — a  is  a  double  hanger  or  Btirrup; 
5  is  a  patent  hanger;  c  is  a  common  mortise. 

The  under  flooring  may  be  spruce  or  hemlock,  V  thick  and  laid  diago- 
nally in  order  to  brace  or  stiffen  the  floor.  On  top  of  this  and  at  right  an^lc 
y/rit^  the  tail  beams  is  laid  the  finished  flooring  which  may  be  white  pine 
\^  tlxick  or  any  other  flooring  material.  The  ceiling  may  consist  of  lathmg 
ftxuS  plastering  bekvw  the  beams  in  the  usual  manner. 


818 


Al.—BUILDINGS. 


Fig.  13.7-Centerin«  for     Fig.   14.— 4-inch   Brick   Arch.— c  i 
Brick  Arch.  wooden  screed  on  which  is  nailed  th 

the  rod;  w,  washer;  a,  angle  iron 
thrust  of  the  arch;  /.  steel  beam. 

Fig.  16.— Hollow   Bricks.  Pig.  16.— « 

Instead  of  the  solid  bricks,  hollow  bricks  are  often  ua 

reduce  the  dead  load  of  the  arch.    Figs.  15  and  16  are  cxamp 

htillow  bricks  and  skew -backs.    They  can  be  manufactured 

pattern. 


Fig.  17.— Corrugated  Steel  and 
Concrete  Floor. 


Fig.  18.— Steel  T 
Concrete  F 


Fig.  19.— Typical  Terta- 
Cotta  Floor. 


Figs.  20. — ^End-Construction 
Tile  Floor. 


Fig.  23. 


r  Cinder  Concrete  between  Screeds^ 


Fig.  24 


t- 18-25.  F^.  26.  Fig.  27.       ^   fS!28. 


I  FLOOR  CONSTRUCTION.    CITY  CODES,  819 

DIGEST  OP  THE  NEW  YORK  CITY  BUILDING  CODE  (1906). 

[Also  District  of  Columbia,  practically  the  same.] 

QUALITY  OF  MATERIALS. 

1.  Line  mortar. — 1  part  lime,  not  >  4  parts  sand;  lime  properly 
ilaked  before  being  mixed  with  the  sand. 

2.  Cement  mortar. — 1  part  cement,  not  >  8  parts  sand;  mixed  before 
adding  water.  Portland  ctnunt'^ cement  that,  when  tested  neat,  will  resist 
tension  of  at  least  120  lbs.  per  sq.  in.,  after  1  day  air  setting:  and  300  lbs.. 
after  1  day  in  air  and  0  days  in  water.  Othsr  c^nunts,  60  lbs.  and  120  lbs., 
respectively. 

8.  Cement  and  lime  mortar. — 1  part  cement.  1  part  lime,  not  >  3  parts 
of  sand  to  each. 

4.  Concrete. — At  least  1  cement;  2  sand;  A  clean  broken  stone  (2  in. 
ring),  or  6  clean  graveL 

5.  Wroufht  iron. — Ultimate  strength  48,000  lbs.  per  sq.  in.;  elastic 
limit  not  <  24,000;  elongation  20%  in  8  ins.  (small  specimens). 

8.  Steel.~Ult  str.  64-64,000;  elastic  limit,  not  <  32.000;  elongation, 
not  <  0.20.    Rivet  steel.  60-58,000  ult  str. 

7.  Cast  iron. — One-inch  square  bar,  64-in.  span,  shall  support  central 
load  of  460  lbs.  before  breaking.  Tensile  strength,  not  <  16.000  lbs.  per 
sq.  in.  (small  specimens). 

EXCAVATIONS  AND  FOUNDATIONS. 

8.  Bearing  capacity  of  soil. — Where  no  tests  are  made  allow  for  soft 
clay,  1  ton  per  sq.  ft.;  ordinary  clay  and  sand  together,  in  layers,  wet  and 
spnngy,  2  tons;  loam,  clay  or  fine  sand,  firm  and  dry.  8  tons;  very  firm, 
coarse  sand,  stiff  gravel  or  hard  clay.  4  tons. 

0.  Presinre  under  footings  of  foundations. — For  warehouses  and  fac- 
tories, full  dead  and  full  live  loads;  for  stores,  light  factories,  churches, 
school  houses,  and  places  of  public  amusement  or  assembly,  full  dead  and 
75  per  cent  of  live  loads;  for  office  buildings,  hotels,  dwellings,  apartment 
houses,  tenement  houses,  lodging  houses,  and  stables,  full  dead  load  and 
60%  of  Hve  load. 

10.  Foundations. — Piles  20  ft.  or  less  in  length,  not  <  5  ins.  at 
enall  end  and  10  ins.  at  butt.  Piles  over  20  ft.,  not  <  12  ins. 
at    butt.        Max   load   per   pilef  40,000    lbs.       Use    Engineering    News 

formula  when  pile  is  not  driven  to  refusal:  P— — — r  .    Safe  load  for  stone, 

brick  or  concrete  piers  in  caissons:  to  rock,  not  >  16  tons  per  sq.  ft.;  to 
firm  gravel  or  hard  clay,  10  tons;  in  open  caissons  or  sheet  pile  trenches, 
8  tons. 

WOODEN  BEAMS.  GIRDERS  AND  COLUMNS. 

11.  Wood  beams. — Minimtim  thickness,  8  ins.  Every  wood  header  or 
trimmer  more  than  4  ft.  long  shall  be  hung  in  stirrup  irons.  All  wood  floor 
and  wood  roof  beams  bridged  with  cross  bridging  spaced  not  >  8  ft.  Safe 

imiform  load  in  lbs.  per  lineal  foot  for  long  spans:  hemlock.  70  -j- ;  spruce 
tnd  white  pine,  M-j-;  oak,  120  -j-;  yellow  pine,  140  -j-;  in  which  b  — 

yrcaudth  of  beam  in  indies.,  (f— depth  in  ins.,  L^- length  in  ft.  For  short 
;pans  the  shear  must  be  considered. 

12.  Timber  for  trusses. — Working  stresses  in  timber  struts  of  pin-con- 
lected  trusses  shall  not  exceed  75%  of  the  working  stresses  established  in 
•ar.  27-8a 

FIREPROOF  BUILDINGS. 
18.    Fireproof  buildings. — For  buildings  exceeduig  12  stories  or  150  ft. 
tte  floors  shall  be  of  stone,  cement,  rock  asphalt,  tiling,  etc..  or  the  sleepers 
n<i  floors  may  be  of  wood  treated  by  some  approved  process  to  render  them 
repmxrf.  ^  . 

" _  _       -.  .  ,.—  Digitized  by  VjOOQIC 

♦  See  Sec.  60.  Foundations,  page  871.  o 


830  47,^BUILDINGS, 

14.  Fireproof  floors. — Shall  be  constructed  with  wrought  iron  or  steel 
floor  beams  calculated  to  deflect  no  more  than  ^-inch  per  foot  of  span 
under  total  (live  and  dead)  load;  and  tie  rods  shall  be  spaced  not  >  8 
times  deplh  of  beam.  (1)  Brick  arches,  springing  from  the  lower  flange  of 
the  steel  beams,  shall  be  designed  with  a  nse  not  <  1  i  ins.  for  each  foot  of 
span,  and  with  a  thickness  not  <  4  ins.  for  spans  of  5  ft.  or  less,  and  not 
<  8  ins.  for  spans  over  6  ft.  They  shall  be  composed  of  good  hard  bride  or 
hollow  brick  of  ordinary  dimensions  laid  to  a  line  on  the  centers,  property 
and  solidly  bonded,  each  lon^e^itudinal  line  of  brick  breaking  joints  with  the 
adjoining  lines  in  the  same  ring  and  with  the  rin«  under  it  when  more  than 
4-in.  arch  is  used;  cement  mortar  joints.  (2)  Hollow  tile  arches  of  hard- 
burned  clay  or  porous  terra-cotta  stxaXl  have  an  effective  depth  not  <  If 
ins.  per  ft.  of  span,  some  allowance  (not  over  6  ins.)  being  made  if  soffit  ca 
arch  is  straight;  if  segmental,  the  depth  of  tile  shall  be  not  <  0  ins.  if  rise 
is  not  <  If  ins.  times  span  in  ft.;  cement  mortar  joints.  (3)  Portland 
cement  concrete  arches,  segmental,  with  rise  not  <  li  ins.  times  span  in  ft. 
Thickness  at  crown  not  <  4  ins.  Mixed  as  per  par.  4.  Arches  shall  be  rein- 
forced and  protected  on  under  side  with  corrugated  or  sheet  steel,  steel  ribs, 
or  metal  in  other  forms  weighing  not  less  than  1  lb.  per  sq.  ft.,  and  having 
no  openings  larger  than  3  sq.  ins.  (4)  Reinforced  floors  of  solid  or  hollow 
Inimed  clay,  stone,  bnck,  or  concrete  slabs  in  flat  or  curved  shapes,  in 
combination  with  wire  cloth,  expanded  metal,  wire  strands,  or  wroueht 
iron  or  steel  bars,  may  be  used,  but  proper  tests  shall  be  made  as  pxx>vided 
in  the  Code. 

IRON  AND  STEEL  CONSTRUCTION. 

16.  Skeleton  construction. — Where  columns  are  xised  to  support  iron 
or  steel  girders  carrying  inclosure  walls,  the  said  coltimns  shall  be  of  cast 
iron,  wrought  iron,  or  rolled  steel,  and  on  their  exposed  outer  and  inner  sur- 
faces be  constructed  to  resist  fire  by  having  a  casing  of  brickwork  not  leas 
than  8  ins.  thick  on  the  outer  sxirfaces,  nor  less  than  4  ins.  thick  on  the  ixmer 
surfaces,  all  bonded  into  the  brickwork  of  the  inclosure  walls.  Exposed 
sides  of  girders  protected  with  4  ins.  of  brickwork;  outer  edges  of  flanges, 
2  ins. 

16.  Steel  and  wrought  iron  columns. — Minimum  thickness  of  raetal.  ) 
inch.  Least  lateral  dimension  ^  length  of  coltmin,  except  as  allowed  in 
par.  26. 

17.  Cast  iron  columns. — Minimum  diameter,  6  ins.;  minimum  thick- 
ness of  metal,  |  in.  Least  lateral  dimension  ^  length  of  column,  except  as 
allowed  in  par.  26.  , 

18.  Steel  and  Iron  girders. — Stiffened  shall  be  used  at  intervals  xMt 
exceeding  120  times  thidcness  of  web  if  the  tmsupported  depth  of  the  web 
plate  exceeds  60  times  its  thickness. 

19.  Rolled  beams  used  as  girders. — Beams  in  pairs  to  form  girders 
shall  be  connected  together  by  bolts  and  separators  at  intervals  of  not  more 
than  6  ft.  Beams  12  ins.  or  more  in  depth  shall  have  2  bolts  to  each  aepsk- 
rator. 

20.  Cast  iron  lintels. — Maximum  span,  16  ft.;  minimimi  thickness  of 
metal.  }  in. 

21.  Painting  of  structural  metal  work. — After  erection  all  work  ^lall 
be  painted  at  least  one  additional  coat.  All  iron  or  steel  used  under  water 
shall  be  inclosed  with  concrete. 

FLOOR  LOADS. 

22.  Floor  loads. — Dead  loads— weight  of  walls,  floors,  roofs,  partitioos 
and  all  permanent  construction.  Live  loads  —  variable  loads  "-all  loads 
other  than  dead  loads.  Live  loads  per  sq.  ft.  of  floor  shall  be  assumed  as 
follows: 

For  dwelling,  apartment,  tenement,  hotel  or  lodging  house,  not  <  60  lbs. 

For  office  ptirpose,  first  floor,        -------       75    •• 

"         •*  all  floors  above  the  first,      -       -       -       **     150    " 

]]  school  or  place  of  instruction,  -  *•  -  -  -  "  75  ** 
II    stable  and  carriage  house  purposes,     -       -       -       -       *'       76    " 

^\    place  of  public  assembly, -"•0" 

,1  ordinary  stores,  light  manufacttuing,  light  storage,  -  "  ISO  •' 
,,  warehouse,  factory,  heavy  stores,  ----'•  ISO  - 
„  roofs  with  pitch  less  than  20*',  per  area  of  roof,  -  '*  60  " 
••  -ij  «  ."  more"  20<»,  per  horizontal  area..  ^-^.1^"  30  '* 
sidewalks,  between  the  curb  and  area  Unes,      ^^^^Iv."     |00    *■ 


d  by  Google 


822  il.— BUILDINGS. 

28.  Tenston  (Direct). — Safe  stress  in  lbs.  oer  sq.  in.:  Rolled  steel,  1«,- 
000;  cast  steel.  16.000;  wroxight  iron,  12,000;  cast  iron,  3,000;  yeUofw 
pine.  1.200;  white  pine,  spruce.  800;  oak.  1,000;  hemlock.  600. 

29.  Shear. — Safe  stress  in  lbs.  per  sq.  in.:  Cast  iron,  3.000.  Web  plates: 
Steel,  9,000;  wrought  iron.  6,000.  Shop  rivets  and  pins:  Steel.  10.000; 
wrought  iron.  7,500.  Filed  rivets:  Steel,  8,000;  wroiight  iron,  6,000. 
Field  bolts:  Steel,  7,000;  wrought  iron.  6,600. 


With 

Across 

With 

Across 

Fiber. 

Fiber. 

Fiber. 

Fiber. 

Yellow  pine 

70 

600 

Locust,      - 

100 

720 

White  pine, 

40 

260 

Hemlock,   - 

40 

275 

Spruce,      - 

60 

320 

Chestnut.  - 

150 

Oak,  -       - 

-       100 

600 

30.  Bending. — Safe  extreme  fiber  stess  in  lbs.  per  sq.  in. :  Rolled  beams. 
Steel,  16,000;  wrought  iron,  12.000.  Rolled  pins,  rivets  and  bolts:  Steel, 
20.000;  wrought  iron.  16.000.  Riveted  beams  (not  flange  section):  Steel 
14,000;  wrought  iron,  12,000.  Cast  iron:  Compression  side,  16.000;  tensioo 
side,  3,000.  Yellow  pine.  1,200;  white  pine,  spruce.  800;  oak,  1,000;  kxmst. 
1,200;  hemlock,  600;  chestnut,  800.  Granite.  180;  Greenwich  stone,  150; 
gneiss  (New  York  City).  160;  limestone,  160;  slate.  400;  marble.  120; 
sandstone,  100;  bluestone  (North  River),  300;  brick  (common),  60;  brick- 
work (in  cement),  30.  Concrete:  (Portland),  1:2:4,  30  lbs.;  1:2:5,  20  lbs.: 
(Rosendale,  or  equal),  1:2:4,  16  lbs.;  1:2:6.  10  lbs. 

31.  Wind  pressure. — All  structures  exposed  to  wind  shall  be  designed 
to  resist  a  horizontal  wind  pressure  of  30  lbs.  for  every  sq.  ft.  of  stuiace  thus 
exposed,  from  the  ground  to  the  top  of  same,  including  roof,  in  any  directkm. 
In  no  case  shall  the  overturning  moment  due  to  wind  pressure  exceed  76% 
of  the  moment  of  stability  of  the  structure.  In  all  structiires  exposed  to 
wind,  if  the  resisting  moments  of  the  ordinary  materials  of  constmctkm 
such  as  masonry,  partitions,  floors  and  connections  are  not  sufficient  to 
resist  the  moment  of  distortion  due  to  wind  pressure,  taken  in  any  direction 
on  any  part  of  the  structiu^,  additional  bracing  shall  be  introduced  sufficient 
to  make  up  the  difference  in  the  moments.  In  calculations  for  wind  bracing, 
the  working  stresses  set  forth  above  may  be  increased  by  50%.  In  buildings 
under  100  ft.  high,  where  the  height  does  not  exceed  four  times  the  average 
width  of  the  base,  the  wind  pressure  may  be  disregarded. 

CONCRETE-STEEL  CONSTRUCTION. 

1.  The  term  "concrete-steel"  shall  mean  an  approved  concrete  mixture 
reinforced  by  steel  of  any  shape,  the  steel  to  take  up  the  tensional  stresses 
and  assist  in  the  resistance  to  shear. 

2.  Concrete-steel  construction  will  be  approved  only  for  buildings 
which  are  not  required  to  be  fireproof  by  the  building  code,  unless  satisfac- 
tory fire  and  water  tests  shall  have  been  made  \mdef  the  supervision  of  this 
bureau. 

3.  Complete  drawings  and  specifications  must  be  filed  with  the  supt.  of 
buildings,  showing  all  details  of  the  construction,  the  size  and  position 
of  all  reinforcing  rods,  stirrups,  etc.,  and  giving  the  composition  of  the 
concrete. 

4.  Execution  of  work  shall  be  under  the  control  of  a  competent  fore- 
man or  superintendent. 

6.    Ojncrete  to  be  mixed  in  the  proportions  of  1  cement,  2  sand,  and  4 
stone  or  gravel ;  or  the  proportions  may  be  such  that  the  resistance  of  the 
concrete  to  crushing  shall  not  be  less  than  2000  lbs.  per  sq.  in.  after  harden-   , 
ing  for  28  days.    The  concrete  is  to  be  what  is  usually  Jcnown  as  a  "wet" 
mixture. 

6.  Only  high-grade  Portland  cements  shall  be  permitted ;  and  shall  de- 
velop a  tensile  strength  of  at  least  300  lbs.  per  sq.  in.  after  1  day  in  water;  J 
at  least  500  lbs.  per  sq.  in.  after  1  day  in  air  and  6  days  in  water;  and  at 
least  600  lbs.  per  sq.  in.  after  1  day  in  air  and  27  days  in  water. 

7.  The  sand  must  be  clean  and  sharp,  free  from  loam  or  dirt,  and  not 
finer  than  the  standard  sample  submitted. 

8.  The  stone  shall  be  clean,  broken  trap  rock,  or  gravel,  of  a  size  thai 
will  pass  through  a  three-quarter  inch  ring. 

It    •     ^^^  ^^^^  ^^^^^  ^^^^  ^^  "^*-  str.  of  64-64,000  lbs.  per  sq.  in.;  an  elastic 
than  20%  m  8  ins.  Digitized  b~    ^^^^^  "^ 


d  by  Google 


824 


il. "BUILDINGS, 


Adhesion — Bond. — For  a  concrete  of  1:2:4  mix,  the  allowable  adhefion 
in  lbs.  per  sq.  in.  of  surface  of  embedment  shall  not  exceed  the  following: 
Onplambarsof  structural  steel,  70;  on  plain  bars  of  high  carbon  steel,  ^ 
on  plain  flat  bars  in  which  width  to  thickne^  is  not  >2  to  1,  50;  on  twisted 
bars  when  twisting  is  not  <  one  complete  twist  in  eight  diameters,  100. 

EXTRACT  FROM  BUILDINQ  LAWS  AND  ORDINANCES  OF 
PHILADELPHIA  (1907). 

Live  Loads  for  Floors. — Lbs.  per  sq.  ft.:  Dwellings,  tenement  houses, 
apartment  houses,  hotels,  hospitsjs  and  asylums,  70  The. ;  office  buildings. 
100  lbs. ;  places  of  public  assembly,  light  manufacturing  and  retail  stores, 
120  lbs.;  storehouses,  warehouses  and  manufactories.  150  Ibe.  and  upward 
in  proportion  to  the  loads  they  have  to  carry. 

Roofs  shall  be  constructed  to  bear  a  safe  weight  of  30  lbs.  per  superfi- 
cial foot. 

Ultimate  Stresses  in  lbs.  per  sq.  in.: 


Cast 
Iron. 


Wrt. 
Iron. 


Mild 
Steel. 


Medi- 
um 
Steel. 


Hem- 
lock. 


Spruce 


Long 

Leal 

Yellow 

Pine 


Tension  (direct) 

Compression  (direct) ... 
Bending — extreme  fiber 

(tension) 

Shear 

Shear — perp.  to  grain.  . 
Shear — parallel  with 

grain 


70.000 
15.000 


50,000 
50.000 


58.000 
58.000 


65.000 
65.000 


30.000  35,000 


40.000 


4.000 
2.100 

8.600 


5.000 
3.000 

4.400 


7.200 
4.500 

6.400 


2.500 
250 


3.000 
800 


4.500 
400 


Working  Stresses*  in 

lbs.  per  sq.  in. 

Cast 
Iron. 

Wrt. 
Iron. 

Mild 
Steel. 

Medi- 

sSmv 

Hem- 
lock. 

Spruce 

YeUow 
Pine. 

Tension 

12,500 
12.500 

14,500 
14,500 

16,250 
16.250 

1,000 
350 

250 

900 

1.250 
500 

300 

1.100 

1.800 

Compression 

11.667 

750 

Ownpression — perp.  to 
grain 

550 

Bending-^xtreme  fiber 
(tension) 

3,750 

L60O 

Shear 

7.500 

8,750 

10.000 

Shear-^perp.  to  grain. . . 

4161 
411 

500 
50 

750 

Shear — parallel  to  grain  . 

w 

*  For  columns,  the  safe  working  loads  p  in  lbs.  per  sq.  in.  may  be  re- 
duced by  the  following  formulas: — 


C^t  iron.      />— - 


11667 


Mild  steel,     p  — 


P 
14500 


Wrought  iron,  ^—- 


13500 


1  + TKnJT- 


Medium  steel,  p^- 


15000r« 
16250 


l-l-- 


13500f« 


l-l-- 


Hemlock.  p—  350-  3.5-^ ;  Spruce. /»— 


llOOOrt 
-  5j :  Yellow  pine.  />  -  750 -  7.5^  - 

In  which  /= length,  r— least  radius  of  gyration,  d  — least  diameter,  all  in 
inches.  The  allowable  reduction  of  live  load  on  colximns  and  girders  rfjall 
be  as  follows:  "For  all  tenement  houses,  hotels,  apartment  houses,  hospitals 
and  office  buildings  the  live  loads  on  columns,  girders  and  foundaticms  may 
be  estimated  by  the  formula  X-  100 --jV A,  and  for  light  mantifactunne 
buildmgs  by  the  formula  X  -  1 00  -§  v//l .  in  which  *'X"  equals  the  pe«»it«e 
foimSi?*^  ^       "*^'  ^^  "-A  "equals  area  carried  by  any  girder,  cohmm  o* 


PHILADELPHIA  BUILDING  CODE.  825 

AltowaUe  PrMsnret  in  lbs.  per  sq.  ft. — Concrete,  16  tons:  brickwork  in 
lime  mortar.  8  tons;  brickwork  in  lime  and  cement  mortar.  12  tons;  brick- 
work in  cement  mortar,  15  tons;  stonework  (rubble)  in  lime  mortar,  5  tons; 
stonework  (rubble)  in  lime  and  cement  mortar,  8  tons;  stonework  (rubble) 
in  cement  mortar,  10  tons. 

Reioforced  Concrete. — Reinforced  concrete  construction  will  be  accepted 
for  fireproof  buildings  of  the  first  class,  if  designed  as  hereinafter  pre 
scribed;  provided,  that  the  aggregate  for  such  concrete  shall  be  clean  brcMOsn 
hard  stone,  or  clean  graded  gravel,  together  with  clean  siliceous  sand  or  fine 
trained  gravel ;  should  the  concrete  be  used  for  flooring  between  rolled  steel 
beams,  clean  furnace  clinkers  entirely  free  of  combustible  matter,  or  suita- 
ble seasoned  furnace  slag  may  be  used;  when  stone  is  used  with  sand  or 
gravel  it  must  be  of  a  size  to  pass  throiagh  a  one-inch  ring,  and  25%  of  the 
whole  must  not  be  more  than  one-half  the  maximum  siee;  and  provided 
further,  that  the  minimum  thickness  of  concrete  surrounding  the  reinforc- 
ing members  of  reinforced  concrete  beams  and  girders  shall  be  2  ins.  on  the 
bottom  and  one-half  inch  on  the  sides  of  said  beams  and  girders.  The 
minimum  thickness  of  concrete  under  slab  rods  shall  be  one  inch.  All  rein- 
forcement in  columns  to  have  a  minimum  protection  of  2  ins.  of  concrete. 

For  wails,  reinforced  concrete  may  be  used  in  place  of  brick  and  stone 
walls,  in  which  case  the  thickness  may  be  two-thirds  of  that  required  for 
brick  walls.  0>ncrete  walls  in  such  cases  must  be  reinforced  in  both  direc- 
tions in  an  api>roved  manner. 

All  steel  reinforcement  shall  be  of  standard  grade  of  structural  steel  or 
iron  of  either  grade  to  meet  the  "Manufactiu^rs'  Standard  Specifications," 
revised  Feb.  3, 1903. 

Slabs,  beams  and  girders  shall  be  designed  on  the  assumption  of  a  load 
four  times  as  great  as  the  total  load  (ordinary  dead  load  plus  ordinary  live 
load).  The  steel  to  take  all  the  tensile  stresses.  The  stress-strain  curve  of 
concrete  in  compression  is  a  straight  line. 

Ratio  of  moduliof  elasticity  of  concrete  to  steel:  Stone  or  gravel  con- 
crete. 1  to  12;  sla^r  concrete,  1  to  15;  cinder  concrete,  1  to  30. 

Allowable  umt  transverse  stressjjbs.  per  sq.  in.)  upon  concrete  in  com- 
pression: Stone  or  gravel  concrete,  600:  slag  concrete,  40(1;  cinder  concrete.  250. 
Allowable  unit  transverse  stress  Obs.  per  sq.  in.)  in  tension:  Iron,  12,000; 
steel,  16,000. 

Allowable  unit  shearing  stress  (lbs.  per  sq.  in.)  upon  concrete:  Stone  or 
gravel  concrete.  75;  slag  concrete,  50;  cmder  concrete.  25. 

Allowable  tuilt  adhesive  strength  (lbs.  per  sq.  in.)  of  concrete:  Stone  or 
gravel  concrete,  50;  slag  concrete,  40;  cinder  concrete.  15. 

Allowable  unit  stresses  (lbs.  per  sq.  in.)  upon  concrete  in  direct  com- 
pression in  columns:  Stone  or  gravel  concrete,  500;  slag  concrete,  300;  cinder 
concrete.  150. 

Allowable  unit  stress  upon  hoop  columns  composed  of  stone  or  gravel 
concrete  shall  not  be  over  1000  lbs.  per  sq.  in.,  figuring  the  net  area  of  the 
cirde  within  the  hooping.  The  percentage  of  longitudinal  rods  and  the 
spacing  of  the  hoops  to  be  such  as  to  permit  the  concrete  to  safely  develop 
the  above  unit  stress  with  a  factor  of  safety  of  4. 

Floor  slabs,  when  constructed  continuously,  and  when  provided  with 
reinforcement  at  top  of  slab  over  the  supports,  may  be  treated  as  continu- 
ous beams,  the  bending  moment  for  unitormlv  distributed  loads  being  taken 
at  not  less  than  WL  •«- 10.  In  case  of  souare  floor  slabs  which  are  reinforced 
in  both  directions  and  supported  on  all  sides,  the  bending  moment  may  be 
taken  at  WL  ■*-  20;  provided,  that  in  floor  slabs  in  juxtaposition  to  the  walls 
af  the  building  the  bending  moment  shall  be  considered  as  WL  +  8,  when 
'einforc^  in  one  direction,  and  if  the  floor  slab  is  square  and  reinforced  in 
x>th  directions  the  bending  moment  shall  be  taken  dsWL  +  16. 

In  columns  the  longitudinal  rods  will  not  be  considered  as  taking  any 
lirect  compression. 

EXTRACT  FROM  THE  BUILDING  LAW  OP  BOSTON  (1909). 

MATERIALS— ALLOWABLE  FIBER  STRESSES. 
[Lbs.  per  square  inch.] 
Timber. — Extrene  fiber  (bending) :  White  pine  and  spruce.  1000;  white 
ak.  1000;  yellow  pine  (long  leaf),  1500.  Shearing  along  grain:  White  pine, 
0;  white  oak,  150:  yellow  pine  (long  leaf).  100.  Compression  perpendicular 
»  gmin :  White  pine  and  spruce.  250:  white  oak,  600;  yellow  pine  (long  leaf), 
M>.    Modulus  of  elasticity:  White  pine.  750.000;  spruce.  900.000;  white  oak, 


826  A7.— BUILDINGS. 

860.000:  3^11ow  pine  (long  leaf),  1.300,000.  Colnmns  (centraHy  loaded  aai 
fUt  ends) :  White  pine  and  spruce,  630  for  L-t-D  »0  to  10,  fi05  for  L-i-D  —10  to 
16.  600  for  L+D- 16  to  20,  626  for  L+D-20  to  26.  490  for  L-t-D~25  to  90; 
white  oak,  810  for  L+D-0  to  10,  766  for  L+I?- 10  to  15,  720  for  L+D- 16  to 
20. 676  for  L+P- 20  to  26,  630  for  L-i-D-26  to  30;  yellow  pine  (long  leaf), 
900  for  L-i-D  -0  to  10.  850  for  L-^D  ->  10  to  16,  800  for  L-i-D  -16  to  207790  for 
L-i-D — 20  to  26.  700  for  L+D — 26  to  30.  No  column  shall  be  used  with  greater 
value  than  L+ D  —  30.  For  eccentric  loads,  see  Methods  of  Computation,  p.  8^. 

Wrought  Iroo  and  Steel  (steel  at  66-66,000). — Extreme  fiber  of  rolled 
beams  or  shapes:  Wrought  iron,  12,000;  steel,  16,000.  Tension;  Wrought 
iron,  12.000;  steel.  16.000.  Compression  in  flanges  of  built  beams:  Wrot^ht 
iron,  12,000;  steel.  16.000.  Shearing  (including  pins  and  rivets,  but  not  bolts): 
Wrought  iron.  9.000;  steel,  lO.OO).  Shearing  (bolts):  80%  of  preceding 
values.  Direct  bearing  (including  pins  and  rivets,  but  not  bolts) :  Wrouglit 
iron,  16.000;  steel,  18,(N)0.  Direct  oearing  (bolts):  80%  of  preceding  values. 
Bending  on  pins:  Wrought  iron,  18.000;  steel,  22^500.  Modulus  of  elas- 
ticity: Wrought  iron,  27,000.000;  steel.  29,000.000.  For  compression  mem- 
bers, use  the  formula:  ,[12,000  for  iron  or  16.000  for  steel]  dividmi  by 
[1  +  (L*  +  20000  f*)  ],  in  which  L  —  length  and  r  —  radius  of  gyration  in  inches. 
Compression  flanges  of  beams  shall  be  proportioned  to  resist  lateral  flexure; 
if  the  ratio  of  unsupported  length  of  flange  to  width  of  flange  does  not  ex- 
ceed 20,  no  allowance  need  be  made;  if  the  ratio  is  70.  the  above  specified 
allowable  fiber  stress  shall  be  reduced  by  one-half;  and  proportionate  for 
values  between  20  and  70. 

Cast  Iron. — Extreme  fiber  stress:  Tension,  8.000;  compression.  16,000. 
Coiumns  (centrally  loaded  and  unsupported  laterally):  Average  stress.  ll.OOQ 
forL+r-10.  10,700  for  L+r-20.  10.400  for  L-i-r-M,  10.000  for  L-i-f^l 
9,800  for  L+r- 60,  9.500  for  L-i-r- 60.  9,200  for  L-i-r- 70.  I.  and  r  in  inches. 
Cast  iron  shall  not  be  used  for  columns  in  bmldings  of  more  than  76  feet  is 
height,  nor  in  cases  where  L-*-r  exceeds  70. 

[Tons  (2000  lbs. )  per  square  foot.] 

Stone  Work,  In  Compression. — First  quality  dressed  beds  and  builds, 
laid  solid  in  mortar  of  one  part  Portland  cement  to  three  parts  sand,  or  one 
part  natural  cement  to  two  parts  sand.  Granite,  60;  marble  and  limestone. 
40;  sandstone.  30.  When  poorer  mortar  is  used  the  above  stresses  shall  be 
lowered  (as  approved). 

Brickwork,  in  Compression. — (1.)  For  first  class  hard-burned  bricks, 
including  piers  in  which  the  height  does  not  exceed  six  times  the  least  di- 
mension, laid  in:  (a)  One  part  Portland  cement,  three  parts  sand,  by  vol- 
ume, dry,  20;  (b)  (Jne  part  natural  cement,  two  parts  sand,  by  volume,  dry. 
18;  (c)  One  part  natural  cement,  one  part  lime  and  six  parts  sand,  by  vol- 
ume, dry,  12;  (d)  Lime  mortar,  one  part  lime,  six  parts  sand,  by  volume, 
dry.  8.    (2.)  For  brick  piers  of  hard-burned  bricks,  in  which  the  height  is 


.  of  hard-bumed  bricks. 

CONCRETE  AND  REINFORCED  CONCRETE. 

Cement  shall  conform  to  the  specifications  of  the  American  Sodrty 
for  Testing  Materials,  as  modified  from  time  to  time  by  that  association. 

Concrete. — When  the  structural  use  of  concrete  is  proposed,  a  specifica- 
tion, stating  the  quality  and  proportions  of  materials,  and  the  methods  of 
mixing  the  same,  shall  be  submitted  to  the  building  commissioner,  who  ma/ 
is.<;ue  a  permit  at  his  discretion  and  under  such  further  conditk>ns,  in  addi- 
tion to  those  stated  below,  as  he  sees  fit  to  impose. 

A.  In  first  class  Portland  cement  concrete,  contadning  one  part  cement 
to  not  more  than  six  parts  mixed  properly  graded  aggregate,  except  in  piers 
or  columns  of  which  the  height  excecas  six  times  the  least  dimension,  the 
compressive  stress  shall  not  exceed  30  tons  of  2000  lbs.  per  sq.  ft. 

B.  In  piers  and  columns  of  first  class  Portland  cement  concrete,  con- 
taining one  part  cement  to  not  more  than  five  parts  mixed  properly  graded 
aggregate,  where  the  height  of  the  pier  or  column  is  more  than  six  times  and 
do«i  not  exceed  twelve  times  its  least  dimension,  the  compreasive  stress 
shall  not  exceed  26  tons  of  2000  lbs.  per  sq.  ft. 

By  "aggregate"  shall  be  understood  all  the  materials  in  the  concrete 
except  the  cement.  Cinder  concrete  shall  be  used  constructively  only  for 
floors,  roofs  and  for  fiUing.  C  r^ofrl^ 

^  Digitized  by  V^OOQLC 


BOSTON  BUILDING  CODE.  827 

Rules  for  the  computation  of  reinforced  concrete  columns  may  be  for- 
mulated from  time  to  time  by  the  building  commiasioner  with  the  approval 
of  the  board  of  appeal. 

In  reinforced  concrete  beams  or  slabs  subjected  to  bending  stresses,  the 
entire  tensile  stress  shall  be  assumed  to  be  carried  by  the  steel,  which  shall 
not  be  stressed  above  the  limits  allowed  for  this  material.  First  class  Port- 
land cement  concrete  in  such  beams  or  slabs,  containing  one  pcit  cement  to 
not  more  than  five  parts  mixed  properly  graded  aggregate,  may  be  stressed 
in  compression  to  not  more  than  506  lbs.  per  sq.  in.  In  case  a  richer  con- 
crete is  used,  this  stress  may  be  increased  with  the  approval  of  the  commis- 
sioner to  not  more  than  600  lbs.  per  sq.  in. 

In  reinforced  concrete  the  maximum  shearing  force  upon  the  concrete, 
when  uncombined  with  compression  upon  the  same  plane  shall  not  exceed 
60  lbs.  per  sq.  in.,  unless  the  building  commissioner  with  the  consent  of  the 
board  of  appeal  shall  fix  some  other  value. 

If  the  embedded  steel  has  no  mechanical  bond  with  the  concrete,  its 
holding  power  shall  not  exceed  the  all6wable  shearing  strength  of  the  con- 
crete. 

Keioforced  Concrete. — Reinforced  concrete  slabs,  beams  or  girders,  if 
rendered  continuous  over  supports  by  being  'unbroken  in  section,  shall  be 
provided  with  proper  metal  reinforcement  at  the  top  over  said  supports  and 
may  be  computed  as  continuous  beams,  as  hereinafter  described. 

The  modulus  of  elasticity  of  the  concrete,  if  not  shown  by  direct  tests, 
may  for  beams  and  slabs  be  taken  as  one-fifteenth  that  of  steel,  and  for  col- 
umns one-tenth  that  of  steel. 

The  reinforcing  metal  shall  be  covered  by  not  less  than  three-fourths 
inch  of  concrete  in  slabs,  and  by  not  less  than  one  and  one-half  inches  of 
concrete  in  beams  and  columns. 

Metbods  of  Conpntatiofi. — Beams  or  girders  of  metal  or  reinforced  con- 
crete shall  be  considered  as  simply  supported  at  their  ends,  except  when 
they  extend  with  tmbroken  cross-section  over  the  supports,  in  which  case 
they  may  be  considered  as  continuous. 

The  span  of  a  beam  shall  be  considered  as  the  distance  from  center  to 
center  of  the  bed  plates  or  surfaces  upon  which  it  rests.  If  it  is  fastened  to 
the  side  of  a  coltimn.  the  span  will  be  measured  to  the  center  of  the  colunm. 
In  slabs,  beams  or  girders  continuous  over  supports,  provision  shall  be 
made  for  a  negative  bending  moment  at  such  supports  equal  to  four-fifths 
of  the  i)Ositive  bending  moment  that  would  exist  at  the  center  of  the  span 
if  the  piece  were  simply  supported;  and  the  positive  bending  moment  at  the 
center  of  the  span  may  be  taken  equal  to  the  negative  bending  moment  at 
the  support. 

In  the  case  of  a  slab  of  reinforced  concrete  with  parallel  ribs  or  girders 
beneath,  the  rib  or  girder  may  be  considered  to  include  a  portion  of  the  slab 
between  the  ribs,  forming  a  T-beam.  The  width  of  the  T-beam  on  top  shall 
not  exceed  one-third  of  the  span  of  the  rib  nor  the  distance  from  center  to 
center  of  the  ribs. 

Reinforced  concrete  columns  shall  be  proportioned  on  the  assumption 
that  the  concrete  and  the  steel  are  shortened  in  length  in  the  samepropor- 
tion.  The  steel  members  shall  be  tied  together  at  intervals  sufficiently 
;hort  to  prevent  buckling. 

If  a  column  is  loaded  eccentrically  or  transversely,  the  maximum  fiber 
(tress,  taking  account  of  the  direct  compression,  the  bending  which  it 
'auses,  its  eccentricitjr  and  the  transverse  load,  shall  not  exceed  the  nmxi- 
num  sillowable  stress  in  compression. 

If  a  tension  piece  is  loaded  eccentrically  or  transversely,  the  maximum 
iber  stress,  taking  account  of  the  direct  tension,  its  eccentricity  and  the 
ransverse  load,  shall  not  exceed  the  maximum  allowable  stress  m  tension. 
An  eccentric  load  upon  a  column  shall  be  considered  to  affect  eccentric- 
Ily  only  the  length  of  column  extending  to  the  next  point  below  at  which 
he  column  is  held  securely  in  the  direction  of  the  eccentricity. 

If  a  piece  is  exposed  to  tension  and  compression  at  different  times,  it 
ball  be  proportioned  to  resist  the  maximum  of  each  kind,  but  the  unit 
tresses  sliafl  be  less  than  those  used  for  stress  of  one  kind,  depending  upon 
le  ratio  and  the  relative  frequence  of  the  two  maxima,         GoOqIc 


838 


il,— BUILDINGS. 


EXTRACT  FROIH  BUILDINQ  LAWS  OF  CITY  OF  BUFFALO  (I9«>). 
CONCBfiTE  CONSTRUCTION. 

Concrete  may  be  used  in  buildings  of  all  classes  whet)  such  constroctioo 
is  approved  by  the  Deputy  Building  Commissioner. 

Regulations  regardmg  the  use  of  concrete  in  hollow  blodcs  and  in  rein- 
forced steel  construction: 

ttdght  of  bnildings. — Buildings  whose  exterior  walls  are  of  hoUow  am- 
creU  blocks  may  be  erected  not  to  exceed  8  stories  in  height,  and  the  thick- 
ness of  such  walls  shall  be  as  given  below  for  brick  walls;  provided,  however, 
that  the  materials  of  construction  are  not  strained  beyond  the  safe  limits: 


Buildings  of  Class  I:    Sale,  stor- 
age or  manufacture  of  merchan- 
dise, and  public  livery,  boarding  or 
sale  stables. 

Buildings  of  Classes  II.  III.  IV': 
all   other   buildin£»,   as   hotels, 
hospitals,  office  buildings,  halls. 
theaters,  etc. 

8 

Basement. 

Story. 

Basement. 

Story. 

1 

Stone. 

Brick. 

Gro'nd 

2 

3 

Stone. 

Brick. 

Gro'nd 

2 

8 

1 

2 
3 

18* 
IS* 
2(r 

12* 
16" 
16" 

12* 

ir 

16' 

12* 
12" 

12" 

18" 
18" 
20" 

12" 
16" 
16" 

ir 

12" 
12" 

12" 
12" 

ir 

Buildings  whose  exterior  walls  are  of  reinforced  concrete  steel  ma^  be 
erected  3  stories  in  height,  and  the  thickness  of  such  walls  shall  be  as  given 
in  the  following  table;  provided,  that  the  materials  of  construction  are  not 
strained  beyond  the  sate  limits: 

Stories.  Basement.       1st  Story.       2nd  Story.      Jlrd  Story. 

1  8"  6"  ..  .. 

2  10"  6"  6" 

3  12"  8"  ••  «• 

Concrete  must  be  mixed  in  the  proportions  of  1  of  Portland  cement. 
2  of  sand,  and  6  of  stone  or  gravel;  or  .the  proportions  may  be  such  that 
the  resistance  of  the  concrete  to  crushing  shall  not  be  less  than  2,000  Ibt. 
per  sq.  in.  after  hardening  for  28  days,  by  approved  test.  The  concrete 
used  in  reinforced  concrete  steel  construction  must  be  what  is  usually  known 
as  a  "wet  mixture." 

''Reinforced  concrete  steel"  shall  be  understood  to  mean  an  approved 
concrete  mixture  reinforced  by  steel  of  any  shape,  so  combined  that  the  steel 
will  take  up  the  tensional  stresses  and  assist  in  the  resistance  to  shear. 

Concrete  construction  will  be  approved  only  for  buildings  which  are  not 
required  to  be  fireproof  by  the  building  ordinances,  imless  fire  and  water 
tests  shall  have  been  made  under  the  sui)ervision  and  to  the  sati^actioa  of 
the  Deputy  Building  Commissioner.  Bach  company  offering  a  systan  of 
concrete  construction  for  fireproof  buildings  must  submit  such  constmctioD 
to  a  fire  and  water  test. 

Inspection  and  tests. — ^The  execution  of  concrete  work  shall  be  confided 
to  workmen  who  shall  be  under  the  control  of  a  competent  foreman  or 
superintendent,  and  persons  erecting  buildings  of  concrete  shall  provide  for 
expert  inspection  of  the  cement  and  inerts  and  a  daily  record  ^all  be  kept 
of  the  tests,  the  temperature  in  which  the  concrete  was  woriced,  and  all 
other  conditions  which  may  be  of  importance  in  the  construction,  and  a 
certified  copy  of  such  record  shall  be  filed  twice  each  week,  or  oftener  if 
required. 

,  Quality  of  materials. — Only  high  grade  Portland  cement  shall  be  ptf- 
mitted  in  concrete  construction.  Such  cement  when  tested,  after  1  day  in 
w  and  6  days  in  water,  shall  develop  a  tensile  strength  of  at  least  600  lbs. 
P«r  sq.  m.;  and  after  1  day  in  air  and  27  days  m  water  shall  develop  t 
tensile  strength  of  at  least  600  lbs.  per  sq.  in.  Other  tests  as  to  fineness, 
«««tancy,  volume,  etc.,  shall  be  made  in  accordance  with  the  standard 


BUFFALO  BUILDING  CODE.  820 

method  prescribed  by  the  Committee  of  the  Am.  Soc.  C.  E.,  as  may  from 
time  to  time  be  directed. 

The  sand  to  be  used  must  be  clean,  sharp  grit  sand,  free  from  loam  or 
dirt. 

The  stone  used  in  the  concrete  must  be  clean  broken  stone  or  gravel, 
of  a  size  that  will  pass  through  a  |-in.  ring.  In  case  it  is  desired  to  use  other 
materials  or  other  kinds  of  atone,  samples  of  same  must  be  submitted  for 
approval. 

Reinforced  concrete  steel  must  be  so  designed  that  the  stresses  shall  not 
exceed  the  following  limits: 

Extreme  fiber  stress  on  concrete  in  compression,  500  lbs.  per  sq.  in. 
Shearing  stress  in  concrete,  60  lbs.  per  sq.  in. 
Concrete  in  direct  compression,  360  lbs.  per  sq.  in. 
Tensile  stress  in  steel.  16,000  lbs.  per  sq.  in. 
Shearing  stress  in  steel,  10,000  lbs.  per  sq.  in. 

Adhesion  of  concrete  to  steel,  not  greater  than  shearing  strength  of 
concrete. 

Modulus  of  elasticity  of  concrete  to  steel,  1  to  12. 

Bending  moments. — ^The  following  assumption  shall  guide  in  the  de- 
termination of  the  bending  moments  due  to  the  external  forces:  Beams 
and  girders  shall  be  considered  as  simply  supported  at  the  ends,  no  allow- 
ance being  made  for  continuous  construction  over  the  supports.  Floor 
plates  when  constructed  continuous  and  when  provided  with  reinforcement 
at  top  of  plate  over  the  supports,  may  be  treated  as  continuous  beams, 
the  bending  moment  for  imiformly  distributed  loads  being  taken  at  not  less 
than  WL-^\0\  the  bending  moment  may  be  taken  H^L-*-20  in  the  case  of 
square  floor  plates  which  are  reinforced  in  both  directions  and  supported 
on  all  sides.  The  floor  plate  may  be  taken  as  part  of  the  beam  or  girder  in 
computing  its  moment  of  resistance  to  the  extent  of  not  more  than  10  times 
the  width  of  that  beam  or  girder. 

Resisting  moments. — ^The  moment  of  resistance  of  any  reinforced  con- 
crete steel  construction  imder  transverse  loads  shall  be  determined  by 
formulas  based  on  the  following  assumptions: 

The  bond  between  concrete  and  steel  is  sufiicient  to  make  the  two  ma- 
terials act  together  as  a  homogeneous  solid. 
The  strain  in  any  fiber  is  directly  proportionate  to  the  distance  of  that 

fiber  from  the  neutral  axis. 
The  modulus  of  elasticity  of  the  concrete  remains  constant  within  the 

limits  of  the  working  stresses. 
The  tensile  strength  of  the  concrete  shall  not  be  considered. 
When  the  shearin£[  stresses  developed  in  any  part  of  the  construction 
exceeds  the  safe  workmg  strength  of  the  concrete,  a  suflficient  amount  of 
steel  shall  be  introduced  in  such  a  position  that  the  deficiency  in  the  resist- 
ance to  shear  is  overcome. 

When  the  safe  limit  of  adhesion  between  the  concrete  and  steel  is  ex- 
ceeded, some  provision  must  be  made  for  transmitting  the  strength  of  the 
steel  to  the  concrete. 

Colmnnt. — ^Reinforced  concrete  steel  may  be  used  for  columns  in  which 
the  ratio  of  length  to  least  side  or  diameter  docs  not  exceed  16.  The  rein- 
forcing rods  must  be  tied  together  at  intervals  of  not  more  than  the  least 
side  or  diameter  of  the  colxmin. 

Tests. — ^Tests  must  show  that  the  construction  will  sustain  a  load  of 
3  times  that  for  which  that  portion  of  the  building  is  designed,  without  any 
Hgn  of  ^liltire. 

*Honow  concrete  blocks  used  for  outside  walls  and  partitions  shall  not 
>e  loaded  to  more  than  160  lbs.  per  sq.  in.  of  available  or  effective  section, 
md  the  hollow  spaces  shall  not  exceed  M  the  area  of  the  blocks  when 
tsing  the  tables  for  thickness  of  walls. 

Untried  methods  of  construction  may  first  require  preliminary  trial 
ests. 

Frost. — ^Thc  influence  of  frost  must  be  excluded  when  concrete  work  is 
one. 


*  For  specifications  for  hollow  concrete  building  bk)cks^  the  dty  of 
liiladelphia,  see  Sec.  26,  Masonry,  page  460.  Digitized  by  V^OOg LC 


830  il.SUILDINGS. 

EXCERPTS  AND  REFERENCES. 

Reinforced-Concrete  Work  at  the  Atlanta  Railway  Terminal  Sta- 
tion (Eng.  News,  April  12,  1906).— Illustrated  details. 

A  System  of  Reinforced-Concrete  Construction  Withoot  Wooden 
Forms  (Eng.  News,  July  12,  1906).— Illustrated. 

Practical  tfints  for  Concrete  Constructors  (By  W.  J.  Douglas.  Eng. 
News,  Dec.  20,  1906,  and  Jan.  24,  1907).— Illustrated. 

A  Reinforced-Concrete  Shop  with  Steel  Roof  Trusses  and  Crane- 
Qirders  (By  W.  P.  Tubesing.    Eng.  News,  Jan.  10,  1907).— Illustrated, 

The  4S-Story  Tower  of  the  JWetrofN>Utan  Life  BnUding,  N.  Y.  CHy 
(By  Purdy  &  Henderson.  Eng.  News,  Jan.  31,  1907). — Illustrated  detaik 
of  column  shoes  and  coltimn  connections. 

Table  Showing  Proportions  of  Value  in  the  Various  Items  of  Con* 
struction  of  Fireproof  Buildings  (By  P.  J.  T.  Stewart.  Eng.  News.  Peb.  7. 
1907) . — ^The  table  embraces  various  kinds  of  buildings  in  New  York,  Chicago. 
Boston,  Baltimore  and  St.  Louis,  and  gives  the  percentage  of  cost  of  about 
50  items  of  construction  arranged  tinder  the  following  headings:  Founda- 
tions, steel  frame,  mason  work.  e<)uipment.  trim  and  finish,  and  general 
expenses.  The  cost  per  cubic  foot  is  also  given.  Cost  of  foundations  varies 
from  2.3  to  24.5%  ot  the  total  cost  of  buDding. 


A  Reinforced-Concrete   Mill  Building  With    Separately-Molded 

bers  (Eng.  News,  July  4,  1907). — Ten  illustrations,  showing  details  of  con- 
struction. 

Stresses  in  Oas-Holder  Qirder  Frames  (By  H.  Stoffels.  En«.  News, 
Aug.  15,  1907). — Dlustrated  diagrams  of  stresses  in  a  single-lift  gas  holder. 
with  three  different  arrangements  of  guide  rollers. 

The  Singer  Buildinc  and  the  City  Investment  Building,  of  New  Voile 
City  (Eng.  News.  Dec.  6,  1907). — Sixteen  illustrations,  including:  Typicsl 
floor  plan,  foimaation  plan,  cast  steel  shoe  for  column  base,  elevation  of 
cupola,  diagram  of  wind  bracing,  details  of  wind  bracing,  typical  column, 
^  *  '  "•  '        • ails  of  ^  * 


column  anchorage,  of  Singer  tower;   foundation  plan,  details  of  cast-ctecl 
bases  of  columns,  foundation  prders.  floor  plan,  typical  column  sections. 
details  of  portal  girders  and  wind  bracing,  of  City  Investment  Building. 
A   Reinforced-Concrete   Building  With    Concrete    Domes:  Cindaaati 


Zoological  Garden  (Eng.  News.  Peb.  20.  1908).— Illustrated  details  oi 
typical  column,  girder  and  dome  construction. 

AdJusUble  and  Portable  Forms  for  Concrete  Building  Coostrvction 
(By  L.  G.  Hallberg.  Eng.  News.  Mar.  6.  1908)  r— Illustrated  details  of  post 
and  form  for  girder,  with  adjustable  and  portable  centering. 

Steel  Construction  for  Long  Span  Hoors  In  the  Chicago  AtUetic 
Assn.  Building  (Eng.  News.  Mar.  19,  1908). — Illustrations  of  steel  framing 
for  ftoor,  and  plan  of  steel  floor  girder  43-ft.  long. 

Reinforced-Concrete  Cantilever  Qirders  In  the  Bogertown  BnMfait, 
Phila.  (Eng.  News.  April  23,  1908).— Illustration  of  the  side-wan-bcaring 
cantilevers,  and  saw-tooth  roof  construction. 

The  10-Story  Reinforced  Concrete  Hostetter  Building,  Plttifcig 
(Eng.  News,  May  14.  1908). — Illiistrated  details  of  column  remforcemest 
and  cast-iron  base. 

A  Reinforced-Concrete  Cold  Storage  Building  (By  W.  P.  Tubesiu. 
Eng.  News,  July  11.  1908). — Illustrated  details  of  wall  and  footings,  »»«V 
and  reinforced-concrete  covered  bridge  between  buildings. 

The  Reinforced-Concrete  Court  House  at  New  Orleans  (Eng.  News, 
July  2,  1908). — Illustrated  details  of  floor  construction. 

A  Steel  Frame  Orand  Stand  at  Dallas,  Tex.  (By  Howard  Arthur. 
Eng.  News,  Aug.  20,  1908). — Illustrated:  Side  elevation,  showing  dimca> 
sions  of  members. 

Conservatory  Buildings  of  Steel  Construction  in  Garfield  PartE, 
S!^f®T>^P"^  News,  Aug.  27.  1908).— fllustrated:  Stress  sheet  of  aicbed 
ribsoIPalm^ouse;  detaUs  of  steel  ribs.       ,,,,,,  .^GoOglc 


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832  il.^BUILDlNGS. 

it  may  be  used  for  fireproofins.  Assiuoptions  in  DesifO. — 43.  The  spas 
length  for  beams  and  slabs  shall  be  the  oist.  c.-c.  of  supports,  but  not  to 
exceed  the  clear  span  plus  the  depth  of  beam  or  slab;  brackets  shall  not  be 
considered  as  reducing  the  clear^pan.  44.  Length  of  columns  shall  be  the 
max.  unsupported  length.  46.  Where  slabs  and  beams  are  figured  as  simple 
beams  the  length  shall  oe  the  clear  dist.  between  supports  excluding  bradcets. 
Loads. — 47.  Weight  of  rein.-conc.  to  be  taken  as  150  lbs.  per  cu.  ft.  49.  The 
roof  shall  be  figured  to  carry  30  lbs.  live  load  per  sq.  ft.  unless  otherwise 
noted.  60.  A  reduction  of  live  load  coming  to  the  coltimn  supporting  the 
floor  below  the  roof  of  5%  to  be  allowed  and  a  further  reduction  of  6%  of 
the  live  load  of  each  story  below  until  tue  total  reduction  shall  amount  to 
60%  of  the  live  load  of  any  floor,  after  which  all  loads  shall  be  figxired  net 
to  the  foundations.  These  reductions  shall  not  apply  to  storage  warehouses. 
61.  No  reduction  of  loads  shall  be  allowed  for  figuring  floor  slabs.  52.  Nor 
none  for  figuring  beams.  63.  A  reduction  of  16%  live  load  may  be  allowed 
in  figuring  the  girders,  except  in  buildings  used  for  storage  purposes.  54. 
In  assummg  the  load  coming  to  the  columns  all  beams  and  girders  shall  be 
considered  as  carrying  a  net  load  consisting  of  100%  each  of  live  load, 
subject  to  the  above  reductions.  Bending  Moments. — 55.  Slabs. — The 
bending  moment  of  slabs  uniformly  loaded  and  supported  at  two  sides  only 
shall  be  taken  as  w^-i-8,  where  wunit  load  and  /-"span.  56.  Continuous 
Slabs. — For  interior  slabs  overhanging  two  or  more  supports  the  bending 
moment  shall  be  taken  as  w/«+12.  The  reinforcement  at  the  top  of  the  slab 
over  supports  must  equal  that  used  at  the  center.  57.  Slabs  Reinforced  in 
Both  Directions.— Slabs  reinforced  in  both  directions  and  supported  on 
four  sides  and  f\illy  reinforced  over  the  supports  (the  reinforcement  passing 
into  the  adjoining  slabs)  may  be  figured  on  the  basis  of  bending  moments 
equivalent  to  wP-t-F  for  load  in  each  direction.  When  span  under  consider- 
ation is  not  continuous,  F— 8;  when  continuous  over  one  support.  F>"10; 
when  continuous  over  both  supports,  F*-12.  The  distribution  of  the  loads 
to  be  determined  by  the  formula:  r— L*-»-(L<— 6<),  in  which  r—projKMtitm 
of  load  carried  by  the  transverse  reinforcement,  L-^span,  fr—oreadth  of 
slab.  58.  The  slab  area  may  be  reduced  by  one-half  as  above  figured, 
when  the  reinforcement  is  parallel  to  and  not  further  from  the  supports 
than  i  of  the  shortest  side.  The  reinforcement  spanning  the  shortest 
direction  shall  be  below  the  reinforcement  spanning  the  longer  directian, 
and  shall  not  be  further  apart  than  2i  times  the  thickness  of  the  floor  in- 
cluding the  finish.  69.  Simple  Beams. — ^The  bending  moment  of  beams 
supported  at  the  ends  only  shall  be  figured  as  of  simple  beams.  60.  Partially 
Restrained  Beams. — ^Beams  supported  at  one  end  and  continuous  at  the 
other  to  be  figuredpartially  restrained  with  a  bendinls  moment  of  A  that 
of  a  simple  beam.  When  the  over-all  vertical  distance  of  the  tension  members 
in  greater  than  |  of  the  total  depth  of  the  beam  the  stresses  in  each  member 
shall  be  computed  in  proportion  to  the  distance  from  the  neutral  axis. 
Beams  supporting  rectangular  slabs  reinforced  in  both  directions  shall  be 
assumed  to  take  the  following  load:  The  beams  on  which  the  shortest  sides 
of  the  slab  rest  shall  take  the  load  of  that  portion  of  the  slab  formed  bjr  the 
isosceles  triangle  having  this  side  as  its  base  and  half  this  side  as  its  he^t. 
The  load  from  the  remaining  portion  of  the  slab  shall  go  to  the  beams  <m 
which  the  long  side  of  the  slab  rests.  62.  Continuous  Beams.— 'When 
beams  or  girders  are  continuous  over  two  or  more  supports,  the  interior 
beams  may  be  considered  as  partially  restrained,  and  the  bending  monients 
at  the  center  and  support  figured  as  f  that  of  a  simple  beam,  unless  the 
concrete  at  the  bottom  of  the  beam  at  the  support  shall  by  this  considera- 
tion receive  excess  compression.  63.  T-Beams. — In  beam  and  slab  construc- 
tion, an  effective  metallic  bond  should  be  provided  at  the  jtxnction  of  the 
beam  and  slab.  When  the  principal  slab  reinforcement  is  parallel  to  the 
girder,  transverse  reinforcement  snail  be  used  extending  over  the  girder 
and  well  into  the  slab.  64. — Where  adequate  bond  between  slab  and  web 
of  beam  is  provided,  the  slab  may  be  considered  as  an  integral  part  of  the 
beam,  but  its  effective  width  shall  not  exceed  4  on  either  side  of  the  bean. 
nor  be  greater  than  6  times  the  thickness  of  the  slab  on  either  side  of 
the  beam.  Measurement  from  the  edge  of  the  web.  05.  In  the  design  of 
T-beams  acting  as  continuous  beams,  due  continuation  should  be  given  to 
the  compressive  stresses  at  the  supports  at  the  bottom  of  the  beam.  Ratfc) 
of  JH<Mlull. — 76.  The  ratio  of  moduli  of  elasticity  of  concrete  to  steel  shall  he 
v2**?fl  S«^^**,?"  ^  *°  ^^-  76.  The  allowable  ten^le  stress  in  reinforcement  to 
^„u  'r"".^^.-  ?«*■  "Q-  »"■  for  medium  steel  and  20.000  lbs.  per  sq.  in.  for 
lugh  elastic  hmit  steel  with  adequate  mechanical  bond.     77.  The  compns- 


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834  iJ.^BUILDINGS. 

Description.  Bog.  Rec 

Alaska  Commercial  Bldg.,  San  Francisco,  eng'g  feattirei Feb.  6,  '01 

Columns  with  connections  for  wind  bracing  and  cantilevers Feb.  20. 01 

Methods  of  hanging  shafting,  etc.,  in  rein. -cone,  buildings Mar.  13.'0Y 

Reinforced -concrete  church,  with  dome,  in  Los  Angeles Mar.  20, 01 

A  light  steel  pier  shed,  roof  53-ft.  span Mar.  27,  Of 

Construction  of  the  Baxter  Bldg.  (rein .-cone),  Portland,  Me...  .Apr.  10.  H 
Methods  of  hanging  wires  and  shafting  to  cone,  beams. ........  .Apr.  24, 01 

Reinf orced-concrcte  dome  of  the  Porto  Rico  Capitol }£aiy  1,  Of 

Types  of  hangers  used  for  piping  in  a  power-house May  15.  '01 

The  Keewatin  rein.-conc.  flour  mill May  29,  Of 

Principal  roof  trusses  and  banqviet  hall  girders.  La  Salle  Hotel . .  .Tune  S,  00 
Steel  details,  floor,  girders,  columns,  cornice  of  Trust  Building  .  .July  3.  '00 
Engine  house:  sep.-molded  roof  members;  engine  and  drop  pits, 

etc Tuly  10.  "09 

Cement  shed,  mixing  building,  measuring  tank,  concrete  plant. .  .July  17,  09 

Section  of  framework.  Copper  Queen  smelter  building July  81,  00 

Details  steel  framework  of  large  coal  storage  shed Sept.  4.  00 

Plans  of  sedimentation  basin.  Goderich,  Ontario Sept.  4,  09 

Plan  of  wood-framed  machine  shop Sept.  4.  09 

Details  concrete  and  steel  work.  Met.  Life  Bldg.,  San  Francisco  .Sept.  11,09 

Details  safety  equipment,  Singer  Building  elevators Sept.  ll.'jj 

A  reinforced-concrete  sawmill Sept.  ll/JJ 

Floor  beam  plans,  typical  columns,  Bank  Bldg.,  N.  Y Oct.  2.  '09 

Structural  steel  frames  of  open  hearth  bldgs.,  Gary,  Ind Oct.  9,  '0* 

Rein.-conc.  joists  with  hollow  tile  fillers.    Tables Oct.  9.  'Oj 

Rein.-conc.  (Quincy  market)  cold  storage  warehouse.  Boston Nov.  13,'OJ 

General  plans  of  Balloon  house,  U.  S.  Signal  Corns Dec.  4.  'W 

Details  of  forms  for  concrete  floor  beams  and  slabs Dec.  11,  'OJ 

Details,  steel  truss  supporting  column,  Martinique  Hotel Ian.  1.   Ij 

Rein.-conc.  grand  stand  at  Minn.  State  Fair  Grounds Tan.  15,  '»\ 

Approx.  cost  of  mill  buildings;  diagrams,  tables Jan.  29,  IJ 

Details,  colvmms,  etc.,  large  steel  frame  rolling  mill Jan.  29,  'IJ 

Cross-section  rein.-conc.  warehouse;  details  machinery Mar.  13.  '!• 

Steel  and  architectural  details,  N.  Y.  Municipal  Building Mar.  19.  l* 

Cast-steel  column-pcdesuls  (4  to  6J  ft.  sq.).  N.  Y.  Munic.  Bldg.  .Mar.  19,  IJ 

Rein.-conc.  girder  beam,  63  ft.  clear  span Mar.  6,   IJ 

12-story  rein.-conc.  bldg.,  48  ft.  x  110  ft.,  without  inter.  columnsMar.  6,  'Ij 

Steel  freight  sheds  at  Winnepeg,  C.  N.  &  G.  T.  P.  Ry Apr.  16,  IJ 

Arrangement  of  reinforcing  at  elevator  and  stairway Apr.  U,  'Ij 

Framework  22d  reg't  armory;  3-hinged  arch;  cantilever May  5,  'JJ 

Rein.-conc.  grandstand.  Minn.  State  Fair  race  track Tune  4.  'IJ 

Formula  for  determining  the  elevation  of  grandstand  seats Jime  4,  [Ij 

Concrete  and  tile  floors  with  2-way  reinforcement June  l5/lf 

Steel  and  architectural  details  of  Chicago  station,  C.  &  N.  W.  Ry  .June  IS.'l 

Structural  details  of  Columbia  Theatre,  San  Francisco June  M,|j| 

Column  sections,  bases  and  splices,  Curtis  bldg.,  Phila 

Concrete  building  with  steel  columns  in  lower  stories 

Saw-tooth-roof  machine  shop  for  Georgia  Ry , 

Heating  and  ventilation  of  Union  Passenger  Sta.,  Wash..  D.  C 

ReinforcedKxincrete  construction  in  the  Hartford  Armory , 

64-ft.  rein.-conc.  arch  for  supporting  warehouse  floor , 

Wall  insulation  of  a  cooling  room Aug.  6,  ]l 

Half  of  steel  roof  truss  for  the  Doe  Memorial  Library Aug.  37.] jj 

Diagram  from  coltimn  formula:  15000  — 60(/  +  r) ' Sept.  8.  'M 

Steel  and  rein.-conc.  grand-stand,  baseball  park,  Chicago Sept.  8,  'J 

Structural  steel  details  in  the  Wick  Bldg.,  Youngstown Sept.  tl]\ 

Details  of  cantilever  beam  in  rein.-conc.  storage  warehotise Oct.  15,  [^ 

Deep  underpinning  (1 2-story  steel  bldg.)  through  sand Oct.  22.  ^ 

Depositing  concrete  by  gravity  in  a  7-story  building Oct.  22,  J 

The  Tacoma  High  School  Stadium  (L.  D.  Howell) ' Oct.  19,  ' 

Structural  details  of  the  Curtis  Bldg.,  Phila..  Pa Nov.  5, ' 

Structiu^l  details  in  the  Soldan  High  School,  St.  Louis Nov.  5.  ]] 

Metal  wall  forms  for  concrete  houses Nov.  H.' 

A  large  concrete  coal  breaker  and  washery  bmlding Dec.  8.  J 

Underpinning  the  Manhasset  Building.  New  York Dec  10. 1 

iypical  beam,  columns  and  floor  reinforcement,  cone,  bldg Dec  19.  J 

iTandstand  of  reinforced  concrete,  Cleveland  (O.)  B.  B.  Club . . ,  Dec  17. 1 


48.— RETAINING  WALLS. 

The  forces  acting  on  a  retaining  wall,  due  to  the  pressure  of  the  earth 
behind  it,  are  not  susceptible  of  exact  determination.  Several  theories 
have  been  advanced  from  time  to  time,  based  on  assumptions  more  or  less 
at  variance  with  practical  conditions,  and  from  these  theories  formulas  have 
been  deduced,  but  they  are  not  relied  upon  with  any  degree  of  certainty. 
We  depend  rather  upon  the  proportions  of  existing  structures  for  otir 
designs.  Some  data  have  been  obtained  from  tests  of  models,  but  the  con- 
ditions imder  which  the  tests  were  made  are  not  considered  sufficiently 
reliable  upon  which  to  base  a  general  working  formula. 

Theory  of  Earth  Pressure  (No.  I).— Any  theory  of  earth  preswire 
diould  be  founded  on  assumptions  clearly  and  carefully  made,  and  leaning 
rather  on  the  side  of  safety  than  otherwise.  It  is  believed  that  in  the 
present  disctission  a  clearer  concep- 
tion may  be  had  by  taking  a  concrete       ^  T^  tf  fM 

example  for  an  illustration.  ~"*^^ * — "^ '■ 

Let  us  consider  an  earth  fill  20 
ft.  high,  level,  and  of  indefinite  ex- 
tent. Imagine  this  fill  to  be  cut  by 
the  vertical  plane  ab;  then  will  there 
be  on  either  side  of  the  plane  a  set 
of  equal  and  symmetrical  forces  act- 
ing  on    the    plane,    in    equilibrium.  . 

What  is  the  nature  of  these  forces,  Qnm^  Um 

their  intensities  and  directions,  and  «•      « 

their  resultants?  ^«-  1- 

Firstly,  it  is  asstimed  that  the  earth  fill  is  dry  and  granular,  in  fact 
sand,  as  that  will  probably  produce  about  the  greatest  pressure*;  also  that 
there  is  no  cohesion  among  the  grains  of  sand  and  hence  there  can  be  no 
tension  in  any  part  of  the  mass.  If  now  the  fill  to  the  right  of  the  plane  ab 
is  removed,  it  is  clearly  evident  that  certain  forces  as  p,  whose  resultant  is 
P  may  be  applied  on  the  right  face  of  the  plane  to  hold  the  fill  to  the  left 
of  it  in  place,  and  maintain  equilibriimi  as  before.  In  Fig.  1  these  forces 
are  represented  as  acting  horizontally,  but  no  assumption  is  being  made 
at  present  as  to  the  direction  of  the  original  forces  on  the  plane  ab  due  to 
the  earth  fill  removed,  nor  to  the  direction  of  the  existing  forces  acting  to 
the  left  of  the  plane  due  to  the  earth  fill  in  place.  It  is  assumed  merely  that 
the  p  forces  represent  in  intensity  the  horizontal  components  of  these  forces, 
in  the  direction  of  the  former  and  opposite  in  direction  to  the  latter. 

Let  us  next  remove  the  plane  a6.  the  forces  acting  to  the  right  of  it.  and 
also  that  portion  of  the  groimd  line  to  the  right  of  a,  if  we  can  so  stretch  our 
imagination.  Immediatelir.  the  sand  will  begin  to  slide  over  fan-like  planes 
radiating  from  a:  There  will  be  a  tendency  for  the  whole  triangular  prism 
as  abd  to  slide  en  masse  on  some  plane  ad,  and  the  general  movement  of 
the  earth  will  not  cease  until  some  plane  bsocis  exposed  and  all  the  material 
above  is  removed.  It  will  further  be  found  that  this  plane  ac  makes  an 
angle  <^— 33**-4r  (about)  with  the  horizontal.  This  angle  is  called  the 
angle  of  repose,  angle  of  friction, t  or  natural  slope  for  that  material.  It  is 
based  on  the  engineer's  slope  of  li  horizontal  to  I  vertical,  which  earth  fill 
in  general  assumes,  and  is  the  slope  at  which  the  material  will  just  barely 
remain  at  rest.  For  instance,  if  we  consider  the  mass  of  earth  aoc  restored 
above  the  plane  ac  and  assume  it  for  the  moment  to  have  stifficient  cohesion 
60  that  no  sliding  plane  above  the  plane  ac  can  develop  through  it,  that  is, 
•ao  part  of  the  mass  abc  can  slide  on  the  other  part,  then  will  the  mass  be 
at  rest,  as  the  tendency  to  slide  on  the  plane  ac  will  jtist  equal  the  resistance 
due  to  friction.  Clearly,  then,  considering  the  prism  abc  as  a  uniud  mass, 
it  is  evident  from  the  foregoing  that  no  horizontal  pressure  would  be  exerted 

*  The  exception  to  this  is  clean,  coarse,  uncemented  gravel:  see  page  838. 
t  The  coefficient  of  friction  —tan  ^.  ^  , 

Digitized  by  VjOOQ  IC 

835  ^ 


886 


48.''RETAINING  WALLS. 


by  it,  and  hence  no  forces  p,  acting  on  the  face  ab,  would  be  needed  to  keep 
it  in  place.  As  such  it  would  exert  a  vertical  force  —  IV, ,  a  normal  force 
W^  cos  ^  =  W- ,  and  a  tangential  force  on  the  plane  ac  equal  to  W,  sin  4  « 
VTt  -  IV.  tan  *-  (W.  XI)  +  U  =  f  IV. .  The  tangent  of  the  natural  slope, 
or  tan  0.  equal  to  }  for  earthwork,  is  commonly  termed  the  coefficUnt  of 
friction  because  it  requires  a  force  a  little  greater  than  }  of  the  normal 
pressure  on  the  natural  slope,  to  move  the  mass.  Hence  the  imited  prism 
abc  is  just  stationary  on  the  1^  to  1  slope  ac,  because  the  total  friction. 

I  W^  -IV.,  the  tangential  force (I) 

Slop€  of  Maximum  Pressure. — Consider  any  triangular  prism  abd.  Fig.  !• 
resting  on  the  sliding  plane  ad  whose  base  is  x,  height  k,  and  length  perpen* 
dicular  to  the  i^aper  is  one — all  in  feet.  The  weight  of  the  material  com- 
posing the  fill  is  taken  at  100  lbs.  per  cu.  ft.  Then,  with  the  center  of 
gravity  at  B,  we  have: 


Vertical  force  or  weight, 
Normal  force  (to  plane  ad). 


HT.^li^^lb..; 


IV.  "W,  cosa- 


lOOkx 


Tangential  force  (on  plane  ad),      H^i  —  PV,  sin  OC- 


Total  friction  (on  plane  ad), 


/-§  W^. 


and  the  resultant  force  R,  parallel  with  the  sliding  plane  ad,  vnS\  equsd  the 
tangential  force  minus  the  total  friction,  or 

j^^lOOhx  h  lOOhx  X  .^ 

2       v;t«+*«       3       \/¥+x* 

By  placing  the  first  difTerential  coefficient  equal  to  zero,  and  solving  for 
maxim  imi, 

dR^(h^  +  x*)i  (50^-66}  M  -  (bO  hhc-Z3\  hc^x  (h*  +  x')'^ ^^ 
dx "  ;t«  +  ir»  " 

whence.  (*«+««)  (50  A«-  66|  hx)  -  50  *«««-  33*  h  jfi. 

or,  ac»+  2  A*  *  -  -5-  (General  equation.) (S) 

Solving  this  cubic  equation  there  is  obtained 

Of-  . 627  A;  whence  a  =«  67*  -hV. 
Hence,  the  maximum  pressure  in  a  direction  parallel  with  th4  slope,  against 
the  vertical  plane  ab,  obtains  when  we  consider  that  the  sliding  plane  makes 
an  angle  a  =  57°-56'  with  the  horizontal;  and  when  /i  -  20,  %  -  12.54.  Sub- 
stituting the  value  of  x  in  equation  (2),  or  the  values  of  OC  and  x  in  the 
following: 

/?*-60Axsin  a  -  33i  *  iP  cos  a (4) 

we  have,  /?=  1^540  X  .847-8360  X  .531  -  6182  lbs.  Hence,  from  the 
above  analysis,  the  resultant  pressure  R,  due  to  the  earth  sliding  on  the 
plane  of  maximum  slope  pressure,  is  6182  lbs.,  which  force  is  attuned  to 
act  parallel  with  the  airection  of  the  sliding  plane,  through  the  center  of 
gravity  B  of  the  mass,  and  intersecting  the  vertical  plane  06  at  a  point 
distant  }  h  below  the  top  of  fill  (Fig.  1). 

In  a  similar  manner  the  total  horizontal  pressure  H  (■■/?  cos  a),  against 
the  wall,  may  be  found;  thus, 

50/t«a:«-33U»* 


H-i?cos  a«" 


(5) 


A>+**        

Placing  the  first  differential  coefficient-j-  equal  to  0  and  aolying,  we  have. 

*"+8  fc«x— 3  W,  and  for  maximum  value  of  H  we  have  *  — 0.8178  fc— 
*2-3?  ft.;  whence  ex:  -  SAMS',  and  //- 16360  (sina-fcosoc)  oosoc- 
H  anSl'iw^PP^^^  horizontally  at  r,  Fig.  1.  N«;lecting  friction  on  slope. 
whTrl  ^'  '"ak'n^  the  lateral  pressure  about  40%  of  the  vertical  pressure, 

wmcn  may  be  considered  a  maximxmj  for  any  earthy  material. 


I 

i 


PRACTICAL  DEDUCTIONS.  837 

AssHmptioHs  Rtgarding  Friction. — Reverting  to  Fig.   1.  there  are  two 

planes  where  friction  mav  be  considered,  namely,  ad  and  ab.     We  have 

tound  (equation  4)  that  the  possible  friction  on  the  plane  od  is  ZSk  hx  cos 

a  "4439  lbs.  which,  deducted  from  the  tangential  force.  50  hx  sin  cc  (or 

I      10621Ibs.).  gives  6182  lbs.,  the  resultant.     Hence,  if  the  friction  is  neglected 

t     our  resultant  will  be  increased  from  6182  to  10621  lbs.,  an  increase  of  nearly 

i      72%.    Should  this  friction,  for  safety,   be  wholly  or  partly  neglected? 

Before  arriving  at  any  conclusion  in  regard  to  this,  let  us  consider  the 

possible  friction  on  plane  ab.     U  a  b  represents  the  back  of  the  retaining 

wall,  the  amotmt   of  possible  friction   will  depend 

upon  the  construction  of  the  wall  itself. 

Let  Pig.  2  represent  a  simple  frame  construction 
to  better  analyze  the  acting  forces.  The  resultant 
force  R  is  resisted  by  the  strut  c  #,  and  hence  the 
stress  in  the  latter  is  equal  and  opposite  to  R.  The 
point  c  is  the  center  of  gravity  of  the  distributed 
earth  pressure  acting  on  the  facing,  which  is  sup- 
ported by  the  stud  ao,  which  facing  is  stiff  enough  to 

resist  bending,  and  which  is  balanced  on  the  pivot  ^   _  . 

or  point  of  support   c.    As  long    as    the   resiiltant  vwm^.Um  • 

pressure  acts  parallel  to  the  plane  a  d.  as  indicated.  Pig.  2. 

there  will  be,  apparently,  unstable  equilibrium;  but  should  it  make  a  less 
angle  than  ex  with  the  horizontal,  then  there  would  be  a  tendency  for  the 
strut  c  e  to  revolve  about  #.  In  doing  so  it  would  tend  to  raise  the  facing 
a  b,  thereby  causing  friction  of  the  latter  against  the  earth  fill.  Indeed, 
as  the  forces  now  act.  the  resultant  R  can  be  transmitted  to  the  strut  c  # 
only  on  the  assumption  that  there  is  sufficient  frictional  force  downward 
on  the  "fill"  face  ot  the  wall  to  resist  the  vertical  component  of  the  stress 
in  the  strut  c  #.  Let  us  examine  this:  Assuming  the  coefficient  of  friction 
of  the  earth  on  the  face  of  the  wall  as  equal  to  f  of  the  normal  pressure, 
there  is  obtained. 
Total  friction  —  f  /?  cos  a 

-2189  lbs.  for/?- 6182: 
-3760  lbs.  for/?- 10621. 
This  friction  on  the  "fill"  face  of  the  wall  will  be  opposed  by  the  vertical 
component  of  the  stress  in  the  strut  c  0,  equal  to 
Rsin  (X 
-5236  1bs.  for/?-6182: 
-8906  lbs.  for/?- 10621. 
Hence  it  is  evident  that  the  wall  may  have  to  be  anchored,  at  a,  an  amount 
equal  to 

Vertical  component  of  /?—  (total  friction +wt.  of  wall) 
of  else  the  strut  c  0  will  have  to  have  a  less  inclination  with  the  horizontal. 
Similarly,  the  preceding  form  of  analysis  may  be  repeated,  but  using 
the  maximtmi  value  of  H  obtained  from  equation  (5)  with  the  angle  ol 
slope  60*-4y. 

Practical  Deductions. — ^The  uncertainty  of  some  of  the  foregoing  assump- 
.ions  makes  the  problem  a  difficult  one  to  solve.  However,  we  are  reason- 
ably certain  that  the  resultant  pressure  on  the  wall  parallel  with  the  sliding 
jlane  ad  (Pig.  1)  is  somewhere  between  6182  and  10621  lbs.  Assuming 
he  latter  as  correct  by  neglecting  friction  on  the  slope  (which  can  obtain 
mly  when  the  wall  begins  to  tip)  we  have  that  the  resultant  normal  pressure 
^  actincT  horizontally  at  c  is 

P-/?  cos  a- 10621  X.631- 6640  lbs. 
rhich  is  equivalent  to  a  horizontal  pressure  per  square  foot  on  the  vertical 
rail  a  b,  varying  uniformly  from  zero  at  b,  to  664  lbs.  at  a.  This  is  equiva- 
snt  to  stating  that  the  horizontal  pressure  per  square  foot  against  the 
staining  wall  at  any  point  below  the  top  is  equal  to  2^o  P^i*  cent,  of  the 
eight  of  a  vertical  column  of  earth,  one  square  foot  in  section,  extending 
•om  the  top  of  the  fill  to  that  point:  that  is,  the  lateral  pressure  is  28ft  per 
2nt.  of  the  vertical  pressure. 

For  Temporary  Shoring,  this  maybe  reduced  to  25  per  cent.,  or  even 
ss,  providea  of  course  that  the  "earth"  is  not  saturated  with  water  so  as 
»  be  in  a  muddy  condition.  Up  to  a  certain  point  of  wetness,  moist  earth 
ill  produce  less  percentage  of  lateral  pressure  than  dry.  granular  earth. 
Few  Permanent  Structures,  the  lateral  pressure  should  oe  assumed  at 
>out  30  per  cent,  of  the  vertical,  and  even  up  to  33 i  per  cent,  in  places 
bjcct  to  considerable  jarring,  as  for  retaining  walls  supporting  railway 


838 


48.^RETAINING  WALLS. 


embankments.     Where  the  weight  of  a  train  or  of  a  structure  falls  within 
the  range  of  the  slope,  it  can  be  reduced  to  an  equivalent  volume  of  earth. 

If  the  material  is  coarse  gravel,  the  ratio  of  lateral  to  vertical  pressure 
may  reach  as  high  as  40  per  cent.,  tor  which  provision  should  be  made. 

Graphical  Solution  of  Preceding  Problem. — ^Fig.  3  is  a  graphical  solution 
for  a  masonry  retaining  wall  20  ft.  high  to  restrain  a  level  earth  fill  of  the 
same  height — the  problem  which  has  engaged  our 
attention  throughout  the  discxission  of  the  theory 
of  eaBth  pressure.  The  weight  of  the  earth  fill  is 
assu^d  at  100  lbs.  per  cu.  ft.,  and  the  lateral  pres- 
sure. 30  per  cent,  of  the  vertical.  Hence  the  re- 
oi*»^,  V  f  30  X  20* 
sultant  lateral  pressure  P ^ —  «  6000  lbs.,  acting 

horizontally  at  a  point  one-thiixl  the  height  from  the 

bottom.     Selecting  the  trapezoidal  type  of  wall,  the 

center  of  gravity  is  foimd  by  asstunin^  the  top  and 

bottom  widths;  laying  off  the  bottom  width  on  either 

side  of  the  top.  and  the  top  width  on  either  side  of  the 

bottom:  and  finding  the  point  of  intersection  of  the 

diagonal  lines  joining  the  outer  points.     The  weight 

of  one  foot  section  of  wall  at  160  lbs.  per  cu.  ft.= 

16500  lbs.,  acting  vertically  through  the  center  of 

gravity.     From  the  intersection  of  the   two  acting 

forces  the  triangle  of  forces  is  drawn  showing  the 

resultant  to  intersect  the  base  within  the  middle  third, 

which  is  good  practice.      ,    .      ,       ^  ,  .  , 

Fig.  i  shows  another  design  for  the  same  in  wnicn 

the  top  width  of  wall  is  one  ft.  instead  of  three.     In 

this  case  the  resultant  falls  outside  the  middle  third, 

and  hence  there  is  tension  on  the  face  ab.    In  addition 

to  this  tension,  the  factor  against  overturning  at  i  is 

lessened,  and  it  is  not  as  desirable   a  type  as  that 

shown  in  Fig.  3. 

Top  of  Fill,  Sloping.— Vp  to   the   present,  we 

have  considered  the  top  of  fill  level,  and  flush  with 

the  top  of  the  wall.     We  will  now  consider  what 

modification  of  pressure  will  be  effected  in  case  the 

surface  of  the  fill  shotdd  slope  either  upward  or  down- 
ward   from  the  back  or,  in  fact,  show  any  profile 

whatever.     Fig.  6,  in  which  ab  is  the  "fill*    face  of 

the  retaining  wall,  shows  the  slopes  of  maximum 

pressure  for:  (1)  a  level  fill  W,  with  maximum  pres- 
sure slope  ad  making  an  angle  of  67°-66'  with  the 

horizontal;   (2)   an  upward  surface  slope  bu,  with 

maximum  pressure  slope  au  slightly  less  than  ad; 

and  (3)  a  downward  surface  slope  bl,  with  maximum 

pressure  slope  al  slightly  greater  than  ad.  It  is  to  be 

noted  that  the  slopes  of  maximum  pressure  au  and 

al  very  nearly  coincide  with  ad,  the  slope  of  maxi- 
mum pressure  which  we  found  for  a  level  fill,  and 

it  might  also  be  stated  here  that  this  slope,   ad, 

may  be  varied  either  way  several  degrees  without  '^'^iu        

materially  affecting  the  resultant  pressure.     Also,  as  6u  and  bl  are  the  upp» 

widlowef  limits  at  which  earth  fill  will  stand    li  to  1).  then  .all  other  poaable 

surface  slopes  must  be  less  than  these,  and  in  approaching  a  level  tlwir 

slopes  of  maximum  pressure  a  u  and  a  I  wUl  approach  a  dm  directum,     i^ 

all  practical  purposes  a  d  may  be  assunted  as  the  slope  of  maxtmum  pressure 

for  any  surface  slope.    This  assumption,  containing  a  small  percentage  oi 

error,  greatly  simplifies  the  method  of  calculation  for  general  cases.     ¥ct 

depressed  surface  slopes,  as  bl,  the  assumption  is  on  the  side  ol  salety. 

while  for  surcharged  walls  with  upward  slopes,  afbu.the  assumption  in- 
volves a  slightly  opposite  effect,  to  counteract  which  it  would  be  wen  to 
have  the  resultant  of  all  the  forces  (earth  and  wall)  cut  the  base  of  the 
retaining  wall  at  least  |  of  the  width  from  the  toe  instead  of  the  customary  t- 
General  Cases. — By  observing  the  following  methods  a  retaining  wall 
may  be  designed  for  any  surface  slope:  (1)  Draw  the  back  of  the  wall,  oft 
(Pigs.  6,  7,  and  8) ;  the  slope  of  greatest  pressure,  au  or  al,  making  an  an^ 


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840  48.— RETAINING  WALLS. 

,  Notation. 

w     —weight  of  earth  in  lbs.  per  cu.  ft.; 
X     —vert,  depth  in  ft.  below  surface,  of  any  (conjugate)  plane  parallel 

with  the  surface  plane  (Pig.  9) ; 
e     wangle  of  inclination  of  conjtigate  plane  with  the  horiaontal; 
^     —angle  of  repose  of  earth,*  or  angle  of  greatest  obliquity; 
p,    —intensity  of  vert.  pres.  in  lbs.  per  sq.  ft.  on  any  conjugatt  plane  at 

depth  X  below  surface; 
p,    —intensity  of  pres.  in  lbs.  per  sq.  ft.,  in  a  direction  parallel  with  the 

conjugate  plane,  against  a  vertical  plane  (as  a  retaining  wall)  at 

depth  X  below  surface. 

Formulas. 
(Surface  plane  assumed  to  be  of  indefinite  extent.) 

In  general,  p,  — w  ar  cos  6 (1) 

and  p^  may  have  any  value  between 


Pig.  9. 


„  -  cos  tf— \/cos*  ^— cos*^  ,^  . 

p,  7w  X  cos  e — - (Sa) 

cos  d>+vcos'  d—C08^^ 


-               ^  _                «cos  O+s/cos*  <?  — cos*^  .«., 

and  p,  ^w  X  cos  8 — - (26; 

cos  tf— Vcos*  fl— cos*^ 
If  A  is  the  height  of  the  retaining  wall,  the  maximum  intensity  of  prcsson. 
at  the  bottom,  may  be  foxmd  by  substituting  h  for  x  in  the  preceding  equa- 
tions; and  as  the  intensity  of  pressure  at  the  top  of  the  wall  is  icro.  the 
average  will  be  one-half  the  maximum.  Hence  the  total  pressure  on  the 
wall  will  equal  the  average  intensity  multiplied  by  the  height  h,  and  this 
to  be  applied  at  a  point  fh  from  top  or  sunace,  and  in  a  direction  paralleJ 
with  the  conjugate  plane. 

If  the  surface  plane  is  horizontal: 
Equation  (1)     reduces  to  p,  — w  x (3) 

'•   <^>  ••   •■  ^-^"'uM <*" 

'•       (^>      ••       ••   ^--'T^* <**' 

If  the  surface  plane  is  inclined  at  the  angle  of  repose  so  that  5  —  ^,  then 
p.  —n;  X  cos  d^w  x  cos  ^ (i) 

For  water,  the  angle  of  repose  ^—0.  and  equations  (4a)  and  (46)  reduce 
to  the  hydraulic  equation 

p^  — w  X (6 


♦  Usxmlly  assumed  at  33^-41'  for  earth  fill,  equal  to  slope  of  14  to  1. 
making  coefficient  of  friction  (-tan  ^) -  |.  r^^^^T^ 

Digitized  by  VjOOv  Ic 


STANDARD  TYPE. 


841 


N.  Y.  C.  &  H.  R.  R.  R.  Standard  Retaining  Wall. 
(W.  J.  Wilgus,  Chief  Engineer.) 


S9MW  Dm  0IOntMH 


■  dilmmimdbfloadiitfmdaanctv  fkrtnnktJoti. 
Fig.   10. 


1. — Cubic  Yards  op  Masonry 

IN  Rbtainino  Walls  (Pio.  10). 

Cu.  Yds.  per  Running  Ft. 

Cu.  Yds.  per  Running  Ft. 

Height 

Height 

Body 
Wall. 

Foundat'n  1 

Body 
Wall. 

Foundat'n 

Coping. 

4' Deep.    1 

Coping. 

4' deep.    . 

5'(r 

0.111 

0.671 

0.833 

18' 0* 

0.111 

3.858 

1.644 

6'(r 

0.868 

0.920 

ivor 

4.204 

1.666 

7'(r 

1.048 

0.932 

20' 0* 

•• 

4563 

1.668 

s'cr 

•• 

1.241 

0.944 

21' 0* 

" 

4.946 

1.744 

yo* 

** 

1.456 

1.032 

22' 0* 

•• 

6.341 

1.756 

\(y(r 

•* 

1.673 

1.044 

23' 0* 

" 

6.740 

1.768 

11' cr 

•• 

1.894 

1.066 

24' 0* 

•* 

6.183 

1.946 

r(r 

•• 

2.136 

1.143 

26' 0* 

•• 

6.629 

1.968 

ycr 

•* 

2.381 

1.166       1 

26' 0* 

•• 

7.078 

1.970 

4'(r 

•• 

2.630 

1.167 

27' 0* 

•• 

7.671 

2.146 

S'O* 

•• 

2.922 

1.343 

28' 0* 

•• 

8.068 

2.158 

e'o* 

•• 

3.217 

1.366 

29' 0* 

•' 

8.667 

2.170 

r<r 

" 

3.616 

1.367       1 

30' 0* 

" 

0.110 

2.346 

EXCERPTS  AND  REFERENCES. 
Deslcns    of    Reiororccd-Concrete    Retainiog-Walls    (By    J.    Lehman. 
I.  News,  Aug.  7,  1902). — Illustrated. 
Typicid    Croo-Sectioo   of    Retaining-Wall,  and   Detafls  of  ExpaiukMi 

It  (Kng.  News.  June  2.  1904). — Illustrated. 

Analysis    and   Design   of   a   Reinforced-Concrete   ReUining-Wall  (By 

?.  Sinks.     Eng.  News,  Jan.  6.  1906). — Comparison  of  cost  with  plain 

rrete.      Olustrated.     Discussion  of  this  article  in  Eng.  News.  Feb.  16, 

5. 


842 


48  ^RETAINING  WALLS. 


High  Reinforced-Concrete  ReUining-Wall  Constructioo  at  Secttle, 
Wash.  (By  C.  F.  Graff.    Eng.  News,  Mar.  9,  1906). — lUustiated. 

Difficult  Reinforced-Concrete  Retaining -Wall  Constructloa  on  the 
Oreat  Northern  R.  R.  (By  C.  E.  Graff.  Eng.  News,  May  3,  1906). — Illus- 
trated. 

The  SUMUty  of  Sea  Walls  (By  D.  C.  Serber.  Eng.  News.  Aug.  ^3. 
1906).— Illustrated. 

Reinfofced-Concrete  ReUining-Wall  Design  (By  E.  P.  Bone.  Bsg. 
News,  April  25.  1907).— Illustrated. 

Comparative  Sections  of  Thirty  Retaining  Walls  and  Some  Notes  oa 
ReUining  WaU  Destai  (By  F.  H.  Carter.  Eng.  News,  July  28.  1910).— 
The  following  table  is  compiled  from  the  dimensions  given  on  the  cross- 
sections: — 


Retaining  Wall. 


Height 
h. 


Top 

Width 

t. 


Bottom 

Width 

b. 


N.  Y..  N.  H.  &  H.  R.  R.  (stone 
masonry) 

Penn.  N.  Y.  &  L.  I.  R.  R.  (concrete) 
wet  gr'd 

Penn.,  N.  Y.  &  L.  I.  R.  R.  (concrete) 

Boston  subway  (cone,  granite  faced) 

East  Boston  tunnel  (cone,  granite 
faced) 

Penn.  Ave.  subway,  Phila.  (stone 
masonry) 

Detroit  ttmnel  (concrete) 

Borough  of  Bronx.  N.Y.  City  ( ) 

HI.  Ont.  R.  R.,  Chicago  (concrete) . . 

B.  &  M.  R.  R.  (1st  claJss  mas.  or  con- 
crete)   

B.&A.  R.  R.    ( )   level  earth 

cmb'k't 

Penn.  R.  R.,  standard  (stone  mason- 

N.  ¥.c''&  H.  R.  R.'  R.'  (.' .' .' .'  y.'.y.) 

Sea  wall,  Lynn  shore  (concrete) 

Sea  wall.  CTradock  Br.  (1:3:6  con- 
crete) 


At  spillway,  Wachusett  dam  ( . 


Mass.  Highway  Comra.  (stone  mason- 
ry)  

Board  Water  Supply,  N.  Y.  (con 
Crete) 

Board  Water  Supply,  N.  Y.  (rubble 
masO 

Board  Water  Supply,  N.  Y.  (cyclo- 
pean  mas.) 

Sea  wall,  Charlcstown  (stone  mason- 
ry)   •• 

Subway  wall,  Boston  Term.  Sta 
(concrete) 

Harbor  wall.  (Charles  river  (cone, 
granite  faced) 

Sea  wall.  Charles  River  (dry  coursed 
rubble) 

Retaining  walls  on  transverse  roads 
in  connection  with  Boulevard, 
New  York  City. — 3  examples  are 
given 

Retaining  walls  designed  for  Cam- 
bridge Main  Street  Subway. — 3 
examples  are  given 


26' 9  " 

23' 0  ' 
18' 0  ' 
13*  6  ' 

17' 0  • 

28'  4  ' 

28'  ir 

33' 2  • 
21' 0  ' 

20' 0  ' 

20' 0  • 

25' 0  • 
28' 0  • 
18' 0  ' 

19'  9  ' 
26'  4  ' 

13'  6  ' 

20'  0  ' 

18' 0  ' 

44'  6  ' 

24'  0  ' 

16' 6  ' 

2^  4  • 

15'  6  ' 


3'0' 

3' 4' 
3*4' 
3'0' 


2'  6' 
8'0' 
2'  4' 

1'5' 

I'O* 

2'0' 

S'O' 
3'0' 
3'0' 

2'0' 

y  r 

2' 4' 

y  r 

8' 6* 
S'O' 
2' 6' 
3'0' 
4' 6* 
4'0' 


12' 0  ' 

15'  9i' 
9'0  • 
S'O  ' 

5'0  • 

12' 4  ' 

13' 7  ' 

12'  If 

9'3r 

8'0  ' 

9'0  ' 

13*8  • 

12*  3r 

9'0  -' 

O'O  ' 

ir  6  ' 

7'0  • 
9'5r 

11'  sr 

24'  OJ* 
12*0  • 

8'  6  ' 
16'  0  • 

9'  6  • 


d  by'GDipgfi^' 


MISCELLANEOUS  DATA.  843 

The  Bradng  off  Trcncbet  and  Ttumcls,  With  Practical  Formulas  for 
EMiih  l>resMirct  (By  J.  C.  Meem.    Trans.  A.  S.  C.  E.,  Vol.  LX). 

A  Reinforced-Coocrete  Retaining-Wall  Alonf  tlie  Bank  of  tlie  Ohio 
River  (By  F.  A.  Bone.    Eng.  NcwsTjune  3,  1909).— lUustratcd. 

Tlie  Design  of  Retaining  Walls  (By  Comra.  on  Masonry  of  the  Am.  Ry. 
Engg  and  M.  of  W.  Assn.  Eng.  Rcc,  Sept.  U,  1909).— Includes  many 
types  of  structxires  an  actual  use,  and  contains  32  illustrated  sections. 

Tables  for  Determination  of  Earth  Pressure  on  Retaining  Walls  (By 
C.  K.  Mohler.  Eng.  News.  Nov.  25,  1909).— (1)  Rankine's  method  after 
Howe;  (2)  Sliding  prism  theory. 

The  Cradcbig  and  Partial  Failure  of  Abutments  and  Retaining  Walls  (By 
C.  K.  Mohler.  Eng.  News,  (Dct.  13,  1910). — Criticism  of  present  methods 
of  design  and  construction. 

Illustrations  of  Various  Types  of  Retaining  Walls. 

Description.  Eng.  News. 

Relnforced-concrete  retaining  walls,  bridge  approaches Nov.  25.' 09 

Eng.  Rec. 

32-ft.  reinforced-concrete  retaining  wall Apr.  3.  '09 

Section.  31-ft.  rein.-conc.  retaining  wall.  C.  B.  &Q.R.R Aug.  21.'09 

Design  of  retaining  walls  for  Steptoe  smelter Feb.  19, '  10 

Conbtned  rein.-conc.  fence  and  retaining  wall Feb.  26.  '10 

Rein.-conc.  retaining  wall  and  roadwav  bridge  and  walk Sept.  24,' 10 

Types  of  French  railway  retaining  walls Nov.  12.  '10 


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49— DAMS. 

Common  Fixed  Types. — A  dam  is  a  structure  designed  to  hold  back  a 
large  body  of  water  in  an  impounding  reservoir,  at  a  higher  level  than 
would  naturally  obtain.  It  should  first  of  all  be  safe,  ana  the  site  should 
be  selected  with  due  regard  to  present  and  future  needs  for  storage.  «xm- 
omy  of  construction,  efficiency  of  head,  outlet,  wasteway,  etc.  With  re- 
spect to  their  structural  features,  dams  may  be  classified  as  follows: 

A  Gravity  dam  is  a  masonry  dam  desijg^ed  to  resist  overturning  by  the 
action  of  gravity  alone.  It  must  also  resist  any  tendency  to  slide  horiion- 
tally  (down-stream)  on  its  base  or  on  any  plane  above  (or  below)  the  base; 
there  must  be  no  tension  in  the  masonry  at  any  point  as  in  the  up-stream 
face  where  it  is  most  likely  to  occur;  and  the  compression  in  any  part  as 
the  down-stream  face,  where  it  is  maximum,  must  not  exceed  the  safe, 
allowable  intensity  per  square  inch. 

An  Arched  dam  is  a  horizontally  curved  (arched)  type  with  ends  rigidly 
braced  against  the  side  walls  of  the  canyon — a  typical  site  for  this  class  erf 
dam.  The  arch  is  designed  to  relieve  partly — not  wholly — gravity  re- 
quirements although  many  engineers  use  the  full  gravity  section  that  would 
be  required  for  a  straight  dam,  thereby  employing  the  arch  to  give  greater 
stabihty,  or  in  other  words,  to  increase  the  factor  of  safety.  Althoxigh  the 
stresses  in  an  arched  dam  cannot  be  determined  with  accuracy,  especially 
as  it  acts  partly  as  a  gravity  dam,  being  "fixedly"  supported  throughout 
its  whole  length,  we  know  that  the  arch  effect  relieves  the  tendency  to  o%*er- 
tumin^,  caused  by  the  action  of  the  water  pressure  on  the  up-stream  face, 
and  this  being  true,  it  is  evident  that  the  base  of  the  dam  can  be  narrowed 
materially.  This  possible  reduction  of  section,  however,  diminishes  as  we 
approach  the  top  of  the  dam  where  the  combined  gravity-,  arch-  and  tem- 
perature stresses  bear  in  increased  ratio  to  the  gravity  stre^es  alone. 
indeed,  it  has  been  claimed  that,  under  certain  conditions,  the  arched  dam 
requires  a  greater  section  near  the  top  than  does  the  gravity  dam,  althous^ 
the  writer  has  never  met  with  such  conditions  in  practice. 

A  Buttressed  dam  is  a  gravity  dam  with  buttresses,  or  thickened  sections, 
spaced  at  stated  intervals  for  the  more  economical  distribution  of  the  material 
than  one  of  uniform  cross-section.  It  may  be  built  of  concrete,  steel- 
concrete,  or  stone  masonry.  The  sections  at  the  buttresses  will  be  larger, 
and  the  sections  between  the  buttresses  will  be  smaller,  than  that  of  an 
equally  safe  gravity  dam  of  uniform  cross-section.  Care  should  be  taken 
in  both  the  design  and  construction  to  avoid  any  possibility  of  tension, 
undue  shearing,  or  excessive  compression  in  any  part  of  the  masonry.  The 
facing  between  the  buttresses  may  be  supported  by  horiiontal  remf(»x«d 
concrete  beams  as  us«i  in  building  construction,  or  by  concrete  or  stone 
masonn^  arches.    The  facing  should  practicably  be  imperviotis  to  water. 

A  Braced  dam  is  a  dam  with  braced  vertical  or  sloping  face.  It  differs 
from  a  buttressed  dam  in  that  the  solid  masonry  buttresses  are  replaced 
by  open  bracing  of  reinforced  concrete,  steel  or  wood.  The  facing  may  be 
ot  the  same  character  of  material,  but  not  connected  with  the  braced  legs 
in  such  a  manner  as  to  form  a  series  of  arches  between  them.  A  good  angle 
for  the  face  of  a  braced  dam  is  a  slope  of  46  degrees  with  the  horizontal, 
in  which  case  the  cost  of  facing  will  generally  about  equal  the  cost  of  bracing. 
But  if  the  facing  is  very  expensive  and  the  bracing  cheap,  this  angle  should 
be  increased.  The  cost  ot  repairs  for  each  should  also  be  considered  in 
determining  the  economic  angle. 

A  Cantilever  dam  is  designed  on  the  cantilever  principle  and  may  be 
braced  or  buttressed.  The  facing  is  supported  by  beams  or  trusses  projec- 
ting beyond  the  upper  limit  of  the  bracing.  It  may  be  framed  of  steel  and 
concrete,  reinforcea  concrete,  steel  or  wood,  or  a  combination  of  these 
materials.  It  should  be  secured  firmly  to  a  natural  bed-rock  or  to  a  con- 
crete anchorage. 

A  Crib  dam  is  a  skeleton,  box -like  structure  weighted  with  filling  and 
usually  faced  to  prevent  undue  leakage.  The  skeleton  structure  may  be 
composed  of  logs  or  of  hewn  or  sawed  timbers,  framed  apd  bolted  into  a  crib. 


Digitized  by  VjOOQ IC 


COMMON  TYPES.    GRAVITY  DAM. 


845 


fined  with  rock,  slag,  gravel  or  other  suitable  material,  sunk  to  the  bottom 
(«rhich  has  been  previously  prepared)  and  preferably  bolted  thereto.  Plank- 
ing makes  a  cheap  facing. 

A  Composite  dam  is  one  composed  of  two  or  more  radicallv  different 
kinds  of  material,  composite  but  not  structural  in  character.  A  good  ex- 
ample  of  a  composite  dam  is  the  common  brush  and  rock  dam,  the  brush 
to  prevent  excessive  leakage  and  the  rock  to  give  stability. 

Jfi  Filkd  dam  is  one  not  strictly  structtiral  in  character,  containing 
little  or  no  cohesion  and  hence  not  capable  of  being  "overturned,"  but 
which,  if  ifeoded  (overtopped)  with  water,  will  disintegrate  and  wash  away. 
It  may  be  composed  ot  any  durable  material  of  specific  gravity  greater 
than  unity,  as  clay,  earth,  sand,  gravel  or  loose  rock.     If  it  is  of  the  finer 
materials  it  is  called  an  Earth  dam;  if  of  the  coarser  (rock),  a  Rock-fill  dam. 
(a)  An  Earth  dam  should  be  composed  of  material  or  materials  which 
will  pack  well  and  allow  but  small  voids,  if  any,  and  which,  under  the  action 
of  water,  will  not  wash,  leaving  large  holes  or  pockets.     "Cement"  gravel 
is  probably  the  best  material  as  it  contains  the  proper  natural  binder  for 
a  solid  mass.     If  materials  are  mixed,  such  as  earth,  sand,  clay,  etc.,  they 
are  better  if  mixed  thoroughly  and  uniformly — if  not,  there  are  liable  to 
be  seams  of  strata  allowing  the  water  to  percolate  and  wash  the  materials. 
The  ratio  of  3  horizontal  to  1  vertical  for  the  wet  slope  and  2  to  1  for  the 
dry  slope  is  ordinarily  good  practice  and  generally  should  not  be  exceeded. 
(2r)  A  Rock-fill  dam  is  composed  of  loose  rock  dumped — not  carefully 
laid — in  place,  with  proper  up-stream  and  down-stream  slopes.     The  up- 
stream slope  may  sometimes  be  as  steep  as  \  horizontal  to  1  vertical  if  the 
rock  facing  is  laid  by  hand,  otherwise  1  to  1  is  the  usual  practice.     The  dry- 
or  down-stream  slope  is  usually  broken,  being  steeper,  say  1  to  1,  for  the 
upper  and  H  to  1  or  li  to  1   for  the  lower  section.     The  facing  may  be  of 
double  planking,  caulked  and  asphalted,  and  nailed  to  wooden  stringers, 
say  6'xo'.  imbedded  in  the  face  rock.     The  thickness  of  the  planking  will 
of  course  be  greater  for  the  (greater  head  of  water. 

STABILITY  OF  GRAVITY  DAMS. 

A  gravity  dam  to  be  safe  must  be  built  on  the  natural,  hard  bed-rock 
not  liable  to  disintegrate,  and  capable  of  withstanding  the  maximum 
intensity  of  pressure  at  the  toe  of  the  dam.  to  resist  overturning.  The 
outlet,  for  drawing  off  the  water  for  domestic  or  commercial  uses,  is  usually 
by  (cast  iron)  pipes  extending  through  the  masonry  wall  of  the  dam  itselt, 
but  preferably  by  tunnel  construction  through  the  solid  rock  at  one  side 
of  and  apart  from  the  dam.  Likewise,  the  wasteway,  for  carrying  off  the 
flood  waters,  should  preferably  be  at  some  other 
point  than  at  the  dam  itself.  In  many  cases,  how- ,, 
ever,  there  is  no  alternative  but  to  let  the  surplus  or 
waste  water  from  the  full  reservoir  flow  over  the  en- 
tire crest  of  the  dam,  or  through  a  specially  provided 

wasteway  in  a  certain  limited  part  of  the  crest. 
When  the  dam  acts  as   a  waste-weir,  i.e.,  with 

the  water  flowing  over  the  crest,  additional    forces 

must  be  considered    as    tending    to    overturn    the 

structure.     There  are    (1)    the  additional   head  of 

water  hi  above  the  top  of  the  dam;    (2)  the  tension 

:>r  suction  at  the  rear  face   of   the  dam,  due  to  a 

partial  vacuum  at  a.  Pig.   1.  caused  by  the  falling 

Krater  taking  up    the    particles   of   air   between    it 

ind  the  rear  face  of  the  dam;  and   (3)  the   pressure 

»f  ice  and  logs  against  the  upper  face.     The  vacuum 

fleet    may  be  lessened  materially  by  rotmding  off 

he  rear   upper  comer  of  the  dam,  ai  shown  in 

^ig.  2. 

Hydrottatic  PlreMure. — In  the  discussion  of  dams  and  the  forces  acting 
gainst  them  it  is  convenient  to  assume  a  section  of  the  dam  and  of  the  col- 
mn  of  water,  etc.  acting,  as  one  foot  thick.  The  weight  of  a  cubic 
>ot  of  water  is  generally  assumed  at  62.5  lbs.,  involving  an  error  of  J  of 
ne  per  cent,  on  the  side  of  safety.  Therefore,  the  pressure  of  one  square 
ot  of  surface  at  a  depth  of  h  feet  below  the  surface  is  62.6  h.  It  will  thus 
s  seen  that  the  intensity  of  pressure  increases  uniformly  with  the  depth. 
id  furthermore  it  is  always  normal  (at  right  angle)  to  the  surface  acted 


S46 


«.— D^AfS. 


upon,  because,  being  a  irictionless  liquid,  the  pressure  is  equal  in  all  direc- 
tions. To  find  the  total  pressure,  then,  on  any  plane  siuiace  one  foot  wide, 
whether  inclined  or  not.  it  is  necessary  only  to  find  the  intensity  of  pressure 
per  square  foot  at  its  "middle  point"  and  multiply  this  result  by  the  length 
of  the  plane.  Moreover,  as  will  be  shown  in  the  next  article,  imder  "Center 
of  Pressure."  the  total  pressure,  instead  of  being  assumed  as  a  distributed 
force,  may  be  assumed  to  act  at  the  center  of  pressure,  i.e.,  at  the  center 
of  gravity  of  pressure  on  any  "rigid"  surface,  thereby  greatly  simplifyibig 
the  calculations. 

The  following  are  common  examples  of  total  pressure,  the  heavy  line 
in  each  figure  representing  the  edge  of  the  plane,  <m$  foot  wid4,  acted  upon: 

(H  and  h  are  in  feet;  pressure  is  in  lbs.  against  the  plane  ah). 


jUst^^^fiss. 


^^/sl9tJSS6l^ 


Fig.  3. 
(1).  Vertical  plane  ab,  just  touching  surface  of  water. 

Total  pressure  -  — 9  ^  '  ^^^  — 2 — 
If  the  surface  of  the  plane  makes  an  angle  6  with  the  vertical,  multiply 
the  abovt  result  by  secant  d. 

(2).  Vertical  plane  ab,  submerged  below  the  surface.     (Pig,  4.) 

Total  pressure  -  62.6  (^y^)  (H  -  h)  ^  62.5  (^4~^)  *** 
(3).  Inclined  plane  ab,  submerged  below  the  surface.     (Pig.  5.) 
Total  pressure  -62.6  (^"y"^)  sec  ^  lbs. 

This  pressure  will  not  be  horizontal,  but  normal  to  the  plane  ab;  ex> 
ample  (2)  illustrates  the  horizontal  component  of  this  pressure. 

The  above  formulas  will  be  found  useful  in  calculating  the  total  pressure 
on  any  section  of  a  dam.  whether  the  face  is  vertical  or  sloping.  The  point 
of  application  of  the  resultant  pressure  will  now  be  discussed. 

Center  of  Pressttre. — If  the  total  pressure  against  any  surface  as  06.  in 
the  preceding  illustrations,  is  concentrated  as  a  single  resultant  force,  this 
force  will  acta/  the  center  of  pressure  ^  and  through  the  center  of  gravity 
of  the  distributed  force.     In  Example  1,  above,  the  resultant  P  of  the 

distributed  force  is  — ~ —  lbs.,  acting  horizontally  through  the  center  of 

gravity  e.g.  of  the  pressure  triangle  a  b  c,  at  a  point  p  on 
the  face  of  the  dam.  distant  f  H  below  the  water  sur- 
face (Fig.  15).  Thtis,  p  is  the  center  of  pressure,  for  the 
head  H,  on  the  plane  ab,  whether  vertical  or  inclined. 
Likewise,  in  Example  2,    the   resxiltant  pressure   on  the 

62  & 
plane  ad  is  P  — -^(//'— A')  lbs.,  and  the  center  of   pres- 
sure. ^,  is  1  (H-f  %,     .  j  feet  below  the  water  surface  (Fig. 

16).     In  Example  3,  the  same  value,  f  f//-f  „     .  j  ,    holds 

true  for  the  distance  to  the  center  of  pressure  below  the 
surface,  while  the  total  pressure  is  of  course   greater— or 

—J-  (H*— fc«)  times  sec  angle  of  inclination  with  the  ver- 
tical.    For  reference, 
lows;— 


these  values  are  tabulated 


b?t?8feglepig. 


d  by  Google 


848 


40.— DAMS. 


cubic  foot  of  water  and  m  is  the  weight  per  cubic 
foot  of  masonry,  we  have,  from  the  preceding: 

w  /f  * 
The  resultant  horizontal  pressure,  P  —  — 5— . 

mbh 
2    ' 

Now,  if  it  is  desired  that  the  resultant,  R,  shall  in- 
tersect the  base,  b,  at  the  edge  of  the  "middle  third," 
as  shown  in  Fig.  10,  we  have  that 

E,      L      K      k. 

Vy  "    3    "*"    3   "  if 


The  total  weight  of  masonry. 


l^-- 


—  TjF,  whence  by  substitution. 


Pig.  10. 


wH*      mbk         b  .         faJln 


(1) 


U  H  ^  h,  this  reduces  to 


(2) 


JL 


:T?5^ 


e 


->._ 


If  w  (water)  -  62.6.  and  m  (masonry)  -  146,*  6-0.654  h (3) 

It  is  desirable,  sometimes,  to  have  the  resultant  cut  the  base  |  b  (instead  of 
i  6)  back  from  the  toe,  in  which  case  we  will  have,  6»=  0.7  A (4) 

Pressure  on  Fonndatlons. — If  two  stiff  pencil  erasers. 
Fig.  11,  are  pressed  moderately   together  by  equal  and 
opposite  forces  W  and  W  applied  neat  the  left  end,  a, 
it  will  be  seen   that  they  do    not  remain   in    contact 
throughout  their  entire  length,  but  separate  at  the  right 
end,  e.    Moreover,  it  will  be  found  that  the  length  of  con- 
tact to  the  right  of  the  applied  force  is  double  the  con- 
tact length  to  the    left,  and   therefore  \  of  the  total 
contact   b.     Similarly,   we   have    in    the    case  of  the         Fig.  11. 
dam  ab  c.  Fig.  10,  that  when  the  reservoir  is  empty  and  consequently  there 
is  no  water  pressure  on  the  face  06.  the  resultant  force  is  W,  the  weight  of 
the  masonry,  acting  as  shown  in  Fig.  11.     Hence,  we  may  say  that  for  a 
triangular  dam  with  a  vertical   face   ab   the   resultant 
weight  when  dam  is  empty  will  produce  a  pressure  in- 
tensity on  the  base  varying  uniformly  from  zero  at  the 
lower  toe,  c,  to  a  maximum  (m  h)  at  the  upper  heel,  a. 
Fig.  12.    The  exact  results   given   above   may  be   de- 
duced   by   mathematical  analysis,  which,  however,  will 
be  omitted  here. 

Let  us  now  consider  the  forces  acting  on  the  plane  a  c.  Pig.  10,  doe  to 
the  water  pressure  P.  Imagine  the  dam  to  be  a  vertical  beam  of  length 
a  b  and  "fixed"  at  the  lower  end,  a  c.  Consider  the  depth  of  the  beam,  b, 
and  the  width  (vertical  with  the  page),  unity.     The  acting  force,  P,  is 

wH*  H 

— 5— ,  the  lever  arm  is  -j,  and  hence  the  bending  moment  about  the  section 

wH^    H     wH* 
a  c  \s  —^'-  •  ■3—-~g-.     The  resisting  moment  of  the  beam  at  the  sectioo 

a  c  isf  I  /  6».     Equating,  /  —  — r^  —  the  compressive  stress  at  c  and  the  tcn- 


sile  stress  at  a,  considering  the    neutral  axis  midway  between, 
reservoir  is  full  of  water,  H  —  /» therefore  /  »■    -rj-  (Pig.  18) . 

By  combining  Figs.  12  and  13  we  are  enabled  to 
obtain  the  vertical  component  of  the  distributed 
stress  on  the  foimdation  or  on  any  plane  above 
same.     In  addition  to  this  there  is  the  horizontal 


If  the 


*  Specific  gravity  = 

jThe  resisting  moment  of 


» 146  +  62.5  =  2.336:  often  assumed  at  2\. 
„  _.jment  of  a  rectangular  beam  about  a  neutral  axis 
Pa^uig  through  the  center  of  section  is  A/,  •=  J  /  X  breadth  of  beam  X  (depth 
of  beam)*;  m  which  /-outer  fiber  stress.  n^^^]^ 

Digitized  by  VjOOQ  IC 


PRESSURE  ON  FOUNDATIONS.  84> 

shear  (  — P)  which  may  bo  considered  as  distributed  in  intensity  varying 
directly  with  the  vertical  pressure  at  any  point.  Hence  the  resultant 
intensities  will  be  parallel  with  the  resultant  a.  Pig.  10. 

Combining  the  stress  due  (1)  to  the  weight  of  the  masonry  dam.  and 
(2)  to  the  water  pressure  on  the  face  a  c,  we  have,  for  the  triangular  dam. 


c -/.-      0-^ ...(6) 

The  result  is  tension  if  "plus,"  compression  if  "minus." 

The  following  example  is  solved  by  equations  (5)  and  (6).  Wt.  of 
water,  v.  is  assiuned  at  62.5;  masonry,  m.  146  lbs.  per  cubic  foot;  see  also 
Pig.   10. 

Example. — ^What  is  the  effect  on  the  resultant  pressure,  R,  Pig.  10, 
when  the  reservoir  is  being  filled  ? 

Solution.— <a)  When  the  reservoir  is  empty  we  have  from  equation  (5). 
/,  —  — 146  A,  that  is,  the  intensity  of  compression  per  sq.  ft.  at  a  is  equal 
to  146  X  height  of  dam  in  feet!  If  the  limiting  pressure  on  masonry  is 
assumed  at  30.000  lbs.  per  sq.  ft.  it  will  be  seen  that  the  limiting  height  of 

30  000 

the  dam  will  be,  fc  —     .  .^    —  2061  feet,  when  the  dam  is  empty,  and  that  the 

pressure  on  the  foundation  tmiformly  decreases  from  80.000  lbs.  per  sq.  ft. 
at  a  to  zero  at  c  (see  Pig.  12).  (b)  If,  now.  the  reservoir  is  gradually  filled, 
the  horizontal  pressure  P  increases  with  //*  and  the  distance  to  center  oi 

pressure  above  the  base  increases  with  g-.    The  resultant  pressure  R  will 

gradually  swing  to  the  right  from  the  vertical  position  W  and  with  increas- 
ing magnitude.  It  will  be  found  also  that  the  intensity  of  pressure  at  a 
wiU  gradually  decrease  with  the  corresponding  increase  of  pressure  at  c. 
while  R  is  traveling  across  the  middle  third  of  the  base.  By  the  use  of 
eqtiations  (5)  and  (6)  the  intensities  of  pressure  /,  and  /,  can  readily  be 
obtained  by  substituting  the  values  of  the  unknown  quantities,  (c)  Lastly. 
we  will  consider  the  reservoir  as  full,  that  is,  the  water  is  assumed  to  be  at 
its  flood  height.  In  this  case.  H  may  be  slightly  less  than,  equal  to,  or  greater 
than,  h.  The  resultant  R,  Fig.  10,  is  now  cutting  the  base  at,  say,  the 
extreme  right  edge  of  the  middle  third,  whence  the  compression  at  a  is 
reduced  to  zero,  while  the  compression  at  c  has  reached  the  maximum. 
Therefore  it  is  evident  from  equation  (6)  that  if  /•  -"O, 

—^"mh (7) 

from  which,  the  value  of  any  factor  may  be  fotmd  by  assuming  values  for 

tlie  other  factors.     Thus,  ^"^ — r*.  which  compare  with  equation  (1). 

I£  /f —  A,  this  reduces  to  equation  (2),  or  6«=/i- /— .     Assuming  water  (w) 

a.t  62.6,  and  masonry  (m)  at  146.  we  have,  6 —  0.654  h,  equation  (8).  If 
y^ow  this  value  of  6  is  substituted  in  equation  (3)  and  tt;a62.5,  we  have, 
^vvlien  reservoir  is  full, 

4  gg  8ffl  62.6  A«  -.^. 

^'  "  "  (0.654 fc)«   ■"  "'OAS^nW  "  -"»*'^ 
rlSi^  same  result  which  was  obtained  for  /.  with  the  reservoir  empty.     It  is 
.g^    he  noted,  also,  that  the  most  economical  type  of  dam  approaches  the 
l^j-jaiffT'^^f  section  with  a  vertical  up-stream  face. 

General  Formulas  for  Prtssttre  on  Foundations. — ^For  any  type  of  gravity 
l^^rn  the  following  formulas  may  be  applied  with  a  reasonable  degree  of 
i^^^^^T^iracy,  or  at  least  sufi^ently  so  for  all  practical  purposes: 

Notation. 
m^       »■  total  weight  in  lbs.  of  "section-foot"  of  masonry  above  plane  a  c. 
»i  width  of  base  a  c  in  feet,  with  center  of  base  at  origin,  o. 


860 


49.— D^AfS. 


F. 


«  distance  in  feet  from  origin  o,  to  point  of  applica- 
tion of  the  resultant,  R,oryac\  +x  if  down- 
stream, —  jr  if  up-stream,  from  o. 

—  vertical  intensity  of  stress  in  ll».  per  sq.  ft.  at  a. 

—  vertical  intensity  of  stress  in  lbs.  per  sq.  ft.  at  c. 
—angle  of  inclination  of  resultant  R  with  the 

vertical. 

—  intensity  of  stress  in  lbs.  per  sq.  ft.,  parallel 

with  R,  at  a. 
—intensity  of  stress  in  lbs.   per  sq.   ft.  parallel 
with  R,  at  c. 


Formulas. 


Fig.  14. 


'■  -  -TO-f) 

'•  --^(-f) 


If  the  result 
is  minus,  the 
stress  is  com- 
pression;  if 
plus,  it  is  ten- 
sion. 


(7) 

(8) 

(9) 

(10) 

Note  that  /.  and  /«  are  vertical  components  of  F.  and  F,;  also  that  when 

+  *  or  —X  is  equal  to  r-,  the  resultant  pressure  cuts  the  base  at  the  edge  of 

2W 
the  middle  third;  whence  /•  is  respectively  equal  to  0  or  to—  —r-,  and  /• 


That  is  to  say.  that  when  the  resol- 


2iy 
is  respectively  equal  to IT^^  ^^  ^• 

tant  cuts  the  base  within  the  limits  of  the  middle  third  there  will  be  no 
tension  in  any  part  of  the  masonry. 

Table  2,  next  page,  is  based  on  allowable  tension  in  the  masonry,  but 
in  acttial  practice  tension  is  not  allowable  in  the  masonry  of  a  gravity  dam. 

Factor  of  Safety  Against  Overturning. — With  the  resultant  pressure  R 
cutting  the  base  at  the  lower  edge  of  the  middle  third,  Fig.  10,  when  the 
reservoir  is  full  and  the  water  pressure  P  is  maximum,  it  is  to  be  noted  that 
the  factor  of  safety  of  the  dam,  against  overturning,  is  2,  because  if  P  is 
doubled,  R  will  pass  through  the  lower  toe  at  c,  whence  the  dam  will  be  oo 
the  point  of  overturning.  The  nearer  to  the  center  of  the  middle  third  that 
R  intersects  the  base,  the  greater  is  the  factor  of  safety.  If  it  intersects 
in  the  middle  third,  the  factor  is  2  or  greater;  if  in  the  outer  third,  the  factor 
is  between  1  and  2;  if  at  the  outer  toe,  c,  the  factor  is  1 ;  if  outside  the  outer 
toe,  the  factor  is  less  than  1,  and  hence  the  dam  will  overturn.  These 
principles  apply  not  only  to  the  triangular  dam  but  to  any  practical  type. 

Shear. — ^The  horizontal  shear  on  any  plane  a  c 
is  equal  to  the  horizontal  component  of  the  total « 
water  pressure  on  a  section-foot  above  that  plane, 
or  equal  to  P  cos  0.  If  FT- the  total  weight  of  the 
masonry  resting  on  the  Joint  oc,  and  /  —  the  coeffi- 
cient of  friction,  then  f  {W+P  sin  ^)— the  total 
resisting  force  due  to  friction.  Hence,  if  the  joint 
ac  is  assumed  to  be  a  horizontal  plane  with  no  ad-  ' 
hesion,  but  simply  friction,  between  the  two  sur^ 
faces  in  contact,  we  have,  for  equilibrium, 

P  cos  e  ^fiW+Pain  0) (11) 

In  ordinary  practice,  f  may  be  assumed  at  |,  hence 
P  cos  d  must  not  exceed  f  {W-\-P  sin  0).  Equa- 
*'on  (11)  may  be  used  safely  in  designing  because 
J  (Vr+P  sin  0)  does  not  represent  the  entire  resisting  force.  In  fact,  hori- 
zontal and  unlaroken  joints  are  avoided  in  practical  construction,  and  hence 
SIS'SJ?^^**  ?*»earing  resistance  is  introduced,  thereby  increasing  the  factor 
of  safety  agamst  slKfing,  materially.  □,„  tized  bv  (^  "  "^" 


Pig.  1& 


Digitized  by  VjOOQ  IC 


d  by  Google 


862 


19.— DilAfS. 


Anthor's  Type  of  Dam. — ^The  author  submits  Pig.  16  as  a  type  which 
may  be  used,  ordinarily,  up  to  200  ft.  in  height,  every  part  to  be  enlaxsed 
proportionately.  The  dimensions  shown  in  the  figure  are  baaed  oq  a 
height  of  unitv.  If  the  proposed  height  of  dam  is  60  it.,  multiply  each  di- 
mension by  60;  if  100  ft.,  multiply  by  100;  if  200  ft.,  multiply  by  200;  etc. 
In  approaching  the  upper  limit  of  height,  care  must  be  used  to  see  that  the 
maxmiimi  allowable  f>ressures  per  square  foot  on  the  base  and  foundations 
are  not  exceeded.  Table  2.  preceding,  may  be  consulted  with  regard  to  the 
pressure  on  foundations.  If  for  any  proposed  height,  say  226  ft.,  the 
pressure  on  the  foundations  would  be  excessive,  the  type  may  be  propor- 
tioned for  a  height  which  will  not  produce  excessive  pressure,  say  tor  200 
ft.,  and  the  side  lines  projected  ftuther  downward,  below  the  E'  level,  the 
necessa^  distance.  Note  that  the  up-stream  face  below  the  'B'  level  is  a 
series  of  chords  touching  an  imaginaiy  parabolic  curve  at  their  vertices, 
while  the  down-stream  Uce  is  a  straight  line;  also  that  above  the  B'  level 
the  up-stream  face  is  vertical  and  the  down-stream  face  is  a  parabola. 
The  design  is  based  on  the  masonry  having  a  specific  gravity  of  2)i,  which 
is  equivalent  to  146.83^3  lbs.  per  cubic  foot,  hence  the  engineer  is  catxtkned 
not  to  use  this  type,  unmodified,  for  masonry  of  less  specific  gravity. 

Calcnlatioos  of  Author's  Type  of  Dam 
(Fig.  16). — ^Thc  triangular  type  of  dam,  with 
an  apex  at  6,  Pig.  10.  is  never  adopted  in 
practice.  The  practical  type  is  never  allowed 
to  come  to  a  point  at  the  top,  but  has  a  cer- 
tain top  width,  say  about  one-tenth  the  height 
of  the  dam,  giving  mass  to  resist  any  forces 
acting  at  the  surface  such  as  those  due  to 
floating  ice,  logs,  etc.  This  width  also  pro- 
vides usually  for  foot-path  and  roadway, 
either  expressly  or  incidentally,  and  for  a 
general  promenade  if  the  dam  is  high  and 
m  a  picturesque  site.  Another  departure 
from  the  triangular  dam  is  the  upstream 
face  a  6,  which  is  battered  more  or  less  in- 
stead of  being  vertical.  With  these  condi- 
tions imposed  the  problem  becomes,  by  com- 
parison, a  complicated  one  when  we  wish 
to  design  a  type  having  practical  lines, 
containing  the  least  amount  of  masonry,  and 
whose  resultant  lines  of  pressure  must  gen- 
erally coincide  with  the  edges  of  the  middle 

third.  In  Pig.  10,  the  triangular  type,  line  ^.  ,-  a  *v-  .  •r  ^t 
E  represents  the  line  of  resultant  pressure  ^^'  ^^Tj^^^^  "  ^^^ 
when  the  reservoir  is  empty,  and  Hne  F  when  Dam.— Umt  Dimensuma. 
fxill.  They  are  both  straight  lines  and  are  drawn  from  b  to  the  base,  cut- 
ting the  latter  in  three  equal  parts.  Likewise  they  will  cut  any  parallel 
plane  above  the  base  in  a  similar  manner,  and  hence  the  triangular  type 
IS  an  ideal  one.  easy  to  calculate. 

There  are  several  methods  in  use  in  designing  dams.  The  "cut-and- 
try"  method  is  the  one  here  presented,  and  Pig.  16  is  the  result  of  the 
"second  trial.*'  It  is  practical,  economical,  safe,  and  pleasing  to  the  eye; 
in  fact,  the  outline  was  determined  not  a  little  by  the  general  effect,  keepotf 
in  mind  certain  well-known  principles. 

Notation. 
h   ""height  of  dam  in  feet  — assumed  as  1; 

t    —width  of  top  of  dam  in  feet     — equal  to  0.1  li; 
w  —specific  gravity  of  water  —equal  to  1; 

m  —specific  gravity  of  masonry     — assumed  as  2}>i; 

P  —total  spec.  grav.  water  pressure  on  dam  above  any  plane  in  questioo; 
IV— total  spec.  grav.  weight  of  masonry  above  any  plane  in  question; 
d   —depth  of  water  above  the  plane  in  question;  or  depth  of  section  coo* 
sidered,  from  top  of  dam  downward. 

Calcitlation. 
.      ?1^-.  1®  represents  the  second  and  final  design.     (The    first  design 
ui  not  shown,  but  had  a  greater  width  at  the  i4' level  and  contained  about 
«  per  cent,  more  masoAry.)     It   is  to  be  noted   that  in  the  following 


TRIAL  METHOD  OF  DESIGN, 


S68 


caktilations  the  horiMontal  position  of  the  centtr  of  gravity  of  the  masonry 
W  above  any  plane  in  question  is  desired,  but  not  the  vertical  position; 
'  likewise,  the  vertical  position  of  the  center  of  pressure  of  the  water  pressure  P, 
above  any  plane,  is  required.  The  vertical  component  of  P,  acting  down- 
ward on  the  sloping  up-stream  face,  will  be  neglected.  This  is  on  the  side 
of  safety,  as,  if  considered,  it  would  throw  the  Une  of  resultant  pressure  for 
"full  reservoir"  inward  toward  the  center  of  the  middle  third.  Calculations 
will  be  made  of  the  forces  above  the  respective  planes  A',  B\  C\  D*  and  E\ 
taken  in  order.  In  other  words,  the  structure  is  considered  as  cut  suc- 
cessively by  these  planes  and  the  problem  consists  in  finding  the  point  of 
applicant  <h  the  resultant  force  on  each  plane,  (a)  for  reservoir  empty,  and 
(6)  for  reservoir  full.  Connecting  all  the  (a)  points  gives  the  line  of  resul- 
tant pressure  when  empty,  and  connecting  all  the  (6)  points  gives  the  line 
of  resultant  pressure  when  full. 

A*  Level. — ^This  plane  is  0.2  A  below  top  of  dam.    Considering  one 
aection-foot  of  dam,  and  the  specific  gravity  of  the 
masonry  equal  2|.  we  have  the  acting  forces  as  shown 
in  Pig.  17.  in  which  W%  and  Wh  act  alone  (above 
the  plane)  when  the  dam  is  empty,  and  the  force  P 
is  added  when  the  dam  is  full.     Or,  we  may  con- 
sider  PV.  +  W^b  — VT   acting   vertically  through    the 
center  of  gravity  of  the  total  section  above  A\  cut- 
ting the  base  at  e  and  being  resisted,  when  empty,  by 
the  equal  and  opposite  force  R,.     But  when  the  res- 
ervoir is  full,  the  added  force  P  will  make  the  resul- 
tant take  the  direction  of,  cutting  the  base  at  /.  and 
being  resisted  by  the  egual  and  opposite   force  Rt. 
Xote  that  the  point  o  is  the  intersection  of  the  vertical  force 
horizontal  force  P,  and  that,  relatively, 
W»»2\  (.10X20)  h\  acting  vertically  through  center  of  rectangle; 
\V^  -2|  (3        \  A*,  acting  vertically  A  X  .036  k  from  left  face  of  para- 

Hence, 
335  X. 20' 


Fig.  17. 

»  W"  with  the 


bolic 
V   -W.  +  Wh 


-j  A*,   acting  vertically   .  0068*  h  to  right  of 

H^.,  that  is,  through  the  point  o. 
^kd^^h  (.2A)>-.02  h\  acting  horizonUlly  .06}  h  above  A'.    Taking 

loments,  we  find  the  distance  e  /  — .06|  ^Tp  "  .0256  h.    It  is  to  be  noted 

iat  both  resultants  intersect  the  A'  base  well  within  the  limits  of  the 
liddle  third. 

B'  Level. — ^This  plane  is  0.4  li  below  top  of  dam  and  is  calculated  in 
ic  same  maimer  as  the  preceding.  Note  that  W,  includes  W^  and 
lat  Wa  includes  Wh.     Then,  relatively. 


-2J  (.10X.40)  h\ 


*W.-^W 


ting  vertically  through  </,  .0208^  to  right  of  W,. 
•«ce.  R,  acts  .0793  h  from  left  hand  face  or  .0007  A 
tside  of  the  middle  third.  For  a  dam  100  ft. 
;li  this  amounts  to  only  \  inch  in  a  total  width  on 
»  B*  level  of  24  ft. — an  amount  insignificant. 
-i<<»-4  (.4A)»-.08W,  acting  0.13J  fc  above  B' 
'ci.    Taking  moments  in  the  case  of  the  full  reser- 

p 
Lx- we  find  thedistancer/ -"0.13}  M-rp-. 0779 A. 

C  L0tfel. — In  Fig.  19.  We  +  Wa  is  the  relative  weight  of  the  masonry 
>-vc  the  B'  level,  while  W,  is  the  relative  weight  of  the  trapezoidal  sec- 
■%  'foot  between  th^  B*  and  the  C  levels.     The  vertical  arrows  indicating 

^  .00<I3  —  '  ,  ^.  See  page  295  for  determining  the  position  of  the 
t«r  of  gravity  of  two  or  more  parallel  forces.         Digitized  by  V^OOglC 


Fig.  18. 


854 


48.— DilMS. 


The   total 


the  weights,  pass  through  the  respective  centers  of  gravity, 
weight  W^  (  "W.  +  W4-^)  intersects 
the  C  plane  at  e,  distant  .  1225  A  from 
the  face  of  the  dam;  or  .0053  h  out- 
side the  limit    of  the  middle  third, 
amounting  to  about  6i  ins.  on  a  total 
base  of  38  ft.  4  ins.  for  a  dam  100  ft. 
high.     For  full  reservoir,  we  have, 
1^  -2*X.062JA», 
W   -2{X.121H 

p  -id«-i(.6fc)«=.18fc«,  acting 
0.20  A  above  c'  level.  Taking  moments 
in  the  case  of   the   full   reservoir  we 

p 
find  the  distance  tf/-.2/t-rp-.  1275  A. 

This  is  on  the  assimiption  that  P  acts  horizontally.  Note,  however,  that 
below  the  B*  level  the  prcssxire  is  really  normal  to  a  sloping  face  and  if  so 
considered  the  resultant,  under  full  reservoir  pressure,  would  cut  the  C 
plane  a  Httle  to  the  left  of  /,  thereby  increasing  the  factor  of  safety. 

V  Level. — Briefly  discussed,  the  relative  weight  of  the  new  trapezoidal 
section-foot,  between  the  C  and  the  D'  levels  is 


Wr  -2J  X.0911H 
IV  =2|  X.212|A«. 
P    -id«-H.8*)«-. 


£.  i^evei. 
W.  -2*  X. 

w  -2ix. 

P     -0"J 


.32^2,  acting  0.26] /»  above  D*  level.  Completing 
the  caiculadon  it  is  found  that  when  the  reservoir  is  empty  the  resultant 
cuts  the  JO'^plane  .1770  h  from  the  up-stream  face,  or  .0008  h  outside  the 
limit  of  the  middle  third,  amounting  to  1  in.  on  a  total  base  of  53  ft.  4  ins. 
for  a  dam  100  feet  high.  When  the  reservoir  is  full  the  resultant  cuts  the 
D  plane  .1720  h  farther  from  the  face,  and  within  the  middle  third. 

E'  Level — For  the  section  between  D'  and  E'  levels, 
X.122tfc», 
C.336%>, 
,_    •  i/r2,  acting  \  h  above  E'  level. 
With  the  reservoir  empty  the  resultant  cuts  the  base  .2882  h  from  the  up- 
stream face,  which  is  .0082  h  within  the  limit  of  the  middle  third.     When 
the  reservoir  is  full  the  resultant  cuts  the  E'  plane  .2182  A  farther  from  the 
up-stream  face. 

For  general  dimensions  and  quantities,  see  Tables  8  and  4,  following. 

QUANTITIES  IN  MASONRY,  ROCK-FILL  AND  EARTH  DAMS. 

Tables  4,  5  and  6,  following,  will  be  found  useful  in  estimating  the  relative 
quantities  in  masonry,  rock-fiD  and  earth  dams,  from  profiles  or  contour  maps 
of  any  particular  site.  Quantities  are  in  cubic  yards  per  100-ft.  section  of 
dam.  For  other  sectional  lengths  the  yardage  will  of  course  be  proportionaL 
Thus,  for  60-ft.  lengths,  divide  by  2;  lor  25  -ft.  lengths,  divide  by  4;  etc 

The  scientific  design  of  masonry  dams,  laid"in  cement  mortar,  is  subiect 
to  more  accurate  determination  than  are  those  of  rock -fill  or  earth.  For 
the  two  latter  classes  we  are  guided  mainlv  by  the  behavior  of  the  types 
that  have  been  constructed,  and  by  carefully  studying  the  causes  of  failure 
of  those  that  have  not  stood  the  test.  The  actual  cross-section  of  the  dam 
itself  is  only  one  of  the  necessary  elements  of  strength.  The  foundations 
should  be  selected  and  prepared  carefully  to  receive  the  superstructure  or 
dam  proper;  the  outlet  constructed  with  care  to  prevent  leakage;  and  the 
wasteway  ample  to  provide  for  flood  discharges. 

A  word  in  regard  to  the  effect  of  profile  on  the  resisting  power  of  a  dam. 
In  our  calculations  we  assume  one  section-foot  of  dam  and  one  sectx>n-foot 
of  water  pressure  acting  against  it — ^the  resultant  forces  in  each  section- 
foot  acting  independently  of  any  other  section-foot.  This  theory  would 
hold  true  m  practice  for  a  straight  dam  of  constant 
height  and  oi  indefinite  length,  but  for  all  ordinary**^ 
cases,  as  for  instance  Fig.  20,  where  the  ground  line 
IS  irregular,  calling  for  different  heights  for  each  • 
section,  it  is  impossible  for  any  section  to  act  inde- 
pendently of  any  other.  Thus,  under  full  reservoir 
head,  the  high  section  A  will  tend  to  deflect  down-  Pig.  20.— 

stream  a  greater  amoimt  than  will  one  of  less  height.  Profile  of  Dam-Site. 


d  by  Google 


866 


4«.— IMM5. 


4. — Specific  Tablb  of  Quantitibs  in  MasokrtDaus— Aotbob'sTtps, 

Fig.  16. 

(See  also  Table  8.) 


Cubic  Yards  of  M nnonry  per  1 00  Lineal  Feet  of  Dam.  fOr  Seetloo 

Depth  <f 

ol 
Section  In 

of  Depth  d  from  Top  (Fl«.  31). 

Top= 

Top- 

Top— 

Top— 

Top- 

Top- 

Top- 

■^- 

Top- 

Top- 

Feet. 

20'. 

is'. 

16'. 

14'. 

13'. 

10*. 

s'. 

4'. 

2*. 

d 

ft- 

ft- 

A- 

A- 

A=. 

*- 

A- 

*- 

A- 

*- 

200*. 

180'. 

160*. 

MO'. 

120'. 

100'. 

so*. 

oo*. 

40'. 

20*. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(11) 

4 

296 

267 

237 

208 

178 

149 

119 

90 

61 

33 

8 

596 

636 

478 

419 

360 

802 

244 

187 

132 

87 

13 

899 

810 

723 

636 

549 

463 

379 

298 

224 

I7t 

16 

1207 

1091 

976 

861 

748 

639 

529 

386 

348 

315 

20 

1524 

1381 

1239 

1099 

961 

827 

701 

688 

511 

4H 

84 

1852 

1683 

1516 

1351 

1191 

1088 

898 

782 

717 

88 

3193 

1998 

1807 

1621 

1442 

1274 

1126 

1017 

966 

88 

2554 

2330 

2118 

1912 

1717 

1539 

1391 

1294 

1260 

86 

2919 

2680 

2448 

2227 

2020 

1837 

1696 

1613 

1600 

40 
44 

3309 

3061 

2802 

2568 

2354 

2173 

2044 

1976 

1985 

8720 

3445 

3183 

2939 

2722 

2550 

2435 

2384 

48 

4153 

3864 

3591 

3343 

3129 

2969 

2869 

2836 

53 

4612 

4311 

4031 

3781 

3577 

3431 

3345 

3333 

66 

5096 

4787 

4504 

4259 

4067 

3935 

3866 

3877 

60 

5612 

5296 

5014 

4778 

4600 

4481 

4431 

4467 

64 

6157 

5840 

5563 

5339 

5176 

5071 

5041 

68 

6735 

6420 

6153 

5943 

5793 

5766 

5696 

72 

7350 

7041 

6786 

6589 

6453 

6385 

6398 

76 

8000 

7702 

7461 

7278 

7157 

7109 

7146 

80 

8692 

8406 

8178 

8009 

7905 

7877 

7941 

84 

9424 

9152 

8938 

8784 

8698 

8690 

88 

10199 

9941 

9741 

9601 

9535 

9550 

92 

11016 

10772 

10586 

10463 

10417 

10456 

96 

11876 

11645 

11473 

11369 

11343 

11409 

100 

12778 

12561 

12404 

12320 

13314 

12407. 

104 

13733 

13519 

13379 

13315 

13832 

108 

14710 

14520 

14399 

14354 

14396 

112 

15739 

15564 

15463 

15438 

15507 

116 

16813 

16653 

16572 

16567 

16664 

120 

17936 

17787 

17726 

17743 

17867 

134 

19084 

18965 

18932 

18965 

Top 

128 

20286 

20187 

20164 

20234 

f-^-i  ' 

132 

21533 

21454 

21451 

21549 

1 

-~ 

w/Kuk  "    '  'f 

186 

22825 

22765 

22785 

22911 

m/Xwi            \ 

140 

24160 

24121 

24165 

24319 

Bi  s* 

144 

25541 

25521 

25592 

148 
152 

26966 

26966 

27065 

^ 

J^^^L       i 

28434 

28458 

28585 

"W^ 

156 

29948 

29996 

30151 

¥ 

\ 

160 

31507 

31581 

31763                                  -[      1                  \ 

164 

33110 

33212 

\ 

168 

34760 

34889 

/                       \ 

178 

36456 

36613 

/                         \ 

176 

38199 
39988 

38383 

1 

'    ' 

^ 

180 

40200  ' 

Fig.  21 

184 
188 

41834 
43705 

Note.— For  absolute  quantitiea,  use  the 

193 

45634 

second  column  only;  the  last  nine  columos 

196 
,.0 

47607 
49630 

are  for  possible  sections  which  must  be  verified 
or  modified  by  trial  calculations. 

d  by  Google 


858 


49.— DAMS. 


6. — ^Tablb  of  Ouantitibs  w  Earth  Dams. 
Fig.  23. 


Area  of 

Up- 

Cubic Yards  of  Earth  per  100  Uneal  Feet  of  Dam.  tor 

Depth  d 

stream 

Section  of  Depth  d,  from  Top  (Fig. 

23). 

of  Sec- 

Face. 

tion 
from  Top 
of  Dam. 

100-ft. 
Long 
and  of 

Top— 

Top- 

Top— 

Top— 

^sr 

Top- 

Top- 

Top- 

'R)p- 

In  Feet. 

Depth  d. 

28' 

26' 

24' 

22' 

18' 

16' 

14' 

12* 

Sq.  Ft. 

(1) 

(2) 

(3) 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(U) 

4 

1077 

563 

533 

504 

474 

444 

41^ 

385 

356 

321 

8 

2154 

1422 

1363 

1304 

1244 

1186 

1126 

1067 

1007 

948 

12 

3231 

2578 

2489 

2400 

2311 

2222 

2133 

2044 

1956 

1867 

16 

4308 

4030 

3911 

3793 

3674 

3566 

3437 

3318 

3200 

3081 

20 

6385 

5778 

6630 

6481 

6333 

5185 

6037 

4889 

4741 

4593 

24 

6462 

7822 

7644 

7467 

7289 

7111 

6933 

6766 

6578 

6400 

28 

7539 

10163 

9956 

9748 

9541 

9333 

9126 

8919 

8711 

8504 

82 

8616 

12800 

12563 

12326 
I52I0 

12089 

11852 

11615 

11378 

11141 

10904 

36 

9693 

15733 

15467 

14933 

14667 

14400 

14133 

13867 

13600 

40 

11770 

19111 

18816 

18519 

18222 

17926 

17630 

17333 

17037 

16741 

44 

12847 

22785 

22459 

22133 

21807 

21481 

21156 

20830 

20504 

20171 

48 

13924 

26766 

26400 

26044 

25689 

25333 

24978 

24622 

24267 

23911 

62 

16001 

31111 

30726 

30341 

29956 

29570 

29185 

28800 

28415 

28030 

66 

16078 

35763 

35348 

34933 

34519 

34104 

33689 

33274 

32869!  32444 

60 

17156 

40711 

40267 

39822 

39378 

38933 

38489 

38044 

37600 

371&5 

64 

18233 

45956 

45481 

45007 

44533 

44059 

43585 

43111 

42637 

4216) 

68 

19310 

51496 

50993 

50489 

49985 

49481 

4897e 

48474 

47970 

47467 

72 

20387 

57333 

56800 

56267 

65733 

56200 

64667 

64133 

53600 

53017 

76 

21464 

63467 

62904 

62341 

61778 

61215 

60652 

60089 

59526  58968 

80 

22641 

69896 

69304 

68711 

68119 

67526 

66933 

66341 

66748  651M 

84 

23618 

76622 

76000 

76378 

74756 

74133 

73511 

72889 

72267  71644 

88 

24695 

83763 

83111 

82459 

81807 

81156 

80604 

79852 

79200  78644 

92 

25772 

91200 

90519 

89837 

89156 

88474 

87793 

87111 

86430^  65744 

96 

26849 

98933 

98222 

97511 

96800 

96089 

95378 

94667 

939661  93244 

100 

27926 

106963 

106222 

105481 

104741 

104000 

103269 

102519 

101778 

101037 

104 

29003 

116289 

114519 

113748 

112978 

112207 

111437 

110667 

109896 

109126 

108 

30080 

123911 

123111 

122311 

121511 

120711 

119911 

119111 

118311 

117511 

112 

31157 

132830 

132000 

131170 

130341 

129511 

128681 

127852 

127022126193 

116 

32234 

142193 

141333 

140474 

139615 

138756 

137896 

137037 

13617SJIS5319 

120 

33311 

151852 

150963 

150074 

149185 

148296 

147407 

146619 

146«80  144741 

124 

34388 

161807 

160889 

169970 

159052 

168133 

157216 

156296 

156378154419 

128 

35465 

172059 

171111 

170163 

169215 

168267 

167319 

166870 

165422  154474 

132 

36542 

182607 

181630 

180652 

179674 

178696 

177719 

176741 

17J753IT4T8I 
1864001 185391 

136 

87619 

193452 

192444 

191437 

190430 

189422 

188415 

187407 

Fig.  23. 

Note.— Area  of  Qp-«tream  face  Is  given  In  order  to  est^aate  tli«  qnaDttty  of 
material  in  the  facing.  '  tized  byX^OOgle 


d  by  Google 


850  49.— ZJililfS. 

Rubble  Concrete  Dam  for  the  Atlanta  Water  ft  Electric  Power  Co. 

(Eng.  News,  Jiily  7,  1904). — Illustrated  section  of  roUway  portion  of  dam 
with  graphical  determinations  of  resultant  pressures.  *Toe  advantages  of 
nibble  concrete  for  many  kinds  of  masonry  work,  and  particularly  for 
massive  structures  like  masonry  dams,  are  gradually  being  recognized  by 
engineers.  In  many  cases  where  large  yardage  of  masonry  is  required  the 
use  of  rubble  concrete  will  effect  a  saving  in  time  and  cost  over  nibUe 
masonry  work  or  fine  concrete  work.  As  an  illustration,  rubble  concrete 
composed  of  40%  large  stone  and  60%  of  1:2J:5  concrete  reouircs  7%  of 
the  volume  to  be  of  cement,  while  rubble  masonry  composed  of  65%  laurge 
stone  and  36%  of  r.2J  mortar  requires  10%  of  the  volume  to  be  of  cement." 

Investigation  of  Stresses  in  High  Masonry  Dams  of  Short  Spans  (By 
G.  Y.  Wisner  and  E.  T.  Wheeler.  Eng.  News.  Aug.  10,  1905).— Relates  to 
the  proposed  curved  Pathfinder  dam  (cross-section:  height  210',  top  width 
lO'.  bottom  width  94',  up-stream  batter  0.15,  down-stream  batter  0.25), 
with  diagrams  giving  results  of  calculations. 

Earth  Dams  with  Concrete  Core  Walls  (By  Clemens  HerscheL  Eog. 
News.  Sept.  7,  1905). 

Computation  of  Height  of  Backwater  Above  Dams  (Eng.  News, 
Nov.  1.  1906;  also  Nov.  29,  1906.  with  tables). 

Large  Reinforced-Concrete  Dam  at  Ellsworth,  Me.  (Eng.  News, 
May  23.  1907). — Illustrated  sectkm;    64  ft.  high. 

Large  Electrically  Operated  dates  for  the  Roosevelt  Dam,  Ariz.  (By 
F.  W.  Hanna.    Eng.  News,  Mar.  30,  1907).— Dlustrated. 

Electrk:ally  Operated  Service  dates  for  the  Shoshone  and  Pathfinder 
Dams   (By  F.  W.  Hanna.    Eng.  News,  Jan.  2.  1908).— Illustrated. 

Reinforced-Concrete  Diaphrams  for  Earth  Dams  (By  B.  M.  Hall 
Eng.  News.  Feb.  6,  1908).— Illustrated. 

Combination  Dam  and  Bridge  of  Reinforced  Concrete  (Eng.  News. 
April  9,  1908).— Illustrated. 

The  Deston  of  Buttressed  Dams  of  Reinforced  Concrete  (By  R.  C. 
Beardsley,    Eng.  News,  April  23.  1908). — Illustrated. 

Progress  on  the  Roosevelt  Dam ;  with  Cost  Data  (By  C.  W.  Soxith. 
Eng.  News,  Sept.  10.  1908). 

Movable  Dams  and  Lock  at  the  Power  Plant  on  the  Chicago  Draia- 
age  Canal  (Eng.  News,  Nov.  12.  1908). — Illustrated. 

Cast-iron  Sluice  dates  for  the  Fens  date  Chamber,  Charles  Rber 
Basin.  Boston,  Mass.    (By  W.  H.  Sears.    Eng.  News,  Feb.  25.  1909).— lUus- 

trated. 

Investigations  of  the  Saturizatlon  of  Earth  Dams  (Eng.  Rec.,  Aug.  21. 
1909). — Results  of  experiments  by  Desmond  Fitzgerald:  1.  Clay  banks 
are  more  completely  saturated  than  well-drained  banks.  2.  Clav  banks  are 
more  slowly  sattirated  and  part  more  slowly  with  their  water  of  satxuatioc. 
8.  In  high  banks  it  is  unsafe  to  have  nothing  but  clayey  material,  a  down- 
stream section  of  well-drained  material  being  essential. 

Partial  Failure  Through  Undermbiing  of  the  ZunI  Dam,  New  Nlexko 
(Eng.  News,  Dec.  2,  1 909) .—Combined  hydraulic  earth  fill,  60.120  cu.  yds., 
up-stream  section;  and  rock  fill,  40,160  cu.  yds.,  down-stream  sectifon 
Up-stream:  slope  3:1,  rock  rio-rap  18  ins.  deep  on  gravel  12  ins.  dee? 
Down -stream:  slope  IJ  :  1.  Illustrated.  The  spillway,  south  abutment 
and  extreme  south  end  of  dam  were  undermined  by  the  p>assage  of  watw 
underneath  a  cap  of  lava  rock  which  flanked  the  dam  and  extended  betwath 
the  spillway. 

The  Eastwood  Multiple-Arch  Dam  (Eng.  Rec.,  Jan.  15,  1910). — Ab6tract 
of  article  by  John  S.  Eastwood,  in  the  "Journal  of  Electricity,  Power  and 
Gas,"  Oct.  30,  1909.  The  Hume-Bennett  dam  consists  of  12  arches,  each 
50-ft.  span,  resting  on  13  buttresses,  the  end  walls  of  the  last  buttress  at 
each  end  being  extended  into  the  opposite  bank  as  a  core  wall,  as  they  are 
above  the  normal  water  line  and  have  no  water  load.  The  elevation  <x  the 
water  line  is  5.300,  that  of  the  crest  of  the  middle  six  arches  is  5.303.  and 
tne  remamder  of  the  crest  to  the  ends  is  5.804  ft.  above  mean  tide  level 
floiS^^*  *  380-ft.  crest  for  any  freshet  that  may  occur  when  the  spillway 
nasnooards  were  accidently  left  in  their  openings.     The  entire  structure 


MISCELLANEOUS  DATA,  861 

rests  on  sound  bedrock.  Mr.  Eastwood  found  that  to  give  the  required 
statnli^  with  the  greatest  economy  it  was  desirable  to  build  the  top  16  ft. 
of  the  dam  with  vertical  arches,  and  all  arches  up  to  20  ft.  high  at  the  spring 
line  were  built  vertical.  All  arches  higher  than  20  ft.  are  carried  vertical 
to  within  16  ft.  of  the  top  at  the  crown  line,  and  then  slope  to  the  founda- 
tions at  an  angle  of  32  deg.  The  arch  ring  thickness  is  increased  as  required 
for  the  water  pressure.  All  of  the  vertical  part  of  the  arch  wall  is  18  in. 
thick:  the  wall  increases  in  thickness  from  this  point  at  the  rate  of  1  ft. to 
each  24  ft.  vertical,  or  a  little  more  than  required  for  water  load.  The 
buttresses  are  all  2  ft.  thick  at  the  top  and  project  8  ft.  from  the  inside 
spring  line  to  the  down-stream  end,  all  comers  being  clipped.  The  batter 
of  the  down-stream  end  is  5  in.  to  1  ft.,  and  of  the  sides  1  m  24  to  the  base 
on  each  side.  Each  buttress  is  finished  on  its  down-stream  end  with  wing 
buttresses  or  counterforts.  The  12  spillway  openings  are  located  in  the 
three  middle  arches  of  the  dam,  the  openings  being  5  x  8  ft.  each,  to  be  closed 
to  any  desired  height  by  means  of  flashboards.  The  structure  was  rein- 
forcea  throughout  when  necessary  by  means  of  railroad  iron  scrap  and  old 
logging  cable.  .  .  .  The  buttress  forms  consist  of  2  x  4  in.  studding 
set  about  20  in.  apart  on  centers  and  spliced  where  not  long  enough  to  reach 
the  top;  a  framework  was  first  built  and  lined  with  12-in.  lumber  of  10  and 
12-in.  widths,  lightly  nailed  to  the  inside  of  the  studs,  the  studs  being  braced 
to  the  trestle.  The  shapes  of  the  cotmterfort  forms  were  such  that  they 
braced  themselves  when  once  boarded  up.  The  arch  forms  were  built  up 
:rom  the  bottom,  using  2  x  4-in.  studding  and  i  x  6  in.  stuff  nailed  on  double. 
.  Crushed  granite  was  used  for  the  coarse  aggregate,  the  crusher- 
tm  being  mixed  with  sand  from  an  adjacent  pit;  the  mix  was  approx.  1:2:4. 
rhe  forms  were  not  removed  for  at  least  a  week  after  the  concrete  was  laid, 
nd  the  walls  were  kept  wet  by  a  night  watchman  and  a  day  crew.  A 
iniod  of  the  different  day's  work  was  made  by  scarifying  the  surface  of  the 
Id  work  and  washing  off  with  a  hose:  dry  cement  was  then  sprinkled  over 
his  surface  and  concreting  begun,  a  few  batches  of  concrete  with  excess  of 
lortar  being  laid  in  contact,  the  work  being  carried  up  as  nearly  level  as 
ossiblc.  Tne  junctions  of  the  walls  were  made  on  the  center  of  buttresses, 
le  reinforcement  being  left  protruding  to  tie  them  together.  .  .  .  The 
ater  face  and  the  parts  of  the  down-stream  face  were  plastered,  the  water 
ce  with  two  coats  of  1  to  li  cement  plaster  and  selected  sand  and  a  wash 
■at  of  neat  cement  on  the  bases  of  the  middle  arches.  A  base  seal  of 
ortar  was  placed  along  the  line  of  contact  with  the  rock.  The 

ructure  contains  2.207  cu.  yds.  of  concrete  and  was  built  in  114  days. 
All  parts  ot  dam  are  m  compression,  max.  stress  187.5  lbs.  per  sq.  m. 
ifety  factor  16)  being  at  bases  of  arch  rings.     Max.  stress  in  shear,  50  lbs. 
r  sq.  in.     Rates  of  overturning,   1  :  3.6.  Cost  of  dam,  in- 

iding  plastering,  about  121  per  cu.  yd.  or  146,000  for  the  structure; 
nent  costing  a  little  over  15.00  per  bbl..  delivered. 

Airbed  Masonry  Dun  at  Las  Vecas,  N.  M.  (By  C.  W.  Sherman.  Bng. 
w9,  Oct.  27,  1910). — Description  and  illustrations.  Also  contains  a 
>Ie  of  23  ctirved  masonry  dams,  giving  max.  height,  base  thickness,  top 
^kness.  max.  stress  in  arch,  radius  of  up-stream  face,  top  length,  charac- 
of  rock,  date  of  building. 

Movairfe  Duns  on  the  New  York  State  Bafce  Canal  (Eng.  News,  Dec.  8. 
0). — Description,  with  14  illustrations,  of  the  type  of  dam  known  as  the 
l^e  dam  with  the  Bould  gates. 

inuatnitions  of  Various  Types  of  Dams. 

Description.  Bng.  News. 

-.  rubble-faced  dam  47'  high  June  13.  1901. 

k-fill  dam  IOC  high  with  steel  core  Jan.     2,  '02. 

tan  dam  (66^  high)  and  reservoir  on  the  River  Nile  Aug.  14,  '02. 

sraxn  masonry  dam  70^  high,  Waterbury,  Conn.  May     7,  "O" 


w^xn  masonry  dam  7v  hijsh,  Waterbury,  Conn.  May     7,  03. 

r  Kalis  masonry  dams  SO^and  152'  hign  Time  18,  '03. 

31W  rein. -cone,  dam  11'  high  (Ambursen  type)  Nov.    5,  *03. 

eel  concrete  dam  llO'  high,  Barossa,  So.  Australia  April    7,  '04. 

e<l  Masonry  dam  230^  his^.  Lake  Cheesman,  Colo.  May   12.  '04. 

>er  dam  SO'  high  on  the  Penobscot  River  Sept.    1.  '04. 

ev-elt  znaaonry  dam  260^  high,  Arizona  Jan.    12,  '05. 

nif  steel  dam  at  Sweinfurt,  Bavaria  Jan.    19,  '06. 
small  concrete  dams — one  on  pile  foundations      Digitized  by    Peb.     9,  06. 


862  4»,—DAMS. 

Description.  Eng.  Ken^ 

Hollow  rein. -cone,  dam  25'  high,  at  Schuylerville  April  27,  '05. 

Debris  Barrier  No.  1,  Yuba  River,  Cal.  June  15.  Oi 

Arched  masonry  dam  80'  high,  Cheyenne,  Wyo.  June  211.  '05- 

Gatun  dam  27(r  to  bed  rock  (Panama  Canal)  July  27,  'OS. 

Pile  foundation  for  movable  dam  July  27,  'Oi. 

Movable  dam  and  lock  of  the  Rice  I.  &  I.  Assn.  Ia.  Sept.  28,  'Oi 

Structural  steel  dams  (F.  H.  Bainbridge)  Sept.  28, 'Oi 

Crib  dam  2(K  high  with  sheet  steel  piling  Nov.    i,  'Oi 

New  Croton  dam,  with  balanced  gate  valve  (Wegmann)  Oct.     4, '08. 

The  Mercedes  curved  masonry  dam  ISC  high  Nov.    l.'Oi 

Collapsible  steel  dam  crest.  Bear  River,  Utah  Oct.     3.  '07. 

*Hauser  Lake  steel  dam,  Missouri  R.,  Mont.  Nov.  14,  07. 

Lock  Gates  of  the  Charles  River  dam  July     9,  '0&- 

Butterfly  dam  on  Chicago  Drainage  Canal  July  22.  08. 

Revolving  segmental  sluice-gates  for  Sterling  dam  Aug.    5,  'Oi 

Plan  and  cross-section  of  Shoshone  dam  Dec.     9,  '09. 

Failure  of  concrete  dam,  10  ft.  high,  at  Danville,  N.  Y.  Jan.    13,  '10. 

Designs  for  rebuilding  the  Austin  dam,  Texas  Apr.   14,  '10. 

Curved  masonry  dams  in  New  South  Wales  May   19.  '10. 

Construction  of  Cataract  Dam,  Sidney,  N.  S.  W.  June  23,  '10 

Reinforced  buttressed  dam,  Ottawa,  Can.  June  30,  '10. 

Dike,  mosquito  extermination  work,  Welfleet,  Mass.  Aug.  11.  '10. 

Design  and  constr.  of  movable  dam  and  lock,  Lockport  Oct.     6,  'Ifi- 

The  La  Prele.  hollow  reinforccd-conc.  dam,  130  ft.  high  Nov.  10,  '10. 

Buttressed  masonry  dam  reinforced  with  steel  I-beams  Nov.  24,  *I0. 

Diamond  drill  borings  for  a  dam,  Clackamas  R.,  Ore.  Dec.  22,  '10. 

Eng.  Rec. 
Experiments  with  rubber  models  of  dams,  to  study  stresses      Mar.    6,  'W- 

Rein.-conc.  dam,  buttressed,  16'  0*  high,  U'  6*  base  Mar.  27.  '0«. 

Section  of  the  Arrowhead  hydraulic  fill  dam  Apr,     3.  '0^ 

Olive  Bridge  dam  (cyclopean  masonry) ;  earth  dike  Sept.    4,  '09. 
Diagram,  principal  stresses  and  planes  in  the  masonry  dam       Oct.     2.  '09. 

Cross-section  of  hydraulic  fill  dam.  South  Carolina  Oct.     2,  'Oft 

Cross-section  Kensico  dam.  Catskill  water  supply  Dec.  25,  '09. 

Cross-section  rock-fill  crib  dam,  power  develop.,  Mont.  Mar.  12,  'Ift 

Construction  plant  for  the  Holter  dam,  Montana  Oct.   20,  '10. 

*See  Eng.  News  of  April  30,  1008.  for  description  of  failure. 


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864  CO.— FOUNDATIONS. 

Tock  shoxild  not  be  so  smooth  as  to  unsafely  decrease  resistance  to  sliding 
of  the  foundation  above.  Especially  should  this  be  looked  after  in  the  caae 
of  a  submersed  pier  or  of  a  dam.  where  the  lateral  pressure,  due  to  the 
current  of  the  stream,  or  to  ice.  logs,  or  hydrostatic  pressure,  would  be 
considerable. 

/I  bed-rock  fotmdation  is  not  always  easily  obtainable  on  account  of  its 
depth  below  the  ground  surface  or.  in  marine  work,  below  the  water  surface. 
It  is  therefore  often  more  economical  to  choose  for  a  fotmdation  bed  a 
poorer  character  of  material  not  so  deep,  thereby  saving  considerable  in 
excavation  but  requiring,  generally,  a  more  expensive  fotmdation  "footing" 
(see  Pigs.  1.  2  and  3).  Hence  it  is  that  often  after  the  excavation  for  the 
fotmdation  is  started  the  plans  are  changed  when  it  has  become  evident 
that  a  strattmi  has  been  reached  that  is  "good  enough'*  for  all  practical 
purposes;  or,  on  the  other  band,  when  the  expected  strattun  as  revealed  by 
the  borinffs  does  not  meet  the  requirements,  and  another  stratum  at  greater 
depth  is  decided  upon.    (Excavation  processes  are  described  farther  on.) 

1. — Actual  Bearing  Pressures  on  Bed  Rock. 
Foundatlona  oj  New  Croton  Dam^ — Calculated  pressures  limited  to  1 5  tons  per  sq.  fL 

at  base  of  dam  on  rock  surface,  the  resultant  pressure  being  kept  within  the 

middle  third  of  section. 
MaiUtaUan  Life  Building,  New  York  City. — Pressure  at  base  of  caissons  on  bed  rock. 

10.8  tons  per  sq.  ft. 
American  Surety  BvUding. — Pressure  at  base  of  calSBons.  7i  tons  per  sq.  ft. 
Oiikn/der  BuUdinO' — ^Pressure  at  base  of  caissons  on  bed  rock.  12  tons  per  sq.  ft. 

(6.)  Hard-Pan. — ^Next  to  solid  rock  there  is  no  better  material  for 
foundation  bed  than  cemented  gravel  or  hard-pan.  When  well  cemented, 
and  in  thick  and  extensive  beds,  it  is  capable  of  sustaining  safely  without 
injury  and  with  comparatively  slight  settlement,  a  quiescent  loading  of 
1()  tons  per  square  foot  («  138.8^8  lbs.  per  sqtiare  inch). 

(c.)  Gravel  and  Sand. — Large,  thick  beds  of  well-compacted  gravel  and 
sand,  free  from  wash  by  the  action  of  water,  can  generally  be  cotinted  on 
to  stxstain  about  8  tons  per  square  foot  of  quiet  loading,  or  equal  to  11 1.1"' 1 
lbs.  per  square  inch.  For  such  a  loading,  however,  the  foundation  bed 
should  be  at  least  10  or  12  feet  below  the  surface  of  the  ground,  and  the 
under  strata  must  be  firm. 

(d.)  Indurated  Clay. — By  the  term  "indurated"  we  mean  the  hard 
variety,  tisually  containing  m  sufficient  quantities  such  binding  materials 
as  carbonate  of  lime,  silicates  of  alumintmi  and  magnesium,  iron  oxides,  etc 
When  in  the  natural  bed,  at  considerable  depth,  and  free  from  the  softening 
action  of  water,  this  material  may  be  loaded  safely  to  6  tons  per  squsue 
foot  (equivalent  to  83.3^^3  lbs.  per  square  inch).  If  it  contains  a  proper 
intermixture  of  gravel  and  sana  it  approaches  hard-pan,  and  the  bearing 
power  is  increased. 

(e.)  Dry  Sand. — Under  the  most  favorable  conditions,  that  is,  where 
the  material  is  confined  as  in  a  deep  trench  and  not  allowed  to  spread  out 
from  the  pressure  above,  and  also  where  it  is  reasonably  dry  and  free  from 
wash,  sand  will  easily  support  a  load  of  4  tons  per  square  foot  ( ->  56.5'^5  lbs. 
per  square  inch).  For  large  buildings,  however,  where  tmeqtial  settlement 
to  any  considerable  extent  would  be  liable  to  produce  crtidcs  in  the  masonry 
walls,  the  maximum  limit  of  allowable  pressure  should  be  fixed  at  3  tons  per 
square  foot.  2^  tons  or  even  2  tons  is  quite  common  practice  under  ordi- 
nary conditions  of  wetness,  but  where  there  is  no  wash  from  running  water. 
For  the  above  conditiotis  the  underlying:  strata  mtist  of  course  be  firm. 
Where  the  amount  of  settlement  is  of  mmor  importance  there  is  really  no 
practical  limit  to  the  bearing  power  of  sand,  hence  the  wide  range  of  values 
assumed.    In  some  instances  lO  tons  per  square  foot  has  been  exceeded. 

2. — ^Actual  Bearing  Pressures  on  Sand. 
WoMhington  Monwnent,  WasMngton,  D.  C. — Pressure  at  base  resting  on  sand  bed  3  ft. 

thick,  about  11  tons  per  sq.  ft.;  and  with  wind  preamire  added,  about  H  tons. 
Piert  of  Brooklyn  Smpmsion  Bridge. — At  base  of  piers.  44  ft.  below  bed  of  rirft, 

proHure  on  layer  of  sand  3  ft  thick  resting  on  bed  rock,  5i  tons  per  sq  ft. 
St.  Paul  Building.  New  York  City.— ConUnuova  grillage  over  entire  area.    Prcosiin 

on  compact  sand.  3.2  tons  per  sq.  ft. 
vroridBuUding.  New  York  City. — Inverted  arches  over  continuous  concrete  foottnfs. 

FTeamire  on  dense,  fine  sand.  4.7  tons  per  sq.  ft. 
aprecMea  Building.  San  FmnciMO.— Continuous  grfllage.     Pressure  on  dense,  vet 

■and.  2i  tons  per  sq.  ft. 


fo 


FOUNDA  TION  BED— BEARING  PRESSURES,  865 

(/.)  Graofl;  (g.)  BoukUrs  and  Gravel. — Some  very  important  structures 
are  tound  on  these  classes  of  material,  both  above  and  under  water.  If 
properl)r  prepared  and  protected  from  lateral  bulging  and  wash  such  a 
oundation  may  be  loaded  with  4  tons  per  square  toot  (  —  56.6'' 5  lbs.  per 
square  inch).  11,  (urther.  it  is  compacted  with  dry  or  moist  sand  not  subiect 
to  wash,  the  bearing  power  will  be  increased,  say  to  6  or  8  tons,  depending 
upon  the  binding  quality  of  the  material  and  on  local  conditions;  if  a 
moderate  quantity  of  clay  is  intermixed  with  the  sand  and  the  resultant 
matrix  is  sufficient  to  fill  the  voids  of  the  gravel  the  higher  value  (8  tons) 
may  be  used  with  safety.  Such  a  material  if  thoroughly  hardenea  would 
(orm  hard-pan. 

3. — Actual  Bbaring  Prbssurbs  on  Gravbl. 
Pkr»  of  CitictMnaH  Stapemiou  Bridoe.-~At  base  of  p'era.  12  ft.  below  low  water. 
pressure  on  gravel  bed  (neglecting  skin  friction  of  piers).  4  tons  per  sq.  ft. 

(A.)  Chy  and  Sand-,  (•'.)  Common  Clay. — Ordinary  soft  clay  or  clay  and 
and.  when  wet.  is  subject  to  considerable  displacement  if  heavily  loaded; 
ind  under  ordinary  conditions  it  is  best  not  to  allow  more  than  1  ton  per 
quare  foot  (  —  13. 8^8  lbs.  per  square  inch)  for  important  buildings  where 
nuch  settlement  would  be  harmful.  But  this  bearing  power  may  be  greatly 
ocreased  by  proper  drainage  or  by  a  close  (lateral)  confinement  of  the 
taterial,  so  that  well-drained  clay  or  such  clay  containing  some  sand  may 
e  loaded  with  2  tons  per  square  loot.  A  naturally  dry  common  clay  bed  of 
on^derable  thickness  and  extent  will  stand  three  tons  with  allowable 
ettlement;  and  this  may  be  increased  to  4  tons  for  a  mixttu«  of  sand  and 
lay  where  the  former  predominates  and  the  latter  is  sufficient  for  a  binder, 
[ard.  firm  clay  unmixed  with  sand  will  also  stand  4  tons  and  if  mixed  as 
binder  with  good,  coarse  sand  the  bearing  power  will  be  greatly  augmented, 
ine  clay  ana  sand  when  thoroughly  saturated  with  water  forms  quick- 
ind. 

4. — Actual  Pressures  on  Clay  and  Sand. 
tpilal  BuOiino,  Albany,  N.  Y. — aay  with  some  sand.    Pressure  allowed.  2  tons 

per  8Q.ft. 
mmmaioml  Library,  WashinffUm,  D.  C. — Ydlow  day  mixed  with  sand.     Pressore 

allowed.  2i  tons  per  sq.  ft. 

(/  )  Sand  and  Loam;  (k.)  Loam. — ^Loam  is  too  spongy  and  compressible 
be  relied  upon,  from  an  engineering  standpoint,  to  support  any  structure. 
d  hence  the  excavation  is  always  carried  through  it  to  some  firmer 
jtKiatkm  bed  beneath.  It  is  a  mixture  of  clay,  sand,  vegetable  mould, 
d  decayed  animal  matter.  But  when  mixed  with  a  large  proportion  of 
id  it  is  less  objectionable  especially  when  well  tamped.  Railway  trestle 
Its  which  rest  on  mud  sills  supported  by  this  material,  arc  frequently 
:>ject  to  considerable  settlement. 

Practical  Tests  of  Soils.— Where  the  bearing  power  of  any  particular 
I  is  in  question  it  may  be  tested  by  loading  a  vertical  timber  of  given 
sa-section  (the  larger  the  better)  and  resting  on  the  soil  at  the  bottom 
a,  pit,  with  a  weight  equal  to  or  greater  than  the  proposed  intensity  of 
iing.  Allowance  will  be  made,  however,  for  the  results  obtained  as  the 
tleznent  due  to  loading  such  a  limited  area  would  be  excessive. 

Sdectioa  of  Site  for  BaUding. — (generally,  the  site  for  the  erection  of  a 
kctttre  is  determined  from  necessity  rather  than  from  choice.  That  is  to 
,  conditkmt  other  than  those  of  local  character  govern  and  fix  the 
xioa.  But  there  are  many  instances  where  other  sites  than  those 
rted  w>nld  have  been  chosen  from  pure  economy  of  cost  of  foxmdation 
direction  been  given  to  its  consideration. 

ExMBinatiofl  of  Soil. — ^The  simplest  and  most  satisfactonr  method  of 
rminins  the  character  of  the  soil  is  by  digging  pits.  This  should  be 
*  generally  before  making  estimates  and  letting  contracts,  on  all  im- 
ant  work  requiring  excavation  in  general,  and  including  foundation 
c  at  no  firreat  depth.  For  the  former  we  may  cite  railroaoT  cuts,  irriga- 
canals,  and  waterways  in  general:  while  for  the  latter,  may  be  men- 
;d  dam  sites,  and  sites  for  bridge  piers,  buildings,  etc.  The  pits  need 
ily  large  enough  for  a  man  to  find  room  to  excavate.  Where>great  depth 
quired  borings  must  be  made.  ized  by  V^DOglC 


866  fO.— FOUNDATIONS, 

Boriofff  in  Soil. — Por  soft  earth  and  clay,  up  to  about  100  feet  in  deptK 
a  common  wood  auger  with  levers,  turned  by  hand,  may  be  used.  It  may 
have  a  diameter  of  li  to  2|  inches  and  be  woiiced  on  the  end  of  a  sectional 
iron  rod  easilv  made  by  any  blacksmith.  It  is  usually  started  by  one-mas 
power,  but  after  being  sunk  a  short  distance  two  or  more  men  may  be  re- 
quired. During  the  process  of  boring,  samples  are  brought  up  and  recorded 
together  with  their  distances  below  the  surface. 

Por  the  harder  strata  and  at  greater  depth,  artesian  well  boring  tools 
are  employed.    (See  Eng.  News,  Vol.  XXI.  page  324.  for  illustrations.) 

Estimating  Loads  on  Foundatiooi. — ^These  loads  include: 

(1.)  Porces  due  to  the  weight  of  the  structure  itself,  so  distributed  as 
to  conform  with  the  reactions,  whether  vertical  or  inclined.  This  is  not 
always  an  easy  matter,  but  the  principle  should  be  kept  clearly  in  mind. 

(2.)  The  live  loads  or  that  percentage  of  them  liable  to  act  in  unison  to 
produce  maximum  stresses  in  any  part  of  the  foundation.  The  term  "live 
loads"  will  here  be  considered  to  embrace  those  loads  for  which  the  structure 
was  principally  designed,  as  for  instance  people,  furniture  and  merchandise 
for  buildings,  water  pressure  for  dams,  etc. 

(3.)  The  wind  loads  (also  other  natural  forces  of  an  accessory  character 
such  as  snow,  pressure  of  ice,  etc.).  considering  possible  tension  in  the 
foundations  as  well  as  compression;  also  shearing. 

(4.)  Temperature  stresses,  due  to  changes  in  temperature  affecting  the 
length  of  certain  principal  members  confined  between  parts  of  the  founda- 
tion, as  for  instance  in  the  two-hinged  steel  arch. 

(5.)  Impact  loads  due  to  moving  machinery,  as  steam  engines,  steam 
hammers,  dynamos,  etc. 

For  Buildings. — ^There  are  two  main  classes  of  foundationa  in  use  for 
buildings,  namely,  continuous  foundations,  and  independent  piers.  Ttw 
latter  are  generally  employed  where  a  siutable,  natiiral  foundation  bed 
exists  only  at  great  depth,  in  which  case  the  continuous  fotmdation  wonM 
be  more  expensive.  As  more  or  less  settlement  always  occurs  after  a  bui)d> 
ing  is  erected,  due  almost  wholly  to  the  constant  pressure  of  the  dead  load,  it  is 
best  to  proportion  the  area  of  all  fotmdation  footings  to  the  dead  load  only, 
using  a  reduced"  and  uniform  working  pressure  for  same,  so  that,  selecting 
that  pier  which  we  will  call  the  "Index  '  pier  or  part  of  fotmdation  which 
sustains  the  least  ratio  of  dead  load  to  total  load,  we  have. 
Reduced  working  pressure  ^  Dead  load  stress  at  footing  of  column  ... 
Allowable  maximum  pressure  "  Maximtmi  stress  at  footing  of  column 

Under  the  subject  of  Buildings,  page  822,  it  will  be  noted  that  for  higli 
buildings  the  maximum  stress  at  footing  of  column  is  reduced  by  diminisi- 
ing  the  live  load  for  each  floor  below  the  top  one  a  certain  percentage,  as  it 
is  not  likely  that  all  floors  "in  column"  will  be  loaded  fully  at  the  same  time. 

It  may  be  stated  here  that  vault  shafts  nmning  up  through  buildings 
should  be  carried  on  a  separate  fotmdation  from  that  of  the  main  building- 
Engine  and  boiler  foundations  should  also  be  independent. 

C^are  should  be  taken  that  the  line  of  resultant  pressure  at  the  founda- 
tion footing  ihould  come  well  within  the  middle  third  if  the  foundation 
bed  is  solid  rock,  and  it  should  be  practically  central  for  any  bed  which  is 
soft  or  springy.  Eccentricity  of  loading  may  unduly  increase  the  intensity 
of  pressure,  and  also  cause  tipping,  cracking,  and  perhaps  rupture,  of  the 
masonry  wall. 

For  City  Building  Codes,  see  Table  6.  following  page. 

For  Dams. — To  save  the  reader  the  time  and  trouble  of  looking  into 
the  matter  it  will  be  stated  that  for  a  gravity  dam  with  reaerVbir  empty. 
it  will  not  be  necessary  to  consider  any  additional  stresses  in  the  mascmn' 
or  on  the  foundation  bed.  due  to  wind  pressure  against  the  down-etream 
face.  Assuming  a  dam  200  ft.  high  with  a  base  of  69  ft.,  and  considering  • 
wind  pressure  of  60  lbs.  per  sq.  ft.  acting  horizontally  (with  no  vatk^ 
component),  then  under  tne  most  tmfavorable  conditions  the  intensity  of 
•tress  at  either  toe  would  not  exceed  0  lbs.  per  sqxiare  inch.  In  calculating 
the  resultant  stress  due  to  any  pressure  at  the  top  of  the  dam,  as  for  inttance 
w^  or  ice,  it  is  necessary  only  to  consider  the  oam  as  a  beam  fixed  at  coe 
end  with  length  equal  to  the  height  of  the  dam  and  with  depth  equal  to  its 
case,  and  assuming  the  neutral  axis  of  the  section  to  bisect  the  ' 


WADS  ON  FOUNDATIONS. 


867 


5. — Bbarinq  Power  of  Soils  for  Buildings. 

I  (Extracts  from  variotis  City  Codes.) 

I  [Loads  are  in  tons  of  2000  lbs.  per  sq.  ft.]   ^ 

i  New  York  (1906). — Where  no  test  Is  made,  different  sous,  exdudinic  mud.  at  bottom 
of  footings,  shall  be  deemed  safe  to  sustain  the  following  loads  per  sq.  ft. :  Soft 
day.  1  ton;  ordinary  day  and  sand  together.  In  layers,  wet  and  springy.  2  tons; 
losm.  day  or  fine  sand,  firm  and  dry.  3  tons;  very  Arm.  coarse  sand,  stiff 
gravd  or  hard  olay,  4  tons,  or  as  otherwise  determined  by  the  Commlsiloner  of 
Buildlnp. 
C/Hai0o  (1907).— If  the  SOU  Is  a  layer  of  pure  day  at  least  15  ft.  thick,  without  ad- 
mixture of  any  foreign  substance  excepting  gravel,  the  load  shall  not  exceed 
1}  toDfl  per  sq.  ft.;  pure  day  In  layers  at  least  IS  ft.  thick,  dry  and  thoroughly 
oompreoed.  2\  tons;  dry  sand,  at  least  15  ft.  thick,  and  without  admixture  of 
day.  loam  or  other  foreign  substance.  2  tons;  day  and  sand  mixed,  H  tons. 
PkUaddpkia  (1907). — Foundations  of  other  materials  than  piles  shall  be  so  propor^ 
tlooed  that  the  loads  upon  the  soil  shall  not  exceed  the  limits  for  the  different 
kinds  of  sou  than  herein  given,  to  wit:  Sand  and  loose  gravd.  3^  tons  per  sq.  ft. ; 
dry.  hard  day.  3i  tons;  cemented  gravd.  6  tons. 
CleMUmd  (1907).— Good,  sound,  natural  earth  shall  not  be  loaded  to  more  than  the 
following:  Qravd  and  coarse  sand  well  cemented,  or  rock  or  hard  shale  unex- 
posed to  the  action  of  air,  frost  or  water,  8  tons  per  sq.  ft;  dry.  hard  day  or  fine 
sand,  compact  and  wdl  cemented.  4  tons;  moderatdy  dry  day  or  dean,  dry 
sand.  2  tons;  soft,  wet  sand.  1  ton;  quicksand  or  alluvial  soils,  i  ton;  the  sand 
underiying  the  City  of  Qevdand  above  the  lake  levd.  commonly  called  "quick- 
sand," when  drained  of  Its  ground  water  without  puddling  or  disturbing  the 
foundation  may  be  loaded,  3  tons.  « 

SanFrancUco  (1910).— Soft  dav.  1  ton  per  sq.  ft ;  sand  and  day  mixed.  2  tons: 
firm,  dry  day,  3  tons;  hard  day,  4  tons;  loam  or  fine,  dry  sand.  3  tons;  com- 
pact sand.  4  tons;  coarse  gravd.  6  tons;  shale  rock.  1 0  tons;  hard  rock.  20  tons. 
BMflaio  ( 1909). — In  no  case  shall  the  soil  under  any  building  be  loaded  with  a  weight 
greater  than  Zk  tons  per  sq.  ft.  If  the  soil  is  composed  of  other  materials  than 
hard  day  or  gravd  then  the  area  of  the  foundation  shall  be  extended  as  directed 
untn  the  pressure  Is  reduced  to  a  safe  limit. 
District  ot  ColumMa  (1906).— (PracUcally  the  same  as  N.  Y.  aty  Code.)  Soft  clay, 
1  ton  per  sq.  ft.;  ordinary  day  and  sand  together.  In  layers,  wet,  2  tons;  loam. 
day.  or  fine  sand,  firm  and  dry.  3  tons;  very  firm,  coarse  sand,  stiff  gravd,  or 
hard  day.  4  tons,  or  as  otherwise  determined  by  the  Inspector  of  Buildings. 

For  Machines,  Dynamos,  9U. — ^The  weight  of  the  machine  as  a  whole  is 
not  alone  to  be  considered.  A  more  massive  foundation  may  be  required 
for  a  light  machine  than  for  a  heavy  machine  with  the  same  weignt  of 
movin^r  parts.  The  foundation  should  be  on  a  natural,  hard  bed,  but 
where  this  is  not  obtainable  the  foundation  itself  should  be  massive  enough 
to  absorb  the  shock  or  impact  of  the  machine.  Manufacturers  usually 
prefer  to  install  their  own  machines  and  prepare  the  fotmdations.  and. 
where  possible,  it  is  best  for  them  to  do  so  on  account  ot  their  practical 
loiowledge  of  the  requirements  of  the  case. 

Types  of  FomidatJoo  Footings: — 


g.  J.— -£.#a5<  dimensions  for  ordi- 
xiary  concrete  footing  imder 
brick  or  rubble  wall  or  pier. 
Where  more  bearing  area  is  re- 
Quircd  on  foundation  bed  the 
offset  and  thickness  arc  increased 
or  the  sides  of  the  footing  sloped, 
as  in  Fifi'  2. 


Fig.  2. — Concrete  footing  with  or 
without  I-beams,  for  heavily 
loaded  walls,  yielding  founda- 
tions, or  both.  One  or  more  of 
the  beams  is  often  imbedded  in 
the  concrete  to  give  stiflness  and 
absorb  shock  due  to  heavy  ma- 
chinery, as  in  power  houses,  etc. 


868 


(O.—FOUNDA  TIONS. 


^^ 


I    I   I   I    I    I    I   I 

CLOnmm 


a 


H b  — l-VV-J. — b  — 4 

b B .-J 


Fig.  8. — I-beam  Footing  for  Inde- 
pendent (isolated)  Piers.    Beams 
to  be  imbedded  in  concrete. 


Problem.— Let  it  be  reqmred  to  de- 
sign a  footing  of  I-beam  construction 
tmder  a  steel  colimin,  carrying  at  bottom 
of  footing  a  maximum  load  of  748,000 
lbs.,  and  on  a  soil  capable  of  sustaining 
3  tons  (6000  lbs.)  per  square  foot. 

Solution. — By  using  formula  (1), 
page  866,  we  find  that  the  reduced 
working  pressure  on  fotmdation  is.  say, 
5200  lbs.  per  square  foot,  hence  the 
total  area  of  the  footing  should  be 
748.000-1- 5200- 143.8  square  feet,  or  say 
a  square  base  of  length  J5- 12  ft.  Now, 
tenUtively,  we  may  assume  that  il  — 

|-3ft.:a-f— 3£t.;6-^-4J  ft.; 

c  -  y  -  U  f t.    Then  for  the  bottom  tier 

of  beams  each  cantilever  arm  a  will  sus- 
tain a  total  upward  pressure  of  5200  X  a 
XB  -  5200X  3X  12  -  187200  lbs.,  pro- 
ducing a  bending  moment  of  1 87200  X 

■j-280,800ft.-lbs.    Using  a  fiber  stress 

of  16000  lbs.  per  square  inch  for  steel 

I-beams  the  above   moment   calls   for 

either  12  9*  21  lb.  beams,  9  10*  25  lb. 

beams,  or  6  12*   31   lb.   beams*.     The 

12*  beams  are  the  more  economical, 

while  the  10*  beams  give  closer  and 

better   spacing  and  wul   be   adopted. 

Similarly,  for  the  middle  tier  of  beams, 

each  cantilever  arm  b  will  sustain    a   total    upward  pressure  (neglecting 

weight  of  lower  tier  of  beams)    of    6200X6XB- 280800  lbs.,    produdi* 

a  bending  moment  of  631800  ft.  lbs.,  and  calling  for  5  20*  65  lb.  beams. 

Lastly,  for  the  upper  tier,  each  cantilever  arm    c   will    (be    assumed    to) 

support  one-quarter  the  total  load  or  187,200  lbs.,  producing   a   bending 

moment  of  140.400  ft.-lbs.,  and  calling  for  5  10*  25  lb.  beams. 

CHher  proportions  may  be  assumed  for  the  areas  of  the  tiers  of  beams 
if  it  is  thought  that  economy  may  result. 

Coffer-Dams. — A  coflfer-dam  is  a  fixed  enclosure  built  in  situ  around  a 
proposed  foundation  for  the  purpose  of  shutting  out  the  water  during  con- 
struction of  the  latter.  Such  a  dam  may  be  formed  by  building  an  earth 
embankment  around  the  site;  by  constructing  a  water-tight  casing  of  any 
material,  as  iron  or  wood;  by  sinking  cribs;  by  driving  sheet  piling;  or  by 
a  combination  of  these  methods.  In  any  event  there  will  be  more  or  less 
leakage,  and  either  hand  or  machine  pximps  will  have  to  be  installed  to  keep 
the  site  dry. 

By  Earth  Embankment. — A  tight  dam  may  be  made  with  gravel  and 
clay,  but  other  soils  may  be  used  if  there  is  a  matrix  sufficient  to  fill  the 
voids.  This  construction  is  used  where  the  water  is  shallow  and  quiet 
or  where  there  is  but  little  current.  The  width  of  dam  at  top  may  vary 
from  3  ft.  upward,  with  side  slopes  of  2  or  2^  to  1.  For  a  depth  greater 
than  5  ft.  other  methods  are  generally  used.  Sometimes  sand  in  bags  b 
employed  to  good  advantage,  especially  where  there  is  some  current. 

By  Water-Tight  Casing. — The  casing  may  be  in  the  form  of  a  Utgt 
wooden  crib  with  single  or  double  shell.  If  of  single  shell,  the  seams  are 
calked  tight,  while  if  the  shell  is  double  the  intervening  space  or  chamber  is 
packed  with  clay  puddle,  to  prevent  leakage.  The  sijse  of  the  Aell  timben 
depends  on  the  depth  of  water  and  also  on  the  interior  bracing.  For  coffer- 
dams in  ordinary  bridge  foundation  work.  12*xl2*  timbers  are  frequently 
^ed,  dove-tailed  or  rather  halved  at  the  joined  ends  or  comers.  The 
pracmg  may  extend  entirely  across  the  crib  from  shell  to  shell,  and  be  re- 
placed  by  shorter  struts  abutting  against  the  masonry  as  the  latter  inter- 

*  Sec  Tables  of  Properties  of  I-beams,  pages  554  and  556. 


COFFERDAMS.    SHEET  PI  UNO, 


869 


cepts  it  in  being  projected  upward.  In  desisnins  the  shell,  remember  that 
the  hydrostatic  pressure  in  lbs.  per  sq.  ft. »  62.6  H,  in  which  H  is  the  depth 
in  ft.  below  the  water  stirface.  (See  Dams,  pa^e  846.)  Thus  for  a  horizontal 
shell  timber  of  length,  say,  6  ft.  between  interior  bracing,  and  whose  center 
is  30  ft.  bebw  the  surface,  we  have,  if  d  equals  thickness  of  shell. 

o     ,.  ^       wP       62.5X30X6X6X12 

Bending  moment  ■■  "S"  ■■ o 

Resisting  moment '^kfbcP;  in  which  /— 1000,  and  6— 12. 
u      .'       jt     62.5X30X6X6X12X6     .^  _.  .     _. 

Equatmg,  cP 8x1000X12 W. 63;  or,  say  d -  8  ma. 

The  desijTQ  of  such  a  crib  is  qiiite  simple  imder  favorable  circumstances, 
but  in  a  swift  stream  with  an  uneven  bed,  part  of  which  may  be  rock,  it 
offers  many  difficulties.  The  bottom  of  the  crib  in  this  case  should  conform 
closely  with  the  rock  bottom.  For  a  silt  bed  the  bottom  of  crib  should  be 
sharpened  to  penetrate  the  silt.  Piles  may  be  driven  to  hold  the  crib  in 
place.  This  leads  to  another  construction,  namely,  that  of  driving  one  or 
more  rows  of  piles  and  sheathing  them,  thus  obtaining  the  same  result  in 
another  way.  The  piles  should  be  well  diagonal-braced  where  necessary  to 
resist  bending,  remembering  that  where  not  so  braced  the  resisting  moment 
of  the  section  in  inch-lbs.  is  —  0.0982  diameter'X  allowable  outer  fiber 
stress  /  of  pile  per  square  inch — say  /  — 1000. 

By  Sinking  Cribs. — ^A  larp^e  crib  coffer-dam  is  sometimes  formed  by 
sinking  severafsmall  cribs  in  line  around  the  site,  and  planking  and  calking 
them  on  the  outside.  The  cribs  are  made  rectangular,  of  squared  timbers 
ramed  in  the  ordinary  manner,  and  containing  cells  or  chambers,  somewhat 
ibove  the  level  of  the  bottom,  to  be  weighted  with  stone  so  as  to  sink  into 
he  river  bed.  Guide  piles  are  often  driven  for  this  work.  In  sinking  cribs 
irhere  there  is  current  two  or  more  clusters  of  piles  may  be  driven  up  stream, 
T  auxiliary  cribs  may  be  sunk  to  which  are  attached  adjustable  steel  cables 
>r  "dropping"  the  cribs  into  position. 

By  Driving  Skett  Piling. — ^This  is  one  of  the  most  common  methods  in 
se,  both  in  wet  ground  and  in  shallow  water;  and  where  it  can  be  employed 
Tectively,  is  simple  and  cheap.  Some  of  the  principal  forms  of  wooden 
leet  piling  are  the  following: 


f.  4. 


-Large  Square 
Piles. 


I    I    I    I 

Fig.  5.— Plain  Single 
Sheeting. 


nn 


X 


x=s 


Pig.  6.— Double  Sheeting. 


!i  !  i!  I  "i 


:jz 


3X 


[>      >      > 


Fig.  7. — ^Triple  Sheeting. 


Fig.  8.— Matched  Piles. 


I<     <     <l 

Fig.  9.— V-Matched  Piles. 


3 


Pig.  10. — ^Tongue-and-Groove  Piles. 


^ 


Ni 

'X 

A 

II. 


-Built    Matched 
Pile. 


Fig.  12.— Built  V-Matched      Fig.  13.— Built  W- 
Pile.  Matched  Pile. 


^^ 


^S 


Fig.  14.  Fig.  15.  Fig.  16qIp 

Figs.  14,  16,  16.— Details  of  Wakefield  Sheet  Piling.       o 


870 


50.— FOUNDATIONS. 


Other  forms  are  in  use  but  they  are  no  improvement  over  the  above. 
The  lower  ends  of  the  piles  are  usually  cut  on  the  slant  so  that  in  driving 
they  will  crowd  against  those  in  place  and  close  the  joints 
(Pig.  17;.  They  are  also  sharpened  so  as  to  "broom"  if 
there  is  solid  rock  bottom.  A  good  method  to  secure 
tight  joints  is  to  drive  from  both  ends  of  the  line  toward 
the  center  and  then  drive  home  a  good  tight-fitting  "key" 
pile.  Sheet  piles  are  usually  driven  between  giiides  or  hori- 
zontal waling  pieces  which  may  be  supported  by  a  row  of 
ordinary  round  piles,  or  sawed  piles,  previously  driven.  After 
the  sheeting  is  driven  it  is  keyed  tightly  or  wedged  in  the 
wales.  Fig.  17. 

Steel  Sheet  Piling  comes  in  many  forms,  some  of  which  are  composed 
of  standard  rolled  sections  riveted  together,  while  others  are  special  roUed 
sections  not  requiring  any  riveting. 


Fig.  18. 
Fig.  18  illustrates  an  interlocking  channel-bar  piling  caisson  driven 
in  place  and  ready  for  excavating.  The  piling  is  that  of  the  Priestedt* 
type.  This  piling  in  place  will  weigh  from  23  to  67.5  lbs.  per  sq.  ft.  Piling 
which  will  weigh  when  interlocked  about  41  lbs.  per  sq.  ft.  will  have  a 
moment  of  inertia  of  60.21  and  a  radius  of  gyration  of  1.6. 


Fig.  19. 
Fig.  10  illustrated  the  plain  rolled  section  as  manufactured  hy  the 
United  States  Steel  Piling  Co.  of  Chicago.  The  actual  coet  of  this 
piling  depends  somewhat  upon  the  specifications.  If  ordered  cut  to  lengths 
It  can  be  furnished  on  cars  at  approximately  $42.00  per  net  ton.  Where  cor- 
ner pieces  are  required  there  is  a  net  extra  of  approximately  $10.00  per 
net  ton  for  the  comers  onljr,  and  there  is  also  a  net  extra  of  $2.00  per  ton 
for  punching  each  piece  with  pulling  holes  where  purchasers  prefer  shop 
punching,  prior  to  sh:pment.    The  above  prices  are  for  August.  1906. 

Chic*a^!°'^^*"''*''*  ^^  ^^^  Priestedt   Interl(^k^mj^^(^^p|^lPar  Co..  of 


d  by  Google 


872 


n  ^FOUNDATIONS. 


6.— Safb  Bbarino  Powbr  of  Pilbs,  in  Tons  ot  2000  Lbs. 

Driven  by  Drop  Hammer. 

[By  Wellington's  Formula  (1)  preceding  page:    P -  2  wfc  +  (*  +  1).) 


Pcnetra- 

tion 
at  Last 

Weight  of  Hammer  in 

Tons,  for  Drop  of  20  Feet.* 

Blow. 

i  ton 

1  ton 

1  ton 

11  tons 

litons 

If  tons 

2  tons 

2iton& 

2*  togs 

Inches. 

(1000 

(1500 

(2000 
lbs.) 

(2500 

(3000 
lbs.) 

(3500 

(4000 

(4500 

(5000 

lbs.) 

lbs.) 

lbs.) 

lbs.) 

lbs.) 

lbs.) 

lbs.) 

H 

17.78 

26.67 

35.56 

44.44 

53.38 

62.62 

71.11 

80.00 

88.89 

\i 

16.00 

24.00 

32.00 

40.00 

48.00 

56.00 

64.00 

72.00 

80  00 

^ 

14.65 

21.82 

29.09 

36.36 

43.64 

50.91 

58.18 

65.45 

7273 

^ 

13.88 

20.00 

26.67 

33.33 

40.00 

46.67 

53.33 

60.00 

66.67 

12.31 

18.46 

24.62 

30.77 

36.92 

43.08 

49.23 

55.38 

61.54 

^ 

11.43 

17.14 

22.86 

28.57 

34.29 

40.00 

45.71 

51.43 

57.14 

10.67 

16.00 

21.33 

26.67 

32.00 

87.33 

42.67 

48.00 

53.33 

1 

10.00 

15.00 

20.00 

25.00 

30.00 

35.00 

40.00 

45.00 

5aoo 

l\i 

8.89 

13.33 

17.78 

22.22 

26.67 

31.11 

35.56 

4000 

44.44 

m 

8.00 

12.00 

16.00 

20.00 

24.00 

28.00 

32.00 

36.00 

40.00 

^H 

7.27 

10.91 

14.55 

18.18 

21.82 

25.45 

29.09 

32.73 

36.36 

2 

6.67 

10.00 

13.33 

16.67 

20.00 

23.38 

26.67 

30.00 

33.33 

2\i 

6.15 

9.23 

12.31 

15.38 

18.46 

21.54 

24.62 

27.69 

30.77 

2H 

5.71 

8.57 

11.43 

14.29 

17.14 

21.00 

22.86 

25.71 

28.57 

Vi 

5.33 

8.00 

10.67 

13.33 

16.00 

18.67 

21.33 

24.00 

26.67 

3 

5.00 

7.50 

10.00 

12.50 

15.00 

17.50 

20.00 

22.50 

25.00 

m 

4.44 

6.67 

8.89 

11.11 

13.33 

15.56 

17.78 

20  00 

22.W 

4 

4.00 

6.00 

8.00 

10.00 

12.00 

14.00 

16.00 

18.00 

2aoo 

6 

3.33 

5.00 

6.67 

8.33 

10.00 

11.67 

13.33 

15.00 

16.67 

6 

2.86 

4.29 

5.71 

7.14 

8.57 

10.00 

11.43 

12.86 

14.29 

The  drop-hammer. — ^This  may  consist  of  a  heavy 
block  of  oak  when  some  hastily  improvised  machine  is 
desired,  but  the  cast -iron  ram  as  shown  in  Fig.  17  is  the 
tvpe  quite  universally  employed.  In  the  illustration 
the  hammer  h  is  engaged  by  the  nippers  n«  and  is 
released  when  the  latter  are  drawn  up  against  the  w^edge 
w  fastened  to  the  guides  «,  at  the  top  of  the  derrick. 
The  hammer  may  also  be  released  at  any  height  below 
the  top  by  pulling  a  tripping  rope  attached  to  the  nip- 
pers. The  hammer  line  or  hoisting  rope  r  runs  over  a  10* 
to  18*  sheave  (2  sheaves  are  fixed  at  the  top-;-one  for 
the  hammer  line  and  the  other  for  the  pile  line)  and 
can  be  operated  either  by  horse  power  or  by  hoisting 
engine.  These  hammers  weigh  from  1200  lbs.  upward, 
2000  to  2500  lbs.  being  a  very  satisfactory  medium 
weight.  Greater  speed  can  be  obtained  by  the  use  of 
a  hoisting  engine  with  a  friction  clutch  or  friction  drum, 
so  that  the  rope  and  hammer  may  be  released  by  the 
engine  driver  at  any  moment.  In  such  a  case  the  ham- 
mer rope  is  fastened  permanently  to  the  hammer  which 
is  level  on  top.  instead  of  being  depressed  as  in  Fig. 
20.  It  is  to  be  noted  that  the  nammer  should  be 
heavier  for  this  method  as  it  has   to   "overhaul"    the 


hammer  rope  in  its  descent, 
efficient. 


Pigs.  20, 

Drop-Hammer 

with  Nippers. 


Such  hammers  weighing  3500  lbs.  are  vcf? 


The  steam-hammer. — Fig.  21  is  an  illustration  of  an  improved  type  of 
steam-hammer t  with  a  "gravity"  action.   The  total  machine,   which  may 

•For  any  other  drop  the  bearing  is  proportional.    Thus,  for  15  ft.  drop. 

Vfe  by  »^:   for  25  ft.  drop,  multiply  by  V4;  etc. 
«»    T  The  Warrington  steam  nammer  as  maniilactured  by  the  Vulcan  Iroo 
ToSTr-^'xP^'*^**?- .  "^^^  fi"^  steam  hammer  for  pile  driving;  was  applied  by 
James  Nasmyth  in  1845.  DgtizedbyGoOgle  *^ 


PILE  DRIVING.  87B 

weigh  as  much  as  6  tons,  is  suspended  from  the  top  and 
between  the  leads  or  gins  of  the  derrick,  like  a  common 
drop-hammer;  but  in  this  case  it  is  allowed  simply  to  rest 
on  the  pile  to  be  driven.  The  ram  h,  whose  weight  is  about 
half  that  of  the  total  machine,  slides  vertically  on  four  circu- 
lar guides  and  is  connected  to  a  piston  rod  operated  from  the 
cvlmder  c.  Steam  is  led  into  the  lower  part  of  the  cylinder 
through  a  flexible  tube,  thus  raising  the  ram  which  is  then 
allowed  to  drop  by  its  own  weight.  The  amount  of  "drop" 
may  be  lessened  il  the  cylinder  is  double  acting. 

The  derrick. — ^The  ordinary  pile  driver  derrick  is  a  simple 
affair  consisting  of  two  upright  leaders  with  guides  for  di- 
recting the  hammer  (Pig.  20).  and  supported  by  a  frame- 
work (for  fore-and-aft  and  lateral  bracmg)  resting  on  a  plat- 
form or  horizontal  frame.  The  frame  may  rest  on  a  scow. 
sn  a  car,  or  on  rollers.    If  on  a  scow,  it  is  usually  fixed;  on 

I  car,  it  is  allowed  to  swing  laterally  arovmd  a  vertical  pivpt; 
)n  rollers,  it  is  given  forward  and  lateral  movement  by  using 

wo  sets  of  wooden  rollers,  one  above  the  other,  at  ri^ht  I 

ingles  to  each  other.    A  tilting  driver  for  driving  batter  piles 
nay  be  constructed  by  allowing  the  leaders  to  swing  on  a  ' 

orizontal  pivot  attached  to  the  i4 -frame  of  the  derrick  near 
he  top:  or  by  pivoting  the  whole  derrick  &ame  on   V-bol- 
ters  which  will  allow  lateral  tipping.    Ratchet  devices  mav 
e  used  for  tilting  the  leads  or  the  derrick  frame,  and  hold- 
tg  them  in  position  while  driving  the   piles.     The   follow- 
g  dimensions  may  be  taken   as  mere    'hints"  for  design 
r  scow  and  heavy   land    derricks:  For  a  60-ft.    derrick, 
ads  8'x  10*:  guides  i'xi'  sheathed  with  4*xK  iron;  spread- 
s  (lateral)  S'xKT  for  height  of  56  ft.  and  total  base  of  18 
;   ladder  strings  (fore  and  aft)    Q'xlTf  for  height   of  60    «*"  ^    t.-i 
and  base  of  18  ft.;   horizontal  bracing  8^x8"  to  S'xlO'    ^t^™  P*^®- 
le  latter  supporting  platforms) ;  diagonal  bracing  4''xl2';       i^nvcr. - 
itform    frame    12^12'   and    12^x14':    caps    (for   supporting    sheaves) 
K2(y.    For  a  height  less  than  60  feet  the  dimensions  may  be  proportioned 
:>ut^  the  square  root  of  the  height ;  thus,  for  a  derrick  30  ft.  high  multiply 
N/i  or  <^.    Less  amount  of  bracing  is  of  course  needed  for  a  low  derrick 

II  for  a  high  one  and  where  it  is  not  over  20  or  25  ft.  the  diagonal  bracing 
not  required.  For  a  steel  frame,  proportion  the  members  for  equu 
mgth  and  stiffness  to  the  above.  A  car-derrick  may  be  made  to  hinge 
^he  foot  of  the  ladder  strings  and  lie  flat  when  not  in  use.  If  a  light, 
table  land  driver  is  required  the  above  proportions  may  be  reduced. 
The  power. — ^This  may  be  either  man.  horse,  steam,  gas,  hydraulic,  pneu- 
ic,  or  electric.  The  first  named  is  now  only  employed  in  driving  ^eet 
i;^,  and  to  a  limited  extent.  The  horse  is  used  frec^uently  in  outlying 
nets  where  it  would  be  expensive  to  ship  a  hoisting  engine  for  the 
ed  amount  of  work  to  be  done.  Steam  is  mostly  employed,  and  usually 
he  hoisting  engine  or  by  operating  the  steam  ham- 

(sec  page  872).  Hydraulic  pressure  may  be  used 
Iriving  piles  for  foundation  work  in  submarine  tun- 
where  a  steady  pressure,  without  shock,  is  abso- 
/  necessary.  For  a  large  amount  of  work  requir- 
everal  drivers,  electric  power,  delivered  from  a 
al  plant,  has  proven  economical.  Fig.  22  is  a  light, 
ble    steam    pOe  driver  for*  height   up   to  50  teet. 

diacronal  bracing  may  be  used  if  deemed  advisa- 
jt  should  not  be  added,  to  increase  the  portable 
t,  unless  the  work  is  heavy  and  demands  it. 
rivinfir  is  often  assisted  by  the  water  jet. 
t^  tvatmr  jet. — If  the  soil  is  sandy  gr^t  assistance 
/infi[  piles  may  be  rendered  by  attaching  the  end  of 
!1  pipe  to  the  foot  of  a  pile  and  playing  a  stream 
er  into  the  sand  as  the  pile  descends.  If  the  ma- 
is  ptire  sand,  driving  often  becomes  unnecessary, 
e  settling  readily  imder  the  weight  of  the  hammer.  Fig,  22. 

e  cases  a  driver  is  not   used  at  all,  the  pile  being    Light,  Portable 
doTvn  by  bringing   some  other   weight   to   bear       Land  Driver. 


874  fO.^FOUNDATIONS. 

upon  it,  as  by  block  and  tackle  or  by  lever.    Softer  wood  for  piles  can  be 
used  in  such  cases  than  would  be  required  for  ordinary  driving. 

Pilt  shoes. — ^These  may  be  used  in  hard  driving  to  prevent  broomnig  of 
pile.  The  shoe  may  be  ot  cast  iron  or  steel,  usually  fitted  to  the  point  of 
pile  after  the  latter  has  been  sharpened  or  shaped  to  receive  it.  Coeoes 
made  of  sheet  steel  are  sometimes  used.  Provision  should  be  made,  by  lugs 
or  straps,  for  spiking  or  bolting  the  shoes  to  the  piles.  Shoes  should  have 
either  a  point  or  an  edge,  for  penetration. 

Comtnon  PiU  Foundations. — ^There  is  danger  in  driving 
piles  too  close.  Instances  are  frequent  when  piles  already 
driven  have  been  weakened  considerably  by  subsequent 
too-close  driving.  2^-V  centers  is  about  as  close  as  ordmary 
piles  should  be  driven,  and  2f-(f  is  much  better;  but 
local  conditions  sometimes  demand  a  minimiun  spacing 
of  2f-fif  or  even   2f,  especially  if  the  piles  are  small. 

Piles  should  be  driven  to  firm  foundation,  and  it  is 
sometimes  necessary  to  drive  them  in  "tandem"  or  one 
above  the  other  to  reach  a  suitable  supporting  soil.  Fig.  28 
shows  the  dowel  connection  used  for  splicing  same,  riles 
spliced  in  this  manner  have  been  driven  considerably  Pig.  23. 
over  100  ft.  in  depth.  Dowel  Splice. 

Cutting  off  piles. — Grades  for  cutting  oflf  piles  are  given  by,  say,  drivios 
a  tack  in  the  side  of  the  pile  either  at  the  desired  level  or  at  certain  established 
distance  below  it.  The  cut-off  is  made  with  a  cross-cut  saw  resting  on  two 
short  horizontal  guide  sticks  nailed  on  opposite  sides  of  pile,  with  top 
edges  at  grade.  For  cutting  ofl-piles  under  water  there  are  several  methods: 
(1)  The  above  method  may  be  employed  sometimes  during  absolute  low 
water,  by  sawing  off  two  or  three  feet  below  the  siuface,  provided  the  cut- 
off is  near  the  river  bottom;  (2)  under  the  same  conditions  as  above  it  may 
be  advisable  to  cut  off  all  the  piles  just  above  the  surface  and  then  nail 
horizontal  guide  strips  on  which  to  suspend  a  "gage"  saw  operated  by  hand 
and  which  will  cut  off  the  piles  at  the  true  level  a  certain  distance  below 
the  jjuides;  (3)  a  circular  saw  fixed  horizontally  at  the  lower  end  ci  a 
vertical  shaft  operated  from  a  scow,  may  be  xised;  (4)  if  the  water  is  too 
rough  or  deep  and  greater  care  is  required  it  is  best  to  cut  the  piles  off 
above  water  as  in  method  number  (2)  and  construct  a  level  platfiorm  on 
which  to  operate  the  circular  saw.  say  4  ft.  diameter,  from  a  movable 
machine  (a  pile  driver  is  sometimes  rigged  up  for  this  purpose)  mounted  on 
rollers. 

Foundations  on  piles  are  of  many  kinds  and  are  discussed  under  Caissoos, 
and  what  follows. 

"Dead-Men." — ^These  are  short  piles  sometimes  "planted"  "throu^  soft 
material  to  a  firm  bed  and  packed  aroimd  the  sides  with  gravel  or  sand. 
wet  and  well  tamped.    They  should  be  well  braced  laterally. 

Iron  Piles. — These  are  cast  iron,  wrought  iron  and  steel,  being  best 
(most  durable)  in  the  order  named.  Cast  iron  piles  may  sometunes  be  used 
to  advantage  in  hard-driving  soil  where  a  wooden  pile  would  broom  and 
where  the  grovmd  becomes  alterably  wet  and  dry.  Steel  shapes,  as  I-beams, 
may  be  used  in  wharf  construction  (fresh  water)  where  considerable  latenl 
thrust  has  to  be  resisted.  They  should  be  coated  with  asphalt  before 
driving. 

Screw  Piles.* — A  screw  pile  consists  of  a  cast  iron  shoe,  shaped  aome 
thing  like  a  cartridge,  surrounded  by  about  1}  turns  of  spiral  duk  thread 
6  feet  more  or  less  in  diameter  and  moxmted  on  the  lower  end  of  a  vertical 
shaft  which,  when  turned,  screws  the  pile  into  the  ground.  The  ^laft  is 
usually  of  steel  and  about  ^  the  diameter  of  the  screw.  Screw  piles  are 
particularly  adapted  to  soft  soil,  but  are  seldom  used  in  this  country  exccpt- 
mg  for  wharf  work,  anchoring  beacons,  and  light -house  construction.  Tntk 
use  in  bridge  fotmdations  has  been  extremely  limited.  The  circtilar  area 
of  the  screw  presents  resistance  against  an  uplifting  as  well  as  downward 
force. 

Disk  Piles.  ^ — A  circular  "disk"  of  cast  iron  fastened  to  the  lower  end 
of  an  iron  shaft  and  sunk  by  the  water  jet  (see  page  873)  is  the  usual  form 

*See  £««.  News,  Oct.  16.  1903. 

t  See  Trans.  A.  S.  C.  E.,  Vol.  VIII,  page  227-87;  Coney  Island  Pier 


d  by  Google 


876 


n.— FOUND  A  TIONS. 


At  the  point  of  the  pile  the  reinforcement  rods  are  brought  together, 
uid  may  be  banded  with  wire,  or  welded.  At  the  top.  the  rods  are  imbedded 
in  concrete;  but  after  driving,  the  concrete  may  be  picked  away  and  the  rods 
exposed  in  order  to  bind  with  the  new-laid  concrete  for  foundations. 


Fig.  28. 


Pig.». 


Fig.  26.  Fig.  27. 

Fig.  26. — Circular,  tapering  pile,  reinforced  with  |**  and  IK*  steel  rods, 

united  at  bottom  of  pile. 
Fig.  27. — Cylindrical  pile,  reinforced  with  expanded  metal. 
Fig.  28. — (Modified)  triangular  pile,  reinforced  with  1'^  steel  rods,  and 

\'°  wire  ties. 
Fig.  29. — "Square"  pile,  reinforced  with  4  —  1"®  steel  rods  with  various 

arrangements  of  {"*  wire  ties.    The  central  hole  is  for  water  jet. 

Concrete  piles  are  made  in  moulds.  They  should  be  kept  sxifficiently 
Wet  while  ciuing.  and  away  from  the  sim.  In  driving,  a  follower  shoidd  bie 
used  to  protect  the  concrete,  at  the  head  of  the  pile,  trom  injury. 


Fig.  30. 

Open  Caissons. — An  "open"  caisson  is  a  water-tight  box  without  a  top, 
in  which  a  masonrv  pier  is  built  and  sunk  on  to  a  prepared  fotindation. 
The  sides  are  detachable  from  the  bottom  (see  Fig.  30),  and  hence  may  be 
removed  after  the  pier  is  sunk  in  place,  and  used  in  the  constructioo  of 
succeeding  piers.  Guide  piles  are  usually  driven  to  assist  in  sinking  the 
caisson. 

The  following  rules  will  be  found  useful  in  proportioning  the  thickness 
of  planking  on  the  sides  of  the  caisson,  and  subject  to  hydrostatic  [>resBaire 
(taking  into  consideration  the  deflection  as  well  as  the  strength):  Hard 
woods:  For  hydrostatic  head  of  36  ft.  make  thickness  of  planking  m  inches 
equal  to  the  unsupported  span  in  feet;  for  4 J  ft.  head  make  the  thickness  ■ 
one-half  of  the  above;  for  mtermediate  heads  make  thickness  directly  pn>- 
P<**J»onal  between  the  two.  Soft  woods:  For  hydrostatic  head  of  SO  ft. 
make  ttuckncss  of  planking  in  inches  equal  to  the  unsupported  span  in  feet; 
^La:  ^*- «ead  make  the  thickness  one-half  of  the  above;  for  intermediate 
neads  make  thickness  directly  proportional  between  the  two.  j 


OPEN  CAISSONS.    PIERS,  877 

Is  proportionSng  the  uprights,  not«  that  for  deep  caisson  work  they 
may  be  braced  by  horizontal  struts  from  side  to  side  or  from  the  sides  to 
the  built  masonry  pier. 

For  the  construction  of  concnu  piers  in  open  caissons,  the  wooden  forms 
are  built  inside  and  separate  from  the  sides  of  the  caisson — cleaving  a  space 
between,  all  aroimd. 

For  lane  or  deep  piers  the  floor  of  the  caisson  may  be  of  two  or  three 
courses  of  12-inch  timber;  and  the  sides  may  be  plamced  with  two  thick- 
nesses of  planking  (the  inner  course  being  laid  diagonally),  or  they  may  be 
composed  of  crib  timbers  dovetailed  or  halved  tc)gether  and  well  drift- 
bohed.   Guide  piles  are  sometimes  driven  in  pairs  instead  of  in  single  line. 

Crib  Pkrf. — A  crib  pier  is  simply  a  wooden  crib  (see  page  869)  or  box 
constructed  of  logs  or  of  squared  timbers  framed  and  bolted  together,  and 
sunk  to  a  natural  or  a  prepared  fotmdation  bed,  by  filling  the  chambers 
with  gravel,  rock,  etc  A  crib  differs  from  a  caisson  in  that  the  latter  is 
supposed  to  be  water-tight.  The  crib  may  or  may  not  have  a  bottom. 
If  it  is  sunk  to  a  natural  bed  the  bottom  is  omitted  (which  is  the  usual 
form)  and  the  sides  are  projected  downward  a  few  feet  below  the  inner 
bracing  and  chamber  floors  so  as  to  cut  into  the  bed  and  get  a  good  stable 
bearing.  The  bottom  of  the  sides  of  the  crib  is  sometimes  extended  by 
bkxrkmg,  to  conform  with  the  natural  bed,  especially  if  the  latter  is  solid 
rock,  in  which  case  the  crib  is  often  bolted  thereto. 

The  crib  may  be  of  rectangular  form  (with  vertical  or  inclined  sides)  or 
it  may  have  a  V-end  up-stream,  and  perhaps  down-stream  also.  The  up- 
stream end  should  be  protected  with  angle  iron  or  steel  rail,  against  floating 
ice  and  k)gs.  In  framing  the  sides,  the  timbers  (say  12'xl2^  may  rest 
squarely  on  each  other  or  be  separated  a  few  inches;  and  framed  into  the 
cross  timbers,  say  every  four  feet  apart.  Interior  longitudinal  timbers  are 
also  framed  in.  about  the  same  distance  apart,  forming  vertical  chambers 
about  4-ft.  square.  The  bottoms  of  these  chambers  are  planked,  to  hold 
the  filling.  All  the  timbers  should  be  securely  drift-bolted  together.  If  the 
crib  is  designated  to  support  a  heavy  superimposed  load  the  chambers 
should  be  made  smaller  by  increasing  the  number  of  longitudinal  and 
transverse  timbers. 

The  crib  is  usually  sunk  direct Iv  on  the  bottom,  if  hard;  but  if  soft,  it 
is  sometimes  sunk  on  a  prepared  pile  foundation,  and  the  bottom  protected 
from  scour  by  a  deposit  of  rip-rap.  If  the  crib  projects  above  low  water  it 
3ecomes  merely  a  temporary  structtu^  as  the  timbers  are  exposed  to  rot. 
i^rib  piers  are  speciaUy  permanent  when  entirely  submerged  below  low 
eater  mark,  and  when  not  subject  to  the  attacks  of  the  iertdo  (see  page  860). 
U  sach,  a  crib  may  act  as  a  sub-fotmdation  on  which  may  be  constructed  a 
oncrete  or  stone  masonry  pier. 

PHe  Piers. — A  pile  pier  is  a  pile  sub-foimdation  projected  upward  to 
ipport  the  superstructtu%  direct.  It  is  at  best  a  temporary  affair  and 
icks  the  lateral  stability  of  masonry-  Pile  piers  and  abutments  are  used 
iTgely  in  every  new  country  where  timber  abotmds,  for  supporting  railway 
id  mshway  bridge  n>ans,  on  account  of  low  first  cost  and  rapidity  of 
tnstruction.  As  Bridge  Engineer  of  a  western  railroad  the  writer  con- 
ructcd  many  of  the  bridges  from  end  of  track,  as  the  latter  was  laid 
.usin£(  little  delay  in  the  tracklaying.  and  utilizing  the  construction  trains 
r  the  transportation  of  material  to  the  bridge  sites. 

A  siniple  form  of  bridge  pier  consists  of  two  or  more  rows  of  piles  (5  or 
3rc  in  a  row),  each  row  capped  with  a  12*xl4''  cap  dapped  \  inch  and 
ift -bolted  with  l''*^20'  drift  bolts.  On  top  of  these  caps,  cross-caps  are 
tft -bolted  to  receive  the  pedestals  of  the  span.  The  inside  rows  of  piles 
ly  be  projected  up-stream  in  the  form  of  a  V.  The  rows  of  piles  should 
sway -braced  with  4''xl2*  planking,  both  longitudinally  and  trans- 
"scly;  secured  at  the  ends,  to  piles  and  caps,  with  screw  bolts;  and 
iblc  spiked  at  intersections  with  piles.  The  outsides  of  piers  maybe 
-athed  all  aroimd  with  3-inch  or  4-inch  planking,  laid  longitudinally  with 
:t  joints.  The  nose  of  the  pier  may  be  driven  with  batter  piles  and 
atned  with  iron  as  a  protection  agamst  ice  and  logs.  Rip-rap  may  be 
»osite<l  around  the  piles,  to  prevent  scour;  also  pile  clusters  may  be 
rexx  up-stream,  as  ice  breakers  or  fenders. 

Tobtilar  VUn* — ^Under  this  heading  the  writer  desires  to  bring  to  the 
sntion  of  the  reader  a  variety  of  piers  which  are  tubular  in  form,  com- 


878  m.— FOUND  A  TIONS, 

posed  of  various  materiak*  sunk  by  variotis  prooeases,  and  occupying 
various  positions  when  in  place.  -  When  we  say  "tubular  in  form'*  we  mean 
that  they  are  composed  ot  a  tubular  "shell"  which  is  lowered  into  position 
and  filled  with,  say,  concrete  or  some  other  equally  serviceable  material. 

Shap€. — ^The  circular  section  is  the  one  most  commonly  iised  and 
hence  it  the  section  is  tmiform  throughout,  the  pier  is  cylindrical  in  form; 
if  the  section  decreases  uniformlv  upward  it  is  conical.  Often  two  cylinders 
of  different  diameters  (the  smaller  one  above)  are  joined  by  a  conical  frus- 
ttun.  They  are  usxially  placed  in  pairs  for  supporting  bridge  trusses,  being 
braced  to  each  other  by  a  web  plate,  or  by  horizontal  and  diagonal  bracing. 
The  center  pier  of  a  drawbridge  may  be  one  large  circular  cyundcr  or  may 
consist  of,  say,  6  or  8  separate  cylinders  surrounding  a  central  one  of  larger 
diameter,  all  braced  rigidly  together.  When  used  singly  for  center  piers  of 
draw  spans  the  oval  or  elliptical  section  is  sometimes  preferred. 

Materials. — Timber  staves,  say  from  6*^  to  12*  thick  and  planed  with 
sides  radial  have  been  constructed  in  the  circular  or  "barrel"  form  similar 
to  the  sides  of  a  water  tank  or  a  section  of  stave  pipe.  The  bottom  is  pro- 
vided with  an  iron  shoe  if  it  is  to  be  sunk  into  the  soil.  Instances  are  on 
record  where  a  masonry  shell,  as  of  brick,  has  been  used  as  a  tubular  pier 
and  sunk  into  the  ground  to  considerable  depths.  But  the  most  commonly 
used  materials  are  the  metals — cast  iron,  wrought  iron  and  steel.  Cast -iron 
shells  with  metal  1-in.  thick,  more  or  less,  and  with  flanges  inside  for  bolting 
the  sections  together,  present  a  smooth  exterior  surface  for  sinking,  and  are 
very  durable.  Wrougnt  iron  and  steel  are  generally  preferred.  The  metal 
is  from  i-in.  to  f-in.  thick  and  the  riveted  tubes  are  composed  of  sections 
from  6  to  6  ft.  in  length.  Both  butt-  and  lap  joints  are  used.  The  cylinders 
are  stiffened  at  the  top  with  an  outside  circular  angle-iron  and  the  top 
covered,  when  finished,  with  a  plate.  There  is  no  reason  whv  a  reinforced- 
concrete  shell  should  not  prove  economical  under  certain  tavorable  con- 
ditions. 

Sinking  in  Place. — ^The  method  of  placing  or  sinking  the  tubes,  or  their 
method  of  support  after  being  placed,  often  determines  the  name  of  the 

8ier.  For  instance,  a  metal  cylinder  encasing  a  cluster  of  piles  is  called  a 
ushing  cylinder  pier,  "Gushing  pier,"  or  Gushing  pile,  named  after  the 
inventor  of  the  system.  If  the  same  cylinder  Jor  usually  two  cylinders)  is 
set  on  a  timber  platform  resting  on  piles,  it  is  called  a  "platform  pier," 
platform  cylinder  pier,  or  simply  a  cylinder  pier.  If  it  is  sunk  in  the  grotmd 
It  may  receive  the  name  of  cylinder  pier,  or  "tubular  pier."  If  sunk  by  the 
pnetunatic  process  (compre^ed  air)  it  is  called  a  "pneumatic  cylinder." 

fmeumatic  tube,  or  pneumatic  pile.  Sinking  the  cylinder  in  place,  in  the 
oundation  bed,  may  be  accomplished  either  by:  (I)  Weighting  the  tube 
with  pig  iron  and  excavating  inside,  whence  it  descends  by  overcoming  the 
frictional  resistance*  on  the  sides;  (2)  Dredging,  when  in  water,  and  kMtding 
as  before;  (3)  Pneumatic  Process,  for  great  depth  xmder  water,  excavating 
in  a  "working  chamber"  under  compressed  air,  as  with  the  pneumatic 
caisson. 

Gushing  Piers. — Fig.  31  illustrates  two  styles  of  casing  and  two  styles  of 
piling  ordinarily  used  for  Gushing  piers.  The  wrought -iron  or  steel  cylinders 
(say  V  to  I*  metal)  are  usually  placed  after  the  piles  are  driven  and  bolted 
together,  but  sometimes  one  ot  more  bottom  sections  (6  to  6  ft.  lengths  each) 
are  set  up  and  riveted  together  in  place  and  then  the  piles  are  driven  inade 
of  them.  Gare  must  be  used  not  to  bulge  the  sides  in  driving.  After  the 
cylinders  are  set  and  connected  with  bracing  (at  least  at  the  bottom)  they 
are  filled  with  concrete,  deposited  in  layers  and  thoroughly  tamped  around 
the  piles.  Soft  silt,  logs,  boulders,  etc.  should  be  removed  (previously) 
from  the  bottom  and  the  cylinders  should  rest  on  as  firm  a  fotmdation  bed 
as  practicable.  The  horizontal  bracing  between  the  cylinders  may  be  com- 
posed of  two  channels  with  pin  connections  to  angles  or  bent  plates  riveted 
to  the  cylinders.  They  may  be  connected  top  and  bottom,  with  tie  plates 
or  lattice  bars,  or  be  reinforced  with  plates.  Two  10*  channels  are  common 
for  small  piers.  Adjustable  rods,  singly  or  in  pairs,  are  often  used  for  the 
diagonal  bracing,  but   stiff  members  are  preferred.      Howe  truss  bracing 

*  The  frictional  resistance  for  cylinder  piers  may  vary  from  about 
300  lbs.  per  sq.  ft.  in  mud,  up  to  as  much  as  say  1600  lbs.  ow  sq.  ft.  in 

gravel.  *^  DgfeedbyGOOgTe 


GUSHING  PIERS.   CY UNDER  PIERS. 


879 


;  been  vsed  considefably  in  the  West  where  timber  is  plentiful:  that  is. 
dS^n2lb»^  of  timber,  say  IQT  to  ir,  tied  witL  horizontal  rods, 
'and  upward.  The  web  brae-  ■  ,, 

is  usuaJJy  sheathed  on  both  |         fi^ 

s  with  Z-in.  planlcing,  projecting 
tie  beyond  high  and  low  water. 
of  the  best  forms  of  bracing  is 
»b  plate  connected  with  the 
dcrs  by  vertical  angles  riveted 
to.  Tne  web  is  stiffened  at  in- 
Isby  horizontal  angle  stiffen- 
Much  of  this  description,  espe- 
that  relating  to  the  bracing, 
3pJy  to  Platform  Piers,  which 
ext  be  described.  Plenty  of 
should  be  used  around  the 
to  prevent  scour.  Ends  of 
louid  be  cut  off  at  different 
yns. 

iorm  Cylinder  Mm.— Plat- 
ers are  constructed  by  driv- 
er more  rows  of  piles,  cap- 
•m  below  low  water  mark 
'  timbers  laid  longitudinally 
!  pier,  and  drift-bolted  to 
;  and  then  laying  a  plat- 
G*  to  12*  timbers  trans- 
;nd  spiked  to  the  caps, 
iders  are  then  placed  on 
oTtn  and    securely  bolted 


Pig.  31. 
;;i^rholS^S;i{ie  biuom  aange  angles.     Sonietimcs  the  ^ile« 
32)7  are  allowed  to  project_  upward  through  the  platform  into 
iers,    thus    forming  ^ 


ncrete   and       p 1  y' 

ling  piers"       I  tr 

y   masonry       I  i    _ 

oj  a  "grif.  ri  I  i   M  t-r 


form  and  Gushing  pier.    The 
re   filled    with  concrete   and 
iJar  to    the   "Gushing 
ibcd.      For  heavy 
[atform   consists   of  a  "gri 
nbcTS  (say  12'xl20   usually 

courses  or    more,  laid    at 

drift-bolted    together   and 

>  piles.    On  this  grillage  the 
laid. 

ic  Cylloder  Plera.— Instead 

ig    cylinder    piers   by  the 

cess    or    on    platforms,  as 

just    described,  they  are 

>  a  firm  foundation  bed 
J  the  material  from  the 
ow  the  bottom,  as  they  descend,  and 
ting  them.  If  the  tubes  are  sunk 
he  material  may  be  removed  often 
isingr  an  orange-peel  bucket  for  this 
;re  this  can  be  done  it  will  be  found 
al.  But  for  deep  foundation  work 
*  process  is  generally  used. 

Rracess. In  Fig.  33,  W  is  the  com- 

-Jcins    chamber,  connected  with  the 
s    air   lock.      When  the  workmen  or 

ttirovi«h.  the  lock  into  or  out  of  the 

oors  <x  axid    h  are  worked  like  the 

lock,    l>ecause  the  compressed  air 

2vtma.tic  process  is  meant  the  plenum 
lir    process.      The  vacuum  process  is 


\ 


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880  S0.^FOUNDATIONS. 

in  TV  is  at  a  higher  pressure  than  the  atmospheric  pressore.  The  compressed 
air,  sand  and  water  pumps  are  on  the  scow.  The  material  excavated  b 
raised  by  a  windlass.  When  the  air  lock  has  been  stmk  to  water  level, 
a  new  section  of  cylinder  is  inserted  and  the  air  lock  placed  above  it. 
Guide  piles  may  be  driven  to  guide  the  descending  cylinders. 

Pneumatic  Poundatioas. — ^The  main  essentials  for  the  prosecution  <^ 
deep  fotmdation  work  under  water,  for  large  bridge  piers,  are: 

(1)  The  pneumatic  caisson  (an  inverted,  air-tight,  "open"  caisson),  wfaidi 

forms  the  working  chamber,  and  supports  the  masonry  pier; 

(2)  The  crib,  a  cob-like  (sometimes  solid  grillage)  construction  of  timbeis 

above  the  pneumatic  caisson,  really  forming  a  part  of  it,  and  on 
which  the  masonry  pier  is  built ; 

(3)  The  coffer-dam  (sometimes  omitted),  built  on  top  of  the  crib  so  that 

masonry  can  be  laid  dry  even  when  below  the  water  level; 

(4)  The  pneumatic  tubes,  consisting  of  air  shafts,  air  locks,  etc.; 

(5)  The  machinenr  scow,  containing  boilers,  air  compressors,  engines,  and 

dynamos  for  lighting; 
(0)  The  excavating  tools,  as  picks,  shovels,  windlass  for  hoisting,  etc. 

(7)  The  sand  lift,  for  forcing  out  the  sand: 

(8)  The  mud  pxmip,  for  pumping  out  the  mud. 

Pig.  34  illustrates  the  first  four  essentials,  and  Fig.  33  shows  the  arrange- 
ment of  main  shaft  and  air  lock,  enlarged.  Note  that  the  air  lock  occupies 
(Pig.  M)  about  a  central  position  in  the  shafts  high  enough  to  be  out  of 
danger  from  flooding,  and  low  enough  to  be  economical.  After  the  pier  is 
sunk  to  bedrock  the  shafts,  as  well  as  the  woxking  chamber,  are  fiUeo  solid 
with  concrete. 

The  main  essentials  will  be  disctissed  briefly  in  detail,  as  follows:* 

The   Pneumatic    Caisson. — ^The     caisson  ^^ 

may  be  separate  from  the  crib,  as  shown  in  ^^       ^rm^'Vf 

Pig.  34,  in  which  case  the  roof  is  supported 
by  longitudinal  and  transverse  trusses  extend- 
ing through  the  working  chamber  (but  not 
shown  in  the  illustration).  But  the  more 
modem  method  is  the  combined  crib  and 
caisson,  by  which  means  the  crib  becomes  a 
part  (sometimes  the  whole)  of  the  truss  sys- 
tem, to  transfer  the  central  weight,  over  the 
chamber,  on    to   the  cutting   edges    of    the 

caisson,  during  the  process  of  sinking.    The    «•     o^      e  f>  i 

combined  crib  and  caisson  is  typically  reprc-  '^^'  84.— Separate  Caisson. 
sented  in  Pig.  35,  which  is  a  general  plan  and  longitudinal  section  of  the 
coffer-dam  and  caisson  for  South  Pier  of  Brooklyn  tower  foundation  oi 
the  new  East  River  Bridge  (Williamsbiu^)  New  York  City.  Pig.  36  shows 
a  vertical  section  of  same,  transverse  to  bridge  axis.  Pigs.  37  to  40 
show  details  of  caisson  for  North  Pier,  and  Pigs  41  to  43  show  details  of 
coffer-dam  for  either  pier. 

The  working  chamber  (Pig.  35)  was  7  ft.  high  and  divided  by  bulkheads. 
All  scams  were  calked  with  two  strands  of  oi^um ;  the  chamber  was  then 
lined  with  8-in.  plank,  the  joints  (and  spikes  to  fasten  them)  being  treated 
as  above,  and  then  painted  with  white  lead,  making  it  air-tight.  Fig.  40 
shows  the  roof  plan  of  caisson. 

The  Crib. — ^Where  a  crib  is  used  above  the  caisson  proper,  it  may  be  a 
solid  grillage,  or  it  may  be  divided  into  separate  vertical  compartments  to 
be  filled  separately  with  concrete  as  the  caisson  is  sunk;  or  the  compart- 
ments may  be  staggered  (offset)  vertically  or  open  so  the  concrete  filling  wfll 
^™^  one  monolithic  mass.  The  accompanjring  illustrations  (FigsTSO  to 
3»)  show  an  open  crib  of  the  latter  type. 

♦ii«  12^?  *U^»trations  of  Williamsburg  bridge  foundations  arc  adapted  from 
me  omcxal  working  drawings. 


PSEUMA  TIC  FOUNDA  TIONS.  881 


Piff.  35. — Combined  Crib  and  Caisson. 
C  Sec  pages  880  and  882.) 

Digitized  by  VjOOQ  IC 


882  Sl^.—FOUNDATIONS. 

The  Coffer-Dam, — ^The  cofiFer-dam  as  applied  to  the  pneumatic  fotrndo" 
tion.  is  really  an  open  caisson  (see  page  876)  resting  on  top  of  the  crib; 
or  it  the  crib  is  omitted,  it  rests  directly  on  the  pnetunatic  caisson.  Bat 
sometimes  the  coflfer-dam  itself  is  omitted,  as  when  the  masonry  is  buflt 
directly  on  the  crib  or  on  the  pneumatic  caisson,  and  its  top  kept  above  hi^ 
water  as  the  pier  sinks.  If  this  is  done,  no  coffer-dam  is  needea  to  shut  out 
the  water.  But  it  is  not  always  safe,  advisable,  or  possible  (economicaUy) 
to  construct  the  masonry  with  the  rate  of  progress  corresponding  with  tne 
sinking  of  the  pier,  and  hence  the  coffer-dam  is  employed.  It  is  usually 
erected  in  sections,  one  above  the  other.  Note  in  Pig.  85  the  substi- 
tuted bracing  against  the  masonry  as  the  latter  is  built  upward.  Figsl  41. 
42  and  43  show  the  bracing  in  detail. 


Section  tnanbversetoBndge^xis 

Fig.  36.— Combined  Crib  and  Caisson.  (See  page  880.) 
The  Freesirtif  Process. — Soft,  flowing  mud  and  quicksand  (especially) 
are  the  most  difficult  materials  to  be  encountered  in  sinking  foundations 
and  shafts,  excavating  for  wells,  or  driving  tunnels*  and  it  nas  naturally 
occurred  to  a  few  inventors  to  devise  means  for  freezing  this  material, 
somewhat  beyond  the  area  to  be  excavated  (leaving  frozen  walls  for  tem- 
porary lateral  support),  so  the  actual  excavation  can  be  made  by  ordinary 
methods,  as  with  the  pick  and  shovel. 

Any  practical  system  consists  essentially  in  driving  a  number  of  tubes 
into  the  ground  around  the  proposed  excavation,  and  a  little  beyond  its 
outer  limits.  These  are  calledi  the  "freezing  tubes"  and  may  be,  say.  from 
4*  to  10*  in  diameter.  They  are  closed  at  the  lower  end  and  should  pene- 
trate the  full  depth  of  the  soft  material.  Inside  of  these  tubes  are  ntted 
the  "circulating  pipes."  about  1*  to  IJ'  diam.,  with  lower  ends  open,  and 
extending  practically  to  the  bottom  of  the  tubes.  The  circulating  pipes  are 
connected  at  their  tops  by  a  "circulating  ring"  into  which  the  freeziog 
liquid  is  pumped ;  descending  through  the  pipes  into  the  lar^e  tubes  where 
by  absorbing  the  heat  from  the  surrounding  soil,  the  latter  is  frozen;  then 
emerging  from  the  tops  of  the  tubes  into  the  "collector  rings"  and  reservoir. 
From  the  reservoir  it  passes  to  the  refrigerating  machine,  and  then  to  the 
pump,  thus  completing  the  cycle.  Certain  modifications  of  this  process 
nave  been  introduced,  but  the  process  in  any  form  is  seldom  used.  The 
circulating  liquid  may  be  a  solution  of  calciimi  chloride  or  brine.  Ammonia 
!?^.  1  "5®  have  been  used  with  success,  with  magnesium  chloride 
circulating  medium. 


uTXjCCsE 

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884 


SO.^FOUNDA  TIONS. 


PlonofBulkheod 
Fig.  38.^Details  of  Caisson.    (See  page  880.) 


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886 


ya.— FOUNDATIONS. 


HUIfthn/ti^i 


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1  •     Cor  of  Top  Section 


*     Section 
•'-^'^  of  Walled- 
CorMlddleSed 


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l(fr|  Section  cf 
'j|G3i«)SonWblI 
1  *JatCbrnearTopHii|^ 


Sedioaad?  parallel  to  Bridge  Aw6     5 


Pig.  41.— Details  of  Ck>flerdam.     (See  pages  880.  882.) 

Digitizeaby 


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SO.—FOUNDA  TIONS. 


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OefQll  of  Ironitr  Anchor 
ingCoffer  Dom  toCoi*>«iOO 

pfmr/nkrixinnRiuA 
Fig.  43.— Details  of  Cofferdam.    (See  pages  880,  882.) 

Masonry  Piers.* — In  sectional  plan,  masonry  piers  are  designed  langely 
to  accommodate  the  superimposed  loadings.  Thus,  for  swing  bridges  thir 
center  pier  would  naturally  be  circular,  octagonal,  hexagonal  or  square — 
the  circle  being  the  most  economical  and  the  square  the  least.  If  the  draw 
is  center-bearing,  the  pier  may  be  of  solid  masonry;  if  rim-bearing.  it  may 
consist  of  a  circular  shell  to  support  the  rim  or  track,  and  perhaps  a  central 
pier  or  core;  the  rim  and  core  may  be  joined  by  steel  struts,  or  concrete 
webs,  radiating  from  the  latter;  or  the  radiating  struts  may  be  used  with 
the  central  core  omitted.  But  there  are  other  considerations  which  affect. 
more  or  less,  the  shape  of  the  center  pier,  namely,  the  sides  of  the  draw 
openings  for  the  passage  of  water  craft  should  be  straight,  or  in  continuous 
line  with  the  up-stream  and  down-stream  arms  of  the  draw  rest;  where  the 
water  way  is  limited  and  the  stream  is  swift,  the  pier  should  be  designed 
to  offer  the  least  resistance  to  the  flow,  to  ice  and  to  logs;  and  lastly,  for 
structural  reasons,  the  sectional  plan  should  be  simple. 


<l 


>  a 


3 


Fig.  44. 


Fig.  46. 


Fig.  46. 


<r=z>^=C>  C^O 


Fig.  47. 


Fig.  48. 


Fig.  49. 


For  ordinary  river  piers  supporting  the  ends  of  spans,  we  naturally 
choose  the  rectangular  section,  or  one  ol  its  modified  forms.  The  modi&ca- 
tions  are  based  on  such  sections  as  will  offer  but  moderate  resistance  to  1^ 
flow  of  the  stream  and  at  the  same  time  economize  in  masonry.  Pigs.  44 
to  49  show  various  sectional  plans  of  piers,  from  the  rectangular  to  the 
double  diamond.  The  right-hand  ends  are  "up-stream."  Note  that  Fig-  46 
shows  two  types  of  ends,  namely,  the  semi-circular  and  the  46**  pointed; 
also  that  the  down-stream  ends  of  Figs.  46,  46  and  47  may  be  either  square, 
or  symmetrical  with  the  up-stream  ends.  Figs.  48  and  49  illustrate  the 
saving  in  masonry  over  Figs.  46  and  46,  respectively,  by  comparing  the  fxill 

*  For  masonry  abutments,  see  Sec.  26,  Masonry,  pages  436  and  437. 


MASONRY  PIERS. 


889 


Hnes  with  the  dotted  (between  the  ends  of  the  latter) ;  and  although  not 
altogether  pleasing  in  appearance  they  may  be  (and  have  been)  used-  as 
concrete  piers  in  replacing  some  existing  cylinder  piers,  where  the  other 
forms  above  would  have  overloaded  the  pile  foundation.  Where  concrete 
piers  are  built  hollow,  or  cobbed  (with  cross  walls),  they  may  generally  be 
reinforced  with  steel  rods. 

Summarizing  in  general,  the  rectangular  type,  Pig.  44,  is  suitable  for  a 
land  pier;  Pig.  46,  with  semicircular  ends,  for  a  land  or  shore  pier;  and 
Fig.  47,  with  circular  arcs  (a.  b  and  c  being  equidistant),  for  a  channel  pier 
in  the  swiftest  current.  By  combining  47  with  46  (semicircular  ends),  using 
the  former  type  below  high  water  and  the  latter  type  above,  there  is  obtained 
a  pier  at  once  efficient,  economical  and  graceful  (see  Pig.  60),  and  suitable 
for  our  deepest  rivers  and  swiftest  currents. 


Fig.  60. — Practical  Type  for  High,  River  Piers. 

CorUtnts  of  Pigrs  by  Prismoidal  Formula. — Where  the  sides  of  the  piers 
batUred  in  straight  lines  the  average  sectional  area  mtdtipUed  by  the 
ical  height  will  give  the  cubic  contents.  The  average  sectional  area  is 
al  to 

I  (top  area +  4  times  middle  area + bottom  area). 
Por   an    ordinanr  masonry   pier  of  rectangular 
s-section.  Fig.  61,  let 
length  of  top  of  pier,  under  coping,  in  ft.; 
width  of  top  of  pier,  under  coping,  in  ft. ; 
height  of  pier  (between  coping  and  footing),  in 

batter  of  masonry  (horizontal-*- vertical). 


Pig.  61. 

L 

,  cubic  contents  in  feet— ^M+  4(w+6A)(/+feA)  +  (w+26/i)(/+26A)]. 

-  kiwi + 6/i(/ + w)  +  46«W] 

the  batter  is  1  in  24,  we  have,  since  &— A, 


contents  in  feet 


-*r^~4) 


hO+w) 


h* 


(1) 
.(2) 

.(3) 


4X6      '    6X8X9J 

in  yards         -  (above,  divided  by  3X  9) (4) 

«r  small  piers,  the  batter  is  usually  1  in  12,  or  f  i^  itfzljb  ^*^  ^*"^®  piers. 


Experience  With  Foundations  in  Boston  (By  T.  R.  Worcester.  Eng. 
W8,  Feb.  5,  1903). — Contains  a  formula  for  the  bearing  power  o£  piles: 
SmM{W  —  p)-hf:  where  5 —area  in  sq.  ft.  of  pile  in  contact  with  the  earth, 
ly  — load  in  lbs.  on  pile.  p»a  factor  for  bearing  of  pile  (  —  6000  to  6000  lbs. 
for  sand  and  gravel,  and  0  for  8ilt),/»a  factor  for  friction  of  soil  (—  100  to 

QAA  11 ..^    e*     j_    ..^e*.    .^>,4. :^i      oaa  *.^    caa  iu.     ^^_  .^    /«.     i-^    i i 


L 


800  SO.— FOUNDATIONS. 

EXCERPTS  AND  REFERENCES. 

Foundations  for  the  New  Singer  Building,  New  York  City  (By  T.  K. 

Thomson.    Trans.  A.  S.  C.  E.,  Vol.  LXIII). 

Pressures  on  Foundation  Footings  for  the  Walls  of  BuUdinn  (Eng. 
News,  Jan.  31,  1901). — Formulas  by  (3ias.  E.  Greene  and  Frank  T.  Daniels. 

Experience  With  Foundations  In  Boston  (By  T.  R.  Worcester.  Eng. 
News,  Feb.  5,  1903). — Contains  a  formula  for  the  bearing  power  of  piles: 

"      "'       '     '       •         "  •  '       ' arth, 

nbs. 

„ ,      _JOto 

300  lbs.  per  sq.  ft.  in  soft  material,  300  to  500  lbs.  per  sq.  ft.  in  mixed 
material.  400  to  600  lbs.  per  sq.  f t.  in  sand  and  gravel) ;  p  and  /  having  been 
determined  by  experiment. 

A  Novel  Tilting  PUe  Driver  (By  J.  H.  Baer.  Eng.  News.  Sept.  3. 1903) 
— Drawing  and  dimensions  of  driver. 

Concerning  the  Holding  Power  of  Anchor  BoUs  (Eng.  News.  Jan.  5, 
1905) . — References  where  data  can  be  obtained. 

A  Novel  Water  Jet  for  Driving  Piles  (By  S.  A.  Jubb.  Eng.  News, 
May  VI 905) .—Illustrated. 

Design  and  Construction  of  High  Bridge  Piers  of  Reinforced  ConcreCc 
(By  W.  M.  Torrence.    Eng.  News,  May  25,  1905).— Illustrated. 

Spread-Foundation  of  Reinforced-Concrete  for  a  Six-Story  Bolidiiig 
(Eng.  News,  July  20,  1905).— Illustrated. 

Construction  of  Cofferdams  (By  T.  P.  Roberts.  Paper,  Engrs.  See 
West.  Pa.,  May  23,  1905;   Eng.  News.  Aug.  10.  1905). 

New  Concrete  Covering  for  Timber  Piles  in  Teredo-Infested  Waters 
(Eng.  News,  Jan.  4,  1906). — A  pipe  armor;   illustrated. 

The  Design  of  High  Abutments  (By  W.  M.  Torrence.  Eng.  News. 
Jan.  11,  1906). — Illustrated;  with  quantities  and  costs. 

A  Form  for  Applying  Concrete  Armoring  to  Timber  Piles  (Eng.  News, 
May  24,  1906).— Illustrated. 

A  Method  of  Manufacturing  Reinforced-Concrete  Piles  by  Rolling 
(A.  C.  Chenoweth.  Eng.  News,  fuly  26,  1906). — Illustrated.  "The  cost  oi 
a  pile  61  ft.  lon^  and  13  ins.  in  dia.  is  about  960.  It  is  reinforced  to  carry 
its  own  weight  in  handling.  A  pile  30  ft.  long  could  be  made  and  dri\%a 
for  II  per  ft.,  so  the  price  of  a  60-ft.  or  100-ft.  pile  would  be  no  guide  for 
estimating  the  cost  oi  shorter  length." 

Allowable  Pressures  on  Deep  Foundations  (By  E.  L.  Corthell.  Eng. 
News,  Dec.  20,  1906). 

Telescoping  Leads  for  Pile  Drivers  (By  H.  P.  Shoemaker.  Eng. 
News.  Nov.  14,  1907).— Illustrated. 

Cost  of  Small  Concrete  Piers  (By  J.  H.  Ryckman.  Eng.  Rec.,  Jan.  it, 
1909). 

Reinforced-Concrete  Caissons:  Their  Development  and  Use  for  Break- 
waters. Piers  and  Revetments  (By  W.  V.  Judson.  Eng.  News,  July  8 
1909). — Illustrated:  Fig.  2  shows  method  of  computing  stresses  in  steel  in 
caisson  (for  breakwater)  shown  in  Fig.  1.  (Figs.  1  and  2  are  not  reproduced 
here.) 

Steel  Sheeting  and  Sheet-Piling  (By  L.  R.  Gifford.  Trans.  A.  S.  C.  £.. 
Vol.  LXIV.,  Sept.,  1909). — Illustrations  of  various  types,  with  discussioas. 

The  Design,  Manufacture.  Driving  and  Cost  of  Reinforced-Concrete 
Piles  (Eng.  Rec,  Mar.  27.  1906).— Two  papers  presented  before  the  Boston 
Soc.  of  C.  E.,  Sept.  16,  1908. 

Caisson  Disease  and  Its  Prevention  (By  Henry  Japp.  Trans.  A.  S.  C.  B.. 
Vol.  LXV.,  Dec,  1909). — Illustrations:  Medical  air-lock  used  in  the  East 
River  tunnels  of  the  Penna.  Tunnel  and  Terminal  R.  R.;  automatic  constant- 
rate  decompression  valve;  automatic  constant-rate  decompression  aund 
ventilating  valve;  air-lock  with  middle  decompressing  chamber. 

The  Sixth  Street  Viaduct.  Kansas  City  (By  E.  E.  Howard.  Trans.  A.  S. 
9  §'  ^?}:  LXV.,  Dec.  1909).— Illustrations:  Details  of  concrete  pier  No. 
^.  kaw  River;  general  details  of  steel  shoes  of  Kaw  River  bridge. 


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51.— WHARVES,  PIERS  AND  DOCKS. 

(References:    Foundations.  Sec.  50;  Breakwaters,  Sec  52.) 

Deflnltioas. — A  wharf  is  essentially  a  platform  structure  projection 
outward  from  the  shore,  and  alongside  of  which  water-crafts  may  be  rooored 
for  the  exchange  of  freight  or  passengers.  The  term  "quay"  is  applied  dis- 
tinctly to  a  wharf  which  skirts  the  shore,  and  runs  about  parallel  with,  and 
extends  to  no  great  distance  beyond,  the  shore  line.  A  pitr,  on  the  other 
hand,  is  a  wharf  which  projects  outward  from  the  shore  a  considetabk 
distance;  is  supported  usually  on  piles  or  piers;  and  hence  has  "open 
waterways"  beneath  the  platform. 

A  Dock  is  an  artificial  receiving  basin  for  water-eraft — for  loading,  un- 
loading, repairing,  etc.  It  need  not  necessarily  be  "closed."  A  commm 
form  of  dock  is  the  ."open"  basin  between  adjacent  wharves  or  piers;  thus. 
we  speak  of  "docking  '  a  vessel,  or  bringing  her  up  alongside  one  of  the 
wharves  or  piers.  Where  the  rise  and  fall  of  the  tide  is  excessive  and  would 
interfere  with  loading  and  unloading,  "closed"  docks  may  be  iised,  as  those 
at  London  and  Liverpool.  These  are  provided  with  gates  which  are  opened 
only  at  full  tide.  It  is  but  a  step  from  the  common  "closed"  dock  to  the 
Graving  Dock.* 

Foundations.— -One  of  the  most  important  features  to  be  conaklercd  in 
the  construction  of  wharves  and  piers  is  the  foundation.  The  kind  o: 
foundation  most  advisable  to  use  will  depend  upon:  (I)  the  uses  for  which 
the  structuire  is  designed;  (2)  the  nature  and  character  of  the  sofl  and 
foundation  bed.  and  depth  of  same;  (8)  the  currents,  tide  limits,  and  depths  i 
of  water;  (4) the  restrictions  by  the  Government,  State  (and  City)  as  called 
for  by  the  established — 

Pierhead  and  Bulkhead  Lines. — Piers  with  open  waterways  may  be 
constructed  to  the  pierhead  lines,  while  wharves  of  solid  construction  may 
be  built  only  to  the  bulkhead  lines.  Where  two  sets  of  lines  exist,  one  set 
established  by  the  Government  and  the  other  set  by  the  State,  the  set 
nearest  the  shore  is  supposed  to  govern.  The  U.  S.  Engineers  have  author-  j 
ity  to  interpret  the  true  position  of  established  Government  harbor  lines, 
and  no  encroachment  is  allowed  beyond  without  the  approval  of  the  Sec'y 
of  War.  Such  approval  may  often  be  obtained  to  meet  certain  exigenaes 
in  local  conditions. 

Construction  Methods. — Common  methods  of  wharf  construction  inside 
of  bulkhead  lines  are:  (a)  By  sinking  timber  cribs  filled  with  stone,  around 
the  sides  (inside)  of  the  wharf  area,  and  then  filling  in  behind  with  earth, 
perhaps  by  dredging  from  the  outside,  (b)  By  constructing  wharf  walls  c( 
stone  or  concrete  masonry,  instead  of  sinking  cribs,  and  filling  in  behind 
them.  C^are  should  be  taken  to  have  these  walls  rest  on  a  good  sub-founds- 
tion  or  foundation  bed.  that  is,  either  natural  or  artificially  prepared,  as 
they  are  really  retaining  walls  of  the  most  treacherous  kind:  the  earth 
backing  is  saturated  and  has  a  fiat  angle  of  pcposc,  and  when  the  wharf  is 
loaded  the  overtuminjj  force  may  be  increased  greatly;  moreover,  the 
resistance  of  the  wall  itself  to  overturning  is  decreased  considerably  when 

*A  Graving  Dock  (commonly  called  a  Dry-dock)  is  an  (excavated  i 
hesin  into  which  a  vessel  can  be  floated,  the  gates  closed,  the  water  forced 
out,  and  the  hull  exposed  for  inspection,  repairs,  cleaning,  painting,  etc  I 

iSee  Paper  No.  1016.  Trans.  A.  S.  C.  E..  Jtme.  1906,  entitled  "A  New  Gravirf 
)ock  at  Nagasaki,  Japan.")  A  Floating  Dock  (commonly  called  a  Floating 
Dry-dock)  is  what  its  name  implies  and  need  not  be  defined.  (See  Paper 
No.  1042,  Trans.  A.  S.  C.  E.,  June.  1907.  entitled  "The  Naval  Floating  Dock 
—Its  Advantages,  Design  and  Construction,"  bjr  Leonard  M.  0>x.  Mr.j 
v-ox  defines  the  "Marine  Railway"  and  the  "Lift  Dock^  aa  additkraal 
forms  of  Repair  Docks.)  J 

ggj  Digitized  by  CiOOgle  I 


CONSTRUCTION  METHODS.  B98 


nerstd  in  waitr.    It  is  a  good  plan  to  back  such  walls  with  stone  spalls 
slag,  before  filling,     (c)  By  any  of  the  n«   '     " 
)pen  piers,  which  will  now  be  explained. 


slag,  before  filling,     (c)  By  any  of  the  methods  tised  in  the  construction 
*  •  •    urill  *  •  •      • 


Piers  are  usually  oC  timber  construction — at  least  the  floors — supported 
piling.  The  latter  may  be  timber-,  screw,-  disk-,  concrete-  or  cylmder-. 
iter  Pila  are  most  commonly  used.  They  are  driven  in  rows  (some  of 
piles  are  frequently  driven  slanting  to  give  lateral  stability),  and  capped 
1  say  12*xlr  timbers  thoroughly  drift-bolted  to  piles.  The  floor  may 
:omposcd  of  one  or  more  thicknesses  of  3*  or  4'  planking  laid  on  say 
14'  stringers  resting  oft  the  caps  and  drift -bolted  or  toe-nailed  thereto, 
uard  from  6'x8'  to  KfxXT^  surrounds  the  edge  of  the  pier.  Snubbing 
5  arc  driven  where  required  near  edge  of  pier,  and  allowed  to  project 
ve  the  floor  level.  Fender  piles,  singly  or  in  cluster,  are  driven  usually 
he  comers  of  piers  to  receive  the  shock  of  vessels  making  landing.  The 
J  of  the  pier  are  thoroughly  sway-braced  with  S^xlO*  to  4^x12*  planking. 
?re  the  soil  is  sandy,  screw  piles  or  disk  piles  are  sometimes  employed, 
long  iron  pier  at  Coney  Island  is  supported  on  disk  piles  with  disks  24' 
md  9*  thick,  the  wrought-iron  shafts  (tubes)  being  8f'  outside  diameter. 
I  piles  are  calculated  to  support  5  tons  or  more  per  sq.  ft.  of  disk  area. 
r  are  sunk  with  the  water  jet.  Where  timber  piles  are  subject  to  the 
:Jcs  of  the  ioredo  nevalis*  (see  page  360)  the  expense  of  repairs  is  con- 
able,  hence  concrete  piles  and  cylinder  piles  are  often  employed. 

•erry  Slipt  and  Bridge  Aprons. — A  ferry  slip  is  a  dock  for  a  ferry  boat; 
tridM  or  apron  being  an  adjustable  roisulway.  for  rise  and  fall  of  tides, 
id  from  the  ferry  in  the  slip.  Probably  the  largest  ferry  boats  in  the 
1  are  those  plying  between  San  Francisco  and  Oakland,  Cal.  Some  of 
lips  in  New  York  City  are  designed  for  boats  260  ft.  upward  in  length, 
iremendous  force  with  which  these  boats  sometimes  strike  the  slips  in 
ng.  especially  during  fc^gy  weather,  requires  the  latter  to  be  constructed 
e  strongest  manner  compatible  with  the  requisite  elasticity,  and  im- 
iments  are  constantly  being  made  in  their  design.  Local  conditions 
be  studied  for  each  particular  case,  as  those  which  flt  one  locality 
not  fit  another. 

he  throat  or  shore  end  of  the  slip  is  usually  made  to  conform  closely 
the  shape  of  the  ferry  boat  for  say  i  to  i  its  length,  and  from  thence 
es  outward  more  or  less  to  the  mouth.  Sometimes  one  wing  only  is 
ied  beyond  the  middle  in  order  to  facilitate  landing,  tmder  certain 
ions  of  wind  and  tide. 

le  foUowing  illustrations  were  prepared  by  the  Dept.  of  Docks  and 
5.  New  York  City,  Chas.  W.  Staniford,  Engineer-in-Chief,  and  were 
icd  the  writer  through  the  courtesy  of  Mr.  S.  W.  Hoag,  Jr.,  of  the 
Bering  Department. 

39th  Strbbt  Ferry.  Manhattan: 

(a)  Plans  of  Crib  with  Dolphin : 
J.  1. — General  Plan  of  Outer  End  of  West  Pier  with  Dolphin, 
rs.  2  to  7. — General  Details  of  Crib. 

(b)  Plans  of  Ferry  Dolphin: 
.  8. — ^Part  Plan  of  Ferry  Dolphm. 
s.  9  to  18. — General  Detail  of  Ferry  Dolphin. 

(c)  Plans  of  Ferry  Bridge. 
.  14. — Part  Plan  and  Cross-Section  of  Bridge. 
5.  15  to  17. — General  Elevation  and  Details  of  Bridge. 


le  pilins  along  the  Seattle  (Wash.)  water  front  is  often  rendered 
ry  this  sea-worm  in  two  or  three  years'  time,  being  almost^mpletely 
ombed.  ^  ^    ^ 

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Fig.  8. — Part  Plan  of  Ferry  Dolphin. 
(For  Details,  see  Figs.  9  to  13,  on  following  page.) 


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61.— WHARVES,  PIERS  AND  DOCKS. 


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(For  Elevation  of  Bridge  and  Details,  see  Figs.  15, 16  and  17, 
on  following  page.) 


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900  &l.— WHARVES,  PIERS  AND  DOCKS. 

EXCERPTS  AND  REFERENCES. 

The  U.  S.  Steel  FloetiM  Drv-Dock  for  Cavtte,  PhUlppine  IslaiMfe  (Br 

J.  S.  Schultz.    Eng.  News,  Dec.  10,  1903).— Illustrated. 

Novel  Steel  Pier  Construction  at  Lome,  Africa  ("Le  Genie  Civil"  of 
July  15,  1906;   Eng.  News,  May  24.  1906).— Illustrated  structural  details. 

The  Terminal  Station  and  Ferry  Hoose  of  D.,  L.  &  W.  R.  R~  at 
Hoboken  (By  C.  C.  Hurlbut.  Eng.  News,  Sept.  20,  1906).— Sixteen  illus- 
trations. 

Steamship  Terminal  With  Concrete  Pile  Pien  at  Bmswlck,  Oa., 
A.  &  B.  Ry.  (Eng.  News,  Dec.  20.  1906).— Illustrated. 

Dock  Walk  at  the  Port  of  Koenifsber^ .  Pnuaia  (Eng.  News.  Aug.  22. 
1907). — Illustrations  showing  methods  of  driving  piles,  and  bracing. 

New  Piers  for  Transatlantic  Steamships.  Chelsea  Improvemeat.  N.  Y. 
City  (Eng.  News.  Jan.  14,  1909).— Twelve  illustrations  and  double-page 
insert. 

Lixht  Reinforced-Concrete  Wharf  Construction,  Madras  Harbor,  India 
(Eng.  News,  Nov.  11,  1909). — Construction  comprises  reinforced -concrete 

giles  (reinforced  with  1-in.  rods)  driven  8  ft.  apart  to  a  depth  of  8  ft.  below 
ottom  and  tied  back  to  an  anchor  by  means  of  30-lb.  old  rails  completely 
encased  in  concrete.  Back  of  these  piles  are  sunk  reinforced -concrete  slabs 
to  a  point  below  river  bottom,  the  slabs  acting  as  a  retaining  wall  to  hold 
back  the  earth.  The  tops  of  the  piles  are  joined  together  by  an  arch  con- 
struction topped  by  a  coping  of  old  rails.  A  1  :  2  :  4  concrete  was  used  for 
all  the  work.     Illustrated. 

Reinforced  Concrete  Wharf  of  the  United  Fruit  Company,  Bocas  dd 
Toro,  Panama  (By  T.  H.  Barnes.  Trans.  A.  S.  C.  E..  Vol.  LXVI..  Mar.. 
1910). — Illustrated,  with  cost  data. 

Illustrations  Useful  for  Reference: — 

Description.  Bng.  News. 
Standard  car-ferry  transfer  bridge                                                Dec.  19,  1901. 

Large  ore  dock  of  the  C.  &  N.-W.  Ry.,  Escanaba,  Mich.  July  80.  '03. 

New  graving  dock  at  Kobe,  Japan  Sept.  24.  *03. 

Omcrcte  dry-dock  at  Kiel,  (Germany  Dec.     3,  '03. 

Details  of  Rcinforced-concrcte  crib-work  wharf  May   26.  '04. 
Details  of  standard  pile  pier,  Dept.  Docks  and  Perries.  N.  Y.     May   18.  '05^ 

Elevation  and  plan  of  fireproof  wharf,  Tampico,  Mex.  June     8.  *0i 

Solid  pier  construction  in  Baltimore  harbor  July   19.  '06. 

Plan  and  details  of  reinforced-concrete  pier,  Atlantic  City  July   26.  '06 

Reinforced-concrete  retaining  wall  and  quay  April  20.  '09. 

Design  of  Ckmcrete  Naval  Dry-Dock,  Pearl  Harbor,  Hawaii  Dec.     9.  '09 

Rein.-conc.  piers  at  U.  S.  Naval  Station.  Philippine  Islands  Dec   15,  '10 

Bng.  Rec. 

Walls,  girders,  ties,  anchorage,  etc.,  Baltimore  piers  May     8.  *09. 

Details  of  ferry  platforms  and  bridges,  C.  R.  R.  of  N.  J.  May   22,  '09. 

Sewells  Point  coal  pier,  Virginia  Ry.  Feb.     6,  '  10. 

Sea- Wall  bulkheads  in  connection  with  streets  and  buildings  Feb.   2ft,  '10. 

Cross-section  of  deck  of  rein.-conc.  deck  of  ore  dock  Nov.  12,  *10. 


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52.— BREAKWATERS. 

Ocfieral  Dliciisslon. — ^This  subject  forma  one  of  the  most  important  in 
River  and  Harbor  Improvements.  The  term  "breakwater"  is  quite  distinct 
from  the  so-called  "reaction  (curved)  breakwater,"  which  latter  belongs 
rather  under  the  head  of  Jetties  (page  905)  and  might  be  termed  a  "break- 
water" jetty  or  "lee"  jetty. 

A  Breakwater  is  an  arm-like  construction  projected  in  the  water  and 
des^ned  to  form  an  artificial  harbor  for  sea-going  crafts.  The  foundation 
is  stone,  rip-rap,  gravel,  etc.,  either  deposited  loose  or  stmk  in  timber  cribs. 
Where  the  timber  cribs  are  used  they  are,  for  permanent  construction, 
projected  upward  only  to  within  about  2  ft.  of  low  water,  thus  forming  a 
tahstnicture  on  which  the  superstructure  is  built.  The  superstructiu^*  is 
best  constructed  of  stone-  or  concrete  blocks  weighing  from  1  to  10  or  15 
tons;  or  of  concrete  deposited  en  masse.  If  the  bottom  is  soft  or  silty,  a 
trench  should  first  be  dredged  on  the  line  of  the  breakwater,  removing  all 
■oft  material  liable  to  cause  trouble  by  excessive  settlement.  This  method 
will  generally  be  more  satisfactory  than  the  one  sometimes  employed  of 
using  a  gravel  core  in  the  breakwater  and  trusting  permanent  settlement 
to  take  place  as  the  breakwater  is  bviilt  up.  Although  the  latter  method 
has  proved  successful  in  some  instances,  there  are  records  of  utter  failure 
during  the  first  heavy  storm  after  completion  of  the  work. 

For  an  excellent  discussion  of  breaJcwater  construction,  see  Paper  No. 
971,  Trans.  A.  S.  C.  E.,  June,  1904,  entitled  "The  Breakwater  at  Buffalo, 
N.  Y.,"  by  Emile  Low.  See  also  Paper  No.  15  of  Transactions,  Vol.  IV— 
Part  A,  page  824,  entitled  "The  Delaware,  Sandy  Bay  and  San  Pedro 
Breakwaters,"  by  C.  H.  McKinstry.  Considerable  valuable  data  on  break- 
water construction  is  contained  in  Vol.  VIII — Part  4,  Annual  Report  (1904) 
of  Chief  of  Engineers,  War  Department  (U.  S.).  The  following  illustrations 
are  from  these  sotirces: 


Fig.  1.— Buffalo  (N.  Y.)  Breakwater. 
Types  off  Breakwaters. — Pig.  1  is  a  plan  of  minimum  cross-section  for 
"eplBCXDg  the  decayed  timber  superstructure  of  a  portion  of  the  old  Buffalo 
treakwater,  with  a  new  superstructure  of  concrete  and  stone  "shell  con- 
traction." The  maximum  cross-section  is  32  ft.  on  the  harbor  side  and 
2  ft.  on  the  lake  side,  making  a  total  width  of  78  ft. 


Fig.  2. — Sandy  Bay  (Mass.)  Breakwater. 
Pis.  2  is  a  plan  of  the  Sandy  Bay  (Mass.)  breakwater,  showing  the  section 
3pted  in  1002. 

*  The  use  of  timber  cribs  projecting  above  high  water  is  becoming  more 
I  rtuare  obsolete.    But  see  Fig.  4.  f^r^r^rt]^ 

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903 


a.—BREA  KWA  TERS. 


FiK-  S  is  a  cross-section  of  the  Delaware  Bay  c 
ftnictcd.  1897-1901.    The  total  length  of  superstnid 


Pig.  3.— Delaware  Bay  Outer  Breal 
139.43  per  lin.  ft.;  toUl  length  of  subetructure.  8( 
per  lin.  ft. 


/ibe* 


Fig.  4.— Oswego  (N.  Y.)  Outer  Brei 
Fif?   4  is  a  cross-section  of  the  Oswego  (N.  Y.)  oi 
crib),  constructed.  1884-1900. 

Averages  Pbr  Lineal  Foot  for  Fici 

Volumeslj 
Cu.Yds. 


Materials. 


Cross -sect  ion  above  mean  low  water. 
Cross-section  below  mean  low  water. 
Total  cross-section  above  sea  bottom 

Rubble  stone 

Capping  stone 

Cost  of  superstructure 

Cost  of  substructure 

Total  cost 

(Approximate  voids:  rubble,  39% 
capping  stone,  10%.) 


Cross-section  above  mean  lake  level. 
Cross-section  below  mean  lake  level. 
Total  cross-section  above  lake  bottom 

Timber 

Stone ■ 

Cost  of  old  structure 

Cost  of  foundation 

Cost  of  new  superstructure 

Total  cost  2970  ft 

Total  cost  570  ft ^^. 


20  37 
106  30 
128  67 
120  14 
8.53 


7.6 
29.81 
37.31 

7.44 
28.20 


..     NpUble  Breakwaters. — ^The  following  table  wai 
the  direction  of  Maj.  Theo.  A.  Bingham.  Corps  of  E 


STATISTICS  OF  BERAKWATERS. 


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904  S2.— BREAKWATERS. 

EXCERPTS  AND  REFERENCES. 

The  Sea  Wall  of  La  Piuita«  Havana  (By  W.  M.  Black.  Eng.  News. 
Nov.  14.  1901). — Illustrated:  Pig.  1  shows  section  through  steps  of  seawall: 
Fig.  3  shows  section  of  concrete  toe  with  projecting  stones  to  check  two.  of 
waves.  The  article  gives  the  composition  of  the  various  concretes  used. 

The  Materials  for  the  Concrete  of  the  Buffalo  Breakwater  (By  Smile 
Low.  Eng.  News.  Sept.  11,  1902). — ^The  gravel  and  sand  were  obtained 
from  the  bed  of  the  Niagara  River  by  means  of  a  so-called  * 'sand -sucker." 
described  as  follows:  The  vessel  consists  of  a  wooden  hull  132  ft.  long. 
30.2  ft.  beam  and  7.2  ft.  depth.  The  propelling  machinery  consists  of  a 
double  non-condensing  engine  w^ith  a  steam  cylinder  14*  dia.  and  IC  stroke. 
The  boiler  is  allowed  to  carry  30  lbs.  steam  pressure.  At  the  bow  is  located 
a  ccntrifugalpump,  driven  by  two  direct -connected  engines  with  cylinders 
9*  dia.  and  9^  stroke.  The  suction  pipe  is  12*  dia.,  and  is  also  a  discharge 
oipe.  Located  on  the  deck  of  the  scow  is  a  large  wooden  box,  86'  long. 
24'  9*  wide  and  3'  10*  deep,  divided  into  two  compartments  by  wooden 
bulkheads  4'  thick.  The  capacity  of  the  box  is  325  cu.  yds.  The  water 
charged  with  gravel  and  sand  is  pumped  from  the  river  bed  (generally  12^ 
deep)  and  flows  into  the  flume,  with  screens  of  \'  wire  spaced  J*  apart  in 
frames  IKx  24".  Five  tables  are  given  showing  various  properties  of  the 
aggregates,  and  data  regarding  the  manufactured  concrete  blocks. 

Wave  Action  in  Relation  to  Engineerinf  Structures  (By  D.D.  Gaillard. 
Professional  Paper  No.  31  of  the  C^rns  of  Engrs.,  U.  S.  A.:  En^.  News. 
Feb.  23,  1906). — Paper  deals  with:  Deflnitions  and  theory;  Height  and 
Length  of  Waves;  Reduction  in  Height  of  Waves  on  Passing  into  a  Closed 
Harbor;  Velocity  of  Waves;  Per  C^nt  of  Wave  Above  Water  Le\'el;  Depth 
in  which  Waves  Break;  Dynamometer  Tests  of  Wave  Force;  Comparison 
of  Theoretical  Wave  Force;  etc.    Tables  and  formulas  arc  given. 

Reinforced-Concrete  Caissons  for  Breakwaters  (By  W.  V.  Tudson.  Eng. 
News,  July  8,  1909). — Illustrated;  plan  of  caisson  and  method  of  computing 
stresses.  Estimated  cost  of  Algoma  breakwater,  if  built  of  stone-filled 
wooden  cribs,  placed  on  pile  foundation  and  capped  with  a  standard  con- 
crete superstructure  (the  cheapest  permanent  form)  was  tl06.18  per  lin. 
ft.  Estimate  for  caisson  breakwater  was  1103.74.  Actual  cost  of  «^^«^>" 
breakwater  was  $75. 67 -I- $2. 62  per  lin.  ft. 

Illustrations  of  Breakwaters,  for   Reference: — 

Description.  Eng.  News. 

Plans  of  crib  breakwater  at  Welland  (^anal  entrance  May  15,  1902. 

Plans  of  concrete  breakwater  at  Bufl^alo  (T.  W.  Symons)  May   29,  '02. 

Section  and  views  of  Cleveland  breakwater  Mar.  23,  '07. 

Concrete  breakwater  at  Harbor  Beach,  Mich.  Mar.  28,  *07. 
Sections  of  breakwaters  in  fishery  harbors  of  Scotland;  Coet    Dec.   22,  '10. 


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53.— JETTIES. 

Qcocral  Dtsctution. — At  the  mouths  of  navigable  rivers  where  there  is 
crois-current,  whether  the  river  empties  into  another  or  into  the  sea,  sand 
bars  are  liable  to  form,  shoaling  the  water  and  obstructing  navigation 
The  cost  of  dredging  deep-water  channels  through  these  bars  and  main- 
taining them  is  sometimes  enormous,  hence  jetties  are  often  constructed  to 
reduce  this  annual  expense. 

Jetties  are  structures  designed  to  change  the  shape  and  velocitv  of  the 
moving  volume  of  water  so  that  it  will  do  the  work,  in  part  at  least,  of 
deefjening  the  channel.  The  voltmie  is  contracted  laterally  and  deepened 
vertically,  and  the  velocity  is  increased,  thereby  cutting  out  the  channel 
and  canyinfi^  the  material  further  on,  some  of  it  out  to  sea. 

•Twin"  jetties  are  formed  by  two  jetty  arms  converging.  One  is  called 
the  "windward"  jetty  and  the  other  the  lee"  jetty.  The  windward  jetty 
is  placed  on  the  side  of  the  channel  on  which  the  sand -drift  predominates; 
the  "lee"  jetty,  on  the  other  side.  As  twin  jetties  are  very  expensive  it  is 
customary  on  large  projects  to  build  one  j^ty  first,  watch  the  effect  of 
scouring  of  channel,  shifting  of  sand  bars,  etc.,  and  then  with  this  addi- 
tional data  plan  the  second  arm.  In  selecting  the  single  jetty,  sometimes 
the  windward-  and  sometimes  the  lee-  jetty  is  chosen.  The  argument  in 
favor  of  the  latter  is  that  the  channel  is  practically  confined  from  further 
movement  "leeward,"  as  the  sand  drifts  from  the  "windward"*  and  is  swept 
cm  or  carried  away  by  the  current;  whereas  with  the  single  windward 
jetty  the  channel  may  fluctuate  in  position  instead  of  remaining  permanent 
and  deep.    Each  particular  case  requires  a  special  solution. 

The  "reaction  breakwater,"  so-called,  is  a  single  S-shaped  jetty  de- 
signed to  increase  the  scour  by  creating  a  ccntrifufi[al  force  to  the  current, 
thereby  narrowing  the  volume  laterally  and  increasing  the  velocity,  similar 
to  the  natural  winding  cuttings  in  river  beds.  The  effect  of  this  type  of  jetty 
has  not  fully  been  demonstrated,  and  will  be  watched  with  much  interest. 

Jetty  Constmctlon. — ^Most  of  the  jetties  now  built  are  of  rock  fill,  that 
is,  rubble  stone  dumped  from  scows  or  trains.  The  trains  are  run  out  on 
temporary  pile  trestles  constructed  along  the  line  of  the  jetty.  The  material 
is  paid  for  by  the  yiutl  or  ton.  Brush  and  rock  are  sometimes  used  but  the 
use  of  brush  has  practically  given  way  to  rock  alone,  especially  on  large 
work,  on  account  ot  the  action  of  the  teredo  and  liability  to  unequal  settlement. 
Small  jetties  and  bank  protections  of  streams  are  often  constructed  by 
driving  two  rows  of  piles,  facing  them  on  the  inside  with  planking,  bolting 
and  bracing  the  rows  together,  and  filling  the  space  between  with  brush 
and  rocJc.  The  brush  is  often  tied  together  m  bundles  or  fascines  (see  Pig.  1). 
The  bottom  layer  is  placed  on  the  bed 
of  the  stream  transversely  to  the  di-  iK'/p" 

i«ction  of  the   jetty,  and   on    these  f<-  •  •  -  -       -  -        /^  t|^ 

are  placed  other  fascines  laying  longi-   "-*  ^ 

tttdmally  between  the  piles.    Between 

the  fascmes  and  the  bottom  of  the 

side     planking,  t    boxes    filled    with  v     i      t>      • 

rock  are  sunk  between  the  piles;  and  *^^-  *• — t^^ascme. 

the  balance  of  the  space  above,  between  the  planking,  is  filled  with  rock, 

formixig  a  pile  crib.    This   type  is  often  used  for  the  protection  of  bridge 

abutments,  and  frequently  as  real  jetties  in  deepening  the  channeL 

EXCERPTS  AND  REFERENCES. 

Tb«  Improvement  of  the  Eatrance  to  Cumberiand  Sound,  Qeorgia 
ajul  Florida  (By  J.  H.  Bacon.  Eng.  News,  May  12,  1003). — Shows  general 
plans  of  the  jetty-work  improvement;  table  of  official  record  of  contract 
Work;    and  table  of  sand  movement  at  Cumberland  Sound. 

Complicated  Reinfforced-Concrete  Jetty-Head,  Thames  Haven,  Eng^ 
land  (Ens.  News,  April  22,  1M9).— Blustrated. 

*  Tlie  terms  "windward"  and  "lee"  relate  to  the  sand  drift  and  not  to 
he  direction  of  the  wind,  although  they  are  frequently  in  the  same  direction. 

t  The  side  planking  consists  of  plank  spiked  or  bolted  to  the  inside  of 
>iles  and  laid  as  far  below  low  water  as  practicable.  r^r^r^n\o 

Digitized  by  VjOOv  IC 

906 


54— EARTHWORK.* 

Uncertain  Cost. — In  any  engineering  work  the  chance  of  an  accurate 
estimate  of  the  cost  diroiniimes  as  earthwork  becomes  the  important  item: 
for  in  the  purchase  of  materials  and  supplies  a  fairly  correct  estimate  may 
be  had  in  advance,  but  where  the  labor  factor  enters  largely  in  a  dirtct  teay 
great  uncertainty  exists.  Especially  is  this  true  where  the  character  of 
work  to  be  performed,  as  in  grubbing,  clearing,  and  "earthwork,"  is  proble- 
matical, the  quality  of  labor  uncertain,  and  the  rate  of  wages  tmstable. 

Before  making  an  estimate  the  engineer  should  consider:  (1)  the  kind 
and  quality  of  material  to  be  handled,  by  diggins  test  pits  and  by  boring: 
(2)  the  most  approved  method  of  doing  the  work;  (8)  the  availability  of 
good  contractors,  superintendents,  and  foremen;  (4)  the  quality  and  price 
of  labor.    These  will  be  considered  in  the  order  mentioned. 

Kind  and  Quality  of  Material. — ^No  contract  should  be  let  or  woric 
started  before  full  information  as  to  the  character  of  the  material  has  been 
obtained.  The  cost  of  pits  and  borings  is  merely  incidental.  Not  only  are 
they  a  practical  guarantee  of  the  correctness  of  the  estimates  but  they  give 
timely  information  necessary  for  the  pruchase  and  proper  disposition  on 
the  work  of  the  necessary  tools  and  machinery.  The  writer  has  seen  steam 
shovels  delivered  where  nothing  short  of  dynamite  could  be  used,  and  the 
expense  of  such  changes  and  incidental  delavs  is  enormous.  For  trendi 
work,  test  i)its  will  generally  determine  in  advance  whether  shoring  plank 
will  be  required,  so  they  can  be  ordered  in  time.  One  of  the  first  things  to 
look  for  is  the  material  "hard-pan,"  "cemented  gravel"  or  "glacial  drift,'* 
as  it  is  variously  termed.  When  not  classified  it  is  a  source  of  contention. 
Lying  beneath  the  soil,  unseen,  it  is  often  from  3  to  5  times  as  expensive 
to  remove  as  is  the  material  above,  especially  in  trench  work  where  it  can- 
not be  loosened  economically  or  handled  with  the  steam  shovel.  It  comes 
between  the  earth  and  the  loose  rock  or  the  sand-rock  classifications  and 
should  be  mentioned  in  specifications.  Stiff  clay  is  sometimes  as  hard  to 
work  as  many  of  the  hard-pans,  and  some  idea  should  be  had  of  the  propor- 
tionate amovmt  of  this  material.  If  it  is  large  the  estimate  of  cost  of  *  earth" 
should  be  raised  accordingly.  Loam  is  about  the  easiest  material  to  ^xovel 
by  hand,  while  sand  and  gravel  are  more  difficult.  Loose  and  solid  rock 
are  considered  under  the  next  subject  heading  (Section  66).  Sandrodc  is  a 
partially  formed  sandstone.  It  may  be  in  various  degrees  of  hardness,  axid 
should  receive  a  separate  classification. 

Approved  Methods  of  Handlinf . — Space  will  permit  only  of  the  briefest 

mention  of  the  methods  employed,  simply  to  recall  them  to  the  attentsoo 
of  the  reader. 

Clearing  and  Grubbing. — After  the  trees  are  cut  down  the  stumps  are 
usually  blown  out  with  giant  powder  (No.  2).  An  effective  method,  how- 
ever, which  is  sometimes  employed,  is  to  snatch  them  out  with  a  donkey 
engine.  This  has  been  done  economically  on  railway  right-of-way  in  the 
State  of  Washington,  where  the  stumpage  is  thick.  Quite  a  commoa 
method  is  to  twist  them  out  by  using  horses  at  the  end  of  a  horisontal 
lever  chained  rigidlv  to  the  stump;  but  only  small  stumps  can  be  removed 
in  this  manner.  The  method  of  burning  stumps  is  a  slow  process  and  not 
generally  resorted  to  on  engineering  wore.  It  takes  many  years  for  stumps 
to  rot.  The  brush-hook  is  very  serviceable  in  cutting  brush,  especiaUT 
small  willows  and  alders.  Grubbing  the  roots  of  trees  is  best  accompli^iea 
with  the  grubbing-hoe  or  mattock.  Strange  to  say,  estimates  for  clearins 
and  grubbing  are  almost  tmiversally  too  low.  The  price  is  tisualhr  ptr 
acre,  or  sometimes  per  station  on  railroad  work.  In  reservoir  wonc  tor 
domestic  water  supply  the  grubbing  must  be  done  most  carefully  in  order 
that  the  top  soil  may  be  removed  imobstructed.     Under  railroad  filb  the 

*  For  earthwork  Tables,  see  Sec.  69,  Railroads,  pag^  1017,  ^ 


900  «zedb,(^oogle 


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908  U.—EARTHWORK. 

There  are  many  graders,  trench  machines  and  excavators  on  the  maxkeL 
many  of  which  are  greatly  overrated  in  efficiency  and  capacity.  Some  of 
them  work  well  in  loose  soils  but  are  useless  in  the  harder  materials  liable 
to  be  encountered.    Caution  should  be  exercised  in  their  selection. 

Under  favorable  conditions  where  there  is  plenty  of  water,  cxcavaticMi 
and  fill  by  hydraulic  method  is  sometimes  the  cheapest.  The  favorsbfe 
conditions  arc  a  gravity  supply  of  water  obtained  with  little  expense,  the 
right  kind  of  material  as  sand  or  fine  gravel,  sufficient  grade  from  cut  to 
fiU,  and  a  short  conveying  distance.  The  material  is  washed  from  the  natural 
bank  by  concentrating  a  stream  from  a  noszle,  or  giant,  and  is  carried  in 
a  sluice  box  under  a  constant  stream  of  running  water.  The  required 
gnule  of  the  sluice  may  be  as  great  as  8  or  10  per  cent  for  very  coarse  ma- 
terial. Earth  dams  constructed  in  this  manner  are  plentiful  m  California. 
Part  of  the  water  front  at  Tacoma.  Wash.,  has  been  filled  by  washing  down 
the  steep  bank  and  sluicing  the  material  into  the  bay.  If  there  is  no  gravity 
supply  and  pumping  is  required  the  chances  of  the  hydraulic  method  being 
the  cheapest  are  greatly  lessened. 

One  other  method  which  may  be  touched  upon  in  this  connection  is 
by  hydraulic  dredging.  By  the  use  of  a  rotary  cutter  and  a  suction  pump 
the  fine  material  from  the  bottom  is  sucked  up  and  forced  into  a  sheet-iron 
pipe  leading  to  the  shore.  Pilling  operations  along  our  water  fronts  bear 
witness  to  the  efficiency  of  this  method.  Material  is  frequently  delivered 
one-half  mile  from  the  dredge,  and  sometimes  to  a  much  greater  distance. 

Supcrintendeoce. — Some  years  ago  a  certain  engineer  known  to  the 
writer  entered  into  a  term  contract  as  Chief  Engineer  with  a  contracting 
firm  at  a  stated  salary  and  a  certain  percentage  of  the  profits.  One  of  the 
first  contracts  securecl  was  for  the  construction  of  headworics  and  a  30-mile 
pipe  line  for  water  works  in  one  of  our  prominent  western  cities.  The 
amount  of  the  contract  was  over  $900,000.00.  The  estimate  was  based  on 
prevailing  prices,  the  prices  for  material  being  guaranteed  in  mpst  cases. 
A  Profit  <?/  26%  was  added  to  all  estimated  costs,  including  materials  fur- 
nished. The  Treasurer*  volunteered  togo  up  and  superintend  the  work, 
as  it  would  be  a  nice  outing  for  him.  They  had  other  contracts  on  hand 
but  this  was  the  largest,  and  the  profit  on  the  steel  pipe  niaterial  akmr, 
delivered,  was  about  950,000.00.  The  wood -stave  pipe  construction  was 
under  an  experienced  man.  The  Treasurer  was  a  fair  book-keeper.  When 
the  work  was  about  half  completed  the  City  Engineer  became  desperate 
and  called  at  the  main  office.  'Pully  a  hundred  thousand  dollars  had  been 
wasted  on  the  line.  Men  all  over  the  line  working  without  sufficient  toob: 
one  gang  of  12  with  only  one  shovel  between  them,  and  no  pick.  Material 
from  the  trench  being  wasted  improperly,  that  had  to  be  used  again  Cor 
back-fill."  Upon  investigation  it  was  found  that  these  were  facts;  Uiat  the 
office  force  was  up  to  its  ears  in  book-keeping:  that  there  was  no  actim 
superintendent  or  line  boss;  that  not  one  of  the  foremen  had  been  fumi^bed 
with  a  profile  of  the  line  or  had  been  instructed  where  to  make  his  spail 
banks;  and  after  the  pipe  had  been  laid,  extra  borrow  pits  had  to  be  opened 
for  back-fill!  It  proved  to  be  an  expensive  "outing,"  and  the  loss  fell  most 
heavily  upon  the  Treasurer  himself  who  was  the  principal  owner.  Here  is 
a  case  where  a  good  superintendent  could  have  saved  the  company  ten 
times  his  salary. 

Good  foremen  keep  track  of  how  much  each  man  is  doing,  know  what 
he  ought  to  do,  and  whether  he  is  doing  a  day's  work.  It  is  a  mistake  to 
drive  men  who  are  resting  occasionally,  as  the  one  who  "keeps  coovinp" 
may  not  be  doing  half  as  much  work.  Poor  foremen  can  wipe  out  the  proaxs 
in  a  contract  even  although  they  may  appear  to  be  "hustlers." 

Labor. — ^The  common  labor  problem  is  a  difficult  one  to  solve.  Generally, 
"white"  labor  is  the  most  profitable  but  it  is  hard  to  secure,  exduai-rdy. 
on  large  work.  Italian  and  Chinese  come  next  in-order.  A  method  com- 
monly employed  with  some  contractors  is  to  select  one  or  two  good  n>en  in 
each  gang,  secretly  pay  them  from  25  to  60  cents  more  per  day  and  let 
them* 'set  the  pace.  '  As  a  further  incentive  a  small  bonus  is  sometimes 
offered  to  the  other  men  if  a  certain  amotmt  of  work  is  accomplished.     In 

.*  There  was  considerable  rivalry  between  the  Treasurer  and  the  Sccre- 
tSTi^  °  ^**°  should  "boss"  the  job.  which  was  acknowledged  to  have  been 
me  best  one  ever  landed  on  the  Pacific  Coast  up  to  that  tSne. 


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910  U.— EARTHWORK. 

and  the  voids  thus  created  being  ftirthcr  increased  by  the  action  of  frost, 
tendinis  to  swell  the  soil.  Hence  it  is  seen  that  soils  may  have  different 
densities,  even  if  of  the  same  composition,  when  lyinff  in  their  natttral  beds. 

The  Effect  of  Water  on  excavated  soils  is  to  settle  them,  mechanically, 
and  to  make  them  more  compact*  with  the  notable  exception  of  cla^.  which 
swells  when  moistened  and  shrinks  again  when  dried.  Thus,  with  roost 
soils  the  water  will  dep>osit  the  finely  suspended  particles  of  matter  into  the 
voids  of  the  coarser  material,  decrease  the  friction,  and  settle  it  into  a 
denser  mass;  while  with  clay  the  admixture  of  water  produces  a  colloidal 
state,  causing  the  mass  to  expand. 

The  Effect  of  Temperature  on  soil-  or  earth  embankment  is  mainly  the 
effect  of  drying  out  the  water,  or  of  producing  frost  action;  the  direct  ex- 
pansion or  contraction  due  to  temperature,  being  extremely  slight,  and 
negligible. 

The  Effect  of  Vertical  Compression  or  Tarring  on  an  earth  embankment, 
is  a  downward  tendency  to  settlement  and  a  lateral  tendency  to  expansioa. 
This  statement  as  to  lateral  expansion  does  not  of  course  take  into  consider- 
ation any  side-surface  slides  of  the  mass,  or  w^ash  of  slopes  from  rain. 

The  Effect  of  Stirring  or  Puddling  is  to  make  the  soil  or  earth  denser  by 
decreasing  the  percentage  of  voids.  The  following  experiment  was  made 
with  coarse  sand,  which  had  all  passed  through  a  {-in.  sieve  (16  meshes  to 
the  inch) :  A  box  of  one  cu.  ft.  capacity  was  filled  with  the  sand,  then  jarred 
to  settle  it.  and  again  filled  to  the  top.  Water  was  then  poured  in.  filling 
all  the  voids  in  the  sand,  the  amount  of  water  used  being  0.342  cu.  ft.,  thus 
measuring  the  voids  in  the  sand  as  34.2% .  The  wet  sand  was  then  tborot^di- 
ly  stirred,  and  settled  in  the  box  to  82.5%  of  its  original  volume,  the  voads 
in  the  stirred  sand  being  therefore  20.2%  of  the  final  volume. 

In  the  following  discussion  the  term  earth  will  be  considered  to  include 
soil. 

Swellage  (w)  of  Earth  takes  place,  usually,  when  it  is  first  dug.  This  is 
due  to  the  loosening  of  the  material,  thus  increasing  the  voids.  The  mote 
thoroughly  it  is  loosened  the  greater  will  be  the  swellage.  But  it  can  im- 
mediately be  Compressed  or  compacted  to  its  original  volume,  or  be  made 
to  Shrink  below  its  original  volume,  if  water  and  sufficient  pressure  are 
applied.  The  Percentage  of  Swellage  is  the  percentage  of  increase  in  volume 
o!  the  loose  material  excavated,  based  on  the  originafvolume  of  the  material 
in  situ. 

Compression  (k)  of  Earth  takes  place,  more  or  less,  in  forming  any 
embankment;  that  is.  the  loose  material  is  compacted  somewhat,  even  by 
its  own  weight,  while  being  placed.  A  low  embankment  formed  by  shovel 
work,  or  by  dumping  from  a  cableway,  or  from  a  train  supported  on  a 
trestle,  especially  dunng  drv  weather,  would  naturally  show  httle  compres- 
sion durirus  the  short  period  of  time  required  in  its  construction;  while  the 
material  forming  a  high  embankment  might  be  compressed  appreciably 
tmder  the  same  conditions  of  construction,  owing  to  the  increased  weight  of 
the  bank  and  the  element  of  time,  both  of  which  are  important  factors. 
If  the  track  were  supported  directly  on  the  embankment  itself,  or  the 
material  delivered  in  wheelbarrows,  or  especially  if  carts  or  scrapers  were 
used,  the  compression  would  be  increased ;  while  if  the  material  were  n>read 
in  thin  layers  and  rolled  with  a  heavy  roller,  the  compression  would  be 
much  greater.  The  Percentage  of  Compression  is  the  percentage  of  re« 
duction  of  volume  in  placing  the  material  in  the  embankment,  based  on  the 
Volume  of  the  loose  material  after  being  excavated. 

Contraction  (c)  of  Earth  in  embankment  continues,  perhaps,  indefinitely ; 
but  the  rate  of  contraction,  under  constant  conditions,  decreases  with  time. 
That  is  to  say,  tmder  the  same  conditions  the  rate  of  contraction  decreases 
as  the  material  in  the  embankment  becomes  more  dense.     The  rate  o4 
contraction,  however,  may  be  increased  by  pressure,  by  jarring  or  «Kair^g 
and  usually  by  moisture  or  sprinkling.     Thus  we  have  as  factors  tending  to 
contract  the  material  in  the  embankment:  The  pressure  of  the  embankraent 
itself,  the  pressure  and  jarring  due  to  mo  vine  trains,  and  the  sprinklins  due 
to  rainfall;  added  to  this,  is  the  wash  of  the  slopes  which,  for  our  imroeoiatc 
purpose,  will  be  included  under  the  present  heading.     The  Percentage  of 
Contraction  in  Embankment  is  the  percentage  of  decrease  in  volume  at  any 
stated  time  after  the  work  is  completed,  based  on  the  volume  of  the  com- 
pacted materials  as  placed  in  embankment. 

Shrinkage  (s)  of  Earth  is  also  measured  in  per  cent,  and  is  the  ratio  of  tl*t 
loss  m  voliune  of  earth  (measured)  in  embankment  at  any  specified   tdro! 


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912 


H^—EARTHWORK. 


2. — Approximatb  Values  of  (1-*)  to  bb  Usbd  in  Formula  (1). 
(k  —  Compression.) 


dasfl. 


Material,  and  Method  of  Placing  In  Embankment. 


<l-»). 


Blaatcd  rock,  large  maaws 

Broken  rock  as  for  riprap:   (a)  Qsreleady  dumped , 

(b)  More  carefully  placed 

Crusbed  trap,  granite  and  the  harder  rocks: 

(a)  Looaely  placed 

(b)  Thoroughly  shaken  In  tnmsportatkm 

(c)  Thoroughly  rolled 

Crushed  limestone,  sandstone  and  the  softer  rocks: 

(a)  Loosely  placed 

(b)  Thoroughly  shaken  In  transportaUoa 

(c)  Thoroughly  rolled 

Quart!  rock  crushed  to  sand,  loose 

Limestone  crushed  to  fine  grains,  loose , 

Glacial  drift,  cemented  grnvd.  day-ond-gravd.  extremely  dense: 

(a)  Cablewasrs  or  wheelbarrows  used,  dry  weather,  low  embankment. 

(b)  Carts  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Material  thoroughly  sprinkled  and  rolled,  blgh  embankment 
Cemented  gravel,  or  day-and-aand.  very  hard,  well  loosened: 

(a)  Cablewajrs  or  wheelbarrows  used,  dry  weather,  low  embankment. 

(b)  Carts  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Material  thoroughly  sprinkled  and  rolled,  high  embankment . 
Cemented  gravel,  muck,  and  compact  hard-pan,  average:. 

(a)  Cableways  or  wheelbarrows  used,  dry  weather.  low  embankment. 

(b)  Carts  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Material  thoroughly  sprinkled  and  rolled,  high  embankment . . 
Clay-cmd-gravel.  ordinary,  well  loosened: 

(a)  Cablewajrs  or  wheelbarrows  used,  dry  weather,  low  embankment. 

(b)  Carts  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Material  thoroughly  sprinkled  and  rolled*  high  embankment 
Clay-sand-gravel  mixture,  average: 

(a)  Cableways  or  wheelbarrows  used,  dry  weather,  low  embankment. 

(b)  Oarti  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Material  thoroughly  sprinkled  and  rolled,  high  embankmoit 
Sand-and-gravel.  compact: 

(a)  Cableways  or  wheelbarrows  used,  dry  weather,  low  emban  kment. 

(b)  CartB  or  scrapers  used,  some  rain,  medlimi  embankment 

(c)  Material  thoroughly  sprinkled  and  rolled,  high  embankment 
Loam,  sandy  loam,  average: 

(a)  Cableways  or  wheelbarrows  used,  dry  weather,  low  embankment. 

(b)  Carts  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Blaterlal  thoroughly  sprinkled  and  rolled,  high  embankment 
Sand  or  gravd.  ordinary: 

(a)  Cableways  or  wheelbarrows  used,  dry  weather,  low  embankment. 

(b)  Carts  or  scrapers  used,  some  rain,  medium  embankment 

(c)  Material  thoroughly  sprinkled  and  rcdled.  high 


.00 
.00 
.80 

.00 

f] 

.77 

.00 

.91 
.74 


.80 
.70 
.00 

.80 
.71 
.60 

.80 
.71 
.60 


.78 
.62 

.80 
.75 
.05 

.85 
.80 
.17 


.80 
.00 

.M 

.00 
.TO 


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d  by  Google 


914 


U.— EARTHWORK, 


the  commencement  and  completion  of  the  work."  The  results  of  the 
measurements,  involving  nearly  44,000  cubic  yards,  are:  Shrinkage  of 
yellow  clayey  soil,  9.25  to  10.15  per  cent;  shrinkage  of  light  sandy  soiij  12.93 
per  cent;  mean  average  shrinkage.  10.3  per  cent.  Based  on  these  expenments 
some  authors  give  the  "shrinkage  of  earth"  as  0  to  13  percent,  while  others 
have  widened  the  range  to  8  to  15  percent.  Most  railroads  use  about  10 
per  cent  as  an  average  working  basis. 

The  Am.  Ry.  Eng.  &  M.  of  W.  Assn.  Committee  Report  for  1907  recom- 
meilds  shrinkage  allowance  for  both  height  and  width  in  new  banks.  30 
replies  favoring  this,  while  two  favored  allowance  for  vertical  shrinkage 
only,  and  two  for  horizontal  shrinkage  only.  The  following  shrinkage 
values  were  recommended: 

Suggested  by       Recommended 
Members.  by  Committee. 

Black  dirt,  trestle  filling 7  to  30%  ISJ* 

Black  dirt,  rai^ng  tmder  traflSc 4- to  20%  5? 

Clay,  trestle  filling 6  to  30%  10^ 

Clay,  raising  under  traffic 2  to  20%  65 

Sand,  trestle  filling 3  to  15% 

Sand,  raising  under  traffic 2  to  15%  59 

In  building  the  Tabeaud  Dam,  1900-1902.  near  Jackson.  Cal..  tests  of 
the  earth  material  used  showed  the  following  average  weights  per  cu.  ft.: 

Dust  dry  soil  (angle  of  repose  36°) 84 .0  lbs. 

Soil  fully  saturated,  52%  moisture  (angle  of  repose  23°) 101.7  Ihs. 

Natural  bank  soil.  19%  moisture  (angle  of  repose  44°) 116.5  Ihs. 

Delivered  from  wagons,  moist  and  loose  (showing  swellage  of  52%)  76 . 6  lbs. 
Loose  dirt  from  dam.  shaken  down  and  measure  istruck  (swellage 

45.6%) 80. §  lbs. 

Material  in  dam.  38%  gravel  and  grit,  thorotighly  sprinkled  and 

rolled  (showing  shrinkage  of  12.4%) 133.0  lbs. 

Experiments  made  by  Mr.  D.  C.  Henny,  on  earth  material  for  the  Cold 
Springs  Dam,  Umatilla  Irrigation  Project,  (3rcgon,show  the  following  results: 


Specific  Gravity. 

Percentage  Voids. 

it 

•  Sample. 

Constit- 
uents. 

Mass. 

Dry. 

Wet 
Rammed. 

Compact. 

A.  Surface  soli 

B.  Fine  subaoU 

C.  Gravel 

8.52 
2.65 
2.90 
2.66 
2.93 

2.64 
2.83 
2.00 
2.87 
2.83 
2.91 
2.84 

1.41 

1.65 
1.91 
0.94 
1.57 

1.75 
1.76 
1.91 
1.95 
2.01 
2.04 
1.88 

59 
54 
42 
74 
55 

50 

47 
42 
41 
47 
47 
41 

49 
43 
37 
68 
49 

89 
41 
83 
35 
43 
40 
35 

44 

45 
34 
65 
46 

38 
89 
84 
82 
29 
30 
84 

3.9 
4.0 
9.2 

1.5 
3.0 

.033 
021 

.659 

D.  Voloanlc  ash 

E.  Goarse   subsoil 

Mixtures: 
B.            C. 

75%      n%.... 

67%         83^.... 

60%         50% 

33%         67%.... 
25%         76%.... 
20%         80%.... 
15%          85%.... 

.019 
.OTt 

.066 

14.7 
20.0 
21.0 
71.7 
18.0 

.Oil 
.076 
.•M 

.991 
Iftl 

*  Sample  A  is  the  12-in.  surface  soil  in  the  bottom  lands,  being  dasker 
in  color  than  the  deeper-lying  soil,  but  containing  a  sensibly  greater  quantity 
of  organic  matter,  as  roots  and  vegetable  fibers.  Sample  B  is  talcen  from 
1  to  I  ft.  below  the  surface,  being  slightly  lighter  in  color  than  A.  and  whh 
less  vegetable  matter.  Sample  C  is  coarse  sand  gravel  and  from  the  steep 
side-hill,  the  mass  of  the  material  being  a  coarse  sand  or  fine  gravel  with  a 
considerable  proportion  of  gravel  that  would  be  retained  on  a  one-inch 
mesh:  also  occasional  large  cobbles,  and  a  scantiness  of  fine  sand.  Saxn^ 
D  is  volcanic  ash,  almost  pure  white  in  color;  when  in  place  it  appears  to  be 
slightly  indurated.  Sample  B  is  a  coarse  soil,  coarser  in  appearance  than 
A  and  B  but  otherwise  greatly  resembling  them;  it  lies  from  1  to  4  ft.  bekiw 
the  suriace.  Samples  A,  B  and  E  all  contain  a  considerable  proportion  ol 
volcanic  ash  and  vegetable  matter,  and  are  fairly  representative  of  soils  is 
that  section  of  the  West.       tMassachusetts  State  Board  of  Health  standaxd. 

tizedbyUOOgle 


SHRINKAGE  DATA, 


015 


Experiments  made  by  Mr.  Emery  Sudler.  on  soils  for  use  in  construc- 
tion of  earth  dam  for  water-works  reservoir,  Baltimore.  Md..  show  the 
following  results: 


Properties  or  Ooadltkm  of  Material. 


Soft,  rotten 
Serpentine  Rock, 
below  the  day. 


Welgbtlnlbs. 
per  cubic 
footwben 


In  place 

Loose 

Compressed  (In  4-ln.  layer  In  6- 
In.  test  pipe,  at  about  160 

^      lbs.  per  sq.  In.) 

Yolame  In  cubic  feet  correspond- 1  Loose  . . 

Ingto  one  cubic  foot  In  place. .  J  Compressed 
AbeorptloD  by  weight 


108. 
74.6 


129.3 
1.45 
.84 
.007 


This  table  shows  that  when  loosened  the  clay  swelled  50%  and  the 
rotten  rock  swelled  45%;  after  being  compressed  the  loose  clay  showed  a 
compression  of  40.7%  and  the  loose  rotten  rock  a  compression  of  42.4%; 
while  the  ultimate  shrinkage  of  the  material  in  place  when  compressed, 
was:  clay,  11.0%  and  rotten  rock,  16.5%. 

Shrinkage  in  Volmie— Vertical  Shrinkage. — If  each  particle  in  an  earth 
embankment  shrinks  vertically  (not  laterally)  how  will  the  settlement  of 
the  top  of  an  embankment  compare  with  the  shrinkage  in  volume? 


I 1 


Fig.  2. 

Solution. — ^Let  the  full  lines,  Pig.  2,  represent  the  original  fill,  and  the 
dotted  lines  the  top  and  slopes  after  vertical  shrinkage.  Then  will  d-s- A 
represent  the  ratio  of  vertical  shrinkage,  as  well  as  shrinkage  in  vol- 
ume.   For 

Final  volume       ^  j^     d)^^'^*\  h^^'^*^ '^^^^ ^l     ^ 

Orifl^al  volume"  2  2     ""    A    "        h' 

earthwork  is  always  measured  in  excavation  where  possible:  but  it 
often  happens  that  a  contractor  will  start  in  on  a  borrow-pit  before  it  is 
cross-sectioned.  For  this  and  other  reasons  it  is  sometimes  necessary  or 
advisable  to  measure  up  the  embankments  as  a  basis  for  payment.  Con- 
siderable judgment  must  therefore  be  exercised  in  the  question  of  "shrink- 
age." 

Perfonnance  of  Work. — ^The  following  items  are  selected  and  digested 
from  the  columns  of  Enginegring-Contracttng,*  and  give  what  may  be  con- 
sidered fair  averages  of  good  work  imder  the  conditions  named.  For 
detailed  information  see  ori^al  articles.  References  are  made  to  the  files 
of  Sftg'r'Contr.  in  the  following  manner;  thus,  E.-C.,  (date,  page). 

Sewer  Trench  In  stiff  day.  wet  and  soft  In  spots,  but  touj?h  digging;  at  West 
Ants  <near  MnwauXee).  Wis.;  by  "Buckeye  Tmctlon  Ditcher,"  a  machine  with 
Ouekets  on  the  periphery  of  a  large  wheel,  operated  by  steam,  costing  about  $4600.00. 
uid  manuisctured  by  the  Van  Buren.  Heck  A  Marvin  Ck)..  of  Findlay.  O.  Estimated 
7erfc»rmanoe  (less  than  actual)  900  lln.  ft.  of  trench  2  ft.  wide  by  7  ft.  deep  in  10  hra. 
it  ooat  of  5  cts.  per  cu.  yd..  Induding  all  items  of  pay  roll.  fuel.  Interest  and  depre- 
•latlon. — B.-C.,  Jan.,  1 906.  p.  7. 


Published  weekly  by  the  Myron  C.  Clark  Publishing  Co.,  Chicago,  111. 


01«  M.— EARTHWORK. 

New  York  Subway.  Earth  excavatloii  In  a  tynleal  section  of  about  )  mSe. 
Brooklsm  Extenalon:  Excavation  proper  (labor  1.60,  materials  and  plant  0.31. 
power  0.02.  dump  cbarges  at  60  cts.  per  load  0.25),  S2.19  per  cu.  yd.*,  bracing  and 
sheeting  Oabor  0.78.  materials  and  plant  0.37).  $1.16  per  ciLyd.;  pumping  and 
draining  Oabor  0.01.  materials  and  plant  0.01.  power  0.01).  $0.03  per  co.  yd.; 
bridges  and  barricades  Oabor  0.10.  materials  and  plant  0.14).  $0.24  per  cu.  yd.; 
backflUlng  (labor).  $0.01  per  cu.  yd.  Grand  total.  $3.62  per  cu.  yd.~jr.<C..  Febw 
1906.  p.  30. 

Panama  Canal.  Cost  per  cu.  yd.  of  mixed  exoavatl(m  (06062  c  y.  hard  ro^ 
254262  c.  y.  soft  rock.  391340  c.  y.  earth),  for  a  total  of  741644  cu.  yds.,  betweea 
July  1.  1904.  and  June  30.  1906:  July,  65.4  c.  Aug..  50.6  c.  Sept..  57.3  c.  Oct.  64.1  c 
Nov.  50.1  c,  Dec.  52.8  c.  Jan.  47.8  c.  Feb.  46.6  c,  Mar.  43.3  c.  Apr.  52.5  c.  May 
83.8  c.  June  102.7  c  Excavators  and  steam  shovels  were  used.  Roughly,  the 
above  costs  Include  up-keep,  depreciation,  etc..  of  plant. — B.-C.,  Feb..  1906.  p.  44. 

Intercepting  Sewers.  CThlcago.  ( 1)  Excavating  with  Ennls  type  derrick,  equipped 
with  a  1  cu.  yd.  Haywood  orange-peel  bucket,  an  8i"by  10"  douUe-<lrum  hoMing 
engine  and  60-ft.  boom.  Cost,  exclusive  of  wear  and  tear  of  machinery.  6.6  cts  per 
cu.  yd.    (2)  Other  methods  were  used  also. — S.-C..  Apr.,  1906.  p.  y6. 

R.  R.  Excavation  with  Elevating  Grader.  7  examples,  by  D.  J.  Hauer.  Ma- 
terial, average  earth  when  dry.  Machine  built  by  the  Natl  Drill  and  Mfg.  Co.  of 
New  York  aty.  Wagons,  drop  bottom  patent  dump,  of  2-yds.  capacity.  (1)  R.  R. 
cut.  400  ft.  long.  45  ft.  wide  on  top.  Coet  (loading  0.130.  handling  0.1 11.  dumplnc 
0.041,  water  boy  0.001.  foreman  0.012).  29.5  cts.  per  cu.  yd.  Av.  output.  206  cu. 
yds.  per  day:  lead,  400  ft.  (2)  R.  R.  cut  about  1400  ft.  long.  20  ft.  wide  and  2  ft. 
deep.  Cost  (loading  0.067,  handling  0.078,  dumping  0.011.  water  boy  0.002.  Coremsa 
0.007),  16.5  cts  per  cu.  yd.  Av.  capacity,  380  cu.  jrds.  per  day:  lead  1000  ft.  (S)  R. 
R.  cut.  30  ft.  roadbed  for  double  track.  CTost  Ooad.  0.046,  haul.  0.072,  dump.  aoic. 
water  O.OOI.  foreman  0.005).  14  cts.  per  cu.  yd.  Max.  output  at  top  of  cut.  510  cu. 
yds.  per  day;  av.  output.  300  cu.  yds;  lead  600  ft.  (4)  R.  R.  cut  for  double  track. 
(Tost  Oood.  0.108.  haul.  0.149.  dump.  0.019.  water  0.003.  foreman  0.010).  28.9  eta. 
per  cu.  yd.  Av.  output.  284  cu.  yds.  per  day;  lead.  700  ft.  (5)  R.  R.  cut.  Cost 
(1.  0.061,  h.  0.077,  d.  0.018.  w.  0.002,  f.  0.006).  16.4  cts.  per  ou.  jd.  At.  output.  417 
cu.  yds.  per  day;  lead,  500  ft.  (6)  R.  R.  borrow-plt.  Cost  (j.  0.098,  h.  0.094.  d. 
0.049,  w.  0.003,  t  0.009),  25.3  Cts.  per  cu.  yd.  Av.  output,  260  cu.  yds.  per  day; 
could  have  been  Increased  If  more  wagons  had  been  used.  Lead.  600  ft.  <  7)  R.  R. 
borrow-plt.  <3o8t  0-  0.153.  h.  0.260,  d.  0.050,  w.  0.002.  f.  0.015).  48  cts  per  ou.  yd. 
Av.  output.  167  cu.  yds.  per  day;  material  hauled  1700  ft. ;  management  Infertor.-- 
^. -C..  Apr..  1906.  p.  102. 

Steam  Shovel  Work  on  Ann  Arbor  R.  R.  In  1895.  Cost  figures  cover  loading; 
hauling  and  placing  under  track,  but  make  no  aUowanoe  for  rental  of  plant,  loeo* 
moUve  or  cars,  nor  for  depreciation  of  plant.  Labor.  $1.15.  Cost  per  eu.  yd. :  Sand. 
7.22  to  13.88  cts  ;  sand  (very  light  face),  17.24  cts.;  sand  (all  work  lowering  br 
hand  charged  against  this  cut),  25.44  cts.;  sand  (light  face).  13.25  eta.;  qulcknad. 
13.98  and  15.95  cts.;  gravel.  8.93  and  14.37  cts.;  gravel  (long  haul).  19.81  eta: 
day.  9.60  to  14.01  cts.;  day  (hard  pan),  17.65  cts.;  sand  and  gravel.  6.48  and  8.56 
cts.;  sand  and  gravel  (very  light  face),  17.31  cts.;  sand  and  clay.  10.49  eta. — S.-C^ 
May  30.  1906,  p.  151. 

Sewer  Tunnel  at  Qevdand.  Using  Hydraulic  Shield.  Sewer,  13i  ft.  dla^  btilt 
of  four  rings  of  No.  l  shale  brick  laid  In  Portland  cem.  mortar.  Shield.  16^  ft.  dla., 
4  ft.  long,  of  f  metal,  and  weight  about  16  tons;  upper  half  provided  with  fioOowcr 
7  ft.  long,  of  r  sted.  bolted  toshldd.  Shldd  pushed  forward  by  12  hydraulic  Jacks. 
5'  dla.  and  26'  long.  Water  led  to  Jacks  bv  pipes  with  swinging  Joint;  av.  pmeauit 
about  700  lbs.  per  sq.  In.,  but  pump  could  devdop  6000  lbs.  Material,  hard,  dry 
quicksand,  sometimes  mixed  with  day.  CTost  of  tunnd  per  Un.  ft.:  8  c  y.  exeav.. 
underground  labor,  at  73  cts.— $5.44:  8  c  y.  excav.,  surface  labor,  at  48  cta» 
$3.82.  2.62  c  y.  brickwork,  underground  labor,  at  $1.12— $2.99;  2.62  c.  v.  brick- 
work, surface  labor,  at  73  cts.«$1.91;  1100  bricks  d$9  per  M«$9.90:  2.1  bhis. 
cement  (1:3  mortar),  at  $l.70-$3.57:  1  c.  y.  sand  at  $l->$1.00;  plant.  60%  of  first 
cost.  diBtributcd  over  1625  lin.  ft.=>$5. 00;  lumber— $1.05;  shafts  or  manholos— 
$1.00.    Total  $35.64.— ^.-C..  July  25,  1906.  p.  22. 

aearing  and  Grubbing  Land;    and  Blasting  Stumps.     Area.  9  acrea; 
6  Ins.  to  3  ft.  in  dla..  with  average  about  20  Ins..  consisting  of  oak.  hlek<UT.  cb 
etc.;  number  of  trees  cut  was  over  1100.  and  number  of  stumps  blasted  was  1212. 
Trees  under  6'  dla.  dasMd  as  brush,  and  stumps  were  grubbed  with  mattorta 
For  blasting  stumps  the  following  were  used:    1  chum  drill.  1  large  auger,  aad 
1  bucket,  costing  in  all  about  $80.     Total  cost    per  acre  was  as  foUowa.  wtth- 
Italian  labor  at  $1.25:    (flopping  $18.84,  grubbing   and   dcaring  $15.53.  ma' ^ 
cord  wood  $10.14.  blasting  $73.73,  grubbing  alter  blasting  $35.26.  grinding 
$0.65.  tools  $9.00:   total  cost  per  acre  $163.25.— l?.-C..Feb.  27.  1907.  p.  92. 

Wash  Drill  Borings,  Deep  Waterways  Survey.  Great  Lakes  to  Atlantic  TWe 
W^Mers.  1897-1900.  The  process  consisted  In  altematdy  "driving  easing^  and 
drtuing"  until  "bottom"  was  reached.  Where  obstrucUoos  were  eoeountered  tliat 
i^JllS*  ^  passed  by  drilling,  they  were  removed  by  puUIng  the  drm  rod  and 
of  tSS  Sf  ^oK  3  or  4  ft.  and  then  firing  a  stick  or  two  of  dynamite  at  the  1 
oi  tne  bole,    (a)  On  the  Tonawanda-Oloott  and  La  SaUe-Lewtoton  Rmttei.  < 


PERFORMANCE  OF  WORK. 


017 


lOK  404  holes  bored  to  an  afrsrefcato  depth  of  9624  ft.  The  cost  of  borings  (hieluding 
total  cost  of  plant)  was  68.63  cts.  per  lio.  ft.,  the  material  betnjr  sand,  gravel,  clay, 
kod  hardpan.  (b)  On  the  Western  Division  of  the  Oswego-Mohawk  Route — fkx>ni 
Onrego  to  Rome— 750  holes  were  bored  to  an  aggregate  depth  of  3371 1  ft.,  and  at 
an  average  cost  of  70.07  cts.  per  lln.  ft.  For  the  Oswego  river  and  harbor  work,  the 
machines  were  mounted  on  nnall  flatboats  with  open  wdls  at  the  center;  and  the 
work  on  Oneida  Lake  was  done  through  the  Ice.  (c)  On  the  Eastern  Division  of  the 
Oswego-Mobawk  Route  there  were  made  290  soundings  by  hand  with  a  sted  rod. 
and  1562  actual  borings,  together  amounting  to  55521  ft.,  aggregate  depth,  at  a 
cost  of  54.19  cts.  per  lln.  ft.  The  borings  varied  from  a  few  feet  to  1 90  ft.  In  depth. 
Four  types  of  machines  were  used,  vis.:  1  Pierce  well-boring  machine.  1  Sullivan 
wash  drill,  and  2  home-made  affairs.  The  material  encoimtered  was.  sand.  20706 
fLf-day.  9880  ft.;  earth.  7611  ft;  sand  and  day.  3176  ft.:  gravel.  2815  ft.;  sand 
and  gravd.  2728  ft.;  sand,  day  and  gravd.  1843  ft.;  quicksand.  1529  ft.;  day  and 
Bbale.  903  ft.;  sand,  loam  and  mud.  900  ft,  day  and  gravd,  760  ft.;  rock.  626  ft.; 
mud,  417  ft;  mlaodlaneous.  1628  ft.  (d)  On  the  Champlaln  Route  from  Ogdens- 
borg  to  Lake  St.  Francis  there  were  148  sand  borings  totalUig  7052  ft.,  and  151 
water  borings  totaling  2123  ft.  The  cost  of  the  9175  ft.  of  borings  was  84.18  cts. 
per  Un.  ft.  (e)  On  the  Hudson  River  Dlvlston  of  the  Cham^aln  Route  57991  lln. 
ft.  of  borings  cost  12.35  cts.  per  Un.  ft.  (0  On  the  Hudson  River  Survey.  Hudson 
to  Troy,  the  borings  were  made  with  an  outfit  mounted  on  a  catamaran  and  on 
scows,  sat.  day.  ooarse  and  fine  sand,  gravd.  and  boulders  were  penetrated.  A 
2Hn-  easing  and  "B  drill  rods."  with  X-blts  were  usnL  In  aU.  1385  borings  were 
made  aggregating  28965  ft.  In  depth  and  costing  25.07  cts.  per  Un.  ft.— J?.-C.. 
Mar.  27.  1907.  p.  131 

Diamond  DriU  Borings.  Deep  Waterways  Survey.  Great  Lakes  to  AUanUe  Tide 
Waters.  1897-1900: 


No.  of  holes. 

Depth  In  feet 

Staodplpe,  feet 

Rock  drflled.  feet 

Cost  of  boring,  per  lln.  ft. 

'  Rental  of  driUIng  outfit. 

Carbon 

Labor. 

TeamstCT. 

Teaming,  extra. 

Superin  tendenoe. 

Repairs. 

Ooal  (and  wood). 

Lumber. . . . 

Core  boxes. 

Freight  and  Express. 

Travdlng  expenses. 

Sundries. 


s 
I 


0.020 
0.225 
0  201 
0.057 


—B.-C..  Mar.  13.  1007,  p.  108. 
R.  R.  Grading  with  Wheded  Scrapers.    Five  examples: 

UiteriaL 

esad.  inft 

oretnan  <f3.00) 

rrapers  ($4.75) 

owing  ($9.20) 

LatclUng  CI6.00)... 

y^den  ($1.60) 

Lsmptng  (men  $1.50) 
atcr  boy  ($1.00). 

•cal  cost  per  ca.yd.  1.273      $.311      $.450      $.430      $.367       $.366       (100.0) 

S.-C..  Sept.  25,  1907,  p.  184. 

Trenchtng  and  BaokflUIng  fbr  Pipe  Sewer.  (}enterv1Ile.  Iowa.  Data  from  which 
>Je  wHa  compiled  was  furnished  by  Mr.  M.  A.  HaU.  engineer  In  charge,  from  dafly 
KjrtB  by  tnspeeton,  and  Mr.  HaU  suggests  adding  1 0%  for  possible  omladons  in 


Ex.  1. 

Ex.2. 

Ex.3. 

Ex.4. 

Ex.  5. 

Av. 

% 

Sandy 

Good 

Wet 

Fine 

Loaro- 

loam. 

day. 

day. 

sand. 

day- 
sand. 

260. 

300. 

400. 

600. 

700. 

432. 

$.017 

$.019 

$.026 

$.024 

$.020 

$.021 

6.0 

.138 

.158 

.216 

.222 

.210 

.189 

61.6 

.052 

.057 

.080 

.073 

.053 

.063 

17.2 

.034 

.037 

.052 

.050 

.030 

.040 

10.9 

.018 

.020 

.028 

.026 

.020 

.022 

6.0 

.008 

.016 

.039 

.027 

.033 

.025 

6.8 

.006 

.004 

.009 

.008 

.001 

.006 

1.5 

918 


bL—EARTHWORK. 


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p— dlA.of  plp«.  mina.:  l»  Hie  of  trench,  widtb  by  dq^:  d 
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blaflUng.  although  bUsting  niAy  be  resorted  to  occaalonaUy.  B.  dt  0.-H9late,  eori. 
BhAle.  soft  triable  saodBtone  and  soapstoDe.  detached  maffles  3  eu.  ft.  to  1  co.  yd. 
CA«».  <t  O. — Shale,  date,  ochre,  which  can  be  removed  with  pick  and  bar.  and  li 
soft  and  loose  enough  to  be  removed  without  blasting,  although  blasting  may  be 
resorted  to  occasionally.  Detached  masses  3  cu.  ft.  to  1  ctL  yd.  Norf.  A  W. — Shait 
soapstone,  and  other  rock  which  can  be  removed  by  pick  and  bar.  and  Is  soft  and 
loose  enough  to  be  removed  without  blasting,  although  blasting  may  be  resorted  to 
occasionally.  Detached  masses  1  cu.  ft.  to  1  cu.  yd.  SotOhem. — {Same  as  NorL  * 
W.)  "Big  Four." — Shale,  coal,  slate,  soft  sandstone,  soapetone.  ooogloaicnte 
stratified  limestone  In  layers  less  than  6  In.  Detached  masses  3  cu.  f t.  to  1  cu.  yd. 
C  B.  A  Q. — Stratified  rock  which  can  be  removed  by  pick  and  bar  and  weightog 
more  than  140  lbs.  per  cu.  ft.    Detached  masses  3  cu.  ft.  to  1  cu.  yd.    Chi,  &  AVl— 

Stratified  rock  which  can  be  removed  by  pick  and  bar and  masses  between 

3  cu.  ft.  and  1  cu.  yd.  OreaX  Nor. — Slato  and  other  rock,  and  loose  enough  to  be  re- 
moved without  blasting,  although  blasting  may  be  resorted  to  occasionally.    Detached 

masses  3  cu.  ft.  to  1  cu.  yd.    A.,T.  A  8.  F. — Hard  shale  or  soapstone hi 

original  or  sUatlfled  position,  boulders  In  gravel,  cemented  gravel,  hardpan ai^ 

other  material  requiring use  of  pick  and  bar  or  which  cannot  be  plowed  with 

10-ln.  plow  and  fr-horse  team.  lU.  Cent. — (No  loose  rock.  Everything  but  solid  rock 
dassed  as  common  excavation.)     N.  P. — Slato,  soft  suidstone,  or  other  rock  ttetn 

ean  be removed  without  Masting.    Detached  rock  between  1  cu.  ft.  and  1  eayd. 

Mo.  P. — All  rock which  requires  for  Its  removal  steam  shovel  or  pick  aod  bar. 

without  blasting,  although  blasting  may  be  resorted  to  at  the  optlOQ  of  the 
contractor.    Detached  masses  1  to  18  cu.  ft. 

EXCERPTS  AND  REFERENCES. 
Some    References    to    Earthwork    and    Especially    to   ShrinkMe. — 

(1).  Notes  on  Earthwork.  By  Geo.  J.  Specht.  Tech.  See.  Pac.  Coast 
Transactions,  May.  1885.  A  collection  and  digest  of  data  on  shrinkase  up 
to  that  time.  (2).  Shrinkage  of  Earthwork.  By  P.  J.  Flynn.  Tech.  Soc. 
Pac.  Coast  Transactions,  read  June  5.  1885.  Refers  to  experiments  oc 
shrinkage,  made  in  India,  and  gives  \ables  of  shrinkage.  Also  gives  nu- 
meroxis  references  and  data.  (3).  Shrinkage — Growth.  J.  C.Nagle.  "A  Field 
Manual  for  Railroad  Ei^finecrs,"  1887.  (4).  Shrinkage  of  Earthwork. 
W.  M.  Patton.  "Civil  Engineering."  Patton  says:  Sand  shrinks  about  10%; 
sand  and  gravel,  8%;  earth  and  loam,  10  to  12%;  gravelly  clay.  8  to  10%; 
puddled  clay  and  soil.  20  to  25%;  rock  excavation  produces  a  lax^r  mass 
by  from  25%  in  cases  of  small  fragments  and  60  or  70%  when  in  blocks 
carelessly  piled  up.  (5).  Shrinkage  of  Macadam  Under  Rolling.  See  Ens> 
News  of  Feb.  11.  1904.  (See,  also.  Kng.  News,  Jan.  14  .1004,  under  Macadaza 
Road  Construction  Along  Charles  River. 

A  Novel  Method  of  Constructing  High  Embankments  in  Swttzeria»4 
(Eng.  News,  Aug.  21,  1902). — By  use  of  temporary  suspension  bridgie; 
illustrated. 

The  Cost  of  Hydraulic  Excavation  for  Embankments  and  for  Plaocr 
Mining  (Eng.  News,  Nov.  27,  1902). — C^st  data  on  several  works,  also 
references  to  other  data. 

The  Buckeye  Trench  Digging  Machine  (Eng  News,  Aug.  6.  1903). — 
Illustrated. 

Discussions  on  Clearing  and  Qrubbhig   (Eng.  News,  Jan.,  1904.) 

Time  Required  to  Load  Wagons  -with  a  Steam  Shovel  (By  J.  S.  Ely. 
Eng.  News,  July  14,  1904).— Table. 

A  Cross-Cttt  Excavating  Machine  for  Drainage  Dttches  (Eng.  Ne-ws, 
Sept.  7,  1905).— Illustrated. 

Machine  for  Spreading  and  Leveling  Material  (Eng.  News.  Jan.  4. 
1906).— Illustrated. 

Cost  of  Steam  Shovel  Work  by  Railway  Force  and  by  Contract  (By 
T.  C.  Sesscr.  Bulletin  81.  Nov..  of  Am.  Ry.  Eng.  &  M.  of  W.  Assn.:  Ei^. 
News,  Jan.  17,  1907). — Work  by  company  force,  18.7  cts.  per  cu.  yrt.: 
contract,  26.0  cts.;  saving,  7.3  cts. 

Excavating  Machines  on  the  N.  Y.  SUte  Barge  Canal  (Eng.  Nev^ 
June  6,  1907).— Illustrated. 

^_  Qravel  Spreader  Used  on  the  Colorado  River  Levee  ConstmctiQa 
(By  li.  T.  Cory.  Eng.  News.  July  11.  1907).— lUustrated.  "Cost  of  w«]«k 
done  by  the  machine  was  about  one-tenth  of  a  cent  per  yafd  of  m&t.eriKl 
spread.    Machine  cost  $300.     Its  operation  required  ^locomotive  and  four 


MISCELLANEOUS  DATA,  921 

An  Untoading  MachliM  for  Dnmpiiig  Cars  in  Bailding  Embank- 
^joU  on  the  Western  Pacific  Ry.  (Eng.  News,  Aug.  22,1007}.— Illustrated; 
consists  of  a  circular  loop  at  end  of  top  of  embankment,  for  cars  to  run 
around  and  dump. 

ffydranlic  Constmctton  of  Larce  Embankmeats  on  the  Clii.«  Mil.  ft 
PuceC  Sound  Ry.  (Eng.  News,  May.  27,  1909). — ^Twelve  illustrations  of  con- 
struction work. 

Macliine  for  Excavatins  Trenches  and  Foundations  in  Frozen 
Qrotind  (Eng.  News,  June  17,  1909.) — Used  in  Winnipeg,  Canada  "In 
that  city  the  frost  penetrates  to  a  depth  of  6  to  6J  ft.  Previous  to  the  in- 
troduction of  this  machine,  all  earth  excavation  during  5  or  6  months  of 
the  winter  had  been  done  oy  hand  picking  or  bv  blasting  the  frozen  earth 
with  black  oowder,  the  former  costing  about  $1.35  per  cu.  yd.,  and  the 
latter  about  11.25  per  cu.  yd.  down  to  93  cents  per  cu.  yd.  By  the  machine, 
the  cost  has  been  reduced  to  from  11  to  30  cents  per  cu.  yd.  The  ("Drop- 
Chisel")  machine  is  illustrated. 

Excavation  Metliods,  Fourth  Avenue  Subway,  Brooldjm  (Eng.  Rec.. 
Dec.  3,  1910). — Described  and  illustrated. 


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55.— ROCK  EXCAVATION. 

Subject  DivUloiu. — Under  "Ouanving"  (see  page  410)   are    discosRd 

the  metnods  of  excavating  "dimension  and  other  stone  for  subeequent  use 
in  masonry  construction.  The  present  subject  deals  with  the  most  approved 
methods  of  excavating  open  rock  cuts  and  trenches  for  railways,  hi^wavs, 
canals,  sewers,  etc.  For  subaqueous  excavation,  including  blasting  imdcr 
water,  see  "Dredging,"  page  927,  and  for  tunnel  work  see  'TunneKng" 
page  933. 

Open  Rock  Cuts. — ^The  cheapest  form  of  open  cut  is  the  side-hill  cut 
(Pig.  1),  in  which  c  is  the  cut,/  the  fill,  and  w  the 
waste.  A  common  method  of  operation  is  to  begin 
drilling  with  holes  a  at  the  bottom  of  the  cut, 
tising  moderate  blasts  and  woricing  back  in  steps 
to  b.  But  where  the  quantity^  in  cut  c  greatly 
exceeds  the  fill  /,  it  is  often  advisable  to  begin  at 
b,  using  deep  holes  and  large  charges  of  explo- 
sives. By  this  means  a  more  effective  use  of  the 
powder  can  be  had  in  not  only  loosening  the  rock 
but  in  wasting  a  large  proportion  of  it  at  the  same 
time.    Solid  rock  is  supposed  to  stand  about  "ver*  Pig.  1. 

tical."  hence  the  drill  holes  b  as  shown.  If  the  material  is  seamy  and  coc- 
tains  more  or  less  loose  rock  the  latter  may  be  taken  'out  to  slope  as  n- 
quired,  but  it  is  not  necessary  to  take  out  the  whole  cut  in  the  same  ^ope.* 

Drilling. — ^The  most  common  form  of  rock  cut  is  the  "thownigh"  cut 
as  shown  in  Pig.  2.  The  rock  is  excavated  in 
benches,  o,  b  and  c,  but  not  so  regularly  as 
shown  in  the  Pig.  tmless  channeling  machmes 
are  used  as  was  the  case  on  the  Chicago 
Canal.  The  rise  or  lift  may  be  assumed  as 
about  equal  to  the  tread,  but  this  depends  on 
the  size  of  blocks  that  can  be  hanaled  eco- 
nomically, the  depth  of  economical  drilling, 
the  qiiality  and  character  of  stone  and  seams, 
and  whether  horieontal  holes  at  the  bottom 
of  rise  are  drilled  to  assist  in  blasting.  The  spacing  of  the  holes  msT 
be  assumed  about  equal  to  their  depth,  if  in  single  row  and  the  rock 
is  not  too  hard.  Por  trap  and  granite  the  spacing  should  be  closer,  ordi- 
narily. The  rise  may  vary  from  a  few  feet  up  to  12  or  even  30  ft.,  tbe 
deeper  holes  requiring  the  larger  drills,  say  8  to  3|  ins.,  and  opetated 
by  machine.  Chum  drills  up  to  3  ins.  in  dia.  (1|*  bar)  may  be  tiaed  for 
vertical  holes  in  soft  rock,  where  machine  drills  are  not  available.  Each 
drill  is  operated  by  two  or  more  men  whoraiseit.  turn  it  'round  a  fittk 
and  let  it  plunge  back  into  the  hole.  Sometimes  the  drill  is  loaded  to 
give  more  weight  and  hence  become  more  effective.  For  two-hand  ham- 
mer drilling  (one  man  holding  and  turning  drill,  and  two  men  striking), 
the  hole  is  usually  started  with  a  1 J  to  IJ-in.  bit  and  using  10-Ib.  hamxners- 
The  dia.  of  bit  is  decreased  with  depth  of  hole,  to  prevent  binding,  anj^ 
the  limiting  depth  is  about  8-ft.  Octagonal  bars  from  t-in.  to  1-in.  are  oscd- 
Por  one-hand  drilling  (hammer  4 J  lbs.),  the  drills  are  usually  1  in  to  If  i^ 
with  octagonal  bars  f-in  to  {-in.  in  dia.  The  minimtim  diameter  of  bofe 
(at  bottom)  for  use  of  dynamite  is  about  I  in.  The  hand  drfll  is  ojKcc 
called  a  jumper.  Rotary  drills,  rotating  drills,  or  augers  are  names  gnsw 
to  (hand  or  machine)  drills  which  bore  solid  holes,  or  annular  rixsgs  aiwc» 
solid  cores.  They  are  generally  used  in  the  softer  rocks  where  heavy  Was» 
arc  required.  Such  drills  can,  however,  penetrate  almost  any  roatenJ 
liable  to  be  encountered,  instances  being  recorded  in  which  borings  ha^ 
been  made  through  imbedded  steel  rails  used  for  foundations.     Core  dnBs 

*  The  writer  knows  of  an  instance  where  a  whole  rock  cut  was  taken  o3t 
to  sk>pe  of  i  to  1,  where  A  of  it  could  have  been  verti«l,  or  at  least  t  to  L 


023 


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924 


65.— /JOCK  EXCAVATION. 


dynamite  proved  to  be  the  best  generally.  The  sticks  were  IJ  x  6  ins^ 
weighing  |  lb.,  and  10  to  25  sticks  were  charged  in  a  hole.  The  price  p>er  lb„ 
including  caps  and  ftise,  was  about  12  cents  and  about  1  lb.  of  dynamite 
was  used  per  cu.  yd.  of  xx)ck. 


iiiiiiiiii ■MiiiiiiimftiiiiiHi»n(<'^     _—— .» 

K sos'a H 

Ctilcago    Moin    Drainage    Channel. 

Fig.  3. 

Channeling  machines  of  the  Sullivan  and  Ingersoll  types  were  used  in 
order  to  secure  smooth  side  walls  to  the  canal.  The  average  machine 
weighed  11000  lbs.,  was  operated  on  a  track  30  ft.  long,  and  struck  250 
blows  per  min.  The  width  of  the  channel  cut  by  the  bit  was  2|  ins.  at  the 
top,  decreasing  |  in.  for  each  2  ft.  of  depth.  The  speed  of  channeling  was  13B 
to  200  sq.  ft.  per  10  hrs.  on  the  upper  lift  (where  the  nx^  was  softer)  and 
about  half  as  much  on  the  two  lower  lifts.  The  lifts  were  12  ft.  each.  The 
cost  of  the  channeling  varied  from  8  to  25  (say  17)  cents  per  sq.  ft.,  or  from 
8  to  7  (say  6)  cents  per  cu.  yd.  excavated. 

Steam  shovels  of  the  Bucyrus  type  were  employed  to  a  limited  extent 
in  loading  rocks  on  cars.  The  cars  were  operated  by  incline  and  hoist 
methods.  But  these  were  generally  more  expensive  than  the  cantilever, 
cableway  and  derrick  methods  of  conveyance  as  shown  in  the  two  following 
tables. 

1. — Cost  in  Cbnts  per  Cu.  Yd.  (Solid). 

I      .      M.     «     I     8     I 

Brown  Cantilever 3.9  4.1     8.0  3.2  1.0  3.6  14.6  0.0  88. S 

Lidgerwood  Cableway..    3.7  3.8     8.4  2.7  1.0  3.6  15.6  0.0  38.8 

Hullett-McMylerDerrick  3.9  4.0     7.4  2.5  1.8  5.8  18.3  0.0  43.2 

HuUett  Conveyor 4.1  3.7     8.5  3.8  1.2  6.2  21.4  0.0  48.9 

Car  Hoist,  No.  1 3.7  3.9     9.1  2.7  0.8  8.124.8  5.1  53.1 

Car  Hoist.  No.  2 3.9  3.6     8.9  3.2  0.9  1.2  22.9  2.3  47.1 

Car  Hoist.  No.  3 4.0  5.0  10.7  3.1  1.2  1.2  26.4  4.8  66.5 

Note. — Shop  repairs,  drill  sharpening  and  plant  rental  not  included. 

2. — Output  in  Cubic  Yards  by  Convbyors.* 


Section. 


Cu.  Yds. 


Cu.  Yds. 
per  10  Hrs. 


Cu.  Yds. 
per  Man  in 

Pit 
per  10  Hrs. 


10 
8 
7 
7 
9 
8 

10 
9 

14 
_    14_ 

*  Compiled  by  Mr.  W.  G.  Potter, 
hour. 


Brown  Cantilever 

Lidgerwood  Cableway 

Hullett-McMyler  Derrick.. . 

Hullett  Cantilever 

Hullett  Conveyor 

Car  Hoist,  No.  1 

Car  Hoist,  No.  2 

Car  Hoist,  No.  3 

Double  Boom  Derrick 

St.  Paul  Derrick 


443.750 
600.725 
180,406 
109.397 
178.839 
181.674 

60,841 
308.581 
324.880 

63.700 


478 
397 
217 
235 
336 
285 
269 
463 
282 
153 


10.45 
10.25 
8.52 
9.91 
6.85 
6.96 
6.98 
6.82 
8.22 
8.22 


Common  labor  received  15  cents  pier 

Digitized  by  VjOOQ  IC 


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926  C6.'-R0CK  EXCAVATION. 

EXCERPTS  AND  REFERENCES. 

The  WeU  Driller  for  Drffling  BUstinc  Holes  (Bng.  News.  Jtme  23. 
1904). — On  the  excavation  work  for  the  Wabash  R.  R.,  in  Ohio,  in  drilling 
brown  sandstone  the  holes  were  put  down  to  a  depth  of  24  ft.  with  a  3*  bit. 
and  the  drill  averaged  two  such  holes  per  day  of  10  hours.  The  cost  ot 
labor,  fuel  and  water  was  about  12^  cents  per  ft.  of  hole  drilled.  In  the 
blue  standstone,  which  is  softer,  an  average  of  60  ft.  per  day  was  drilkd. 
Formerly,  with  chum  drills  by  hand,  the  cost  in  brown  sandirtone  has  been 
38  cents  per  ft.  of  hole,  the  holes  being  20  to  30  ft.  deep;  the  steam  drills, 
up  to  depths  of  20  ft.,  and  in  sandstone  no  harder,  reducing  this  coct  but 
very  little.  The  well-drill  holes  being  large  (3*)  are  never  sprung"  more 
than  three  times  in  the  sandstone,  whereas  the  steam-driU  holM  (Ip)  most 
be  sprung  4  or  6  times. 

Methods  of  Sabaqyeoas  Rock  Excavation,  Buffalo  Hafhor,  N.  Y. 
(Eng.  News,  July  6. 1906). 

Rock  Excavatioa  by  Mechanical  Power  Instead  of  Expk»sives  (Bng. 
News.  June  26.  1908). — Editorial  on  the  Lobnitz  rock  breaker  and  similar 
machines. 

lUnstrations  of  Machines,  Tools,  etc 
Description.  Eng.  News. 

Austrian  drill  boat  with  screw-operated  spuds  May  26,  '10. 

Bng.  Rec. 
Excavating  submerged  rock  with  a  drill  boat,  N.  Y.,  N.  H.  & 
H.  R.  R.  Jan-     8,  '10. 


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d  by  Google 


Lit  wean 
clayey  i 
(someti 


928  ^.—DREDGING, 

grapple  dredge,  (3)  the  bucket  elevator  dredge,  (4)  the  hydraulic  drtedc 
Each  of  these  is  particularly  adapted  to  certain  kinds  of  dredging  and  the 
are  many  modifications. 

The  Dipper  dredge  (Fig.  1)  is  really 
a  long-hanafed  dipper  or  shovel  which 
is  filled  by   pressuig   the    scoop    down 
into  the  mud  while  bcin^  swung  radi- 
ally outward.     The  material  is  dumped 
through   the   bottom   of    the     bucket, 
which    is   movable     (usually    hinged). 
This   is   the    best    all-around    type   of 
dredge   for  general  use.     The   buckets 
average  1  to  2  cu.  yds.,  but  may  be  of  i 
any  size  up  to  6,  10  or  even  15  cu.  yds.  | 
capacity.    They  are  capable  of  working  I 
in  very  soft  and  very  hard  material  and  ' 


are  geneijilly  useful   around    wharves, 

and  for  channel  and  canal  excavation. 

30  ft.  of  water  is  about  the  limiting  .   Fig.  1. 

depth  for  good  work.  Dipper  Dredge. 

The  Clam-shell  bucket  (Fig.  2)  is  suspended  from  a  derrick  boom  or 
scow  and  is  a  form  of  grapple  dredge.  The  bucket  is  lowered  with  ja^a 
open,  and  sinks  into  the  mud  by  its  own  weight. 
The  jaws  are  then  closed  arouncf  the  material  and 
the  bucket  is  raised  and  dumped.  The  capacity 
of  a  clam-shell  bucket  is  about  the  same  as  that 
of  a  dipper,  but  it  is  especially  adapted  to  deep 
dredging. 

The  Orange-peel  bucket  (Fig. 
3)  is  another  form  of  grapple, 
and  may  have  3  or  more  seg- 
ments which  arc  open  during 
its  descent  and,  after  pressing 
into  the  mud,  are  closed.  In 
addition  to  its  regular  work  in 
dredging,  it  is  frequently  em- 
ployed m  excavating  inside  of 
cylmders  which  are  being  sunk 
for  foundations. 

The  (Bucket)  Elevator 
Dredge  or  bucket  ladder  dredge 
consists  of  an  endless  ladder 
chain  to  which  buckets  are  at- 
tached. These  buckets  scoop  Fig.  2.  Pig.  3. 
up  the  material  from  the  bot-  Clam-shell  Bucket.  Orange-peel  Bucket- 
torn,  are  elevated  to  the  top  of 

the  ladder,  and  the  material  is  dumped  in  a  chute  or  on  a  belt  conviero 
which  deposits  it  as  required.  They  are  particularly  adapted  to  "sk:ir 
dredging  in  soft  material  for  canal  work,  etc.  They  leave  a  smooth  bot 
tom.  The  buckets  may  have  a  capacity  of  say  Vio  to  V»  cu.  yd.  each,  ani 
a  speed  of  30  to  40  ft.  per  min. 

For  discussion  of  sub-aqueous  electric  power  cable,  sec  Eng.  Nfws,  ui 
7.  1003,  and  Aug.  13,  1903. 

The  Hydraulic  Dredge*  is  used  in  the  improvement  of  waterways  vij 

in  the  reclamation  of  low  lands.  It  works  best  in  fine  material  ^^''^ 
remains  suspended  in  a  swift-moving  volume  of  water.  The  pricci:.«i 
features  of  the  hydraulic  dredge  are  the  rotary  butter  or  stirrer  to  kwsd 
the  material  and  keep  it  in  suspension,  and  the  centrifugal  pump  to  pun:| 
the  suspended  material  up  into  the  delivery  pipe  and  to  its  dcstxnaii>'* 
If  the  material  is  light  anci  loose  the  rotary  cutter  is  sometimes  replaced  b 
the  water-jet,  but  ordinarily  the  cutter  is  better,  and  must  be  used  -*3 
compacted  materials.  Sand  is  handled  easily,  but  if  it  is  sharp  and  M 
It  wears  out  the  pumps  quickly.  Coarse  gravel  is  out  of  the  question.  Sci 
clayey  mud  is  probably  the  best.  The  delivery  pipe  is  of  sheet  iron  or  st« 
(sometimes  wood -stave  pipe),  with  an  average  diameter  of  say  10  to  20ir» 


*  For  valuable  data  on  Dredges,  see  Eng.  Ntws  of  July  28.  1904. 


TYPES  OF  DR 


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930 


Sd.—UREDGfXG. 
Driluno. 


BaUard'0 
Reef. 


LtmeKfl 
CroaBln^ 


[Worked 

D rtU  hoore  ]  Delayed . : 

iTotaJ 

Number  of  holet  drilled. 

Number  of  feet  drilled 

Ft.  per  hr.,  actual  work.   

Ft,  per  cu.  yd.,  pay  material 

Ft.  per  cu.  yd.,  total  eic 

Distance  between  bolos 

Averaee  depth  of  boles 

Avemee  depth  of  pay  material 

pprcenta«e  of  drflllnii  below  pay  deptJi 

No.  of  lbs.  of  60*i  dynamite 

LbflL  per  cu.  yd.,  pay  material 

Lbs.  per  cu.  yd.,  total  excav 

Total  cost  of  drilling 

Cost  per  cu.  yd.,  pay  material 

Coflt  |)er  cu.  yd.,  total  excav 

Owt  per  lln.  ft.  drlUod 

Coet  per  drill  hour 


24.442 

982 

25.424 

30.023 

191.850 

7.9 

2.6 

1.4 

5ft, 

6.2  ft. 

I.OfU 

84.0  % 

110.305 

0.5 

0.8 

$59,235 

10.80 

SO.  4  4 

10.31 

12.25 


37,746 

1.278 

39.024 

29.236 

240.591 

6.4 

2.4 

1.9 

6ft. 

8.2  ft. 

5.0  ft, 

37.5  % 

222.396 

2.2 

1.8 

$105,245 

$1.04 

$0,865 

$0.44 

$2.69 


Note. — 75%  dynamite  often  produce  the  best  results. 

Dr.RRICK  SCOWft. 


Cost  per  aq.  yd.  of  area  Improved 

Cost  por  cu.  yd.  of  materlai  removed  by 
diver 


Ballardi 
Reef, 
at  $9.70 
•     11.2  moa. 
I        $10,865 
Tug  service 
Included  In 
klredglng. 

I         $0.0475 
I         $5.73 


.ln»e  Klin 
CroflBlng. 
'  3.0  mos. 
at  $9.70 

$12,610 

Tugservfi 

Included  I 

dredging 

$0.22 


Sum  MARY  OP  Cost. 


Ballard's    |   LJme  KQ 
Reef.        <    Croasing 

Droflt'ing 

$102,000 
69.235 
10.865 

$55.72 

Drilling 

105,24 

Derrick  Scows. 

12.61 

Totals 

$172,100 

$2.32 
$1.27 

$173,57 

Cofit  per  cu  yd.  of  pny  material 

$1.71 

Cost  per  cu.  yd.  of  total  eicavaUon 

$1.42 

Qold  Dredginff. — This  has  become  a  verv  profitable  ind 
of  the  streams  of  California.  Mr.  W.  P.  Hammon,  who  h 
experience  in  this  class  of  work,  writes  the  author  from  h. 
under  date  of  Sept.  12,  1906.  as  follows: 

In  handling  gravel  In  our  work  we  use  elevator  dredgee  entlrv 
dredge  not  being  so  eflflclent  or  economical;  In  fact.  In  most  place 
the  latter  la  altogether  Impracticable  for  the  reason  that  where  1 
boulders  are  frequent.  In  the  operation  of  a  bj^draullc  dredge,  tbc 
2^  *-  ^^^  Intake  of  the  suction  pipe  thereby  preventing  gold  Irom 
now  of  water. 

froTn^»i**^®  operated  elevator,  dredgee  with  steam  and  dectrlo  c 
nomipny^t®*^^'^**^,.'^^'^^^'"  that  electric  power  Is  at  least  50  pe 
eSSk  ^  ^LJ?*****'""^  <*'  ^^^  8Teat  convenience  dectrtdty  baa  o 
^fd^Jb^^rtS^  ''^  P°^"  *«'  '*  cents  per  kUowatt-bour.  and  w 


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982  S6.— DREDGING. 

Cutters  for  HydnuUc  Dredces  Woridof   io  Hard  Material  (Eng.  News. 

June  16,  1906).— Used  at  Alameda,  Cal.    Illustrated. 

The  Work  of  a  Ladder  Dredge  and  Belt  Conveyor  System  on  the  Fox 
River,  Wisconsin  (By  L.  M.  Mann.    Eng.  News, Oct.  25. 1906).— Illustrated. 

Dredging  Operations  at  Warroad.  Lake  of  the  Woods,  Minn.,  by  U.  S. 
Gov't  (By  Emile  Low.    Eng.  News,  Nov.  29,  1906).— Cost  data. 

The  Frahling  System  of  Suction  Dredging  (By  John  Reid.  Ens. 
News,  Mar.  6,  1908). — ^Table  of  comparison  of  this  type  with  American 
hydraulic  hopper  dredges. 

Large  Elevator  Dredge  for  Work  in  Boston  Harlx>r  (Eng.  News,  Jan.  27, 
1910). — Capacity  of  each  bucket  is  U  cu.  yds.  and  the  bucket  chain  is 
driven  ordinarily  at  a  rate  of  14  buckets  per  min.,  so  that  the  dredging 
capacity  with  full  buckets  would  be  1.100  cu.  yds.  per  hour.  This  has  been 
exceeded  by  more  than  30%  for  shorter  periods  in  actual  use.  For  driving 
the  bucket  chain,  a  double  tandem  compound  steeple  engine  is  provided, 
with  cylinders  12x16  ins.  by  18-in.  stroke.  This  is  entirely  separate 
from  the  engines  for  driving  the  vessel's  propeller  shaft.  The  ladder 
frame  is  of  steel  and  is  of  sufficient  length  to  woric  at  a  depth  of  51  ft. 
After  a  year's  service,  the  buckets  with  their  pins  and  busniiigs  are  re- 
ported in  good  condition  and  the  general  loss  of  time  and  cost  of  repairs  is 
said  to  compare  favorably  with  that  of  a  dipper  dredge  on  the  same  class 
of  work.  The  material  encountered  at  different  parts  of  the  channel  in- 
cluded hardpan,  clay,  stone  and  gravel.  The  ordinary  yardage  for  a  single 
day's  work  was  about  8,000,  and  under  favorable  conditions  as  much  as 
10,800  cu.  yds. 

Working  Costs  of  Gold  Dredging  in  Califomla  (By  Charles  Janin  and 
W.  B.  Winston.  Mining  and  Scientific  Press,  July,  1910).— The  total  oper- 
ating expense  per  cu.  yd.  varies  from  9.23  cts.,  for  difficult  digging,  down  to 
2.30  cts.  for  easy  diggmg  (fine  gravel). 

Illustrations. 
Description.  Eng.  News. 

Light-draft  stem-wheel  suction  dredge  for  Niger  river  Jime  16,  'IOl 

Eng.  Rec. 
Gold  dredging  and  rock  crushing  in  California  July   16,  'IQl 


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934 


l^.— TUNNELING, 


converging  toward  each  other  at  their  points.  This  "center  cut"  is  then 
widened  laterally  into  a  "heading"  from  which  the  bench  bek>w  is  easily 
worked  by  vertical  drilling  supplemented  by  horizontal  drilling  at  the  sides 
of  the  section.  Sometimes  a  central  core  is  left  to  support  the  centering 
temporarily.  There  are  various  modifications  of  the  above.  They  differ 
essentially  however  from  the  prevailing  Biux>pean  method  of  first  driving  a 
"drift"  at  the  bottom  of  the  section  and  working  upward.  In  either  methc^. 
where  possible,  the  work  progresses  in  benches  so  two  or  more  drilling  gangs 
may  be  employed  at  the  same  time.  Headings  and  drifts  are  often  advanced 
a  few  hundred  feet  beyond  the  main,  full  section — sometimes  a  thousand 
feet  of  more. 

DrilUnff  and  Blasting. — Hand  drilling,  and  even  steam  drilling,  as  being 
supplanted  by  drills  operated  with  compressed  air  or  electricity.  Where 
the  necessary  water  power  is  available  hydraulic  drills  are  used,  and  some- 
times show  great  economy  over  any  other  power;  at  the  same  time  each 
drill  is  supplied  with  a  jet  of  water  for  cleanmg  out  the  hole  and  laying  the 
dust  in  the  tunnel.  Compressed  air  has  the  advantage  of  incidentally 
ventilating  the  tunnel.  Electricity  becomes  economical  as  the  depth  of 
tunnel  increases  from  the  face  or  portal. 

Drills  may  be  mounted  on  tripods,  on  cars,  on  columns  (one  or  two 
drills  to  each  column)  which  brace  against  the  top  and  bottom  of  the  tunnel 
and  have  a  wide  range  of  action,  on  bars  which  brace  against  the  sides  of 
the  tunnel,  etc.  The  size  of  an  air  drill  is  denoted  by  the  inner  diameter 
of  the  cylinder. 

Dynamite  of  high  grade,  say  75%  down  to  60  or  60,  is  used  in  c^iter- 
cut  blasting  in  hard  rock,  as  granite,  trap,  basalt,  syenite,  gneiss,  etc.. 
while  for  soft  or  seamy  rock  and  for  trimming  up  on  the  sides  ox  the  tunnel 
a  lower  grade  of  dynamite,  say  40%,  is  better. 

The  'Radialaxes"  channebng  machine,  manufactured  by  the  Ing^soll- 
Rand  Co.,  has  been  used  to  some  extent,  and  its  general  efficiency  will  be 
watched  with  interest. 

Timbering. — In  hard,  solid  rock,  timbering  is  not  required  and  the 
finished  tunnel  is  often  left  rough  without  lining.  But  in  loose,  seamy 
rocks  and  in  the  common  soils,  the  sides  and  roofs  have  to  be  supported. 
Round  timbers  are  generally  used  for  timbering  because  they  are  cheaper, 
although  sawed  timbers  are  more  easiljr  framed  and  handled.  In  very 
loose  material,  lagging  or  sheeting  is  driven  longitudinally  of  the  tunnel 
behind  transverse,  segmental  girts,  or  it  may  be  driven  transversely  behind 
longitudinal  girts.  The  girts  are  supported  by  timber  props  or  struts,  sise 
about  12  X  12  ins.  if  sawed.  Another  method  is  to  omit  the  lagging  and  lay 
the  longitudinal  girts  close  together,  supported  by  segmental  ribs  of  timbers. 
If  these  sc^nnental  ribs  are  placed  close  together  even  the  sprts  mmj  be 
omitted.  Pigs.  2  and  3  show  simple  types  of  rafter  timbenng  in  smaH 
tunnels  in  which  the  lower  space  is  left  open. 


Fig.  2.  Pig.  3. 

Lining. — ^The  lining  may  be  of  timber,  brick,  stone  masonry,  concrete, 
etc.  In  subaqueous  work  the  lining  is  frequently  of  cast  iron,  steel  or  rein- 
forced concrete.  The  thickness  of  plain  concrete  or  brick  lining  in  the  upper 
or  arched  section  will  of  course  depend  largely  upon  the  kind  of  material 
through  which  the  tunnel  is  driven.  In  loose  material  of  considerabto  depth 
the  thickness  of  the  concrete  lining  may  be  assumed  at  not  less  than  2  ft.  for 
a  single  track  railroad  tunnel,  and  somewhat  more  for  a  double  trade 
tunnel.      This  thickness  increases  gradually   in  the  lower  bench  wal^ 


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Q36  SI.—TUNNEUNG. 

S  or  a  times  as  much.  If  we  add  to  this  about  10  cubic  feet  per  man  for 
foulins  by  dust  and  gases  from  explosions,  we  have  a  basis  for  estimating 
the  minimum  number  of  cubic  feet  of  air  which  must  be  supplied  at  the  head- 
ing. This  must  be  increased  when  men  are  working  in  ditterent  parts  of  the 
timnel  and  also  when  locomotives  are  employed  to  handle  the  cars.  The 
purity  of  the  atmosphere  can  be  aided  materially  by  the  use  of  compressed 
air  drills  and  also  by  the  use  of  the  waterjet  in  the  drill  holes  and  by  wat«r 
sprinkling  elsewhere  to  lay  the  dust.  The  carbonic  acid  gas  exhaled  in 
breathing  may  be  aiigmented  by  "lire  damp"  or  carburetted  hydrogen  gas 
which  lies  pocketed  in  rocks  in  the  coal  measures,  sometimes  encountered 
by  railway  and  other  ttmnels. 

Vertical  shafts  in  tunnel  construction  are  sometimes  sunk  to  increase 
the  niunber  of  headings  and  push  the  work,  but  the  cost  of  sinking  them 
and  the  subsequent  cost  of  Handling  timnel  excavation  throtigh  them  is 
very  great.  These  shafts  are  left  open  for  ventilation  after  the  tunnel  is 
completed.  It  is  a  serious  question  however  whether  they  are  of  much  value 
for  this  purpose.  The  best  ventilator  is  an  express  train  running  down- 
grade through  the  txmnel  and  emitting  little  or  no  (black)  smoke,  in  which 
case  the  tunnel  shaft  is  not  only  of  no  aid  but  a  positive  hindrance  to  clear- 
ing the  tunnel.  A  central  shaft  is  sometimes  beneficial  if  located  in  about 
the  middle  of  a  very  long  tunnel  which  point  also  happens  to  be  the  stunmit 
of  two  ascending  grades;  but  usually  where  the  whole  tunnel  is  on  one 
grade  the  shaft  is  rather  a  drawback.  Artificial  ventilation  is  accompUAied 
usually  by  forcing  air  through  pipes  to  the  center  of  the  ttmnel,  or  by 
suction  at  the  ends  (through  closed  doors),  or  both.  With  the  advent  of 
electricity  in  the  operation  of  trains  the  aiJfficulty  disappears. 

**Shield"  Method. — ^This  method  is  employed  in  boring  subways  and 
subaqueous  tunnels.  The  shield  consists  of  a  cylindrical  steel  shell  with  a 
cutting  edge  pressed  against  the  head  of  the  tunnel  to  be  excavated.  A 
detachable  hood  is  provided,  when  boring  through  gravel  and  sand,  to 
replace  the  upper  and  side  portions  of  the  cutting  edge.  As  the  excavation 
progresses,  the  whole  shield  is  pressed  forward  b}r  hydraulic  jacks  or  shovixig 
rams;  and  in  order  to  preserve  true  alinement  in  the  finished  tunnel  it  is 
necessary  to  steer  the  shield  by  exerting  more  pressure  on  some  of  the  jades, 
thereby  giving  the  shield  a  certain  "lead"  or  angular  direction,  either  later- 
ally or  vertically,  or  both.  It  is  sometimes  necessary  also  to  ^ve  the  ^ield 
a  constant  lead  in  one  direction  in  order  to  produce  a  true  almement  when 
passing  through  certain  classes  of  material.  For  subaqueous  ttmneling, 
where  compressed  air  is  u.sed.  the  shield  is  a  very  complicated  machine,  ana 
the  progress  of  the  work  hinges  largely  on  its  proper  design.* 

"Dredging"  Method. — ^This  method  was  employed  by  McMuIlen  8c 
McBean.t  sub-contractors,  in  the  construction  of  the  west  half  of  the  river 
portion  of  the  Harlem  River  Tunnel,  New  York  City,  for  the  Rapid  Transit 
Railroad.    Mr.  McBean  describes  the  work  as  follows: 

First  a  channel  was  dredged  across  the  river  bottom  to  within  a  few  fleet  of  the 
full  depth  of  excavation  required  to  build  ttie  tunnel.  In  this  channel,  fooDdatloa 
piles  and  a  row  of  specially  prepared  heavy  timber  sheeting,  along  each  side  and 
acroBS  the  ends,  were  driven  and  cut  off  to  a  true  plane  about  25  ft.  Mow  the  surtsee 
of  the  water.  This  sheeting  forms  the  sides  and  ends  of  a  pneumatic  working  chamber. 
For  the  roof  of  this  chamber  a  platform  of  tlml>er  40  Ins.  In  thickness  and  extendlBg 
the  full  width  and  length  of  the  tunnel  section,  was  built  and  sunk  and  rested  on 
the  cut  off  sheetinK  which  formed  the  sides  and  ends  ss  above  described.  Stmidtaiie> 
ously  with  pumping  the  water  from  under  this  roof,  oompressod  air  was  Coreed  Into 
the  chamber  under  a  pressure  corresponding  to  the  pressure  of  ihe  water  above  the 
roof.  Inside  this  chamber  the  west  half  of  the  tunnel  was  buflt  and  then  tbe  Umbcf 
roof  was  removed. 

**Caisson'*  Method. — ^This  consists  in  btiilding  and  sinking  caiflKms  to 
the  reqtiired  level  below  the  surface  of  the  river  bed  and  later  connecting 
them  tcMether  so  that  they  form  sections  of  the  completed  tunnel.  See  Eng, 
Ntws  of  Feb.  15,   1906,  and  April  11,   1907,  for  illustrated  deacriptioci  oi 

.,     *  See  articles  on  "The  Construction  of  the  Pennsylvania  R.  R.  Ttmnels 
Under  the  Hudson  River  at  New  York  City,"  by  James  Forgie,  in  Eng.  News 
^«^  18,  190«.  and  Feb.  28.  1907. 
T  Mr.  D.  D.  McBean  is  credited  with  the  design  of^this  method  of  tun- 

"*•  Dgtized  by  Google 


t^rcTunm 


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938  57,— TUNNEUNG, 

Caacade  Tunnel.— (1897-1900.)  Single  track*  through  OMoade  ICts..  onOrcftt 
Northern  Ry.  Length  13813  ft.  =  2.62  miles.  Clear  width  16  ft.;  dear  height  above 
base  of  rail.  21.5  ft.  Concrete  lining,  a  to  3^  tt.  thick,  replacing  temporary  timber 
lining. 

Stampede  Tunnd. — ( 1 886-88.)  Single  track,  through  Cascade  Mts..  on  Northeni 
Pacific  R.  R.  Length  9850  ft.—  1.87  miles.  Contract  price  $118  per  lln.  ft..  wltho«tt 
masonry  lining. 

Busk  Tunnel. — (1890-93.)  Single  track,  through  Rocky  Mts..  on  Colorado  Mid- 
land R.  R.    Length  9395  ft.- 1.78  mUes.    aear  width  15  ft ;  dear  height  21  ft. 

Musconetoong  Tunnd. — (1872-75.)  DoubI»-track  R.  R..  on  E^Mton  and  Amboy 
(L.  V.  R.  R.).  Length  4879  ft.;  dear  width  26  ft.;  dear  height  21  ft.  (H.  a  Drtnkflr. 
author  of  "Tunndlng."  was  a  reddeat  engineer  on  this  work.] 

EXCERPTS  AND  REFERENCES. 

A  Proposed  VentllatlnK  System  for  the  Park  Ave.  Tunnel,  N.  Y.  City 

(By  A.  H.  Gary.    Eng.  News,  Aug.  8,  1901).— lUustrated. 

Sabaqoeous  Tunnel  Siphons  of  the  Mass.  Pipe  Line  Qas  Co.  (W.  W. 
Cummings.  Jl.  Assn.  of  Eng.  See.,  June,  1901;  Eng.  News,  Oct.  3,  1901). — 
lUiistrated  details. 

Difficult  Woric  in  Repairing  a  Swiss  RaUway  Tunnel  (Bng.  News, 
Sept.  26,  1902). — Shows,  by  illustration,  method  of  centering  for  caving 
roof. 

Freezing  Process  for  Building  the  River  Tunnels  of  the  P.  R.  R.  at 
N.  Y.  City  (By  Charles  Sooysmith,  Inventor.  Eng.  News,  Dec.  4.  1902).— 
Illustrated. 

Methods  of  Work  Adopted  in  Constructing  the  Chicago  Telephone 
Tunnels  (Eng.  News,  Feb.  19,  1903).— Illustrated. 

Tunnel  at  Michel  Creek  Loop,  Crow's  Nest  Pass  Line,  Can.  Pac.  Ry. 
(By  C.  R.  Coutlec.    Eng.  News,  April  2,  1903). — lUustrated. 

Construction  of  the  SImplon  Tunnel  (Eng.  News,  Atig.  13,  20.  27 
1903). — (Complete  description  of  the  tunnel  and  its  construction.  Illtis- 
trated. 

The  Pennsylvania  R.  R.  Tunnel  Under  the  North  River,  N.  Y.  City 
(Eng.  News,  Oct.  15,  1903). — Complete  detailed  description  of  method  ot 
construction.     Illustrated. 

The  East  River  Division  of  the  Penn.  R.R.  Tunnel,  at  N.  Y.  City 
(Eng.  News,  Oct.  29,  1903).— Illustrated. 

The  Cost  of  Concrete  Tunnel  Lining  and  of  Tunnd  Excavation  (By 
Geo.  W.  Lee.  Eng.  News,  Dec.  17.  1903). — Illxistrated  sections  with  cost 
data. 

Remarkable  Progress  of  the  Hudson  River  Tunnel  for  the  N.  Y.  & 
N.  J.  R.  R.  Co.  (Eng.  News,  Nov.  10,  1904).— Illustrations  of  shield. 

Waterproofing  the  P.  R.  R.  Tunnek  at  New  York  (Eng.  News, 
June  29,  1905). — Specifications. 

Concrete  Stringers  and  Tracks  in   Mine  Shafts   (Eng.  News.  Jan.  25, 

1906).— Illustrated. 

The  Ventilation  of  Tunnels  (By  C.  S.  Churchill.  Trans.  A.  S.  0.  B^ 
Vol.  LVII). — Includes  the  ventilation  of  subways. 

Tunnel  Lining  Work  in  the  Far  West  (Eng.  News,  Dec,  0.  1906).— 
Descriptive  and  illustrated  article  on  lining  and  rclining;  masonry  and 
timber. 

The  Construction  of  the  P.  R.  R.  Tunnels  Under  the  Hudson  River 
at  N.  Y.  City  (By  James  Forgie.  Eng.  News.  Dec.  13.  20.  1907).— Complete 
Description  of  the  tunnel  and  its  construction.  Plans  of  shield.  Tables 
VI  and  VII  (Eng.  News,  Feb.  28):  Comparative  Statement  Giving  Partic- 
ulars  of  Some  of  the  Principal  Tunnels  (Railroad  and  Other  Than  Raihtiad) 
(Constructed  Under  Waterways.     Very  comprehensive. 

Alpine  Railway  Tunnel  Data  (Eng.  News,  Dec.  5,  1907).— TabK 
giving:   Particulars  of  the  Pour  Principal  Alpine  Railway  Tunnels. 

Records  in  Rock  Tunneling  (Eng.  News,  April  2,  1908}.— Qiows 
I>roRre88  figures—greatest  advance  made  in  any  one  month,T  in  Icet,  for  a 
wngle  heading,    fc,  also.  Eng.  News.  Nov.  19.  lOOS^OOglC 


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940  hT.—TUNNEUNG, 

Description.  Bog.  News. 

Cross-flection  of  Cascade  tunnel,  for  electric  S3rstem  ^  Nov.  18,  'OJl 

Lining  and  grouting  tunnels  in  water-bearing  material  Nov.  25,  *09l 

Railway  tunnels;  cross-sec.,  grades,  lining,  drainage  Tune     2,  '10. 

Reconstruction  Washington  St.  Txinnel  under  Chicago  river"  July    21,  *1(L 

Typical  sections  of  ttmnels,  Catskill  aqueduct  Oct.    20.  '10. 

Eng.  Rec 

Concrete-lined  tunnel,  V  xV,  Los  Angeles  aqueduct  July     8,  'OSi 

Sections  of  the  Washington  St.  tunnel.  Chicago  I>ec.   11,  'OS. 

The  Bergen  Hill  4-track  tunnel.  Erie  R.  R-  Dec.   18,  '00. 

Sections  of  Main  St.  Subway,  Cambridge.  Mass.  Jan.      1. '10. 

Relining  railroad  tunnel  with  cast-iron  segments  Jan.      1,  *10. 

TerryviTle  tunnel,  double  track,  N.  Y..  N.  H.  &  H.  R.  R.  Feb.   26,  '10. 

Construction  of  tunnel  for  Great  Western  Power  Plant  July   10.  '10. 

Section  of  tramway  and  pipe  subway  in  Kingsway,  London  Dec.   10.  '10. 


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58.— SURVEYING,    MAPPING    AND 
LEVELING. 

Ctre  of  InttmmMiti. — ^The  correct  use  of  stirveying  instruments  takes 
into  consideration  their  lack  of  precision.  No  instrument,  however  carefully 
it  may  be  adjusted  in  the  shop  or  field,  will  remain  permanently  accurate 
with  ordinary  field  use.  New  instruments  hold  their  adjustments  better 
than  old  ones  because  the  parts  of  precision  are  less  worn.  With  good  care 
in  handling^  the  life  of  an  instrument  can  be  doubled  without  decreasing 
its  duty.  For  the  Level,  there  is  but  one  main  object  of  adjtistment,  namely, 
to  preserve  a  horiMontal  plant  of  sight  around  a  vertical  axis.  For  the  plam 
Transit  it  is  necessary,  m  addition  to  the  above  "horiiontal  plane"  acfiust- 
ments,  to  preserve  a  vtrtical  plant  of  sight  passing  through  the  point  ot  t^e 
suspended  plumbbob.  Note  that  when  the  instruments  arc  out  of  adjust- 
ment these  "planes"  of  sight  are  warped  into  "cones"  of  sight,  with  the 
apex  of  the  cone  at  the  center  of  the  telescope;  hence  the  adjustments  con- 
sist in  changing  "cones"  into  "planes"  of  sight. 

To  Adjust  the  Level.* — In  running  a  line  of  levels,  if  the  back-sights  and 
fore-sights  are  of  equal  length  the  results  of  the  leveling  will  be  accurate 
even  if  the  instrument  is  out  of  adjustment,  as  shown  in  Fig.  L  Thus,  the 
elevation  of  each  of  the  turning  points    at 

R  will   be   accurately  determined,  but  the    I        m       i   _^__^_^ 
"height  of  instrument"  in  each  case  will   "n       ^       J,         J^  |  , 

be  wrong  because  the  lines  of  sight  are  "         L         jL   A    I 

not  level.     For  general  leveling,  however,  .  L   R 

the  instrument  should  be  adjusted  so  that  Fig.  L 

all  sights  will  be  leveL 

First,  the  cross-hairs,  or  line  of  collimation. — "Set  up"  the  level  firmly 
(although  it  need  not  be  accurately  leveled)  with  one  diagonal  pair  of  leveling 
screws  /  in  line  with  the  teleeoo(>e.    Open  the  clips  c  c.  Fig.  2,  so  the  tele- 


Fig.  2.— -The  Level. 

cope  wiU  be  free  to  revolve  in  the  Ys.  Adjust  the  eye-glass  t  by  the  milled 
crsid  #',  SO  the  cross  hairs  appear  distinctly.  Sight  the  telescope  7  on  a 
i slant  point  (at  the  intersection  of  horizontal  and  vertical  lines)  about 
^O  to  360  feet  away,  as  this  is  the  usual  length  of  sight  for  accurate  leveling. 
rove  the  object  glass  o  by  the  milled  head  </  so  that  the  object  is  seen 
iist-inctly  without  "parallax"  (i.  e.,  without  the  cross-hairs  "dancing"  or 
^p>earizig  to  move  away  from  a  straight  line  of  sight).  With  the  bubble 
it>«  below  the  telescope,  as  shown  in  the  illustration,  move  the  line  of 

*  See  also  "peg-adjustment"  described  in  the  fourth  adjustment  of  the 

•^  Digitized  by  V^OOQIC 

941 


042 


S8.SURVEYING,  MAPPING  AND  LEVELING. 


sight,  by  means  of  the  leveling  screws  I  and  the  tangent  screw  t,  so  the 
intersection  oi  the  cross-hairs  will  cover  the  distant  point.  Now,  theoretic- 
ally, if  the  telescope  is  revolved  in  the  Ys  by  revolving  the  bubble  tube 
completely  around  it,  the  cross-hairs  are  in  adjustment  if  their  inteisectioo 
oontmues  to  cover  the  distant  point.  That  is,  the  line  of  sight  is  akmg  tbe 
central  axis  of  the  telescope  and  pierces  the  center  of  the  obiect  glais. 
When  either  cross-hair  leaves  the  distant  object  it  is  out  of  aajxistmsot. 
The  cross-hairs  are  stretched  across  a  circular,  movable  ring  or  diaphrago, 
called  the  rgHcuk^  held  in  position  by  four  adjtisting  screws  s.  To  move  the 
horizontal  cross-hair  upward,  loosen  the  top  screw  and  tighten  the  bottotn 
one.  (See  also  Fig.  6.)  The  reverse  operation  will  lower  it.  Similarly,  the 
vertical  cross-hair  can  be  moved  laterally  by  the  two  side  screws.    That 


Fig.  3. — ^Level  Telescope. 

screws  are  turned  with  capstan  or  adjusting  pins.  To  adiust  Ut9  horimmiai 
cross-hair  bring  it  on  to  the  distant  object,  with  the  bubble  tube  below  the 
telescope;  revolve  the  telescope  half  rotmd,  in  the  Ys,  brin«[ing  the  bubble 
tube  above;  correct  ons-hcUf  the  variation  from  the  distant  object,  by  operat- 
ing the  top  and  bottom  screws  s.  Repeat  until  accurately  adjusted.  The 
vertical  cross-hair  can  be  adjtisted  in  the  same  manner. 

Secotid,  the  bubble  tube. — ^With  the  clips  e  open  as  before.  Icvd  the 
instrument  and  lightly  clamp  the  telescope  over  one  set  of  leveling  screws  t, 
by  means  of  the  tangent  clamp.  Now  level  the  bubble  B  accuratelv,  gently 
lift  the  telescope  out  of  the  Ys  and  set  it  back  reversed,  end  for  end.  If  the 
•bubble  is  still  level  it  is  in  adjustment.  If  it  moves  either  way  from  a 
central  position  it  is  out  of  adjustment.  Correct  om-kalf  the  variation  irom 
the  central  position  with  the  leveling  screws  and  the  balance  by  operating 
the  capstan  nuts  n  at  the  right-hand  end  of  the  tube  as  shown  in  Pv.  % 
thus  rising  one  end  of  the  tube  to  a  level  position.  Repeat  (after  levding 
the  instrument  again  with  the  leveling  screws  /)  until  the  bubble  remains 
central  in  the  tube  upon  reversing  the  telescope  in  the  Ys. 

Third,  the  Ys. — In  the  two  previous  adjustments,  we  have  fixed  the 
line  of  sight  centrally  through  the  telescope,  and  adjusted  the  bubble  tube 
parallel  with  it.  It  now  remains  to  adjust  the  Ys,  in  which  the  telescope 
rests,  to  the  same  level,  so  that  when  the  instnunent  is  leveled  up  the 
vertical  center  pin  will  be  truly  vertical,  and  the  line  of  sight  truly  horisontal 
in  any  direction.  To  do  this,  level  up  the  instnmient  carefully,  and  start 
with  the  telescope  over  one  set  of  the  leveling  screws  /.  With  the  telescope 
clamped  firmly  m  the  Ys.  swing  half  round  on  the  vertical  center  pin  so  the 
telescope  will  rest  over  tne  same  screws  but  reversed  in  direction.  Coneci 
one-half  the  variation  of  the  bubble,  from  the  central  position,  with  the 
leveling  screws  /,  and  the  balance  by  means  of  the  large  capstan  nuts  N, 
operated  with  large  adjusting  pins,  and  similar  to  the  nuts  »  described  in 
the  second  adjustment.     (Level  up  and)  rep^it,  with  the 


until  adjustment  is  effected.  The  adjustment  may  be  repeated  over  the 
other  set  of  screws  in  order  to  test  the  workmanship  of  the  vertical  center 
pin  and  bearings,  but  it  is  rarely  done. 

To  Adjust  the  Transit.— Even  with  a  transit  considerably  out  of  adjust- 
ment, leveling  can  be  done  by  using  equi-distant  back-  and  fbrr  sights; 
straight  hues  can  be  run  by  half-revolving  the  alidade  (commonly  called 


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944  S8.— SURVEYING,  MAPPING  AND  LEVEUNG. 

the  telescope  vertically  downward  and  fix  a  law  point  on  the  line  of  sight. 
Now  revolve  the  alidade  180^,  sight  again  on  the  high  point  and  get  another 
low  point  beside  the  first  one.  A  point  midway  be- 
tween the  two  low  points  will  lie  in  a  vertical  plane 
passing  through  the  high  point.  The  adiustment 
can  then  be  made  on  the  standard,  using  these  two 
fixed  points. 

Third,  the  vertical  hair  or  line  of  collimation. 
— By  the  two  preceding  adjustments  we  have 
secured  a  vertical  axis  for  the  alidade,  and  a  hori- 
zontal axis  for  the  telescope.  It  now  remains  to  ad- 
just the  vertical  cross-hair  in  the  telescope  so  that 
m  revolving  through  a  vertical  circle  the  line  of 
sight  will  describe  a  vertical    plane    instead  of  a  Fig.  ft. 

"cone,"  or  in  other  words,  so  that  a  straight  line  may  be  produced  by 
"reversing  the  instrument  (telescope).  Set  up  the  instrument  on  fairly 
level  ground.  Sight  on  a  fixed  point  a.  Fig.  7,  reverse  the  telescope  ver^ 
tically.  and  set  a  point  b  on  line  in  the  opposite  direction  from  a;  revolve 
the  alidade  180^,  set  the  instrument  agam   on  a, 

reverse  the  telescope,  and   set   a   point  c  on  line  ^.     _^— — # 

opposite  the  point  b.  Correct  the  vertical  cross-  _.—-^.— 5Sfes^~I-4e- 
hair  by  moving  it   laterally   so   the   line  of  sight   •  ^*~"*— -Jj^ 

strikes  d{cd^\d>).   This  is  done  by  operating  the 
side  capstan-heiaded  screws  c  which  move  (laterally)  p».     « 

the  diaphragm  ring  orreticule  to  which  thecross-hairs  '^^  '• 

are  attached.  Repeat  the  whole  operation  until,  on  reversing,  the  first  and 
second  points  (6  and  c)  coincide  at  e,  on  the  straight  line  produced.  If  the 
"vertical"  cross-hair  is  not  truly  perpendicular  (which  can  be  tested  by 
sighting  at  a  plumb-string)  it  should  be  made  so  during  this  adjustment. 
This  is  done  by  loosening  two  adjacent  screws  of  the  reticule  and  tapping 
gently  against  their  heads  in  the  direction  required. 

Fourth,  the  telescope  bubble. — ^This  is  generally  accomplished  by  what 
is  called  the  "peg-adjustment."  sometimes  also  adopted  in  the  adjustment 
of  the    engineer  s    level.    Two  leveling  pegs,  a 
and  b,  are  driven  nearly  level  and  about  260  ft. 
apart  (Fig.  8).    The  instrument  is  set   up  at  i4. 
alxjut  a  foot  from  the  rod  at  a,  and  rod  readings 
are  taken  at  a  and  6,  these  readings  being  resp)ec-     x"^ 
tively  i4,  and  Ay..     Similarly,    with  the   instru- 
ment at  B,  readings  Bb  and  B.  are  taken.  Then*  pjg,  g, 
from  the  nature   of  the  problem, 

i4.-B.-Av-Bb  db  2c (1) 

in  which  c->the  inclination  of  the  line  of  sight  from  the  horizontal,  between 
the  two  rods.  Now  with  the  instrument  at  B,  fix  a  point  on  the  rod  at  a, 
at  elevation  B»±c  above  the  peg;  sight  the  telescope  on  this  point,  using 
the  horizontal  cross-hair;  and  bring  the  telescope  bubble  to  a  level  in  the 
tube  by  raising  or  lowering  one  end  of  the  latter,  with  the  adjusting  screws. 
Equation  (1),  m  practice,  will  determine  whether  c  is  +  or  — .  Repeat  the 
above  for  a  new  and  more  refined  adjustment. 

Fifth,  the  vertical  arc  or  circle. — If  the  transit  has  an  attachment  for 
reading  vert  ical  angles,  it  is  desirable  that  the  angle  shall  read  scro  whea 
the  telescope  is  honzontal.  To  adiust  the  vertical  arc  or  circle,  level  up  the 
instrument,  and  then  level  the  telescope  by  the  attached  bubble.  Adjoit 
the  vernier  (attached  to  the  standards)  so  the  zero  mark  will  coincide  with 
the  zero  of  the  vertical  circle  or  arc.  If  the  vernier  is  not  adjustable,  reoord 
the  "index  error"  to  be  used  with  all  vertical  angles  measured. 

The  Solar  Attachment. — ^This  is  a  small  instniment  attached  to  the 
upper  part  of  the  transit  telescope,  for  determining  the  meridian,  latitiule, 
time,  etc.  It  is  used  largely  in  government  land  surveying  where  the 
section  and  township-lines  are  supposed  to  run  in  the  direction  of  the 
principal  points  of  the  compass. 

Fig.  8  illustrates  the  solar  apparatus  manufactured  by  the  Messrs. 
Gurlcy,  of  Troy.  New  York. 

_,^5^  .*??***•  shown  represent  those  supposed  to  be  drawn  upon  the  eooesvt 
»JiII?^«^  *^.*»?*^«»-  When  the  telescope  Is  set  horizontal  by  Its  spirit  levei.  tbe 
noar  angle  wfli  be  In  the  plane  of  the  horlaon.  the  pdar  axis  wiu  point  to  the  i       ' 


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t&e'Amf"*'  ^Kmuller.  1881 
^  A«encan  Ephemerii  or  Nkutical  Atoaiuc 


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948  m.-^SURVEYING,  MAPPING  AND  LEVELING. 

Computation. 
Deollnatlon  at  Greenwich  noon«  7  a.  m.  standard  time  75th 

^^      meridian -  P  32' Sr  eouth 

Hourty  change-  68.5'.    Change  for  7*  hou«=.  58.5  X  7*         -        7'  ay  eouth 

Dedlnatlon  at  2  p.  m  -      -      -      -      -      —  r  40'  12*  aouth 

Average  vertical  angle  by  observation  -  -  31*  03'  00* 
Correction  tor  refraction  -       -       -       -   =»         l'  40* 

TrucalUtude -Sl-'OrzO' 

LaUtude  of  Thayer  School    -  43®  42'  10» 
Station  about  1  mile  south  »  1'  00" 

LaUtude  of  sUUon         -  43*'  41'  10" 
rvi.x  P7  <:»  i/sln  »  a  X  sin  (^  3  -  co-decl.) 

^^^^^^      V siQ  00-alt.X  Bin  oo-lat. 

where  S-co-dcd.+oo-alt+oo-lat. 
c*-decl.-   9l»  40'  ir 
co-alt.-    58«  68'  40* 
co-lat.-   46«  18'  50* 


S-196"  57' 42* 


i5-    980  28'  51' 

co-ded.-    •l"  40'  12* 

4  5-oo-ded.-     6<»  48'  39* 

log  sin   98*'  28'  51'  -    9.996225 

••       •       6<»  48'  39*  -    9.074052 

a.C     "     "     58"  58' 40*  =-    0.067035 

a.C.     "     "     46*  18' 50*  —    0.140781 


19.277093 


log  cofl  i  PZS  -    9. 638546 
JPZS-    64*  12' 40" 
PZS=I28«  25' 20* 
Axlmuth  of  sun  from  north      "•  128*  25"  20* 
Amde  between  sun  and  mark  »   42*  06'  15' 

Angle  north— station— mark    —  170*  31'  35* 
*'I1  a  rtngle  observation  Is  made,  the  altttude  must  be  changed  br  tbe  aemi- 

16' 
diameter  (16')  and  the  horizontal  angle  by.  not  16'.  but   js^nfu*    Ttiedlliedni 

angle,  whose  edge  Is  the  verUoal  line  tbroogh  the  Instrument  subtended  by  the 
SSS-dlimetcr.^mles  with  the  altttude  of  the  sun.  from  16'  for  alt.-0*.  to  4^  Itor 
SL-67*on  June  2 let.  in  this  latitude  (43*  42')." 

Meridian  from  the  North  Star.— Polaris  is  a  distant  "fixed"  star  called 
the  north  star.  It  lies  about  in  line  with  the  two  "pointers  of  the  '"big 
dipper"  (the  two  stars  farthest  from  the  "handle  )  and  ^«ng  ita  op«i  toe. 
It  isthe  brightest  star  of  a  cluster  of  three  forming  one  end  of  Uracr  Mmor 
and  can  be  recognized  easily.*  The  earth's  axis  ifproduced  wiU  never  piecce 
the  north  star,  but  wabbles  around  it  m  a  circle.  This  makea  the  star 
aooear  to  move  in  a  circle  around  the  truefnorth  point  (Fig.  14),  and  hence 
we  oonsider  the  pole  P  as  fixed,  and  the  star  to  move   around  it-     The 

*The     accompanying  \         \        J  y 

diagram  will  aid  m  finding  <=i>        ?-      4?        ^<- 

Polaris  at  any  time  of  the        "*^-^     .     .  1  ^       jun 

while  facing  the  north,  in  ^.                        or         ^30  '^  A.    _^ 

such  a  position    that    the  y*                  JB^^H :.VMay"* 

month,  during  which  the  J^                          "  ^Qitfe^i€r  ^PSSll,m 

observation  is  made,  will  *-Mov.                           Vffitw  kfiSlS 

wjint   vertically    upward.  ^^                V*r^J~^  i 

Polaris  crosses  the  merid-  ^^        J^•          i.^  v^ 

ian  on  April  10th  of  each  y       \       %^ 

year  at  about  noon.  /        *1    r^  "^ 


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9M 


SS.— SURVEYING,  MAPPING  AND  LEVEUNG, 


2. — Azimuth  op  Polaris  at  Elongation  Jan.  1. 
For  Various  Years  and  Latitudes. 


Lat. 

1900.0 

1905.0 

1906.0 

1907.0 

1908.0 

1909.0 

1910.0 

Yearir 
Decroaae. 

o 

o      » 

0       » 

0         i 

o        » 

0         ' 

0         » 

0          » 

•   ' 

+  25 

1   21   2 

1   19.4 

I   19.1 

I   18.7 

1   18.4 

1   18.1 

1   17.7 

0  0.35 

26  ! 

21.8 

20.1 

19  8 

19.4 

19.1 

18.7 

18.4 

0.35 

27 

22.5 

20.8 

20.5 

20.1 

19.8 

19.4 

19.1 

0.35 

28 

23.3 

21.6 

21.3 

20.9 

20.5 

20.1 

19.8 

0.35 

29 

24.1 

22.4 

22.1 

21.7 

21.3 

20.9 

30.  S 

0.86 

30 

1  24.9 

1  23.1 

1  22.8 

1  22.4 

1  22.1 

1   21.7 

I  21.3 

0  0.36 

31 

29.8 

24.0 

23.6 

23.2 

22.9 

22.5 

22.2 

0.36 

32 

26.7 

24.9 

24.5 

24.1 

23.8 

23.4 

23.1 

0.37 

33 

27.7 

25.9 

25.5 

25.1 

24.7 

24.3 

24.0 

0.87 

34 

38.7 

26.9 

26.5 

26.1 

26.7 

25.3 

26.0 

0.36 

35 

1  29.8 

1  27.9 

1   27.6 

1   27.1 

1   26.8 

1   26.4 

1  26.0 

0  0.38   «• 

36 

30.9 

29.0 

28.6 

28.2 

27.9 

27.6 

27.1 

0.39  S 
0.39  « 
0.40  1 
0.40  "3 

37 

32.1 

30.1 

29.7 

29.3 

29.0 

28.6 

28.2 

38 

33.3 

31.4 

31.0 

30.6 

30.2 

29.8 

29.4 

39 

34.7 

32.7 

32.3 

31.8 

31.4 

31.0 

30.6 

40 

1   36.0 

1   34.0 

1   33.6 

1   33.2 

1   32.8 

1  32.4 

1   32.0 

0  0.41  i 
0.41   E 

41 

37.5 

35.4 

35  0 

34.6 

34.2 

33.8 

33.4 

42 

39.0 

36.9 

36.5 

86.0 

35.6 

86.2 

34.8 

0.42    J 

0.43  5 

43 

40.6 

38.5 

38.1 

37.6 

37.2 

36.8 

36.8 

44 

42.3 

40.1 

39.7 

89.2 

38.8 

38.4 

37.9 

0.44  ^ 

45 

1  44.0 

1   41.8 

1  41.4 

1  40.9 

1   40.6 

1  40.1 

1  89.6 

0  0.44   1 

46 

45.9 

43.7 

43.2 

42.7 

42.3 

41.9 

41.4 

0.45  ^ 

47 

47.9 

45.6 

45.1 

44.6 

44.2 

43.7 

43.3 

0.46  1 
0.47  1 

48 

49.9 

47.7 

47.2 

46.7 

46.3 

45.8 

45.3 

49 

62.1 

49.8 

49.3 

48.8 

48.4 

47.9 

47.4 

0.48  Z 

50 

1   54.4 

1   52.0 

1   51.5 

I   61.0 

1   50  6 

1   60.1 

1  49.6 

0  0.40  i 

61 

56.9 

54.4 

54.0 

53.6 

63.0 

52.5 

62.0 

0.40  1 

52 

59.5 

57.0 

56.4 

65.9 

55.4 

54.9 

54.4 

0.51   * 

63 

2  02.2 

69.6 

59.1 

68.6 

58.1 

57.6 

57.1 

0.52  5 

54 

05.1 

2  02.5 

2  02.0 

2  01.5 

2  00.9 

2  00.4 

1   59.9 

55 

2  08.3 

2  05.6 

2  05.0 

2  04.4 

2  03.9 

2  03.4 

2  02.8 

0  0.56  1 

56 

11.6 

08.8 

08.2 

07.7 

07.1 

06.6 

06.0 

0.56   1 

67 

15.1 

12.2 

11.7 

U.l 

10.5 

10.0 

09.4 

0.57 ; 

58 

18.8 

15.9 

16.3 

14.7 

14.2 

13.6 

13.0 

O.SS  * 

59 

22.8 

19.8 

19.2 

18.6 

18.0 

17.4 

16.8 

0.60  5 

60 

2  27.1 

2  24.0 

2  23.4 

2  22.8 

2  22.1 

2  21.5 

2  20.9 

0  0.62   S 

61 

31.7 

28.5 

27.9 

27.2 

26.6 

25.9 

26.3 

0.64   3 

62 

36.7 

33.4 

32.7 

32.1 

31.4 

30.8 

30.1 

0  66 ; 

63 

42.1 

38.6 

38.0 

37.3 

36.6 

35.9 

35.2 

0.69  £ 
0.70^ 

64 

47.8 

44.3 

43.6 

42.9 

42.2 

41.6 

40.8 

65 

2  54.1 

2   50.4 

2  49.7 

2   49.0 

2  48.3 

2  47.6 

2  46.8 

0  0.73 

66 

3  00.9 

57.1 

56.3 

55.6 

54.8 

54.1 

63.3 

0.T6 

67 

08.3 

3  04.4 

3  03.6 

3  02.8 

3  02.0 

8  01.2 

8  00.4 

0.79 

68 

16.4 

12.3 

11.5 

10.7 

09.8 

09.0 

08.2 

o.u 

69 

25.3 

21.0 

20.1 

19.3 

18.4 

17.6 

16.7 

0.86 

70 

3  35.2 

3  30.6 

3  29.7 

3  28.8 

3  27.9 

8  27.0 

3  26.1 

0  0.91 

71 

46.1 

41.3 

40.3 

39.4 

38.4 

37.5 

86.  S 

0.06 

72 

68.2 

63.2 

52.1 

51.1 

60.1 

49.1 

48.1 

1.01 

Ex.— Elongation  of  Polaris  for  Lat  A'(  +  )38'>-30'  dunng  June- July, 
1914.  or  4i  years  after  Jan.  1,  1910.  is  I'^-W  minus  ik  times  <r-0'.40- 
!•- 28^.2. 


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952  6B.— SURVEYING,  MAPPING  AND  LEVEUNG, 

noon  of  a  civil  day,  and  each  is  24  hrs.  in  length.  Thus,  the  A.  hi  of  a 
civil  day  corresponds  to  the  last  half  of  the  preceding  astronomical  day, 
each  lapping  by  12  hrs.* 

In  making  an  observation  on  Polaris  for  azimuth,  it  is  necessary  to  know: 
(1)  the  latitude  of  the  place  of  observation,  which  may  be  obtained  from  a 
map;  (2)  the  mean  local  time  of  observation,  which  can  be  calculated  from 
the  particular  "standard  time"t  used  in  that  locality  when  the  longitude  <rf 
the  place  of  observation  is  known:  (3)  the  horizontal  measured  angle  fnom 
Pokuis  to  the  previously  established  base  line,  explained  under  ui),  pre- 
ceding, together  with  the  mean  local  time  of  observation;  (4)  the  hour 
angle  of  Polaris  at  time  of  observation,  to  be  calculated  from  Parts  I  and  II 
of  Table  3;  (5)  the  azimuth  of  Polaris  from  the  hour  angle,  date,  and  lati- 
tude of  place  of  observation,  to  be  obtained  from  Table  4.  (G)  Find  the  sum 
or  difference  of  the  azimuth  and  the  measured  angle,  explamed  xmder  (a) 
preceding,  and  lay  it  off  in  the  right  direction  from  the  established  base  line. 

Practical  Examplb  op  Usb  op  Tables  8  and  4. 
Place  of  observation,  lat.  41«N..  long.  lOO^W.:    Mountain  time,  8  30  p.m.. 
Nov.  8.  1911;  measured  angle  from  Polaris  eastward  to  base  line.  V — 40*.    Find  tbe 
astmuth  of  Polaris,  and  the  angle  of  base  Une  with  true  merkUan?   Then  we  liav»— 

*     m 

Standard  time  of  observation  (merld.  105®  W) 8  30.0 

Formertd.  100"  W..  add  5x  4  m. 20.0 

Mean  local  Ume  of  obs..  1 91 1.  Nov.  8 8  60. 0 

Equivalent  time  to  Nov.  7  (add  24  h.) 32  60.  0 

k     m 

Astrom.  time  U.  C  Polaris.  Nov.  It  (Table  3.  Part  I) 10  48. 0 

Reduction  to  Nov.  7  (Table  3.  Part  II)||  Subtract 23. 6      10  34. 4 

Hour  angle  of  Polaris  at  observation. 22  26.  < 

Subtract  from 23  60. 1 

Time  argument  for  Table  41 1  30. 5 

Aslmuth  of  Polaris,  at  observation  (lat.  4r) 0°  38*.  6    S. 

Measured  angle  eastward  from  Polaris  to  base  Une. r*  40^       £. 

Angle  of  base  line  eastward  from  true  meridian 3*  16*.  5   & 

Therefore  lay  oft  angle  3®  16'.5  westward  from  base  Une  to  true  merMlao. 

♦Civil  time  P» Af. ■» astronomical  time  with  the  P.M.  omitted;  thus. 
6.30  P.  M.  -  6h  30m  of  the  same  date.  Civil  time  A.  Af ..  + 12  hrs,  -astixmo- 
mioal  time  of  the  preceding  date*  thus,  5.30 i4.  Af.  June  2—  17h  80kn  June  1. 
Astronomical  time  under  izh  —  civil  time  P.  Af  of  the  same  date*  thusSh  JIQm 
—  6.30  P.Af.  of  same  date.  Astronomical  time  over  12h,  with  12  hra.  de- 
ducted from  it —  civil  time  A.  Af .  of  the  following  date;  thus.  I7h  SQm 
Jime  1  -  6.30  A.  M.  Jime  2. 

t  Standard  railway  time  for  longitude  west  from  Greenwich:  Inter- 
colonial time,  for  60**  west.  Eastern  time,  for  76*  west;  Central  time,  for 
90**  west;  Mountain  time,  for  105**  west;  Pacific  time  for  120**  west.  15® of 
longitude- 1  hr.  of  time  (1**=«4  m.);  15'  of  long.-l  mln.  of  time  (!'— 
4  sec.);  15*  of  long.-  1  sec.  of  time  (l'-0.6|  sec.).  Ex.— The  place  <rf 
observation  is.  say,  108**  west,  and  the  observer  has  Mountain  time:  hence 
the  mean  local  time  is  3X4  m.  — 12  m.  slower  than  his  watch.  For  MB* 
west  it  would  be  12  m.  faster  than  his  watch.  West  of  standard  time  meri- 
dian means  deduct',  east  means  add. 

X  This  is  the  nearest  date  preceding,  in  the  table.  Values  are  given  m 
Part  I  for  the  Ist  and  16th  of  each  month;  and  in  Part  II  the  reductioa  is 
given  for  succeeding  dates.  ^    ,      ^        ^ 

IJCJaution. — Be  sure  to  use  the  same  "Diff.  for  I  day  m  Part  n  as 
obtained  from  Part  I,  and  opposite  the  day  o£  the  month  Smblract;  don't 
add. 

tSee  "£x."  below  Table  3. 


d  by  Google 


d  by  Google 


964  58.— SURVEYING,  MAPPING  AND  LEVEUNG. 

4. — Azimuth  op  Poijutis 
(The  hour  angles  are  expressed  In  mean  solar  time.    The  occurrence  of  a  period  after 


Star  and  Azimuth.  I  Polaris  above  the  Pole. 

W.  of  N.  when  hour  angle  Is  less  than       I  To  determine  the  true  meridian,  the  asi- 
_il>«  A8-.  I     muth  win  be  laid  oft  to  the  euf  fT' 


Note.--From  the  "Ex."  below  Table  3.  preceding  page,  we  ftad  that  the  imper  tdh 
mlnatlon  of  Polaris  occurs  at  lO.ZOi  P.  A£.  on  Nov.  8. 1914:  and  that  the  time  of  obser^attea 
if*. K^.^^^^0^-'^-°^<'^  local  tlmcorlh.  30.5m.  eariler.  Henoe  the  position  of  IHilsjls 
?iii  4™Si*'  observation  Is  Just  to  the  rlghtof  U,  Fig.  14.  p.949.  Moreover,  tliestar^  toer 
t!i^^t^  ?^*^'^'lon  Is  23h.  56. 1 m.  minus  Ih.  30  5m.>-22h.  25.6m..  which  corrcaponfc 
tjl^n  i#*i^  ^lY*^"  *°  \P^  practical  example  preceding.  Have  graphically  Uk  mind  thepo^- 
Mon  or  the  sUir.  and  1  u  apparent  motion,  and  the  calculaUons  become  simple. 


AZIMUTH  OF  POLARIS.  966 

Land  Survbyors. 

e  or  of  an  boor  ancle  Indlcatea  (hat  Its  value  le  (H.  5  greater  than  prlnted.1 


~>11IC  HlUOUiiUWvr  VUluiiiuibivii  wi  M  uicuiovrvvuio  i  i  ii.  •nux,  u^iuicui  Bii/ci   viJC 

upper  (nilmlnatlon.  The  time  of  eastern  and  of  western  elongation  occurs 
lately 5h.55in.  before  and  after  the  time  of  upper  culmination.  Hence  the 
ioneitloa  may  be  obtained  from  the  above  table.  See  also  Fig.  14.  p.  949.  and 
p.  950.  lor  data  In  thla  connection.  r^^^^T^ 

Digitized  by  VjOOv  IVL 


iS.—SURVEYING,  MAPPING  AND  LEVEUNG. 


4a.«-PoLARi8,  1912,  FOR  Mbrioian  of  Orbbnwich. 
Civil  Date  and  Clock  Time. 


Date 

Upper  Cul- 
nuDatlon. 

Eloofa^tlon. 

Dedl- 

Date 

Upper  Cul- 
mmatlon. 

Elongation* 

DedK 

1912. 

Q'tlOQ. 

1912. 

Lat40*. 

B'ttOB. 

+88  50 

+88  51 

Jan. 

hm 

hm 

m 

Mar. 

hm 

hm 

# 

1 

6  47.4  PJI. 

W.E.  0  46.4  A.M. 

30.8 

1 

3  50.5  P.M. 

W.  E.  8  45.6  P.M. 

r.f 

a 

6  43.5 

0  43.6 

31.0 

2 

2  46.6 

8  41.7 

r.5 

8 

6  39.6 

0  38.6 

31.1 

3 

2  42.6 

8  37.7 

37.2 

4 

6  35.6 

0  34.6 
0  30.7 

31.3 

4 

3  88.7 

8  33.8 

17.6 

5 

6  31.6 

31.5 

5 

3  84.7 

8  29.8 

36.7 

6 

6  37.7 

0  36.7 
)l23.8 

31.6 

6 

3  30.8 

8  25.9 

16.4 

6  33.7 

31.7 

7 

3  26.9 

8  23.0 

M.l 

g 

6  19.8 

0  18.8 

31.8 

8 

3  33.9 

8  18.0 

25.8 

} 

6  15.8 

0  14.9 

31.9 

9 

3  19.0 

8  14.1 

tS.6 

10 

6  11.9 

0  10.9 

31.9 

10 

3  15.0 

8  10.1 

15.3 

11 

6    7.» 

0    7.0 

,  31.9 

11 

3  11.1 

8    6.3 

35.1 

12 

6    4.0 

/          0    8.0  A.M. 
I        11  59.1  P.M. 

«.. 

13 
13 

3    7.3 
3    3.3 

8    3.3 
7  58.3 

24.9 
24.6 

13 

6    0.0 

11  55.1 

32.0 

14 

1  59.8 

7  54.4 

34.4 

14 

5  66.1 

11  51.3 

33.0 

15 

1  55.8 

7  60.4 

34.1 

U 

5  52.1 

11  47.2 

33.1 

16 

1  51.4 

7  46.6 

28.9 

16 

5  48.3 

11  43.8 

83.3 

17 

1  47.5 

7  43.6 

23.6 

17 

5  44.3 

11  39.8 

33.2 

18 

1  43.5 

7  88.6 

23.3 

18 

5  40.1 

1  35.4 

32.3 

19 

1  39.6 

7  34.7 

22.9 

19 

5  86.8 

1131.4 

32.3 

20 

1  35.6 

7  30.7 

23.6 

80 

5  32.4 

11  37.5 

33.4 

21 

1  31.7 

7  26.8 

23.3 

21 

5  38.4 

11  23.5 

32.4 

22 

1  27.8 

7  22.9 

23.0 

22 

5  24.5 

11  19.6 

32.4 

23 

1  23.8 

7  18.9 

21.7 

23 

5  20.5 

11  15.6 

32.3 

24 

I  19.9 
1  16.0 

7  15.0 

21.4 

34 

5  16.6 

11  11.7 

32.3 

25 

7  11. 1 

21.1 

25 

5  18.6 

11    7.7 

32.2 

26 

1  13.0 

7    7.1 

20.9 

36 

6    8.7 

11    3.8 

33.3 

27 

1    8.1 

7    3.3 

20.7 

27 

5    4.7 

10  59.8 

32.1 

28 

1    4.1 

6  59.3 

28.4 

38 

5    0.8 

10  55.9 

32.1 

29 

1    0.8 

6  55.3 

28.1 

29 

4  56.8 

10  51.9 

83.0 

30 

0  56.8 

6  51.4 

19.8 

80 

4  52.9 

10  48.0 

32.0 

31 

0  53.8 

6  47.4 

19.5 

31 

4  48.9 

10  44.0 

32.0 

Feb. 

4  45.0  P.M. 

W.E.  10  40.1  PJ^. 

82.0 

Apr. 

0  48.4  P.M. 

W.  E.  6  43.6  PJt. 

W.I 

3 

4  41.0 

10  36.1 

82.0 

2 

0  44.5 

6  39.6 

18^8 

3 

4  37.1 

10  32.3 

33.0 

3 

0  40.6 

6  35.6 

Si 

4 

4  33.1 

10  28.3 

31.9 

4 

0  36.6 

6  31.7 

B 

4  39.3 

10  24.3 

81.8 

5 

0  33.7 

6  37.8 

17.8 

6 

4  25.3 

10  20.8 

31.6 

6 

0  28.7 

6  33.8 

17.5 

7 

4  21.8 

10  16.4 

31.6 

0  24.8 

6  19.9 

17J 

8 

4  17.8 

10  13.4 

31.3 

8 

0  20.9 
0  16.9 

6  16.0 

17.0 

9 

4  13.4 

10    8.5 
10    4.5 

31.2 

9 

6  13.0 

16.7 

10 

4    9.4 

31.1 

10 

0  13.0 

6    8.1 

16.1 

11 

4    5.5 

10    0.6 

31.0 

11 

0    9.1 

6    4.3 

16.1 

12 

4    1.6 

9  56.6 

30.8 

12 

0    5.1 

6    0.3 

U.8 

13 

3B7.6 

9  52.7 

30.7 

13 

0    1.3  P.M. 

W.  E.  5  66.3  P.M. 

16.5 

14 

3  53.7 

9  48.8 

30.6 

14 

U  57.8  A.M. 

E.  E.  6    3.3  A.M, 

U.3 

15 

3  49.7 

9  44.8 

30.5 

15 

11  53.4 

5  58.3 

14.9 

16 

8  45.8 

9  40.9 

30.4 

16 

11  49.4 

6  54.8 

14.S 

17 

3  41.8 

9  36.9 

30.2 

17 

11  45.5 

6  50.4 

142 

18 

3  37.9 

9  33.0 

30.0 

18 

11  41.6 

5  46.3 

13.9 

19 

3  33.9 

9  29.0 

39.9 

19 

11  87.6 

6  43.5 

136 

30 

3  30.0 

9  25.1 

39.7 

20 

11  33.7 

5  88.6 

U.3 

21 

3  26.0 

9  21.1 

29.4 

21 

11  29.8 

5  34.7 

I3.t 

22 

3  22.1 

9  17.2 

29.2 

23 

11  25.9 

6  30.8 

I3.« 

23 

3  18.1 

9  13.2 

29.0 

23 

11  21.9 

5  26.8 

13.5 

24 

3  14.3 

9    9.8 

28.8 

24 

11  18.0 

5  23.9 

13.3 

25 

3  10.8 

9    5.8 

28.6 

25 

11  14.1 

6  19.0 

13.1 

26 

8    6.3 

9    1.4 

28.4 

26 

11  10.8 

6  15.1 

11.8 

27 

3    2.4 

•  8  57.5 

28.2 

27 

11    6.8 

5  11.1 

11.5 

38 

2  68.4 

8  53.5 

28.1 

28 

11    2. 
10  58. 

6    7.3 

11.1 

39 

2Si-5 

8  49.6 

27.9 

29 

5    3.3 

19.8 

30 

3  60.5 

8  45.6 

27.7 

30 

10  54. 

4  59.3 

10.5 

31 

10  50.5 

itized  by  V 

4  66.4 

joogle 

16.3 

TABLES  OF  POLARIS,  JP12. 


9Ub 


.ARI8,  1013,  VOR  Meridian  op  Grbbnwich. — Continued. 
Civil  Date  and  Clock  Time. 


' 

HonpMon. 

Dedl- 

Date 

Upper  Cul- 

Dedl- 

n'Uon. 

1912. 

mination. 

Lat.40». 

Q'tlon. 

+88  50 

+  88  50 

h  m 

» 

^"T 

hm 

hm 

• 

[.  ] 

3.K.  4  55.4  A.lf. 

10.2 

6  51.5  A.U. 

E.E.  0  56.4  AJf. 

1.6 

4  51.5 

9.9 

2 

6  47.6 

0  52.5 

.7 

4  47.4 

9.7 

3 

6  43.7 

0  48.6 

1.7 

4  43.7 

9.4 

4 

6  39.8 

0  44.7 

.7 

4  39.7 

9.2 

5 

6  35.9 

0  40.8 

1.7 

4  35.8 

8.9 

6 

6  32.0 

0  36.9 

1.7 

4  31.9 

8.7 

7 

6  28.0 

0  33.9 

.7 

4  28.0 

8.5 

8 

6  24.1 

0  29.0 

1.7 

4  24.0 

8.3 

9 

6  20.3 

0  25.1 

.7 

4  20.1 

8.0 

10 

6  16.3 

0  21.2 

1.8 

4  14.3 

7.8 

It 

6  12.4 

0  17.3 

.9 

4  12.3 

7.5 

12 

6    8.5 

0  13.4 

.0 

4    8.3 

7.2 

13 

6    4.6 

0    9.5 

.1 

4    4.4 

6.9 

14 

6    0.7 

0    5.6 

.    3.2 

4    0.5 
8  64.0 

6.7 
6.5 

15 

5  56.7 

/          0    1.6  A.M. 
I         1157.7  P.M. 

},., 

8  52.7 

6.3 

16 

5  52.8 

11  53.8 

8.5 

3  48.8 

6.1 

17 

5  48.9 

11  49.9 

2.6 

3  44.8 

6.9 

18 

5  45.0 

11  46.0 

2.7 

8  40.9 

5.8 

19 

5  41.1 

11  43.1 

3.7 

3  37.0 

5.6 

20 

5  37.3 

11  38.3 

2.8 

3  33.1 

5.5 

21 

5  33.3 

11  34.2 

2.9 

3  29.2 

5.3 

22 

5  29.3 

11  30.3 

3.0 

3  25.2 

6.1 

23 

5  25.4 

.11  26.4 

3  21.3 

4.8 

24 

5  21.5 

11  22.5 

8!2 

3  17.4 

4.6 

25 

5;7.6 

11  18.6 

3.4 

3  13.5 

4.4 

26 

5  13.7 

11  14.7 

8.6 

3    9.6 

4.2 

27 

6    9.8 

11  10.8 

3.7 

3    5.6 

4.0 

28 

5    5.9 

11    6.8 

8.9 

3    1.7 

3.9 

29 

5    1.9 

1    2.9 

4.1 

2  57.8 

3.7 

30 

4  58.0 

0  59.0 

4.3 

31 

4  54.1 

10  55.1 

4.4 

M 

E.E.  3  53.9  A.M. 

3.6 

n 

4  50.2  A.M. 

E.E.IO  51.2  P.M. 

4.6 

2  50.0 

8.5 

2 

4  46.3 

10  47.3 

4.7 

2  46.1 

3.4 

3 

4  42.4 

10  43.4 

4.9 

2  42.1 

3.3 

4 

4  38.5 

10  39.4 

5.0 

2  38.2 

3.2 

5 

4  34.5 

10  35.5 

5.2 

2  34.3 

3.0 

6 

4  30.6 

10  31.6 

5.4 

a 

2  30.4 

2.9 

7 

4  26.7 

10  27.7 

5.6 

2  26.5 

2.8 

8 

4  22.8 

10  23.8 

5.8 

2  22.6 

2.6 

9 

4  18.9 

10  19.9 

6.0 

3  18.6 

2.5 

10 

4  15.0 

10  16.0 

6.3 

2  14.7 

2.3 

11 

4  11.1 

10  12.0 

0.6 

2  10.8 

2.2 

12 

4    7.1 

10    8.1 

6.8 

2    6.9 

2.1 

13 

4    3.3 

10    4.3 

7.1 

2    3.0 

2.1 

14 

3  59.3 

10    0.3 

7.3 

159.1 

2.0 

15 

3  55.4 

9  56.4 

7.5 

155.2 

2.0 

16 

3  51.5 

9  52.5 

7.7 

151.2 

2.0 

17 

8  47.6 

9  48.5 

7.9 

147.3 

2.0 

18 

3  43.6 

9  44.6 

143.4 

1.9 

19 

3  39.7 

9  40.7    • 

8.4 

139.5 

1.9 

20 

3  35.8 

9  36.8 

8.6 

125.6 

1.8 

31 

3  31.9 

9  82.9 

8.9 

131.7 

1.7 

22 

3  28.0 

9  29.0 

9.2 

127.7 

1.7 

23 

3  24.1 

9  25.0 

9.6 

123.8 

1.6 

34 

3  20.1 

9  21.1 

9.8 

119.9 

1.5 

25 

3  16.2 

9  17.2 

10.1 

116.0 

1.5 

26 

3  12.3 

9  13.3 

10.4 

112.1 

1.5 

27 

3    8.4 

9    9.4 

10.7 

1   8.3 

1.5 

28 

3    4.5 

9    5.4 

11.0 

1   4.3 

1.6 

29 

3    0.5 

9    1.5 

11.2 

1   0.4 

1.6 

30 

3  56.6 

8  57.6 

1.5 

0  56.4 

1.6 

31 

2  52.7 

8  53.7 

1.7 

32 

2  48.8 

8  49.8 

12.0 

956c 


6S.^SURVEYING,  MAPPING  AND  LEVELING. 


4a. — Polaris,  1012,  for  Mbridian  op  Grbbnwich.— <^ncluded. 
Civil  Date  and  Clock  Time. 


D»te 

Upper  Cul- 

Elongation. 

DeoU- 

Date 

Upper  Cul- 
mination. 

Elongation. 

DedJ- 

1912. 

mination. 

Lat.40*. 

n'tlon. 

1912. 

UA.ifr>. 

■tin. 

+88  50 

4*50 

Sep. 

hm 

hm 

• 

Not. 

hm 

hm 

1 

2  48.8  A.M 

E.E.  8  49.8P.M. 

12.0 

1 

10  45.4  P.  If. 

W.E.  4  44.4  A.M. 

34.9 

i 

2  44.9 

8  45.9 

12.3 

S 

10  41.4 

4  40.5 

3S3 

3 

2  41.0 

8  41.9 

12.6 

8 

10  37.5 

4  96.5 

3i.« 

4 

2  37.0 

8  38.0 

12.9 

4 

10  33.6 

4  32.e 

«.• 

B 

2  33.1 

8  34.1 

13.2 

5 

10  29.6 

4  28.7 

34.1 

6 

2  29.2 

8  30.2 

13.6 

6 

10  25.7 

4  24.7 

31.7 

7 

2  25.3 

8  26.3 

14.0 

7 

10  21.8 

4  20.8 

374 

8 

2  21.4 

8  22.3 

14.4 

8 

10  17.8 

4l6.t 

ri 

9 

2  17.4 

8  18.4 

14.7 

9 

10  13.9 

4  12.9 

r.r 

10 

2  13.5 

8  14.5 

15.1 

10 

10    9.9 

4    9.0 

381 

11 

2    9.6 

8  10.6 

15.4 

11 

10    6.0 

4    5.0 

385 

12 

2    5.7 

8    6.6 

15.7 

12 

10    2.1 

4    1.1 

S.» 

13 

2    1.7 

8    2.7 

16.0 

13 

9  58.1 

3  57.2 

3»J 

14 

I  57.8 

7  58.8 

16.S 

14 

9  54.2 

3  53.2 

».l 

16 

1  53.9 

7  64.9 

16.6 

16 

9  60.3 

3  49.3 

4C.4 

16 

1  50.0 

7  51.0 

16.9 

16 

9  46.3 

8  45.4 

4fl.i 

17 

1  46.1 

7  47.0 

17.3 

17 

9  42.4 

3  41.4 

«.T 

18 

1  42.1 

7  43.1 

17.7 

18 

9  38.4 

3  37.5 

411 

19 

1  38.2 

7  39.2 

18.0 

19 

9  84.5 

3  33.5 

41.3 

20 

1  34.3 

7  35.3 

18.4 

20 

9  30.6 

8  29.6 

41.4 

21 

1  30.4 

7  31.3 

18:8 

31 

9  26.6 

3  35.7 

4I> 

22 

1  26.4 

7  27.4 

19.2 

22 

9  22.7 

3  21.7 

41.2 

23 

1  22.6 

7  23.5 

19.6 

33 

9  18.7 

3  17.8 

42J 

24 

1  18.6 

7  19.6 

19.9 

34 

9  14.8 

3  13.8 

42J 

25 

1  14.7 

7  15.6 

20.3 

25 

9  10.9 

3    9.9 

4SZ 

U 

1  10.7 

7  11.7        . 

20.6 

26 

9    6.9 

3    6.0 

434 

27 

1    6.8 

7    7.8 

20.9 

27 

9    3.0 

3    2.0 

43.1 

28 

1    2.9 

7    8.9 

21.3 

28 

8  59.0 

3  58.1 

44.3 

29 

0  59.0 

7    0.0 

21.6 

29 

8  55.1 

8  54.1 

44.4 

30 
Oct. 

0  55.1 

6  66.0 

22.0 

30 
Dec. 

8  61.1 

2  50.2 

44J 

1 

0  51.1  A.M. 

E.E.  6  52.1P.M. 

22.3 

8  47.2  P.M. 

W.E.2  46.3  A.M- 

4SJ 

2 

0  47.2 

6  48.2 

22.7 

2 

8  43.3 

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45  .i 

3 

0  43.3 

6  44.3 

23.2 

3 

8  39.3 

8  38.4 

41.7 

4 

0  39.4 

6  40.3 

23.6 

4 

8  35.4 

8  34.4 

46.1 

5 

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24.0 

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6  32.5 

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24.8 

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8  23.5 

2  22.6 

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11 

8    7.8 

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12 

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12 

8    3.8 

8    2.9 

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13 

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E.E.  6    5.0P.M. 

27.0 

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32.8 

28 

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29 

6  66.7 

0  55.8 

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4  56.2 

33.6 

30 

6  62.8 

0  51.8 

g.l 

4  52.3 

34.0 

31 

6  48.8 

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10  49.3 
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4  48.3 
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34.4 
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6  44.9 

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TABLB 

4c. — Polaris.  191 
(To  accoi 


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966 


BS.— SURVEYING.  MAPPING  AND  LEVELING. 


Tmpes. — ^The  best  form  of  tape  for  general  surveving  is  a  100-ft.  steel 
ribbon  with  graduations  to  feet,  tenths,  and  hundredths.  The  sero  end  of 
the  tape  should  be  the  end  of  the  steel  rtbbon  itself,  and  it  mav  be  provided 
with  a  small  handle  or  a  large  detachable  handle,  the  latter  for  continuous 
line  measurements.  The  100-ft.  end  should  also  be  provided  with  detadt* 
able  handle  so  it  can  be  wound  in  a  box. 

Every  city  surveyor  should  keep,  in  his  office,  a  standard  tape  tested  by 
the  U.  S.  Coast  and  Geodetic  Dept.  at  Washington,  and  certified  to  as  coc- 
rect  at  a  certain  standard  temperature,  say  60*  P.,  and  for  a  certain  puD,  say 
10  to  15  lbs.,  when  uniformly  supported.  This  should  be  used  as  a  test  tape 
only,  and  never  for  field  work.  The  advantage  of  such  a  standflird  over  a 
fixed  base  (as  on  a  pavement)  is  that  the  temperat\ire*of  the  tapes  need  sot 
be  taken  during  the  test.  Nor  is  it  necessary  to  use  the  spring  balance^  as 
the  tapes  can  be  brought  to  practically  the  same  tension  without  it.  It  is 
necessary  of  course  to  use  the  same  pull  for  the  field  measurements  and 
this  is  one  of  the  tricks  of  chaining,  t  The  "misuse"  of  the  thermometer  in 
the  field  is  often  a  source  of  "error."  That  is  to  say,  the  temperature  of  the 
thermometer  will  never  indicate  the  temperature  of  the  tape,  exactly 
Both  will  be  aflected  diflFercntly  by  the  sun's  rays,  surrounding  air.  wind 
and  temperature  of  grotmd.  The  best  chaining  is  done  on  cloudy  days  acd 
in  still  air. 

Temperature  corrections  should  be  added  to  a  measured  length  between 
two  fxea  points  in  the  field  when  the  temperature  of  the  tape  is  aboue  the 
standard  temperature;  subtracted  when  below.  Reverse  the  above  when 
laying  out  a  fixed  distance,  as  setting  one  point  from  another. 

5. — ^Tbmpbraturb  Corrbctions  IK  Pbbt  pbr  100  Pbbt. 
Note. — Use  signs  as  per  tabic  for  measurements  between  fixed  objects. 
Reverse  signs  in  table  when  laying  out  fixed  distances. 

(From  the  author's  "Railway  Right -of- Way  Surveying."  t) 


100-foot  Tape  Standard  at  following  Temperatures. 

40° 

45° 

60° 

56° 

60° 

65» 

7V> 

75«» 

80* 

89» 

0^ 

5° 

10« 

-.027 
-.023 
-.02 

-.03 

-.027 

-.023 

-.033 

-.03 

-.027 

-.037 
-.033 
-.03 

-.04 

-.037 

-.033 

-.043 
-.04 
-  .037 

-.047 
-.043 
-.04 

-.05 
-.047 
-.043 

-.0531 

-.06 

-.047 

-.057 
-.OM 
-.05 

r 

10- 

20* 
25" 

-.017 
-.013 
-.01 

-.02 

-.017 

-.013 

-.023 

-.02 

-.017 

-.027 

-.023 
-.02 

-.03 

-.027 

-.023 

-.033 

-.03 

-.027 

-.037 
-.033 
-.03 

—  .04 

-.037 

-.033 

-.043, 

-.04 

-.037 

-.04- 

-.043 
-.04 

ir 

! 
1 

30« 
35° 
40« 

-.007 
-.003 

-.01 

-.007 

-.003 

-.013 

-.01 

-.007 

-.017 
-.013 
-.01 

-.02 

-.017 

-.013 

-.023 

-.02 

-.017 

-.027 
-.023 
-.02 

-.03 

-.027 

-.023 

-.033 

-.03 

-.02^ 

-.027 
-.033 
-.03 

35» 

45« 
50° 
55« 

+  .003 
+  .007 
+  .01 

+  '.  003 
+  .007 

-.003 -.007 

—.003 

+  .003 

-.003 

-.013 

-.01 

-.007 

-.017 
-.013 
-.01 

-.02 

-.017 

-.013 

-.023*— .027 
-.02    -.021 
-.017-. 02 

4r 

65» 

i 

60° 
65° 
70° 

+  .013+  .01   I+.007 
+  .017+  .013+  .01 
+  .02    +.017+.013 

+  .003 
+  .007 
+  .01 

+  !663 

+  .007 

-.003 
+  !663 

-.007 

-.01 

-.007 

-.003 

-.013-. 017] 
-.01  I-.013 
-.007 -.01 

75° 
80° 

85° 

+  .023 
+  .027 
+  .03 

+  .02  !+.017 
+  .023+.02 
+  .027+  .023 

+  .013 
+  .017 
+  .02 

+  .01 
+  .013 
+  .017 

+  .007 
+  .01 
+  .013 

+  .003 
+  .007 
+  .01 

+  .*66j 
+  .007 

-.003 
+  !663 

-.00: 
-.003 

7F 

90O 

95«» 

100° 

+  .033 
+  .037 
+  .04 

+  .03    +.027 
+  .033 +.03 
+  .O37I+.O33 

+  .023!+. 02  I+.017 
+  .027 +.023 +  .02 
+  .03  I+.027I+.023 

+  .013 
+  .017 
+  .02 

+  .01 
+  .018 
+  .017 

+  .007 
+  .01 
+  .013 

+  -0«| 
+  .007 
+  .01 

io<r 

*  The  tapes  should  lie  unwotmd  in  the  same  atmosphere  for  some  Ihtk 
time  before  making  the  test. 

t  On  very  accurate  city  work  it  is  often  desirable  to  let  the  rhaJntTyn 
"ff  u'^".***  l>alance  until  they  get  accustomed  to  the  proper  tenakm. 
attcr  which  it  may  be  discarded  generally,  or  used  only  occasionally  to  keep 
them  m  tune.        %  Published  by  McGraw-Hill  Book  Company.  New  Yortt. ! 


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9M 


S8.^SURVEYING,  MAPPING  AND  LEVEUNG. 


0. — Tablb  of  Pbbt  and  Chains  (Guntbr's  or  Surtbtor's). 

(1  chain- 100  links;  1  link- 7.02  ins.) 

(a)  Chains  to  Feet  (Exact). 


Ch'ns. 

Feet. 

Chains. 

FMt. 

Chains. 

Feet. 

nh^ina 

Feet. 

riMfcina 

FMC 

.01 

.66 

.21 

13.86 

.41 

27.06 

.61 

40.36 

.81 

58.41 

.02 

1.82 

.22 

14.62 

.42 

27.73 

.63 

40.92 

.82 

S4.13 

.03 

l.M 

.23 

15. li 

.43 

l^.Zl 

.68 

41.58 

.83 

54.71 

.04 

2.64 

.24 

15.84 

.44 

29.04 

42.24 

.84 

56.44 

.05 

3.30 

.25 

16.50 

.45 

29.70 

42.90 

.85 

M.lf 

.06 

3.96 

.26 

17.16 

.46 

30.36 

43.56 

.86 

56  76 

.07 

4.62 

.37 

17.82 

.47 

81.02 

44.22 

.87 

57.42 

.08 

5.28 

.28 

18. 4C 

.48 

81.68 

44.88 

.88 

6S.i8 

.09 

5.94 

.29 

19.14 

.49 

82.84 

45.54 

.89 

S8. 74 

.10 

6.60 

.30 

19.80 

.50 

88.00 

46.20 

.90 

ft.  49 

7.26 

.31 

20.46 

.51 

83.66 

46.86 

.91 

€0.06 

7.92 

.32 

21.12 

.62 

34.32 

47.52 

.92 

fe.;2 

8.5S 

.33 

21. 7J 

.53 

34.98 

48.18 

.98 

61. 3S 

9.24 

.34 

22.44 

.54 

35.64 

48.84 

.94 

68.14 

9.90 

.35 

23.10 

.55 

36.30 

49.50 

.95 

e3.;6 

10.56 

.36 

23.76 

.56 

36.96 

50.16 

.96 

63.M 

11.22 

.37 

24.42 

.67 

87.62 

50.82 

.97 

C4.62 

11.88 

.88 

25.08 

.58 

38.28 

51.84 

.98 

C4.6I 

13.54 

.39 

25.74 

.59 

38.94 

52.14 

.99 

•5.84 

.20 

13.20 

.40 

26.40 

.60 

39.60 

58.80 

1.00 

M.09 

(6)  Feet  to  Chains. 

Feet. 

Chains. 

Feet. 

Chains.     Feet. 

Chains. 

Feet. 

Chains. 

FWk 

Chataa 

1 
2 

.015^16 
.030^30 

3 

4 

.045^45          5 
.060^60          6 

.076^75 
.090^90 

7 
8 

.106^06 
.121^21 

9 
10 

.126^8« 

Note. — ^The  inverted  caret  indicates  repeating  decimal;    thus,  1ft.*- 
0.016  16  15  15 chain. 


Ex.— Reduce  18  dk.  46  /.[to  feet? 

Solution'. 

.18  ch- 11.88  ft.  .'.18  ch- 1188.00ft. 

.46ch-29.70ft.  ..46/    -     29.70ft. 


Ans.  18ch46l  -1217.70ft. 

Or.  mult.  18.46  by  66. 


Ex.— Reduce  482.78  ft.  to  db.  and  /? 

Solutifmx 

400ft.-6.060«ch.    .70ft.-. 0106 ck. 

80ft.-1.2121ch.    .08ft.-. 0006 ch. 

2ft.-0.0808ch.  

Ans.  7ch.  8L41L 
Or,  divide  482.73  by  6  and  11. 


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CHORDS  FOR  PLATTING  ANGLES, 


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064 


^.--SURVEYING.  MAPPING  AND  LEVEUNG. 


Farm  Survejiac. — ^Let  it  be  required  to  make  a  survey  of 
about  150  acres,  locating  the  roads,  fences,  buildings, 
determining  the  acreage,  and  making  the  map.  As 
the  farm  is,  say,  about  80  miles  from  the  city  the  sur- 
veyor decides  that  he  will  prepare  to  spend  one  day  in 
the  field,  only. 

The  Equipment  consists  of  1  transit.  2  100-ft. 
tapes,  2  flaiBf  poles  (Fig.  19).  12  pins  (Fig.  20)  with  red 
flannel  tied  at  their  tops  to  prevent  losing  them,  1  axe. 
1  hatchet,  1  transit  plumbbob  (Pig.  21),  1  plumbbob 
(Fig.  22)  for  each  of  the  men,  1  steel  frost  pin  (Fig. 
23)  if  tne  ground  is  frozen,  and   the  stakes  (Fig.  24). 


farm  ol 


>e> 


D 


V 

Fig.  26. 


Fig.  19.    Fig.  2a 


Fig.  21.     Fig.  22.  *    Fig.  28. 

hubs  (Fig.  25),  tacks,  etc.  (The  stakes  may  perhaps  be  procured  on  the 
groimd,  but  it  is  often  cheaper  to  take  them  from  tne  office.)  Pour 
men,   say,  besides  the  chief  of  party,  comprise  the  woridng  outfit. 

The  Traverse  of  the  farm  is  represented  (Fig.  26)  by  the  broken  instm- 
ment-line  A  B  C  D  EA,  which  closelv  follows  the  fence  lines  (not  shown). 
In  running  around  the  farm  with  this  transverse,  lettered  or  numbered 
stakes  are  set  on  the  instnmient  lines  opposite  all  bends  in  the  fence  lines; 
these  stakes  are  located  by  base  line  measure- 
ments, and  from  them  the  offset  distances  are 
measvired  to  the  fences,  thus  completely  tying- 
in  the  farm  boundary.  Any  buildmg  as  H  may 
be  located  by  running  a  spur  instrument  line 
from  some  pomt  on  the  traverse,  as  B.  The  trav- 
erse itself  is  determined  by  the  lengths  of  the 
measured  base  lines.  A  B,  BC*  CD,  etc..  and 
by  the  measured  angles  at  A^  B,  C.  etc.  Inaccu^ 
racies  in  measurement,  both  m  base  line  distances 
and  in  angles,  will  usually  creep  into  the  work  p.     ^n 

and  hence  the  traverse  will  seldom  close,  that  is,  '**•  '^' 

it  will  have  to  be  adjusted.  Absolute  errors,  however,  can  be  eliminated 
by  meastiring  the  base  lines  twice  and  by  "repeating"  all  angles,  and 
these  should  be  examined  carefully  before  leaving  the  Held. 

The  Adjustment  of  the  Traverse  may  be  made  in  several  ways,  but 
the  simplest  and  most  practical  is  as  follows:  Let  A,  B,  C,  etc.,  be  the 
interior  angles,  measured  in  the  field,  at  the  respective  comers  of  the  tra- 
verse (Fig.  26).  The  sum  of  these  angles  should  equal  540^  ( » 180*  X 
number  oT sides—  360^)  if  there  is  perfect  accuracy  in  the  field  work.  If  the 
angles  add  up  to  within  a  few  minutes  of  540*'this  variation  may  be  propor- 
tioned among  all  the  angles  so  their  sum  will  eqiial  540*^.  But  greater 
weight  should  be  given  to  those  measured 
angles  with  the  (long^t  and)  clearest  fore- 
sights, as  A,  especially  if  the  angle  "doubled" 
accurately  when  measured  in  tne  field;  and 
less  weight  should  be  given  to,  say.  C  and  D,  j^  , 
especially  if  the  anales  did  not  double"  orp  ' 
"repeat  properly.  Having  adjusted  the  angles  I 
(Fig.  27)  so  their  sum  is  540**,  assume  one 
side  of  the  traverse  as  a  base  line,  say  A  B, 
and  cut  the  exterior  of  the  traverse  into  right 
angle  triangles  as  shown  by  the  dotted  lines; 
calculate  the  angles  a,  c,,  ca  and  #.  from  the         Cc^r  P«-  27. 

:tized  by  VJWV. 


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066  SS.—SURVEYINC,  MAPPING  AND  LEVEUNG. 

The  Office  Plan  is  made  on  heavy  manila  detail  paper  The  adjusted 
traverse  is  shown  in  red  ink.  Angle  points  on  the  instnunent  lines  are  izidi- 
cated  by  being  enclosed  in  a  small  triangle;  and  ordinary  hubs,  at  other 
points,  by  a  small  circle.  The  property  lines  are  in  black  (India)  ink,  as  are 
also  the  outlines  of  buildings.  Lanes  may  be  indicated  bv  parallel  dotted 
black  lines,  and  streeU  by  full  shaded  lines.  Fences  may  be  shown  by  fine 
black  lines  (imless  they  mark  the  property  boundary)  and  shotild  be  lettered 
"Ftnce,"  "Stone  wail, '  etc.;  or  tney  may  be  indicated  by  broken  lines  as 
for  instance  alternate  dashes  and  dots.  All  corrected  measurements  aad 
angles  are  given  on  the  office  plan  as  they  appear  in  the  field  book  or  cako' 
lation  book,  and  cross  reference  is  made  to  each  other.  The  lettering  i* 
slanting,  and  is  made  bv  single  strokes  of  the  pen.  including  names  o£  streets, 
buildings,  etc.  All  information  should  be  recorded,  including  the  acmige 
of  the  property.  This  is  usually  obtained  by  calculating  the  area  of  the 
traverse  and  making  the  necessary  additions  and  subtractions  when  tbe 
boundary  line  of  the  property  is  respectively  exterior  or  interior  to  tbe 
traverse  lines.  Field  measurements  are  taken  i  n  such  a  way  as  to  simpKfy  office 
calculations.  Both  magnetic  and  true  north  are  shown.  The  title  is  prefer- 
ably in  the  lower  right-hand  comer  and  should  include  the  name  of  the 
property  (owner),  location,  date  of  survey  and  by  whom,  reference  to  field 
Dook,  date  of  plan,  and  scale.  The  author  has  found  it  convenient  to  cm 
out  a  small  46^  triangle  from  the  lower  right-hand  comer  of  the  plan  so  that 
when  the  plans  are  lying  in  the  case  drawer,  the  thumb  can  be  inserted  and 
the  number  of  the  plan  sought  can  be  seen  readily.  The  plan  numbers  are 
adjacent  to  the  comers  so  cut. 

The  Finished  Map  which  is  furnished  to  the  owner  of  the  property  is  oa 
mounted  white  paper  with  rough  surface.  Paragon  paper  or  its  equal  is 
recommended.  The  transfer  is  made  with  the  steel  or  needle  point  from 
the  office  plan.  All  instrument  lines  are  omitted,  but  the  property  lines  are 
shown  with  distances  and  angles  just  as  though  the  instrument  lines  had 
actually  traced  them  and  they  were  the  real  traverse.  In  other  words,  the 
property  line  traverse  should  contain  sufficient  data  so  it  can  be  plotted  to 
'close,  and  also  be  described  in  deed.  All  lines  should  be  in  India  ink.  The 
slant -block  lettering,  plain  or  fancy,  is  easy  to  make,  neat,  and  clean.  The 
upright  Roman  lettering  for  street  names  is  peiliaps  more  desirable  than 
the  block  lettering,  but  requires  greater  care  in  proportioning  and  executkm. 
The  title  should  be  in  taste  with  the  general  map,  neat  and  compact.  It 
should  always  include  the  scale,  date,  and  surveyor's  name.  It  is  a  mistake 
to  color  a  map  too  highly.  The  property  boundary  may  be  shaded  with  a 
diluted  carmine,  and  the  streets  tinted  with  burnt  sienna.  Buildinss  may 
be  tinted  with  the  proper  colors*  to  represent  wood,  brick.  ^ 
stone,  etc.  The  nortn  point  should  be  neat  and  artistic  but  not 
coarse.  It  should  be  placed  in  a  position  to  "balance"  the 
map.  The  border  may  consist  of  a  heavily  leaded  line  be- 
tween two  finer  lines;  or  one  of  the  latter  may  be  omitted. 
The  comers  are  generally  made  as  in  Fig.  80,  but  may  be 
curved  to  various  patterns.  pjg  jq^ 

City-Lot  SarveylnK. — ^The  functions  of  the  surveyor  ai%  almost  jndidal 
in  character.  No  statutes  are  framed  or  can  be  framed  to  meet  all  cases  of 
confficting  deed  lines.  These  conflicts  arise  from  inaccurate  surveys  in  the 
past  when  land  was  cheap,  and  also  from  improper  wording  of  deeds  of 
conveyance.  The  inaccurate  surveys  were  due  in  part  to  the  use  of  chains 
which  were  longer  or  shorter  than  the  present  standard.  This  is  the  caose 
of  much  of  the  "surplus"  and  "deficiency"  existing  in  many  of  oxir  city 
blocks,  amounting  in  some  cases  to  several  inches  per  himdred  feet.  Jersey 
City.  N.  T.,  is  a  notable  example  of  surplus,  some  of  the  blocks  being  4  ins. 
per  100  rt.  too  long.  The  sensible  way  is  to  distribute  this  surplus  propor- 
tionately or.  in  other  words,  to  use  the  same  length  of  chain  by  whtck  Ae  biocks 
were  lata  out  originally.     But  this  cannot  be  hold  to  in  all  cases  because 


■ai 


♦Technical  or  conventional  colors  may  be  purchased  in  liquid  form 
(26  cts.  per  bottle)  in  the  following  colors:  1  cast  iron.  2  wrought  iron,  J 
steel.  4  copper,  5  brass,  6  machinery,  7  leather,  8  light  wood,  9  cUurk  -wood. 
10  brick.  11  stone.  12  brown  stone,  13  Prussian  blue,  14  gamboge,  15  yellow 
ochre,  16  Vermillion,  17  burnt  sienna.  18  carmine.  The  same  may  be  pur- 
chased in  water  colors  (10  cts.  per  halt  pan)  with  the«xceptipn  that  Chinese 
white  IS  substituted  for  bumt  sienna  (17).         ized  by  LjOOQ IC 


J^SH^S 


CITY  LOTS.    GOVERNMENT  LAND,  957 

be  lines  have  been  estftbliahed  by  mutual  consent,  expressed  or 
Perhaps  one  or  more  buildings  have  been  erected  and  have  absorbed 
\ot  quite  all  the  surplus  in  the  block.  If  on  the  other  hand  there 
lency  of  total  measurement,  we  have  a  more  serious  problem  to 

Those  having  the  prior  deeds  are  apt  to  oppose  any  proportionate 
^n  of  the  * 'deficiency."  throwing  it  entirely  in  the  last  lot  con- 
Sxistins  buildings  have  much  to  do  with  the  solution  of  these 

The  puzpose  of  the  surveyor  is  to 
!  any  benefits  or  losses  as  equally  as 
with  injustice  to  no  one.  It  is  well  to  re- 
hat  in  making  out  deeds  of  original 
ice  of  lots,  the  description  of  each  lot  _j  ^  , 
►e    referred   to  the    same    street   line.  ^  ^^   a 

Fig.  31.  the  west  line  of  Ist  St.  may  *>  ^c.  a.^ 

ed  as  the  initial  base  of  all  lots  in  block    "*       '  *      •" 

he  width  of  lot  8  should  read  *'26  ft.  Pig.  31. 

ess"  to  the  east  line  of  2nd  St. 

t  lines  in  small  cities  should  be  fixed  by  stone  monuments  set  on 
nes  at  the  street  intersections.  As  the  cities  grow  in  size  these 
nts  are  bound  to  be  disturbed,  but  they  have  served  their  pxirpose 
nience  for  ready  use.  Offsets  to  buildings  may  now  be  usea  or  the 
nt  points  trannerred  to  the  manholes*  which  have  supplanted  the 
Dntunents.  The  point-  selected  on  the  buildinff  should  be  such  as 
lily  be  described,  as  abov$  or  btlow  the  wattr  took',   the  comer  of  a 

is  the  best,  as  being  definite.  Where  sewers,  water  works  and 
IT  lines  have  been  introduced  more  rapidly  than  substantial  build- 
re  been  erected,  it  is  quite  customary  to  transfer  the  stone  monu- 
rom  the  centers  to  the  comers  of  the  streets,  say  on  3-ft.  to  10-ft. 
nes. 

•enmiefit  Land  Ssnrsyiiif. — ^The  following  is  a  digest  of  General 
'ffice  "Circular  on  Restoration  of  Lost  and  Obliterated  Comers  and 
sion  of  Sections,"  Revision  of  June  1,  1909. 

"obliterated"  comer  is  one  where  no  visible  evidence  remains  of  the 
:  the  original  surveyor  in  establishing  it*  but  it  is  not  a  "lost"  comer 
)cation  nas  been  preserved  beyond  all  question  by  acts  of  land- 
,  and  by  the  memory  of  those  who  knew  and  recollect  the  true  situs 
original  monument. 

Synopsis  op  Acts  or  CoNORxas. 

Y  30.  178S.  PrescrlblDg  mode  of  survey  tor  the  "Westem  Territory,  said 
y  to  be  divided  into  "townships  of  six  miles  square,  by  running  lines  due  N 
and  others  oosslnK  them  at  right  angles."  as  near  as  may  be.  Further  pro- 
hat  the  Arst  line  running  N  and  S  should  be  on  the  Ohio  river,  at  a  point  due 
i  the  westem  t^mlnus  of  a  line  run  as  the  south  boundary  of  the  State  of 
and  the  first  line  running  E  and  W  should  begin  at  the  same  point  and  extend 
h  the  wbole  territory.  In  these  Initial  surveys  only  the  exterior  lines  of  the 
aps  were  surveyed,  but  the  plats  were  marked  by  subdivisions  into  sections 
square,  numbered  from  1  to  36.  commencing  with  No.  1  in  the  southeast  comer 
township,  snd  running  from  5  to  JV  in  each  tier  to  No.  36  in  the  northwest 

of  the  towQditp:  mile  comers  were  established  on  the  township  lines.    The 

embraces  what  Is  known  as  the  "Seven  Ranges"  In  Ohio. 

AY  18,  1796.    "Territory  northwest  of  the  River  Ohio,  and  above  the  mouth 

Keatueky  River."  Section  2  provided  for  dividing  lands  "by  N  and  .5  lines 
•cording  to  the  true  meridian,  and  by  others  crossing  them  at  right  angles,  so 
[orm  townships  o(  6  miles  square."  etc.    Also  that  "one-halt  ot  said  townships. 

them  sltemateiy.  should  be  subdivided  Into  sections  containing,  as  nearly  as 
)e.  640  seres  each,  by  running  through  the  same  each  way  parallel  lines  at  the 
t  every  two  miles;  and  by  marking  a  corner  on  each  ot  said  lines  at  the  end  ot 

mae."  Also  that  "the  sections  shall  be  numbered,  respectively,  beginning 
So.  1  in  the  northeast  seeUon.  and  prooeding  west  and  east  alternately  through 
jwnsbip,  with  progressive  numbers  till  the  36th  is  completed.!" 
lAT  10. 1800.  Amendatory  to  the  foregoing.  "Townships  west  ot  the  Musklng- 
wbleh  sre  dtreeted  to  be  sold  in  quarter  townships,  to  be  subdivided  Into  half 
>ns  ot  320  seres  each,  as  nearly  as  may  be.  by  rumUng  parallel  Unes  through  the 
;  trook  S  to  IF.  snd  from  iS  to  ^.  at  a  distanoe  ot  one  mile  from  each  other,  and 

*  Four  maiks  with  a  cold  chisel  on  the  fixed  iron  rim  and  ati^uadrant 
Its  will  determine  the  tme  center.  Digitized  by  CjOOQIc 

tThlsiDSthodotnamberlngsecUonBlsstllllnuse.  o 


908  S8.— SURVEYING.  MAPPING  AND  LEVELING. 

marfclng  oornen,  ftt  the  dlitanoe  of  eacb  half  mUe  on  the  llnei  nmnliig  fMm  S  to 
W,  and  ftt  the  dlatanoe  of  each  mile  on  thoee  running  from  StoN.  And  the  Intertor 
lines  of  townships  Intersected  by  the  Muskingum,  ftnd  ol  sll  townships  lyln^  east  of 
that  river,  which  have  not  heretofore  been  actually  subdivided  Into  sectlODa,  shall 

also  be  run  and  marked .   And  In  all  cases  where  the  exterior  lines  of  the  tova- 

shlp  thus  to  besubdlvlded  Into  sections  or  half-sections,  shall  exceed  or  shall  not  extcad 
six  miles,  the  excess  or  deficteicy  shall  be  specially  noted,  and  added  to  or  dedoelsd 
from  the  western  or  northern  ranges  of  sections  or  half -sections  In  su^  tawoatb^ 
according  as  the  error  may  be  in  running  the  lines  from  StoW  or  from  3  to  N," 

JUNB  1.  1796.  Act  "regulating  the  grants  of  land  appropriated  tor  mlUtarr 
servloes.  etc.  provided  lor  dividing  the  "U.  8.  Military  Tract,"  In  Ohio,  into  tovi- 
shlps  5  miles  square,  each  to  be  subdivided  In  quarter  towndiJps  oontaming  4fM 


March  1.  1800.  Amendatory  of  the  foregoing  act.  Seetlon  6  enacted  that  the 
Secretary  of  the  Treasury  was  authorised  to  subdivide  the  quarter  townships  Into 
lots  of  100  acres,  bounded  as  neariy  as  practicable  by  paralld  lines  160  perdtes  in 
length  by  100  perches  In  width.  |l  perch—  1  rod— 16.5  ft.— i  chaln.1  These  sntodl- 
vlslons  Into  lots  were  made  upon  the  plats  in  the  office  of  the  Secretary  of  the  Treasury 
and  did  not  agree  with  the  actual  survey  made  later,  many  fractional  lots  being 
entirely  crowded  out.  This  fact  may  explain  some  of  the  difficulties  met  with  ta 
the  district  thus  subdivided. 

Fkbruabt  11. 1805.  This  act  directs  the  subdlvMon  of  land  Into  quarter  sectloos. 
and  provides  that  all  comers  marked  In  the  ftdd  shall  be  established  as  the  proper 
comers  of  the  sections  or  quarter  sections  which  they  were  Intended  to  designate, 
and  that  comers  of  half  and  quarter  sections  not  marked  shall  be  placed  as  nearty  is 
possible  "equidistant  from  those  two  comers  which  stand  on  the  same  line."  Also 
tb&t  "the  boundary  line  actually  run  and  marked  (In  the  field)  shall  be  established  as 
the  proper  boundary  linos  of  the  sections,  or  subdivisions,  for  which  they  were  In- 
tended, and  the  length  of  such  lines  as  returned  by  either  of  the  surveyors  sTnicssliI 
dull  be  hdd  and  conddered  as  the  true  length  thereof  and  ttie  boundary  lines  whidi 
shall  not  have  been  actually  run  and  marked  as  aforesaid  shall  be  aaoertalned  by 
mnning  straight  Hues  from  the  established  oomers  to  the  opposite  ctKrespoDdlnc 
comers,  but  In  those  portions  of  the  fractional  townships  where  no  such  opposite  <x 
ocHTespondIng  comers  have  been  or  can  be  fixed,  the  said  boundary  lines  diall  be 
ascertained  by  running  from  the  established  comers  due  N  and  S,orE  and  W  lines. 
as  the  case  may  be.  to  the  water  course.  Indian  boundary  line,  or  other  extenul 
boundary  of  such  fractional  township." 

April  24,  1820.  This  act  provides  for  the  sale  of  public  lands  In  holf-qoaiter 
sections,  and  requires  that  "In  every  case  of  the  dlvldon  of  a  quarter  sectloo  the 
line  for  the  dlvldon  thereof  shall  run  N  and  8, and  fractional  seetHma.  con- 
taining 160  acres  and  upward.  duUl  In  like  manner,  as  neariy  as  practlcahle.  be 
subdivided  Into  half-quarter  sections,  under  such  rules  and  regulatlona  as  may  be 
prescribed  by  the  Secretary  of  the  Treasury:  but  fractional  sections  containing  less 
than  160  acres  shall  not  be  divided." 

May  24.  1 824.  This  act  provides  "that  whenever,  in  the  opinion  of  the  Preddent 
of  the  U.  S..  a  departure  from  the  ordinary  mode  of  surveying  land  on  any  river, 
lake,  bayou  or  water  course  would  promote  the  public  Interest,  he  may  direct  the 
surveyor-general  In  whose  district  such  land  la  dtuated.  and  where  the  change  h 
Intended  to  be  made,  under  such  rules  and  regulations  as  the  Prestdeat  may  ne* 
scribe,  to  cause  the  lands  thus  dtuated  to  be  surveyed  In  tracts  of  two  acres  In  width, 
fronting  on  any  river,  bayou,  lake,  or  water  course,  and  running  haek  the  depth 
of  forty  acres." 

April  5.  1 83  2.   This  act  directed  the  subdivldon  of  the  public  lands  hito  qnaiter- 

Suarter  sections;  that  In  every  case  of  the  dlvldon  of  a  half-quarter  seotloo  the 
Ivldlng  line  should  run  S  and  w.  and  that  fractional  sections  should  be  subdivided, 
under  rules  and  regulations  prescribed  by  the  Secretary  of  Ihe  Treasury.  Usder 
this  provldon  the  Secretary  directed  that  fractional  sections  containing  less  than 
160  acres,  or  the  redduary  portion  of  a  fractional  section,  after  the  subdlvtskm  lata 
as  many  quarter-quarter  sections  as  it  Is  susceptible  of.  may  be  subdivided  Into  lota 
each  containing  tne  quantity  of  a  quarter-quarter  sectlcm  as  neariy  as  practicable, 
by  so  laying  down  the  line  of  subdivldon  that  they  shall  be  20  chains  wfcto.  whlcb 
distances  are  to  be  marked  on  the  plat  of  subdivldon.  as  are  also  the  areas  of  the 
quarter-quarters  and  redduary  fractions. 

These  two  last  acta  provided  that  the  comers  and  contents  of  half-quarter  and 
quarter-quarter  sections  should  be  ascertained  as  neariy  as  possible  In  the  nuimer 
and  on  the  prlndples  prescribed  In  the  act  of  February  1 1.  180S. 

Genzral  Rules  from  the  FoRsoomo  Acn. 

UL  Boundaries  establUhed  and  retumed  by  the  duly  appointed  Oovenuneot 
Burveyors.  when  approved  by  the  surveyor  general  and  accepted  by  the  govenuneol. 
are  unchangeable. 

2nd.  Original  township,  section,  and  quarter-section  comers  established  by  thd 
government  surveyors  must  stand  as  the  true  comers  which  they  were  Intended  M 
ropresent,  whether  the  comers  be  In  place  or  not. 


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•70  SS.SURVEYING,  MAPPING  AND  LEVELING. 

me— ufement  from  ttie  ooni«n  med  In  tlie  ortftoal  flurrey  to  det«nnliie  iU  pooltloii: 
meuuremenU  from  comers  on  tlie  opposite  aide  of  tlie  panllel  will  not  contn)!. 
<c)  A  mlBBlDg  dosing  corner  orlglnaUy  estebllshed  during  tlie  sarrey  of  s  sUndnid 
p«irsUel  as  a  oomer  from  wlUoh  to  project  surreys  »tntth  will  be  restored  to  its  ortglnsl 
position  by  considering  It  a  standard  comer  and  treating  it  accordingly,  (d)  Ttaers- 
tore,  from  the  preceding,  using  proportionate  measurements,  we  baTe:  "As  the 
original  field-note  distance  between  tbe  selected  known  comers  Is  to  the  new  measure 
of  said  distance,  so  Is  tbe  original  field-note  length  of  any  part  of  the  line  to  the 
required  new  measure  tbereoL  («)  As  existing  original  comers  must  not  be  disturbed, 
discrepancies  betweoi  tbe  new  and  the  original  fleld^K>te  measurements  of  tbe  Une 
joining  the  selected  original  comers  will  not  affect  measurements  beyond  said  oofnen. 
Proportionate  measurements  are  to  be  used  between  them.  (/)  After  haTlng  diecked 
each  new  locaUon  by  measurement  to  tbe  nearest  known  comers,  new  ooniets  wll 
be  established  permanently  and  new  bearings  and  measurements  taken  to  ptomincBt 
objects,  and  recorded  for  future  reference. 

2.  ReataratUm  of  toumahip  comers  common  to  lour  towiuMp$  — ^Two  cases:  IM, 
Where  the  position  of  the  original  comer  has  been  made  to  depend  upon  moMure- 
ments  on  two  lines  at  right  angles  to  each  other:  A  line  will  first  be  ran  oonneoOng 
the  nearest  identified  original  comers  on  the  merldlooal  township  lines,  north  and 
south  of  the  missing  comer,  and  a  temporary  oomer  will  be  plaieed  at  the  fwoper 
proportionate  distance,  thus  determining  the  oomer  in  a  north  and  south  directloa 
only.  Next,  tbe  nearest  original  comers  on  the  latitudinal  township  lines  wfll  be 
connected  and  a  point  thereon  detMmlned  In  a  stnUlar  manner,  near  the  interaeotloa 
with  the  meridional  line  just  run.  The  intersection  of  these  two  lines  will  define  the 
position  tor  establishing  the  true  comer,  ffid. — Where  the  original  oomer  has  been 
located  by  measurements  on  one  line  only;  for  example,  as  a  guide  meridian:  Resio* 
ration  of  comer  is  effected  by  proportionate  measurements  on  said  line,  as  prertoosly 
exi^ained. 

3.  Ree$tabHshment  of  comers  common  to  two  lotnuMp*. — The  two  Dearest  known 
comers  on  the  township  line  (the  same  not  being  a  base  or  a  ootreetlon  line)  to  be 
corrected  as  in  case  No.  1.  by  a  right  line,  and  the  mfaMng  comer  established  by 
proportionate  distance,  and  to  be  "checked"  upon  by  measurements  laterally  to 
nearest  known  section  or  quarter-section  comers. 

4.  RetauMishment  of  closing  comers. — Measure  from  the  quarter-section,  seeUon. 
or  township  corner  east  or  west,  as  the  case  may  be,  to  the  next  preceding  or  sue- 
ceedlng  comer  In  the  order  of  original  establishment,  and  reestablish  the  mtsshif 
corner  by  proportionate  measurement. 

5.  ReesuMishment  of  interior  section  comers. — Same  manner  as  coners  eonunou 
to  four  townships.  When  a  number  of  comers  are  missing  on  all  aides  of  Um  cos 
sought  to  be  reestablished,  the  entire  distance  must  be  measured  between  tbe  neareal 
existing  reco^Ued  comers  both  N  and  S.  and  B  and  W,  In  aeoordance  with  tbe 
rule  laid  down,  and  the  new  comer  reestablished  by  proportionate  meaeurement. 

6.  Reestabtisfanent  of  qtuirter-^ctUm  comers  on  townsMip  boundaries. — Only  one 
set  of  quarter-section  comers  are  actually  marked  in  the  fidd  on  township  lines. 
and  they  are  established  when  the  township  exteriors  are  run.  When  double  seoUon 
comers  are  found,  the  quarter-section  comers  are  considered  generally  as  stwsdlng 
midway  between  the  comers  of  their  respective  sections,  and  when  required  to  be 
established  or  reestablished,  they  should  generally  be  so  placed. 

7.  Reestaiilisfmtent  of  quarter-seetUm  comers  on  dosing  section  Hnm  tthtMm 
fractional  sections.— yixuX  be  reestabllBbed  according  to  the  original  measureoient  of 
40  chains  from  the  last  Interior  section  comw.  or  rather  that  distance  corrected  by 
proportional  measurement  of  original  field  notes  and  the  new  measurement  oe 
dosing  line. 

8.  ReeatablishmerU  of  interior  quaner-wction  comers. — Tbe  missing  quarter- 
comer  (in  the  later  surreys)  must  be  estaMlshed  equidistant  between  the  sectloa 
comers  marking  tbe  line,  according  to  the  Add  notes  of  the  original  survey. 

9.  Wlure  double  comers  were  originally  esUMished,  one  of  isMcA  ie  standing.  Id 
reestablish  the  other.— It  being  remembered  that  the  comers  eetablisbed  when  the 
exterior  township  linos  were  run.  bdong  to  the  sections  in  tbe  townships  north  sad 
west  of  those  lines,  the  surveyor  must  first  determine  beyond  a  doubt  to  which  s 
tbe  existing  comer  belon«cs.    This  may  be  done  by  testing  the  comas  and  dl 

to  witness  trees  or  other  objects  noted  in  the  original  field  notes  of  the  survey. 

by  remeasuring  distances  to  known  comers.  Having  detwmlned  to  which  townaMp 
tbe  existing  comer  bdongs.  the  missing  comer  may  be  reestablished  in  line  north  or 
south  of  the  existing,  as  the  case  may  be.  at  the  distance  stated  In  the  fidd  notes 
of  the  original  survey,  by  proportionate  measurement,  and  tested  by  i 
to  the  opposite  corresponding  comer  of  the  section  to  which  the  i  ' 
belongs. 

SuBDrvisioN  or  Sections. 

^.♦.ii-v'??^**'****^  °1  sections  into  quarter  sections.-^Rwi  straight  Unes  from  the 
SrSSJS^^*'"*^'""***^®"  corners.  U.  &.  surveys,  to  the  opposite  correspoodlsg 
Si  SSkn%.P^'°^  of  intersection  of  these  lines  wUl  be  the  10011  center  of  the  sectkn. 
w  upon  the  lines  dosing  on  the  north  and  west  boundaries  of  a  towMhlp.  the 


GOVERNMENT  LAND  SURVEYING.  »71 


ectloB  eoriMra  are  eiCabllfllied  by  tbe  IT.  8.  deputy  euiteyoti.  but  In  Bab- 
such  awtloae  Mild  quartw-cornen  ibould  be  so  placed  as  to  ault  the  calca- 
r  the  areas  of  the  quarter  sections  adjolnjng  the  township  boundaries  as 
I  upon  the  ofOclal  plat,  adopting  proportionate  measurements  where  the 
•orements  of  the  north  and  west  boundarfes  of  the  seetkm  differ  from  the 


vbdMxkm  of  tractUmal  teetUma. — Where  opposite  corresponding  comers  have 
or  cannot  be  flxed.  the  subdivision  lines  should  be  ascertained  by  running 
established  comers  due  N.  8.  IT  or  FT.  as  the  case  may  be.  to  the  water  course, 
mindary  line,  or  other  boundary  of  such  fractional  section,  (a)  The  law 
the  section  lines  surveyed  and  marked  in  tbe  field  by  the  U.  8.  deputy  sur« 
be  due  N  and  8m  S  and  W  lines,  but  m  actual  ezperlenoe  this  Is  not  always 

Hence,  in  order  to  carry  out  the  spirit  of  the  law.  It  will  be  necessary  In 
Jie  sabdlvMonal  lines  through  fractional  sections  to  adopt  mean  courses 
B  section  lines  are  not  due  lines,  or  to  ran  Mat  subdivision  line  parallel  to 

IF.  or  ^  boundary  of  the  section,  as  conditions  may  require,  where  there 
oette  sectional  line. 

ubdMjtioi^  of  quarter  tectums  into  cuarftfr-^Morfsrt.— Preliminary  to  the  sub- 
f  quarter  sections,  the  quarter-quarter  comers  will  be  established  at  points 
>etween  the  section  and  quarter-section  comers,  and  between  quarter  ooi^ 
the  center  of  the  section,  except  on  the  last  half  mile  of  the  lines  dosing  on 
or  west  boundaries  of  a  township,  where  they  should  be  placed  at  20  chains, 
nate  measurement,  to  the  north  or  west  of  the  quarter-section  comer, 
quarter-quarter  section  comers  having  been  established  as  directed 
e  subdivision  tines  of  the  quarter  section  will  be  ran  straight  between 
oofrespondlng  quarter-quarter  section  comers  on  the  quarter-section 
a.  The  intersection  of  the  lines  thus  run  will  determine  the  place  for  the 
nmon  to  the  four  quarter-quarter  sections. 

ibdMsUm  offraeHmaiqtittrter  sections.— Tt^  subdivision  lines  of  fractlotnal 
ctlons  wni  be  ran  from  properly  established  quarter-quarter  section  comers 
ue  /V,  iS.  JV  or  IT.  to  the  lake,  water  course,  or  reservatlmi  which  renders 
s  fractional,  or  parallel  to  the  east,  south,  west,  or  north  boundary  of  the 
'CtKm.  as  conditions  may  require.    (See  par.  2  (a).) 

roportUnuUe  measurement. — By  "proportionate  measurement"  Is  meant  a 
ent  having  the  same  ratio  to  that  recorded  In  the  original  field  notes  as 
of  Main  used  In  the  new  measurement  has  to  the  lenoth  of  chain  used  In 
al  survey,  assuming  that  the  original  and  new  measurements  have  been 
made.  For  example:  the  length  of  the  line  from  the  quarter-section  comer 
!t  side  of  sec  2.  T.  24  N.,  R.  HE.  Wisconsin,  to  the  north  line  of  the  town- 
he  United  States  deputy  surveyor's  chain,  was  reported  as  45.40  chains, 
e  county  surveyor's  measure  Is  reported  as  42.90  chains;  then  the  distance 

quart^Hiuarter  section  comer  should  be  located  north  of  the  quarter- 
nier  would  be  determined  as  foUows  As  46.40  dialns.  the  Govemment 
t  the  whole  distance.  Is  to  42.90  chains,  the  county  surveyor's  measure  of 
distance,  so  Is  20.00  chains,  original  measurement,  to  18.90  chains  by  the 
rveyor^  measure,  tiiowlng  that  by  proportionate  measurement  In  this  case 
tr-quarter  section  comer  should  be  set  at  1 8.90  chains  north  of  the  quarter- 
raer,  instead  of  20.00  chains  north  of  such  comer,  as  represented  on  the 
it.  In  this  manner  tiie  discrepancies  between  original  and  new  measure- 
equitably  distributed. 

UsBPtTL  Tablbs  in  Public  Lands  Survbts. 
(From  the  Manual  of  1902.) 
system  of  rectangular  surveying,  authorized  by  law  May  20.  1785 
<J7).   was  first   employed  in  the  survey   of  u.  S.  public  lands  in 

of  Ohio. 

boundary  line  between  the  States  of  Penn.  and  Ohio,  known  as 
's  line,"   in   longitude  80*  32*  20*  west  from  Greenwich,  is  the 

to  which  the  first  surveys  are  referred.  The  townships  east  of 
to   R.,  in  Ohio,  are  numbered  from  south  to  north,  commencing 

1  on  the  Ohio  River,  while  the  ranges  are  numbered  from  east  to 
rinning  with  No.  1  on  the  east  boundary  of  the  State,  except  in  the 
lignated  **U.  S.  Military  Land,"  in  which  the  townships  and  ranges 
bered ,  respectively,  from  the  south  and  east  boundaries  of  said  tract. 
:  1876,  ntmibered  and  locally-named  principal  meridians  and  base 
e  bera  established  as  shown  by  Table  8,  following. 


d  by  Google 


d  by  Google 


PUBUC  LAND  SURVEYS— TABLES. 


973 


9.— Azimuths  of  thb  Sbcant.  and  Ofpsbts.  in  Fbbt,  to  thb  Parallel. 

Arguments:  latitude  in  left-hand  column,  and  distance  from  starting 

point  at  top  of  table. 

(For  example  of  use  of  table,  see  Fig.  32.) 


AjUmuUw  sDd  Offlsets  at— 

I>eflect'n 
Angle 

andnat. 

tan.  to 
Rod.  66ft 

OmilM. 

*-«.. 

I  mOe. 

HmllM. 

2niilM. 

2»mlk.. 

3inil«. 

M 

Sr  58'.  6 
I.MN. 

8y»  58'  7 
0.S7N. 

89*  59-.  0 
0.00 

89*  59'.2 
0.67  S. 

89*  59'.  5 
1.15  8. 

89*  59-.7 
1.44  8. 

99*(E.orW.) 
1.54  S. 

3'90'.2 
0.691m. 

Jl 

Sr  68'.  4 
2.01  N. 

89«  68'.6 
0.91  N. 

89*  58'.9 
•JOO 

89*  59*3 
0.70  S. 

89*  69'.8 
1.20  S. 

89*  59*.  7 
1J0&. 

90*(E.orW.) 
1.60  S. 

3'  07*.  4 
0.721m. 

n 

Sr  58'.4 
TMfL 

89*  58'.6 
0.94  N. 

89*  68'.  9 
0.00 

89*  59'.2 
0.73  & 

89»  59'.  6 
1.25  S. 

89*  69'.7 
1.56  S. 

90*(E.orW.) 
1.67  S. 

3'  IS-.O 
0.751m. 

3S 

2.17  N. 

Sr  58*.  6 
0.97  N. 

89®  58'.8 

89*  59'.  1 
0.76  S. 

88^  54'  4 
1.30  8. 

89*59*7 
1.62  S. 

99*(E.orW.) 
1.73  S. 

3'  22'.« 
0.78  las. 

u 

8««  58^.2 
2.25  N. 

89*  58'.  6 
1.01  N. 

SV*  58'. 8 
0.00 

89*  59'.  I 
0.79  S. 

89*  59'.4 
1.35  S. 

89*  59'.  7 
1.69  S. 

90*(E.orW.) 
IJOS. 

3'  30*.  4 
0.81  im. 

IS 

Sr  58'.2 
2.33  N. 

ar  58'.  5 

I.OSN. 

89*  58'.8 
0.00 

89*  69'.! 
0.82  S. 

89*  59'.4 
1.40  S. 

89*  59*. 7 
1.75  S. 

90*(E.orW.) 
1.87  S. 

3'  38*.  4 
0.84  im. 

u 

89-58M 
2^N. 

8r»  58'.  4 
1.09  N. 

8r»  58'. 7 
0.00 

89*  59'.0 
0.85  S. 

89*  59'.  4 
1.46  8. 

89»  59'  7 
1.82  8. 

99*(E.orW.) 
1.94  S. 

3'  46'. 4 
0.87  ias. 

J7 

8««  58'. 0 
2.51  N. 

89*  59'.  3 
1.13  N. 

89«»  58'.  6 
04M> 

89*  58.9 
0.88$. 

89»  69'  3 
1.51  S. 

89*  69'  7 
1.89  S. 

99*  (E.  or  W.) 
2.01  S. 

3*  65'.  0 
0.901m. 

38 

89«  58'.  0 
2.41  N. 

89*  58'.  3 
1.17  N. 

89«»  68'.  5 
0.00 

89*  58'  9 
0.91  S. 

89»  59'.  3 
1.56  S. 

89*  59'. 7 
1.95  8. 

99*(E.orW.) 
2.08  S. 

4  03'.  6 
0.931m. 

39 

Sr  57'. 9 
2.70  N. 

89«  58'. 2 
I.2IN. 

8r»  68'. « 
0.00 

89*  58'  9 
0.94  S. 

89*  59'.  3 
1.62  S. 

89*  59'.  7 
2.02  S. 

90*(E.orW.) 
2.16  S. 

4'  I2'.« 
0.971m. 

40 

Sr  57'.8 
2.79  N. 

89*68'.l 
I.2SN. 

89*  68'.  5 

ouw 

89*  68'.  9 
0.98  S. 

89*  59'. 3 
1.68  S. 

89*  59'.7 
2.10S. 

90*(E.orW.) 
2J24S. 

4'.  21'.  6 
14N>im. 

41 

8y»  57'.  7 

2.89  N. 

89«68'.0 
1.30  N. 

89*  58'.  4 
0.00 

89*  58'  8 
1.02  S. 

89*  59'.2 
1.74  S. 

89*  59'.6 
2.17  S. 

99*(E.orW.) 
2J2S. 

4'  31'.2 
1.041m. 

42 

89*  57'.7 
34N>N. 

89»  58'.0 
1.35  N. 

89*  58'. 4 
0.00 

89*  68'.8 
1.05  S. 

89*  59'.  2 
1.80  S. 

89*  69*.« 
2.25  S. 

90*(E.orW) 
2.40  S. 

4'  40*.  8 
1.08  iM 

43 

Sr  57'.6 
3.11  N. 

Sr  58'.0 
1.40  N. 

89*  58'.  4 
0.00 

89*  58'.  8 
1.08  8. 

89*  59'.  2 
1.86  S. 

89*  59'.6 
2.33  S. 

90*(E.orW.) 
2.48  S. 

4'  59'.8 
1.12  im. 

44 

89*  57'.5 
3.22  N. 

89*  57'.  9 
1.45  N. 

89*  58'.  3 

89*  58'. 7 
1.12  S. 

89*  59'.2 
1.93  S. 

89*  59'.6 
2.41  S. 

99*(E,orW.) 
2.57  S. 

5'  0!'.0 
1.16  im. 

45 

89«  57'. 4 
3.33  N. 

89*  57'.8 
1.50  N. 

89*  58'.  3 
0.00 

89*  88'.  7 
1.16  S. 

89*59'.! 
2.00  S. 

89*  69'.  5 
2.49  S. 

90*(E.orW.) 
2.66  S. 

6' 11*.  8 
1.20  im. 

46 

«9«  57'.3 
3.44  N. 

89*  67'.  7 
1.55  N. 

89*  58'.  2 

89*  58'.  6 
1.21  S. 

89*59'.! 
2.07  S. 

89*  59'.  5 
2.59  S. 

90*(E.orW.) 
2.76  S. 

5'.  22-.  8 
lJ241as. 

47 

«9«  57'.2 
3.S7N. 

89*  57'.  6 
1.61  N. 

89*58'.! 
0.00 

89*  58'.  6 
1.25  S. 

89*59'.! 
2.14  S. 

89*  59'. 5 
2.67  S. 

90*(E.orW.) 
2.86  S. 

5'  34*.  2 
1.28  im. 

48 

89«  57'.  1 
3.70  N. 

89*  57'.  6 
1.66  N. 

89*  58'.  0 
0.00 

89*  68'.  5 
1.30  & 

89*  59'.0 
2.22  S. 

89*  59'.  & 
2.78  S. 

90*(E.orW.) 
2.96  S. 

5'  46*.  2 
lJ3im. 

49 

«9«  57'. 0 
3.A2N. 

89*  57'.  5 
1.72  N. 

89*  68'.  0 
0.00 

89*  58'.  5 
1.34  & 

89*  59'.0 
2.30  S. 

89*  59'. 5 
2.87  S. 

90*(E,orW.) 
3.06  S. 

5'  58*.  6 
1.381m. 

SO 

sr*  56'.! 
3.96  N. 

89*  57'.  4 
1.78  N. 

89*  57'.^ 
0.00 

89*  58'.  4 
1.39  S. 

89*  59'.0 
2.38  S. 

89*  59'.  5 
2.97  S. 

90*(E.orW.) 
3.17  S. 

8'  11'.4 
1.43  im. 

N 

,    /^"»»rd  Standard    ?aro\\€\ 

MtfaT   Secant  Line     s&Ut—*- 


'^figolar 


'^SSShtT 


Digitized  by  VjOOQ  IC 

Fig.  32. — E^mple. 


974 


^.—SURVEYING,  MAPPING  AND  LEVBUNG. 


10. — ^AziMUTHS  OF  THB  TaMOBNT  TO  THB  PaRALLBL. 

The  azimuth  is  the  smaller  angle  the  tangent  makes  with  the  true  meridian 

and  always  measured  from  the  north  and  towards 

the  tangential  points. 


LaU- 
tude. 

ImUe. 

2niiks. 

3inilcs. 

4iiili«. 

.»^ 

.— . 

o 

30 
31 
32 

0         t           » 

89   59  30.0 
89  59  28.8 
89  59  27.5 

o       t          m 

89  68  59.9 
89  68  57.5 
89  68  65.0 

p  #   • 
89  68  29.9 
89  58  26.3 
89  58  22.5 

0       1         m 

89  57  59.9 
89  57  56.0 
89  57  50.0 

89  67  29.9 
89  57  23.8 
89  57  17.5 

9       »         m 

89  56  59.8 
89  56  52.5 
89  56  45.0 

33 
34 
35 

89  59  26.2 

89  59  24.9 
89  59  23.S 

89  58  52.5 
89  58  49.9 
89  58  47.2 

89  58  18.7 
89  58  14.8 
89  68  10.8 

89  57  44.9 
89  57  89.7 
89  57  34.4 

89  57  11.2 
89  57  04.6 
89  66  58.0 

89  56  37.4 
89  56  2f.i 
89  56  21.5 

3d 
37 
38 

89  59  22.2 
89  59  20.8 
89  59  19.4 

89  58  44.4 
89  58  41.6 
89  58  38.8 

89  68  06.8 
89  58  02.5 
89  57  68.2 

89  57  28.9 
89  57  23.3 
89  57  17.5 

89  66  61.1 
89  66  44.1 
89  56  36.9 

89  56  13.4 
89  66  05.0 
89  55  55.3 

39 
40 
41 

89  59  17.9 
89  59  1S.4 
89  59  14.8 

89  68  35.8 
89  58  32.8 
89  58  29.6 

89  67  S3. 7 
89  67  49.2 
89  57  44.4 

89  57  11.6 
89  57  06.6 
89  56  59.3 

89  65  29.6 
89  56  2L9 
89  66  14.1 

89  55  47.5 
89  55  58.3 
89  55  28.5 

42 
43 
44 

89  59  13.2 
89  59  11.6 
89  59  09.8 

89  58  26.4 
89  58  23.1 
89  58  19.6 

89  67  39.6 
89  57  34.6 
89  57  29.5 

89  56  52.8 
89  66  46.2 
89  56  39.3 

89  56  06.0 
89  55  57.7 
89  65  49.1 

89  65  lt.8 
89  55  09.8 
89  54  58.9 

4$ 

4« 
47 

89  59  08.0 
89  59  06.2 
89  59  04.3 

89  68  16.1 
89  68  12.4 
89  58  08.6 

89  67  24.1 
89  67  18.6 
89  67  12.9 

89  56  82.1 
89  56  24.8 
89  56  17.1 

89  65  40.2 
89  66  31.0 
89  66  21.4 

8t  54  48.2 
89  54  87.2 
89  54  2&7 

48 
49 
50 

89  59  02.3 
89  59  00.2 
89  58  58.1 

89  58  04.6 
89  56  00.5 
89  57  56.2 

89  67  06.9 
89  67  00.7 
89  56  54.3 

89  56  09.2 
89  56  00.9 
89  55  52.6 

89  56  11.6 
89  55  01.2 
89  54  60.5 

8f  54  18.8 
8t  54  0L4 
8t  58  48.5 

LaU- 
tude. 

7  miles. 

8niUes. 

9niU«s. 

lOmUes. 

II  miles. 

I2mfla«. 

30 
31 
32 

o   »    • 

89  56  29.8 
89  56  21.3 
89  56  12.5 

p   #  • 
89  55  59.8 
89  56  60.0 
89  65  40.0 

o   •    • 

89  55  29.8 
89  55  18.8 
89  6i  07.6 

89  54  69.7 
89  54  47.6 
89  54  86.1 

o    ^    • 

89  64  29.7 
89  54  16.3 
89  54  02.6 

9        »         m 

89  58  59LT 
89  53  45.1 
89  53  Sai 

33 
34 
35 

89  66  03.6 
89  65  54.5 
89  55  45.2 

89  55  29.9 
89  55  19.4 
89  55  08.8 

89  54  56.1 
89  54  44.4 
89  64  32.3 

89  54  22.3 
89  64  09.3 
89  53  55.9 

89  63  48.5 
89  53  34.2 
89  53  19.5 

89  53  14.8 
89  52  59.1 
89  52  42.1 

36 
37 

38 

89  56  35.6 
89  55  25.8 
89  56  15.7 

89  54  67.8 
89  54  46.6 
89  54  35.1 

89  54  20.0 
89  54  07.4 
89  63  64.5 

89  53  42.3 
89  63  28.2 
89  68  13.9 

89  53  04.5 
89  52  49.1 
8t  62  33.2 

89  52  26.7 
89  52  09L9 
89  51  52.5 

39 
40 
41 

89  55  05.4 
89  54  54.7 
89  54  43.7 

89  54  23.3 
89  64  11.1 
89  63  58.5 

89  53  41.2 
89  53  27.6 
89  68  13.4 

89  52  59.1 
89  52  43.8 
89  62  28.2 

89  62  17.0 
89  62  00.2 
89  61  4S.0 

89  51  34.9 
89  61  16.6 
89  50  57.8 

42 
43 
44 

89  64  32.4 

89  54  20.8 
89  54  08.7 

89  53  45.6 
89  53  32.3 
89  53  18.6 

89  62  68.8 
89  52  43.8 
89  52  28.4 

89  62  12.0 
89  51  55.4 
89  51  38.2 

89  51  26.1 

89  61  06.9 
89  60  48.0 

89  50  U.A 

89  50  1&5 
89  49  57.8 

45 

46 
47 

89  53  56.3 
89  53  43.4 
89  63  30.0 

89  53  04.3 
89  52  49.6 
89  52  34.3 

89  62  12.3 
89  61  56.7 
89  51  38.6 

89  61  20.4 
89  51  01.9 
89  50  42.9 

89  50  28.4 

89  60  08.1 
89  4t  47.2 

89  49  88.4 
89  49  14.2 
89  48  51.4 

48 
49 
50 

89  53  16.1 
89  53  01.7 
89  52  46.6 

89  52  18.4 
89  52  01.9 
89  51  44.7 

89  51  20.7 
89  51  02.1 
89  50  42.8 

89  50  23.0 
89  50  02.4 
89  49  40.9 

89  49  26.8 

89  49  02.6 
89  48  39.0 

89  48  87.8 

89  48  02.8 
89  47  87.1 

Note. — For  example  of  use  of  table,  see  Fig.  33,  next  page. 


PUBLIC  LAND  SURVEYS— TABLES. 


976 


11. — Offsbts.  in  Chains,  from  Tanobnt  to  Paiiallbl. 
[Chains.] 


Lat- 

MUes 

itude. 

Deg. 

1 

2 

3 

4 

6 

6 

7 

8 

9 

10 

U 

12 

30 
31 
32 

O.OM 
0.006 
0.006 

0.023 
0.024 
0.025 

0.053 
0.055 
0.067 

0.09 
0.10 
0.10 

0.14 
0.15 
0.16 

0.21 
0.22 
0.23 

0.29 
0.30 
0.31 

0.37 
0.39 
0.40 

0.47 
0.49 
0.51 

0.58 
0.60 
0.63 

0.71 
0.74 
0.76 

0.84 
0.88 
0.91 

33 
34 
35 

0.007 
0.007 
0.007 

0.026 
0.027 
0.028 

0.069 
0.061 
0.064 

0.10 
0.11 
0.11 

0.16 
0.17 
0.18 

0.24 
0.25 
0.25 

0.32 
0.33 
0.35 

0.42 
0.43 
0.46 

0.53 
0.55 
0.57 

0.65 
0.68 
0.70 

0.79 
0.82 
0.86 

0.95 
0.98 
1.02 

36 
37 
38 

0.007 
0.008 
0.008 

0.029 
0.031 
0.032 

0.066 
0.068 
0.071 

0.12 
0.12 
0.13 

0.18 
0.19 
0.20 

0.26 

0.27 
0.28, 

0.36 
0.37 
0.38 

0.47 
0.48 
0.60 

0.59 
0.61 
0.64 

0.73 
0.75 
0.78 

089 
0.91 
0.96 

1.06 
1.10 
1.14 

39 
40 
41 

0.008 
0.008 
0.009 

0.033 
0.034 
0.035 

0.074 
0.076 
0.079 

0.13 
0.13 
0.14 

0.20 
0.21 
0.22 

0.29 
0.30 
0.32 

0.40 
0.41 
0.43 

0.52 
0.64 
0.66 

0.66 
0.68 
0.70 

0.81 
0.84 
0.87 

0.99 
1.02 
1.06 

1.18 
1  22 

1.26 

42 
43 
44 

0.009 
0.009 
0.010 

0.036 
0.038 
0.039 

0.082 
0.085 
0.088 

0.14 
0.16 
0.16 

0.23 
0.24 
0.24 

0.33 
0.34 
0.35 

0.44 
0.46 
0.48 

0.58 
0.60 
0.62 

0.73 
0.75 
0.79 

0.90 
0.93 
0.97 

1.09 
1.14 
1.18 

1.31 
1.35 
1.40 

45 

4« 
47 

0.010 
0.010 
0.011 

0.040 
0.042 
0.044 

0.091 
0.094 
0.097 

0.16 
0.17 
0.17 

0.25 
0.26 
0.27 

0.36 
0.37 
0.39 

0.49 
0.51 
0.53 

0.64 
0.66 
0.68 

0.81 
0.84 
0.87 

1.00 
1.04 
1.07 

1.22 
1.26 
1.31 

1.46 
1.50 
1.66 

48 
49 
50 

0.011 
0.012 
0.012 

0.046 
0.046 
0.048 

0.101 
0.104 
0.108 

0.18 
0.19 
0.19 

0.30 

0.40 
0.42 
0.43 

0.66 
0.67 
0.69 

0.71 
0.74 
0.77 

0.91 
0.93 
0.97 

1.12 
1.16 
1.20 

1.35 
1.40 
1.45 

1.61 
1.67 
1.73 

Note. — For  uae  of  above    table,  sec  example  below    (Fig.  33). 
that  in  the  table  the  offsets  are  in  chains,  and  not  in  feet. 


Note 


Pig.  33.— Example  of  use  of  Tables  10  and  11,  for 
latitude  45  deg.  34.5  m.  N. 


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976 


^.—SURVEYING,  MAPPING  AND  LEVEUNG. 


12. — CORRBCTION  OF   RAK1>OlfS. 

Links  and  Minutes  of  Arc,  showing  departure  in  running  80.00  chs.  at  any 
course  from  1  to  60  minutes  (or  difference  in  latitude  foi  90^  minus 
angle). 


An- 

De- 

An- 

^J 

An- 

D^ 

An- 

De- 

An- 

De- 

An- 

De- 
part- 
ure 

gle. 

parture 

gle. 

parture 

gle. 

parture 

gle. 

parture 

gle. 

parture 

gle. 

Min. 

Links. 

Mln. 

Links. 

Mln. 

Links. 

Mln. 

Links. 

Min. 

LlnkB. 

Mln. 

Unka. 

n 

11 

25} 

21 

49 

31 

Jll 

41 

95} 

51 

119 

12 

28 

22 

51» 

32 

42 

98 

61 

U6 

7 
H 

13 
14 

1^ 

23 
24 

S» 

33 
34 

77 

I?! 

43 
44 

102} 

53 
54 

m 

15 

35 

25 

68* 

35 

45 

105 

55 

128} 

u 

16 

^ 

26 

60} 

36 

84 

46 

1071 

56 

130} 

f 

17 

27 

63 

37 

9 

47 

109} 

57 

133 

18 
19 

42 
44^ 

28 
29 

^ 

38 
39 

S 

112 

i'4 

58 

59 

!^ 

10 

m 

30 

m 

30 

70 

40 

93} 

50 

60 

140 

Remarks. — ^Table  12,  showing  the  departure  or  falling  at  80  chains 
distance,  for  any  number  of  minutes  up  to  60*  can  also  be  used  in  finding 
the  minutes  of  correction  of  a  random  course  corresponding  to  the  number 
of  links  of  falling.  For  distance  less  than  1  mile,  the  links  ol  falling  miist  be 
proportionately  increased;  for  example,  if  the  falling  at  70  chiuns  is  28 
links,  the  correction  of  the  course  will  be  14  minutes  for  32  links.  For 
township  exteriors  and  other  long  lines,  the  number  of  links  of  falling  must 
be  divided  by  the  number  of  miles  to  bring  the  calculation  to  the  basis  of 
the  table. 

Table  12  may  be  used  to  determine  the  return  from  the  random  course, 
also,  by  keeping  in  mind  clearly  just  what  is  being  done. 


d  by  Google 


PUBLIC  LAND  SURVEYS— TABLES, 


877 


ONVBRGBNCT  OP  MbRIOIANS  SIX  IflLBS  LONG  AND  SIX  IflLBS 
RT,  AND   OTHBR  RBLBVANT  DATA,  TO   LATITUDE   70*  NORTH. 


Oonveggeucy. 

Dllferenoe  of  longitude 

Dlflerence 

Of  latitude 

per  range. 

tor— 

3n  the 

taraUel. 

Angle. 

In  arc. 

In  time. 

1  mile  In  arc. 

1  Tp.  In  arc. 

Limka. 

*     » 

'          m 

Seconds. 

41. • 

3     0 

6     0.36 

24.02 

43.6 

3     7 

6     4.02 

24.27 

45.4 

3  15 

6     7.93 

24.53 

0'871 

5'.  225 

47.2 

3  23 

6  12.00 

24.80 

49.1 

3  30 

6  16.31 

26.09 

J 

50.9 

3  38 

6  20.95 

25.40 

53.7 

3  46 

6  25.60 

25.71 

54.7 

3  65 

6  30.59 

26.04 

0'.870 

6'.221 

56.8 

4     4 

6  35.81 

26.39 

68.8 

4   13 

6  41.34 

26.76 

60.9 

4  22 

6  47.13 

27.14 

63.1 

4  SI 

6  53.22 

27.55 

65.4 

4  41 

6  59.62 

27.97 

0^.869 

6'.217 

87.7 

4  51 

7     6.27 

28.42 

70.1 

\          6     1 

7   13.44 

28.90 

72.6 

5  12 

7  20.93 

29.39 

75.2 

5  23 

7  28.81 

29.92     ; 

77.8 

6  34 

7  37.10 

30.47     1 

0'.869 

5'.212 

80.6 

5  46 

7  45.79 

31.05     1 

83.5 

5  69 

7  65.12 

31.67 

86.4 

6  12 

8     4.83 

32.32 

89.6 

6  25 

8  15.17 

33.01 

92.8 

6  39 

8  26.13 

83.74 

0'.868 

5'.  2  07 

96.2 

6  54 

8  37.75 

34.52 

99.8 

7     9 

8  50.07 

35.34 

103.5 

7  25 

9     8.18 

36.22 

107.5 

7   42 

9  17.12 

37.14 

111.6 

8     0 

9  31.97 

88.13 

0'.867 

5'.  2  02 

116.0 

8  19 

9  47.83 

39.19 

120.6 

8  38 

10     4.78 

40.32 

125.6 

8  59 

10  22.94 

41.52     1 

130.8 

9  22 

10  42.42 

42.83     ' 

136.3 

9  46 

11     3.38 

-     44.22     , 

O'.fiee 

5M98 

142.2 

10  11 

11  25.97 

45.73 

148.6 

10  38 

11   50.37 

47.36 

156.0 

11     8 

12   16.82 

49.12 

162.8 

11   39 

12  45.55 

51.04     i 

170.7 

12   13 

13   16.88 

53.12 

0'.866 

5M95 

179.3 

12  51 

13  51.15 

55.41 

1 

188.7 

13  31 

14  28.77 

57.92 

1 

199.1 

14   IS 

15  10.26 

60.68 

0'.866 

5'.  193 

Rbmarks  on  Tablb  13. 
second  column  of  Table  13  contains  the  convergency  of  two 
IS  six  miles  long  and  six  miles  apart,  measured  on  a  parallel  of 
When  the  parallel  of  latitude  passing  through  the  south  end  of 
ridians.  and  forming  the  south  boundary  of  the  township  of  which 
dians  form  the  meridional  boundaries,  is  coincident  with  a  tabular 
given  in  the  first  column,  the  required  convergency  will  be  ob- 
irectly  from  the  second  column  (see  Fi^.  34) ;  while  for  other  than 
alar  latitudes,  it  will  be  obtained  by  simple  proportion  (Fig.  35). 
d  column  contains  the  angle  of  convergency.  (abc,  Figs.  34  and  35.) 
the  purpose  of  computing  convergency  within  the  boundaries  of  a 
township,  said  boundaries  may  be  regarded  as  straight  lines  and  the 
p  a  plane  figure,  generally  a  trapezoid;  the  convergency  of  any 
liar  part  thereof,  bounded  by  meridional  and  latitudinal  section 
ill  be  determined  as  follows:  Multiply  the  convergency  for  the 
p,  determined  as  above  directed,  by  the  length  of  the  tract  in  miles 


078 


iS,-SURVEYING,  MAPPING  AND  LBV  RUNG, 


and  decimals  of  a  mile,  divided  by  6,  and  the  product  by  the  width  of  the 
tract  divided  by  6;  the  resulting  product  will  be  the  convergency  required. 
(See  Fig.  34.) 

To  obtain  the  convergency  of  the  meridional  botmdaries  of  any  tract 
bounded  by  section  lines,  or  other  lines  of  legal  subdivision,  within  p  town- 
ship, proceed  as  follows:  Divide  the  tract  into  the  least  possible  number  of 
rectangtilar  parts  and  compute  the  convergency  for  each  tract:  then,  take 
the  sum  of  the  con vergencies  thus  determined.  (See  example.  Pig.  3^.  The 
convergency  of  two  meridians  %f  equal  length,  in  the  same  latitude,  is  |m> 
portional  to  their  distance  apart;  e.  g.,  the  conveigency  of  two  meridians 
6  miles  long,  separated  by  6  ranges,  latitude  88^  is  56.8  lks.X5  — 2.84 
chains. 

0>nvergency  of  meridians  in  the  same  latitudes,  and  not  exceeding  24 
miles  in  length,  may  be  computed  by  an  approximate  proportion,  whidi 
combines  the  advantages  of  convenience  with  an  accuracy  sufficient  for  the 
ordinary  wants  of  the  land  siu^eyor;  the  proportion  is  this:  Th»  ccsitus 
of  the  latitudes  are  to  each  other  as  the  iengths  of  the  intercepted  paraUels. 
The  following  example  illxistrates  the  use  of  this  rule: 

The  distance  between  the  Principal  Meridian  and  first  ranjse  line  west. 
in  latitude  42^  39^  07',  is  6  miles:  what  is  the  convergency  of  the  two  range 
lines  at  the  Base  Line,  the  meridional  distance  being  24  miles? 

cos  42"  39^07*  :  cos  43"  ::  480.00  chs  :  477.31  chs..  which  proportion  may 
be  worked  with  natural  cosines,  or  more  expeditiously  by  logarithms,  as 
follows: 

a.  clog  cos  42"39'0r  0.138427 

log  cos  43"  0.864127 

log  480.00  2.681241 


log 
The  difference. . . 


477.30 


2.678706 


2.76  chs.  is  the  convergency  required. 


o^— 0>nvergency  on  the  Parallel. 
abc  =  Angle  of  (Convergency. 

Table  13;  opposite  Latitude  44",  will  be  found  70. 1 
links,  the  convergency. 

North  Boundary  =  480.00  -  0. 70  «  479  30  chs. 

For  Convergency  of  the  meridians  sh  and    fg,  we 
have: 

70. 1 X  8  X  8  =  17. 16  Links,  as  in  the  text. 


Required  the  0>nvergency  for  a  Township  in  Lat. 

38"  29^  N. 
From  Table  13: 

Convergency  in  Latitude  38", »  56.8  Links; 
39".  "58.8      " 

Difference 

Also;  29'-0".48; 

then.  0".48X  2.0  =  0.96  links;  • 

ac"  66.8-1-0.96-67.76  links,  the  convergency  required. 
North  boundary- 478.86- 0.58* -478.28  chains. 

*  Taken  to  nearest  whole  link. 
Tabular  Convergency,  is  80.6  links. 
Omvergency  for  the  tract  abcdefgh: 
Conv.  of  A;    80.6x8X1-22.39  links; 

•      ••    B;    80.6X«X|- 13.42     " 

"      "   C;    80.6X1X1-   8.96     " 


£mf'mi§e»e 


Pi8.8& 


t 

L 


Convergency  Required  —44.77     *' 

Also; 

Conv.  for  E.  tract  is  17.92     " 

•  S.W.  ••       ••  17.91     •• 

Total  convergency  80.60  links,  for  Townsh^  by  Gc>^.  86. 


9KiM 

\ 

: 
1 

i^  ^ 

A 

\ 

B 

Lj 

C 

r  .  1 

Laith^e 


d  by  Google 


980 


^.^SURVBYING.  MAPPING  AND  LEVELING, 


14. — Lbnoth  of  a  Dborbb  of  Latitude. — Concluded. 


i 

39» 

40» 

AV* 

43» 

43* 

44» 

45» 

A^ 

47. 

4r 

i 

» 

Cha^m 

CAoliw 

Chatnt 

Cftaim 

Chtsbu 

CHaim  Cfuins 

Chaina 

Chains 

Chains 

0 

5618.05 

5619.00 

5619.96 

5620.92 

5621.88 

6622  86  6523  81 

5624.78 

5625.76 

5526  78 

0 

18.07 

19.02 

19.97 

20.93 

21.90 

22.86 

23.83 

24. 80 

25.77 

26.73 

1 

3 

18.08 

19.03 

19.99 

20.95 

21  91 

22.88 

23.85 

24.82 

25.78 

26  75 

3 

3 

18.10 

19.05 

20.00 

20.96 

21.93 

22.89 

23.86 

24.83 

26.80 

26.76 

3 

4 

18.11 

19.06 

20.02 

20.08 

21.94 

22.91 

23.88 

24.85 

25.82 

86  78 

4 

5 

18.13 

19.08 

20.04 

21.00 

21.96 

22  93 

28.90 

84.86 

85  83 

26  80 

8 

6 

18.15 

19.10 

20.05 

21.01 

21  98 

22.94 

23.91 

84  88 

25.86 

26  81 

6 

7 

18.  IS 

19.11 

20.07 

21.03 

21.99 

22.96 

23.93 

24.00 

25.86 

26.83 

7 

8 

18.18 

19.13 

20.08 

21.04 

22.01 

-ft.  98 

23.94 

24.91 

25  88 

26.84 

8 

9 

18.19 

19.14 

20.10 

21.06 

32.02 

22  99 

28.96 

24.83 

25.90 

26.86 

9 

10 

18.21 

19.16 

20.12 

21.08 

22.04 

23.01 

23.98 

24.94 

25.91 

26  88 

10 

II 

18.22 

10.18 

20.13 

21.09 

22.06 

23.02 

23.99 

24.96 

25  93 

26.89 

II 

13 

18.24 

19.19 

20.15 

21.11 

22.07 

23.04 

24.01 

24.98 

25  94 

36  91 

13 

la 

18.26 

19.21 

20.16 

21.12 

22  09 

23.06 

24.02 

24.99 

25.96 

26.92 

13 

14 

18.27 

19.22 

20.18 

21.14 

22.11 

23.07 

24.04 

28.01 

25.98 

26.  M 

14 

15 

18.29 

19.24 

20.20 

21.16 

22.12 

23.09 

24.06 

25.03 

85.99 

86  96 

IS 

16 

18.30 

19.25 

20.21 

21.17 

22.14 

23  10 

24.07 

26.04 

26.01 

26  97 

16 

17 

18.32 

19.27 

20.23 

21  19 

22.16 

23.12 

24.09 

26.06 

26.02 

26.99 

17 

18 

18.34 

19.29 

20.24 

21.20 

22.17 

23.14 

24.11 

26.07 

26  04 

27.00 

18 

19 

18.35 

19.30 

20.26 

21.22 

22.19 

23  15 

24.12 

26.09 

86.06 

87.08 

19 

30 

18.37 

19.32 

20.28 

21  24 

22.20 

23.17 

24.14 

85.11 

26.07 

87.04 

79 

31 

18.38 

19.33 

20.29 

21.25 

22  22 

23  19 

24.16 

26.12 

26.09 

27  05 

31 

33 

18.40 

19.35 

20.31 

21.27 

22.23 

23.20 

24.17 

25.14 

26.10 

27  07 

33 

3S 

18.41 

19.37 

20.32 

21.29 

22.26 

23.22 

24.19 

26.15 

26.12 

27.09 

33 

34 

18.43 

19.38 

20.34 

21.30 

22.27 

23.23 

24.20 

25.17 

25  14 

87.10 

34 

3S 

18.45 

19.40 

20.36 

21.32 

22.28 

33.26 

24.22 

25.19 

26.15 

87.18 

as 

36 

18.46 

19.41 

20.37 

21.33 

22.30 

23.27 

24.23 

25  20 

26.17 

27.13 

36 

37 

18.48 

19.43 

20.39 

21.35 

22.31 

23.28 

24.26 

25.22 

26  19 

27.15 

37 

38 

18.49 

19.45 

20.40 

21.36 

22.33 

23.30 

24.27 

26.23 

26  20 

27.17 

38 

39 

18.51 

19.46 

20.42 

21.38 

22.36 

23.31 

24.28 

25.25 

26.82 

87.18 

30 

30 

18.53 

19.48 

20.44 

21.40 

22.86 

23.33 

24.80 

85.87 

26  23 

87.80 

30 

31 

18.54 

19.49 

20.45 

21.41 

22.38 

23.35 

24.33 

26.28 

26.25 

27.21 

31 

33 

18.56 

19.51 

20.47 

21.43 

22.40 

23.36 

24.33 

26.30 

26.27 

r.83 

33 

33 

18.57 

19.53 

20.48 

21.46 

22.41 

23.38 

24.35 

26.32 

26.28 

27.85 

33 

34 

18.59 

19.54 

20.50 

21.46 

22.43 

23.  «D 

24.36 

25.33 

26.30 

r.88 

34 

38 

18.60 

19.56 

20.62 

21.48 

33.44 

83.41 

84.88 

25.35 

26  31 

r.88 

38 

36 

18.62 

19.57 

20.53 

21.49 

22.46 

23.43 

24  40 

25.36 

26  33 

27.89 

36 

37 

18.64 

19.59 

20.55 

21.51 

22.48 

23.44 

24.41 

25.38 

26.35 

87.31 

J7 

38 

18.65 

19.60 

10.56 

21.63 

22.49 

23.46 

24  43 

26.40 

26  36 

r.33 

38 

39 

18.67 

19.62 

20.68 

21.64 

22.61 

23.48 

24.44 

25.41 

26-38 

r.34 

39 

40 

18.68 

19.64 

20.60 

21.66 

22.52 

23.49 

24.46 

25.43 

26.39 

zr.u 

40 

41 

18.70 

19.66 

20.61 

21.67 

22.64 

23.51 

24.48 

26.44 

26  41 

87.87 

41 

43 

18.72 

19.67 

20.63 

21.59 

22.56 

23.62 

24.49 

25.46 

26.43 

87.89 

43 

43 

18.73 

19.68 

20.64 

21.61 

22.67 

23.54 

24.61 

26.48 

26.44 

r.4l 

43 

44 

18.75 

19.70 

20.66 

21.62 

22.69 

23.66 

24.52 

26.49 

26  46 

27.48 

44 

48 

18.76 

19.72 

20.68 

21.64 

22.60 

23.67 

24.54 

26  51 

26  47 

37.44 

4S 

46 

18.78 

19.73 

20.69 

21.65 

22.62 

23.69 

24.66 

26.62 

26.49 

r.45 

46 

47 

18.79 

19.75 

20.71 

21.67 

22.64 

23.60 

24.67 

26.64 

26.61 

27.47 

47 

48 

18.81 

19.76 

20.72 

21.69 

22.66 

23.62 

24.69 

25  56 

26.52 

r.49 

48 

49 

18.83 

19.78 

20.74 

21.70 

22.67 

23.64 

24.61 

26.57 

26.54 

37.60 

49 

80 

18.84 

19.80 

20.76 

21.72 

22  69 

23  65 

24  62 

25.59 

26.56 

87.58 

s» 

81 

18.86 

19.81 

20.77 

21.74 

22.70 

23.67 

24.64 

25.61 

26.57 

47.58 

51 

S3 

18.87 

19  83 

20.79 

21.75 

22.72 

26.69 

24  66 

25  62 

26.69 

87.50 

sa 

H 

18.89 

19.84 

20.80 

21.77 

22.73 

23  70 

24  67 

26  64 

26.60 

87.57 

SJ 

84 

18.91 

19.86 

20.82 

21.78 

22.75 

23.72 

24.69 

2665 

86.62 

87.68 

S4 

88 

18.92 

19.88 

20.84 

21.80 

22.77 

23.73 

24  70 

25  67 

26.64 

87.60 

88 

86 

18.94 

19.89 

20.85 

21.82 

22.78 

23.75 

24.72 

26  69 

25.65 

87.61 

86 

87 

18.95 

19  91 

20.87 

21.83 

22.80 

23.77 

24.73 

26  70 

26.67 

87.63 

57 

88 

18.97 

19.92 

20.88 

21.85 

22.81 

23.78 

24.76 

26.72 

26  68 

r  65 

88 

89 

18.98 

19.94 

20.90 

21.86 

22.83 

23.80 

24.77 

26.73 

26.70 

87  66 

99 

60 

5519.00 

5519.96 

5520.92 

6621.88 

6522.86 

5523.81 

5524.78 

5625.75 

6526.72 

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d  by  Google 


083 


S8.— SURVEYING,  MAPPING  AND  LEVELING. 


16. — ^Lbnoth  op  a  Dborbb  of  Lonoitudb. — Concluded. 


i 

39" 

400 

AV 

43* 

43« 

44«» 

4r 

^ 

4r 

4r 

i 

» 

^JMfu 

Chains 

Chains 

Chans 

Chains 

Chains 

Chains 

Chains 

Chains 

Chains 

» 

0 

4306.73 

4244.47 

4181.91 

4118.06 

4062.96 

3986.62 

3919.06 

3850.88 

3780.33 

3709.28 

f 

1 

04.72 

43.44 

80.85 

16.99 

51.87 

86.60 

17.91 

49.12 

79.16 

08.03 

1 

3 

08.71 

42.41 

79.80 

15.91 

60.77 

84.88 

16.78 

47.97 

77.98 

86.88 

3 

3 

02.70 

41.37 

78.75 

14.84 

49.67 

83.87 

16.64 

46.81 

76.80 

05.69 

a 

4 

01.89 

40.84 

77.69 

ia.76 

48.58 

88.15 

14.60 

45.85 

75.68 

04.44 

4 

8 

4300.68 

39.81 

76.64 

18.69 

47.48 

81.88 

13.86 

44.60 

T4.45 

08.84 

f 

6 

4299.67 

38.27 

76.68 

11.61 

46.38 

79.91 

12.23 

43.84 

73.27 

08.06 

6 

7 

98.65 

37.24 

74.52 

10.53 

46.28 

78.79 

11.09 

42.18 

72.00 

3700.85 

7 

8 

97.64 

36.20 

73.47 

09.46 

44.19 

n.68 

09.95 

41.02 

70.92 

3699.65 

6 

9 

96.63 

36.17 

73.41 

08.38 

43.09 

76.66 

08.81 

89.86 

89.74 

98.46 

9 

10 

95.61 

34.13 

71.86 

07.80 

41.99 

75.44 

07.87 

88.70 

68.56 

97.88 

M 

II 

94.60 

33.10 

70.30 

06.82 

40.89 

74.32 

06.58 

87.54 

67.88 

96.06 

11 

13 

93.59 

32.06 

69.24 

06.14 

89.79 

73.20 

06.89 

86.38 

66.20 

94.86 

13 

13 

92.57 

31.02 

68.18 

04.07 

88.69 

72.08 

04.35 

35.22 

65.02 

93.66 

13 

14 

91.66 

29.99 

67.12 

02.99 

87.69 

70.96 

08.11 

84.06 

68.84 

98.48 

14 

18 

90.54 

28.95 

66.07 

01.91 

86.49 

88.84 

01.97 

88.90 

68.66 

91.88 

If 

16 

89.62 

27.91 

66.01 

4100.83 

85.39 

68.72 

3900.83 

81.-74 

61.48 

90.60 

16 

17 

88.51 

26.87 

63.95 

4099.75 

84.29 

67.69 

3899.69 

80.58 

60.80 

88.86 

17 

18 

87.49 

25.84 

62.89 

98.67 

33.19 

66.47 

98.54 

89.42 

59.12 

87.66 

IS 

19 

86.48 

24.80 

61.83 

97.58 

38.09 

65.86 

97.40 

88.86 

57.94 

86.46 

19 

30 

85.46 

33.76 

60.77 

96.60 

80.98 

64.83 

96.86 

r.09 

66.76 

85  88 

30 

31 

84.44 

22.72 

59.71 

95.42 

29.88 

68.11 

96.18 

85.93 

65.57 

84.06 

31 

23 

83.42 

21.68 

68.65 

94.34 

28.78 

61.98 

n.97 

24.77 

64.89 

82.86 

33 

23 

82.40 

20.64 

67.58 

93.26 

27.67 

60.86 

92.83 

83.60 

53.21 

81.66 

33 

34 

81.39 

19.60 

56.52 

92.17 

36.67 

59.73 

•1.68 

88.44 

68.02 

80.46 

34 

38 

80.37 

18.56 

56.46 

91.09 

25.47 

68.61 

90.54 

81.88 

50.84 

79.85 

38 

36 

79.85 

17.52 

64.40 

90.01 

24.36 

67.49 

89.40 

80.11 

49.66 

78.05 

36 

37 

78.33 

16.48 

53.44 

88.92 

83.26 

56.36 

88.25 

18.95 

48.47 

76.85 

37 

38 

77.31 

15.43 

62.27 

87.84 

22.15 

66.24 

87.11 

17.78 

47.29 

75.64 

38 

39 

76.29 

14.39 

51.21 

86.75 

81.06 

54.11 

86.96 

16.88 

48.10 

74.44 

39 

30 

75.27 

13.35 

50.14 

85.67 

19.94 

68.98 

84.81 

15.45 

44.92 

78.84 

39 

31 

74.24 

12.31 

49.08 

84.58 

18.84 

51.86 

83.67 

14.29 

43.73 

72.03 

31 

33 

73.22 

11.26 

48.02 

83.50 

17.73 

50.73 

82.52 

13.12 

42.55 

70.88 

33 

33 

72.20 

10.22 

46.95 

82.41 

16.62 

49.60 

81.37 

11.95 

41.80 

89.  U 

38 

34 

71.18 

09.18 

45.89 

81.33 

15.52 

48.48 

80.23 

10.79 

40.18 

88.48 

34 

38 

70.16 

08.13 

44.82 

80.84 

14.41 

47.85 

79.08 

09.62 

88.99 

87.81 

38 

36 

69.13 

07.09 

43.75 

79.15 

13.30 

46.22 

77.93 

08.45 

37.80 

66.01 

36 

37 

68.11 

06.04 

42.69 

78.07 

12.19 

45.09 

76.78 

07.28 

36.62 

64.80 

37 

38 

67.09 

05.00 

41.62 

76.98 

11.09 

43.96 

75.68 

06.11 

35.43 

63.59 

38 

39 

66.06 

03.96 

40.65 

75.89 

09.98 

48.83 

74.48 

04.95 

84.84 

88.89 

39 

40 

65.04 

02.90 

89.49 

74.80 

08.87 

41.71 

78.34 

03.78 

83.06 

81.18 

40 

41 

64.01 

01.86 

38.42 

73.71 

07.76 

40.58 

72.19 

02.61 

31.86 

59.97.41 

43 

62.99 

4200.81 

37.35 

72.62 

06.65 

39.45 

71.04 

01.44 

80.67 

58.76 

43 

43 

61.96 

4199.76 

36.28 

71.53 

05.54 

38.32 

69.89 

3800.27 

29.48 

87.56 

43 

44 

60.93 

98.72 

35.21 

70.44 

04.43 

37.18 

68.74 

3799.10 

88.80 

88.85 

44 

48 

59.91 

97.67 

34.14 

69.35 

03.32 

36.06 

67.58 

97.98 

r.ii 

55.14 

48 

46 

58.88 

96.62 

33.08 

68.26 

02.21 

34.92 

66.43 

96,76 

85.98 

53.93 

46 

47 

57.85 

95.57 

32.01 

67.17 

4001.10 

33.79 

66.88 

95.69 

24.73 

58.78 

47 

48 

56.83 

94.52 

30.93 

66.08 

3999.98 

32.66 

64.13 

94.41 

83.53 

51.51 

48 

49 

55.80 

93.47 

29.86 

64.99 

98.87 

31.53 

68.98 

83.84 

88.84 

60.80 

49 

80 

54.77 

92.42 

28.79 

63.90 

97.76 

30.39 

61.88 

92.07 

81.15 

49.89 

•9 

81 

53.74 

91.37 

27.72 

62.81 

96.65 

29.26 

60.67 

90.90 

19.96 

47.88 

81 

83 

52.71 

90.82 

26.65 

61.71 

95.53 

28.13 

59.58 

89.73 

18.77 

46.67 

S3 

83 

51.68 

89.27 

25.58 

60.62 

94.42 

26.99 

58.36 

88.56 

17.58 

45.46 

S8 

84 

60.66 

88.22 

24.51 

59.53 

93.31 

25.86 

67.81 

87.88 

16.88 

44.88 

84 

85 

49.63 

87.17 

23.43 

58.43 

92.19 

34.73 

56.06 

86.80 

15.19 

43.03 

S8 

56 

48.59 

86.12 

22.36 

57.34 

91.08 

23.59 

54.90 

86.03 

14.00 

41.82 

SO 

87 
88 
89 

47.66 

85.07 

21.29 

66.25 

89.96 

22.46 

58.75 

83.86 

12.80 

40.61 

S7 

46.53 

84.02 

20.21 

65.15 

88.85 

21.32 

53.69 

88.68 

11.61 

89.40 

ss 

45.50 

82.96 

19.14 

54.06 

87.73 

20.19 

61.44 

81.61 

10.41 

88.18 

S9 

60 

4844.47 

4181.91 

4118.06 

4052.96 

3986.62 

3919.06 

8850.88 

3780.88 

3709.22 

9836.97 

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LEVEUNG— CURVATURE  AND  REFRACTION.  »87 

LeveUng  Correctioa  for  E«rth*s  Curvature  and  Refraction. — A  Itvel 
"surface"  arotind  the  earth  is  a  spheroid.  Now  this  spheroid  is  of  the 
exact  size  and  shape  of  the  "mean"  earth  when  every  point  of  its  surface  is 
at  zero  elevation,  corresponding  generally  with  mean  sea  level.  This  is  the 
datum  spheroidal  "plane"  used  in  leveling.  Any  "plane"  above  said  datum, 
i.  e.,  at  a  higher  elevation,  if  extended  around  the  globe,  will  form  a  spher- 
oidal level  surface  whose  perpendicular  distance  from  the  datum  plane  will 
be  constant  at  points  of  eqtial  latitude;  but  will  decrease  gradually  from 
the  eauator  toward  the  poles.  Hence,  a  meridian  line  of  levels  if  run  at  a 
con^erable  height  above  the  datum  plane  would  be  subject  to  correction; 
but  the  error  is  generally  so  small  compared  with  other  errors  that  it  is 
disr^arded  in  practical  leveling. 

Ordinary  sources  of  error  m  leveling  are  eliminated  by  taking  equal 
back-sights  and  fore-sights  and  by  using  other  pre- 
cautions. Those  due  to  curvattire  of  the  earth  and 
refraction  of  light  rays  passing  thro\igh  the  atmos- 
phere must  be  corrected,  where  a  single  sight  is  taken 
on  a  distant  object  from  a  fixed  position  of  the  level. 
Let  t  (Fig.  37)  be  the  point  of  sight  of  the  telescope 
and  let  it  be  required  to  find  the  elevation  of  the 
point  f  upon  which  rests  a  leveling  rod  hp.  Let  the  Pig.  87. 

point  /  on  the  rod  be  at  the  same  elevation  as  f,  then  Ip,  the  desired  height. 
IS  the  height  of  instrument  above  p,  and  the  radius  of  the  curve  tl  is  the 
radius  of  the  earth.  If  no  atmosphere  were  present  to  cause  refraction,  the 
line  of  si^ht  would  be  the  horizontsd  line  th,  but  on  account  of  refraction 
the  real  hne  of  sight  takes  the  curve  tr  whose  radius  is  about  7  times  the 
radius  of  the  earth;  hence  W— 7  times  hr,  or  rl^^lihl  (nearly).  Now  as  tr 
and  tl  are  short  curves  of  very  large  radii  we  may  consider  them  as  para- 
bolas and  intersecting  the  leveling  rod  at  angles  of  90^.  If  D  represents 
the  horizontal  distance  from  instrument  to  rod,  we  have,  from  the  nature  of 
the  problem,  that  hr,  rl  and  kl  are  each  proportional  to  D^,  Moreover, 
while  the  correction  for  curvature  adds  to  the  apparent  elcAration  of  the 
distant  object,  the  correction  for  refraction  subtracts  from  this  bv  about  if 
part.  The  combined  (difference)  correction  for  curvature  and  refraction  is 
additive,  as  per  the  following  table. 


d  by  Google 


988 


l».— SURVEYING.  MAPPING  AND  LEVEUNG. 


17. — CORRBCTION  FOR  EaRTH'S  CuRVATURB,  AMD  RbPRACTION. 

(Add  "Curvature  and  Refraction"  to  apparent  Elevation  of  object.) 


Curva- 
ture 

Dis- 

CX)rrecUon In  Feet  lor— 

Dis- 

Correction In  Feet  tor  — 

Dis- 

tance. 

and 

tance 

Curvar 

tance. 

Curva- 

Feet. 

Refrao- 

MUefl. 

Curva- 

Retrac- 

- tureand 

Miles. 

Curva- 

Retno- 

ture  and 

Uon. 

ture. 

tion. 

Refrao- 
Uon. 

ture. 

tton. 

Retrao 
tton. 

300 

.002 

1 

0.7 

0.1 

0.6 

34 

771.0 

108.0 

663.3 

400 

.003 

2 

2.7 

0.4 

2.3 

36 

817.4 

114.4 

703.0 

600 

.006 

3 

6.0 

0.8 

5.2 

600 

.007 

4 

10.7 

1.5 

9.2 

36 

864.8 

121.1 

743.7 

700 

.010 

5 

16.7 

2.8 

14.4 

37 
38 

913.5 
963.5 

127.9 
134.9 

785.6 
828.6 

800 

.013 

6 

24.0 

3.4 

20.6 

39 

1014.9 

142.1 

872.1 

900 

.017 

7 

32.7 

4.6 

28.1 

40 

1067.6 

149.6 

918.1 

1000 

.020 

8 

42.7 

6.0 

86.7 

1100 

.026 

9 

54.0 

7.6 

46.4 

41 

nil. 7 

167.0 

M4.7 

1200 

.030 

10 

66.7 

9.8 

B7.4 

42 

43 

1177.0 
1233.7 

164.8 
172.7 

1012.3 
1061.0 

1300 

.035 

11 

80.7 

11.3 

69.4 

44 

1291.8 

180.8 

lUl.O 

1400 

.040 

1     12 

96.1 

13.4 

82.7 

46 

1361.2 

189.2 

1162.0 

1500 

.046 

13 

112.8 

16.8 

97.0 

1600 

.052 

14 

130.8 

18.3 

112.5 

46 

1411.9 

197.7 

1412.3 

1700 

.0^9 

15 

150.1 

21.0 

129.1 

47 
48 

1474.0 
1637.3 

206.3 
215.2 

1267.7 
IS33.I 

1800 

.066 

16 

170.8 

23.9 

146.9 

49 

1602.0 

224.3 

1377.7 

1900 

.074 

17 

192  8 

27.0 

165.8 

50 

1668.1 

233.5 

1434.6 

2000 

.082 

18 

216.2 

30.3 

181.9 

2200 

.099 

19 

240.9 

33.7 

207.2 

61 

1735.6 

243.0 

1493.6 

i400 

.118 

20 

266.9 

37.4 

229.5 

62 
63 

1804.2 
1874.3 

252.6 
262.4 

1551.6 
1611.9 

2600 

.139 

21 

294.3 

41. 2 

253.1 

64 

1946.7 

272.4 

1673.3 

2800 

.161 

22 

322.9 

45.2 

277.7 

55 

2018.4 

282.6 

1736.8 

3000 

.184 

23 

353.0 

49.4 

303.6 

3200 

.210 

24 

384.3 

53.8      330.5  II 

56 

2092.6 

292.9 

1799.6 

3400 

.237 

25 

417.0 

58.4 

368.6 

57 
58 

2167.9 
2244.6 

303.5 
314.2 

1864.4 
1930.4 

3600 

.266 

26 

451.1 

63.1 

388.0 

69 

2322.7 

325.2 

1997.6 

3800 

.296 

27 

486.4 

68.1 

418.3 

60 

2402.1 

336.3 

3066.8 

4000 

.328 

28 

523.1 

73.2 

449.9 

4200 

.362 

29 

561.2 

78.6 

482.6 

61 

2482.8 

347.6 

2136.3 

4400 

.397 

30 

600.5 

84.1 

516.4 

62 
63 

2564.9 
2648.3 

369.1 
370.8 

3305.8 

2277.5 

4600 

.434 

31 

641.2 

89.8 

551.4 

64 

2733.0 

382.6 

2350.4 

4800 

.472 

32 

683.3 

95.7 

587.6 

66 

2819.1 

394.7 

3424.4 

5000 

.512 

33 

726.6 

101.7 

624.9 

66 

2906.5 

406.9 

2499.6 

Ex. — ^The  rod  reading  on  an  object  distant  3200  ft.  from  the  levd  is 
6.00  ft.;  and  the  height  of  instrument  (H.  I.)  is  300.00  ft.  Find  the  eleva- 
tion of  the  object. 

Ans. — ^The  apparent  elevation  is  295.00  ft.;  and  the  tru$  elevation  is 
296.21  ft. 


d  by  Google 


18. — Allov 


Distance. 

Dtotanoe. 

MOea. 

Feet. 

1 

528 

125 

660 

25 

1320 

333 

1760 

5 

2640 

625 

3300 

r 

75 

3960 
5280 

I. 

25 

CCOO 

1. 

5 

7920 

1. 

75 

9240 

2 

10560 

2. 

5 

13200 

3 

16840 

4 

21120 

5 

26400 

C 

31680 

8 

42240 

10 

62800 

12 

63360 

15 

79200 

20 

105600 

25 

132000 

30 

158400 

40 

211200 

50 

264000 

fO 

316800 

70 

369600 

10 

422400 

M 

476200 

100 

125 

150 

175 

200 

250 

300 

350 

400 

450 

500 

*  Error  (in  feet)  levelin 

.oie 


d  by  Google 


990 


B8.— SURVEYING,  MAPPING  AND  LEVELING. 


EXCERPTS  AND  REFERENCES. 

The  PUme-TaUe  for  Small  Topocraphlcal  Surveys  (By  W.  P.  Bullock. 
Eng.  News.  May  29,  1902). — Sketch  illustrating  use. 

A  City  Eogineer'a  Card  Index  of  Plans  and  Notes  (By  A.  H.  Pratt. 
Eng.  News,  April  16,  1903).— Cards  illustrated. 

Some  Remarkable  Records  in  Taking  Soundings  Thromrh  (pe  on 
Lake  Superior  (By  G.  A.  Taylor.  Eng.  News.  Mar.  24,  1904).— The  obst  of 
the  soundings  was  3  cents  each  for  field  work  alone. 

Boring  Soundlnc  Holes  Through  Ice  (Eng.  News.  May  26,  1904).— 
niustrated  details  of  ice  auger. 

A  Rapid  Method  of  Takh^  Soundings  in  ShaHow  Water  (By  A.  E. 
Collins.    Eng.  News,  June  16,  1904.) — Device  illustrated. 

Electrical  Devk:es  for  Deep  Borehole  Surveying  (By  H.  P.  Marriott. 
Eng.  News,  July  27.  1906). — Includes  19  illustrations. 

Methods  of  Rod-Holding  in  Stadia  Surveying  and  Descrlptkin  cf  a 
New  Stadia  Slide  Rule  (By  A.  L.  Bell.  Eng.  News.  Nov.  9.  1906).— Stadia 
formulas:   illustrated. 

Wash  DriU  Borings:  (I)  On  New  York  State  Barce  Canal:  (2}  On 
the  Deep  Waterways  Survevs;  (3)  For  the  Rapid  Transit  Commission,  N,  Y 
City  (Eng.  News,  Jan.  17.  1907).— Methods  and  cost  data. 

Cost  of  Earth  Anger  Borings  on  the  N.  Y.  State  Barge  Canai  (By 
Emile  Low.    Eng.  News,  Mar.  21    1907). 

Testing  Steel  Tapes  at  the  Natk>nal  Bureau  of  Standards  (By  H.  T. 
Wade.    Eng.  News,  Aug.  13,  1908).— Illustrated. 

North-Points  for  Maps  (By  A.  W.  Bedell.  Eng.  News,  Oct.  7,  1909).— 
Over  40  different  designs  of  north  points  illustrated. 

Description  of  Four  Stadia  Surveys  and  Their  Cost  (By  A.  W.  Tidd. 
Eng.  News,  Oct.  21.  1909). — Illustrations: — Typical  portkm  of  topc^raphkal 
map;  Page  of  stadia  notes:  Portion  of  page  ot  traverse  notes:  Stadia  rod: 
Diagram  for  reading  diflferences  of  elevation  from  stadia  notes:  Diagram  for 
reducing  stadia  readings  to  distance;  Protractor  for  plotting  stadia  notes; 
Device  tor  interpolating  contours. 

Summary  op  (k>8TS. 


Detail 
topography. 

Topography  for 
5-ft.  contours. 

Deens 
Bridge. 

The  Hem. 
locks  site. 

Lower  End 
cf  basin. 

West 
Branch. 

Area,  in  acres 

2392 
17990 
5 

27 
7i 
$171  50 
$181.10 

29 

11 

84 

$0.81 
$0.85 

61 
1010 
8600 

1310 

3215 

52350 

200 

Number  of  Shots 

Length  of  traverse,  in  feet 

Number  of  traverses  

781 

10520 

9 

Number  of  courses 

26 

8 

$t60.40 

$190.40 

6 

20 

168 

$2.94 

$3.74 

62 

16 
$434.40 
$614.40 

82 
2.4 

40 

$0.33 
$0.89 

\16 

Days  work,  Sat.-  full  day 

Total  cost,  excl.  transportation  - 

Total  cost,  incl.  transportation.  . 

Acres  surveyed  per  day 

Shots  per  acre 

Feet  of  traverse,  per  acre 

Cost  per  acre,  excl.  transporta- 
tion   

Cost  per  acre,  incl.  transporta- 
tion   

3 

$77  80 
$107.80 
67 

3.9 
62 

$0.39 

$0.54 

Illustrations. 

Description. 
Concrete  boundary  monuments,  with  costs 


Digitized 


by  Google 


Eng.  Rer. 
Jan.     1.  '10. 


of  steam 
OO  inhabi- 
M)0.000  or 
5.  $2,000.- 
operating 
t.    There 

0  18.8  sq. 

ire  depen- 
upon  the 

1  adopted 
nbjects  of 
i  locating 
cular  line 
reduction, 
especially 
Eul,  in  the 

ivestment 
1  building 
I  works  of 
ofpopula- 
opulation 
he  capac- 
;er  supply 
;  they  are 
'  without 
[icient  for 
z&use  the 
exceeded 
On  the 
manufac- 
ansion  of 
purchased 
d.  There 
nt  on  the 
lade.  ma- 
cient  and 

the  above 
the  start 
I,  and  the 
The  New 
new  road 
System  is 
The  first 
vn  strong 
and  there 
if  become 
.  and  the 
Exceptions 
Southern 
z  (coal,  in 

«8sity.  as 
ent  eleva- 


d  by  Google 


992  Si.— RAILROADS. 

tions  above  aea  level;  (2)  to  reduce  distance,  as  in  passing  over  a  long  range 
of  hills  instead  of  around  it;  (3)  to  reduce  tne  cost  of  constniction  incident 
to  deep  cuttings,  high  embankments  and  long  ttmnels. 

The  "ruling*  ^lade  on  a  location  is  the  maximum  ^rade  allowable  on 
any  part  of  the  hne.  and  is  sometimes  called  the  "limiting"  grade.  Poo* 
mountainous  sections  it  is  generally  fixed  at  about  2%,  more  or  less,  and 
arbitrarily  adhered  to*  by  the  locatmg  engineers.  Sometimes,  however,  the 
ruling  grade  is  changed  after  location  is  begun.  If  a  low  mountain  pass  is 
discovered  it  may  be  decreased;  if  certain  unforeseen  difficulties  are  en- 
countered in  the  topography  of  the  country  it  may  be  increased.  It  is 
alwavs  best  to  have  the  heavy  grades  bunched  together  continuously  if 
possible  and  not  scattered  throughout  the  line.  By  this  arrangement  tney 
may  be  taken  from  the  class  of  "limiting"  grade,  for  single  engine  trains, 
and  placed  in  the  cla^  of  "pusher"  grade,  where  assistant  engines  or  ptishers 
can  be  operated  economically  at  one  point.  In  this  way  the  limiting  grade 
proper,  on  the  line,  may  be  said  to  be  lowered,  which  is  decidedly  advan- 
tageous to  the  reduced  operating  expenses  of  the  road. 

The  Traction  Force  of  a  locomotive  is  the  train  resistance  which  it  can 
overcome.  It  cannot  exceed  the  "adhesion"  of  the  driving  wheels  lo  the 
rails;  the  "adhesion"  should  not  exceed  the  "cylinder"  power  of  the  engine: 
the  "cylinder"  power  should  not  exceed  the  "boiler '  power.  We  wiU 
assume  then,  that  the  engine  is  properly  designed:  that  the  cylinder  power 
is  a  little  in  excess  of  the  adhesion,  and  that  the  boiler  power  is  just  suffi- 
cient to  cause  slipping  of  drivers,  when  using  sand.  Then  tractive  force 
equals  adhesion.  Tne  adhesion  or  tractive  force  may  be  asstuned.  for  our 
•resent  purpose,  at  \^  the  total  weight  on  the  driverSt  that  is,  this  force  can 
exerted  horizontally  in  moving  the  train. 

The  train  resistance  on  a  level  track  comprises  rolling  friction  proper, 
journal  friction,  reduced  effect  of  traction  due  to  curvature,  air  resistance, 
etc.  We  will  assume  it  to  be  about  8  lbs.  %  fer  short  ton  or  Vsjo  the  total 
weight  of  train — engine,  tender  and  cars.  Hence,  using  the  same  unit  of 
weight  throughout, 

ns      ^'      t           Total  wt.  on  drivers     Total  wt.  of  train    _    .         .  ^  ,.. 

Traction  force— j — 55 —Tram  reostAnce  (I) 

Total  wt.  of  train  —  62.5 X total  wt.  on  engine  drivers (2) 

Gross  car  loads—  d2.6Xtotal  wt.  on  drivers-wt.  of  engine  and  tender. .  .(3) 

Net  car  loads— 62.5 X total  wt.  on  drivers— wt.  of  engine,  tender  and 

empty  cars .(4) 

The  effect  of  an  ascending  grade  on  train  resistance  is  calculated  easily. 

The  level-grade  tractive  force  is  simply  increased  by  the  total  weight  of 

train X the  rate  (or  %)  of  the  grade\\.    Hence,  for  any  ordinary  grade  aasa 

using  the  same  unit  of  weight  throughout,  we  have,  from  (1), 

T      *•      t           Total  wt.  on  drivers    «,^,^*^./t.      ^       * 
Tractive  force- j —Total  wt.  of  tram  (ii«-)-rate  of 

grade) • («) 

rwx  ^  1     .     t  ^    ,         Total  wt.  on  drivers  ,_. 

Total  wt.  of  train  -  -jTi^-r-r;: — : — / — i- (® 

.01 6 -H  4  X  rate  of  grade 

\t  ^    f     of\    c       J       Total  wt.  on  drivers      ^^-  _^ 

Max,  rate  (or  %)  of  grade  -  .^,  ^  ,    ^ — j— .004 (7) 

4  X  total  wt.  of  tram 


e? 


*  Compensation  amounting  to  .04  (or  .05)  %  of  grade  per  degree  oi 
curve  is  introduced  in  order  to  equalize  the  tractive  resistance, 
t  May  vary  from  i  to  i;  recent  experiments  give  0.23  to  0.235. 
X  May  vary  from  4  to  10;  7  to  8  lbs.  is  usually  assumed. 
II  This  is  a  slight  approximation.    The  rate  (or  %)  of  grade  is  equal  to 

-7-  or  tangent  a  (Fig.  1),  the  angle  of  inclination  which 
grade  Kne  makes  with  the  horizontal,  whereas  the 
multiplier  should  6*  y  or  sine  a.  For  such  slight  in- 
clinations as  railroad  grades  the  error  is  inappreciable. 
It  won  the  side  of  safety.  0^,.^^, 


d  by  Google 


094 


m.—RAILROADS. 


1. — ^Ratio  op  Total  Weight  op  Train,  T,  to  Wbioht  on  Drivers, 
FOR  Various  Grades. 
(Weight  on  Drivers,  D,  Assumed  as  Unity.)  , 

Calculated  from  Formula  6.  preceding. 


D, 


Rat©  ol  Grade. 

Total 

Wt. 

of  Train. 

Rate  of  Grade. 

Total 

Wt. 

of  Train. 

Rate  of  Grade. 

Total 

of  Train. 

Per  100. 

^•r 

T 
D 

Per  100. 

Ft.  per 
Mtte. 

T 
D 

PerlOO. 

liSt 

T 
D 

Uvel 

Levd 

62.50 

1.00 

52.800 

K.86 

2.00 

105.600 

10.42 

0.02 

1.056 

59.52 

1.02 

53.856 

17.61 

2.02 

106.656 

10.33 

0.04 

2.112 

56.82 

1.04 

54.912 

17.36 

2.04 

107.712 

10.25 

0.06 

3.168 

54.35 

1.06 

65.968 

17.12 

2.06 

108.768 

10.16 

0.08 

4.224 

52.08 

1.08 

67.024 

16.89 

2.08 

109.824 

10.08 

0.10 

5.280 

60.00 

1.10 

68.080 

16.67 

2.10 

110.880 

10.00 

0.12 

6.336 

48.08 

1.12 

59.136 

16.45 

2.12« 

111.930 

•.92 

0.14 

7.392 

46.30 

1.14 

60.192 

16.23 

2.14 

112.998 

•  .84 

0.16 

8.448 

44.64 

1.16 

61.248 

16.03 

2.16 

114.048 

9.77 

0.18 

9.504 

43.10 

1.18 

62.804 

15.82 

2.18 

115.104 

9.69 

0.20 

10.560 

41.67 

1.20 

63.360 

15.63 

2.20 

116.160 

9.62 

0.22 

11.616 

40.82 

1.22 

64.416 

15.43 

2.22 

117.216 

•.54 

0.24 

12.672 

39.06 

1.24 

65.472 

15.24 

2.24 

118.272 

9.47 

0.26 

13.728 

37.88 

1.26 

66.528 

15.06 

2.26 

119.328 

9.40 

0.28 

14.784 

36.76 

1.28 

67.578 

14.88 

2.28 

120.384 

9.83 

0.30 

15.840 

35.71 

1.30 

68.640 

14.71 

2.30 

121.440 

9.26 

0.32 

16.896 

34.72 

1.32 

69.696 

14.53 

2.32 

122.496 

•  .19 

0.34 

17.952 

33.78 

1.34 

70.752 

14.87 

2.34 

123.552 

9.12 

0.86 

19.008 

32.89 

1.36 
1.38 

71.808 

14.20 

2.36 

124.608 

9.06 

0.38 

20.064 

32.06 

72.864 

14.04 

2.38 

125.664 

8.9f 

0.40 

21.120 

31.25 

1.40 

73.920 

13.89 

2.40 

126.720 

8.98 

0.42 

22.176 

30.49 

1.42 

74.976 

18.74 

8.43 

127.776 

8.87 

0.44 

23.232 

29.76 

1.44 

76.032 

13.59 

2.44 

128.838 

8.  SO 

0.46 

24.288 

29.07 

1.46 

77.088 

13.44 

2.46 

129.888 

8.74 

0.48 

25.344 

28.41 

1.48 

78.144 

13.80 

2.48 

130.944 

8.6S 

0.60 

26.400 

27.78 

1.60 

79.200 

13.16 

2.50 

132.000 

8.6S 

0.52 

27.456 

27.18 

1.52 

80.256 

13.02 

2.62 

133.056 

8.6f 

0.54 

28.512 

26.60 

1.64 

81.312 

12.89 

2.54 

134.112 

8.60 

0.56 

29.668 

26.04 

1.56 

82.368 

12.76 

2.56 

135.168 

8.45 

0.58 

30.624 

25.51 

1.58 

83.424 

12.68 

2.58 

136.224 

8.39 

0.60 

31.680 

25.00 

1.60 

84.480 

12.50 

2.60 

137.280 

8.SS 

0.62 

32.736 

24.51 

1.62 

85.536 

12.38 

2.62 

138.336 

8.28 

0.64 

33.792 

24.04 

1.64 

86.592 

12.25 

2.64 

139.392 

8.21 

0.66 

34.848 

23.58 

1.66 

87.648 

12.14 

2.66 

140.448 

8.17 

0.68 

S6.904 

23.15 

1.68 

88.704 

12.02 
11.90 

2.68 

141.604 

8.U 

0.70 

86.960 

22  73 

1.70 

89.760 

2.70 

142.560 

8.06 

0.72 

38  016 

22.32 

1.72 

90.816 

11.79 

2.72 

143.616 

8.01 

0.74 

39.072 

21.93 

1.74 

91.872 

11   68 

2.74 

144.672 

7.%% 

0.76 

40.128 

21.55 

1.76 

92.928 

11.57 

2.76 

145.728 

7.91 

0.78 

41.184 

21.19 

1.78 

93.984 

11.47 

2.78 

146.784 

7.88 

0.80 

42.240 

20.83 

1.80 

95.040 

11.36 

2.80 

147.840 

7.81 

0.82 

43.296 

20.49 

1.82 

96.096 

11.26 

2.82 

148.896 

7.7f 

0.84 

44.352 

20.16 

1.84 

97.152 

11.16 

2  84 

149.952 

7.71 

0.86 

45.408 

19  84 

1.86 

98.208 

11.06 

2.86 

151.008 

7.07 

0  88 

46.464 

19.53 

1.88 

99.264 

10.96 

2.88 

152.064 

T.tt 

0.90 

47.S20 

19.23 

1.90 

100.320 

10.87 

2.90 

163.120 

7.88 

0.92 

48.576 

18  94 

I    92 

101.376 

10.78 

2.92 

154.176 

7.83 

0.94 

49.632 

18  66 

1   94 

102.432 

10.68 

2.94 

156.232 

7.49 

0.96 

50.688 

18.38 

,      1 .  96 

103.488 

10.59 

2.96 

156.288 

7.44 

0.98 

61.744 

18.12 

1.98 

104.544 

10.60 

2.98 

157.344 

7.40 

1.00 

52.800 

17.86 

1     2.00 

105.600 

10.42 

3  00 

158.400 

7.88 

,  Note.— To  find  the  ffross  weight  of  train  h9hind  ike  Undtr:  Multiply  the 
weight  of  the  driving  wheels  by  the  figures  under  "Total  wt.  of  Traai,"  far 
tne  particular  grade,  and  deduct  weight  of  engine  and  tender. 
pageSSa       °**  freight,  multiply  this  result  by  f,  approximately;  bat  sec 


TRACTION  ON  GRADES.    GRADE  REDUCTION,  995 

The  Allowable  Expense  for  Grade  Reduction  will  now  be  considered. 
A  few  hints  only  can  be  given  and  these  based  on  data  of  very  general 
character.   Let  Pig.  2  represent  a  modem  freight  train,  in  which 

Pig.  2. 

D  •  weight  on  engine  drivers  (consolidation  type) ; 
L  —  weight  of  locomotive  and  tender—  1.726  2>; 

T  °>  weight  of  train  (multiplying  values^  in  preceding  Table  by  Dj  ; 
C  -  weight  of  loaded  cars,  which  (see  Table  D  -  (^  -  I.726J  D\ 

F  -  weight  of  net  freight  hauled,  which-  ?  In"""  ^•^2*)  ^'  approx. 

We  will  assume  that  trains  are  made  up  and  hauled  over  a  Division  of 
1 00  miles,  without  regard  to  the  nature  of  the  traffic  on  the  balance  of  the 
road;  that  there  are  1.000,000  tons  of  freight  annually,  hauled  by  138-ton 
engines  with  80  tons  on  drivers;  that  the  cost  per  train  mile  is  $1.00; 
and  that  no  pusher  engines  are  used. 


Pig.  3. 

Ques. — ^What  will  be  the  ruling  grade*  on  the  Division,  provided  a 
saving  of  $200,000  can  be  efTected  in  cost  of  construction  for  each  0.1% 
grade  above  a  level  grade;  the  interest  value  of  money  being  at  the  rate  of 
5  per  cent? 

Ans. — ^We  can  calculate  readily  the  cost  of  hauling  this  freight  by 
ietennining,  for  various  grades,  from  the  preceding  discussion:  .(1)  The 

net  freight  F— f  (^~  1.725 j  D,  hauled  per  train;     (2)    The  number  of 

:  rains  per  year  required  to  haul  the  1,000,000  tons;  (3)  The  total  cost  of 
laul,  at  $1.00  per  train  mile.  Column  (4),  in  the  following  table,  gives  the 
ncreased  cost  of  the  annual  haul  for  any  grade  over  that  for  a  grade  0.1  per 
rent  less.  Column  (6)  shows  the  annual  interest  on  the  $200,000  at  5  per  cent, 
v'hich  equates  nearly  with  $9910  in  column  (4).  opposite  a  2%  grade,  which 
9  therefore  the  required  ruling  grade.  Any  other  rate  of  interest  than  5  per 
ent  would  equate  differently  and  give  a  different  ruling  grade.  Of  cotu^e 
»tlier  considerations  naturally  affect  the  problem  to  a  greater  or  less  extent. 
Reraxaks. — Problems  of  this  character  are,  in  their  nature,  extremely 
oTicrete.  and  therefore  cannot  be  truly  represented  by  merely  abstract  for- 
nulas,  which  serve  only  as  gtiides.  For  instance,  the  probable  increase  in 
Lit ure  traffic  (either  immediate  or  remote)  should  be  taken  into  account, 
f  the  future  traffic  Is  almost  certain  to  be  immediately  and  largely  increased, 
he  grade  reduction  should  be  proportionately  great.  Another  fact  to  be 
ome  in  mind  is,  that  the  cost  of  grade  reduction  after  track  is  laid  is  much 
rcater  than  before,  and  especially  so  when  under  heavy  traffic.  But,  as  a 
^mpensating  effect,  the  road  is  better  able  to  stand  this  extra  expense  at 
^ch  a  time,  both  as  to  available  cash  and  traffic  economy.  The  "Lake 
hore"roaa  has  expanded  hundreds  of  thousands  of  dollars  in  reducing 
rades  hy  a  small  fraction  of  one  per  cent  for  a  distance  of  a  few  miles,  and 
hile  this  work  was  goinff  on  the  writer  counted  on  one  Sxmday,  27  sections 
f  a  "single  freight  train. 

*  Of  coiu^e  the  grade  must  be  assumed  to  be  long  so  the  momentum  of 
le  train  cannot  be  counted  on  as  affecting  the  problem. 


996 


S» —RAILROADS. 


2. — Cost  op  Haul  on  Various  Gradks. 

And  detennination  of  Ruling  Grade. 

(See  preceding  discussion.) 


Total  Cost 

Increased 

No.  Of 

Of  Hauling 

Cost  of 

Interest 

arade 

Net  Freight 

Trains 

1.000.000 

Haul 

on 

per 

per  Train. 

per  Year 

Tons  at  (1 

over  that 

(200.000 

Remarks. 

100. 

Tons. 

Required. 

per 
Train  MUe 

for  grade 
0.1  lower. 

at  5%. 

(1) 

(2) 

(3) 

(4) 

(5) 

Level 

3472.9 

287.9 

$28,790 

0 

0.1 

2758.6 

362.5 

36.260 

17.460 

0.2 

2282.6 

438.1 

43.810 

7.560 

Direct  loss  If  grade  to  reduced  below 
2% :  but  justiflcd.  poaslbly.  If  based  on 
future  increased  traffic,  higher  cost  per 
train  mUe,  or  lower  ooft  for  grade  re- 
duction or  interest. 

0.3 

1942.0 

514.9 

51.490 

7.680 

0.4 

1687.1 

592.7 

69,270 

^.780 

0.5 

1488.9 

671.7 

67.170 

7.900 

0.6 

1330.0 

751.8 

75.190 

8.020 

0.7 

1200.3 

833.1 

83.310 

8.120 

0.8 

1091.7 

916.0 

91.600 

8,290 

0.9 

1000.3 

999.7 

99.970 

8,370 

1.0 

922.0 

1084.6 

108.460 

8,490 

1.1 

854.0 

1171.0 

117.100 

8.640 

1.2 

794.6 

1258.5 

125.850 

8,750 

1.3 

742.0 

1347.7 

134,770 

8.920 

1.4 
1.5 

695.1 
653.4 

1438.6 
1530.4 

143.860 
153.040 

9.090 
9,180 

1.6 

615.7 

1624.1 

162,410 

9.370 

1.7 

•      581.4 

1719.9 

171.990 

9.580 

1.8 

550.6 

1816.3 

181.630 

9.640 

1.9 

522.6 

1913.6 

191.360 

9,780 

2.0 

496.9 

2012.7 

201.270 

9.910 

$10,000 

Ruling  Grade. 

2.1 

472.9 

2114.8 

211.480 

10.210 

2.2 

451.7 

2218.0 

221.800 

10.320 

2.3 

430.6 

2322.5 

232.250 

10.460 

a»5 

2.4 

411.7 

2428.9 

242.890 

10.640 

di 

2.5 

394.0 

2538.1 

263.810 

10.920 

1^^ 

2.8 

377.4 

2649.5 

264.950 

11.140 

2.7 

362.0 

2762.4 

276.240 

11.290 

2.8 

347.7 

2875.9 

287,590 

11.360 

2.9 

334.4 

2991.5 

299,150 

11.560 

^lil 

3.0 

321.4 

3111.1 

811,110 

11.960 

III 

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GRADIENT  AND  CURVATURE  ECONOMICS,  997 

Cmvtttuf9t*  with  imcnastd  Diskxnct,  in  a  line  may  ariae  from  four  primaty 
considentions,  namely,  (1)  to  increast  tkt  revtnut  of  the  road  by  paasmg 
through  towns  not  on  an  air  line  between  terminal  points;  (%)  to  f€duc4  cost 
of  construction,  as  by  avoiding  deep  cuts,  high  ^Is.  long  tunnels,  expensive 
bridge  crotsings,  etc.;  (Z)  to  r«duc9  cost  of  operaiion,  as  by  avoiding  steep 
grades;  and  (4)  to  rmiuct  cost  of  mainttnanc;  as  by  choosing  a  line  with  a 
permanent  roadbed,  cheaply  maintained,  instead  of  a  "structural"  line 
mvolving  much  expense  in  repairs  and  renewals. 

(1).  In  a  new  cotmtry,  thinly  settled  and  without  competing  roads, 
an^  departure  from  an  economically  located  "air"  line,  to  tap  a  lateral 
region.  IS  justifiable  when  the  "richness"  of  that  region  is  about  proportional 
to  the  additional  cost  of  reaching  it,  assuming  that  the  cost  per  mile  of  such 
changed  Une  as  well  as  its  future  growth  of  business  will  be,  say,  proportional 
to  that  of  the  whole  line.  If  there  is  any  question  on  tnis  latter  point  it 
noay  better  be  tapped  by  a  spur.  The  population  of  a  region  is  in  no  wise 
the  only  safe  criterion  on  which  to  base  probable  business.  A  cattle-raising 
country  s^raely  populated  is  very  deceptive  in  this  respect. 

(2).  We  have  just  considered  a  case  (1)  where  incr«Med  curvature 
(and  distance)  on  a  line  would  be  justified  by  an  increase  in  revenue  about 
prop'irtional  to  the  iHcr9ased  costot  the 
fine.  Let  ABC,  Pig.  4.  be  such  a  line 
giviitf[  increased  revenue  over  the  direct 
^tAaC.  We  will  consider  now  whether  k^^'^"'^^'^^^k^r        if 

some  change  in  location  from  AaC  would     ' ft^TT^  a  ■      ^^w         C 

be  justified  by  r^ductd  cost  of  constnution.  Fig.  4. 

of  such  amount  that  the  annual  interest  on  same  would  be  equal  to  the  in- 
creased net  revenue  received  incase  (1)?  In  the  first  case  the  line  ilBC  is  con- 
sidered mon  9xp€nsio9  to  construe  than  the  line  AaC,  while  in  the  present 
case  the  longer  line  is  cheaptr.  As  a  matter  of  fact  there  is  no  relation 
between  the  two  cases,  although  at  first  glance  there  appears  to  be.  In  the 
former  case  we  are  increasing  our  business  say  prooortionately  to  our  in- 
vestment by  running  the  line  through  B.  In  tne  latter  case  we  are  not 
willing  to  mcrease  tne  length  of  our  line  to  pass  through  B,  but  rather 
through  some  point  B*  (where  there  is  no  business)  so  that  tk€  annual  in- 
CT9as9  in  tkg  optraHttg  ex^nsts  on  tht  ling  A  B*C  ovr  that  of  AaC  shall  not 
exceed  the  interest  on  the  decreased  cost  of  construction.  The  actual  cost  of  the 
Une  between  A  and  C  is  another  matter.  This  should  be  fixed  within  certain 
limits,  however,  having  due  regard  to  the  amount  and  quality  of  traffic 
between  O-O^,  the  terminal   centers-of-gravity  of  haul;  and  also  to  the 

?iuality  of  the  improvements  made  on  those  parts  of  the  line  A  O  and  C  (7. 
f  the  bulk  of  traffic  is  "through"  traffic.  O  and  O'  may  be  considered  practi- 
cally to  be  at  the  terminal  pomts  of  the  line. 

(3).  Let  us  now  suppose  that  instead  of  a  deep  cut  or  tunnel  on  the 
line  AaC  (Pig.  4)  as  in  the  preceding  case  (2}.  we  are  confronted  with  a 
long  ridge  i^ch  will  have  to  be  surmounted  with  heavy  grades  if  the  "air" 
line  is  to  be  maintained.  Here  we  may  resort  to  the  expedient  of  selecting 
some  route  9B  AbC,  carxying  with  it  reduced  grades  and  increased  curva- 
ture and  distance.  In  fixing  the  new  route  we  now  apply  the  opposite  rule 
to  that  of  case  ^3):  The  Une  should  pass  through  some  point  b  so  that  the 
innual  decrease  tn  the  operating  expenses  on  the  line  AbC  over  that  of  AaC 
ihould  exceed  the  interest  on  the  increased  cost  of  construction. 

(4).  The  cost  of  maintenance  should  generally  be  considered  as  a  part 
>f  the  "operating"  expenses  in  the  two  preceding  casesL  (2)  and  (3).  But 
he  term  may  have  a  greater  significance  apart  from  sucn  association.  Two 
ines  having  equally  o^ectionable  grades  may  be  constructed,  (a)  following 
he  naturu  contour  ot  the  country,  and  (6)  shortening  the  distance  and 
uttins  out  curvature  by  the  use  of  bridges  and  trestles.  The  difference  in 
est  of  maintenance  and  renewals  in  favor  of  (a)  may  outweigh  all  other 
onaiderations  against  it.  The  increased  curvature  would  have  to  be  con- 
idermble  to  become  a  serious  matter,  as  the  cost  of  maintaining  curved 
rack  is  but  slighthr  more  than  that  tor  maintaining  straight  track.  The 
fe  of  ties  in  curved  track  is  shortened  from  3  to  5%  annually  per  degree  of 
urvatune.  The  excess  cost  per  train  mile  is  inappreciable  for  a  sughtly 
icreased  length  of  line  (not  at  all  proportional  to  the  length),  and  it  is 
\so  but  slightly  a£Fectea  by  the  introduction  of  moderately  flat  curves. 
teep  grades  are  especially  to  be  avoided.  ^  . 

*  CurvaU^re  is  used,  generally,  in  this  discussion,  in  its^broadest  &nse  as 


908  BQ.—RAILROADS, 

Locatloii  of  the  Uim. — ^This  comprises  three  main  operations,  as  follows: 

B.  Reconnoissance,  or  general  field  inspection. 

C.  Preliminary  Survey,  with  instruments. 

D.  Location,  or  final  determination  of  the  line. 

Topographical  maps  of  many  sections  of  the  country  may  be  had  from 
the  Government  and  from  the  several  States.  Those  of  the  geological  sur- 
veys are  especially  valtiable  in  fixing  the  general  route  of  the  line  in  the 
reconnoissance  and  in  the  subsequent  detailed  surveys. 

B.— THE  RECONNOISSANCE. 

This  is  the  Field  Bxamination  necessary  in  fixing  the  "critical"  points 
on  the  line,  prior  to  the  preliminary  survey,  in  order  to  reduce  the  expense 
of  the  latter.  It  picks  out  the  low  mountain  passes,  the  ttmnel  locations, 
and  the  favorable  river-  and  other  crossings.  If  well  conducted  it  may 
dictate  also,  within  close  limits,  the  ruling  grade  and  maximum  curvature. 
The  principal  instruments  used  are  the  aneroid  barometer,  thermometer, 
pedometer  (if  on  foot),  cyclometer  (  if  by  wheel),  odometer  (if  by  wagon). 
These  three  latter  are  used  for  measuring  the  distance  traveled.  A  hand 
level  will  be  found  useful,  also  a  pocket  compass,  if  detailed  information  is 
necessary  in  any  particular  locality.  The  thermometer  is  used  in  coonec- 
tion  with  the  aneroid  barometer.  The  transit  with  stadia  is  often  used 
advantageously  at  this  early  stage.    (See  Stadia  Reduction  Table,  page  984.) 

The  Aneroid  Barometer  is  useful  in  determining  the  altitude  of  any 
point  above  sea  level,  or  the  relative  difference  in  altitude  between  two  or 
more  points.  It  consists  of  a  small, 
circular,  air-tight  box,  in  vacuo,  with 
one  side  sensitive  to  the  pressure  of  the 
atmosphere  outside.  The  heavier  the 
atmospheric  presstire  (the  lower  the 
altitude)  the  more  it  is  pressed  inward, 
and  this  movement  is  multiplied  ana 
transmitted  to  a  recording  index,  like 
the  hand  of  a  clock,  which  denotes  the 
pressure  in  inches  (on  the  inner  circle) 
corresponding  to  the  mercurial  column 
of  an  ordinary  barometer.  It  is  to  be 
noted  that  outside  the  mercurial  scale 
there  is  also  a  direct  reading  scale,  to  ' 
hundreds  of  feet,  giving  the  direct  alti- 
tude approximately.  All  aneroids  now 
sold  by  the  best  makers  are  "compen- 
sated' for  change  or  difference  in  tem- 
perature (see  Fig.  6);  but  this  does  not  „. — 
mean  necessarily  that  they  arc  absolutely  *^*8-  o. 

exact,  but  merely  that  they  are  nearly  so  and  may  be  used  "singly"  with  i 

degree  of  accuracy.  When,  however,  extreme  acciiracy  is  reomred  in  gel- 
ting  the  difference  in  elevation  between  two  stations — one  called  the  upper 
station  and  the  other  the  lower  station— two  compensated  aneroids  are 
used,  one  at  each  station.    Readings  are  taken  at  the  satw  lim#  and — 

The  dL^erence  in  elevation -(tf -A)  (^^  j^  "*"  0 (D 

in  which  //«  reading  in  feet  on  elevation  scale  at  upper  station; 

It  — reading  in  feet  on  elevation  scale  at  lower  station; 
r«  temperature  in  degrees  Fahrenheit  at  upper  station; 

/■"temperature  in  degrees  Fahrenheit  at  lower  station. 
If  the  temperature  at  both  stations  is  60**F.  it  is  seen  that  H  —  h  represents 
the  true  difference  in  elevation,  and  there  is  no  correction  for  temperature. 
Of  course  the  aneroids  will  have  to  be  compared  by  taking  observatioas 
together  at  some  station  and  the  difference  or  index  error  noted  for  subae- 
quent  observations.  The  author  has  seen  it  stated  by  some  of  otir 

prominent  writers  that  the  smaller  aneroids  of  If  to  2*  inches  diameter  give 
as  accurate  results  as  the  larger  ones.  The  author's  observations  are  to  the 
contrary  and  are  confirmed  by  the  following  from  Meanv.  Keuffel  &  Esaer. 
New  York  City:  "All  our  aneroids  are  compensated  and  their  readings  do 
not  require  any  further  corrections  than  the  one  referred  to  [formula  (1) 


RECONNOISSANCE  SURVEY,    BAROMETER.  999 

preceding).  It  is  our  judgment  that  the  small  pocket  aneroids  are  less  accu- 
rate than  the  larger  ones;  not  only  are  the  dials  of  the  larger  instruments  more 
ckMelv  graduated  and  permit  of  finer  reading,  but  the  larger  instruments 
are  also  more  sensitive  on  account  of  the  larser  size  of  their  vacuum  boxes. 
Furthermore,  the  instrumental  error  arising  from  the  elastic  reaction  of  the 
counter  spring  and  rocker  is  greatly  reduced." 

The  Mercurial  Barometer  is  seldom  used  in  railroad  reconnoissance, 
having  been  supplanted  by  the  aneroid,  previously  described.  The 
aneroid  is  much  more  convenient  to  carry;  there  is  no  correction  for  lati- 
tude nor  for  variation  in  gravity  due  to  altitude  above  the  earth.  For 
extremely  acctirate  work,  however,  in  establishing  absolute  elevations  above 
sea  level,  the  mercurial  barometer  is  used.  The  following  Tabler  are  from 
Appendix  10.  Report  U.  S.  Coast  and  Geodetic  Survey  for  1881. 


8. — Baroubtric  Elbvations  for  Tbupbraturb  50^  p. 
(For  use  with  Mercurial  Barometer.) 
Note. — For  temperatures  other  than  50*.  see  Correction  Table,  No.  4. 
(Elevation  in  Feet  above  sea  level.] 


Hekbt 

_ 

" 

of 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

Rem. 

Barom. 

Ins. 

11 

27336 

27090 

26846 

26604 

26364 

26126 

25890 

25656 

25424 

25194 

12 

24966 

24740 

24516 

24294 

24073 

23854 

23637 

23421 

23207 

22995 

13 

22785 

22576 

22368 

22162 

21958 

21757 

21557 

21358 

21160 

20962 

1 

14 

20765 

20570 

20377 

20186 

19997 

19809 

19623 

19437 

19252 

19068 

15 

18886 

18705 

18525 

18346 

18168 

17992 

17817 

17643 

17470 

17298' 

^ 

1« 

17127 

16958 

16789 

16621 

16454 

16288 

16124 

15061 

15798 

15636 

1 

17 

15476 

15316 

15157 

14999 

14842 

14686 

14531 

14377 

14223 

14070 

"S 

18 

13918 

13767 

13617 

13468 

13319 

13172 

13025 

12879 

12733 

12589 

•» 

19 

12445 

12302 

12160 

12018 

11877 

11737 

11598 

fl459 

11321 

11184 

3s 

20 

11047 

10911 

10776 

10642 

105U8 

10375 

10242 

10110 

9979 

9848 

21 

9718 

9589 

9460 

9332 

9204 

9077 

S951 

8825 

8700 

8575 

^l 

22 

8451 

8327 

8204 

8082 

7960 

7838 

7717 

7597 

7477 

7358 

23 

7239 

7121 

7004 

6887 

6770 

6654 

6538 

6423 

6308 

6194 

gQ 

24 

6080 

6967 

5854 

5741 

5629 

5518 

5407 

5296 

5186 

6077 

1 

25 

4968 

4859 

4751 

4643 

4535 

4428 

4321 

4215 

4109 

4004 

26 

3890 

3794 

3690 

3586 

3483 

3380 

3277 

3175 

3073 

2972 

27 

2871 

2770 

2670 

2570 

2470 

2371 

2272 

2173 

2075 

1977 

:§ 

28 

1880 

1783 

1686 

1589 

1493 

1397 

1303 

1207 

1112 

1018 

5 

29 

934 

830 

736 

643 

550 

458 

366 

274 

182 

91 

30 

000 

—91 

—181 

—271 

—361 

-451 

-540 

-629 

-717 

-805 

Ex.  1. — The  mean  temp,  of  two  stations  whose  diff.  of  elev.  is  desired 
£««     60** F.    The  barom.  reading  at  upi^er  station  is  24.62  ins.;   and  at  lower 
^^^ation.  28.165.     Find  the  difference  in  elevation  of  the  two  stations. 
Solution. — Using  proportional  differences — 

Elev.  upper  station  (24.62  ins.)    -    5385  ft. 
Elev.  lower  station  (28.165  ins.)  «    1720  ft. 

Ans.— Diff.  in  elevation.. . .    -   3665  ft. 


d  by  Google 


leoo 


SQ.'-RAILROADS. 


i. — Barombtric  Correction  Tablb  for  Tbmpbraturb. 
(To  be  used  in  connection  with  Table  3,  preceding.) 
Note. — Mult,  value  obtained  from  Table  3,  by  the  Coefficients  in  this 
table. 

[Coefficients.] 


Mean 

Coef. 

Difl. 

Mean 

Ooef. 

DIfl. 

Mean 

C9oef. 

DIIL 

Temp. 

perDeg. 

Temp. 

pcrDeg. 

Temp. 

per  Dog. 

0» 

.8975 

.00219 

30» 

.9620 

.00214 

60» 

I.'«2f2 

.00210 

ICP 

.9194 

.00214 

AQP 

.9834 

.00216 

700 

1.0472 

.00205 

zap 

.9408 

.00212 

B0« 

1.0049 

.00213 

80» 

1.0677 

.00202 

30O 

.9620 

60« 

1.0262 

90« 

1.0879 

Ex.  2. — Now  for  any  other  mean  temp,  of  the  two  stations  than  6©"  P., 
say  05**  P.,  we  find  the  coef.  for  mean  temp,  in  Table  4.  and  mult,  this  into 
the  result  obtained  from  Table  3  for  60**  F.  Thus,  for  65®  F.,  the  coef.  is 
1.0262+. 00210X5-  1.0367.  Solving  Ex.  1,  for  a  mean  temp,  of  66* F.,  we 
have  3665X1.0367"  3800  ft.-difif.  in  elev.  of  the  two  sUtions. 


C.— THE  PRELIMINARY  SURVEY. 

The  Organization  for  the  preliminary  survey,  as  ordinarily  conducted, 
comprises  full  parties  for  transit-,  level-,  and  topographic  work.  This 
survey  consists  m  developing  a  broken  line  on  the  groimd,  that  can  be  used 
later  as  a  base  in  projectmg  the  final  location.  The  preliminarv  Une  diouM 
be  nearly  identical,  practically,  with  the  final  location  so  that  the  latter  will 
be  "fully  covered"  by  the  topography.  In  cases  where  it  is  evident  that 
any  part  of  the  location  will  be  radically  different  from  the  preliminary  line 
as  run,  a  new  preliminary  line  should  be  run  immediately  covering  that 
portion,  and  the  old  line  abandoned"  and  marked  so  in  the  note  books. 
Equated  stationing  should  be  used  instead  of  introducing  the  terms  "kug 
station"  or  "short  station." 

The  Locating  En^eer  will  select,  usually,  some  critical  point  where 
the  line  has  to  come,  m  both  position  and  elevation,  for  a  starting  point  c^ 
the  survey.  Where  a  movmtain  range  has  to  be  crossed  it  is  customary  to 
begin  at  the  summit  and  work  down,  but  this  does  not  always  hoki.  If 
there  is  no  pass  low  enough,  and  a  tunnel  is  imperative,  it  is  often  necessary 
to  make  a  quick  topographical  survey  "along"  the  main  range,  nmning 
transverse  lines  from  the  main  summit  line  at  points  where  it  is  thought  the 
length  of  tunnel  will  be  the  least,  at  the  desired  elevation.  This  will  nc^ 
necessarily  be  at  the  "pass"  and  may  be  a  considerable  distance  from  it. 
(In  connection  with  tunnel  location,  the  geological  formation  should  be 
studied  and  also  the  possibility  of  one  or  more  shafts  to  facilitate  construc- 
tionO 

The  Transit  man  should  be  careftil  to  hold  closely  to  any  grade  line 
which  may  have  been  decided  upon  from  the  reconnoissance  data.  For  this 
purpose  tnc  transit  should  be  provided  with  a  Gradienter  Screw  by  which 
the  telescope  may  be  inclined  to  the  required  grade.  It  consists  of  a  clamp 
and  slow-motion  screw,  so  that  one  complete  revolution  of  the  latter  raises 
or  lowers  the  line  of  sight  of  the  telescope  1  foot  vertically  in  a  horizontal 
distance  of  100  feet.  The  edge  of  the  bead  is  divided  into  100  parts  iat 
minute  readings,  and  the  number  of  complete  turns  of  the  screw  are  indU- 
cated  by  a  graduated  bar.  Stakes  are  set  every  100-ft..  or  station,  and 
hubs  at  every  transit  point.  In  a  true  preliminary  line  no  curves  are  nm. 
but  it  is  sometimes  convenient  to  fit  in  a  curve  around  a  hillside  to  facilitate 
the  work  of  topography  and  later  location.  The  accuracy  with  which  pre- 
liminary lines  are  run  depends  somewhat  upon  the  circumstances  of  the 
case.  The  policy  of  the  Southern  Pacific  R.  K.  Co.  is  to  nm  very  accurate 
preliminary  siu^cys  so  that  the  subsequent  location  can  be  calculated  to  a 
nicety  in  the  office.  Magnetic  bearings  should  be  taken  at  every  poation  of 
the  transit,  as  a  check  on  the  angles. 


Digitized 


by  Google 


PRELIMINARY  SUR\ 


5. — Grades  in  Fbbt  pbr  1 
Part  I.   fFeet  d 


d  by  Google 


1002 


».— RAILROADS, 


7. — Gradb  Angles  Corrbsp'd'o  to  Ratbs  op  Graob  in  Pbbt  pbk  100-Pt. 
Part  I.    [Grade  Angle.]  


Ft.  per 
too  ft. 


3  26 
6  53 
10  19 
13  45 

17  11 


20  38  20  58 


24  04 
27  80 
30  57 
34  23 
37  49 


01  52 


1  12  11 
I  15  37 
1  19  03 


21 
3  47 
7  13 
10  39 
14  00 
17  32 


24  24 

27  51 
31  17 
34  43 
38  09 


41  15  41  35 
44  41 


45  02 

48  08  48  28 
51  34 
55  00 
58  2ft 


51  54 
55  21 
58  47 


1  05  19 1  05  39 1  06  06|l 
1  08  45I1  09  0& 


1  12  32 


I  36  14 .  

1  39  40ll  40  01 


43  06 
46  32 


2  00  16 
2  03  42 


1  56  56(1  57  111  57  321 


41 

4 

7  34 
11  00 
14  26 
17  53 
21  19 
24  45 
38  II 
31  38 
35  04 
38  30 
41  56 
45  23 
48  49 
52  15 
55  41 
59  07 


I  02  131  03  341 


.  09  26 

1  12  52 


1  15  581  16  181 


19  44 


1  19  24.  .,  ,. 

1  22  29 1  22  50|l  23  11 
.  25  56 

1  29  22  

1  32  481  33  081  33  291  83  50|l  34 
1  36  351  36  551 


40  21 
.  43  27  I  43  47 . 
1  46  531  47  131 


^ -..  ,.  55 

1  49  581  50  191  50  391  51  001  51  21 

53  24  1  53  45  1  54  051  54  26  1  54  47 

13 


37  2  00  582 
.  .»  ,.2  04  03  2  04  24  2 
2  07  08|2  07  292  07  502 
2  10  34!2  10  552  11  162 
2  14  00.2  14  21  2  14  4 


.03 


1  02 
4  28 
7  54 
11  21 
14  47 
18  13 
21  39 
25  06 
28  82 
31  58 
35  24 
38  51 
41  17 
45  43 
49  09 
63  36 
66  02 
59  28 
02  54 
06  20 
00  47 
13  13 


10  391  17 
20  051  20 


23  31 
26 
SO  24 


37  16 
40  42 
44  08 

47  34 


.04 


1 
6 
8 
12 
15 

18 
22 

26 
20 
32 
36 
39 
42 
46 
49 
53 
56 
1  00 
1  03  1S|1  03 


06 
1  10 


.05 


1  23 
1  27 
1  30 


1  37 
1  41 
1  44 

1  47 


41 
07 

33|l  13 
oai  17 

26^1  20 
52  1  24 
18*1  27 
441  81 
101  34 
361  37 
1  41 


02 


2  04 

6  30 
8  66 
12  23 
16  49 
10  15 
23  41 
26  08 
29  84 
33  00 
36  26 
39  53 
43  19 
46  45 
60  11 
53  37 
57  04 
09|l  00  30 
351  03  561 
1  07  321 


1  07 

1  10  28|l  10  48|l 


14  151 


29*1  44 


57  521  68 
U  01 


01  18 
04  44 


2  05 


31 

57 

2  15  022  15  23 


1  48 
1  51 
1  56 

1  68 
392  01 
052  05 

2  08 
2  12 
2  15 


20  1  17  41 
461  21  07 
121  24  33 
39|l  27  59 1 
1  31  25|1 
1  34  61 
57 1  38  18 1 
23  1  41  44 1 
49 1  46  10 1 
151  48  36 


I  52  02 
1  56  281 
1  68  641 
I  02  20!2 


2  24 

6  51 
0  17 
12  43 
16  09 

19  36 

23  02 
26  38 

20  64 
33  21 
36  47 
40  13 
43  39 

47  06 
60  32 
63  58 
57  24 
00  511 
04  171 
07  431 
II  0«1 
14  SMI 
18  011 

21  281 

24  641 
2S2ei 
31  4«l 
36  121 
38  381 
42  041 
46  801 

48  561 
63  821 
55  481 
50  161 
02  41 


.08 


2  45 

6  11 
9  38 
13  04 
16  30 
19  56 
23  23 
16  49 
30  15 
33  41 
87  08 
40  84 
44  00 
47  26 
60  62 
64  19 
67  45 
01  II  1 
04  37 
08  041 


.09   P.  P. 


11  30 
14  56 

18  22  1 
21  48  1 
25  14  1 
28  401 
32  07  1 
35  33  1 
38  591 
42  251 
46  51 
49  17 
62  43 
56  091 
69  351 


Ex.  1.— Rate  of  grade -1.937  ft. 
per  100  ft.  Then  grade  angle  — 
1*>00'20'+1S'-1''06'36'. 


03  012 
25|2  05  46i2  06  07^  06  37  2 

09  532 
17|2  12  38j2  12  58J2  13  19  2 
2  16  04!2  16  24  2  16  45  2 


8  06l 
6  32, 

9  5g 
13  24 

le  51 

20  17 
2j  43 

27  09 
90  36, 

34  oa 

87  28 
40  54 
44  21 

47  47 
61  13 

H  n 

68  06 
01  82 
04  58 

08  24 
11  50 

16  16 
18  43 
23  09 
25  85 

28  01 
32  27 
85  53 
39  19 
U  45 

48  12 

49  Z3 
53  04 
66  30 
58  56 
03  22 
06  A¥ 
10  14 
13  40 

17  06 


11 

10 
I  18 


n 


Ex.  2. — By  inverse  operation, 
the  rate  of  grade  may  be  obt^ied 
when  grade  angle  is  given. 


Part  IL     [Grade  Angle.] 


Ft.  per 
100  ft. 


2  17  26 


5 
6 
7 
8 
9 

10 


2  20  522  24  182  27  44  2  31  102  34  362  38  01  2  41  27 


5  42  38 


.4 


2  55  m  58  36  3  03  093  05  27 
52  3  36  18  3  39  43 


2  61  45 

3  26  01  3  29  27 

4  00  154  03  40J4  07  0614  10  3l|4  13  56 

4  34  26  4  37  51 

5  08  34 


4  41   16;4  44  414  48  06 


.5 


5  11  595  15  235  18  48 


5  23  12 


5  46  02  5  49  26  5  52  505  66  16 


3  08  53 

3  43 

4  17  21 

4  51 

5  26 

5  59  39 


.6 


3  12 

3  46  34 

4  20  46 

64 

29 

6  03  03 


304  64  654 


58  2015  01 
32  25^5  25 


22 

3  49  59^3  53  24^3  56 
'        4r  8flh  31 
85 
88 


45  5 


6  06  276  09  516  13  14* 


2  44  53{2  48  19(   3J5 

3  19  10|3  22  36,22  " 


P.P. 


OIU122 

H$  AS 


{»J  05 

Ex.    3. —  By   direct    operation:    I  Ex.   4. — By  inverse  operation* 

Rate   of  grade -4.26  per    100   ft.       Grade  angle  -  2*>  42' S«-.    tSSti 
Then  grade  angle -2»2(P  or.  I   of  grade  per  100  ft. -4. 73*. 

Notbs 
m-m?'^fe°^y  6?/J^.T^*^  ^^  transit  by  the  uae  of  the  gradienter  attach^  I 
mcnt.    Sec  also  Table  No.  8.  following.  «^«cn*j 


GRADE  ANGLES  AND  RATES  OF  GRADES. 


1003 


8.— Oradbs  in  Pbet  pbr  Mils  Rbducbd  to  Pbbt  pbr  100- Ft. 
[Grade  in  Feet  per  100  Ft.] 


Ex.  1.— The  grade  of  a  road  is  96.3  ft.  per  mile- (1.79924 +  .00668)  ft. 
per  100  ft. 

9. — Gradb  Anolbs  Corrbspondino  to  Gradbs  in  Fbbt  pbr  Milb. 
[Grade  Angle.] 


Ft. 


rupa 

MBe. 


7^ 


P.P. 


<  31 
IS  01 
19  32 
M  03 

33  33 
39  04 
45  34 
B2  05 
98  30 


39 
7  10 
18  40 
20  U 
20  42 

83  12 

39  43 
46  13 
62  44 
59  15 


1  18 
7  49 
14  19 
20  50 
27  21 

83  61 
40  22 
40  53 
53  23 
59  54 


1  57 
8  28 
14  tS 
21  29 
28  00 

34  30 
41  01 
47  32 
54  02 
t  00  33 


061 


06 
1  11  37 
1  18  07 
1  24 
1  31 


38! 


,7— . 


t  87 
1  44 

BO 

1  57 

03 


05 
1  12  16 
1  18 

25 

31  47 


461 


551 


391 


88  17 

44 

51 

57 

04 


481 
181 
09^1  57  48 1 
392  04  182 


08  24^ 

1  12 
19  25 
26  56 

1  32 

1  88  56 
45  27 
51  67 
68  2: 
04  67 


07  03 

13  34 

1  20  04 

1  26  35 


2  36 
9  07 
15  38 
22  08 
28  39 

35  09 
41  40 
48  11 
64  41 
01  12 

07  42 
14  13 
20  43 
27  14 
33  44 


3  15 
9  46 
16  17 
22  47 
29  18 

35  49 
42  19 
48  50 
65  20 
01  51 


3  54 
10  25 
16  56 
23  26 
29  57 

36  28 
42  58 
49  29 
55  59 


4  33 
11  04 
17  35 
24  05 
30  36 

37  07 
43  37 
50  08 
56  381 


1  02  30^1  OS  09, 


5  13 
11  43 
18  14 
24  44 
31  15 

37  46 
44  16 
50  47 

57  17 
03  48;i 


08  21 
14  52 
21  22 
27  531 
34  231 


1  09  001  09 


i9|l  03 
!9]l  10 


181 


1  39  351  40  141  40  53 

1  46  06  1  46  45  I  47  24 

1  52  361  53  15|1  53  54 

1  59  06  1  59  45,2  00  24 

2  05  362  06  152  06  54  2  07  33t2  0 


.    3  10  092  10  482  11  27>2  12  06 


,1 


15  311  16  10^1  16  491 

22  01  1  22  40!l  23  I9|l 

28  321  29  nil  29  50,1 

35  0211  35  41  1  36  20  1 


41  321  42  11)1  42  50 

1  48  03h  48  42.1  49  21 

1  51  33.1  55  12|l  55  51 

2  01  03  2  01  42|2  02  21 


12p  08  51 


2  12  452  13  24  2  14  03  2  14  422  16  21 


5  52 
12  22 
18  53 
25  24 
31  54 

38  25 
44  5^1 
61  26 
67  57 
04  27 

10  58 
17  28| 
23  58, 
30  29 
36  59 

1  43  30 
50  00 

1  56  30 

2  03  00 
2  09  30 

2  16  00 


39* 

'I  * 

2  8 

3  12 

4  16 
5I  20 

e!  23 

7  27 

8  31 

9f  35 


4' 


12 
16 
20 
24 
28 
32 
91  36 


Ex.  1. — ^The  grade  of  a  road  is  95.3  ft.  per  mile;   hence,  grade  angle  =- 

10  or  51'  +  ir. 


1004  !».— RAILROADS. 

The  Lcvelman  starts  usually  from  an  established  bench  mark  (B.  Af .). 
frequently  at  an  assumed  elevation,  as  near  as  possible  to  the  correct  eleva- 
tion above  sea  level.  He  follows  closely  behind  the  transitman,  taking 
elevations  on  the  ground  at  every  station  and  also  at  intermediate  points 
where  the  profile  demands.  He  should  keep  the  transit  at  the  correct  eleva- 
tion  at  every  transit  point  and  sometimes  give  levels  ahead  of  the  transit. 
He  establishes  temporary  bench  marks  on  every  transit  hub,  and  permanent 
bench  marks,  say,  every  half  mile.  Thev  shoiud  be  described  accurately  in 
the  note  book  by  exact  stationing  on  the  line  and  bjr  distance  to  right  or 
left  of  same.  Check  levels  should  be  nm  every  10  miles,  more  or  less.  If 
work  is  slack,  the  level  man  can  often  aid  the  topographer  over  certain 
stretches  by  taking  side  levels.  Two  rodmen  can  often  be  used  to  great 
advantage.  The  combined  target-  and  self-reading  rod  is  the  best — the 
former  for  turning  points,  and  the  latter  for  ordinary  ground  elevations. 

The  Topographer  gets  the  ground  elevations  at  stations  on  the  center 
line  from  the  levelman,  either  the  night  before  or  during  the  day,  at  intervals. 
His  duties  are  to  take  such  notes  that  contour  lines  can  be  platted  accu- 
rately on  the  maps.  It  is  perhaps  needless  to  say  that  in  some  cases  topog- 
raphy should  be  taken  extremely  accurate,  smd  especially  so  if  the  loca- 
tion lines  are  determined  primarily  in  the  office.  Perhaps  the  most  common 
method  of  taking  topography  is  with  the  hand  leveljxjr  elevation,  and  by- 
pacing,  for  distance.  Often  the  (cloth)  tape  is  used.  There  are  two  methods 
of  keeping  the  notes:  (1)  To  give  the  relative  elevation  at  right  an^le  to 
the  center  line  at  each  station,  and  the  distance  out*  to  each  break  in  the 

+  4  3 
groimd,  as        '  ;  and  (2)  to  "sketch  in"  the  contour  lines  directly  in  the 

field.  Giving  the  distances  out  from  center  Hne.  The  clinometer  is  very 
useful  in  moderately  sloping  country.  The  transitman  may  often  help  the 
topographer  on  very  steep  hillsides  by  taking  vertical  slope  angles  at  right 
angle  to  the  line. 

The  Mapping  consists  in  platting  the  instrument  line  from  the  transit 
notes,  and  the  topography  or  contour  lines  from  the  topography  notes. 
The  former  may  be  platted  with  a  protractor  or  by  tangent-  or  chord 
deflection,*  from  each  previous  tangent  line;  or  a  base  (say  north  and 
south)  may  be  established  on  the  map  from  which  each  tangent  line  is  laid  off 
by  calculated  angle.  Sometimes  the  lines  are  platted  from  calculated  latitudes 
and  departures  of  the  angle  points  or  points  of  intersection  (P.  I.'s)  of  the 
tangents.  This  latter  methoa  has  the  advantage  of  acctiracy.  The  magnetic 
bearings  are  a  check  on  the  calculated  bearings  of  each  tangent  and  erzoxs 
of  reading  angles  in  the  field,  both  in  amount  and  direction. 

D.— THE  LOCATION  SURVEY 

The  Location  is  the  Objective,  or  the  desired  end  sought;  the  other 
surveys  are  simply  means  to  this  end.  The  reconnoissance  may  sometimea 
be  reduced  to  a  mere  inspection  of  the  country  in  a  most  casual  manner. 
The  preliminary  survey  may  often  consist  in  running  a  few  compass  lines 
to  determine  the  general  route,  or  even  these  may  be  omitted.  But  the 
location  survey  consists  in  the  nnai  establishment  on  the  ground  of  the  Hne 
as  it  is  to  be  built:  running  in  the  tangents  and  joining  them  with  the 
proper  curves.  Of  course  there  are  generally  minor  changes  in  the  Kne 
during  its  construction,  but  these  subsequent  changes  might  bo  considered 
part  of  the  location  proper. 

The  Profile  and  (trades  are  subjects  for  constant  study;  the  latter  even 
after  the  road  is  constructed  and  m  operation.  The  grade  line  ^— base  of 
cut  or  top  of  fill,  and  is  called  sub-grade  during  construction)  is  usually 
adjusted  to  the  profile  by  the  use  of  a  fine  thread  stretched  over  the  latter 
in  various  positions,  studying  at  the  same  time  the  "equalization  of  cuts 
and  fills."  ay  this  phrase  we  do  not  mean  necessarily  that  the  ouantities 
in  the  cuts  should  equal  those  in  the  fills,  although  this  might  hold  true  for 
certain  saw-toothed  profiles  or  profiles  with  short  haul  from  cut  to  fill;  and 
especially  where  the  material  in  the  cuts,  instead  of  borrowed  material, 
would  naturally  be  used  in  the  fills.  If  the  material  in  cuts  is  rock,  ar»d 
borrowed  material  may  be  had  more  cheaply  for  the  fills,  the  grade  line 
would  naturally  be  raised  to  reduce  the  cost  of  cutting.  Generally,  it  may 
be  stated  that  the  grade  line  is  so  adjusted  that  the  quantities  in  cut  are 

*  See  Table  of  Chords,  page  969.  D,g,,ed  by  GoOglc 


d  by  Google 


1006  SQ.— RAILROADS. 

angle  y  is  called  the  deflection  angle  per  station  and  is  always  equal  to 

1  the  central  angle  per  station:  or  i  the  degree  of  curve.  D.  Fxx>zn  this 
It  will  be  seen  that  the  total  deflection  angle  to  any  point  on  the  cxirve,  from 
a  tangent  to  the  curve  at  instrument  point,  is  equal  to  i  the  total  central 


Fig.  7. — Circular  Horizontal  Curve. 

angle  subtended  by  the  two  points.    Thus,  the  deflection  angle  to  point  2 

is  2X§;  to  point  3.  is  3  X  y.  and  to  the  P.  T.,  is  (3+«)  X  y.  in  which  x  is 

any  dtcimal  part  of  a  100-ft.  station.  If.  in  Fig.  7,  the  degree  of  curve 
D^ZQP-W,  and  ji;  —  60  ft.,  we  have  that  the  total  deflection  to  the  end  of 

curve  or  point  of  tangent  P.  7.  -  (3  +  *)  X y  =  S.ex^'^^    -0°-iy;  and  that 

the  total  central  angle— 12*^36'.  Moreover,  the  central  angle  subtended  bv 
the  total  length  of  curve,  from  the  P.  C.  to  the  P.  T.,  is  eaual  to  the  angle 
of  intersection  I  at  the  point  of  intersection  P.  I.  of  the  adjoinixig  tangents 
ii  and  7*2  produced.  The  portion  of  a  tangent  produced  which  lies  between 
the  P.  I.  and  the  P.  C.  or  P.  T.  is  variously  termed  the  "semi-tangent." 
"tangent  distance"  or  "vertex  distance."  The  length  of  a  curve  is  the  dis- 
tance between  the  P.  C.  and  P.  T.,  measured  in  chord  lengths,  and  not  the 
true  length  of  the  arc.  Thus,  in  Fi^.  7,  if  the  last  chord  x  is  A  of  a  100-ft. 
station,  the  total  length  of  curve  is  360  feet.     If  the  degree  of  curve  is 

3^-30' 
3**-30',  the  radius  =-60  + sin  — 5 —  —  1637.28  ft.:   and  if  the  angle  of  inter- 

12^-*  30* 
section   /   is    12*>-36',   the  semi-tangent  -  radius  X  tan  ^ -180.76  ft. 

The  last  is  simply  the  solution  of  a  right-angle  triangle  with  hypothenose 
joining  o  and  P.  /.,  and  with  angle  at  the  base  (at  o)  equal  to  y.  The  "ex- 
ternal" is  the  shortest  distance  from  the  P.  /.  to  the  curve,  and  is  measured 
along  the  hypothenuse  just  mentioned.  Cleanly,  it  is  the  length  of  the 
hypothentise  minus  the  radius,  and  in  the  present  instance  is  equal  to 

12"—  36' 
radius  X  exsec*  — s °  ^-^^  ^*'  ^  fitting  a  curve  in  between  two  adjoin- 
ing tangents  of  a  preliminary  sxirvey,  the  external  distance  is  often  of 
primary  importance  in  arbitrarily  fixing  the  position  (and  degree)  of  the 
curve.  When  the  degree  of  the  curve  is  determined  the  semi-tangenta  are 
calculated  and  laid  off  from  the  P.  /.,  and  the  curve  nm  in  as  explained 
above. 

*  Exaecant— secant— 1. 


d  by  Google 


CIRCULAR  CURVES. 


1007 


10. — ^Raoii  or  English  Cukvbi,  in  Pbbt.*    (Chords  100  Feet.) 

Note. — See  Foot-note  for  using  this  table  for  Metric  curves. 
[Radii  in  Feet.] 


Ifla- 
utes. 

Decree  of  Carre. 

0" 

■• 

3» 

3» 

4« 

5» 

•• 

r 

V 

lanmte 

5729.65 

2864.93 

1910.08 

1432.69 

1146.28 

955.366 

819.020 

1 

343775. 

6635.72 

2841.26 

1899.53 

1426.74 

1142.47 

953.723 

817.077 

t 

171887. 

5544.83 

2817.97 

1889.09 

1420.85 

1138.69 

950.093 

815.144 

3 

114592. 

6456.81 

2795.06 

1878.77 

1415.01 

1134.94 

947.478 

813.238 

4 

85943.7 

5371.56 

2772.53 

1868.56 

1409.21 

1131.21 

944.877 

811.303 

5 

68754.9 

5288.92 

2750.35 

1858.47 

1403.46 

1127.50 

942.291 

809.39? 

6 

57295.8 

5208.79 

2728.52 

1848.48 

1397.76 

1123.82 

939.719 

807.490 

7 

49110.7 

5131.05 

2707.04 

1838.59 

1392.10 

1120.16 

937.161 

805.611 

8 

42971.8 

5055.59 

2685.89 

1838.82 

1386.49 

1116.52 

934.616 

803.731 

9 

38197.2 

4982.33 

2665.06 

1819.14 

1380.92 

1112.91 

932.066 

801.860 

10 

34377.5 

4911.15 

2644.58 

1809.57 

1375.40 

1109.33 

929.569 

799.997 

U 

31252.3 

4841.98 

2624.39 

1800.10 

1369.92 

1105.76 

927.066 

798.144 

U 

28047.8 

4774.74 

2604.51 

1790.73 

1364.49 

1102.22 

934. C76 

796.299 

13 

20444.2 

4709.33 

2584.93 

1781.45 

1359.10 

1098.70 

922.100 

794.462 

14 

24555.4 

4645.69 

2565.65 

1772.27 

1353.75 

1095.20 

919.637 

792.634 

IS 

22918.3 

4583.75 

2546.64 

1763.18 

1348.45 

1091.73 

917.187 

790.814 

16 

21485.9 

4533.44 

25r.92 

1754.19 

1343.15 

1088.28 

914.750 

789.003 

17 

20222.1 

4464.70 

2509.47 

1745.26 

1337.65 

1084.85 

912.326 

787.210 

\% 

19098.6 

4407.46 

2491.29 

1736.48 

1332.77 

1081.44 

909.915 

785.405 

19 

19093.4 

4351.67 

2473.37 

17r.75 

1327.63 

1078.05 

907.517 

783.618 

20 

17188.8 

4297.28 

2455.70 

1719.12 

1322.53 

1074.68 

905.131 

781.840 

21 

16370.3 

4244.23 

2438.29 

1710.56 

1317.46 

1071.34 

902.758 

780.069 

22 

15626.1 

4192.47 

2421.12 

1702.10 

1312.43 

1068.01 

900.397 

778.307 

23 

14946.7 

4141.96 

2404.19 

1693.72 

1307.45 

1064.71 

898.048 

776.553 

24 

14323.6 

4092.66 

2387.50 

1685.42 

1302.50 

1061.43 

895.712 

774.806 

25 

13751.0 

4044.51 

2371.04 

1677.20 

1297.58 

1058.16 

893.388 

773.067 

2« 

13222. 1 

3997.49 

2354.80 

1669.06 

1292.71 

1054.92 

891.076 

771.336 

27 

12732.4 

3951.54 

2338.78 

1661.00 

1287.87 

1051.70 

888.776 

769.613 

28 

12277.7 

3906.64 

2322.98 

1653.01 

1283.07 

1048.48 

886.488 

767.897 

29 

11854.3 

3862.74 

2307.39 

1645.11 

1278.30 

1045.31 

884.211 

766.190 

30 

11459.2 

3819.83 

2292.01 

1637.28 

1273.57 

1042.14 

881.946 

764.489 

31 

11089.6 

3777.85 

2276.84 

1629.52 

1268.87 

1039.00 

879.693 

762.797 

32 

10743.0 

3736.79 

2261.86 

1621.84 

1264.21 

1035.87 

877.451 

761.118 

33 

10417.5 

3696.61 

2247.08 

1614.22 

1259.58 

1032.76 

875.221 

759.434 

34 

10111.1 

3657.29 

2232.49 

1606.68 

1254.98 

1029.67 

873.002 

757.764 

35 

9822.18 

3618.80 

2218.09 

1599.21 

1250.42 

1026.60 

870.795 

756. 101 

2^ 

9549.34 

3581.10 

2203.87 

1591.81 

1245.89 

1023.55 

868.598 

754.445 

37 

9291.29 

3544.19 

2189.84 

1584.48 

1241.40 

1020.51 

866.412 

752.796 

38 

9046.75 

3508.02 

2175.98 

1577.21 

1236.94 

1017.49 

864.238 

751.156 

39 

8814.78 

3472.59 

2162.30 

1570.01 

1232.51 

1014.50 

862.075 

749.521 

•«0 

8594.42 

8437.87 

2148.79 

1562.88 

1228.11 

1011.51 

859.922 

747.894 

41 

8384.80 

3403.83 

2135.44 

1555.81 

1223.74 

1008.55 

857.780 

746.274 

43 

8186. 16 

8370.46 

2122.26 

1548.80 

1219.40 

1005.60 

855.648 

744.661 

4-3 

7994.81 

3337.74 

2109.24 

1541.86 

1215.30 

1002.67 

853.527 

743.056 

44 

7813.11 

3305.65 

2096.39 

1534.98 

1210.82 

999.762 

851.417 

741.456 

40 

7639.49 

3274.17 

2083.68 

1528.16 

1206.57 

996.867 

849.317 

739.864 

4« 

7473.42 

8243.29 

2071.13 

1521.40 

1202.36 

993.988 

847.228 

738.279 

4r 

7314.41 

3212.98 

2058.73 

1514.70 

1198.17 

991.126 

845. 148 

736.701 

40 

7162.03 

8183.23 

2046.48 

1508.06 

1194.01 

988.280 

843.080 

735.129 

49 

7015.87 

3154.03 

2034.37 

1501.48 

1189.88 

985.451 

841.021 

733.564 

So 

6875.55 

3125.36 

2022.41 

1494.95 

1185.78 

982.638 

838.972 

732.005 

5f 

6740.74 

3097.20 

2010.59 

1488.48 

1181.71 

979.840 

836.933 

730.454 

^ 

6611.12 

3069.55 

1998.90 

1482.07 

1177.66 

977.060 

834.904 

728.909 

S3 

6486.38 

3042.39 

1987.35 

1475.71 

1173.65 

974.294 

832.885 

727.370 

C4 

6366.26 

3015.71 

1975.93 

1469.41 

1169.66 

971.544 

830.876 

725.838 

'>f$ 

6250.51 

2989.48 

1964.64 

1463.16 

1165.70 

968.810 

828.876 

724.312 

^ 

6138.90 

2963.71 

1953.48 

1456.96 

1161.76 

966.091 

826.886 

722.793 

^T 

6031.20 

2938.39 

1942.44 

1450.81 

1157.85 

963.387 

824.905 

721.280 

^^ 

5927.22 

2913.49 

1931.53 

1444.72 

1153.97 

960.698 

822.934 

719.774 

»9 

5826.76 

2889.01 

1920.75 

1438.68 

1150.11 

958.025 

820.973 

718.273 

,o 

5729.65 

2864.93 

1910.08 

1432.69 

1146.28 

955  366 

819.020 

716.779 

^  Table  10,  abovQ,  may  be  used  for  Metric  curves:    Radii  of  curves  in 
-.fc^rxs  — values  in  above  table  mult,  by  t^o  chord  in  meters.     Ex. — For 

1637  28 
^^yj-Ki  — 20  meters,  and  degree  of  curve—  3*  SV:    Radius  —  — -.-  -  meters. 


1008 


m.—RAILROADS, 


10. — Radii  of  English  Curves,  in  Pbbt. — Concluded. 
(Chords  100  Ft.) 
Note.— See  Foot-note  preceding  page,  for  use  of  this  table  for  Metric  curves. 
[Radii  in  Feet.] 


a 

Degree  of  Curve. 

Degree  <a 

8o 

y 

IV> 

12" 

W* 

16** 

I8« 

Curve. 

0' 

716  779 

637.276 

0* 

673.686 

478.339 

410.275 

369.265 

319.623 

iTViy 

287. SIS 

1 

715.291 

636.099 

2 

671.784 

477.018 

409.306 

358.623 

319.037 

10 

28S.SS3 

2 

713.810 

634.928  1  4 

569.896 

475.705 

408.341 

357.784 

318.453 

20 

283.267 

3 

712.336 

633.761 

6 

568.020 

474.400 

407.380 

367.048 

317.871 

30 

280.968 

4 

710.865 

632.599 

8 

566.156 

473. 102 

406.424 

366.316 

317.298 

40 

878.  T46 

5 

709.402 

631.440 

10 

564.305 

471.810 

406.473 

355.586 

316.715 

50 

276.541 

6 

707.945 

630.286 

12 

562.466 

470.626 

404.626 

354.859 

316.139 

2P0' 

874.  S7I 

7 

706.493 

629.136 

14 

560.638 

469.249 

403.683 

354.136 

315.566 

10 

273.2M 

8 

705.048 

627.991 

16 

658.823 

467.978 

402.646 

353.414 

314.993 

20 

270.  ISS 

9 

703.609 

626.849 

18 

557.019 

466.716 

401.712 

362.696 

3U.426 

30 

268. 0C3 

10 

702.175 

626.712 

20 

555.227 

466.459 

400.782 

351.981 

313.860 

40 

266. 0B4 

U 

700.748 

624.579 

22 

663.447 

464.209 

399.857 

351.269 

313.295 

60 

864.018 

12 

699.326 

623.450 

24 

651.678 

462.966 

398.937 

350.660 

312.732 

jyv 

263.042 

13 

697.910 

622.326 

26 

649.920 

461.729 

398.020 

349.864 

312.172 

10 

260.  MB 

14 

696.499 

621.203 

28 

648. 174 

460.600 

397.108 

349.150 

311.613 

20 

2».18i 

15 

695.095 

620.087 

30 

646.438 

459.276 

396.200 

348.460 

311.056 

SO 

256.2S 

16 

693.696 

618.974 

32 

544.714 

458.060 

395.296 

347.752 

310.802 

40 

254.431 

17 

692.302 

617.865 

34 

643.001 

456.850 

394.396 

347.057 

309.949 

60 

852.599 

18 

690.914 

616.760 

36 

541.298 

455.646 

393.601 

346.366 

309.399 

23f»V 

250.793 

19 

689.532 

616.660 

38 

539.606 

454.449 

392.609 

346.676 

308.850 

10 

849.013 

20 

688.156 

614.563 

40 

637.924 

453.259 

391.723 

344.990 

306.303 

20 

247.258 

21 

686.785 

613.470 

42 

636.253 

452.073 

390.838 

344.306 

307.759 

90 

845.529 

22 

685.419 

612.380 

44 

534.693 

450.894 

389.959 

343.625 

307.216 

40 

243.825 

23 

684.039 

611.295 

46 

532.943 

449.722 

389.084 

342.947 

306.676 

50 

242.144 

24 

682.704 

610.214 

48 

631.303 

448.556 

388.212 

342.274 

306.136 

340  y 

240.48? 

25 

681.354 

609.136 

50 

529.673 

447.395 

387.845 

341.598 

305.699 

10 

238.853 

26 

680.010 

608.062 

52 

528.053 

446.241 

386.481 

340.928 

305.064 

20 

237  ..841 

27 

678.671 

606.992 

54 

526.443 

445.093 

385.621 

340.260 

804.531 

30 

235.652 

28 

677.338 

605.926 

56 

524.843 

443.951 

384.765 

339.695 

304.000 

40 

234.064 

29 

676.008 

604.864 

58 

623.252 

442.814 

383.913 

338.933 

303.470 

50 

832,537 

30 

674.686 

603.805 

ll» 

13*» 

15° 

ir» 

«>• 

35-0' 

231.011 

31 

673.369 

602.750 

0' 

521.671 

441.684 

383.065 

338.273 

302.943 

10 

229.506 

32 

672.056 

601.698 

2 

520.100 

440.659 

382.220 

337.616 

302.417 

20 

286.080 

33 

670.748 

600.651 

4 

518.539 

439.440 

381.380 

336.962 

301.893 

30 

226.555 

34 

669.446 

599.607 

6 

516.988 

438.326 

380.543 

336.310 

301.371 

40 

825.106 

35 

668.148 

598.567 

8 

515.443 

437.219 

379.709 

335.660 

300.861 

80 

223.680 

36 

666.856 

597.530 

10 

613.909 

436.117 

378.880 

335.013 

300.333 

10 

232.271 

37 

665.568 

596.497 

12 

512.386 

435.020 

378.054 

334.369 

299.816 

S0.879 

38 

664.286 

695.467 

14 

510.869 

433.929 

377.231 

333.727 

299.302 

80 

219. 5M 

39 

663.008 

594.441 

16 

609.363 

432.844 

376.412 

333.088 

298.789 

SO 

218.166 

40 

661.736 

593.419 

18 

607.866- 

431.764 

376.697 

332.451 

298.278 

40 

216.611 

41 

660.468 

592.400 

20 

506.376 

430.690 

374.786 

3^.816 

297.768 

50 

215.469 

42 

659.205 

591.384 

22 

504.896 

429.620 

373.977 

331.184 

297.260 

37*0* 

214.163 

43 

657.947 

590.372 

24 

503.426 

428.557 

373.173 

330.655 

296.755 

10 

212.893 

44 

656.694 

589.364 

26 

601.962 

427.498 

372.872 

329.928 

296.250 

20 

211.620 

45 

655.446 

588.359 

28 

500.507 

426.445 

371.574 

329.303 

295.748 

30 

210.862 

46 

654.202 

587.357 

30 

499.061 

425. 396 

370.780 

328.689 

295.247 

40 

269.119 

47 

653.963 

586.359 

32 

497.624 

424.354 

369.989 

328.061 

294.748 

50 

267.661 

48 

651.729 

585.364 

34 

496.195 

423.316 

369.202 

327.443 

294.251 

as'O' 

206.^8 

49 

650.499 

584.373 

36 

494.774 

422.283 

368.418 

326.828 

293.766 

10 

805.480 

50 

649.274 

683.385 

38 

493.361 

421.256 

367.637 

326.215 

893.262 

20 

264.896 

51 

648.064 

583.400 

40 

491.966 

420.233 

366.859 

325.604 

292.770 

80 

263.125 

52 

646.838 

581.419 

42 

490.559 

419.215 

366.085 

324.996 

292.279 

40 

261.669 

53 

645.627 

580.441 

44 

489.171 

418.203 

365.315 

324.390 

291.790 

50 

260.616 

54 

644.420 

579.466 

46 

487.790 

417.195 

364.547 

323.786 

291.303 

29^(f 

196.696 

55 

643.218 

678.494 

48 

486.417 

416.192 

363.783 

323.184 

290.818 

10 

196.666 

56 

642.021 

577.526 

50 

485.051 

415.194 

363.022 

322.685 

290.334 

80 

167.476 

87 

640.828 

576.561 

52 

483.694 

414.201 

362.264 

321.989 

889.851 

30 

166.365 

58 

639.639 

676.699 

54 

482.344 

413.212 

361.610 

321. 3M 

889.371 

40 

165.666 

59 
60 

638.466 

574.641 

56 

481.001 

412.229 

360.758 

330.801 

288.898 

50 

194.246 

637.276 

573.686 

58 

479.666 

411.250 

360.010 

320.211 

288.414 

J0»0' 

193.185 

« 

' 

60 

478.339 

410.275 

369.265 

319.633 

887.989 

CIRCULAR  CURVE  TABLES. 


1009 


11.— *SBlfI-TANOBNTS  AND  EXTBKNALS  TO  A  1*^  ENGLISH  CURTB,  IN  PSBT.t 

(Chords  100  Peet.) 
Note. — See  Foot-note  for  using  this  table  for  Metric  curves. 


J 


1 
i 

3 

4 
5 
« 

7 
S 
t 

10 

!1 

12 

13 

14 

16 

1< 

17 

18 

19 

20 
21 
22 


Ex- 
ternal. 


.22 

.87 

1.96 

3.49 

6.46 

7.86 

10.71 

13.99 


Dis- 
t&ace. 


0.00 
50. 

100.01 
130.04 
200.08 
250.16 
300.28 
350.44 
400.66 
17.721460.93 
21.89  501.28 
26.50  661.70 
31.66  603.21 
37.07  662.81 
43.03  703.61 


23 
24 
2S 
2ft 

27 

28 

29 

30 

31 

22 

33 

34 

35 

36 

37 

38 

39 

10 

II 

(2 

J3 

(4 

\5 

6 

7 

8 

9 

0 


49.44 
66.31 
63.63 
71.42 
79.67 
88.39 
97.68 
107.24 
117.38 
128.00 
139. 1 
150.71 
162.81 
175.41 
188  61 
202.12 
216.26 


428.50 
449.98 
472.08 
494.82 
5I8.2C 
542.23 
566.94 
592 


764.32 
805.26 
856.30 
907.49 
968.81 
1010.3 
1061.9 
1113.7 
1166.7 
1217.9 
1270.2 
1322.8 
1376.6 
1428.6 
1481.8 
1636.3 
1689.0 


230.90  1643.0 

246.08  1697.2 

261.80  1761.7 

278.05  1806.6 

294.86  1861.7 

313.22  1917.1 

330.16  1972.9 

348.64  2029.0 

367.73  2085.4 
387.38 
407.64 


2142.2 
2199.4 
2257.0 
2314.9 
2373.3 
2432.1 
2491.3 
2661.0 
3611.2 
2671.8 


8.333 
8.335 
8.338 
8.340 
8.347 
8.363 
8.360 
8.370 
8.378 
8.392 
8.403 
8.418 
8.433 
8.450 
8.468 
8.488 
8.508 
8.632 
8.663 
8.582 
8.600 
8.633 
8.667 
8.700 
8.717 
8.767 
8.800 
8.833 
8.867 
8.917 
8.960 
9.000 
9.033 
9.083 
9.150 
9.183 
9.233 
9.300 
9.350 
9.400 
9.467 
9.533 
9.600 
9.650 
9.733 
9.800 
9.867 
9.950 
10.033 
10.100 


031  H  95 


ternal. 
B 


692.32 
618.39 
646.17 
673.66 
700.89 
729.85 
769.58 
790.06 
821.37 
863.46 
886.38 
920.14 
964.76 
990.24 
1026.6 
1063.9 
1102.2 
1141.4 
1181.6 
1222.7 
1265.0 
1308.2 
1352.6 
1398.0 
1444.6 
1492.4 
1641.4 
1591.0 
1643.0 
1695.8 
1749.9 
1806.3 
1862.2 
1920.6 
1980.4 
2041.7 
2104.7 
2169.2 
2235.5 
2303.5 
2373.3 
2444.9 
2518.5 
2594.0 
2671.6 
2751.3 
2833.2 
2917.3 
3003.8 
3092.7 
3184.1 


Semi-Tangent. 


Dl8- 

tanoe. 


8-T 


2671.8 
2732.9 
2794.5 
2856.7 
2919.4 
2982.7 
3046.5 
3110.9 
3176.0 
3241.7 
3308.0 
3376.0 
3442.7 
3511.1 
3580.3 
3650.2 
3720.9 
3792.4 
3864.7 
3937.9 
4011.9 
4086.9 
4162.8 
4239.7 
4317.6 
4396.5 
4476.5 
4557.6 
4639.8 
4723.2 
4807.7 
4893.6 
4980.7 
6069.2 
6159.0 
6250.3 
6343.0 
5437.2 
6533.1 
6630.6 
5729.7 
6830.6 
5933.2 
6037.8 
6144.3 
6252.8 
6363.4 
6476.2 
6591 . 2 
6708.6 
6828.3 


Dlfl. 

for 

O-IO* 

£ 
6 


m 

Add 


10.183 

10.267 

10.367 

10.450 

10.660 

10.633 

10.733 

10.850 

10.950 

11.050 

11.167 

11.283 

11. 

11.533 

11.650 

11.783 

11.917 

12.060 

12.200 

12.333 

12.500 

12.650 

12.817 

12.983 

13.150 

13.333 

13.617 

13.700 

13.900 

14.083 

14.317 

14.617 

14.750 

14.967 

16.217 

15.450 

15.700 

16.983 

16.233 

16.633 

16.800 

17.117 

17. 

17 

18 

18 

18 

19 

19 

19 


?.433 
r.750 
).083 
).433 
J.800 
).I67 
).567 
).950 


.034 
.035 
.036 
.036 
.037 
.038 
.039 
.040 
.040 
.041 
.042 
.043 
.044 
.044 
.046 
.046 
.047 
.048 
.049 
.060 
.051 
.052 
.053 
.054 
.055 
.056 
.057 
.058 
.059 
.060 
.061 
.062 
.063 
.064 
.065 
.066 
.067 
.068 
.070 
.071 
.072 
.073 
.076 
.076 
.078 
.079 
.080 
.082 
.083 
.085 
.086 


Examines  of  Use 
of  TalMe. 


Nou. — Where  «x- 
ftfrnol*  are  required 
accurately,  add  the 
following  correc- 
tion to  result  ob- 
tained from  table: 
(a)For/-0«>to50«, 
Cor.- +  . 000003  PD. 
(b)For/-IOO«, 
Cor.-  +. 00004  PD. 
In  which  /  —  Inter- 
section angle,  and 
D—degree  of  curve, 
both  In  degrees. 

t2fa*"+  IS?i+  I 


These  results,  to 
hundredths,  are 
closer  than  wfll  or- 
dinarfljr  be  meas- 
ured In  the  field. 
Note  that  the  cor- 
rections are  very 
small  and  can  gen- 
erally be  disre- 
garded when  /  and 
/>  are  small. 


♦  Semi-tansents  and  externals  are  (almost  exactly)  inversely  proi>or- 
>nal  to  the  degree  of  curve  D,  for  the  same  intersection  angle  /. 

t  Table  11,  above,  may  be  used  for  Metric  curves:  Semi-tanjgents  and 
temais  in  meters  —  values  in  above  table  mult,  by  ^  chord  in  meters. 
c. — For  chord  —  20  meters,  and  intersection  angle  =  12**;  thejj  semi-tang" 

^^  mctem,  and  external  =  —^  meters,  for  a  1*>  curve.  ^OOglc 


1010 


m.'^RAILROADS, 


13. — Mnnms  and  Sbconds  Rbducbd  to  Decimals  or  a 
Dbgrbb  or  Hour.* 
(Either  Angular  Measure  or  Time  Measure.) 
Note.     See  Foot-note  regarding  use  of  this  table. 
[Decimals  of  a  Degree  or  Hour.] 


P.P. 

H  i;*:SS 

11 « 

^*  «|.e8iii 


Seooods. 


i(r 


ly 


3(r 


35*      w     iy     w    sy 


2 

3 
4 
6 
6 
7 
8 
9 
10 
U 
12 
13 
14 
15 
16 
17 
18 
19 
20 
21 
22 
23 
24 
25 
26 
27 
28 
29 
80 
31 
32 
83 
34 
35 
86 
87 
38 
89 
40 
41 
42 
43 
44 
46 
46 
47 
48 
49 
60 
61 
68 
63 
64 
56 
66 
67 
68 
69 


00000 
01667 
.03333 
05000 
06607 
08333 
10000 
.11667 
J3833 
15000 
16667 


21667 
23333 
25000 
26667 
28333 
300M 
31667 
.33333 


.35000 
36667 
.38333 
40000 
41667 
.43333 
.45000 
.46667 
48333 
50000 
51667 
.53333 
55000 
56667 
.58333 
.60000 
.61667 
63333 
65000 
66667 
68333 
70000 
71667 
.73333 
75000 
76667 
78333 
80000 
81667 
83333 
85000 
86667 


91667 
93333 


95000 

96667 


.00139 

01806 

03472 

05139 

06806 

.08472 

.10139 

.11806 

.18472 

.16139 

.16808 

.18472 

.20139 

.21806 

.21472 

.25139 

.26806 

.28472 

.30139 

31806 

.33472 

.35139 

.36806 

.38472 

,40139 

41606 

.43472 

45139 

46806 

48472 

60139 

.51806 

.53^72 

.55139 

56806 

.68472 

.60139 

.61806 

63472 

.65139 

66806 

68472 

.70139 

71806 

.73472 

75139 

76806 

78472 

80139 

81806 

83472 

.85139 

86806 

.88472 

90139 

.91806 

93472 

95139 

96806 

98472 


.00278 

01944 

08611 

05278 

06944 

,08611 

.10278 

11944 

.13611 

.15278 

,10944 

,18611 

20278 

.21944 

.23611 

.25278 

.26944 

.28611 

.30278 

.31944 

.33611 

J5278 

.36944 

.38611 

.40278 

.41944 

.43611 

.45278 

.46944 

.48611 

.50278 

.51944 

,53611 

55278 

.56944 

.58611 

,60278 

.61944 

63611 

.65278 

.66944 

.68611 

.70278 

.71944 

73611 

.75278 

76944 

78611 

80278 

81944 

.83611 

.85278 

86944 

88611 

90278 

.91944 

93611 

.95278 

96944 

98611 


00417 
02063 
03750 
05417 
07083 
08760 
10417 
12083 
13750 
16417 
17083 
18750 
.20417 
22083 
.23750 
.25417 
.27083 
,28750 
.30417 
.32083 
•33760 
.35417 
37083 
.88750 
.40417 
.42083 
.43750 
.45417 
.47083 
.48750 
.50417 
.52083 
.53750 
.55417 
.57083 
.58750 
,60417 
.62083 
63750  I 
.65417 
.67083 
68750 
70417 
72083 
.73750 
.75417 
77083 
.78750 
.80417 
82063 
83750 
85417 
.87083 
.88750 
.90417 
.92083 
.93750 
.95417 
.97083 
.98760 


00656 
02222 


05556 
07223 


10566 
,12222 
,13889 
,15556 
.17222 
18889 
.20556 
22222 
.23889 
,25556 
.27222 
28889 
30556 
32222 
33889 
.35556 
.37222 


.40556 
42222 
43889 
,45556 

47222 


62222 
53889 
55556 

67222 
58889 
60556 
62222 


65556 

67222 
68889 
70556 
72222 
73889 
75556 
77222 
,78889 
,80556 
,82222 
,83889 
.85556 
.87222 
.88889 
.90556 
.92222 
.93889 
.95556 
.97222 
9S889 


00694 
02361 
04028 
06694 
07361 
09028 
10694 
12361 
,14028 
15694 
17361 
,19028 
20694 
22361 
24028 
.35694 
,27361 
,29028 
.30694 
,82361 
.34028 
.35694 
.37861 
.89028 
,40694 
42361 
.44028 
45694 
47361 
49028 
60694 
52361 
54028 
55694 
.57361 
59028 
60694 
.62361 
64028 
65694 
.67361 
69028 
70694 
72361 
.74028 
.75694 
77361 
79028 
70694 
.82361 
84028 
85694 
87361 
.89028 
90694 
.92361 
.94028 
.95694 
.97361 
.99028 


008S3 
02500 
04167 
05833 
07500 
09167 
10833 
12500 
14167 
15833 
17500 
19167 
20833 
23600 
24167 
2688S 

r500 

29167 
30833 
82500 

34167 
S583S 

87500 
39167 
40833 
42500 

44167 
45833 
47500 
49167 
,50833 
52500 
54167 
,55833 
.57100 
69167 
60833 
62500 
64167 
.65833 
67500 
.69167 
70833 
72500 
74167 
.76833 
.77500 
.79167 
80833 
82500 
84167 


00971 
02639 


05972 
07639 


87500 
89167 
90833 
.92500 
.94167 
95833 
97500 
99167 


10972 

12639 

14306 

11972 

17639 

19306 

20972 

22639 

24300 

25972 

27639 

29306 

30972 

33639 

S4306 

,35972 

37639 

39306 

,40973 

,42639 

.44306 

,45972 

,47639 

.49306 

.50973 

.52639 

.64306 

.55973 

.67683 

.69806 

.60973 

.62639 

.64306 

.65973 

67639 

69306 

70978 

72639 

74306 

.75973 

77639 

.79306 

80973 

82639 

84306 

.85972 

87639 

89306 

90973 

92639 

94306 

.95973 

97639 

99306 


01111 
03778 
04444 
06111 
07n8 
09444 
lllll 
12778 
14444 
16111 
17778 
19444 
21111 
22778 
34444 


01250 
02917 
04583 
06250 

.07917 
09583 
11250 
12917 

.14583 


01389.01628 


03058 
04723 
06389 
06056 
09722 
11389 


021M 
04861 
06S23 
06m 
01661 
11538 


14722 
.16250L 16388 


13056. 131M 
n.  14861 


26111 

27778. 

29444 

81111 

82778. 

86111 
87778 


41211 
4»78. 


46111 
47778 


.17917 
19583 

31250 
.22917 
34583 
36360 
37917 
39583 
31256 
83917 
34583 
36250 
87917 
,39583 


18056. 
19722. 
21389. 
23066 
34733 


16528 
18194 
19e<l 
21538 
23194 
34861 
26I38 
.28194 


397n 

813M(.S181B 

83196 

.S473^.34»l 

36389.36538 

38056^.38194 
39861 
41838 
43196 
44881 
46338 

48m 


89722 
41389 


43096 


81111 
,63778 


43917. 
44583. 
4625C. 
47917 . 

.48733 
5129C  .61389 
52917 


66111 

^n8 


83056 

6458^.84723 
56256. 8638S.S6S28 

.87917.68851.88191 


61528 
53194 
64861 


89444|.  89581^.59732 

.612! 
,62778^.63917^ 
.64444. 6461 


66111 
.87778 
,69444 

71111 
.72778 


.74444 .74583 


.76111 
77778 

.79444 
81111 


.82778.82917 


66350 

67917 
69583 

7125« 
.7291 


.81389 
88066 
84732 


86111 
87778 
89444 
91111 


94444 
96111 
97778 
99444I 


7626C 
77917 
79583 
81250 


862SC 
.87917 
89583 

.9125C 


82778.92917 


.94583 

96250 
97917 


89722 
71389 
73061 


.74723 
76389 


81938 
83194 


88194 

71938 
.73194 
.74861 

76838 
.78194 

79861 

81138 


7805C.; 
79783.; 
81381  .1 
83061.83194 


89723 


8BI9I 


81380.81888 
93098  .88194 
94722.84861 
96389  .8038 
8806<.8et»4 


*^x.  In  Angular  measure: 


20*-  35'  17-  -  20»  35'  15*  +  3»  -  3848808  tfsf . 


MINUTES  TO  DEGREES.    CURVE  PROBLEMS. 


1011 


The  Various  Problems  in  Simple  Curves  may  all  be  solved  without  the 
use  of  fonnulas.  It  is  necessary  only  to  draw  a  sketch  of  the  conditions  of 
the  problem  for  any  particular  case,  set  down  the  known  data  governing  the 
case,  and  solve  tngonometrically  for  the  unknown.  The  position  of  the 
center  of  the  circle  or  circular  arc  is  the  key  to  all  solutions.  A  few  hinu 
will  be  given  to  illustrate: 

To  move  a  curve  ^shown  in  full  lines.   Fig.  8)  ^^ 

joining  two  tangents  (Tt  and  Tj).  so  it  will  end 
(dotted  lines)  in  a  parallel  tangent  (Ts):  The  dis- 
tance moved  (  — m)>-'the  perpendicular  distance 
between  the  tangents  ((i)-i-8ine  of  intersection  angle 

To  dutnge  the  radius  r  (full)  to  r'  (dotted)  so  that               Fig.  8. 
curve  ending  in  tangent  To  shall  end  in  parallel  tan- 
gent  Ti  (Fig.  9):   The  end  of  the  new  curve  lies  on         y^ ->»^ 

the  k>ng  chord  as  shown.     Then  n^d-*-an  -j.and  ^        ^^\y      -^ 

f-/ - -J -i-ain-s-;  therefore  r'—r—  fd-#- 2  8in*-5-)  ,  in    .         «.     « 

which  rf— perpendicular  distance  between  Tt  and  T%.    Or.  r'^T'-d-*'  (1- 
cos  /)  —  r— d+vcrs  /.    The  reverse  holds  true  when  radius  is  increased. 

To  join  a  curve  (c)  and  a  point  (P)  by  a  ton-  ••      r    A 

gent(Ti):  The  tangent  Ti  and  the  curve  c  fit  ^J'^'^nL 

the  contour  line  around  the  hill  //,  and  it  is     'Vv  H,A^v^ 
proposed  to  throw  ofT  a  tangent  Tj,  from  some 
point  on  the  curve,  so  it  will  pass  through  the 
point  P,  ahead.    One  practical  method  of  doing 
this  in  the    field    is  to  assume  the  position  fj,.     ^^^ 

of  the  P.  r.,  turn  the  angle    for  the  tangent  '*•  *"• 

ahead,  measure  the  distance  and  offset  to  P,  and  from  this  data  calculate 
the  true  position  of  the  P.  T..  and  "move  ahead"  or  "back  up"  accordingly. 
If,  bowever,  the  position  of  the  point  P  has  been  located,  the  position  of  the 
P.  T.  can  be  fixed  acctirately  by  calculation.  Reduce  the  location  of  P 
(no  matter  how  located)  to  the  distance  d  from  the  center  of  the  circle  at  o, 
and  calculate  the  angle  a.  The  distance  r  is  the  radius  of  the  curve.  This 
gives  a  calculated  tie  from  the  P.  C.  to  P.    Now 

,I  +  yt»^ (1) 

and  Tan  ^---3-^;  ory«  +  **-rf* (2) 

y     a  —  X 

ft 
Equating  (1)  and  (2).  Jjr-r».  or*— j (3) 

From  which  y,  tan  0  {"~)  ./  ("  a  — 90^+0),  etc.,  can  be  foimd. 

Com|X>und  Curves  are  made  up  of  two  or  more  curves  of  different  radii, 
directly  joining  each  other,  and  curving  in  the  same  direction.  They  are 
not  difficult  of  analysis.  They  key  to  the  solution  of  any  problem  lies  i" 
cutting  the  data  in  the  right  shape  and  work-  ^ 

ng  from  the  centers  of  the  curves.    Fig.  1 1  >^%    ^i^,. 

leeds  no  explanation  other  than   that  the  ^       ^X /♦/'**- 

^.  C.  C.  is  the  point  of  compound  curve,  and  't    "{"^^  '^  ■/^'^•'_  ^ 

he   total   angle  of  intersection  between  tan-  V^"^^""*^  V?  ^^^s5^' 

rents  7*1  and  Tt  is  the  stmi  of  the  separate  in-    ^   ^^         E        ^v   x 
ersectxm  angles  /  and  i.    Note  also  that  the    j>^  v*\  i    ^^'    X. 

ength  of   tangent  to  the  P.  C.  C.  is  equal  to  ^^  \  |»v  X 

he  S'T  of  the  large  curve  +  the  s-t  of  the  \       [7 

mall  curve;  hence  the  total  vertex  distances.  \     [0| 

^  and  r,  from  the  P.  C.  and  P.  T.,  respcc-  \j^ 

ively,  bear  a  relation  to  the  rest  of  the  data.  \j 

'he  following  table  illustrates  a  few  simple  w 

Toblems  and  solutions  which   may  be  had  „.     * 

-om  Fig.  11.    The  known  quantities  are  indi-  ^**f-  H- 

ated  by  letters;  and  the  answers  required,  by  blank  spaces  in  each  line, 
he  formula  for  solution  in  each  case  is  at  the  right.  Problems  with  other 
ata  may  be  reduced  to  these  forms  before  solving. 


1012 


m.—RAILROADS. 


18. — Solutions  of  Compound  Curve  Problbms. 
(See  Fig.  11). 
NoU. — Capital  letters  refer  to  the  curve  of  larger  radius;  small  Iett«n 
to  curve  of  smaller  radius. 


No. 

ADgles  of 
IntenectloD. 

Radii. 

Vertex 
Dtotaoc's 

Solution. 

I+i 

I 

i 

R 

T 

V 

V 

(Descriptions  refer  to  Fig.  11.) 

f+i 
l+i 
/+i 
/+* 
I+i 

I 
Jo 

i 
ri 

R 
R 

, .    R 

T 

r 
r 

T 
T 

(Solve  for  8-T,  t-U  small  triangle.  V,  r. 

V 
V 
V 

V 

V 
V 
V 
V 

1  (/+<). 

f  ft- r- 1«  vers  (/+ 0  -  V  sin  (/+01 + «f8 1- 

and  r-ft  sin  (/+0-  (ft- r)  sin  i~  F  «• 

(/+0. 

Vera  i- [ft  vers  (7+0- F  sin  (/+01+ 

(ft — r) :  and  o*- ft  sin  (/4- 0  —  (ft— r)  sin  i— 

..    R 

If  cos  (7+0. 

Tan  i7-lft  vers  (7+0- F  sin  (7+01-I- 
(ft  sin  (I+i)—  F  006  (7+0— vl:  and  ft— r 

1  o 

ri 

..    R 

l^lftsln  (7+0- F  cos  (7+0-r|-«-it|n  i. 
ft- r- (0 sin  (7+0- r  vers  (7+ 01+ vera/: 

^and  V^'iR-r)  sin  7+r  sin  (/+0— »  cos 

1(7+0. 

Vers  /-(»  sin   (7+0-r  vers  a+OI-s- 
(ft— r) ;  and  F>"  (ft—  r)  sin  7+  r  sin  (7+  <> 

l-PCO8(7+0. 

[Tan   i7-lt>  sin   (7+0-r  vers   (7+0l-#- 
(F+oco8(7+0— rsln  (7+0:  andft— r» 

ilF+r  cos  (7+0-r  sin  (7+OI-»-8ta  7. 

Note. — For  Nos.  1,  2  and  6,  either  /  or  «  may  be  given. 

Reversed  Curves  should  be  avoided,  especially  for  main  line  traffic 
This  may  be  done  by  "separating"  the  two  simple  curves  on  either  side 
of  the  point   of  reversed  curve  (P.  R.  C.)   and  joining  them  by  a  short 


Fig.  12. 

tangent.  The  curves  may  be  separated  by  moving  them  back  from   th« 
P.  C.  and  P,  T.,  or  by  making  them  "sharper."   To  find  the  relation  exist- 
ing between  the  known  and  unknown  data  ia  Fig.  12: 
Let  d  =  the  length  of  the  line  joining  the  P.  C.  with  the  P.  T.\ 

a«the  angle  which  the  line  d  makes  with  Tx\ 

/9— the  angle  which  the  line  d  makes  with  T\. 
Then  sin  A  —  i  (cos  a  +  cos  ;9)   from  which  the  angle  A,  is  obtained: 
/-a+900-^; 
i-^+90<»-i4=/-a+j9; 

and  /?  —  ((/ sin  i4)-^(sin  /  +  sin  i) (1) 

,  In  Fig.  13  the  distance  d  is  measured  between 
pointson  two  tangents  Ti  and  Tz\  and  the  angles/  and 
«,  which  the  line  d  makes  with  these  tangents,  are 
known.  It  is  required  to  fit  in  a  reverse  curve  of  com- 
n^on  radius  R', 

^"taniZ  +  tanJi*  ogtizedbyGoC  pj^  j^ 


COMPOUND,  REVERSED  AND  EASEMENT  CURVES.     lOlt 


The  Cubic  Parabola  is  the  principal  form  of  parabolic  curve  used,  and 
is  fundamental  of  most  so-called  spiral-  or  easement  curves.  The  equation 
of  the  cubic  parabola  is  y  — nx*.  in  which  x  is  the  abscissa,  and  y  the  ordi- 
nate to  any  point  (,  Fig.  14.  The  constant  n  is  a  decimal,  and  may  have 
any  value:  small  for  a  flat  curve,  and 
large  for  a  sharp  curve.  If  the  cubic  para- 
bola is  laid  off  by  deflection  angles  from 
the  point  o  on  the  tangent  T,  then  the 
deflection  angle*  to  point  1  is  d;  to  point 
2,  id;  to  point  3,  9d;  to  point  4,  IW:  to 
point  6,  2W;  etc.  That  is,  while  the  ordi- 
nate y  to  any  point  p  is  proportional  to 
*•,  the  deflection  angle  is   proportionate  _. 

to  at*.    It  is  to  be  noted  also  that  x   is  '^^'  **• 

measured  along  the  tangent  produced  and  not  along  the  curve.  The  effect 
of  this  is,  of  course,  to  gradually  increase  the  lengths  of  the  "stations"  from 
point  01  as  4-6 >  8-4  >  2-3  >  1-2  >0-l.  For  this  reason  the  cubic  parabola 
has  never  been  popular,  but  has  given  way  to  the  spiral  curve.  Both  of 
them  are  very  flat  at  the  ends  and  grow  rapidly  sharper  toward  the  center 
of  the  curve. 

The  Spiral  Curve  is  a  modification  of  the 
cubic  parabola.  It  is  based  on  chords  of  equal 
kngth,  with  the  curve  compoutuUd  at  the  end 
of  each  chord.  The  chords  may  be  of  any 
length  from  10  ft.  to  60  ft.,  while  30  ft.  is 
quite  usual.  The  degree  of  curve  of  the  first 
arc,  subtended  by  the  chord  0-1,  is  the  com- 
mon difference  for  the  degree  of  curve  of 
successive  arcs.  Thus,  if  the  central  angle 
of  the  curve  0-1  is  A,  then  0-1  will  incline 


at  an  angle  of  \A  with  the  tangent  T:    1-2,  at  an  angle  of  M  X  4 

2-3.  MX9-4H:    3-4,  MX16-8A;   4-5.  M  X25- 12M:  etc.    Thi 

be  proved  by  making  the  central  angles  A,  2A,  ZA,  iA,5A,^  respectively. 


Pig.  16. 

.  2i4; 

lA ;  etc.    This  can 


at  an  anKJe  oi  9/1   wiiu  me  ukiiifeni,   i  ,     1- 

2-3.  MX9-4H:    3-4,  MX16-8A;   4-5. 

be  proved  by  making  the  central  angles  A,  -    .  .    .  .  ,  - 

The  offsets  from  tangent  T  to  points  1,  2,  3,  etc.  are  calculated  successively, 

knowing  the  length  of  chords  and  their  angles  of  inclination  with  Ti  as  are 

also  the  horizontal  distances  between  the  offset  lines,  as  xu  ^a.  etc.    Then. 

the  tangent  of  the  deflection  angle  from  o  to  any  point  on  the  curve  is  —   . 

X 

Simple  Easement  Curves  are  sometimes  approximated  from  simple 
curves,  as  follows:  Run  out  the  regular  simple  curve  from  the  tangent  T 
SIS  riiown  dotted.  Lay  off  the  required  curve  in- 
sid£,  by  measuring  the  offset  distance  d  from 
the  outer  curve.  Lay  off  the  point  P.  S.  of  the 
spiral  starting  from  toe  tangent,  and  also  the 
?nd  of  the  spiral  at  the  P.  C.  C.  where  it  joins 
he  new  curve,  equidistant  from  the  point  c,  which 

fis€cts  the  offset  distance  d  at  the  P.  C,    The     j ^ 

iffset  distance  may  average  from  2  to  4  ft.;  and  p 

he  distance  from  P.  5.  to  P.  C.  may  vary  from  Pig.  10. 

1^0   ft.  to   100  ft.    The  writer  can  recommend  these  curves  for  fast-train 

ervicc     Note  that  the  inner  curve  may  be  "run  in"  directly  with   the 

nstnunent,  the  outer  curve  being  omitted. 

E.— RIGHT  OF  WAY. 
FiHiis  of  Locfttioik— After  the  final  location  is  adopted  it  is  filed  with  the 
ccretary  of  State  for  the  particular  State  through  which  the  line  is  pro- 
•<:ted.  The  following  is  a  typical  description  of  location:  Beginning  at  a 
ake  oa  the  shore  of  Huron  Bay.  near  high-water  mark  and  westerly 
-yont  325  feet  from  the  westerly  comer  of  the  old  stone  fort  in  the  town  of 
:.aznford,  cotmty  of  Huntoon,  and  State  of  Ohio;  thence  north  84**  30' 
^est,  four  thotisand  three  hundred  ten  (4310)  feet  to  a  stake  in  the  county 
•ad  in  front  of  Judge  Phtchard's  farm-house;   thence  by  a  ctirve  to  the 

♦  Approximately:  but  almost  exact  for  flat  curves.  To  be  strictly  exact, 
e  **»»a<«ra/ taKfral  of  the  deflection  angle"  should  be  substituted  for  "de- 
r<rtion  angle." 

t  The  Raiboad  Spiral,"  by  W.  H.  Searles,  contains  tables  for  laying 
-t  any  spiral  In  the  field,  with  instrument  at  any  point  on  the  spiral. 


1014 


S^.—RAILROADS. 


right,  with  a  raditis  of  nineteen  hundred  ten  (1910)  feet,  a  distance  of  three 
hundred  fifty  (350)  feet  to  a  stake;  thence  by  a  tangent  to  said  curve 
North  74**  West,  12662  feet  to  a  stake etc. 

Purchase  and  Condemnation. — The  Real-Estate  Agent  of  the  road  is 
provided  with  maps  of  the  located  line  showing  land  lines,  owners'  names, 
and  widths  of  right-of-way  desired  through  the  various  parcels  of  land. 
The  usual  width  is  100  feet,  but  this  should  be  exceeded  in  tne  case  of  heavy 
cuts  and  fills.  The  following  table.  No.  14.  will  be  useful  for  reference  in 
this  connection.  Where  land  cannot  be  purchased  at  a  reasonable  figure  it 
may  be  condemned  and  the  condemnation  price  so  fixed  is  called  an 
"award.** 

Oftentimes  the  award  may  include  a  parcel  of  land  of  considerable  size. 
not  required  strictly  for  right-of-way  purposes.  In  such  cases  it  is  a  great 
mistake  for  the  R.  K.  O).  to  dispose  of  any  of  this  land  without  first  con- 
sidering whether  it  is  liable  to  be  needed  lor  a  passing  siding,  or  for  a  spur 
track  to  some  prospective  manufacturing  plant.  The  writer  can  instance 
many  cases  in  which  supposed  surplus  property  has  been  disposed  of  at  a 
low  figure  and  repurchased  for  an  amoimt  four  or  five  times  as  great. 

14. — ^Tablb  for  Finding  Width  of  Rioht-of-Wat  for  Cuts  and 

Fills. 
Note. — ^Total  width  between  slope  stakes— width  of  base  of  roadway -i- 
sum  of  horiiontal  distances  for  slopes  (from  table). 

[Horizontal  Distance  in  Feet  for  One  Slope.] 


u 

Side  Slope. 

&^ 

itol. 

itol. 

itol. 

}  to  1. 

1  tol. 

litoi. 

litol.l 

If  tol. 

2  tol. 

2itol. 

litol. 

A 

.8 

1 

2 

3 

4 

6 

6 

7 

8 

9 

10 

8 

1.6 

2 

4 

6 

8 

10 

12 

U 

16 

18 

20 

12 

2.4 

3 

6 

9 

12 

15 

18 

21 

24 

27 

38 

16 

3.2 

4 

8 

12 

16 

20 

24 

28 

32 

36 

40 

20 

4.0 

5 

10 

15 

20 

25 

30 

39 

40 

45 

SO 

24 

4.8 

6 

12 

18 

24 

30 

36 

42 

48 

94 

80 

28 

5.6 

7 

14 

21 

28 

35 

42 

49 

66 

63 

70 

32 

6.4 

8 

16 

24 

32 

40 

48 

56 

64 

72 

88 

36 

7.2 

9 

18 

27 

36 

45 

64 

63 

72 

81 

98 

40 

8.0 

10 

20 

30 

40 

50 

60 

70 

80 

90 

108 

44 

8.8 

11 

22 

33 

44 

65 

66 

77 

88 

ft 

118 

48 

9.6 

12 

24 

36 

48 

60 

72 

84 

96 

108 

128 

62 

10.4 

13 

26 

89 

52 

66 

78 

•1 

104 

117 

130 

66 

11.2 

14 

28 

42 

56 

70 

84 

M 

112 

126 

148 

60 

12.0 

15 

80 

45 

60 

75 

90 

109 

120 

135 

158 

64 

12.8 

16 

32 

48 

64 

80 

96 

112 

128 

144 

168 

68 

13.6 

17 

34 

51 

68 

86 

102 

119 

136 

153 

tro 

72 

14.4 

18 

36 

64 

72 

90 

108 

126 

144 

162 

180 

76 

15.2 

19 

38 

57 

76 

95 

114 

133 

162 

171 

198 

80 

16.0 

20 

40 

60 

80 

100 

120 

140 

160 

180 

201 

84 

16.8 

24 

42 

63 

84 

105 

126 

147 

168 

189 

316 

88 

17.6 

22 

44 

66 

88 

110 

132 

154 

176 

198 

2» 

92 

18.4 

23 

46 

69 

92 

115 

138 

161 

184 

207 

238 

96 

19.2 

24 

48 

72 

96 

120 

144 

168 

192 

216 

248 

100 

20.0 

25 

50 

75 

100 

125 

190 

179 

200 

225 

298 

104 

20.8 

26 

52 

78 

104 

130 

156 

181 

206 

JM 

268 

108 

21.6 

27 

54 

81 

108 

136 

162 

189 

216 

243 

278 

112 

22.4 

28 

66 

84 

112 

140 

168 

196 

224 

292 

288 

116 

23.1 

29 

58 

87 

116 

145 

174 

208 

232 

261 

298 

120 

24.0 

30 

60 

90 

130 

150 

180 

210 

240 

270 

388 

Ex. — Width  of  base  of  roadway- 28  ft.;  height.  48  ft.  (ground  skipe 
aboQt  level;)  side  slopes.  IJ  to  1.  Then  width  between  slope  sttdces— 28-»- 
?P+60— 148  ft.  (Retaining  walls  are  often  used  to  narrow  the  requirrd 
nght-of-way.) 


d  by  Google 


1016  m.— 'RAILROADS. 

P.— CONSTRUCTION. 

Earthwork  Calciikitioiis.--The  preliminary  and  location  sunrey  maps 
and  profiles  should  give  all  the  information  necessary  to  estimate  the  cost 
of  constructing  the  Ime.  Borings  should  be  made  or  test-pits  dug  occasioc- 
ally  in  order  to  classify  the  material  in  excavation.  Several  methods  an 
used  in  maldng  preliminary  estimates  of  earthwork,  and  the  three  following 
are  worthy  of  note: 

(1). — ^The  cross-section  at  each  station,  and  at  intermediate  points  if 
necessary,  may  be  plotted  on  cross-section  paper  from  the  profile  and 


Pig.  17. 

topography  notes,  as  shown  in  Pig.  17.  The  distances  D,  J,  H,  k  (and  p) 
are  then  scaled  and  used  in  the  following  formula  for  area  of  cioap  ocction 
in  "cut,"  and  similarly  in  "fill:*' 

Areainsq.  ft.-J[p(D-l-<i)-l-10(H+A)] (1) 

where  10  ft.  is  i  the  width  of  roadbed  in  excavation.  Por  quantities  in  fin. 
10  would  be  replaced  by  7,  if  the  roadbed  is  to  be  14  ft.  wide.  The  cubical 
contents  in  feet  of  tjie  sohd  figure  of  which  the  above  cross-section  is  coo- 
sidered  as  the  "average  area"  is  found  by  multiplying  this  area  bv  \  the  sum 
of  the  distances  to  the  adjacent  cross-sections  on  either  side.  The  sHmma- 
iion  of  the  contents  in  cubic  feet  is  reduced  to  cubic  yards,  as  the  cost  price 
is  in  that  denomination.    (Use  planimeter  if  preferred.) 

(2) . — If  the  topomphy  has  been  taken  with  a  clinometer  and  the  groond 
Hne  is  straight,  as  m  Pig.  18.  instead  of  broken  as 
shown  in  Fig.  17,  there  are  three  methods  in  use  for 
determining  areas: 

(a). — Plat  the  ground  line  G  by  means  of  the 
profile  height  h  and  the  angle  of  incUnation  a;  scale 
G  and  H.  Then,  for  the  etched  portion  or  cut: 
Area—iC//— C;  in  which  C  is  the  area  of  triangle 
below  roadbed  base,  to  V.  In  the  figure,  the  con- 
stant C  is  100  sq.  ft.  It  varies  with  the  side  slopes 
and  width  of  roadbed.  (Use  planimeter  if  preferred.) 

(b). — Prepare  tables  of  areas  for  various  heights  A,  and  various  ground 
slopes  a;  ana  for  the  standard  roadbed  and  side  slopes.  Por  loose  rock  in 
excavation  the  side  slope  may  be  say  ^  :  1;  in  embankment,  1  :  1.  Earth 
1  :  1  for  cut,  and  H  :  1  for  fill.  The  calculation  of  the  table  may  be  based 
on  the  following  formula: 

Area  required,  cut  or  fill  -  \{h-\-v)*  cosMcot(^+  a)  +cot(j9-  a)]-C (1) 

In  which  Area  required  —  area  of  the  etched  portion  in  Piij.  18, 
A— center  height  of  cut  or  fill, 
V  — vertex  distance  below  roadbed, 
a  °- angle  of  ground  slope  with  the  horixontal. 
^»  angle  of  side  slopes  with  the  horizontal, 
cT-area  of  triangle  (ht.— t/)  below  roadbed. 
When  ^—46**  the  formula  is  somewhat  simplified.    It  is  to  be  noted  that 
(A-hv)  may  be  assumed  as  imity  for  various  ground  and  side  sk>pes,  axid 
afterward  expanded  by  squares,  finally  deductmg  the  value  of  the  constant 
area  C.    The  gxotmd  slope  must  not  intercept  the  roadbed. 

(c). — ^Tables  may  be  prepared  giving  correction  areas  for  slopes,  to  be 
added  to  tables  for  "level  sections"  (see  C^ase  3).  instead  of  tables  of 
actual  areas  as  previously  described.  From  Pig.  18  it  will  be  seen  that 
sloping  ground  always  gives  a  plus  correction,  as  the  small  triangle  below 
the  elevated  side  of  the  groxmd  line  G  is  greater  than  the  one  above  the 
depressed  side.    The  correction  tables  may  be  for  areas  of  cross-section,  or 


CONSTRUCTION.    EARTHWORK.  1017 

for  cubic  yards  or  cubic  feet  per  station  of  100  ft.,  60  ft.,  etc.    See  Table  22, 
page  1090;  also  Table  27,  page  1030. 

(3).— Tables  of  "level  sections"  may  be  used  in  preliminary  estimates 
where  the  ground  is  fairly  "level;"  or  in  connection  with  the  previously 
described  correction  tables,  where  the  transverse  ground  line  is  sloping. 
These  tables  may  be  calculated  from  the  following  formula,  modified  from 
formula  (2),  page  1016,  by  making  a^-O.   and  using  the  previous  notation: 

i4— Area  required  — (A +t;)* cot  0—C (3) 

Or,  giving  C"  ( — 1»*  cot  0)  its  value  in  terms  of  v  and  jJ, 

A''ih*  +  2kv)cot  fi   (3) 

When  the  side  slopes  are  1  :  1,  ^-46**,  and 

A'-{h+v)*-C''h*+2hv (4) 

When  the  side  slopes  are  U  :  1, 

.4  - i  (A+t;)«-C-i  (A«+  2hv); (5) 

and  similarly  for  any  other  side  slope. 

These  t£U)les  may  be  copied  on  profile  paper  in  the  form  of  cubic  yards 
per  lOO-ft.  station,  and  arranged  so  that  tne  quantities  can  be  reaid  off 
directly  by  matching  the  zero  of  the  table  to  the  grade  line  of  the  profile, 
and  reading  the  quantity  opposite  the  grotmd  line.  The  profile  tables  are 
usually  to  feet  in  height;  or  to  feet  and  half  feet. 


List  of  Earthwork  Tables,  Pollowino. 
(And  also  tables  relevant  thereto.) 

Table  No.  Description.  Page. 

18.    Multiplication  table,  up  to  60x60 1018-1019 

iSa.  Multiplication  table,  up  to89X35 1020 

( 9.    End  areas  reduced  to  cu.  yds.  per  station  (Equiv.  1-10) 1021 

iO.    End  areas  (1-27000)  reduced  to  cu.  yds.  per  station 1022-1027 

ri .    Method  of  calculating  earthwork  tables 1028-1029 

12.    Pormulas  for  calculating  ground-slope  quantities 1030-1033 

'3.    Level  sections:  HeighU.  0-60 ft. ;  Roadway.  14  ft. ;  Slopes.  IH  to  1     1034 

4,  "  ••  .  ••       60-120"  "  14"       '^      IHtol     1036 

5.  "  "  "  0-60  "  "  16  "  "  Itol  1036 
5.  "  "  "  0-60"  "  16"  "  IHtol  1037 
7.        "           "              "          0-60"           "          18  "       "          Itol     1038 

with  corrections  for  ground  slopes 1039 

{.      Level  sections ;  Heights.  60-100  ft. ;  Roadway,  18  ft. ;  Slopes,  1  to  1     1040 

with  corrections  for  ground-slopes 1041 

L  Formulas  for  extending  tables  of  level  sections  to  any  side  slopes  1042 
at.  Factors  for  extending  tables  of  level  sections  to  other  widths 

and  slopes 1042 

Level  sections;  Heights,  0-60  ft. ;  Roadway.  18  ft. ;  Slopes.  IH  to  1     1043 

0-60  "  "  20  "       "         Htoi     1044 

0-60  "  "  20  "       "         >^tol     1046 

0-60  "  "  20  "       "  Itol     1046 

0-60  "  "  22  "        "  1  to  1     1047 

0-60  "  "  24  "       "       IH  to  1     1048 

0-60  "  "  26  "       *•       IHtol     1049 

0-60  "  "  28  "       "  Itol     1050 

0-60  "  "  28  "       "       mtol     1061 

0-60  "  "  30  "       "  Itol     1052 

*'       60-100"  "      14-30"       "  Itol     1053 

"       60-100"  "      14-30"       "       IHtol     1054 

S>rismoidal  correction  table 1057-1068 


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i018  SH.— RAILROADS. 


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I 


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MULTIPLICATION  TABLE,    AREAS  TO  CU,  YDS. 


1021 


19. — Unit  and  Decimal  Areas  of  Cross-Section  Reduced  to 
Cu.  Yds.  per  100-Ft.  Station. 
(See  Table  20,  following,  for  general  use.) 
Note. — ^Thc  values  in  the  table  are  cu.  yds.  per  lOf^h.  station  corres- 
ponding to  the^  unit  area  in  the  first  coltunn  when  used  in  the  proper  decimal 
place  or  denomination  as  per  headings  of  columns. 

[Cu.  Yds.  per  100-Ft.  Station.] 


4 

mh. 

H 

T 

Thons. 

ta 

t 

Units 

1  Decimals 

|t 

M 

(7) 

(0 

(5)            (4) 

(3) 

(2)           (1)        (.1)(.2) 

|2 

o 

.    o 

o     o  , 

O 

o    o .  oo 

h 

1 

3  703  704 

370  370 

37  037 

3  703.7 

370.4 

37.04 

3.70 

0.37 

.04 

1 

2 

7  407  407 

740  741 

74  074 

7  407.4 

740.7 

74.07 

7.41 

0.74 

.07 

2 

3 

11  111  111 

1  111  111 

111  HI 

11  111. 

1  111.1 

111.11 

11.11 

1. 11 

.11 

3 

(7) 

(6) 

(5) 

(4) 

(3) 

(2) 

(1) 

(.1) 

(.2) 

4 

14  814  815 

1  481  481 

148  148 

14  815. 

1  481.5 

148.15 

14.81 

1.48 

.15 

4 

6 

18  518  519 

1  851  852 

185  185 

18  519. 

1  851.9 

185.19 

18.52 

1.85 

.19 

5 

fi 

22  222  222 

2  222  222 

222  222 

22  222. 

2  222.2 

222.22 

22.22 

2.22 

.22 

6 

(7) 

(6) 

(5) 

(4) 

(3) 

(2) 

(1) 

(.1) 

(-2) 

7 

26  925  926 

2  592  593 

259  259 

25  926. 

2  592.6 

259.26 

25.93 

2.59 

.26 

7 

8 

29  629  630 

2  962  963 

296  296 

29  630. 

2  963.0 

296  30 

29.63 

2.96 

.30 

8 

9 

33  333  333 

3  333  333 

333  333 

33  333. 

3  333.3 

333.33 

33.33 

3.33 

.33 

9 

Ex. — ^The  average  sectional  area  of 
one  station  (100  ft.)  of  the  Culebra  cut 
was  40600  sq.  ft.  Find  the  cu.  yds.  in 
the  statioti? 


Solution. — Prom  above  Table 


4  (5)  »  148  148 
6  (3)  -       


2  222 
150  370  cu.  yds. 


Ans. 


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1022 


m.'-RAILROADS. 


20. — Cubic  Yards  in  100-Ft.  Station,  for — 
(Column  headings  are  Units  of  numbers  in  first  coltmin.) 

[Cu.  Yds.,  from  formula   «     -  .] 


Area. 

Sq.Ft. 

0. 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

P.P. 

.^ 

0.0 

3.7 

7.4 

11.1 

14.8 

18.5 

22.2 

26.9 

29.6 

33.3 

1-! 

37.0 

40.7 

44.4 

48.1 

51.9 

56.6 

69.3 

63.0 

66.7 

70.4 

2-. 

74.1 

77.8 

81.5 

86.2 

88.9 

92.6 

96.3 

100.0 

103.7 

107.4 

3-. 

lll.l 

114.8 

118.5 

122.2 

126.9 

129.6 

133.3 

137.0 

140.7 

144.4 

4-. 

148.1 

151.9 

155.6 

159.3 

163.0 

166.7 

170.4 

174.1 

177.8 

181.5 

5-. 

186.2 

188.9 

192.6 

196.3 

200.0 

203.7 

207.4 

211.1 

214.8 

218.5 

6-. 

222.2 

225.9 

229.6 

233.3 

237.0 

240.7 

244.4 

248.1 

251.9 

255.0 

7-. 

259.3 

263.0 

266.7 

270.4 

274.1 

277.8 

281.6 

286.2 

288.9 

292.6 

»-. 

296.3 

300.0 

303.7 

307.4 

311.1 

314.8 

318.5 

322.2 

325.9 

329.6 

9-. 

333.3 

337.0 

340.7 

344  4 

348.1 

351.9 

365.6 

369.3 

363.0 

266.7 

i  »0-- 

370.4 

874.1 

377.8 

381.5 

385.2 

388.9 

392.6 

896.3 

400.0 

403.7 

3    11~ 

407.4 

411.1 

414.8 

418.6 

422.2 

425.9 

429.6 

433.3 

437.0 

440.7 

•5  12-. 
8  13-. 

444.4 

448.1 

451.9 

455.6 

459.3 

463.0 

466.7 

470.4 

474.1 

477.8 

481.5 

485.2 

488.9 

492.6 

496.3 

500.0 

603.7 

607.4 

511.1 

514.8 

^  14-. 

518.5 

522.2 

625.9 

529.6 

633.3 

637.0 

640.7 

644.4 

648.1 

651.9 

555.6 

559.3 

563.0 

666.7 

670.4 

574.1 

577.8 

681.5 

685.2 

588.9 

592.6 

596.3 

600.0 

603.7 

607.4 

611.1 

614.8 

618.5 

622.2 

625  9 

3.7 

^  17-. 

629.6 

633.3 

637.0 

640.7 

644.4 

648.1 

651.9 

655.6 

659.3 

663.0 

1     .4 

«  1&-. 
1  19-. 

?  20-. 

666.7 

670.4 

674.1 

677.8 

681.5 

685.2 

688.9 

692.6 

696.3 

700.0 

3   .; 

703.7 

707.4 

711.1 

714.8 

718.5 

722.2 

725.9 

729.6 

733.3 

737.0 

n4.i 

3  l.l 

4  1.5 

740.7 

744.4 

748.1 

751.9 

755.6 

759.3 

763.0 

766.7 

770.4 

5t  19 

^21-. 

777.8 

781.5 

785.2 

788.9 

792.6 

796.3 

800.0 

803.7 

807.4 

811.1 

6  2  2 

.22-. 

814.8 

818.5 

822.2 

825.9 

829.6 

833.3 

837.0 

840.7 

844.4 

848.1 

7  3  ( 

7  23-. 

851.9 

855.6 

859.3 

863.0 

866.7 

870.4 

874.r 

877.8 

881.5 

8852 

8   3  0 

w  24-. 

888.9 

892.6 

896.3 

900.0 

903.7 

907.4 

911.1 

914.8 

918.5 

922.2 

9I3.3 

|2^. 
•3  2ft-. 

925.9 

929.6 

933.3 

937.0 

940.7 

944.4 

948.1 

951.9 

955.6 

959.3 

963.0 

966.7 

970.4 

974.1 

977.8 

981.5 

985.2 

988.9 

992.6 

996.3 

38 

S  27-. 

a  2ft-. 

1000.0 

1003  7 

1007.4 

1011.1 

1014.8 

1018.5 

1022.2 

1025.9 

1029.6 

1033.3 

1       4 

1037.0 

1040.7 

1044.4 

1048.1 

1051.9 

1055.6 

1059.3 

1063.0 

1066.7 

1070.4 

2      8 

^29-. 

1074.1 

1077.8 

1081.5 

1085.2 

1088.9 

1092.6 

1096.3 

1100.0 

1103.7 

1107.4 

3  11 

4^1  5 

■0  30-. 

llJ:: 

1111.1 

1114.8 

1118.5 

1122.2 

1125.9 

1129.6 

1133.3 

1137.0 

1140.7 

1144.4 

1148.1 

1151.9 

1155.6 

1159.3 

1163.0 

1166.7 

1170.4 

1174.1 

1177.8 

1181.5 

^23 

1185.2 

1188.9 

1192.6 

1196.3 

1200.0 

1203.7 

1207.4 

1211.1 

1214.8 

1218.6 

7  2: 

§  33-. 

1222.2 

1225.9 

1229.6 

1233.3 

1237.0 

1240.7 

1244.4 

1248.1 

1251.9 

1255.6 

fA3.t 

O  34-. 
7  36-. 

1259.3 

1263.0 

1266.7 

1270.4 

1274.1 

1277.8 

1281.5 

1285.2 

1288.9 

1292.6 

9)3  4 

1296.3 

13OO.0 

1303.7 

1307.4 

1311.1 

1314.8 

1318.5 

1322.2 

1325.9 

1339.6 

1333.3 

1337.0 

1340.7 

1344.4 

1348. 1 

1351.9 

1355.6 

1359.3 

1363.0 

1366.7 

2  37-. 

1370.4 

1374.1 

1377.8 

1381. S 

1385.2 

1388.9 

1392.6 

1396.3 

1400.0 

1403.7 

5  3ft-. 

1407.4 

1411.1 

1414  S 

1418.5 

1422.2 

1425.9 

1429.6 

1433.3 

1437.0 

1440.7 

^39-. 

1444.4 

1448. 1 

1451.9 

1455.6 

1459. a 

1463.0 

1466.7 

1470.4 

1474. 1 

1477.8 

|40.. 

1481.8 

1485.2 

1488.9 

1492.0 

1496.3 

1500.0 

1503.7 

1507.4 

1511.1 

1514.8 

s  *>- 

1518.5 

1522.2 

1525.9 

1529.6 

1533.3 

1537.0 

1540.7 

1544.4 

1548.1 

1551.1 

"  42-. 

1555.6 

1559.3 

1563.0 

1566.7 

1570.4 

1574.1 

1577.8 

1581. C 

1585.2 

15S8.S 

43-. 

1592.6 

1596.3 

1600.0 

1603.7 

1607.4 

1611.1 

1614.8 

1618.1 

1622.2 

1625. S 

44-. 

1629.6 

1633.3 

1637.0 

1640.7 

1644.4 

1648. 1 

1651.8 

165S.( 

1669. S 

1663.C 

45-. 

1666.7 

1670.4 

1674.1 

1677.8 

1681. E 

1685.2 

1688.S 

1692. ( 

1696.2 

1700.  ( 

4ft-. 

1703.7 

1707.4 

1711.1 

1714.7 

1718.B 

1722.2 

1725.  S 

1729. C 

1733.2 

1737. C 

47-. 

1740.7 

1744.4 

1748.1 

1751.9 

1755.6 

1759.3 

1763. C 

1766.7 

1770.  ■( 

1774. 1 

4ft-. 

1777.8 

1781.5 

1785.2 

1788.9 

1792.6 

1796.3 

1800. C 

1803.1 

1807.^ 

1811. 

49-. 

1814.8 

18l8.fi 

1822.2 

1825.9 

1829.6 

1833.3 

1837. C 

1840.1 

1844.4 

1848. 

80-. 

1851.9 

1855.6 

18.59.3 

1863.0 

1866.7 

1870.4 

1874.1 

1877.« 

1881.! 

1885.1 

rl 

Ex,-Av 

erase  area  of  cross 

-section 

32 

I.    -1 

188.9 

of  sta 
for  8U 

Lion  IS 
ition? 

321.4 

sq.ft. 

Find 

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e         ( 

P.  P.c 

-H^. 

.4-_ 

_J.5 

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1024 


SH.— 'RAILROADS. 


20. — Cubic  Yards  in  100-Ft.  Stations,  for — 
(Column  headings  are  Units  of  numbers  in  first  colimin.) 


[Cu 

.  Yds., 

from  formula  ^^.J 

Area. 

Sq.Ft. 

0. 

1. 

s. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

P.P. 

lOfr-. 

3703.7 

3707.4 

3711.1 

8714.8 

3718.8 

8722.2 

3726.9 

3729.6 

3733.8 

3787.0 

101-. 

3740.7 

8744.4 

3748.1 

3751.9 

3765.6 

3769.3 

3763.0 

8766.7 

3770.4 

3774.1 

102-. 

8777.8 

3781.6 

3785.2 

3788.9 

3792.6 

8796.3 

8800.0 

3803.7 

3807.4 

8811.1 

103-. 

3814.8 

3818.5 

382^.2 

3825.9 

3829.6 

3833.3 

3837.0 

3840.7 

3844.4 

8848.1 

104-. 

3861.9 

3855.6 

3869.3 

3863.0 

3866.7 

3870.4 

3874.1 

•8877.8 

8881.6 

3885.2 

!(»-. 

3888.9 

8892.6 

8896.3 

8900.0 

3903.7 

8907.4 

S9U.1 

3914.8 

3918.8 

8928.2 

106-. 

3925.9 

3929.6 

3933.3 

3937.0 

8940.7 

3944.4 

8948.1 

3951.9 

8966.6 

8959.3 

107-. 

3963.0 

8966.7 

3970.4 

3974.1 

8977.8 

8981.5 

3985.2 

3988.9 

8992.6 

3996.3 

!(»-. 

4000.0 

4003.7 

4007.4 

4011.1 

4014.8 

4018.5 

4022.2 

4025.9 

4029.6 

4033.3 

109-. 

4037.0 

4040.7 

4044.4 

4048.1 

4051.9 

4055.6 

4069.3 

4063.0 

4066.7 

4070.4 

|ll(^. 

4074.1 

4077.8 

4061.6 

4086.2 

4068.9 

4092.6 

4096.8 

4100:0 

4103.7 

4107.4 

1  111-. 

4111.1 

4114.8 

4118.6 

4122.2 

4125.9 

4129.6 

4133.8 

4137.0 

4140.7 

4144.4 

1  1 12-. 
8  113-. 

4148.1 

4151.9 

4155.6 

4159.3 

4163.0 

4166.7 

4170.4 

4174.1 

4177.8 

4181.8 

4185.2 

4188.9 

4192.6 

4196.8 

4200.0 

4203.7 

4207.4 

4211.1 

4214.8 

4218.6 

^  114-. 

4222.2 

4225.9 

4229.6 

4233.3 

4237.0 

4240.7 

4244.4 

4246.1 

4251.9 

4255.6 

t  115-. 

4259.3 

4263.0 

4266.7 

4270.4 

4274.1 

4277.8 

4281.8 

4285.2 

4288.9 

4292.6 

4296.3 

4300.0 

4303.7 

4307.4 

4311.1 

4314.8 

4318.6 

4322.2 

4325.9 

4329.6 

3' 

«  117-. 

4333.3 

4337.0 

4340.7 

4344.4 

4348.1 

4351.9 

4365.6 

4359.3 

4363.0 

4366.7 

1     .« 

-,  n»-. 

4370.4 

4374.1 

4377.8 

4381.6 

4385.2 

4388.9 

4392.6 

4396.3 

4400.0 

4403.7 

2     .? 

1  "*"• 

4407.4 

4411.1 

4414.8 

4418.6 

4422.2 

4426.9 

4429.6 

4433.3 

4487.0 

4440.7 

3  1  1 
1.5 
1.} 

?  "0-. 

4444.4 

4448  1 

4451.9 

4456.6 

4469.3 

4468.0 

4466.7 

4470.4 

4474.1 

44n.8 

^  121-. 

4481.5 

4485.2 

4488.9 

4492.6 

4496.3 

4600.0 

4503.7 

46C7.4 

4511.1 

4514.8 

2J 

.  122-. 

4518.5 

4622.2 

4525.9 

4529.6 

4533.3 

4637.0 

4540.7 

4544.4 

4648.1 

4661.9 

2( 

7  123-. 

4655.6 

4559.3 

4563.0 

4566.7 

4570.4 

4574. I 

4577.8 

4581.5 

4685.2 

4588.9 

J.« 

^  124-. 

4592.6 

4596.3 

4600.0 

4603.7 

4607.4 

4611.1 

4614.8 

4618.6 

4622.2 

4626.9 

3.  J 

1  125-. 

4629.6 

4633.3 

4637.0 

4640.7 

4644.4 

4648.1 

4651.0 

4686.6 

4659.3 

4663.0 

•S  126-. 

4666.7 

4670.4 

4674. 1 

4677.8 

4681.5 

4686.2 

4688.9 

4692.6 

4096.3 

4700.0 

3  1 

«  127-. 
S  12S-. 

4703.7 

4707.4 

4711.1 

4714.8 

4718.5 

4722.2 

4726.9 

4729.6 

4783.3 

4737.0 

1     .4 

4740.7 

4744.4 

4748.1 

4751.9 

4765.6 

4769.8 

4763.0 

4766.7 

4770.4 

4774.1 

• 

^12^. 

4777.8 

4781.6 

4786.2 

4788.9 

4792.6 

4796.8 

4800.0 

4803.7 

4807.4 

4611.1 

1  1 
15 

•e  130-. 
i  131-. 

4814.8 

4818.5 

4822.2 

4826.9 

4829.6 

4833.3 

4837.0 

4840.7 

4844.4 

4646.1 

4861.9 

4866.6 

4859.3 

4863.0 

4866.7 

4870.4 

4874.1 

48n.8 

4881.6 

4885.2 

23 

8  133-. 
5  134-. 

4888.9 

4892.6 

4896.8 

4900.0 

4903.7 

4907.4 

4911.1 

4914.8 

4918.5 

4922.2 

IT 

4925.9 

4929.6 

4933.3 

4937.0 

4940.7 

4944.4 

4948.1 

4951.9 

4956.6 

4986.3 

3.0 

4963.0 

4966.7 

4970.4 

4974.1 

4977.8 

4981.5 

4986.2 

4968.9 

4998.6 

4996.3 

34 

1  135-. 

5000.0 

6003.7 

5007.4 

6011.1 

6014.8 

5018.5 

5022.2 

6025.9 

6029.0 

5083.3 

&  13»-. 

6037.0 

5040.7 

6044.4 

6048.1 

5061.9 

6055.6 

6059.8 

5063.0 

6066.7 

6070.4 

«  137-. 

5074.1 

6077.8 

6081.6 

6085.2 

6088.9 

5092.6 

6096.3 

6100.0 

6103.7 

6107.4 

5  138-. 

5111.1 

5114.8 

5118.5 

5122.2 

5126.9 

6129.6 

6133.3 

6187.0 

6140.  T 

6144.4 

;i39-. 

5148.1 

5151.9 

6165.6 

6159.3 

6163.0 

6166.7 

6170.4 

6174.1 

6177.8 

6181.5 

a  U&-. 

6185.2 

5188.9 

6192.6 

5196.3 

6200.0 

5203.7 

6107.4 

5811.1 

5814.8 

5216.5 

"  142-. 

5222.1 

5225.9 

5229.6 

5233.8 

5237.0 

5240.7 

5244.4 

5248.1 

6261.9 

52S6.6 

6259.3 

6263.0 

5266.7 

5270.4 

5274.1 

5277.8 

6881.8 

6866.2 

6288.9 

52926 

143-. 

6296.3 

6300.0 

5303.7 

5307.4 

6311.1 

5314.8 

5318.0 

5382.2 

U26.9 

5329.6 

H4-. 

5333.8 

5337.0 

6340.7 

5344.4 

6348.1 

5351.9 

5365.6 

5859.8 

5863.0 

5866.7 

146-. 

6370.4 

5374.1 

6877.8 

5381.6 

5385.2 

5888.9 

S392.6 

5896.8 

5400.0 

6408.7 

14S-. 

5407.4 

6411.1 

6414.8 

5418.5 

5422.2 

5425.9 

5429.6 

5433.8 

5437.(1 

5440.7 

147-. 

5444.4 

5448.1 

5451.9 

6455.6 

6459.8 

6468.0 

5466.7 

6470.4 

6474.1 

64n.8 

148-. 

5481.5 

5485.2 

5488.9 

6492.6 

5496.3 

5600.0 

5608.7 

650T.4 

6611.1 

6514.8 

14»-. 

5518.6 

5522.2 

5626.9 

6629.6 

5633.3 

5587.0 

5540.7 

65a.4 

5548.1 

5661.9 

150-. 

6555.6 

6659.3   5563.0 

.•5566.7 

5570.4 

5574.1 

5577.8 

6681.6 

5686.8 

5968  9 

Ex. — ^Average  area  of  cross- 
section  IS  1295.3  sq.  ft.  Find 
yardage  for  sUtion? 


1295.   -4796.8 
(P.  P.  Col.)       .8-       l.l 


^ns.  4707.4  cu.  yds. 


d  by  Google 


1026 


m.— RAILROADS. 


20. — Cubic  Yards  in  100-Ft.  Station,  por — 
(Column  headings  are  Units  of  numbers  in  first  column.) 

lOOA. 
3X9* 


[Cu.  Yds.,  from  formula  ■ 


^.1 


Ex. — ^Average  area  of  cross- 
section  18  2436.2  sq.ft.  Find 
yardage  for  station? 


2486.   -0022.2 

Ans.  0022.9  cu.  yds 


EART 

-Given  , 
>ve  deciin 


d  by  Google 


1028  m^RAILROADS. 

21. — Mbthod  of  Calculating  Earthwork  Tablbs  for  Lbvbl 

Sbctions. 
(PxY>m  a  page  of  the  writer's  calculation  of  Table  26,  page  1037.) 

ist. — Select  foolscap  paper,  horizontally  ruled 

Snd. — Draw  vertical  lines,  in  pencil,  to  represent  the  decimal  points  of 
numbers  in  columns  1,  2.  3.  4,  5,  etc.;  thus  insuring  the  figures  bdng  "is 
coltunn"  and  saving  considerable  time  in  making  decimal  points. 

Srd. — Let  w— width  of  roadway,  in  ft.  (tf— 16  in  the  present  case); 
5 "the  side  slopes  of  excavation  or  embankment  (thus,  in  the  present  case, 
using  slopes  oi  IJ  to  1,  5-1.6):  A  =  hcight  of  level  cuttiiwr.  in  ft.;  and 
jj  — quantity  in  cu.  yds.  per  100-tt  station  for  a  level  cut  or  nil  ground  line. 

Then  0''i2sh  +  2w)j  •  ~:  or,  '{2sk+2w)h-^',  or.  -(sA+u.)A~^. 

Sometimes  one  and  sometimes  another  of  the  above  equations  will  be  ioond 
most  convenient,  depending  upon  s  and  h. 

4th. — Calculate  Q  for  A—  0.1  as  for  line  c.  column  1*: 

(?-(2xl.6X0.1  +  2xl6)0.lX~-  6.981  cu.  yds.      Similarly. 

for  A-0.2,  C?-(2X  1.6X 0.2  +  2X  16)0.1X:^- 12.074  cu.  yds. 

wX  V 

.'.Diff.  for  0.1ft.  from  A- 0.1  to  A- 0.2  ft.- 6.093  cu.  yds.  (See  opp.  line  1) 
This  number,  6.093,  forms  a  primary  base  for  calculatingall  the  Differences 
(see  nimibers  in  italics)  in  the  following  table;  and  these  Differences  increase 
by  a  constant  increment  which  will  next  be  explained. 

6th. — Find  the  successive  Diflferences,  lines  1,  3,  5,  7,  etc.  (in  Italics),  by 
calculating  the  constant  incremental  increase  t  for  the  particular  stope  s 
(in  the  present  case  5—1.6)  and  for  the  successive  increase  in  hdght  a  (in 
the  present  case  d  — 0.1  ft.);  and  adding  this  increment  successively,  using 
the  first  Difference,  6.093,  as  a  base.    Now  the  value  of  ♦  in  cu.  yds.  for  any 

25 

slope  ■"  35715  cu.  yds.;  therefore  for  slope  of  IJ  to  1.  as  in  the  present  case. 

»-i  =  0.111^1.  Hence  we  have  for  Differences  in  column  1:  6.098+O.liri 
-6  204  (line  3):  6.204+ O.lin- 6.316  (line  6);  6.316+0.1 11^1 -M2« 
(line  7) ;  etc.  Now  glancing  down  the  coltmin  we  notice  a  similarity  of  the 
three  groups  of  numbers,  the  number  (Difference)  in  each  group  being .» 
unit  larger  than  the  corresponding  one  in  the  group  above.  Henoe  it  i« 
essential  that  these  Differences  be  arranged  in  groups,  each  successive  group 
of  Differences  being  set  down  from  the  preceding  group  by  mental  calculation. 
Note  in  this  connection  also  that  the  Differences  in  successive  columns  are 
increased  by  3.000  from  those  in  the  same  line  in  the  preceding  column. 
Thus,  6.093^  9.093,  12.098,  etc.,  indefinitely.  Now.  hs  to  the  number  of 
Differences  m  each  group,  before  repetition  occurs:  m  the  present  case  this 
number  is  9  because  » —  | ;  for  a  slope  of  1  to  1,  «  —  JV.  therefore  if  27  Differ- 
ences are  arranged  in  each  column  they  will  increase  by  2.000  in  line  hori- 
zontally, when  the  slope  is  1  to  1.  Hence,  the  number  of  Differences  in 
each  column  should  be  arranged  for  the  particular  slope.  For  a  slope  of 
li  to  1,  as  in  the  present  case,  any  number  of  groups  of  9  will  be  convenient. 

6th. — By  successive  addition,  the  quantities  for  each  successive  height  k 
may  now  be  obtained .  Thus,  for  A  -  0. 3  ft .,  0  - 1 8. 2 78  cu.  yds. ;  for  A  - 1  ft.. 
0-64.816  cu.  yds.;  for  A -9. 7  ft.,  (?-  1097.638  cu.  yds.,  etc 

Remarks. — ^The  value  of  5  at  foot  of  each  column  is  the  sum  of  the  Differ- 
ences (in  italics)  in  that  column.  Only  one  column  need  be  added  (these 
values  of  S  are  simply  for  checking  the  r^ular  additions  in  each  colunin} 
as  the  successive  sums  will  increase  by,  in  the  present  case,  27X8—81. 
Note  method  of  checking  each  column  by  lines  a,  h  and  c. 

*  See  table  on  opposite  page.  °  9' '^'^  ^^  GoOglc 


d  by  Google 


1030 


gtj—RAJUX>ADS. 


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D^zed  by  Google^ 


rHWORK-^GROUND-SljOPE  QUANTITIES. 


1081 


llxll^l 


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1032 


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THWORK-CROUND'SLOPE  QUANTITIES. 


1039 


d  by  Google 


1084  9i.^RAILR0ADS. 

28.~Lbvbi.  Sbctions  (Earthwork);  Height.,  <MM>  Ft. 
Basb  of  Roadway,  14  Ft.    Sidb  Slopbs,  IHto  1. 
Note. — ^The  last  two  colmnns  enable  txs  to  laae  any  other  base  than  14  ft: 
Ex.— Given  height,  84.6  ft.;  roadway  12  ft.    Then  we  have.  8401.4- 
(261.86+  8.70)  -  8146.8  dx.  yds.     (For  Ht.  >60  ft.,  see  Tables  24,  41.) 
[Cu.  Yds.  per  100-Ft.  SUtion.] 


d  by  Google 


lARTHWORK  TABLES— LEVEL  SECTIONS.  1035 

•Lbtbl  Sbctions  (Bartkwoik);  Hbiobt.  60-130  Ft. 
LSB  or  Roadway,  14  Ft.    Sidb  Slopbs,  1H  to  1. 
le  last  two oolumns enable tis  to  uae anyother  base  than  14  ft.: 
m  height,  04.5  ft.;   roadway  15  ft.    Then  we  have,  54513+ 
JO)  -  54868  Ctt.  yds.    (See  also  Table  41.) 
[Cu.  Yds.  per  100-Pt.  Station.] 


d  by  Google 


1036  SQ.^RAILROADS, 

25. — ^Lbvbl  Sbctioks  (Earthwork) ;  Hbiobt,  <MW  Ft. 
Base  of  Roadwat,  16  Ft.    Sidb  Slopbs,  1  to  1. 
Note. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  14  ft.: 
Ex. — Given  height,  20.3  ft.;  roadway  14  ft.    Then  we  have.  2729.2- 
(148.15+2.22)-2678.8cu.  yds.    (For  Ht.  >60  ft.,  see  Tables  28.  40.) 
[Cu.  Yds.  per  100-Pt.  Station.] 


d  by  Google 


EARTHWORK  TABLES— LEVEL  SECTIONS,  1037 

-Lbvbl  Sections  (Earthwork) ;  Hbioht.  0-60  Ft. 
ASB  OP  RoAOWAT,  16  Pt.    Sidb  Slopbs,  1H  to  1. 
le  last  two  columns  enable  us  to  use  any  other  base  than  1 8  ft.: 
Ml  height,  89.7  ft.;  roadway  14  ft.     Then   we  have,  11109- 
)  - 10816  cu.  yds.     (For  Ht.  >60  ft. ,  see  Tables  24.  41.) 
[Cu.  Yds.  per  100-Ft.  Station.] 


TET^nOgle 


1038  B»— RAILROADS. 

27. — ^Lbvbl  Sections  (Earthwoxk);  Hbxobt,  0~60  Ft.    Also — 
Basb  op  Roadway,  18  Pt.    Sidb  Slopbs,  1  to  1. 
Note. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  18  ft.: 
Ex.— Given  height,  14.8  ft.;  roadway  19  ft.    Then  we  have,  1797.9+ 
1(103. 70+  6.93)  - 1862.7  cu.  yds.     (For  Ht.  >80  ft.,  see  Tables  28.  40.) 
[Cu.  Yds.  per  100-Ft.  Station.] 


d  by  Google 


EARTHWORK  TABLES,  WITH  GROUND  SLOPES.        1030 


— C0RSBCT10N8  FOR  Ground  Slopbs  Not  Lbvbl. 

Basb  or  Roadway.  18  Ft.    Sidb  Slopbs.  1  to  1. 
(Sm  £xplanation  and  Formulas  in  Table  22.) 
Note.— a-aoale  of  around  slope  {G.  S.)  to  right  of  left  of  center  line; 
!  "G.  S.- 1:10."  "G.  5.-2:10."  etc.,  means  tan  a.  Up  or  ( + )  slopes  from 
center  indicate  additive  corrections,  and  down  or  ( — )  slopes  subtract- 
from  quantities  in  table  oxp  opposite  page  for  level  sections. 
iitive  (+)  and  tubtractive  (-)  Corrections  in  Cu.  Yds.  per  100-Ft.  Sta.] 


^J  <■ 

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a.  8.-5:10. 

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1157 

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1984 

1068 

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5    438 

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1252 

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5400 

1800 

1  1   609 

1400 

934 

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1293 

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5602 

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968 

2489 

1340 

3871 

1659 

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1936 

1   647 

1604 

1003 

2579 

1388 

4011 

1719 

6017 

2006 

1   666 

1557 

1038 

2670 

1438 

4153 

1780 

6230 

2077 

1       686 

1612 

1074 

2763 

1488 

4297 

1842 

6446 

2149 

1       606 

1667 

nil 

2857 

1538 

4444 

1905 

6667 

2222 

1   620 

1723 

1148 

2953 

1590 

2593 

1969 

6891 

2297 

1   647 

1780 

1186 

3051 

1643 

4746 

2034 

7119 

2373 

/   668 

1838 

1225 

3150 

1696 

4900 

2100 

7350 

2450 

'   690 

1896 

1264 

3251 

1750 

6057 

2167 

7586 

2528 

711 

1956 

1304 

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1806 

5216 

2235 

7824 

2608 

783 

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6378 

2305 

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3563 

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1976 

5708 

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8563 

2864 

2204 

1469 

3779 

2035 

5878 

2519 

8817 

2989 

1040  n.—RAILROADS. 

28.^Lbvbl  Sbctions  (Earthwork);  Hbigbt,  60-100  Ft.    Also— 

Basb  of  Roadway.  18  Ft.    Sidb  Slopbs.  1  to  1. 
Note. — The  last  two  columns  enable  us  to  use  any  other  base  than  18  ft.: 
Ex.— Given  height.  88.6  ft.;  roadway  17  ft.    Then  we  have,  84008- 
i(061.86+  3.70)  -  34680  cu.  yds.    (See  also  Table  40.) 
[Cu.  Yds.  per  100-Ft^Station.] 


Note'ihsit  Base,  Slope,  and  Cu.  yds.  in  above  table  may  all  be  multiplie<i 
by  the  same  factor;  thus,  using  factor  oiHior  height  of  06.3  ft.,  we  hav« 
13800  cu.  yds.  for  base  of  12  ft.  and  slopes  H  to  1. 

'  ExampUs  cf  Use  of  Table  S8. 
Ex.  1 . — Find  the  number  of  cu.  yds.  in  Solution : 

a  100-ft.  station:    roadway  18  ft.,  excav.    Level  cutting 18000  cu.yn*- 

slopes  1  to  1,  grotmd  slope  3  in  10  straight    Up  slope,  add . . . .   4114   " 
across,  and  center  height  63  ft?  23014   "     " 

Down  slope,  sub. .   2216   " 

Ahs 20799   "     " 

Ex.  t. — Same,  but  slope  "up"  4  in  10       Solution:  + 18900  cu.yds. 

to  left  of  center,  and  "down"  1  in  10  to  +    6400   "     .. 

nght?  _      878   " 


..iteoogt^"" 


EARTHWORK  TABLES,  WITH  GROUND  SLOPES. 


1041 


— CORRBCTIONS    FOR    GROUND    SlOPBS    NoT    LbVBL. 

Basb  of  Roadwat,  is  Ft.    Sidb  Slopes.  1  to  1. 
(See  Explanation  and  Formulas  in  Table  22.) 
i. — a «"  angle  of  sround  slope  (G.  S.)  to  right  or  left  of  center  line; 
5.-1:10,    "(7.  5.-2:10."  etc..  means  tan  a.     Up  or  (  +  )  slopes 
i  center  indicate  additive  corrections,  and  down  or  (  —  )  slopes  sub- 
,  from  quantities  in  table  on  opposite  page  for  level  sections. 
e  (  +  )  and  subtract ive  (-)  Corrections  in  Cu.  Yds,  per  100-Ft.  Sta.] 


aa-i:io. 

0.8.-2:10. 

a.  a 

-3:10. 

O.  a -4:10. 

aa-5:io. 

a« 

-6».7 

a- 

-11».8 

o- 

-ir'.7 

a- 

■21®.8 

a" 

-26«.6 

4- Up 

—  Down 

+  Up 

-Down 

+  Up 

-Down 

+  Up 

-Down 

+  Up 

—  Down 

980 

802 

2204 

1469 

3779 

2035 

6878 

2519 

8817 

2939 

1008 

825 

2269 

1512 

3889 

2094 

6049 

2593 

9074 

3025 

1037 

848 

2334 

1556 

4001 

2154 

6223 

2667 

9335 

3112 

1067 

873 

2400 

1800 

4114 

2215 

6400 

2743 

9600 

3200 

1097 

897 

2467 

1645 

4229 

2277 

6579 

3820 

9869 

3290 

1127 

922 

2535 

1690 

4346 

2340 

6760 

2897 

10141 

3380 

1157 

947 

2604 

1736 

4464 

2404 

6944 

2976 

10417 

3472 

1188 

972 

2674 

1783 

4584 

2468 

7131 

3056 

10696 

3665 

1230 

998 

2745 

1830 

4706 

2534 

7320 

3137 

10980 

3660 

1253 

1024 

2817 

1878 

4829 

2600 

7511 

3219 

11267 

3756 

1284 

1051 

2889 

1926 

4953 

2667 

7706 

8302 

11557 

3852 

1317 

1077 

2963 

1975 

5079 

2735 

7901 

3386 

11852 

3951 

1350 

1105 

3038 

2025 

5207 

2804 

8100 

3471 

12160 

4060 

1384 

1132 

3113 

2075 

5337 

2874 

8301 

8558 

12462 

4151 

1417 

1160 

3189 

2126 

5467 

2944 

8505 

3645 

12757 

4252 

1452 

1188 

3267 

2178 

5600 

3015 

8711 

3733 

13067 

4356 

1487 

1216 

8345 

2230 

5734 

3088 

8920 

3823 

13380 

4460 

1532 

1245 

3424 

2283 

5870 

3161 

9131 

3913 

13696 

4665 

1557 

1274 

3504 

2336 

6007 

3236 

9344 

4005 

14017 

4672 

1593 

1304 

3585 

2390 

6146 

3309 

9560 

4097 

14341 

4780 

1630 

1334 

3667 

2445 

6287 

3385 

9779 

4191 

14669 

4890 

1667 

1364 

8760 

2500 

6429 

3462 

10000 

4286 

15000 

5000 

1704 

1394 

3834 

2556 

6672 

3539 

10223 

4381 

15335 

6112 

1742 

1425 

3919 

2612 

6717 

8617 

10449 

4478 

16674 

5225 

1780 

1456 

4004 

2669 

6863 

3696 

10678 

4576 

16017 

5339 

1818 

1488 

4091 

2727 

7013 

3776 

10909 

4676 

16363 

5464 

1857 

1519 

4178 

2785 

7163 

3857 

11142 

4776 

16713 

5671 

1896 

1552 

4267 

2844 

7314 

3938 

11378 

4876 

17067 

5689 

1936 

1584 

4356 

2904 

7467 

4021 

11616 

4978 

17424 

5808 

1976 

1617 

4446 

2964 

7622 

4104 

11857 

5081 

17785 

5928 

2017 

1650 

4538 

8025 

7779 

4188 

12100 

6186 

18150 

6060 

2069 

1684 

4630 

3086 

7987 

4274 

12346 

5291 

18519 

6173 

2099 

1717 

4723 

8148 

8096 

4359 

12694 

5397 

18891 

6297 

2141- 

1752 

4817 

1211 

8257 

4446 

12844 

5505 

19267 

6422 

21SS 

1786 

4912 

3274 

8420 

4634 

13098 

5613 

19647 

6549 

2226 

1821 

5007 

3338 

8584 

4622 

13353 

5728 

20030 

6677 

2269 

1856 

5104 

3403 

8760 

4712 

13611 

6833 

20417 

6806 

2312 

1892 

5202 

3468 

8917 

4802 

13872 

5945 

10807 

6936 

2356 

1927 

5300 

8534 

9087 

4893 

14136 

6058 

21202 

7067 

2400 

1964 

5400 

3600 

9257 

4985 

14400 

6171 

II600 

7200 

2445 

2000 

5500 

m; 

9429 

5077 

14668 

6286 

22002 

7334 

-G.  5.—  +  2  in  10  to  left  of  center,  and  -  3  in  10  to  right;  center 
JO  ft.  Then  add  8667  cu.  yds.  to,  and  subtract  3385  cu.  yds.  from. 
1.  yds.  obtained  from  table  of  level  sections  on  opposite  page. 

Interpolations  for  TabU  28. 
—When  center  height  is  in  feet  and  tenths,  interpolate  for  tenths 
from  table. 

—When  the  ground  slope  is  intermediate  between   those  slopes 
to  head  the  columns,  direct  interpolation  will  be  close  enough  for 
'  purposes  for  preliminary  estimates,  etc.     Otherwise,  use  the  exact 
\  in  Table  22. 
-When  the  roadway,  w,  is  greater  or  less  than  18  ft.,  multiply 

1  table  by  i^j^)  -  d  a  tized  by  GoOglc 


lOIS 


l^RAJLROADS. 


29. — POMMULAS  POR  EXTBNOINO  TaBLBS  OP  LSVBL  SkCTIOKS  TO  iS^ 
SiDB  SlOPBS. 


iPor  Use  with  Tables  with  Slopes 
IHtol. 
w^K^.    •¥■  means  add  to      \  the  quanti- 
*  —  means  sttb.  from  |  ties  in  table. 


For  Use  with  Tables  with  Sk?< 

ltd. 
■4-  means  add  to       >  the  qo^^ 
~  means  sub.itom  f  ties  is u^ 


•  iVotr. — Quantities  in  brackets  []  are  +  or  —  anas  in  •9'^.- *'^^ 
change  in  cross-section  by  change  in  side  slope,  and  correspond  with  ar^ 
[A]  in  Table  20.  Hence,  the  cu.  yds.  to  be  added  or  subtrscted  ffisjr  v 
obtained  from  U4]  by  the  use  of  Table  20. 

2ga.— Factors  (F)  pob  Extbkdino  Tablbs  (D  o»  Lbtbl  SBcnfflO  tc 
GivBN  SiDB  Slopbs  (Pirst  Column)  and  Widths  op  Roadwat  UQ. 
(Tables  24.  28.  40  and  41  are  not  included  here.) 


Note. —  /?=width  of  bottom  of  canal  or  railway  cut,  or  top  «  ^^^ 
ment.    R  may  be  increased  or  decreased  by  consulting  the  ls«t  two c^^ 
of  the  tables  referred  to.  ^^i  ]«  1 

r*  ^^  — To  find  the  number  of  cu  yds.  in  a  100-ft.  station  for  « <*™L^ 
ft.  wide  at  bottom  and  with  side  slopes  IH  to  1:  Consult  Table  «  aaa  »^  I 
wply  the  cu.  yds.  corresponding  to  any  given  height  by  the  factor  6.  I 


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1044  Bi.^RAILROADS, 

31. — ^Lbvbl  Sbctxons  (Earthwork);  Hbioht.  0-60  Ft. 
Basb  of  Roadway,  30  Ft.    Siob  Slopbs.  K  to  1 . 
Note. — The  last  two  columns  enable  tis  to  uae  any  other  base  than  20 ft.: 
Ex.—Given  height.  43.9ft.;  roadway  18  ft.     Then  we  have.  6036.8- 
(3l8.52+6.67)-4711.1  cu.  yds. 

[Cu.  Yds.  per  100-Pt.  Station  ] 


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EARTHWORK  TABLES— LEVEL  SECTIONS,  1045 

82. — ^Lbvbl  Sbctions  (Earthwork);  Height.  0-60  Pt. 
Basb  op  Roadway,  30  Ft.    Sidb  Slopbs  H  to  I. 
'>fote. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  20  ft.: 
Ix. — Given  height.   18.1  ft.;    roadway  22  ft.    Then  wc  have  1947.4+ 
.33  +  0.74) -2081.6  cu.  yds. 

[Cu.  Yds.  per  100-Ft.  Station.] 


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1046  ».— RAILROADS. 

83. — ^L^VBL  Sections  (Earthwork) ;  Hbioht,  0-60  Pt. 
Basb  of  Roadway,  30  Ft.    Sidb  Slopbs  1  to  1. 
Note. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  20  ft.: 
Ex.— Given  height,  64.7  ft.;  roadway  21  ft.    Then  we  have.   15134+ 
i  (400.00+5.19)  - 16337  cu.  yds.    (For  Ht.  >60  ft.,  see  Tables  28.  40.) 
[Cu,  Yds.  per  100-Ft.  Station.] 


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EARTHWORK  TABLES—LEVEL  SECTIONS. 


1047 


34.— Lbybl  Sections  (Barthwork);  Hbiobt,  0-60  Ft. 
Basb  of  Roadway,  22  Ft.    Sidb  Slopbs,  1  to  1. 
Note.— The  last  two  coltxmns  enable  tis  to  use  any  other  base  than  22  ft.: 
Ex.— Given  height.  17.2  ft.;   roadway  24  ft.    Then  we  have,  2497.2+ 
>.93-l- 1.48)  -  2624.6  cu.  yds.    (For  Ht.  >60  ft.,  see  Tables  28. 40.) 
iCu.  Yds.  per  lOO-Ft.  Station.] 


Ht. 
Ft. 


.0 


.2 


.7 


Width 
of  2  Ft. 
CiLYdsl 


86.2 
177.8 
277.8 
885.2 
500.0 
822.2 
751.9 
888  9 
1033.31048. 


8.2 
94. 
187. 
288.2 
396. 
511. 
634. 
765.2 
903. 


1200. 

1300. 

1528. 

1703.0 

1885.: 


1185.2 
1344.4 
1511.1 
1685.2 
1866.7 
5  62074, 

16  b251.92271.l 

17  2456.62476. 

18  2666.72688 
6.22907.4 

I  13111.13134.1 
3344.43368. 
3585.23609.7 
3833.33868 
8.94114. 
i  k35l.94378, 
I   4832  24649.7 
4900.04928.' 
5185.26214. 
5477.85607. 
5777.85808. 
6685.26116. 
6400  06431. 
«7ta.26754 
7061.97085. 
7388.97423 
7733.37768. 
1.2  8120. 


8444.48480.1 
8811.1  8848. 
6185.21233. 
9566.79606. 
Wwtf.  V  PW4. 
10361  1I392 
10756  16796 
11167  11208 
11866  11627 
12011  18064 
12444  11488 
1J886  12980 
13933  P8379 

'i3786  ^::: 

14J6lh4lf9 
I47S  14770 
1006  18848 

20066  xmu 

10t78  I6IS7 
ia«78  l< — 
17186  PI 


16. 

103.1 

197.2 

298.7 

407.6 

623.9 

647.6 

778.7 

917.2 

211063. 1 

81216.4 

81377.2 

21545.3 

1720. 

21903.9 

92094.2 

92292. 

82497.2 

22709 

2929. 

3157. 

23392. 

3634. 

63883.9 

9  4140.9 

64406. 

4677.2 
24956.4 
16243.1 
45537 
25638, 
36147.6 
9^. 
6 
18.7 


24.8 
112.2 
207.0 
309.2 
418.9 
535.9 
660.3 
792.2 
931.4 
1078.1 
1232.2 
1393.7 
1562.6 
91738.9 
1922.6 


38. 
121  3 


319.9 


548. 

673.2  686.1 


41.7 
130.6 
226.9 
330.6 
441 
560, 


60. 
139. 
236.9 


945. 
1093. 
1248.0 
1410.2 
1579.9 
1756.9 
1941.3 


2111 


2118.72133. 
03312.22332.4 


82731.4 
82952.2 
23180.3 
03416.9 
23668.9 


2753.2 

2974.7 

3203. 

3439.9 

3683.6 


3909.23934.7 


4167.0 


4193. 


34432.24459.1 


819 

960.2 

108.3 

1263.9 

1426 

1597. 

1775. 

1960. 

22152. 
2352. 
2560, 
2775.0 
2997, 

63226. 
3463, 
3708.3 
3960. 

24219. 


341 

453.2 

572.4 

699 

833 

974.7 

1123.6 

1279.9 

9 1443.6 


96787. 
27111 


2  7803.17838, 


4704.81 
4984.8 
6272.2 
5667.0 
6869.2 
6178.9 

.9 
6820.3 
7152.2 

4 


4732, 

5013.2 

5301.; 

5596.1 

5899.9 

6210.2 

6528. 


4  4760. 

5041.7 
35330. 
95636.9 


21614.7 

01793.2 

21979.1 

82172. 

82373. 

22581. 

2796. 
23019. 
93250. 
9  3488. 

3733. 
23986. 
44245. 

4613. 
24788, 

5070. 
65368.9 

5656.9 


5930.65961 


.2 
8)8617. 2|8653. 7 


6853. 

7185. 

7525. 

7873. 

8228.0 

8590. 


28885.38922.6  8959.98997 


09260.99298.9 


9336.9 


29643.99682.69721.3 


910034 
10432 
10837 
11260 
11670 
12097 
12632 
12974 
18424 
13885  18881 


14817 
16206 
16788 
16877 
16779 
17888 


10074 
10472 
10878 
11291 
11713 
12140 
12570 
18019 
13469 
13927 
14392 
14866 
15845 
16882 
16327 
16829 
17339 


2  8626, 


10113 
10512 
10919 
11333 
11755 
12184 
12620 
13064 
13516 
13973 
14439 
14912 
15393 
15881 
16377 
16880 
17890 


6241.7 

06560.2 

2  6886. 

87219. 

87560. 

27908. 

8263, 

i.9 

2 

9375. 

9760. 

10153 

10553 

10960 

11376 

11797 

12227 

12664 

13108 

13560 

14019 

14486 

14960 

15442 

15931 

16427 

16931 

17442 


6273.2 

6692.4 

6919. 

4  7253.: 

27594. 

37943. 


68. 9| 
149. 
247. 
352.2 
464.8 
584 
712.2 
8470 
989.2 
1138.9 
1295.9 
1460.3 
1632.2 
1811.4 
1998.1 
4  2192.2 
22393.7 
32602.6 
92818. 
93042. 
2  3273.7 
03512.2 
23758.1 
84011.4 
84272. 
24540.3 
04815.9 
2  5098. 
5389.2 
5687.0 
35992.2 
6304. 
6624.8 
16952.2 
27287.0 
7  7629.2 
67978. 
8335.9 


67.6 
158.7 


76.3 
168.2 


257.2  267.4 
363.1  374.1 
476.4  488.2 


697.2 
726.3 
860.9 
1003.9 
1164.2 
1312.0 
1477.2 
1649.8 
1829.8 


2017.2  2036.3 
2212.02231.9 
2414.22434.9 
2623.92645.2 
92840.92863.0 


63065.3 
3297.2 
3536.4 
3783.1 


4937.24063.0 


2  4298.7 
4667.6 
4843.9 

95127.6 
5418.7 
5717.2 
6023.1 

86336.4 
6657.2 
6986.3 


'663.9 


98014 


98299.9 
8663.6  87()0.3|8737. 
9034.7 


09413.2 
29799.1 
10192 
10593 
11001 
11417 
11840 
12270 
12708 
13153 
13606 
14066 
14533 
15008 
15490 
15980 
16477 
16981 
17493 


9072.2 

9461.4 

9838.1 

10232 

10634 

11043 

11459 

11883 

12314 

12752 

13198 

13651 

14112 

14580 

15056 

15539 

16029 

16527 

17032 

17545 


9109.8 


9877.2 

10272 

10674 

11084 

11501 

11926 

12357 

12796 

13243 

13697 

14159 

14628 

15104 

15588 

16079 

16577 

17083 

17596 


609.7 
738.6 
874.9 
1018.6 
1169.7 
1828.2 
1494  1 
1667.4 
1848.2 


3088.2 
3320.8 
3560.8 
3808.2 


4326.2 
4594.9 
4871.9 
5166.3 
5448.2 
5747.4 
6054.1 
6368.2 
6689.7 
7018.6 


7320.9  7354.9 


7698.6 
2|8049.7 
8408.2 
28774.1 
9147.4 
9528.2 
9916.3 
10312 
10715 
11125 
11543 
11968 
12401 
12841 


13: 

13743 

14206 

14676 

15162 

16636 

16128 

16627 

17134 

17648 


7.41 

14.81 

22.22 

29.63 

37.04 

44.44 

51.85 

59.26 

66.67 

74.07 

81.48 

88.89 

96.30 

103.70 

111.11 

118.52 

125.93 

133.33 

140.74 

148.15 

155.56 

162.96 

170.37 

177.78 

186.19 

192.59 

200.00 

207.41 

214.81 

222.22 

229.63 

237.04 

244.44 

251.85 

259.26 

266.67 

274.07 

281.48 

288.89 

296.30 

303.70 

311.11 

318.52 

325.93 

333.33 

340.74 

348. 15 

355.56 

362.96 

370.37 

377.78 

885.19 

392.59 

400.00 

407.41 

414.81 

422.22 

429.63 


% 

P.P. 

7.41 


.74 
1.48 
2.22 
2.96 
5|  3.70 
4.44 
6.19 
6.93 
6.67 


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1048  SO.-^RAILROADS. 

36.— Lbvbl  Sbctions  (Earthwork);  Hbxght.  fh60  Ft. 

Base  of  Roadway,  24  Ft.    Side  Slopes,  IHto  I. 

Note. — ^The  last  two  coliunns  enable  us  to  use  any  other  base  than  24  ft: 

Ex.-— Given  height,   43.1ft.:  roadway    22  ft.    Then  we  have.  141«- 

(318.52  +  0.74)  - 13832  cu.  yds.    (For  Ht.  >60  ft.,  see  Tables  21. 41.) 

[Cu,  Yds.  per  100-Ft.  Station.! 


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EARTHWORK  TABLES— LEVEL  SECTIONS.  1049 

80. — ^Lbvsl  Sbctions  (Earthwork);  Hbioht,  0-60  Ft. 
Babb  op  Roadway,  26  Ft.    Sidb  Slopbs  IH  to  1. 
*fote. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  26  ft.: 
£x.— Given  height,  22.2  ft.:  roadway  27  ft.     Then  we  kave,  4875.8+ 
12.90+ 1.48)  -4968.0  cu.  yds.   (For  Ht.  >60  ft.,  see  Tables  24.  41.) 
(Cu.  Yds.  per  100-Ft.  Station.] 


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1050  m.^RAILROADS. 

87.— ^Lbvbl  Sbctxons  (Earthwork);  Hbiobt,  0-M  Pt. 
Basb  of  Roadway,  28  Ft.    Sidb  Slopes,  1  to  1. 
Note. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  S8  ft.: 
Ex. — Given  height.  57.5  ft.;   roadway  20  ft.    Then  we  have,  18208- 
(422.22+  8.70)  - 17782  cu.  yds.    (For  Ht.  >60  ft.,  see  Tables  28, 40.) 
(Cu.  Yds.  per  100-Ft.  Station.] 


d  by  Google 


EARTHWORK  TABLES—LEVEL  SECTIONS, 


10«1 


88.— Lbtbl  Sbctions  (Barthwork);  Hbiobt.,  0-60  Ft. 

Ba8b  or  Roadway,  28  Pt.    Sidb  Slopbs,  1H  to  1. 

3te.— Tl)e  last  two  columns  enable  us  to  use  any  other  base  than  28  ft.: 

c. — Given  height,  83.0  ft.;  roadway  SO  ft.    Then  we  have,  9750.4+ 

4+4.44)-10^5.3cu.yds.    (PorHt.  >00  ft.,  see  Tables  24. 41.) 

(Cu.  Yds.  per  100-Pt.  Station.] 


1062  ».— RAILROADS. 

30.— -Lbvbl  Suctions  (Earthwork);  Hbiort.  <M(0  Ft. 
Basb  op  Roadway,  30  Pt.    Sidb  Slopbs,  1  to  1. 
Note. — ^The  last  two  columns  enable  us  to  use  any  other  base  than  30  ft.: 
Ex.— Given  height.  41.1  ft.;  roadway  32  ft.     Then  we  have,   10829+ 
(303.70+0.74)'»  11127  cu.  yds.     (PorHt.  >60  ft.,  see  Tables  28, 40.^ 
[Cu.  Yds.  per  100-Pt.  Station.] 


d  by  Google 


EARTHWORK  TABLES— LEVEL  SECTIONS.  106S 

40.~Lbtbl  Sbctions  (Earthwork);    Hbight,  60-100  Pt. 
Basbs  of  Roadway,  14-JO  Ft.    Sidb  Slopes,  1  to  1. 
Note. — ^The  last  two  columns  enable  us  to  tise  any  other  base  than  given : 
Ex.—Oiven  height.  71.5  ft.;  roadway  32  ft.  Then  we  have,  20879+630 
•  27409  CO.  yds.    (See  also  Table  28.) 

[Cu.  Yds.  per  lOO-Ft.  Station.] 


d  by  Google 


1064 


m.—RAILROADS. 


41.^LByBL  Sbctions  (Earthwoik) ;   Hbigbt.  60-100  Ft. 
Basbs  or  Roadway,  14-30  Ft.    Sidb  Slopbb,  IH  to  I. 
Note. — The  last  two  columns  enable  us  to  use  any  other  base  thanghpcix: 
Ex.— Given  height.  68.6  ft.:  roadway  32  ft.  Then  we  have,  S8679+567 
-  34186  cu.  yds.    (See  also  Table  24.) 

(Cu.  Yds.  per  100-Pt.  Station.] 


Ht. 
Ft. 

Width  Of  Roadway  In  Feet. 

WIdtt  WWtU 

nff  9.  V*^  nf  lAPL 

OI  Z  f  b>|<Hllrb 

14 

16 

18 

20 

22 

24 

26 

28 

80 

Ca.YdaCa.Tds 

1 

«0 

23111 

23556 

24000 

34444 

84889 

25333 

25778 

26222 

26667 

444.44 

2223.2 

.6 

23472 

23920 

24368 

24816 

25264 

26713 

26161 

26609 

27067 

448.16 

2240.7 

61 

23835 

24287 

24739 

25191 

25643 

26094 

26546 

26998 

27450 

451.85 

23S9.S 

.5 

24201 

24657 

25113 

25568 

26024 

26479 

36985 

87390 

27846 

456.56 

2277.8 

1 

62 

24570 

25030 

25489 

25948 

26407 

26867 

27326 

r785 

28244 

459.26 

2396.3 

.6 

24942 

25405 

25868 

26331 

26794 

27257 

27720 

28183 

38646 

462.96 

2314.8 

63 

25317 

25783 

26260 

26717 

27183 

27650 

28117 

28583 

29050 

466.67 

2333.3 

.5 

25694 

26164 

26636 

27105 

27575 

28046 

28516 

28987 

29457 

470.37 

2351. 9 

a 

64 

26074 

26548 

27022 

27496 

27970 

28444 

28918 

29393 

29867 

474.07 

2370.4 

3 

.6 

26457 

26935 

27413 

27890 

28368 

28846 

29324 

29801 

30279 

477.78 

2388.9 

S 

65 

26843 

27324 

27806 

28287 

28769 

29250 

29781 

30213 

30694 

481.48 

2407.4 

« 

.5 

27231 

27716 

28201 

28687 

29172 

29657 

80142 

80627 

31113 

485.19 

242S.9 

•s 

66 

27622 

28111 

28600 

29089 

29578 

30067 

30556 

31044 

31633 

488.89 

2444.4 

.6 

28016 

28509 

29001 

29494 

29987 

30479 

30972 

31464 

81957 

492.58 

2463.0 

^ 

67 

28413 

28909 

29406 

29902 

30398 

30894 

81391 

31887 

82383 

496.30 

2481.5 

.B 

28813 

29313 

29813 

80313 

80813 

31313 

81813 

32313 

32813 

600.00 

2500. 0 

1 

68 

29215 

29719 

80222 

30726 

31230 

31733 

82237 

32741 

33244 

503.70 

2518.5 

.5 

29620 

30127 

80636 

31142 

31650 

32157 

32664 

83172 

33679 

507.41 

2S37.t 

.9* 

69 

30028 

80539 

81050 

31561 

32072 

32583 

33094 

34117 

611.11 

2S36.6 

^ 

.5 

30438 

30953 

81468 

31983 

32498 

33012 

33527 

34042 

84557 

514.81 

2574.1 

a 

70 

30852 

31370 

31889 

82407 

32926 

33444 

33963 

34481 

35000 

518.58 

2582.6 

.5 

31268 

31790 

83313 

82835 

33357 

33879 

34401 

84924 

35446 

622.22 

2611.1 

£ 

71 

31687 

32213 

32739 

33265 

33791 

34317 

34843 

85369 

85894 

625.93 

2629.6 

.5 

32109 

32638 

33168 

33698 

34227 

34757 

35287 

35816 

36346 

529.63 

2648.1 

a 

72 

32533 

83067 

33600 

34133 

84667 

85200 

85733 

86267 

36800 

533.33 

2666.7 

rt 

.5 

32961 

33498 

34035 

34572 

35109 

35646 

36183 

36720 

87257 

637.04 

3685.2 

>^ 

73 

33391 

33930 

34471 

85012 

35553 

36093 

36634 

87175 

37717 

640.74 

2703.7 

1 

.5 

33824 

34368 

34912 

36467 

36001 

36546 

37090 

87635 

88179 

544.44 

278  2 

74 

34259 

84807 

35356 

35904 

36452 

37000 

37548 

88096 

38644 

548.15 

r40  7 

O 

.5 

34698 

85250 

85801 

36353 

36905 

37467 

38009 

88561 

39113 

551.85 

27S9.3 

2 

75 

35139 

35694 

36250 

36806 

37361 

37917 

38472 

89028 

39683 

656.56 

27T7.8 

2 

.5 

35583 

86142 

36701 

37261 

37820 

88379 

88938 

39498 

40057 

659.36 

2796.3 

76 

36030 

36593 

37156 

37719 

38281 

38844 

89407 

39970 

40533 

668.96 

2814.8 

.3 

.5 

36479 

37046 

37613 

38179 

38746 

39313 

89879 

40446 

41013 

666.67 

2833.3 

-B 

77 

36931 

37602 

38072 

38643 

39213 

39783 

40354 

40924 

41494 

870.37 

2351.9 

.S 

.5 

37387 

37961 

38535 

39109 

39683 

40257 

40831 

41405 

41979 

674.07 

2870.4 

78 

37844 

38422 

39000 

39578 

40156 

40733 

41311 

41889 

42467 

677.78 

2H8.9 

« 

.5 

38305 

38887 

39468 

40050 

40631 

41212 

41794 

42375 

42957 

661.46 

2907.4 

•0 

79 

38769 

39354 

39939 

40524 

41109 

41694 

42280 

42865 

43450 

866.19 

2925.9 

> 

.6 

39235 

39824 

40412 

41001 

41590 

42179 

42768 

43357 

43946 

686.88 

2944.4 

80 

39704 

40296 

40889 

41481 

42074 

42667 

43859 

43853 

44444 

693.58 

2963.0 

5 

81 

40650 

41250 

41850 

42450 

43050 

43660 

44250 

44850 

45450 

600.00 

3000.0 

82 

41607 

42215 

42822 

43430 

44037 

44644 

45252 

45859 

46467 

607.41 

3037.0 

ns   . 

83 

42576 

43191 

43806 

44420 

45035 

45650 

46265 

46880 

47494 

614.81 

3074.1 

§J 

84 

43556 

44178 

44800 

45422 

46044 

46667 

47289 

47911 

48533 

683.28 

311L1 

it 

85 

44546 

45176 

45806 

46435 

47065 

47694 

48324 

48954 

49583 

626.83 

8148.1 

86 

45548 

46185 

46822 

47459 

48096 

48733 

49370 

50007 

50644 

687.04 

3185.2 

ll 

87 

46561 

47206 

47880 

48494 

49139 

49783 

50428 

51078 

51717 

644.44 

S3tt.S 

88 

47585 

48237 

48889 

49541 

50193 

50844 

61496 

52148 

52800 

661.85 

8858.3 

e^'V 

89 

48620 

49280 

49939 

60598 

01257 

51917 

52576 

53336 

53694 

669. 2< 

3891.3 

l^ 

90 

49667 

50333 

51000 

51667 

52333 

53000 

53667 

54333 

56000 

666.67 

Sis 

&t 

91 

50724 

51398 

52072 

52746 

53420 

54094 

54768 

56443 

56117 

674.07 

3370.4 

«  5. 

92 

51793 

52474 

53156 

53837 

64519 

55200 

55881 

66863 

67344 

681.48 

3487.4 

"S  o 

93 

52872 

53561 

64250 

54939 

55628 

56317 

57006 

87694 

88383 

688.89 

8444.4 

5 

94 

53963 

54659 

55356 

56062 

56748 

67444 

66141 

8863T 

89831 

666.30 

36B1.9 

il 

95 

55065 

55769 

56472 

57176 

57880 

58583 

59287 

SOffl 

66691 

708.70 

SS-f 

96 

56178 

66889 

57600 

58311 

69022 

69733 

60444 

61166 

6166 

711.11 

Si.* 

^^ 

97 

57302 

58020 

58739 

69457 

80176 

60894 

61618 

68381 

718.61 

8I9.0 

•S 

98 

58437 

59163 

59889 

60615 

61341 

62067 

62783 

68611 

716.96 

Sit 

^ 

99 

69583 

60317 

61050 

61783 

62517 

68350 

63M3 

64717 

ULU 

9mi 

100    i  B0r41 1  61481 

62m    63963 

63704 

64444 

•5188 

fm.14 

Sm 

SLOPE-STAKING.    PRISMOl DAL  FORMULA, 


lOU 


Pig.  10. 


Slopt-S(ildfl|<is  one  of  the  first  operations  after  the  location  has  been 
idopted  and  filed  with  the  proper  authorities  to  secure  condemnation  rights. 
t  coosiits  of  settinff  slope-stakes  at 
otnts  where  the  side  slopes  of  cut  and  fill 
itersect  the  ground  line;  and  embraces 
\so,  in  its  widest  sense,  intermediate 
.TOSs-sectioning"  as  shown  in  Fig.  19. 
be  iUustmtion  shows  the  "grade  rod" 
ethod,  which  is  considered  the  best, 
le  "gnde  rod"  is  the  difference  in  ele- 
tioo  between   the  height    of  instru-  _  ^.  ... 

•nt  and  the  top  of  fill  or  bottom    of  cut.  for  the  station  at   which 
>  slope  stakes  are  to  be  set ;  and  is  used  directly  with  ground-rod  readings. 
us,  for  the  left-hand  slope  stake.  10.2+  2.3 « 12. 6  « distance  belcw  top  of 
and  is  marked  - 12.5.    The  '  distance  out"  (from  center  line  stake) 

— 12  5 
•esponding  to -12.5  is  12.6 Xli+ 7.0-26.8.    Hence       '  :    »  the  pod- 

/O.o 

of  the  sbpe  stake.    Sometimes  two  or  three  trials  have  to  be  made  to 
rt  the  point  which  will  give  the  proper  relation  between  elevation,  and 
ince  from  center, 
rhe  field  notes  are  kept  as  shown  at  the  bottom  of  sketch,  Pig.  10; 

are  on  the  right-hand  pa^e  of  the  note  book,  under  Ltft  -  Center  •  Right, 
he  left-hand  pagtaTeS(aium,Grad€El4vcUum,+S.,  H.  I.,  —5.,  B.  M.  and 
r  Rod,  if  the  complete  records  of  bench  marks  and  turning  points  are 
*  Sometimes,  however,  the  records  of  the  turnings  are  kept  on  loose 
5  and  thrown  away  and  the  balance  of  the  above  notes,  including  the 
section  notes,  are  all  on  the  left-hand  page,  with  an  added  column 
'round  Ekvation;  the  right-hand  page  being  reserved  for  office 
ations  of  quantities  in  excavation  (including  solid  rock,  loose 
nd  earth)  suid  embankment.  The  first  named  method  is  the  best  as 
is  a  complete  record  of  all  field  operations.  The  office  copy  may  be 
form  last  mentioned;  and  it  is  best  to  copy  the  field  notes  every  day 
ce  record. 

"fliwork  Computation  from  cross-section  notes  as  in  Pig.  19,  is 
yy  cutting  the  figure  up  into  triangles,  rectaxigles  and  trapezoids, 
n  be  calculated  directly  from  the  field  notes.    Thus,  the  area  of  the 

mdhalfof  thefigure-^X(26.2-7.0)  +  7.0xi5i±ill.    In  this 

te  that  the  intermediate  cross-section  is  taken  7.0  ft.  out  from 
Dne-hsdf  width  of  roadbed^  a  wise  thing  to  do  where  practicable 
d  an  intermediate  elevation  is  necessary)  as  it  simplifies  office 
on.    On  the  left-hand  side  this  was  not  done  and  we  have  for  area 

Uf  of  fi«ur,:     11.0X  (Ik^ll*)  +  U.SX  (i^^^*)  -  12.»X 

—  )  .     The  deduction  is  for  the  triangle  outside  the  slope  at  T,  as 

luded  in  the  previotis  quantities.  Pig.  17,  page  1016,  presents  the 
orzn  of  sketch  for  computation  and  this  will  obtain  when  only  the 
:  or  fill  is  driven  in  addition  to  the  slope-stake  notes.    Thus,  area 

D-hd),aLndBTe&c+d^^(H+h). 

ction    is   called  a  "three-level" 

rtomoktal  Formula  and  Pris- 
Tectlon  Formula  are  used  for 
'^  determination  of  the  vol- 
rismoids,  "wrhcre  the  method 
£LS**  will  not  suffice.  The  fol- 
jssion  is  based  on  the  "three- 
>n.  F'xg.  20. 

t  — the  ntunbcr  of  the  station,  as  1095+50;  Gradg  EUvatum-^ 
n.  of  sul>-srrade,  i.  e.,  bottom  of  cut  or  top  of  fill;  +5— back- 
rcxi  reading  on  the  bench  nMtrk  (B.  M.)  to  determine  the  height 
it  (//.  /.)  :  —S  — fore-sight,  or  the  rod  reading  to  determine  the 
tvamizis  point  (7.  P.)  or  B,  A/.,  from  the  H.  7. 


Pig.  20. 


1056 


BO.— RAILROADS. 


Let  E   «area  of  the  end   section   £, 
#—   "        **.       "  "        #, 

m=   '*        "       middle  "        m, 
L  — pcrp  dist  between  E  and  e, 
H,  H„  Hx  =  respective  elevations  above  roadbed  at  S, 
hjh,  fct  —         "  "  "  "  #, 

Dt%  D\  >"  respective  distances  out  from  center  at  E, 
D~Dr+a, 
dt,  di  « respective  distances  out  from  center  at  #, 

d~dr  +  di. 

VT- one-half  width  of  roadbed  at  £, 
w-»       **  **  **  #. 

5,  — solidity  or  voliune  by  end  areas, 
Vp  —volume  by  prismoidal  formula. 
Cf  —  onsmoidal  correction  volume  —  ±  (S.  —  Vp  ). 

Then.  E-yCA  +  D.)  +  y  (H,+/f,). 

g^^{dr  +  d,)  +  j{hr+hi),  and  since  IV-w, 

m-^~^(D  +  rf) -1-^  (//,  +  //,  +  *,+*.). 
By  end  areas  in  cu.  ft., 

S  ''^iE+e)^^[HD  +  kd  +  W(Hr  +  Hi  +  hr+fh)] (1) 

By  prismoidal  formiila.  in.  cu.  ft., 

Vf''jiE+im+e)^^[HD+kd+ZW(H,+Hi+hr+hO-¥ 

{H+h)(D  +  d)] (2) 

By  prismoidal  correction,  in  cu.  ft., 

Cp-(S.-Kp)-^(HD+W-fcD-H(i)-^(//-A)(Z?-rf) (3) 

By  prismoidal  correction,  in  cu.  yds.  for  100-ft.  station. 

^'  "T2^^^"*^  ^^"*^"  3T4  ('^-^X^-^') 

-0.308642(H-A)  (D-d) (4) 

The  correction  C,  is  to  be  subtracted  if  (H~h)  (D  —  d)  is  posUivt  (usual). 
The  corrccton  C,  is  to  be  added  if  (/f  —  A)  (D—d)  is  ii^^aiw  (rare). 

The  Prismoidal  Correction  table  on  pages  1067-8  is  made  up  from  the 
following  equivalents,  which  may  be  used  direct,  if  desired: 


(H-kHD-d). 
(Feet.) 

Pris.  Cor.  C^ 
for  100-Ft.  Sta. 
(Cubic  Yards.) 

(H-hHD^d). 
(Feet.) 

Pris.  Cor.  C, 
for  100-Ft.  Sia. 

(Cubic  Yards.) 

1 
2 
3 
4 
6 

.308  642 

.617  284 

.925  926 

1.234  568 

1.543  210 

6 
7 
8 
9 
10 
) 

1.861  853 
3.160  494 
2.409  ISO 

2.777  778 
3.086  430 

Example. — The  following  cross-sections  were  taken  at  stations  1  and  i, 
roadbed  20  ft.  wide,  and  side  slopes  1  on  1: 


Sta.  2. 


Sta.  1. 


LKPT. 

CBNTBR. 

RIGHT. 

+  6.4 

16.4 

+  4.2 

+  3.1 

13. r 

+  8.7 
18.7 

+  5.6 

+  4.3 
14.3' 

~.      A-4.2:  d- 16.4+ 18.1-39 1 


//-5.5:  D- 18.7+ 14.8- J3.0 


Fmd  the  quantity  of  earth  to  be  removed  from  Station  1-2? 

.  Solution.~By  end  areas.  5,    -491 .11  Cu.  Yds. 

Pnsmoidal  correction  for  {H-h)  (£>-d).  +  4.65  -      1.40       " 
Therefore,  by  prismoidal  formula,  quantity -  489 .  71       "        Ana. 


PRISMOIDAL  FORMULA  AND  CORRECTION. 


1057 


100 


42. — pRisMOiDAL  Corrections* 

[Cu.  Yds.  per  100-Ft.  Station.] 


t-if;rT7(«-*>(^-««I- 


*) 

Tenths. 

S)      .0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

) 

.     .3086 
i.     .6173 
I     .9259 
I.     1.235 

.0309 
.3395 
.6481 
.9568 
1.265 

.0617 
.3704 
.6790 
.9877 
1.296 

.0926 
.4012 
.7099 
1.019 
1.327 

.1236 
.4321 
.7407 
1.019 
1.358 

.1543 
.4629 
.7716 
1.080 
1.389 

.1852 
.4938 
.8024 
l.Ul 
1.420 

.2160 
.6247 
.8333 
1.142 
1.451 

.2469 
.5556 
.8642 
1.173 
1.481 

.2778 
.5864 
.8950 
1.204 
1.512 

►.     1.543 
.     1.852 
.     2.160 
.     2.469 
.     2.778 

1.574 
1.883 
2.191 
2.500 
2.809 

1.605 
1.914 
2.222 
2.531 
2.840 

1.636 
1.944 
2.253 
2.562 
2.870 

1.666 
1.975 
2.284 
2.593 
2.901 

1.697 
2.006 
2.315 
2.624 
2.932 

1.728 
2.037 
2.346 
2.654 
2.963 

1.759 
2.068 
2.377 
2.685 
2.994 

1.790 
2.099 
2.408 
2.716 
3.025 

1.821 
2.130 
2.438 
2.747 
3.056 

.     3.086 
.     3.395 
.     3.704 
.     4.012 
.     4.321 

3.117 
3.426 
3.735 
4.043 
4.352 

3.148 
3.457 
3.765 
4.074 
4.383 

3.179 
3.488 
3.796 
4.105 
4.413 

3.210 
3.518 
3.827 
4.136 
4.444 

3.241 
3.549 
3.858 
4.167 
4.475 

3.272 
3.580 
3.889 
4.197 
4.616 

3.303 
3.611 
3.920 
4.228 
4.537 

3  333 
3.642 
3.951 
4.259 
4.568 

3.364 
3.673 
3.981 
4.290 
4  599 

.     4.629 

.     4.938 

5.247 

5.556 

5.864 

4.660 
4.969 
5.278 
5.586 
5.896 

4.691 
5.000 
5.308 
5.617 
5.926 

4.723 
6.031 
5.339 
5.648 
5.957 

4.763 
5.062 
5.370 
5.679 
5.988 

4.784 
5.093 
6.401 
5.710 
6.019 

4.815 
6.123 
6.432 
6.740 
6.049 

4.846 
5.154 
5.463 
5.772 
6.080 

4.877 
5.185 
5.494 
5.802 
6.111 

4.907 
5.216 
5.524 
5.833 
6.142 

6.173 
6.481 
6.790 
7.099 
7.407 

6.204 
6.512 
6.821 
7.130 
7.438 

6.235 
6.543 
6.852 
7.160 
7.469 

6.265 

6.574 
6.883 
7.191 
7.600 

6.396 
6.606 
6.914 
7.222 
7.531 

6.327 
6.636 
6.944 
7.253 
7.562 

6.858 
6.667 
6.975 
7.284 
7.693 

6.389 
6.698 
7.006 
7.315 
7.623 

6.420 
6.728 
7.037 
7.346 
7.654 

6.451 
6  759 
7.068 
7.377 
7.685 

7.716 
8.024 
8.333 
8.642 
8.950 

7.747 
8.056 
8.364 
8.673 
8.981 

7.778 
8.086 
8.395 
8.704 
9.012 

7.809 
8.U7 
8.426 
8.735 
9.043 

7.840 
8.148 
8.457 
8.765 
9.074 

7.870 
8.179 
8.488 
8.796 
9.105 

7.901 
8.210 
8.519 
8.827 
9.136 

7  932 
8.241 
8.549 
8.858 
9.167 

7.965 
8.274 
8.582 
8.891 
9.200 

7.994 
8.302 
8.611 
8.920 
9.228 

9.259 
9.568 
9.877 
10.19 
10.49 

9.290 
9.599 
9.907 
10.22 
10.52 

9.321 
9.630 
9.938 
10.25 
10.56 

9.362 
9.660 
9.969 
10.28 
10.59 

9.383 
9.691 
10.00 
10.31 
10.62 

9.414 
9.722 
10.03 
10  34 
10.65 

9.444 
9.753 
10.06 
10.37 
10.68 

9.475 
9.784 
10.09 
10.40 
10.71 

9.508 
9.817 
10.12 
10.43 
10.74 

9.537 
9.846 
10.15 
10.46 
10.77 

10.80 
11. 11 
11.43 
il.73 
12.04 

10.83 
11.14 
11.45 
11.76 
12.07 

10.86 
11.17 
11.48 
11.79 
12.10 

10.90 
11.20 
11.51 
11.82 
12.13 

10.93 
11.23 
11.54 
11.85 
12.16 

10.96 
11.27 
11.67 
11.88 
12.19 

10.99 
11.30 
11.60 
11.91 
12.22 

11.02 
11.33 
11  64 
11.94 
12.25 

11  05 
11.36 
11.67 
11.98 
12.28 

11.08 
11.39 
11.70 
12.01 
12.31 

12. 85 
U.65 

la.oo 

13.27 
13.  U 

12.38 
12.69 
12.99 
13.30 
13.61 

12.41 
12.72 
18.02 
18.83 
18.64 

12.44 
12.75 
13.06 
13.36 
13.67 

12.47 
12.78 
13.09 
13.40 
13.70 

12.50 
12.81 
13.12 
13.43 
18.73 

12.53 
12.84 
13.15 
13.46 
18.77 

12.56 
12.87 
13.18 
13.49 
13.80 

12.59 
12.90 
13.21 
13.52 
13.83 

12.62 
12.93 
13.24 
13.65 
13.86 

13.80 
14.20 
14.51 
14.81 
15.12 

13.92 
14.23 
14.54 
14.85 
16.15 

18.95 
14.26 
14.67 
14.88 
16.19 

13.98 
14.29 
14.60 
14.91 
15.22 

14.01 
14.32 
14.63 
14.94 

15.25 

14.04 
14.35 
14.66 
14.97 

16.28 

14.07 
14.38 
14.69 
15.00 
15.31 

14.10 
14.41 
14.72 
15.03 
15.34 

14.14 
14.44 

14.75 
15.06 
16.37 

14.17 
14.48 
14.78 
15.09 
15.40 

15.43 

15.46 

15.49 

16.52 

15.56 

16.59 

15.62 

16.65 

15.68 

15.71 
,1 

DrncOt 

cm  totx 

tsubtra 
addtd 

cUdvrh 

en(H- 

'h)(D 

-rf)  is 

positive 
ieealive 

.   (Usu 
.  (Rar 

c.) 

1058 


».— RAILROADS, 


42.— Prismoidal  Corrections*  t-^g^g?^^""*^  (D-d)].— Condudci 
[Cu.  Yds.  per  100-Ft.  Station.] 


(H-*) 

Tentlil. 

(D-d) 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

50. 

15.43 

15.46 

15.49 

15.62 

15.56 

15.59 

15.62 

15.66 

15  68 

15.  Tl 

61. 

15.74 

15.77 

15.80 

15.83 

15.86 

15.90 

15.93 

15.96 

15  99 

i6.a 

62. 

18.06 

16.08 

16.11 

16.14 

16.17 

16.90 

16.23 

16.27 

16.30 

16.U 

63. 

16.36 

16.39 

16.42 

16.45 

16.48 

16.51 

16.54 

16.57 

16  60 

16.44 

54. 

16.67 

16.70 

16.73 

16.76 

16.79 

16.82 

16.86 

16.88 

16.91 

16.N 

55. 

16.98 

17.01 

17.04 

17.07 

17.10 

17.13 

17.16 

17.19 

17.22 

17.25 

56. 

17.28 

17.31 

17  36 

17.38 

17  41 

17.44 

17.47 

17.60 

17.58 

17.56 

67. 

17.59 

17.62 

17.65 

17.69 

17.72 

17.75 

17.78 

17.81 

17.84 

17.8? 

58. 

17.90 

17.93 

17.96 

17.99 

18.02 

18  06 

18.09 

18.12 

18.15 

18.lt 

69. 

18.21 

18.24 

18  27 

18.30 

18.33 

18.36 

18.40 

18.43 

18.46 

18.4* 

60. 

18.52 

18.55 

18.58 

18.61 

18.64 

18.67 

18.70 

18.73 

18.77 

18.8i 

61. 

18.83 

18.86 

18.89 

18.92 

18.95 

18.98 

19.01 

19.04 

19.07 

19,11 

62. 

19.14 

19.17 

19.20 

19.23 

19.26 

19.29 

19.32 

19.35 

19.38 

19.41 

63. 

19.44 

19.48 

19  51 

19.54 

19.57 

19.60 

19.63 

19.66 

19.69 

19.71 

64. 

19.75 

19.78 

19.81 

19.85 

19.88 

19.91 

19.94 

19.97 

20.00 

20.06 

66. 

20.06 

20.09 

20.12 

20.15 

20  19 

20.22 

20.25 

20.28 

20.31 

20.34 

66. 

20.37 

20.40 

20.43 

20.46 

20.49 

20.53 

20.56 

20.59 

20.62 

2115 

67. 

20.68 

20.71 

20.74 

20.77 

20.80 

20  83 

20.86 

20.90 

20.93 

an 

.    68. 

20.99 

21.02 

21.05 

21.08 

21.11 

21.14 

21.17 

21.20 

21.23 

21.27 

I- 
3??: 

21  30 

21.33 

21.36 

21.39 

21.42 

21.45 

21.48 

21.51 

21.54 

21.57 

21.61 

21.64 

21  67 

21.70 

21.73 

21.76 

21.79 

21.82 

21.85 

21.88 

21.91 

21.94 

21  98 

22.01 

22.04 

22.07 

22.10 

22.13 

22.16 

22.19 

8     72. 
a     73. 

22.22 

22.26 

22.28 

22.J1 

22.35 

22.38 

22.41 

22.44 

22.47 

23. » 

22.53 

22.56 

22.59 

22.62 

22.65 

22.69 

22.72 

22.75 

22.78 

23.61 

•«     74. 
S     75. 

5??: 

22.84 

22.87 

22.90 

22.9B 

22.96 

22.99 

23.02 

23.06 

28.09 

23.12 

23.15 

23.18 

23.21 

23.24 

23.27 

23.30 

23.33 

2S.36 

23.40 

23.43 

23.46 

23.49 

23.52 

23.55 

23.58 

23.61 

23.64 

28.67 

23.70 

a.  73 

23.77 

23.80 

23.83 

23.86 

23.89 

23.92 

23.95 

23.98 

24.01 

24.04 

^"    78. 

24.07 

24.10 

24.14 

24.17 

24.20 

24.23 

24.26 

24.29 

24.32 

24  35 

80. 

24  38 

24.41 

24.44 

24.48 

24.51 

24.54 

24.57 

24.60 

24.63 

24U 

24.69 

24.72 

24.75 

24.78 

24.81 

24.86 

24.88 

24.91 

24.94 

24.»: 

i    81. 

"5    82. 

S    83. 

84. 

25.00 

26  03 

26.06 

25.09 

25.12 

25.15 

25.19 

25.22 

25.21 

25.» 

25.31 

26.34 

25.37 

25.40 

25.43 

25.46 

25.49 

25.62 

25.56 

25  i» 

26.62 

25.65 

25.68 

25.71 

25.74 

25.77 

25.80 

25. 8S 

25.86 

tiM 

25.93 

25.96 

25.99 

26.02 

26.05 

26.08 

26.11 

36.14 

26.17 

26.21 

85. 

26.23 

26.27 

26.30 

26.33 

26.36 

26.39 

26.42 

26.45 

U.iM 

26  » 

86. 

26.54 

26.57 

26.60 

26  64 

26.67 

26.70 

26.73 

26.76 

26.79 

26.a 

87. 

26.85 

26.88 

26  91 

26  94 

26.98 

27.01 

27.04 

r.07 

27.16 

».u 

88 

27.16 

27.19 

27.22 

27.25 

27.28 

27.31 

27.35 

27.88 

2T.41 

27.44 

89. 

27.47 

27.60 

27.63 

27.66 

27.59 

r.62 

27.66 

27.69 

27.72 

27.75 

90. 

27.78 

27.81 

27.84 

27.87 

27.90 

27.93 

27.96 

r.99 

28.02 

21  •« 

91. 

28.09 

28.12 

28.15 

28.18 

28.21 

28.24 

28.r 

28.30 

28.33 

7LU 

92 

28.40 

28.43 

28.46 

28.49 

28.52 

28.65 

28.58 

28.61 

28.64 

28-C 

93. 

28.70 

28.73 

28.77 

28.80 

28.83 

28.86 

28.89 

28.92 

28.95 

28.N 

94. 

29.01 

29.04 

29.07 

29.10 

29.14 

29.17 

29.20 

29.23 

29.26 

n.% 

95. 

29.32 

29.35 

29.38 

29.41 

29.44 

29.48 

29.51 

29.54 

29.57 

29.<0 

96. 

29.63 

29.66 

29.69 

29.72 

29.75 

29.78 

29.81 

29.85 

29  88 

»n 

97. 

29.94 

29.97 

30.00 

30.03 

30.06 

30.09 

30.12 

30.15 

30.19 

80.C 

98. 

30.25 

30.28 

30  31 

30  34 

30.37 

30.40 

30.43 

30.46 

90.49 

31.53 

99. 

30.56 

30.69 

30.62 

30.65 

30.68 

30.71 

30.74 

30.77 

30.80 

9B.S 

100. 

30.86 

30.90 

80.98 

30.96 

30.99 

81.02 

81.06 

30.08 

31.11 

31.14 

*  Correction  to  be  subtracted  when  (H-h)  (D-d)  im  posUwe.  CUsaaJ.) 
added  **  "       "ntffolM*.  (Rare.) 


EARTHWORK  COMPUTATION,    HAUL,    ROADBED.      1069 

Comction  for  Conrature,  in  earthwork  computation,  is  very  often 
neglected.  Let  A,  Pig.  21.  be  the  total  area  of  the  cross-section  at  any 
station  on  a  cunre;  dx  the  horizontal  distance 
from  the  center  of  the  section  to  the  center 
of  gravity  oi  A*\  R  the  radius  of  the  curve. 
Then  the  correction  for  ctirvature  may  be  em- 
bodied by  using  a  new  area,  A^^A  1 1  ±^)  » 
and  maintaining  the  distance  between  stations 
as  measured  on  the  center  line;  j^  to  be  added 


Pig.  21. 


if  Ra*  the  radius  to  the  center  of  gravity  of  A,  is  greater  than  R,  and  sub- 
tracted ii  Ra<R.  This  is  based  on  the  theory  that  the  volume  of  a  solid 
of  revolution  is  eqiial  to  the  area  revolved  multiplied  by  the  length  of  the 
path  traced  by  its  center  of  gravity.   From  this,  we  have.  Volume  for  one  sta- 


tion-ilXlOO 


(>41 


but  this  is  clearly  equal  to  100  A  <  —  100i4 


04)- 


one  case  the  length  of  station  is  maintained  while  the  area  of  the  section 
is  considered  to  be  increased  or  decreased;  in  the  other  case  the  reverse  is 
assumed. 

'^HatU"  is  a  term  applied  to  the  average  "lead"  or  horizontal  distance 
between  the  cenitrs  of  gravity  of  the  same  material  "in  place"  and  "in  fill." 
In  Fig.  22.  let  G.  L.  be  the  grade  line.  H  the  haul. 
F.  H.  the  free  haul,  and  O.  H.  the  overhaul  or  paid 
hatil.  Then,  overhaul— haul  — free  haul.  The  free 
haul  may  be  500  ft.  more  or  less,  according  to  the 
specifications  and  contract.  The  centers  of  gravitv 
are  determined  after  the  division  lines  d  are  fixed. 
from  the  estimated  quantities,  in  much  the  same 
way  as  the  center  of  gravity  of  A,  Fig.  21.  was  determined.  "Shrink- 
age" is  a  refinement  which  may  be  considered  if  the  quantities  are  large. 
"Waste"  and  "borrow"  will  affect  haul,  and  notes  should  be  made  (on  the 
profile)  of  the  manner  in  which  all  material  on  the  work  has  been  handled. 

Roadbed. — ^The  sUndard   roadbed   cross-sections   should   be   adopted 
before  the  grade  line  is  established,  in  order  to  equalize  cuts  and  fills,  where 


Fig.  23. 


aecesaary,    during   construction, 
•ftrds.u 


Each    road    has  its  own    standard  or 

rather  standards,  for  the  cross-section  varies  with  the  amount  of  traffic, 
tiei^ht  of  embankment,  whether  on  tangent  or  curve,  main  or  branch 
£ne,  etc.  Fig.  23  shows  about  the  minimum  width  of  roadway  that  should 
30  considered,  namely,  14  ft.  and  18  ft.  at  sub-grade  for  embankment  and 
'xca. vation,  respectively.  These  should  be  increased  rather  than  diminished, 
jsi>ccially  if  on  the  main  line,  with  high  embankment,  on  a  long  curve, 
inder  heavy  traffic.  The  width  of  roadway  in  embankment  on  existing 
•oads  varies  from  12  ft.  (minimum  for  cheap  roads)  to  20  ft.  Allowance 
ntist  be  made  for  shrinkage  of  embankment  as  the  width  of  roadbed  cA  stib- 
Tode  will  narrow  three  times  the  amount  of  vertical  shrinkage,  when  side 
loi>es  arc  IJ  to  1.  For  double  track  lines  the  roadbed  for  single  track  is 
ncreased  by  the  distance  between  track  centers,  say  13  ft.  The  size  of 
litches  in  cuts  will  depend  on  the  length  of  cut,  amount  of  drainage,  and 
Iop»e  of  ditch.    Drain  tile  should  be  placed  below  the  frost  line. 

♦  A  —  Oi-l-at-l-oi-l-a*:  and  JA=[a2((ii-Jv)+a3((fi  +  <f3)  +  a«(<'t+<i«)M-*'i- 


1060  m.—RAILROADS, 

Rails  and  Fastenings. — Rails  are  roHed  usoaUy  in  30-ft.  lengths, 
although  33-ft.  rails  have  lately  been  introduced  on  main -line  track.  Shorter 
lengths.  varyin|:  by  two  feet,  or  even  by  one  foot,  are  furnished  for  pre- 
serving "opposite'  or  "broken"  joints  in  track  laid  on  curvM,  and  for 
switch  "leads,"  etc.  Rails  arc  designated  by  the  "weight  per  yard."  as 
60-lb..  70-lb..  80-lb.,  etc.  For  instance,  a  30-ft.  80-lb  rail  will  weigh  800 lbs. 
In  order  to  decrease  the  number  of  existing  standard  rail  sections  and  the 
consequent  expense  in  rolling,  as  well  as  to  improve  the  type  and  facilitate 
quick  delivery  from  the  mills,  the  Am.  Soc.  of  C.  E.,  in  1893,  adopted  a 
standard  type  called  the  "American  Society  Standard,"  shown  in  Fig.  24 
and  in  Table  43,  following. 

Splices  for  rail  joints  have  developed  from  the  primitive  "chair" 
which  simply  gave  vertical  support  to  the  rail  joint  plaoeci  directly  over  the 
tie,  to  the  'fish  plate"  (invented  in  the  early  40  s)  which  gave  mrtical 
stiffness  to  the  joint  (see  Fig.  27.  below),  and  later  to  the  "angle  bar" 
which  gives  lateral  as  well  as  vertical  stiffness  to  the  joint.  Many  improved 
forms  of  angle  bars  have  appeared  on  the  market  from  time  to  time,  but 
only  those  of  uniform  cross-section,  that  can  be  rolled  continuously,  haw 
become  standard.    Figs.  24,  26  and  28  show  standard  types. 

Bolts  for  fastening  the  splice  bars  to  the  rail  are  often  provided  with 
lock-nuts  to  prevent  the  bolts  from  working  loose,  or  at  least  £rom  wotking 
loose  too  rapidly.  One  of  the  simplest  and  perhaps  most  common  forms  is 
a  steel  ring  of  square  or  hexagonal  section  cut  beveled  with  sharp  comers 
and  forming  a  complete  spiral  curve  of  one  turn.  This  is  placed  on  the  bolt 
and  when  the  nut  is  screwed  on,  the  spiral  form  of  the  lock-nut  is  compressed 
to  a  nearly  circular  form,  and  the  sharp  points  pressing  against  the  steel  on 
cither  side  prevent  the  nut  and  bolt  from  loosening.  Weights  and  dimen- 
sions of  splice  bolts  are  given  in  Table  43. 

Tablr  43,  giving  standard 
dimensions  of  rails,  splice 
plates  and  bolts,  will  be 
found  on  the  two  following 
pages.  The  accompanying 
illustrations,  Figs.  24,  26  and 

27,  are  also  a  part  of  this  ^ 

table,  as  per  references  given 
therein.  Fig.  24  is  the  Am. 
Soc.  C.  £.  Standard  rail  sec- 
tion (see  pages  1061-2).  Figs. 
26  and  27  are  Penn.  Steel  Co. 
standards  (see  page  1062). 
Figs.  25  and  28,  with  tables 
of  dimensions,  will  be  found 
on  pages  1061  and  1062.  re- 
spectively. Fig.  24. 


Pig.  27.  Digitp^y  google 


RAILS.  SPUCES  AND  BOLTS. 


1061 


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S§^ 

RAILS  AND  FASTENINGS.    MIDDLE  ORDI NATES,      1068 

For  Single  Track,  the  number  of  80-ft.  nils  required  per  mile  of  track 

-^^—^^-352;  of  38-ft.  rails.  320;  of  50-ft.  rails,  211.2.  Tke  number  of  jftorf 

ms  (of  2000  lbs.)  per  mile  of  single  track—  1.76Xwt.  in  Ibe.  of  single  rail 
er  vd.;  thusjtnere  are  required  176  short  tons  of  100-lb.  rails  per  mile  of 
iigle  trade.  The  number  of  long  tons  (of  2240  lbs.)  per  mile  of  single  track 
'  VXwt  in  lbs.  of  single  rail  per  yard.;  thus,  there  are  reqxured  r67^  long 
ms  of  100-lb.  rails  per  mile  of  single  traick.  For  00-lb.  rails,  mult.  176  and 
S7^,  respectiTely,  by  A;  for  80-lb.  rails,  mult,  by  A;  etc. 

44.^Wbight  of  Rails  per  Yard  Reduced  to  Tons  per  Mils  or 

Single  Track. 

(Short  tons  at  2000  lbs.;  long  tons  at  2240  lbs.) 


m. 

Short 

Long 

Wt. 

Short 

Long 

Wt.  , 

Short 

Long 

ard. 
Lbs. 

Tons 

Tons 

\^d. 
Lbs. 

Tons 

Tons 

Lbs. 

Tons 

Tons 

11^. 

MUc. 

1^. 

^L 

^e. 

aES. 

8 

14.08 

12V7 

56 

98.56 

88          76 

133.76 

119«/7 

12 

21.12 

18»/7 

57 

100.32 

89V7 

78 

137.28 

122«/7 

16 

28.16 

25i/7 

60 

105.60 

94«/; 

80 

140.80 

125»/7 

26 

44.00 

39»/7 

62 

109.12 

97»/7 

85 

149.60 

133«/7 

30 

52.80 

471/7 

64 

112.64 

100«/7 

90 

158.40 

I4IV7 

35 

61.60 

65 

65 

114.40 

102V7 

95 

167.20 

149«/7 

40 

70.40 

62«/7 

68 

119.68 

ioe«/7 

100 

176.00 

157i/T 

45 

79.20 

7OS/7 

70 

123.20 

110 

105 

184.80 

165 

50 

88.00 

78^/7 

72 

126.72 

113»/7 

no 

193.60 

172«/7 

52 

91.52 

8IV7 

75 

132.00 

117«/7 

120 

211.20 

188«/7 

Note. — ^Values  in  above  table  are  exact.  Fractions  of  long  tons  may  be 
teed  to  decimals  of  long  tons  and  to  potmd  equivalents  as  follows: 
M4286  1.t.-320  1bs.:  f  - 0.28571  1. 1.- 640  lbs.;  f  » 0.42857  1. 1.- 960 
«-0.57143  l.t.- 1280  lbs.;  f-0.714291.t.- 1600  lbs.;  f-0.857141.t.- 
Mbs. 

Yiiddle  Ordinates  for  "bending"  (curving)  rails,  to  be  laid  on  curves, 
be  obtained  from  the  following  formulas: 


g^  (practically  exact) ;  or,  M*  — 


.001L*D 
9X6 


(nearly  exact) . 


-,,,     .004L«D  ,        ,  ,, 

or,  M"  -  —J^f~  (nearly  exact) . 


.(1) 
.(2) 


3L* 

'  ■5j5"(P*'*ct*ca^^y  c^cact); 

lich  M'  — middle  ordinate  to  the  cturvcd  rail,  in  ft  ft; 
Af"  — middle  ordinate  to  the  curved  rail,  in  incfus; 
L— len^h  of  rail  in  feet; 
i?—radius  of  curve  in  feet; 
D  ■>■  degree  of  curve  in  degrees  and  decimals. 
crte  that  in  the  above  formulas  either  the  radius  or  the  degree  of  curve 
yc  tased,  both  being  exact  for  the  flat  curves,  say  up  to  4°  or  5°.   For  a 
rail  and   10*  curve,  the  "radius"  formula  gives  Af'- 0.196  (exact), 
tlie    "degree  of  curve"  formula  gives  M' -0.200  (2%  large);  same 
r  20**  curve  gives  Af'  — 0.391  and  M'=- 0.400,  respectively,  instead  of 
the  correct  value.     For  shorter  rails  the  errors  decrease,  hence  it 
I   that  either  formula  may  be  used  for  all  practical  purposes. 


d  by  Google 


1064 


Si.'-RAILROADS, 


45. — ^MiDDLB  Ordinatbs  in  Inchbs  for  Curving  Rails. 

(Degrees  of  ctirve  and  radii  are  for  100-ft.  chords.) 

For  Ordinates  in  Feet,  see  Table  46. 

Note. — Ordinates  are  practically  proportional  to  the  square  of  length  of 

rail.   Thus,  for  60-ft.  rail,  mult,  value  for  30,  by  4;  for  45-ft.  rail,  mult  value 

for  30,  by  2Hl  for  8-ft.  rail,  divide  value  for  16.  by  4;  etc. 

[Middle  Ordinates,  in  Inches.] 


Length  of  Rail,  or  Arc,  in  Feet. 


T  K?*^*^iA —  *^  reduction  of  inches  and  fractions  to  decimals  of  a  foot,  see 
labie  10,  page  223.  No  particular  refinement  is  necessary  in  curvins  raiU: 
ordmates  to  the  nearest  Ji'  are  close  enough,  usually. 

1  ne  quarter  ordinates  are  practically  thnec-fourths  the  middle  ordinate 


ORDINATES  FOR  CURVING  RAILS. 


1065 


40. — ^MiDDLB  Ordinatbs  in  Pbbt  for  CimviNo  Rails. 
(Degrees  of  curve  and  radii  are  for  100-ft.  chords.) 
For  Ordinates  in  Inches,  see  Table  45. 
Note.— Ordinatcs  are  practically  proportional  to  the  square  of  length  of 
Thus,  for  60-ft.  rail,  mult,  value  for  30,  by  4;   for  45-ft.  rail,  mult. 
le  for  30.  by  2H\  for  8-ft.  rail,  divide  value  for  16,  by  4,  etc. 


[Middle  Ordinates,  in 

Feet.] 

Rad- 

his. 
Feet. 

Length  of  RaU.  or  Arc  In  Feet. 

100 

60 

33 

30 

28 

26 

24 

22 

20 

18 

16 

14 

12 

10 

11459.2 

.109 

.027 

.012 

.010 

.008 

.006 

.006 

.004 

.004 

.003 

.002 

.002 

.001 

.001 

B729.7 

.217 

.054 

.024 

.020 

.016 

.013 

.011 

.009 

.008 

006 

.005 

.004 

.003 

.002 

88l9.fl 

.327 

.082 

.036 

.029 

.028 

.021 

.018 

.016 

.013 

.010 

.008 

.006 

.004 

.003 

1864.9 

.436 

.109 

.047 

.038 

.034 

.029 

.025 

.021 

.017 

.014 

.011 

.008 

.006 

.004 

2392.0 

.546 

.136 

.059 

.049 

.043 

.037 

.031 

.027 

.022 

.018 

.014 

.010 

.007 

.005 

1910.1 

.655 

.164 

.071 

.058 

.051 

.044 

.037 

.031 

.026 

.022 

.017 

.012 

.009 

.006 

1637.8 

.763 

.191 

.083 

.070 

.061 

.052 

.043 

.037 

.031 

.025 

.020 

.015 

.011 

.008 

1433.7 

.872 

.218 

.095 

.079 

.069 

.060 

.050 

.042 

.035 

.029 

.023 

.018 

013 

.009 

1373.6 

.982 

.245 

.107 

.088 

.077 

.067 

.056 

047 

.039 

.032 

.026 

.020 

.015 

.010 

1146.3 

1.090 

.273 

119 

.099 

086 

.074 

.063 

.053 

.044 

.035 

.029 

.022 

.016 

Oil 

1043.1 

1.199 

.300 

.131 

108 

.094 

.082 

.070 

.059 

.048 

.039 

.032 

.024 

.018 

.012 

95&.4 

1.308 

.327 

.143 

.117 

.103 

.088 

.076 

.064 

.052 

.042 

.034 

.026 

.019 

.013 

881.9 

1.417 

.354 

.154 

.128 

113 

.097 

.083 

.069 

.057 

.046 

.037 

.028 

.021 

.014 

819.0 

1.525 

.381 

.166 

.137 

.120 

104 

.088 

.074 

.061 

.049 

.039 

.030 

.022 

.015 

764.5 

1.634 

.408 

.178 

.146 

.127 

.111 

.094 

.079 

.065 

.053 

.042 

.032 

.024 

.016 

716.8 

1.743 

.436 

.190 

.158 

.137 

.119 

.100 

.085 

.070 

.066 

.045 

.034 

.025 

.017 

674.7 

1.851 

.463 

.203 

166 

.145 

.126 

.106 

.090 

.074 

.060 

.048 

.036 

.027 

.018 

637.3 

1.9S1 

.490 

214 

.175 

.153 

.133 

.112 

.095 

.078 

.063 

.050 

.038 

.029 

.019 

603.8 

2.069 

517 

.225 

.187 

.163 

.141 

.119 

.101 

.083 

.067 

.054 

.042 

.031 

.021 

173.7 

3.178 

.545 

.237 

.196 

.171 

.148 

.125 

.106 

.087 

.071 

.057 

.045 

.032 

.022 

521.7 

1.394 

.598 

.261 

.216 

.188 

.163 

.139 

.117 

.096 

078 

.063 

.049 

.036 

.024 

478  3 

2.611 

.653 

.284 

236 

.206 

.179 

.161 

.128 

.105 

.085 

.069 

.053 

.039 

.026 

441.7 

3.828 

.707 

.308 

.254 

.222 

.192 

.163 

.138 

.113 

.092 

.075 

.057 

.042 

.028 

410.3 

3.043 

.761 

.332 

.276 

.239 

.207 

.175 

.148 

.122 

.099 

.080 

.061 

.045 

.030 

383.1 

3.258 

.816 

.356 

.295 

.257 

.223 

.188 

.159 

.131 

.106 

.085 

.065 

.049 

.033 

359.3 

3.474 

.870 

,379 

.313 

.273 

.236 

.200 

.170 

.139 

.113 

.091 

.070 

.052 

.035 

338.3 

3.688 

.924 

.403 

.333 

.290 

.252 

.213 

180 

.148 

.120 

.096 

.074 

.055 

.037 

319.6 

3.903 

.978 

.426 

.351 

.306 

.266 

225 

.190 

.156 

.127 

.103 

.078 

.058 

.039 

303.9 

4.117 

1.031 

.450 

.871 

.324 

280 

.238 

.201 

.165 

.134 

.108 

.083 

.061 

.044 

387.9 

4.330 

1.085 

.473 

392 

.341 

.296 

.250 

.212 

.174 

.141 

.114 

.087 

.066 

.041 

274.4 

4.543 

1.138 

.496 

410 

.357 

.309 

.262 

222 

.183 

.148 

.120 

.091 

.069 

.046 

263.0 

4.756 

1.192 

.520 

430 

.375 

.325 

.275 

.233 

.191 

.155 

.126 

.096 

.072 

.048 

350  1 

4.968 

1.245 

.543 

.450 

.390 

.338 

.287 

.243 

.199 

.162 

.131 

.100 

.075 

.050 

240.8 

5.178 

1.298 

566 

469 

.408 

.354 

.299 

.253 

.208 

.169 

.137 

.104 

.078 

.052 

231.0 

5.390 

1.351 

.588 

486 

.424 

.367 

.311 

.263 

.216 

.176 

.142 

.108 

.081 

.054 

323.3 

6.600 

1.404 

.612 

.506 

.441 

.383 

.323 

.274 

.226 

.183 

.148 

.112 

.084 

.056 

214.2 

5.810 

1.457 

.635 

.524 

.467 

.396 

.335 

.284 

.233 

.190 

.153 

.116 

.087 

.058 

206.7 

6.019 

1.510 

.658 

645 

.476 

.411 

.348 

.294 

.242 

.197 

.158 

.120 

.090 

.060 

199.7 

i.226 

1.563 

.681 

.564 

491 

.424 

.361    .303 

250 

.203 

.163 

.124 

.093 

062 

193  2 

6.434 

1.615 

.704 

.582 

.507 

.438 

.373  '313 

.259 

.210 

.168   .128 

.096 

.064 

Note. — ^For  reduction  of  decimals  of  a  foot  to  inches  and  fractions,  see 
le  10.  page  223.    No  partictilar  refinement  is  necessary  in  curving  rails: 
nates  to  the  nearest  n'  are  close  enoiigh,  usuallv. 
The  quarter  ordinates  are  practically  three-fourths  the  middle  ordinate. 


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1066 


m.— RAILROADS. 


47.— Chord  Lbnotbs  op  Curvbd  Rails. 

(Degrees  of  curve  and  radii  are  for  100-ft.  chords.) 

[Chord  Lengths,  in  Feet.] 


o 

Radius. 
Feet. 

LengtH  of  Rafl.  or  Arc  In  Feet. 

1^ 

100 

50 

33 

30 

26 

22 

18 

14 

»• 

2 
4 

6 

2864.9 
1432.7 
956.4 

99.995 
99.980 
99.954 

49.999 
49.997 
49.994 

33.000 
32.999 
32.998 

30.000 
30.000 
29.999 

26.000 
26.000 
26.000 

22.000 
22.000 
22.000 

18.000 
18.000 
18.000 

14.000 
14.000 
14.000 

le.oM 
lion 

8 
10 
12 

716.8 
573.7 
478.3 

99.919 
99.871 
99.818 

49.990 
49.983 
49.977 

32.997 
32.996 
32.994 

29.998 
29.997 
29.996 

25.999 
26.998 
25.997 

22.000 
21.999 
21.998 

18.000 
18.000 
17.999 

14.000 
14.000 
14.000 

10.0DO 

10.  iW 
lOMft 

14 
16 
18 

410.3 
869.3 
319.6 

99.753 
99.677 
99.593 

49.969 
49.960 
49.949 

32.991 
32.988 
32.985 

29.993 
29.991 
29.989 

26.996 
25.994 
25.993 

21.997 
21.997 
21.996 

17.999 
17.999 
17.998 

18.999 
13.999 
13.999 

16.696 
10.000 

loooe 

20 
22 
24 

287.9 
262.0 
240.5 

99.498 
99.394 
99.281 

49.937 
49.924 
49.910 

82.982 
32.978 
32.974 

29.986 
29.984 
29.981 

25.991 
25.989 
25.987 

21.995 
21.994 
21.993 

17.997 
17.996 
17.996 

13.999 
13.998 
13.998 

9.911 
9.991 
9.99S 

26 
28 
30 

222.3 
206.7 
193.2 

99.157 
99.027 
98.887 

i9.894 
49.878 
49.860 

32.970 
32.965 
32.960 

29.978 
29.974 
29.970 

25.985 
25.983 
25.980 

21.992 
21.990 

21.988 

17.995 
17.994 
17.993 

13.998 
13.997 
13.997 

9.991 
9.9?* 
9.9»» 

Note. — For  reduction  of  decimals  of  a  foot  to  inches  and  fractkms.  see 
Table  10.  page  223. 


To  Find  the  Dborbb  of  Curvature  of  Laid  Track. 
(See  Formulas  1  and  2.  and  Notation,  page  1068.) 

On  maintenance  work  it  is  often  necessary  to  find  the  degree  of  curva- 
ture of  laid  track,  on  a  curve  which  has  been  more  or  less  shifted  and  de- 
ranged by  the  trackmen;  and  then  to  run  in  a  regular  or  a  spiral  curve 
which  will  best  fit  the  existing  track:  so  as  to  require  the  least  possible 
shifting  of  the  latter. 

From  the  approximate  formtilas  (1)  and  (2),  page  1063,  it  will  be  seen 
that  there  are  direct  ratios  between  the  degree  of  ctu-ve  (2?),  the  curved 
length  of  rail  (L),  and  the  middle  ordinate  (Af)-  If  Z>  is  in  degrees,  and  L 
and  M  in  feet,  we  have,  by  transposition. 

2>«  — j^ —  (approxmiate) (3) 

For  a  100-ft.  length  of  rail,  L-lOO,  hence, 

Z?— 4.6  M  (approximate) (*1 

-4.58  M  (nearly  exact) (5. 

For  a  30-ft.  length  of  rail,  L— 30,  hence, 

Z?=50  M  (approximate) («> 

="51  M  (nearly  exact) Ci) 

For  a  21'  3*  length  of  rail, 

P— the  middle  ordinate  in  htmdredths  of  a  foot. (8) 


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d  by  Google 


1068 


S^.'-RAILROADS. 


Track  SpOccSt  or  railrocul  spiket-as  tHey  are  commonly  called,  are  square 
in  cro8s-6ection.  with  a  flared  hook  head  and  wedge  pomt.  Spikes  ot  the 
same  size  vary  considerably  in  weight,  but  the  following  table  shows  an 
average,  and  assumes  10660  spikes  per  mile  of  single  track. 


49. — ^Track  Spikbs. 


Size  Meas. 
Under 

Average 
Wt. 

Average 
Number 

Quantity  of  Spikes  per 
Mile  of  Single  Track. 

Rails  Used. 
Weight  per 

Head. 

of  100 

per  Keg 

Ties  2  feet  c.  to  c. 

Yani. 

Spikes. 

of 

4  spikes  per  tie. 

Inches. 

Poimds. 

200  Potmds 

Pounds. 

Pounds. 

Kegs. 

64  X 
6|x 

[ 

66.67 

300 

7040 

86.20 

76tol00 

\ 

63.33 

376 

6630 

28.16 

46  ••     76 

6  x; 

60.00 

400 

6280 

26.40 

40  "     66 

6   X 

44.44 

460 

4690 

23.47 

85  "     40 

4ix 

37.74 

630 

3990 

19.93 

30  "     36 

4    X 

33.33 

600 

3620 

17.60 

25   '     36 

4ix^ 

29.41 

680 

3110 

15.63 

20   •     30 

4    xX 

27.78 

720 

2930 

14.67 

20  "     80 

3ix$ 

22.22 

900 

2360 

11.78 

16  "     25 

4    xi 

20.00 

1000 

2110 

10.56 

16  *•     26 

3ixl 

16.81 

1190 

1770 

8.87 

16  •'     20 

3    x| 

16.13 

1240 

1700 

8.62 

16  ••     20 

2ix| 

14.98 

1340 

1680 

7.88 

8  *•     16 

Note. — ^There  are  4  spikes  per  tie.    The  above  table  assumes  the  ties  to 
be  spaced  24'  centers.    For  other  spacing  allow  as  follows: 
For  main  line,  1 6  ties  to  30-ft .  rail,  incrtast  values  in  cols.  4  and  6  by  ^. 

17       •'       33-ft.   *•        *•  A. 

18       ••       33-ft. Jfc. 

"  sidings,       14       "       30-ft.   "   decrfOM      "         '*  "         "   ^. 


Rail  Joints  are  almost  tmiversally  "square."   That  is,  the  rails  are  cut 
ofi  square  as  they  come  from  the  rolls.    Such  a  joint  is  sh6wn  at  5  in  Pig.  29. 


^^^ 


L 


Fig.  29. — Square,  Miter  and  Lap  Joints. 

In  the  same  Fig.  the  "miter"  joint  is  shown  at  M,  and  the  "lap"  joint  at  L 
The  miter-  or  beveled  joint  is  made  by  sawing  off  the  rails  on  a  bevel  of. 
say,  46**  to  60**  or  66".  The  advantage  claimed  was  that  hnger  rails  could  be 
used  with  reduced  effect  of  "hammering"  on  rail  ends  by  trains,  as  the  open 
joints  caused  by  temperature  contraction  of  rail  would  be  robbed  of  their 
ill  effects  if  beveled.  Steel  rails  will  vary  about  .0008  of  their  lenfrlh  under 
a  change  of  temperature  of  120®  F.;  hence  30-ft.,  rails  if  laid  with  dosed 
joints  at  +  100°F.  will  have  between  \  and  A  hi«  joints  when  the  tempcra- 
ttire  falls  to  20*^  below  zero.  The  miter  joint  has  never  come  into  goieral 
use.  It  was  formerly  used  quite  extensively  on  the  Lehigh  Valley  K.  R., 
and  may  now  be  seen  there,  but  it  has  generally  been  replaced  with  the 
square  rail  joint.  The  lap-  or  scarf  joint,  L^  claims  the  advantage  of  the 
miter  joint  above  mentioned;  in  addition,  it  is  free  from  danger  of  any 
projecting  point  catching  a  wheel  flange,  especially  if  the  track  is  curved. 
It  the  lap  IS  long  the  joint  is  stiffened  vertically,  a  decided  advantage.  It  is 
seldom  if  ever  emptoyed  in  the  United  States. 


TRACK  SPIKES.    RAIL  JOINTS,    CROSS  TIES. 


1060 


"Shims"  are  pieces  of  wood  or  iron  iaierted  at  raaljoints  when  track  is 
laid,  in  order  to  give  the  proper  spacing  of  joint.  The  thickness  of  the 
shim  depends  upon  the  temperature.  A  good  rule  for  thickness  of  shim 
is  the  foibwing: 

S-.00128L(r-O 
in  viiich  5 -thickness  of  shim,  in  Itlhs  of  an  inck\ 
Z." length  of  rail,  in  feet; 

r- "hottest"  temp,  to  be  expected  in  that  locality,  in  degs.  F. 
/■"prevailing  temp,  when  track  is  laid,  in  degs.  r. 
The  Suspended  Joint  (i.  e.,  where  the  joint  comes  between  two  sup- 
porting ties)  has  practically  superseded  the  "supported"  joint  which  rests 
directly  on  a  single  tie  with  the  usual  spacing.  But  better  still,  by  far,  is  the 
use  of  three  ties  doselv  spaced  at  each  joint  with  angle-  or  splice  bars  long 
enough  (say  3i  to  4  ft.)  to  get  direct  support  from  the  two  outside  ties. 
Such  an  arrangement  may  properly  be  called  a  3-tie  "supported"  joint. 

Alternate.  Staggered  or  Broken  Joints  are  usually  preferred  on  main 
line  to  the  "opposite"  or  "even"  joints.  The  advantages  of  "broken"  joints 
are:  (1)  The  intensity  of  shock  due  to  passing  trains  is  reduced  about  50% 
although  the  number  of  shocks  is  doubled;  (2)  the  track  can  be  kept  m 
better  surface  and  line  on  tangents;  (3)  on  curves,  one  line  of  rails  stiffens 
he  other  at  the  joints  and  aids  in  preserving  uniform  curvature  even  if  the 
ails  were  not  curved  properly  prior  to  laying.  The  advantage  of  "opposite" 
oints  is  purely  one  of  cost  in  tracklaying.  and  hence  for  second-class  yards, 
ir  for  slow  train  service  generally,  they  may  do. 

Crass  Ties. — Ordinary  track  ties  are  usually  8  or  8}  ft.  long;  bridge  ties 
M*  single  track.  12  ft.;  and  switch  ties,  up  to  15  ft.  or  more  m  length. 

TablesfiOand  51,  respectively,  give  the  number  of  cubic  feet  and  feet 
oard  measure  in  ties  of  various  dimensions. 

Tables  52  and  53  are  bills  of  switch  ties  for  No.  6  and  No.  8  frog,  respec- 
vely.  To  find  the  bill  of  material  for  any  other  frog:  Draw  the  switch  to 
ale.  and  scale  off  the  lengths  of  ties.  (For  turnouts  and  switches,  see 
i^e  1075.) 


50. 


-Cubic  Fbbt  in  Woodbn  Tibs  of  Various  Dimensions. 
[Cubic  Feet.] 


rth. 

Sectional  Dimension.  Id  Inches. 

J 

6x8 

6x» 

6X10 

7X8 

7x9 

7x10 

8x10 

8x  12 

9x10 

9x12 

1       .028 

.031 

.035 

.032 

.036 

.042 

.046 

.056 

.052 

.063 

2       .056 

.063 

.069 

.065 

.073 

.081 

.093 

.111 

.104 

.125 

3       .083 

.094 

.104 

.097 

.109 

.122 

.139 

.167 

.156 

.188 

6        .167 

.188 

.208 

.194 

.219 

.243 

.278 

.333 

.313 

.375 

9        .250 

.28! 

.313 

.292 

.328 

.365 

.417 

.600 

.469 

.563 

.333 

.875 

.417 

.389 

.438 

.486 

.556 

.667 

.625 

.750 

.W7 

.750 

.833 

.778 

.875 

.972 

1.111 

1.333 

1.250 

1.500 

1.000 

1.125 

1.360 

1.167 

1.313 

1.458 

1.667 

2.000 

1.875 

2.250 

2.000 

3.250 

3.500 

2.333 

2.625 

2.917 

3.333 

4.000 

3.750 

4.500 

2.M7 

3.000 

3.333 

8.111 

3.500 

3.889 

4.444 

6.333 

5.000 

6.000 

6      2.833 

3.188 

3.542 

8.306 

3.719 

4.132 

4.722 

6.667 

5.313 

6.375 

3.000 

3.375 

8.750 

3.500 

3.938 

4.375 

6.000 

6.000 

5.625 

6.750 

3.333 

8.750 

4.167 

3.889 

4.375 

4.861 

5.556 

6.667 

6.250 

7.500 

3.667 

4.125 

4.583 

4.278 

4.813 

5.347 

6.111 

7.333 

6.875 

8.250 

/  4.000 

4.500 

6.000 

4.667 

5.250 

5.833 

6.667 

8.000 

7.500 

9.000 

1  4.333 

4.875 

6.417 

5.056 

5.688 

6.319 

7.222 

8.667 

8.125 

9.750 

1  4.067 

5.250 

5.833 

5.444 

6.125 

6.806 

7.778 

9.333 

8.750 

10.500 

1  5.000 

5.625 

6.250 

5.833 

6.563 

7.292 

8.333 

10.000 

9.375 

11.250 

/  5.333 

6.000 

6.667 

6.222 

7.000 

7.778 

8.889 

10.667 

10.000 

12.000 

1  5.607 

6.375 

7.083 

6.611 

7.438 

8.264 

9.444 

11.333 

10.625 

12.750 

1  6.000 

6.760 

7.500 

7.000 

7.875 

8.750 

10.000 

12.000 

11.260 

13.500 

X. — A  tie  rx»'xl0'6'  will  contain  (4.375+. 219-)4.594  cu.  ft.; 
such  ties  at  48  lbs.  per  cu.  ft.  will  weigh  220,500  lbs. 


and 


d  by  Google 


1070 


m.— RAILROADS. 


51. — ^Pbbt  Board  Mbasurb  (B.  M.)  in  Woodbn  Tibs  op  Vaxiovs 

DiMBNSIONS. 

(See  also  Table  4.  Section  20.) 
[Ft.  B.  M.J 


Lgth. 

Sectional  Dimenalon.  In  Inches. 

6x8 

6x9 

6x  10 

7x8 

7x9 

7X10 

8X  10 

8X12 

9X10 

»xU 

.33 

.38 

.42 

.89 

.44 

.49 

.56 

.67 

.63 

.75 

.67 

.75 

.83 

.78 

.88 

.97 

1.11 

1.33 

1.25 

1.S6 

1.00 

1.13 

1.26 

1.17 

1.31 

1.46 

1.67 

2.00 

1.88 

2.2S 

2.00 

2.25 

2.50 

2.33 

2.63 

2.92 

8.83 

4.00 

S.75 

4.91 

3.00 

3.38 

3.75 

3.50 

3.94 

4.38 

5.00 

6.00 

5  63 

6.7$ 

4.00 

4.50 

5.00 

4.67 

5.26 

6.83 

6.67 

8.00 

7.60 

9.M 

8.00 

9.00 

10.00 

9.33 

10.50 

11.67 

13.33 

16.00 

16.00 

18.  M 

12.00 

13  50 

15.00 

14.00 

15.75 

17.50 

20.00 

24.00 

23.50 

27.69 

24.00 

27.00 

30.00 

28.00 

81.50 

35.00 

40.00 

48.00 

46.00 

54.66 

32.00 

36.00 

40.00 

87.33 

42.00 

46.67 

53.33 

64.00 

60.06 

72.66 

8    6 

34.00 

38.25 

42.50 

89.67 

44.63 

49.58 

56.67 

68.00 

63.76 

76.50 

36.00 

40.50 

45.00 

42.00 

47.25 

52.50 

60.00 

72.00 

67.50 

81.00 

40.00 

45.00 

50.00 

46.87 

62.50 

58.33 

66.67 

80.00 

75.00 

90.00 

44.00 

49.60 

55.00 

51.33 

57.76 

64.17 

73  33 

88.00 

83.60 

99.06 

48.00 

54.00 

60.00 

56.00 

63.00 

70.00 

80.00 

96.00 

90.00 

108.01 

52.00 

58.50 

65.00 

60.67 

68.25 

76.83 

88.67 

104.00 

97.60 

117.M 

56.00 

63.00 

70.00 

65.33 

73.50 

81.67 

93.33 

112.00 

105.00 

126.60 

60.00 

67.50 

76.00 

70.00 

78.76 

87.60 

100.00 

120.00 

]12.8e 

135.90 

64.00 

72.00 

80.00 

74.67 

84.00 

93.33 

106.67 

128.00 

110.00 

144.60 

68.00 

76.50 

85.00 

79.33 

89.25 

99.17 

113.33 

136.00 

127.50 

153.60 

18 

72.00 

81.00 

90.00 

84.00 

94.50 

106.00 

120.00 

144.00 

136.00 

162.00 

Ex.— A  tie  S'xlO'xn'r  will  contain  (80.000+ 1.607-)  81.607  ft.  B.  M.; 
and  1000  such  ties  will  contain  81067  ft.  B.  M. 


62. — Bill  of  Switch  Tibs  for  No.  6  Froo. 
(S'xlO*  is  a  good  size;  lengths  are  given  to  nearest  3*.) 


Length 

Length 

ii 

Length 

6-$ 

Length 

6p. 

Length  ij" 

Length 

2 
6 
2 
3 

8'  3* 
8'6' 

1 

2 
2 

1 

9'  3* 

9'  6* 

9' 9* 

10'  0* 

1 
1 
1 
1 

10'  3* 
10'  6" 

10'  r 
irc 

1 
1 
1 

1 

11'  8* 
11' 6' 
11'  9* 
12' 0* 

1 

1 
1 

1 

12' 6*       1 
12' 9*       3 
13' 0*       1 
13'  3* 

ir  «* 

14' O' 

14' 3* 

Total  lin.  ft.  in  above  bill,  using  exact  lengths—  380  lin.  ft. 
Total  lin.  ft.  in  above  bill,  using  1-ft.    lengths—  303  lin.  ft. 


63. — Bill  of  Switch  Tibs  for  No.  8  Proo. 
(8'xlO*  is  a  good  size;  lengths  are  given  to  nearest  V.) 


IS. 

Lgth.j^S" 

Lgt;h. 

it 

Lgth. 

111 

Lgth. 

M 

Lgth. 

^9 

Uth. 

Lgth. 

2 
3 
3 
3 

8'  0' 
8'  3^ 
8'  6' 
8'  9* 

3 
2 
2 

1 

9'  O' 

9'  y 

V  6* 
9'  9' 

2 

1 
2 

1 

10'  0* 

10'  r 

10'  9^ 

1 
1 
2 

1 

11'  0* 
11'  3* 
11'  6' 
11'  9* 

1 
2 
1 

1 

12'  or 

12'  V 
12'  6' 
13'  r 

1 
1 

2 
3 

13'  or 

13'  8* 
13'  •• 
14'  C 

1 

2 

14'  r 
14'  tr 

Total  lin.  ft.  in  above  bill,  using  exact  lengths  — 484  lin.  ft.. 
Total  lin.  ft.  in  above  bill,  using  1-ft.    lengths -806  lin.  fgle 


CROSS  TIES,    TIE  PLATES.   RAIL  BRACES.  1071 

"Winter  cut'*  ties  are  the  best,  and  hewed  ties  are  better  than  sawed. 
Planing  imofoves  sawed  ties  in  shedding  water  and  preventing  decay. 
Creoeoting  lengthens  the  Ufe  of  ties,  and  the  creosote  oil  in  ties  so  preserved 
tias  a  beneficial  effect  on  spikes  in  preventing  rust. 

Wooden  ties  are  the  only  kind  used  to  any  great  extent  in  t  be  United  States 
it  the  present  time.  The  okl  stone*  tie  has  been  abandoned.  When  the 
rooden  tie  is  supplanted  it  will  probably  be  by  the  steel  tie.  the  steel* 
:oncrete  tie,  or  the  steel-paper  tie;  and  then  only  gradually  and  on  roads  <^ 
he  first  class. 

Oak  ties  are  the  best,  and  white  oak  is  the  best  variety  as  it  holds  the 
pikes  better.  The  other  varieties  frequently  used  are  bur  oak,  post  oak, 
hestnut  oak  and  red  oak.  Together  they  comprise  at  least  one-half  of  the 
3tal  number  of  ties  in  use.  The  average  life  of  the  best  oak  tie  is  about 
ight  years,  varying  inversely  with  the  humidity  of  the  atmosphere,  and 
epending  upon  the  amotmt  of  traffic,  position  in  the  track  (whether  on 
arves  or  tangent),  etc.  Chestnut  ties  will  last  about  as  long  as  oak  but  do 
3t  hold  a  spike  as  well.  C^edar  ties  are  the  longest  lived,  but  they  do  not 
ear  well  under  heavy  traffic  unless  tie-plates  are  used,  in  which  case  they 
ill  last  about  twice  as  long  as  oak.  Red  cedar  is  not  now  readily  obtainable. 
bite  cedar  being  much  more  plentiful.  Next  to  oak,  the  vanotis  varieties 
pine  furnish  most  of  the  ties  now  being  used:  Yellow  pine,  in  the  South 
Id  East;  loblolly  pine  in  the  Southwest;  California  mountain  pine.  Oregon 
oe  (Douglas  fir  or  Washington  pine),  on  the  Pacific  0>ast;  Michigan  pine 
the  Northwest;  etc.  In  the  New  England  States,  hemlock  and  spruce  are 
jch  used,  although  inferior  to  the  Southern  vellow  pine.  Black  walnut  is 
id  in  the  middle  West,  and  redwood  in  (^lifomia.  The  life  of  redwood  is 
i>ut  up  to  that  of  cedar  if  tie-plates  are  used,  the  wood  being  very  soft. 

Tu  PlaUs  are  used  on  wooden  tics,  particularly  those  of  soft  wood,  to 
rvent  the  rails  from  cutting  into  them;  otherwise  the  life  of  such  ties 
uld  be  measured  by  the  amoimt  of  heavy  traffic  passing  over  them, 
her  than  by  their  resistance  to  the  action  of  the  weather,  etc.  The  Ufe 
loft  ties,  then,  may  be  increased:  (1)  by  creosoting,  to  resist  the  action 
;he  weather,  as  already  explained;  (2)  by  the  use  of  tie  plates,  to  resist 
asion. 

The  usual  construction  of  tie  plates  consists  simply  of  flat,  plain  or 
)cd  plates  sa^r  ffx  8".  with  bottom  lugs  or  flanges  say  f  deep,  which  are 
■-en  into  the  tie.  The  plate  is  provided  with  2,  8  or  4  square  holes  gaged 
he  rail  flange,  for  spiking.  In  the  earlier  patterns  there  were  lugs  above 
plate  on  one  or  both  sides  of  the  rail  flange,  but  in  more  recent  designs 
e  are  omitted.  Figs.  80  to  33  show  types  ot  the  Servis,  Walhauper,  Fox 
Diamond  tie  plates. 


""^^  I6rvsnr-ir 


Pig.  81.  Fig.  82.  Pig.  88. 


"he  thickness  of  metal  may  vary  from  i^'  to  |*.  The  cost  of  tie  plates 
rely  nominal.  Varying  from  5  to  16  cents  each.  They  are  used  generally 
rtaxn  points  instead  of  universally,  as  at  rail  joints,  where  there  is 
hammering ;  on  heavy  grades  where  sand  is  much  used ;  on  expensive 
B  tics  and  switch  ties:  on  curves;  and  in  places  generally  where  the 
'al  of  ties  would  be  unusually  expensive,  as  at  stations  and  crossings, 
1  tunnels. 

m7  Braces  are  designed  to  resist  the  outward  lateral  thrust  of  the  rail 
»  passinfiT  trains;  hence  they  are  placed  on  the  outside  of  rail,  pressed 
afirainst  it,  and  spiked  solidly  to  the  ties.  The  most  primitive  form  of 
ace,  and  one  which  may  be  seen  in  almost  any  yard,  at  switches,  is 

x:>ne  tics  were  tried  in  the  early  days  on  the  Boston  &  Worcester  R.  R. 
^rt  of  tbc  B.  &  A.  R.  R.  system)  but  were  abandoned  on  account  of 
rt    and    also    b^uiuae     they  did    not    furnish    a    sufficiently  elastic 


1072 


b^.^RAlLROADS. 


a  bent  fish-plate  with  one  end  pressing  against  the  web  of  the  rail,  just  tinder 
the  head,  and  the  other  end  spiked  to  the  tie.  Many  pat- 
terns are  made  of  cast  iron  or  cast  steel.  Pig.  34  shows  the 
AUdns  brace  of  forged  steel;  and  Pig.  86  shows  the  Edwards 
brace,  being  a  combination  mil  brace  and  tie  plate.  Rail 
braces  are  used  on  curves  and  at  switches,  and  in  general 
where  double  spiking  is  insufficient. 

St«9l  Ties  are  much  used  in  Europe  and  somewhat  in  the 
United  States,  but  are  at  present  avoided  here  on  account 
of  the  expense  as  compared  with  wooden  ties.     Those  in 
Europe  are  generally  of  the  trough  type.    Figs.  36.  37  and 
38  show  a  special  I-beam  section,  after  the  original  design 
of  Mr.  C.  Buhrer,  roadmaster  of  the  L.  S.  &  M.  S.  Ry..  and        _.     ,_ 
manufacttired  by  the  Camesie  Steel  Co.,  for  the  Bessemer  &       "«•  ^*- 
Lake  Erie  Ry.    The  tie  is  8^  6*  long  and  weishs  19.36  lbs.  per  ft.    Sectk» 
A  -  B  of  Pigs.  37  shows  the  depression  lug  6'  from  ends  of  tie  to  prevent 


//j'—H^-^^'" 


.4-nr-" 


=<^=^ 


6l  TV 


rrs:7i 


g-rtP*.--      !«.. ^ 4'i^V 


■.•4«-jrf'-»k — 0^-^ 


H'*! 


Sid*  Ci«va-rlon. 

Figs.  36. 


^V 


^•ctton    A-B 

Figs.  37. 

lateral  movement  in  the  ballast.    Figs.  38  show  details  of  rail  fastenings, 
including  those  atjoint  where  angle  splice  bars  are  vised.* 

Concrete-SUel  Tits  may  be  said  to  be  in  the  experimental  stage.  Tbost 
interested  in  these  types  may  find  designs  of  the  ICampbell  tie  and  tb« 
tPercival  tie  in  Eng.  News,  Oct.  6,  1906,  page  849. 

*  For  fun  description,  see  Eng.  News,  Auto.  24.  1906.  page  202. 
t  Mr.  R.  B.  Campbell.  Gen.  Man.,  the  Elgm,  JoUet  &  Eastern  Ry. 
;  Mr.  H.  E.  Percival,  Galveston.  Tex. 


TIES-STEEL,  CONCRETE.   BALLAST.    TRACK  GAGE.    1078 

Ballast  may  be  broken  stone,  gravel,  cinders,  sand  or  dirt.  The  first 
lamed  is  by  £ar  the  best  and  should  be  of  about  the  size  that  will  pass 
hrough  a  2^  in.  ring.  Most  roads  using  a  great  amount  of  broken  stone  have 
hdr  own  quarries  and  rock-cnishing  plants  instead  of  breaking  the  stone 
)y  hand.  Portable  stone  crushers  are  also  used.  The  advantages  of  broken 
tone  and  aravcl  over  the  finer  materials  are:  (1)  good  drainage.  (2)  firm 
•earing  and  solid  ballast  packing  for  the  ties;  (3)  absence  of  frost,  (4)  lack 
f  retention  of  moisture  to  rot  tne  ties,  (5)  freedom  from  dust,  unpleasant 
3  passengers  and  injurious  to  the  wearing  parts  of  the  rolling  stock. 

For  estimating  the  amoimt  of  ballast  per  mile  of  track,  a  sketch  should 
e  drawn  of  the  ballast  cross-section  desired  (see  Fig.  23,  pase  1059)  and 
om  this  deduct  the  cubic  contents  of  the  ties  from  Table  60,  page  1060. 
htis  from  the  figure,  we  have, 

11.  ft.,  gross,  of  ballast  per  lin.  ft.  of  single  track «  0.6 

edact  for  tie  (O'x  8*  -  S'  spaced  24'  centers)  by  table  »   1 .  883 

1.  ft.,  net^of  ballast  per  lin.  ft -   8. 167 


1. 3rds.  net  of  ballast  per  mile«8.167X 


6280 
27 


- 1697. 


mce  1600  cu.  yds.  of  ballast  per  mile  of  single  track  is  the  very  least 
It  can  be  assumed.  This  is  for  a  depth  of  12  ins.  and  a  top  width  of  8  ft. 
nerally  the  ballast  is  much  deeper  and  wider,  say  18*  below  top  of  tie, 
j  10  to  12  ft.  wide. 

Qafe  of  Track  and  Wheels. — The  minimum  "Standard"  Gage*  of  track 
the  United  States  and  Canada  (also  in  England  and  most  European 
tntries)  is  4'  8\'.  On  roads  where  this  minimum  gage  is  used  for  straight 
dk,  the  gage  is  widened  for  track  on  curves,  say  about  A'  per  eadi 
ree  of  curvature,  as  per  the  following  table. 

64. — Incrbasb  IK  Gage  for  Various  Dborbbs  op  Curvature. 
(Based  on  about  A*  per  degree  of  curve.) 


.of 
ire. 

r 

2o 

30 

4* 

6'* 

e** 

70 

s^ 

9** 

lO*' 

ir 

120 

ir 

14« 

in 

A' 

A' 

r 

A* 

i' 

i' 

A' 

r 

A' 

r 

r 

A' 

r 

r 

>n  some  roads  in  the  U.  S.,  mostly  in  the  South,  the  "Standard"  Gage 
9*.  This  is  true  also  of  some  main-line  freight  tracks  on  the  P.  R.  R. 
m.  In  such  cases  the  gage  is  seldom  widened  for  ordinary  curves. 
i  is  also  another  "Standard"  Gage  employed  by  a  very  few  roads, 
4'  8K.  which  may  be  considered  to  be  a  compromise  between  the  two 
above  mentioned. 

ig.  80  shows  the  Master  C&r  Builders'  (M.  C.  B.)  standard  wheel  (and 
I  sase.  which  has  become  universally  standard.    Note  that  the  side 


Fig.  39. 
the  wheels  is  §'  for  a  4'  8K  gage,  and  that  for  a  4'  9^  gage  it  would 

^ge  of  track  is  the  distance  between  "inside  heads,"  or  "gage  sides." 


1074 


Si.— RAILROADS, 


The  following  data  regarding  ga^^es  will  be  found  uaeftil  in  oonnectioc 
with  the  calculation  of  turnouts,  switches,  crossovers,  crossings,  etc. 

56. — Various  Gages  and  Half  Gages  op  Track,  in  Pert  and  Meters 
WITH  Logarithmic  Values. 


Gage 

Gage 

Gage 

i 

J. 

s. 

K. 

g. 

Log 

g. 

Log.            2- 

2' 

Log. 

2- 

Log. 

Ft.  Ins. 

Ft. 

Meters. 

Ft.  Ins. 

Ft. 

Meters. 

2    0 

2. 

.3010300 

.6096 

9.7850458 

1    0 

1. 

ooooooo 

.3048 

9.4M01SB 

2    3 

2.25 

.3521825 

.6858 

9.8361983 

1    li 

1.125 

.0511525 

.3429 

9.5U168S 

2    6 

2.5 

.3979400 

.7620 

9.8819558 

1    3 

1.25 

.0969100 

.3810 

9.560l2Sg 

2    9 

2.75 

.4393327 

.8382 

9.9233485 

1    4i 

1.375 

.1383027 

.4191 

9.6223185 

3    0 

3. 

.4771213 

.9144 

9.9611371 

1    6 

1.6 

.1760913 

.4572 

9.0601071 

3    3 

3.25 

.6118834 

.9906 

9.9958992 

i    7i 

1.625 

.2108534 

.4953 

9.«»48I92 

3    « 

3.5 

.5440680 

1.0668 

0.0280838 

1    9 

1.76 

.2430380 

.5334 

9.7270B1I 

3    9 

3.75 

.5740313 

1.1430 

0.0580471 

1  lOi 

1.875 

.2730013 

.6715 

9.757W71 

4    0 

4. 

.6020600 

1.2192 

0.0860758 

2    0 

2. 

.3010300 

.6096 

9.7ffi»IS6 

4    3 

4.25 

.6283889 

1.2954 

0.1124047 

2    li 

2.125 

.3273589 

.6477 

9.8118747 

4    6 

4  5 

.6532125 

1.3716 

0. 1372283 

2    8 

2.25 

.3521825 

.6858 

9.8StttO 

4    H 

4.7083 

.6728672 

1.4351 

0.1568830 

2    4^ 

2.3542 

.3718372 

.7176 

9.88W3I 

4    8i 

4.7292 

.6747847 

1.4415 

0.1588005 

2    41 

2.3646 

.3737547 

.7207 

t.ssmis 

4    9 

4.75 

.6766936 

1.4478 

0.1607094 

2  4 

2.375 

.3766636 

.7219 

9.85M794 

5    0 

5. 

.6989700 

1.6240 

0.1829858 

2    6 

2.5 

.3^79400 

.7630 

6    3 

5.25 

.7201593 

1.6002 

0.2041751 

2   n 

2.625 

.419129} 

.8001 

9!9lil451 

5    6 

5.6 

.7403627 

1.6764 

0.2243785  1  2    9 

2.76 

.4393327 

.8382 

9  9133481 

9    9 

5.75 

.7596678 

1.7526 

0.2436836  |  2  m 

2.875 

.4586378 

.8763 

9!  941031 

6    0 

6. 

.7781513 

1.8288 

0.2621671 

|3    0 

3. 

.4771213 

.9144 

9.9611371 

Fi 


Various  Track  Gages  are  used  in  different  countries  as  follows:  In  the 
United  States,  Canada,  England  and  most  European  countries,  the  standard 
'age  is  A'  B^""  1.435  meters.  This  is  true  of  Austria,  Switzerland,  Gennany. 
France,  Himgary,  Italy.  iSweden,  and  Balkan.  In  Russia,  the  standard 
gage  is  1.524  meters  with  the  exception  of  the  Warschau-Wien  and  Wars- 
chau-Bromberg  which  have  a  standard  of  1.436  meters.  In  Spain,  the 
standard  is  1.076  meters,  and  this  gage  also  prevails  mostly  in  the  East 
Indies,  Argentine  and  Chile.  It  corresponds  to  the  old  English  gage  of 
6'  6'.  The  gage  of  the  Great  Western  R.  R.,  in  England,  was  changedlrom 
7  ft.  Hn  connection  with  4'  8i')  wholly  to  standard  gage  in  1890.  In  Ireland, 
the  standard  gage  is  S'  3*.  Narrow  gages  are  used  in  many  cotmtrks 
In  Norway.  Cape  Colonies,  South  Australia,  Japan  and  Java,  a  gage  of  ^  6* 
is  used  largely.  In  Brazil,  Algiers.  Greece  and  Corsica,  1  meter  is  conunon. 
Gages  of  1  meter,  0.75m.  and  0.60m.  are  used  to  some  extent  in  Germany 
for  narrow  gage  extensions,  etc.  Many  roads  in  Switzerland  are  of  !•• 
gage.    The  gage  of  the  Festiniog-Bahn.  in  Wales,  is  only  0.591  meter. 

The  "Best"  Standard  Gage,  for  universal  inter*traffic,  has  gradually 
sifted  down  to  that  of  about  4'  Si*.  Wide  gages  of  6  to  6  ft.,  and  narrow 
gages  of  3  to  8}  ft.,  have  been  changed  to  the  above  standard  almost  uni- 
versally throughout  North  America,  and  the  chances  are  that  the  sane 
standardization  will  prevail  ultimately  in  South  America  also.  Pertxnect 
to  this  question,  the  writer  has  lately  been  of  the  opinion  that,  with  the 
enormotis  locomotives  now  being  built,  and  with  the  limited  head  room,  a 
wider  gage,  say  5'  3*  to  5'  6*  would  have  been  a  better  standard  to  adopt 
than  the  present  one.  Prom  the  standpoint  of  the  locomotive  mannfaic- 
turer,  the  following  letter,  tmder  date  of  September  8,  1006,  from  the 
Baldwin  Locomotive  Works,  Bumham,  Williams  &  Co.,  of  Philadelphia,  in 
reply  to  a  query  from  the  writer,  is  interesting: 

Your  favor  of  September  4th  was  dtily  received. 

The  capacity  of  any  railway,  as  an  instrument  fbr  transportatkm  of  goodie  k 
proportionate  to  its  gage.  In  fact,  the  practicable  weight  of  looomotlvea  and  tke 
practicable  capacity  of  cars,  increase  directly  in  proportt(m  to  Increased  wfcltli  of 
gage.  In  designing  some  of  the  heaviest  locomotives  now  required  fbr  treli^t  tnJfe. 
it  would  be  a  great  comfort  if  the  gage  were  wider  than  4'  8i'.  As  a  broad  pvopoil- 
tlon,  however,  we  do  not  think  that  even  the  congesyon  of  traffle  upon  the  prtaet|Mi 
trunk  lines  has  yet  reached  a  point  limited  by  the  size  of  locomottveB.  nor  thai 
wwer  gage  than  4'  8J'  has  generally  become  necessary. 


TRACK  GAGES,    TURNOUTS,  SWITCHES,  FROGS.        107* 

Tnraoutf  and  Switches.— A  turnout  (for  switching  trains  from  one  track 
to  another)  consists  essentially  of  a  switch,  a  frog,  and  the  connecting 
"lead"  rails. 

Switches  may  be  classed  under  three  main  heads,  namely,  the  stub- 
switch,  the  split-switch,  and  the  Wharton  switch.  Where  there  is  a  double 
turnout  from  the  same  track,  the  diverting  switch  is  called  a  three-throw 
switch.  Fig.  40  shows  a  double  "slip"  switch,  very  useful  in  switching-yards 


or  economizing  room,  and  particularly  adapted  to  sharp  crossings,  with 
nterchangeable  traffic.  For  instance,  a  train  may  pass  from  either  track 
n  one  side  of  the  crossing  to  either  track  on  the  other,  by  operating  the 
witches  s.  In  the  Pig-,  the  switches  are  set  for  "crossing  traffic"  on  tracks 
la  and  Bb.  It  is  to  be  noted  that  the  outside  curved  rails  c  are  continuous 
iroughout.  The  letters  F  denote  position  of  frogs;  and  P^  the  points  of 
vitches.  A  singh  slip  switch  has  but  one  curved  rail  c  with  its  correspond- 
g  gage  rail,  instead  of  two  as  shown  in  Fig.  40. 

Frogs  are  devices  for  allowing  the  flafiges  of  wheels  to  pass  unobstructed 
ong  one  rail  crossing  another  rsul.  There  are  three  distinct  classes,  namely. 
Iff  or  rigid  frogs,  spring  or  spring  rail  frogs,  and  movable^point  frogs. 

Stiff  frogs  may  be  made  up  of  rail  sections,  or  of  solid  steel  castinjgs. 
g.  41  illustrates  the  shape  of  a  stiff  rail  frog,  the  heads  of  rails  only  being 


Fig.  41. 

m.  LW  and  RW  are  left-  and  right-wings  respectively:  and  MP  and 
aure  main-  and  side-points.  Note  that  the  "point  of  frog"  is  at  the 
section  of  the  outside  lines  of  MP  and  SP  and  a  little  beyond  the  blimt 
t  of  tongue.  AH  frogs  are  designated  by  numbers.  Thus,  if  we  let  L 
1  the  length  from  pomt  of  frog  to  heel,  and  W  equal  the  width  at  heel. 

•frog  number"  »-pp..* (1) 

range  from  numbers  4  to  24.  but  the  ustial  limits  are  6  and  12,  while 
9  are  i>erhaps  the  most  common.  We  will  show  further  on  how  the 
lumber  determines  practically  the  radius  or  degree  of  the  turnout 
and  it  will  be  seen  also  what  bearing  the  kind  of  switch  and  length  of 
ive  on  the  problem,  for  any  particular  gage  of  track. 
lid  cast  manganese  steel  frogs  will  greatly  outwear  the  ordinary  rail 
ay  about  0  to  1.  while  they  cost  about  4  or  6  times  as  much.  They 
3  had  "one-sided"  or  "double  sided"  depending  on  whether  the  heavy 
is  mainly  on  one  track,  or  is  "balanced."  There  is  a  saving  in  cost  of 
25%  in  favor  of  the  former. 


ajgrainst  tbe  tongue  by  the  spring,  thus  forming  practically  a  con- 

5  the  ratio  L  +  W  is  constant  for  any  given  frog,  its  number  may 
determined  by  measuring  the  distance  L\  from  the  theoretical  point 
to  a  point  wnere  IV'  — say  4*;  then  «— L'-*-4. 


1076 


».'~RAILROADS. 


56.~Propbrtibs  op  Froo  Angles  ^  — 
With  Logarithmic  Values. 
Note. — ^Logarithmic  values  are  exact  for  the  given  frog  numbers;  the 
frog    angles  are  to   the  nearest   second.     (Angles   to  the  nearest  athrate 
are  close  enou^,  usually.) 

For  values  of  cosec  ^  and  cot  ^,  see  Table  64. 
Part  I.— Properties  of  Prog  Angles,  ^. 


Frog 

Frog 

Nat 

Log 

Nat 

Log 

Nat 

Log 

Nat    |Lof 

NoT 
n. 

A.*. 

Sln^ 

Sin  ^ 

Cos# 

COS  ^ 

Tan  ^ 

Tan  ^ 

8eo  ^ 

Dec 

4 

U^IS'OO* 

.246154 

9.3912067 

.969231 

9.9864272 

.253968 

9.4047794 

1.03175 

*H 

12  40  49 

.219512 

9.3414588 

.975610 

9.9892761 

.225000 

9.3521816 

I.OIIOO 

5 

11  25  16 

.198020 

9.2967086 

.980198 

9.9913138 

.202020 

9.3053948 

1.02030 

5M  10  23  20 

.180328 

9.2560628 

.983607 

9.9928214 

.188338 

9.2632416 

1.016C7 

6 

9  31  38 

.165517 

9.2188433 

.986207 

9.9939680 

.167832 

9.2248753 

1.0U90;  -♦ 

e^ 

8  47  51 

.152941 

9.1845244 

.988235 

9.9948604 

.154762 

9.1896640 

I.OIOM    2  . 

7 

8  10  16 

.142132 

9.1526919 

.989848 

9.9955684 

.143590 

9.15712S5 

1H 

7  37  41 

.132743 

9.1230128 

.991150 

9.9961396 

.133929 

9.1268732 

1.00893    uS 
1.00784  J2fe 

8 

7  09  10 

.124514 

9.0952169 

.992218 

9.9966071 

.125490 

9.0086090 

m 

6  43  69 

.117241 

9.0690810 

.993103 

9.9969944 

.118056 

9.0720865 

1.00094  i:: 

9 

6  21  35 

.110769 

9.0444192 

.998846 

9.9973192 

.111456 

9.0471000 

1.006l»  C^ 

9H 

6  01  32 

.104972 

9.0210750 

.994475 

9.9975939 

.105556 

9.02S4811 

i.oeuo  -? 

10 

5  43  29 

.099751 

8.9989157 

.995012 

9.9978285 

.100251 

9.0010871 

i.oeei?  o ' 

i.ooiujrs 

10^ 

527  09 

.095023 

8.9778270 

.995475 

9.9980304 

.095456 

8.9797966 

U 

5  12  18 

.090722 

8.9577109 

.996876 

0.9982054 

.091097 

8.9596056 

1.00414    1^ 

UH 

4  58  45 

.086792 

8.9384821 

.996226 

9.9983580 

.087121 

8.9401239 

1.00379 

•^'" 

12 

4  46  19 

.083189 

8.9200655 

.996534 

9.9984920 

.083478 

8.9215734 

1.00348 

!| 

12H 

4  34  52 

.079872 

8.9023957 

.996805 

9.9986103 

.080128 

8.9037854 

1.00321 

13 

4  24  19 

.076809 

8.8854147 

.997046 

9.9987151 

.077037 

8.8866996 

1.00291 

II 

14 

4  05  27 

.071338 

8.8533184 

.997452 

9.9988921 

.071520 

8.8544263 

1.00255 

15 

3  49  06 

.066593 

8.8234264 

.997780 

9.9990349 

.066741 

8.8243915 

1.00222 

1« 

3  34  47 

.062439 

8.7954561 

.998049 

9.9991517 

.062561 

8.7963043 

1.00196 

17 

3  22  10 

.058773 

8.7691756 

.998271 

9.9992486 

.058874 

8.7699289 

1.00173 

•0-3 

18 

3  10  56 

.055513 

8.7443926 

.998458 

9.9993298 

.055598 

8.7460628 

1.00154 

jg 

19 

3  00  54 

.052595 

8.7209457 

.998616 

9.9993985 

.052668 

8.7215473 

1.00139 

20 

2  51  51 

.049969 

8.6986987 

.998751 

9.9994571 

.050031 

8.6992415 

1.00125 

S 

21 

2  43  40 

.047593 

8.6775346 

.998867 

9.9995076 

.047646 

8.6780270 

1.00113 

22 

2  36  14 

.045431 

8.6573530 

.998967 

9.9995513 

.045478 

8.6578017 

1.00103 

23 

2  29  27 

.043458 

8.6380670 

.999055 

9.9995895 

.043499 

8.6384776 

1.0009S 

24 

2  23  13 

.041649 

8.6196003 

.999132 

9.9996230 

.041685 

8.6199773 

1.00087 

6  6 

Vers  ^-sin  ^.tan  y-2  sin*  y- 


tinuous  main  line  rail.  When  a  train  takes  the  SP  rail,  the  RW  is  crowded 
open  by  the  wheel  flange,  but  springs  back  after  the  train  has  passed 
Spring-rail  frogs  are  "rights"  and  "lefts**  and  hence  care  must  be  used  in 
ordering  them.  Other  types  are  the  Vaughan,  Wood,  Ajax.  Eureka,  etc. 
Double  spring  rail  frogs  are  seldom  used. 


Fig.  42. — Spring  Rail  Frog.  "^ 

Movable-Point  Frogs  are  shown  in  Fig.  43,  as  manufactured  by  Wm.  \ 
^^^^A  J*"'  *  ^'  PhUadelphia.    Note  that  this  type  might  well  be  used  I 
m  rig.  40  at  the  central  frogs  F.    The  cut  is  self-explanatory.    The  movabk 
__  pomts  also  may  be  of  manganese  steel  if  required.  J 


FROGS.    FROG  ANGLES— PROPERTIES  OF. 


1077 


ND  Propbrtibs  of  J^  Proo  Anolbs  -?. 

With  Logarithmic  Valubs. 
Note. — Logarithmic  values  are  exact  for  the  given  frog  numbers:  the 
;  angles  are  to  the  nearest  second.    (Angles   to  the  nearest  minute 
close  enough,  usually.) 

Part  IL— Properties  of  H  Prog  Angles,  y. 


■  4- 

Nat 

Log 

Nat 

Log^ 

Nat 

Log 

Nat 

Log 
Sec 

S.a4 

8.o4 

cx-4 

C0.4 

Tan^ 

Tan^ 

Sec^ 

2 

• 

jofn'zr 

.124035 

9.0935433 

.992278 

9.9966333 

.125 

9.0969100 

1.00778 

«  20  25 

.110432 

9.0430931 

.993884 

9.9973356 

.111111 

9.0457575 

1.00615 

5  42  38 

.099504 

8.9978393 

.995037 

9.9978398 

.1 

9.0000000 

1.00499 
1.00412 

>A.|M 

5  11  40 

.090536 

8.9568201 

.995893 

9.9982128 

.090909 

8.9586073 

^ 

1 

4  45  49 

.083045 

8.9193160 

.996546 

9.9984973 

.083333 

8.9208188 

1.00347 

4  23  55 

076696 

8.8847755 

.997055 

9.9987189 

.076923 

8.8860566 

1.00295 

1 

4  06  08 

.071247 

8.8527670 

.997459 

9.9988950 

.071429 

8.8538720 

1.00255 

3  48  51 

.066519 

8.8229457 

.997786 

9.9990370 

.066667 

8.8239087 

1.00222 

"j* 

£S 

3  84  86 

.062378 

8.7950334 

.998053 

9.9991534 

.0025 

8.7958800 

1.00195 

' 

i 

3  21  59 

.058722 

8.7688011 

.998274 

9.9992499 

.058824 

8.7695511 

1.00173 

c 

1 

3  10  47 

.055470 

8.7440684 

.998460 

9.9993308 

.055556 

8.7447275 

1.00154 

•" 

3  00  46 

.052559 

8.7206457 

.998618 

9.9993993 

.052632 

8.7212464 

1.00138 

S 

1 

2  51  45 

.049938 

8.6984278 

.998752 

9.9994578 

.05 

8.6989700 

1.00125 

2  43  35 

.047565 

8.6772889 

.998868 

9.9995081 

.047619 

8.6777807 

1.00113 

7 

k 

8  36  09 

.045408 

8.6571292 

.998969 

9.9995518 

.045455 

8.6575773 

1.00103 

2  29  23 

.043437 

8.6378622 

.999056 

9.9995899 

.043478 

8.6382722 

1.00094 

^« 

k 

2  33  09 

.041631 

8.6194122 

.999133 

9.9996234 

.041667 

8.6197888 

1.00087 

g 

0 

2  17  26 

.039968 

8.6017129 

.999201 

0.9996528 

.04 

8.6020600 

1.00080 

V 

0 

8  12  09 

.038433 

8.5847057 

.999261 

9.9996791 

.038462 

8.5850267 

1.00Q74 

9  * 

3  02  43 

.035693 

8.5525652 

.999363 

9.9997232 

.035714 

8.5528420 

1.00064 

f 

1 

1  64  83 

.033315 

8.5226375 

.999445 

9.9997589 

.033333 

8.5228787 

1.00056 

1  47  24 

.031835 

8.4946380 

.999512 

9.9997880 

.03125 

8.4948500 

1.00049 

1 

i 

1  41  05 

.029399 

8.4683333 

.999568 

9.9998122 

.029412 

8.4685211 

1.00043 

*l- 

1  85  28 

.027767 

8.4435301 

.999614 

9.9998325 

.027778 

8.4436975 

1.00039 

H 

1  30  27 

.036307 

8.4200661 

.999654 

9.9998497 

.026316 

8.4202164 

1.00035 

s 

1  36  56 

.024992 

8.3978043 

.999688 

9.9998643 

.025 

8.3979400 

1.00031 

1  31  50 

.023803 

8.3766276 

.999717 

9.9998769 

! 023810 

8.3767507 

1.00028 

S 

1  18  07 

.022781 

8.3564351 

.999742 

9.9998878 

.022727 

8.8565473 

1.00026 

1  14  43 

.021784 

8.8371396 

.999764 

9.9998974 

.021739 

8.3372422 

1.00024 

1  1137 

.020629 

8.3186645 

.999783 

9.9999068 

.020833 

8.31875881  1.00022 

|-sin^.tan^-2sin»f 


Pig.  43. 


aoogle 


1078 


m,— RAILROADS, 


Crossing  Progrs  are  usully  rigid,  and  made  up  of  rail  sections  with  periiaps 
cast  steel  frog  jtinctions.  There  is  a  form  of  movable  frog  consisting  of 
short  pieces  of  rail  on  miniature  turntables  that  can  be  turned  in  any 
desired  direction,  thus  making  a  continuous  rail  of  either  track. 

Stub  Switches. — ^The  stub  switch  is  the  cheapest  and  most  primitive 
form.  Its  use  is  now  confined  to  second-class  yards  and  spur  connectioDS 
with  sMings,  having  disappeared  entirely  from  main  yards.  It  should  never 
be  used  for  main  Ime  connection.  Fig.  44  illustrates  the  essential  featwes. 
The  head  blocks  if  B  are  at  j  f 

the  junction  of  the  switch  ^il^^^ 

rails  5  with  the   main    lead  Santm  a-^ 

(rail)  Af  L  and  turnout  lead 
(rail)  TL,  which   "lead"  to 

the   toe   of  frog;   also  with  A 

the  continuous  main  line  rail  ** 

M  and  turnout  rail  T.  The  » 
"throw"  of  the  switch  is 
clearly  the  distance  between 
the  gage  sides  of  rails  M  and 
TL  or  ML  and  T,  at  the  head 
blocks,  and  is  tisually  6,  5} 
(or  6)  ins.*  The  switch  rails 
are  tied  together  with  a  front 
rod  and  three  or  more  back 
rods.  The  length  of  switch 
rails  is  governed  by  the  frog 
niunber  or  by  the  degree  ot  ' 
turnout  curve.  The  follow- 
ing table  was  calculated  by 
the  author  in  1887  while  he 
was  Resident  Engineer  of  a  «.     ^. 

western  toad  and  was  used  by  ,' 7  .     . 

the  foremen  in  laying  out  all  switches,  mcludmg  the  termmal  yards  st 
Toledo.  The  sharpest  frog  was  No.  9,  and  the  table  was  used  for  both  stub 
and  split  switches;  but  for  frog  numbers  higher  than  9  the  table  does  not 
apply  strictly  to  the  latter.  The  virtue  of  the  table  lies  in  the  offset  dis- 
tances between  the  gage  sides  of  ML  and  TL  rails,  Fig.  44,  as  given  in  the 
last  seven  columns  but  one.  These  offsets  are  measured  at  points  10-,  20-, 
30-ft..  etc.  from  theoretical  point  of  frog  (Fig.  41).  By  this  means  the 
position  of  Uie  TL  rail  is  fixed  quickly,  and  from  it  the  T  rail  is  gaged.  TTie 
efficiency  of  the  work  per  gang  was  increased  from  two  switches  in  tinee 
days  to  one  switch  per  day,  in  broken  stone  ballast. 


67. — ^Tablb  por  Laying  out  Switches.    Gaob  4'  8H'-   Throw  fi*. 


Turnout 
Curve. 


De-     Ra- 
gree.    dlus. 


Theo- 
reti- 
cal 

Lead 


Stub 
Switcb. 

t 


RaU 


Split 
Switch. 

t 


OflSet  distances  In  ft.  from  g»gt 
side  of  main  lead  to  gage  aide  of  I  ^ 
turnout  lead  at  following  dl»>  Iz 
tanoes  from  point  of  tng.  I  , 


I  Oft.  20ft.  30ft.  40ft.  50ft.  60fl.  TOCV  h 


9  32 
8  10 
7 

6  22 
5  43 
5  12 
4  46 


Ft. 
16  58|  339.0 
12  26    461.4 


602.7 
762.8 


6  05    941.7 


5  02 
4   14 


1139.4 
1356. 


Ft. 
56.5 
65.9 
75.3 
84.8 
94.2 
103.6 
01113.033. 6179. 4 


Ft. 
16.9 
19.6 
22.5 
25.3 


Ft. 

39.6 
46.3 
52.9 
59.5 


28.066.1 
30.872 


Ft. 
54.6 
61.3 
67.9 

74 
81 
87 
94.4 


Ft. 

1.51 
1.3t 
1.16 
04 
0.951 
0.86  1 
0.80 


51 


Ft. 
2.73 
2. 

2.1 


Ft. 

3.65 

.13 

.99 

1.96^2.74 

.628 

38  2 

17 


782 
64  2 


Ft. 


3.74 

3 

S.39 


14 

3.92 


OS 
3. 87  4. 2 

2.76|3.26  3.S8  4.«3 


*  Distance  between  rail  heads  should  be  about  8  ins.;  and  the  tbxtm  is 
equal  to  this  distance  plus  width  of  railhead. 

t  "Rail"  means  switch  rail;  "lead"  means  distance  from  point  oC  frog 
to  toe  of  stub  switch  (if.  B.),  or  to  point  of  split  switch. 

Digitized  by  VjOOQ  IC 


CROSSING  FROGS.   STUB  SWITCHES. 


1070 


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STUB  SWIT.-HES.    TURNOUT  CURVES, 


c 


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d  by  Google 


loss 


n.-'^iAILROADS. 


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TURNOUTS  FOR  ANY  CAGE,    TURNOUT  CURVES.     108S 

Ttimotit  Curves  for  Stub  Switches  are  simple  curves.    In  staking  them 
est  on  the  ground  it  is  necessary  only  to  set  two  stakes,  one  marked  P.  F., 

-r 


Pig.  46. 

•ppoaite  the  point  of  frog,  and  the  other  marked  P.  5.,  opposite  the  point  of 
witch.  They  should  be  set  on  the  frog  side  of  the  track  to  indicate  the 
lirection  of  the  turnout.  The  P.  F.  is  usually  located  about  half  a  frog 
enfirth  from  a  rail  joint  to  save  one  cut  of  rail.  No  refinement  is  necessary 
n  the  calculation  of  turnouts,  and  the  following  formulas  may  be  used 
vhere  the  main  track  is  straight,  as  in  Fig.  46: 

Let  ^*"frog  angles  central  angle  of  turnout  curve; 

M  —  frog  number  (see  Fig.  41); 

/—theoretical  lead  to  point  of  main  frog; 

f»  theoretical  lead  to  point  of  crotch  frog: 

C""ga8e  of  track; 

K  —  radiiis  of  turnout  curve; 

5 -switch  length,  P.  S.  to  H.  B.: 

m  — middle  ordinate  of  turnout  curve; 

9— quarter  ordinates  of  turnout  curve. 

I  — throw  of  switch. 
All  distances  in  feet. 

Then,  tan -J- •^; 

cot^-l-2H; 

n-Jcot|-^-V^T2i; 

-R-f +  vers  ^-y  -2fn«; 

-/+ain^--|-; 

/-2£K-gcot|-  (/2+|)sin^: 

*-2nV7<  -  VaKl; 
<-s«+2/?; 
.  m— f-i-4  (nearly); 

fl-?^«  +  4  -  A«  (nearly). 
All  the  above  formulas  may  be  used  with  perfect  safety  for  field  work. 
Other  formtdas  may  be  deduced  from  these  by  transposing  or  equating. 


1084  SQ.—RAILROADS, 

Double  Turnouts  (—three-throw  turnouts)  require  two  main-line  Iroes 
and  one  crotch  frog.  If  the  two  turnouts  are  opposite  and  of  equal  radii, 
then.  Fig.  46,  4>\  the  angle  of  the  crotch  frog,  is  equal  to  double  the  central 

angle  ^.    But   (^+y)  ▼««  ^"  "f*  **®^**  ^^®"  ^-3"*"  (^"^1^)  *  ^™ 
which  ^'  is  obtained. 

Further,  if  n'— the  number  of  the  crotch  frog, 

and  ^  » the  crotch  frog  (point)  distance  from  the  P,  5.,  we  have, 
J?- 4  n'»g  (nearly)  -  2  «»g; 
n'  -  » -»-  vT  (nearly)  -  0. 7071  n  (nearly) ; 
r-0.707/ (nearly). 
Hence  W  and   V  are  respectively  equal  to  n  and  I  multiplied  by  0.707 
(nearly).    See  Table  58. 

Curved  Main  Track. — The  above  remarks  apply  to  turnouts  from 
straight  main-line  track,  in  connection  with  the  stub  switch.  It  is  to  be 
remembered  that  nearly  all  the  formulas  used  in  practical  track  work  are 
approximate  and  close  enough  to  the  exact  values,  which  may  be  obtained 
by  trigonometric  calculation.  We  will  show  now  how  the  foregoing  formulas 
may  be  applied  to  turnouts  from  curved  main-line  track.  In  order  to  illus- 
trate we  will  consider  Fig.  46  to  be  warped  so  the  main  line  is  curved  instead 
of  straight: 

Let  r*« degree  of  curve  of  turnout  from  straight  track; 
<*— degree  of  curve  of  tiunout  from  curved  main  line; 

M*  =  degree  of  curve  of  main  line  after  curving. 
Then  <**-=  T^+M**  when  main  line  is  curved  toward  turnout; 

<«  —  7^— Af  o  when  main  line  is  curved  away  from  turnout. 

For  instance,  a  No.  9  frog  calls  for  a  7**  30'  curve  from  a  straight  track; 
it  calls  for  10**  3tK  ctirve  from  the  inside  of  a  3**  main-line  curve;  and  for  a 
4°  30^  curve  from  the  outside  of  a  3^  main-line  curve.  Hence,  when  tlie 
two  curves  are  in  the  same  direction  we  have  to  find  their  difTerence,  sjod 
when  in  opposite  directions  we  have  to  find  their  stmi,  to  get  the  degree  of 
curve  /**  in  Table  68,  preceding,  and  the  desired  frog  number,  m.  correspoad- 
ing  thereto. 

Split  Sxvitches. — In  otir  consideration  of  the  stub  switch,  which  is  really 
for  second-class  track  work,  we  have  asstuned  all  frogs  in  the  turnout 
curves  to  be  curved,  whereas  they  are  straight,  and  should  be  so  considered 
in  first-class  track  work  where  the  split  switch  is  used,  although  formerly 
this  refinement  was  not  considered  necessary.  This  introduces  a  shon 
tangent  in  the  turnout  at  the  point  of  frog.  Moreover,  split  switch  points 
are  straight  and  it  is  now  customary  to  take  this  fact  into  consideration 
in  calculating  the  turnout  curve,  which  really  extends  only  from  the  heel  of 
switch  (P.  C.)  to  the  toe  of  frog  (P.  T.),  joining  the  two  short  tangents 
above  mentioned,  instead  of  from  point  of  switch  to  point  of  frog  as  assumed 
in  Table  57,  preceding. 

The  following  is  the  practice  of  the  Weir  Frog  Co.,  of  Cincinnati,  Ohio: 


d  by  Google 


TURNOUTS  FROM  CURVES.    SPUT  SWITCHES, 


1085 


1. — ^TuRKOUTs  POR  Split  Switches  and  Sprino  Frogs.  Gaob  4'  8J'. 
(Curve  is  Tangent  to  Switch  Angle  at  Heel  of  Switch  and  to  Frog 
Angle  at  Toe  of  Frog.) 


Fig.  47. 
(a). — Switch  and  Frog  Variable. 


" 

Distance 

.         _ 

o. 

k. 

Frog 
Angle. 

Radius 

of 
Curve. 

R, 

Degree 

of 
Curve. 

Switch 

Angle. 

a. 

Switch 
Length. 

worn  Point 

of  Switch  to 

Actual 

Point  of 

Lgth 

of 
Frog. 

Length 

of  Main 

Point  of 

Frog. 

Frog. 

\ 

M«  15' 

125.868' 

46»  49' 

3«»  20'  29' 

7 

6' 

33'  9     • 

6'0' 

3'    9    • 

m 

ir  41' 

164.569' 

350  22' 

" 

' 

36'  7     ' 

6'  0' 

3'    9     • 

\ 

ll'lB' 

202.054' 

28»S9' 

T  30'  27* 

10 

0* 

43'  1H' 

6'  0* 

3'  10     • 

^ 

10*  13' 

244.318' 

23»  37' 

'• 

46'  3^- 

6'  6* 

3'  lOH* 

; 

9«  SB' 

289.453' 

19»  53' 

I'  40'  16- 

15 

0* 

57'  2H.' 

6'  8* 

4'     3     • 

^ 

8»  48* 

343.249' 

16*  45' 

" 

• 

60'  3     • 

7'0- 

4'    6     • 

8*  lO* 

403.942' 

14«  13' 

•• 

• 

63' 4     • 

7'  0* 

4'    6H' 

H 

r»  38* 

468.794' 

W  15' 

• 

' 

66'  ZW 
69' 0«- 

V  6- 

6'    0     • 

1 

70  o»' 

535.773' 

10»42' 

" 

• 

8'  0* 

5'     3     ' 

1 

«•  tv 

678.440' 

8«>27' 

" 

74' 2     • 

10'  0* 

6'    4H' 

1 

8»44' 

855.803' 

6«  42' 

" 

79'  5M- 

84'042- 

11'  0* 

V     \%' 

B«  \V 

1048.987' 

5«  28* 

" 

12' 0- 

V    8     • 

4»4e' 

1259.507' 

4"  33' 

88'  6X' 

14'  0* 

8'    9     • 

(b).— 15  Ft.  Switches. 


90  82' 

231.21 

24»  56' 

1»40'16» 

15'  0* 

63'    9     •  1 5'  0* 

8'  0* 

V  W 

335.50 

17'>08' 

" 

•• 

60*     I     • 

•• 

1 

70  09* 

461.08 

120  27' 

•• 

'• 

64'     \H' 

" 

•• 

«•  22' 

609.62 

9»25' 

•• 

" 

IV  \WK' 

•• 

" 

1 

5»  44' 

783.02 

7«  19' 

77'    \H' 

(c).— 18  Ft.  Switches. 


9«  32' 

228.97 

25«»  15' 

l<»  23'  34' 

18'  0* 

n:  g{: 

16'  0" 

8'0' 

fp  \V 

331.04 

IT  22' 

" 

" 

•• 

( 

r  09' 

453.04 

12«  40' 

•• 

70*    7     ' 

" 

•• 

1 

••22' 

596.05 

90  37. 

•• 

*' 

76'   m' 

" 

•• 

1 

S«  44' 

761.28 

70  32' 

t* 

82'    7     • 

d  by  Google 


1086 


SH.—RAILROADS, 


62.— Three-Throw  Turnouts.    Split  Switches. 
Gage  4'  8H' I  Throws  S". 


^^i^fe^^H-^P"^^' 


Fig.  48. 


Dtetancclrom 

Length  or 

Main  Line 

Crotch  Frog 

Crotch  Frog 

Point  of  Switch  to 

Length  of 

ActuallUIn 

Frog  No. 

Number. 

Angle. 

Actual  Point  of 

Crotch  Frog. 

PolnioC 

Crotch  Frog. 

Crotch  Fraic. 

4 

2.76 

20O  34' 

29'  9H' 

5'0' 

3'    3    • 

iH 

3.12 

18»  12' 

31' 8    • 

5'0' 

3'    3    • 

B 

3.51 

16*  14* 

37'  6«* 

6' 6* 

3'    6    • 

B^ 

3.83 

140  63' 

39' 2    • 

6'6» 

3'    6    • 

6 

4.21 

13®  34' 

41' 0%' 

6'0- 

3'    9     • 

7 

4.56 
4.91 

120  32' 
1 1®  37' 

42'  9W* 
44'  SH' 

6'0- 
6'0» 

3'    9     • 
8'  10     • 

8 

5.26 

10®  52' 

46'  OM* 

6'e» 

3'10^» 

5.58 

10»  14' 

47'6W» 

6'  6» 

3'  !»><• 

9 

6.20 

9®  14' 

60'  IH' 

7'0* 

4'    6     • 

10 

6.84 

8*  21' 

62' 8H' 

7'0- 

4*    ««• 

1 1 

7.57 

r  33' 

57' 8^' 

8'  0* 

5»     3     • 

12 

8.17 

7«  00' 

60'  OH  ' 

9'0' 

y  II     • 

Split  switches  are  made  either  stiff  or  with  springs. 


d  by  Google 


TURNOUTS,   SPUT  SWITCHES. 


1087 


The  following  is  the  practice  of  the  Buda  Manufacturing  Co.: 
St.— TuKNouTS  FROM  Stiuigrt  Track.    Split  Switcubs. 


Fig.  49. 
(a). — Properties  of  Turnouts. 


Frog 

Frog 

Rsdlusof 

Degree  Of 

Lead. 

Length  of 

Mld-Ord, 

Number. 

Angle. 

Curve. 

Curve. 

Curve. 

of  Curve. 

14»  ly 

121.841' 

48«?7' 

43'    9H' 

26'    9H' 

Sff 

!!•  25' 

193.991' 

29»  52' 

50*    4H- 

33'    Oh^' 

9032' 

283.525' 

20"  19' 

66'    8    ' 

38*  llH* 

8    ' 

8»10' 

393.603' 

14'  36' 

62'  10^' 

44'    7H- 

iH' 

T^IC 

6I6.219' 

11»    8* 

68'    2H' 

49'    6j|- 

7H- 

6«  22' 

657.734' 

8«»36' 

73'    6W 
78'  llrf- 

54'  lOil- 

6H' 

10 

5M4' 

841.083' 

6»49' 

59'    «H' 

6ji" 

Frogs. 


Fig.  60. 
(b). — Properties  of  Frogs. 


Angle. 

Length. 

Actual 

Theoretical 

Spread. 

>. 

Point  to 

Point  to 

Point  to 

Point  to 

Hed. 

Toe. 

Heel. 

Toe. 

Heel. 

Toe. 

U»  16' 

6'0- 

3'    7    ' 

2'    5    • 

3' 9' 

2' 3* 

loi]- 

6?i' 

1  !•  36' 

7'0' 

V  3H- 

r    SH' 

4' 6' 

2' 6* 

6    ' 

^32' 

S'O* 

5'    0    • 

3'    0    • 

5' 3* 

2' 9* 

lOH- 

6}4' 

8»  10* 

9'0' 

5'    8H' 

3'    3H' 

e'O* 

3'0' 

lOA- 

6H' 

70  10* 

lO*©* 

6'    2     ' 

3' 10    ' 

6'6- 

3' 6* 

9.H" 

6M' 

e^'za' 

11' 0* 

6'  lOH' 

4'     Ih' 

7'  3* 

3' 9* 

9^- 

5    • 

S*  44' 

12'  0* 

7'    7     • 

4'    5     • 

8'0* 

4'0' 

-^' 

^H* 

Formulas  for  Split  Switchbs. 
(a). — Assuming  Frog  to  be  curved. 


S'^haagth  of  switch  rail; 
/  —  throw  of  switch ; 
X  —  sw^itch  angle; 
S— £ro«  angle; 
^-"radiuB  of  turnout  curve; 


-R+f 

in  feet. 


/-lead. 


1088 


S^.-^RAILROADS. 


Formulas  (Approxiomte): 


Sin  a—  — •; 


/-i+ 


g-t 


/?'-- 


tan  i  (0+a)' 


Fig.  £2. 


cos  a  —  cos  0 

(b). — Asstiming  Frog  to  be  Straight. 
Notation: 

/-straight  length  of  frog  to  P.  F.,  in  feet. 
Balance  of  notation  as  on  preceding  page. 
Formulas  (Approximate): 

Sin  a  — — ;  

g-<-/8in  ^ 
"tan  i(0+a)' 

Note. — Switches  can  be  planned  cptiphically  very  easily  by  drawing 
them  to  scale  and  scaling  the  dimensions.  After  the  switch  length  and 
switch  angle  are  drawn  for  one  rail,  the  frog,  with  angle  ^  and  length  /. 
may  be  "slid"  long  the  other  "rail"  until  the  semi-tangents,  s-t,  are  equal. 

Wharton  Stviuh. — ^The  virtue  of  the  Wharton  switch  lies  in  the  fact  that 
no  frog  is  necessarv  for  a  turnout  curve  from  the  main  line,  for  which  it  is 
especially  designed,  and  that  the  main  line  rails  are  therefore  unbroken. 
Fig.  53  is  a  general  plan  of  the  switch  as  patented  April  2,  1901.  showing  it 
in  position  tor  main-line  traffic.  The  switch  rails  are  on  a  grade,  rising  fzcun 
the  points,  and  when  thrown  over  and  set  for  the  siding  the  wheels  of  the 
train  ride  up  on  them,  clearing  the  flanges  from  the  main  track.  The  trip 
rail  is  pivoted  so  that  when  the  switch  is  set  for  the  siding,  the  end  G  of 

fuard,  nearest  the  point  of  switch,  swings  outward  and  hugs  the  main  rail, 
[ence,  a  train  commg  heel  on,  on  the  main  line,  crowds  the  trip  rail  inward 
and  throws  the  switch  automatically,  for  the  main  line. 


,  rx/i: 


f—M"^—'J9  — 


\-  -AL -*■»'■ H  *^- 


Sitle  Vk0  of  Derafn/ fbnf 


t^l'i*^ 


4Vi' 1 

Fig.  53.^Wharton  Switch.    (See  also  Pig.  43.) 

Digitized  by  V^OOQ  IC 


WHARTON  SWITCH,    LADDER  TfUiCKS, 

(W.—Laddbr  Tracks.    Spacing  of  Proos. 
(Any  Ga^e.) 
oal  (Direct)  Distanc 
Points,  id  in  Feet.] 


1089 


(Any  Ga^e.)  ^ 

Part  I.— Diagonal  (Direct)  Distances  d  between    Prog 


Part  II. — Horizontal  Distances  h  between  Prog  Points,  [h  in  Peet.1 


d  by  Google 


1090  SQ.—RAILROADS. 

65. — Crossovbrs.    Spacing  of  Proos. 
Gaob-4'8H'. 
Part  I.'Lengths  5  (Feet)  of  Straight  Track  between 
Frog  Pointa. Pig^M. 


HH 

"f-      1  l>- 

o 

Sf 

»-*>-  _ 

S^" 

d  by  Google 


CROSSOVERS^FROG  SPACING.  1091 

flfi. — CR0880VBRS.    SPACiNo  OF  Progs. — Conduded. 
Gaob-4'8H'.      • 
Part  m. — Direct  Distances  D  (Pcct)  between  Prog  Points. 


EXCERPTS  AND  REFERENCES. 

Train  RflsisUnce  PonniiiRS  (By  J.  G.  Crawford.  Eng.  News.  Oct.  31, 
01). — ^Also  diagrams  of  train  resistance  curves  representing  various 
■mulas. 

Holbrook's  Spiral  Corves  (Bng.  News.  June  13  and  Aug.  15.  1901).— 
rmulas  and  tables. 

Tnuuitlon  Curves  (By  W.  B.  Lee.    Trans.  A.  S.  C.  £..  Vol.  XLVI). 

Oravi^  Yards,  Switches  and  Frogs  of  the  Chicago  Transfer  and 
aring  Co.  (Eng.  News.  Jan.  2,  1902).— Illustrated. 

The  Weehawken  Inclined  Railway  (By  C.  L.  Duenkel.  Bng.  News. 
.    16,    1902).— Dlustrated. 

The  Rutland-Canadian  Railway  and  Its  Stmctures  (By  J.  W.  Burke. 
'.  News,  Jan.  15,  1903). — Illustrations  of  turntable  machinery  for  swing 
ge,  details  of  overhead  steel  highway  bridge,  masonry  cattle  pass, 
onry  box  culvert,  surface  cattle-^uard. 

LarKcst    Capacity   Qondola   Cars;  Chicago   &  Alton  Ry.  (Eng.  News. 
26,  1903). — Illustrated.    Capacity.  80.000  lbs.;  weight.empty,  31,000 
2,0O0  lbs.;   length  over  end  sills,  30  ft. 

in  Automatic  Mhie  Car  Tipple  (Bng.  News,  May  21,  1903).— Blus- 
<1. 

Mrmmt  Freight  Car  hi  the  Worid  (Bng.  News,  July  2.  1903).— Blus- 
j.  Capacity,  300.000  lbs.;  weight.  196.420  lbs.;  length  of  car  over 
103  ft.  10}  ins. 


teel  Ties  on  BesMmer  &  Lake  Erie  R.  R.  (Eng.  ^^^®^iS,  1903). 
istrated. 


1002  S^.—RAILROADS, 

Cott  of  Railway  Ballast  (W.  C.  Cushins.  Bng.  News.  Mar.  81,  1904). 
— Record  of  experimental  test  of  three  difierent  sizes  of  broken  stone  ballast 
on  B.  &  O.  Ry.,  with  cost  of  each:  Average  cosU  per  ft.  of  double  track. 
11.  to  11.50. 

A  Conduit  Electric  Raflway  in  Londoo  (Bng.  News.  April  21.  1004). 
— Illustrated. 

Standard  Qirder-Ran  Track  Construction  f6r  City  StfMta.  Pan. 
R.  R.  (Eng.  News.  Aug.  11.  1904).— lUuBtrated:  Croao  oection  of  rail,  and 
details  of  track  construction. 

Screw  Spikes  for  Railway  Track  (Bng.  News,  Aug.  S5,  1004).— 
Illustrated:   7  forms  of  spikes,  and  machine  tor  driving. 

Reinforced-Concrete  Ties,  Ulster  ft  Ddawara  Ry*  (Bng.  News. 
Oct.  6.  1904).— Illustrated. 

Transfer  Tables  Without  Pits  and  TravaUng  on  Corfts  (Bng.  News. 
Oct.  6.  1904).— Illustrated. 

Cost  of  Electric  RaUway  Power  Production  and  Transmlarion  la 
the  SUte  of  Indiana  (By  A.  S.  Richey.  Bng.  News.  Feb.  10.  100^.— 
Efficiencies:  Step-up  transformers.  94%;  transmission  lines.  07%:  step- 
down  transformers.  93%;  rotary  converters,  80%;  direct-ctirrent  distri- 
bution, 80%;  combined  efficiency,  54%. 

The  Cost  for  Concrete  Fence  Posts  (Eng.  News,  tfar.  0,  1005). 

The  San  Pedro,  Los  Angeles  &  Salt  Lake  Ry.  (Eng.  News.  June  22. 
1905). — Illustrations  of  standard  roadbed  cross-sections. 

A  Table  of  Turnout  Curves  and  Crossings  (By  J.  H.  Milbum.  Bng 
News,  July  13,  1905). — Including  frog  ntimbers  10.  12,  15.  Hand  20. 

Some  Records  of  Maintenance-of*Way  Costs  on  American  Rail- 
ways (Eng.  News,  July  27,  1905).— Tables. 

Concrete  Ties  on  the  L.  S.  &  M.  S.  Ry.  (Bng.  News.  Aug.  17.  1005) 
— Illustrated.  (See,  also.  Eng.  News  of  Oct.  5,  1905,  for  descriptions  and 
illustrations  of  the  Campbell  and  Percival  ties. 

Electric  Equipment  and  Reconstruction  of  the  New  Yoric  Terminal 
Lines  and  Qrand  Central  Station,  N.  Y.,  C.  &  H.  R.  R.  R.  (Bng.  News,  Nov.  15. 
1905). — Numerous  illustrations,  with  2-page  insert, 

Switch  Leads  for  Narrow-Oage  Track  (Eng.  News,  Dec  7,  1005).— 
Tratman's  formula. 

Reinforced-Concrete  Pence  Posts  (By  P.  L.  Wonneley,  Jr.  Bng. 
News.  Jan.  18,  1906). — Illtistrations  of  posts,  molds  for  making,  wire  attach- 
ment, etc. 

Summit  or  Hump  Yards  for  Qravity  Switchfaig  (Bng.  News,  Mar.  22, 
1906).— Illustrated. 

Curving  Rails  by  Power;  Nashville,  Chattanooga  &  St.  Louis  Ry. 
(By  G.  P.  Blackie.    Eng.  News,  May  31.  1906). — Illustration  of  mechaxusn:. 

Track  Construction  of  Underground  Railways  (Bng.  News,  Aug.  2. 
1906). — Illustrated. 

A  New  Snow  Scraper  for  Use  on  Locomotives  (Bng.  News.  Axxg.  9. 
1906).— The  Root  scrapei^— illustrated. 

Some  Tables  and  Other  Data  for  Railway  Locating  Engineers  (By   I 
C.  P.  Howard.    Eng.  News.  Sept.  13. 1906).— Formulas:  WeighUof  bridges; 
spiral  curves.    Tables:     Spiral   curves;   excavation   tables,    embankment 
tables;   box  culverts;  areas  for  waterways;  contents  of  retaining  walls  and 
abutments;   weights  of  trusses,  plate  girders  and  viaducts;  etc. 

Track  Construction  for  Railway  Tunnels  (Bng.  News,  Sept.  20, 
1906).— Illustrated. 

Devices  to  Keep  Railroad  Switches  Prom  BaconUng  Clogged  With 
Snow  and  Ice  (By  P.  G.  Shaw.  Eng.  News.  Oct.  18.  1900).— Two  systems 
described:  Gas  heating,  and  oil  heating. 

J     Bumping  Posts  are  illustrated  and  described  in  Bng.  Newt,  Oct.  2$, 

A   Simplined   Method   of   Uying   Out   Transition   Cnrvas  (By  T.  A«rf 

Ross.     Eng.  News.  Nov.   15,   1906).— Transition  curve  table  suitable  foH 

SDceda  ni  aVwrw..*-    oa  .-i i ^^1 


speeds  of  about  30'mUcs' per 'hour. 


MISCELLANEOUS  DA  TA,  1003 

Wooden  Tkt  Baited  in  CoocrtCe,  illustrated  in  Bng.  News.  Jan.  17. 
17.    See,  also,  discussions  of  Jan.  31  and  Feb.  7,  1007. 

A  Nois^Deadening  Experiment  on  the  Chicago  Elevated  Loop  (Bng. 
W8,  Feb.  21.  1007).— Illustrated. 

Tosts  of  Holding  Power  of  RaUway  Spikes  (Bng.  News.  Mar.  7. 1007). 
Testa  made  by  Mr.  Roy  I.  Webber,  Instr.  of  Civ.  Bng..  Unjv.  of  111.,  and 

results  arc  given  in  Bulletin  No.  6,  issued  by  the  Experiment  Station. 
ew  spikes  and  plain  spikes;  direct  pull  and  lateral  displacement. 

A  New  System  of  Block  Signaling  on  the  P.  R.  R.  (Bng.  News, 
y  0,  1007).— Illustrated. 

New  Ralls  for  the  Chicago  Street  Railways  (Bng.  News.  May  23. 
)7).— Specifications.    Illustrated  section  of  120-lb.  grooved  girder  ml. 

Experience  With  Wide-Base  RaiU  on*  the  A^  T.  &  S.  P.  Ry.  (Bng. 
ws,  June  18.  1007). — Illustrated  section  of  101-lb.  rail,  5}' high  and  6|' 
1th  of  base.    The  rail  was  desired  with  the  idea  of  giving  a  larger  bear- 

ttpon  the  ties,  and  using  it  without  tie-plates.  The  rail  was  not  easy  to 
L  and  the  mills  experienced  great  difficulty  with  it.  The  results  are 
d  to  have  been  satisfactory  as  far  as  the  effect  upon  the  ties  was  con- 
ned, but  it  has  been  found  that  the  rails  break  very  readily  in  the  base, 
e  rail  joints  have  20*  splice  bcus,  with  four  i'  bolts  spaced  6*  c.  to  c. 
ese  bars  weigh  about  75  lbs.  per  pair. 

A  New  lOO-lb.  RaU  Sectfon  (Bng.  News.  June  27,  1007).— Qlus- 
ited  (O'high,  and  5i' width  of  base).  Table  of  dimensions  of  heavy 
Is  compares  this  rail  with  the  A.  S.  C.  E.  (100-lb.).  Dudley  or  N.  Y.  C.  R.  R. 
)0-lb.).  and  the  A.,  T.  &  S.  P  (101-lb.— see  above). 

Notes  on  Recent  Rail  Design  (Eng.  News,  July  26.  1007).— Blus- 
ited  section  of  00-lb.  rail;  6|' high,  bV  width  of  base. 

Standard  Turntable  Pit;  Seaboard  Air  Line  Ry.  (By  Philip  Aylett. 
ig.  News,  Aug.  16,  1007).— For  70-ft.  tumUble.    Dlustrated  details. 

Sfando-Phase  Electric  Tractton  on  the  Rochester  Division  of  tlie 
IsRTk.  (By  W.  N.  Smith.    Bng.  News,  Oct.  17,  1007).— Illustrated. 

A  Tracklaylng  Machfaie  With  Rail  Carriers  (Bng.  News.  Nov.  28, 
07). — Illustrated.  Performance:  Rails  33  ft.  long,  2  to  2i  miles  of  track 
d  per  day  with  1  foreman.  4  men  to  operate  the  machine  and  feed  ties 
d  raUs.  o  men  to  distribute  and  space  ties,  8  spikers,  4  nippers,  and  1 
Ice  peddler. 

New  Interiocklng  Plant,  Hoboken  Terminal  Yard,  D^  L.  ft  W.  Ry. 
ng.  News,  Jan.  30,  1008).— Illustrated. 

Qeneral  Formulas  for  Simple  Curves  (By  T.  C.  Locke.  Bng.  News, 
if.  26.  1008). — Diagram  and  numerous  formulas,  prepared  aild  used  on 
bway  track  work. 

Train  Resistance  (Bng.  News.  Mar.  20,  1008). 

New  Steel  RaU  Spedfkatfons  of  P.  R.  R.  (Eng.  News,  Aprfl  16. 1008). 

New  Rail  Sectk>ns  and  Specifications  of  the  Am.  Ry.  Assn.  (Bng. 
w»,  May  14,  1008).— Two  types  illustrated:  A  and  B,  eadh  rolled  at  60-, 
\  80-,  00-,  and  100-lb.    Tables  of  properties. 

Standards  of  Track  Construction  on  American  Railways  (Bng.  News. 
a«  4.  liN)8). — Four  large  tables  comprising  tabulated  data  from  60  rail- 
ids:  Table  1. — Standard  Practice  as  Applied  to  Rails  and  Rail  Joints 
ifl|  weight  per  yard;  length:  type  of  section:  lightest  in  main  track, 
eororoke 


M  Joints;  type;  square  or  Droken;  number  of  bolts;  size  of  bolts;  spac- 
t  of  bolts;  nutlock;  nuts.    Splice  bars;  length;  weight  per  pair.    Special 

e tented  joints  used).  Table  2. — Standard  Practice  as  to  Ties  and  Plates 
;  wood,  and  where  obtained;  average  life  in  main  track:  cost;  re- 
tod  £or  wear  or  decay  mainly;  size,  length,  thickness,  widtn;  number 
V  l3-ft.  rail:  spacing  at  joints;  preservative  process;  number  of  treated 
^1  tase.  Tie-plates;  make;  size;  weight;  where  used).  Table  3. — 
■Urd  Practice  as  to  Progs  and  Switches  (Progs;  standard  pattern; 
K  or  rigid;  numbers,  for  main  track;  numbers,  for  yards;  flangeway 
■^fd  rail.  ins.  Switches;  standard  pattern;  length  of  switch  rail. 
■Otneous).  Table  4. — Standard  Practice  as  to  Spikes,  Ballast  and 
Hl^otection  (Spikss;  style;   size;  screw  spikes  used.    BallMtt  kind 


1M4  m.^RAILROADS. 

used;  size  of  stone;  depth  under  tie.  Qnard  rafls  for  corres;  on  wliat 
curves;  flangeway,  ins.;  are  tie  rods  or  bars  used  to  hold  gage  on  sharp 
curves?) 

Readjustment  of  Curves  and  Tangents  in  MalntcwanceN  off-Way 
Work  (By  W.  H.  Wilms.    Eng.  News,  Sept.  17,  1908).— Dlustratcd. 

Some  Special  Designs  of  Rails  and  Tle-Platas  (Eng.  News,  Oct.  15, 

1908). — Illustrated  sections  of  85>lb.  rails  for  Western  Pac.  Ry.  {^'  x  i^O 
and  Great  Nor.  Ry.  (5'  x  6*);  also  plans  of  four  tjrpes  of  metal  tie-plates 
in  use  on  different  railways. 

Cast  Manganese-Steel  Ralls  on  Curves,  Boston  Elev.  Ry.  (By  H.  U. 

Steward.  Eng.  News,  Oct.  22  1908).— Table  showing  comparative  life  ol 
rails  of  ordinary  Bessemer,  high  carbon  Bessemer,  mdkel-steel,  manganese^ 
steel  and  open-hearth. 

A  Study  of  Rail  Pressures  and  Stresses  in  Track  Prodoced  by  DV- 
ferent  Types  of  Locomotives  on  Curves  (By  E.  E.  Stetson.  Bulletin  No.  lOi 
Oct.,  1908,  Am.  Ry.  Assn.;  Eng.  News.  Nov.  26.  1008).— Extensive  tabic; 
and  analytic  disctission  of  pressures  and  stresses. 

A  Wedge  RaU  Fastening  for  Steel  Tics  (Eng.  News,  Dec.  24.  1908).— 
Illustrated.  It  requires  no  bolts  or  clamps;  tne  width  of  gage  can  bt 
varied  as  required  by  wear;  neatness  of  gage  can  be  obtained,  even  if  the 
rail  section  is  not  exact;  gives  greater  resistance  to  sheaiiiu;.  aa  compared 
with  bolts;  the  fastening  can  be  insulated;  and  it  is  impossible  for  derailed 
wheels  to  destroy  the  fastening. 

New  RaU  Specifk^ttons  for  the  P.  R.  R.  (Eng.  News.  Jan.  14. 1909). 

A  1300-Volt  Diract-Current  Electric  RaUway  (Eng.  News.  Jan.  2L 
1909).— The  Pittsburg,  Harmony.  Butler  &  New  Castle  Ry.  Table  <d 
horse  powers. 

The  Disadvanttfes  of  Concrete  Foundations  for  Railway    Croasinp 

(By  R.  P.  Black.  Eng.  News,  April  29.  1909).— (1)  The  concrete  gives  too 
rigid  a  bearing  imder  frogs,  causing  an  anvil  blow  at  frogs  which  soon  wears 
down  the  points,  especially  at  flat  crossing,  on  account  of  the  greater  dis- 
tance between  points.  ( 2)  This  anvil  or  solid  blow  is  hard  on  bolts,  especiallr 
when  high  speed  is  maintained  over  frogs.  (3)  In  a  high  speed  track  con- 
crete cracks  away  from  timbers  on  accotmt  of  the  excessive  jar.  (4)  It  is 
hard  to  maintain  a  good  surface  on  the  track,  as  the  concrete  footing  dors 
not  permit  of  raising.  (5)  The  ri^id  bearing  is  hard  on  equipment.  <e)  Tb« 
concrete  foundation  for  crossing  is  a  failure.  The  only  case  where  it  can  be 
used  to  good  advantage  is  where  traffic  is  light,  speed  low  and  an^  ci 
crossing  9(f*  more  or  less. 

Earthwork  CakruUtioiis  for  Side  HiU  Work  (By  R.  S.  Beard.    Bng. 

News,  Jime  10,  1009. — Diagrams,  formulas  and  tables. 

A  Railwav  Transfer  Table  Witlioiit  a  Pit  (By  H.  V.  MiUer.  Bng.  News, 
July  16,  1909).— Illustrated. 

Standard  Specifkations  for  Structural  Steel  for  Buildings  (Proc  A.  S. 
T.  M..  Vol.  IX.,  1909).— Adopted  Aug.  16,  1909. 

Standard  Specifications  for  BeMemer  and  for  Open-Hearth  Stael  RaAi 

(Proc.  A.  S.  T.  M.,  Vol.  IX..  1909).— Adopted  by  Aug.  16.  1909. 

Taper  Curves  Used  on  Southern  Padfk:  R.  R.  (Oct.  28.  1909).— Tables. 

formulas  and  illustrations. 

Special  Type  of  Track  Constructkm  for  Tunnels  and  Sobwajn  (Bng. 
News,  Aug.  19,  1909).— Illustrated,  with  tables  of  cost. 

Tie-Plates  and  Braces  for  Guard  Ralls  on  Sluup  Corves;  Natal  Govt  RyiL 

(Eng.  News,  Nov.  11,  1909). — Dlustrated  description. 

Street  Railway  Track  Construction  and  Pavfaw  (Report  of  Comm.  q« 
Way,  Am.  St.  and  Interurban  Rat.  Eng'g  Assn.,  Oct.  4  to  8.  1909;  Ei« 
News.  Nov.  11.  1909).— Use  of  T-RaiU  lii  Paved  Streets ^-Reoommend; 
tions:  (1)  Pot  track  construction  where  type  of  pavement  will  permit,  aa  9 
macadam  or  other  shallow  pavement,  the  T-tail  weighing  not  lest  than  fl 


MISCELLANEOUS  DA  TA.  1095 

lbs.  per  yd.  adopted  at  "recommended  practice"  by  the  Am.  Ry.  Eng.  and 
M.  of  W.  Assn.,  1M8.  (2)  For  heavy  service  in  connection  with  deep  block 
pavements,  a  T-rail  7  ins.  hi^h  with  a  6-in.  base.  17/32-in.  web  and  a  head 
of  2|in8.  wide  and  1-11/16  ms.  deep,  weighing  about  100  lbs.  per  yd.,  as 
illustrated  (not  reproduced  here).  (3)  For  light  service,  in  connection  vriih 
deep  block  pavement,  a  T-rail  7  ins.  high,  6-in.  base,  7/16-in  web.  2i  by 
1-9/32  in.  head,  and  weighing  80  lbs.  per  yd.,  as  illustrated  (not  reproduced 
here).  (4)  For  heavy  service  in  connection  with  deep  block  pavement  on 
streets  where  traffic  is  confined  to  the-  railway  strip,  etc.  (cities  of  large 
class),  the  half-grooved  (or  "Trilby")  section  recommended  in  1907.  Other 
Subjects  Discussed: — ^Track  in  paved  streets:  Opinions  of  City  Engineers, 
etc.,  as  to  St.  Ry.  track  construction;  Widening  gages  on  curves;  Cost  and 
life  of  steel  ties:  Wear  of  gage  lines  of  rails  on  tangents;  Creosoted  wood- 
block pavement:  Spacing  of  ties;  Setting  of  concrete  foundation;  Life  of 
rail  jomts  on  paved  streets;  Efficiency  of  electrically  brazed  and  soldered 
rail  bonds;  Discussions  on  rails,  ties,  foimdations,  paving. 

Train  Resistance  by  Various  Formalas  (Eng.  Rec..  June  4.  1010).— 
Table  of  train  resistance  in  pounds  per  ton  by  various  formulas:  (1)  Am. 
Ry.  Eng.  &  M.  W.  Assn.,  Bulletin  114.  p.  4;  (2)  Ditto.  Bulletin  84,  p.  100; 
(3)  Am.  Loco.  Co.,  Bulletin  1001.  p.  3;  (4)  Am.  Ry.  Eng.  &  M.  W.  Assn., 
Bulletin  120,  p.  26.  Experiments  indicate  that  train  resistance  increases 
with  the  speed. 

Ekmeotary  Theory  of  the  Qyroscope  in  the  Brennan  MononiB  Car  (By 
E.  V.  Huntington.  Eng.  News,  July  21,  1910). — Discussion  of:  (a)  Steady 
precession;  (b)  Accelerated  precession;  (c)  Application  to  the  monorail  car; 
fd)  Efficiency  of  the  Brennan  apparatus;  (e)  Proportions  of  the  car;  (f) 
Proofs  of  theorems.     Dlustrated. 

The  Track  and  Line  Constraction  of  Electric  RaUways  (Eng.  News,  Oct. 
17,  1910). — ^Tabular  results  of  inquiries  as  to  general  lines  of  practice  on  18 
nterurban  railways  and  1 7  street  railways  in  various  parts  of  the  country, 
rhe  tables  are:  (I)  Length,  track  arrangement  and  ballasting;  (II)  Grades 
nd  curves;  (III)  Rails  and  rail  joints;  (IV)  Ties  and  tie-plates;  (V)  Frogs, 
witches  and  switch-stands;  (VI)  Pole  equipment;  (VII)  Line  and  car  equip- 
lent,  signals,  etc.  These  tables  are  accompanied  by  a  general  discussion 
f  prevailing  practices. 

Monntahi  Rack  Railways,  and  the  Jungfrao  Ry.  hi  Switzerland  (By  E. 
.  Corthell.  Eng.  News,  Oct.  27.  1910). — Includes  a  table  of  67  railways 
I  Europe.  Asia  and  Australia,  and  North  and  South  America,  givinp;  date 
:  building,  ^age  of  track,  length,  grades  of  adhesion  and  rack,  kind  of 
action,  mimmum  curve  on  rack,  number  and  weight  of  locomotives,  and 
ain  weight. 
Track  Construction  on  the  Chkago  Street  Railways  (Eng.  News,  Nov. 
1910). — "The  complete  reconstruction  of  the  street  railway  tracks  in 
licago  was  one  of  the  requirements  of  the  new  system  of  mxinicipal  regu- 
Lion  and  the  agreement  between  the  city  and  the  companies,  which  went 
to  effect  about  three  years  ago,  and  by  which  the  city  exercises  a  strong 
ntrol  over  the  construction,  equipment,  operation  and  financial  affairs 
the  street  railways."  The  supervision  of  this  work  is  in  the  hands  of  a 
•ard  of  Supervising  Engineers,  composed  of  Bion  J.  Arnold.  George  Weston, 
irvcy  B.  Fleming,  John  Z.  Murphy  and  A.  L.  Drum.  This  article  gives 
istrated  descriptions  of: — (1)  Types  of  track  construction  (grooved 
der  rails  on  steel  ties  embedded  in  concrete;  same  with  wooden  ties; 
lOVcd  girder  rails  on  wooden  ties  on  broken  stone  ballast;  T-girder  rails 
:h  brick  paving;  tram-head  girder  rails  on  wooden  ties  in  macadam). 
Track  material  (rails,  with  table;  railjoints;  ties;  tic-plates;  spikes  and 
bars;  switches  and  frogs).  (3)  Foundation  and  paving  (broken  stone; 
Crete;  paving;  track  spacing;  track  grade  and  street  grade;  curves  at 
«t  intersections).     (4)  Methods  of  construction.     (5)  Track  deflection. 

Tfie  Electric  Bolt  Lock  as  Applied  to  Interlocking  (Report  of  Committee 

Power    Interlocking,  presented  at  annual  meeting  of  Railway  Sip;nal 

1..  Oct.  11-13.  1910;  Eng.  News,  Nov.  3,  1910).--The  principal  ment  is 

ty. 

Gravity  Freight  Classification  Yard  for  the  P.  R.  R.  at  Northumberland. 

(By   W.   A.  MacCart.     Eng.  News,  Nov.  17,  1910).— Dlustrated  des- 


1096  SO.—RAILROADS. 

Important  Dlastratioiis  for  Referaooe. 

Description.  Eng.  News. 

Railway  ditching  machine  for  small  cuts  and  fills  Jan.   20.  '10. 

Ties:  rein.-conc,  stcel-and-wood,  steel -and -concrete  Feb.   1%  '10 

Track  construction  with  114-Ib.  rails,  Belgium  Apr    14.  '10. 

120- ft.  turntable  for  Malet  locomotives.  A.  T.  &  S.  P.  Ry.  June  23>  '10. 

American  electric  locomotives  (tables)  Aug.     4,  '10. 

The  design  of  the  electric  locomotive  Aug.     4, '10. 

How  to  run  transition  curves  without  tables  (C.  P.  Howard)  Oct.    13.  '10. 

Concrete  and  timber  snow  sheds  on  Gt.  Nor.  Ry.  Dec.    15,  '10. 

A  deflection  recorder  for  track  switches,  N.  Y.,  O.  &  W.  Ry.  Dec   32.  '10. 

Bng.  Rec 

Street  railway  tract  construction  in  Charlotte,  N.  C.  Apr.   24.  *09. 

Curves  showing  relation  of  train  resistance  to  velocity  July   31,  '09. 

Track  details  on  German  railroads;  anti-creeper  Tan.    20,  '10. 

Cross-sections  of  single  and  double  track  roadbed  Feb.   10, '10 

Elevated  car  storage  yard,  Interborough  Rap.  Tr.  Co..  N.  Y.  Oct.    15.  '10. 


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60.— HIGHWAYS. 

A.— TRACTION. 

Power  of  a  Hone. — It  is  aenerally  estimated  that  an  average  horse 
weighing  1200  lbs.  can  exert  a  force  of  100  lbs.  for  a  day  of  10  hours  at  the 
rate  of  2^  miles  per  hr.,  on  a  fairly  level  n^de;  and  for  a  short  haul  he  can 
exert  a  force  of  2i  times  the  above,  or  250  lbs.  A  constant  force  of  100  lbs. 
at  2{r  miles  (13200  ft.)  per  hr.  is  equal  to  just  two-thirds  of  a  horsepower 
(H.  P.),  and  for  10  hrs.  it  is  equal  to  6f  horsepower-hours,  or  13  200  000 
ft.-lbs.  of  work. 

Effect  of  Road  Surfaces  on  Tractioo^ — ^The  tractive  force  required  to 
move  one  ton  of  2000  lbs.  on  various  kinds  of  level  roads  is  approximately 
as  follows: 

F  W  F:W     -  A 

Earth  road 100  lbs.  per  ton  of  2000  lbs.- 1:20     -  .06 

Macadam  road 40"  "  "      "    -1:60     -.02 

Granite  bkxdcs 30"  '*  "      "    -1:661   -.016 

Brick  pavement....   26"  "  "      "    -1:80     -.0126 

Asphalt  pavement..  20  "  "  "      "   —1:100  —.01 

From  I   8  "  "  "      "    -1:260  -.004 

Steelrails JTi"  "  "      "   -1:266|- .00375 

To...(  7  "  "  "      "   -l:286f-.0036 

Experiments  in  Iowa  showed  the  following  tractive  resistances:  Brick 
3avement,  26.4  to  68  lbs.  per  ton;  asphalt  pavement,  23.3  to  67.8  lbs.  per  ton. 
See  page  1142.) 

Effect  of  Qradea  on  Traction. — In  the  above  case,  if  we  let  F— the 

F 
ractive  force,  and  H^  — the  load,  then  will  -r^  —  ^4,  the  tangent*  of  the  angle 

f  repose,  or  grade  of  the  road  at  which  the  load  wotild  just  begin  to  slide 
r  descend  of  its  own  weight.  Hence,  if  F  lbs.  are  required  to  move  a  load 
/  on  a  level,  it  is  clearly  evident  that  2F  lbs.  would  be  required  to  haul  it 
p  a  grade  ^—i4,  3F  lbs.  up  a  grade  G  — 2^4,  etc.,  approximately.  This  propo- 
tion  is  often  erroneously  neglected,  the  usual  formula  given  being,  F—  WG, 
I  which  F— tractive  force,  Ir  —  load,  and  G— grade.  The  correct  formulas 
•e: 

F-W(i4+C7)  in  ascending (1) 

F'-W  iA-G)  in  descending (2) 

p 
lence  ^""A  +  G  "*  *^<*o^"« (3) 

Records  of  actual  tests  appear  in  various  works  stating  that  a  horse 
lich  can  pull  1000  lbs.  on  a  level  road,  can  pull   only   900  lbs.  up  a  1% 


ide.  810  lbs.  up  a  2%  grade,  760  lbs.  up  a  2J%  grade,  720  lbs.  up  a  2i% 
ide,  640  Hm.  up  a  3i%  grade,  640  lbs.  up  a  4%  grade.  600  lbs.  up  a  il% 
idc,  400  lbs.  up  a  6%  grade,  and  260  lbs.  up  a  10%  grade. 


Problem. — On  an  extremely  bad  earth  road  it  requires  a  constant  force 
» 100  Ite.  to  pull  1000  lbs.  on  a  level.  What  would  be  the  maximum  allow- 
e  grade,  assuming  that  F  could  be  increased  to  260  lbs.  while  ascending 

Solution. — ^Transposing  eguation  (3),  above,  we  have,  since  i4— 100+1000, 
MaximtiTrt  grade,  G^r  +  W—A 
250      100 

"lOOO    1000 

-0.16=15%.    Ans. 


*  Approximately:  see  Sec.  50,  Railroads,  page  992. 

1097  Digitized  by  Google 


1098  9fS.— HIGHWAYS, 

B.— ROADS  AND  STREETS. 

Definitions. — ^A  Street  is  a  public  way  in  a  city  or  town,  and  consists 
generally  of  a  roadway  and  two  sidewalks.  A  Road  consists  essentially  of  a 
xoadway  or  public  thoroughfare  through  a  county  district,  and  with  or  with- 
out sidewa^.  City  streets  are  usually  paved,  while  roads,  and  roadways  of 
streets  in  small  towns,  are  merely  surfaced.  Roads  and  streets  may  be  classed 
according  to  the  kind  of  surface  or  pavement,  the  selection  of  which  wiU 
depend  upon  the  kind  and  amount  of  traffic,  grades,  cleanliness  desired, 
material  available,  climate,  allowable  first  cost,  cost  of  maintenance,  etc 

Dirt  Roads,  sometimes  di«itfied  by  the  name  Earth  Roads,  are  the 
pioneers  in  any  new  country.  Dirt  from  the  sides  is  simply  thrown  up  into 
the  center,  forming  a  sort  of  crown  for  lateral  shedding  of  rain  water.  In 
the  Middle  West,  dirt  roads  are  constructed  very  rapidly  and  cheaply  by 
plowing  one  or  two  furrows  on  either  side,  and  usuig  scrapers  in  casting  th» 
material  up  for  the  crown  of  the  road.  Where  extensive  road -making  is 
contemplated,  it  is  well  to  figure  on  regxilar  road-making  machines. 

Corduroy  Roads  are  probably  among  the  first  in  any  new  country,  and 
in  thinly  populated  sections  generally,  to  supplant  the  common  dirt  load  in 
low.  marshy,  wet  ground.  The  typical  corduroy  road  consists  of  itmnd 
sticks  of  wood  a  few  inches  in  diameter,  laid  transversely  across  the  xxiad. 
These  are  sometimes  supplemented  with  half-round  stidcs.  or  slabs  frxnn 
saw-mills.    At  best  they  are  but  makeshifts,  and  give  way  sooner  or  later  to 

f>lank-  or  other  construction  of  surface  of  a  smoother  character  and  calling 
or  less  tractive  ixjwer  in  hauling.  Corduroy  roads  are  often  improved  by 
crowning  them  with  gravel,  using  sticks  or  poles  as  a  foimdation. 

PUnk  Roads  are  ustially  the  first  form  of  improvement  in  timbered 
sections  where  there  is  much  rainfall.  On  many  of  our  old  maps,  in  variotxs 
sections  of  the  country,  we  may  see  the  "Old  Plank  Road"  shown  in  dotted 
lines.  The  typical  plank  streets  now  being  constructed  in  otir  small  towns  of 
the  Pacific  Northwest  are  composed  of  planking  8*  to  4'  thick,  laid  trans- 
verselv,  and  spiked  (or  not)  to  longitudinal  wooden  stringers  of  size  say  4' 
by  l(r,  more  or  less,  spaced  about  4-ft.  centers. 
The  sidewalk  planking  is  ustially  about  V  thick,  suigimif^ 

laid  with  a  slope  of  about  K  per  ft.  toward  the  \ 

ctu-b.  A  simple  gutter  is  shown  in  Fig.  1.  For 
the  roadway,  the  planking  is  sometimes  laid 
level  from  .gutter     to  gutter,  and    sometimes  ^g^g^g 

crowned  in  the  form  of  a  paratx)la,  the  quarter 
points  being  {  the  height  of  the   middle.     The  „.     . 

method  sometimes  adopted  of  laying  the  middle  *^*'  *" 

third  of  the  roadway  level,  and  the  sides  sloping,  is  particularly  objectional^ 
because  of  the  two  continuous  longitudinal  joints  formed  aJong  the  edges 
of  the  level  portion.  If  the  street  is  on  a  steep  prade,  it  is  generally  best  to 
have  the  longitudinal  stringers  imder  the  planking  "broken"  and  not  "con- 
tinuous," in  order  to  prevent  excessive  wash  of  the  soil.  Two  nails  are  tised 
at  each  intersection  of  plank  with  stringer.  Barbed  wire  nails  are  most 
commonly  preferred.  Sometimes  the  planks,  if  very  heavy,  are  simplx  laid 
on  the  stringers  without  spiking,  but  this  method  is  objectionable.  The 
stringers  should  be  imbedded  firmly  in  the  ground. 

Qravel  Roads  are  excellent  when  properly  made.  Angular,  tnt  gravel  is 
the  best;  smooth,  sea-polished  gravel  will  never  bind  properly  unless  a 
binder  is  added,  and  that  increases  the  expense.  After  the  gravel  has  been 
screened,  'i'  to  li',  it  is  spread  on  the  ground  in  3*  or  4'  layers  and  thor- 
oughly compacted,  after  sprinkling,  with  a  steam  road  roller  weighing  fx^ 
3  to  10  tons.  A  small  quantity  of  clay  added  to  the  gravel  acts  asabinder 
and  it  is  still  further  improved  if  mixed  with  crushed  gravel  or  small  broken 
limestone.    Sand  should  not  be  used. 

Gravel  Walks  are  constructed  practically  in  the  same  manner.  The 
mam  thing  to  look  out  for  in  gravel  construction  is  good  drainage,  as  the 
V  ^  iS*?^  1  ^  easily  softened  when  saturated.  Tfle  or  box  under-drains 
SSIil  *u  *^  ^  *^^  °*^  ^®  surplus  water,  and  their  proper  use  greatly 
2,^???w  rt^  *^5*  °'  repairs.  Coal  tar  is  sometimes  used  with  gravel  in 
nawcing  foot-walks,  but  the  result  is  usually  unsatisfactory. 


ROADS  AND  STREETS.    PAVEMENTS,  1090 

BrokMKStoiM  PSivancot  has  undeisone  rapid  improvement  since  the 
advent  of  the  rock  crusher  and  the  steam  road-roller.  The  original  Telford 
and  Macadam  methods,  about  1825.  have  been  supplanted  by  more 
modem  methods  of  construction.  In  providing  for  a  good  pavement,  imder- 
drainage  should  be  provided  when  required;  a  sub-^rade  should  be  prepared 
by  removing  all  perishable  matter  and  the  top  sod;  the  under-soil  should 
be  compacted  and  a  fotmdation  of  gravel  prepared  when  necessary,  if  the 
best  results  are  expected.  The  bnucen-stone  shotdd  not  be  larger  than  2* 
for  the  softer  rock  or  li'  for  the  harder,  and  if  clean  it  should  not  (generally) 
be  screened,  as  the  stone  dust  and  chips  make  good  binders.  A  soft  stone 
foundation  and  a  hard  stone  surface  are  the  best.  Sand  and  gravel  may  be 
employed  to  fill  the  voids,  but  very  little  if  any  clay  or  loam  should  be 
used.  Crushed  granite  should  never  be  used.  Trap  or  basalt  is  best  for  the 
nirface,  and  limestone  for  the  bottom.  The  material  is  spread  in  layers  of 
ibout  4'  to  4i'.  sprinkled  sufficiently,  and  compacted  with  steam  road 
x>llers  weighing  5  to  10  tons.  It  will  roll  to  about  A  the  spread  thickness. 
Phe  thickness  of  broken  stone  pavement  is  usually  from  6*  to  10*.  althotigh 
['  is  auite  common.  It  is  to  be  noted  that  a  thin  pavement  laid  on  a  good 
rravel  fotmdation  is  often  superior  to  a  much  thicker  pavement  laid  directly 
•n  the  soil.  The  rolling  shotdd  begin  at  the  sides  and  work  toward  the 
rown  of  the  road. 

ffydranlk-Ccatirt  Pavemtnt  consists  of  a  3*  to  0*  concrete  base  tmder- 
iTing  a  wearing  surface  composed  of  one  part  hydratilic  cement  to  two  parts 
nely  crushed  rock,  H'  or  more  in  thickness.  The  concrete  base  may  rest 
a  a  gravel  or  cinder  bed.  The  finished  stirface  may  be  fltished  with  a  1  to  1 
lod  and  cement  mixture. 

Cerntni  Sidewalks  tisually  consist  of  a  1'  to  li'  wearing  surface  com- 
>sed  of  a  1  to  1  sand  and  cement  mixttire.  overlaying  a  8^  to  4'  concrete 
ise  resting  on  cinders.  The  wearing  surface  is  often  flushed  with  a  ptire. 
nearly  pure,  cement  mortar. 

Wood-Block  Pavements  have  given  good  results  when  properly  con- 
ructed,  but  the  expense  of  preparing  good  fotmdations  necessary  to  keep 
e  blocks  in  even  stirface  is  considerable.  The  bejt  fotmdation  is  a  layer  of 
Dcrete,  say  4'  or  more  in  thickness,  and  this  is  the  practice  in  Europe 
lere  this  kind  of  pavement  has  reached  its  highest  perfection.  It  is  also 
coming  standard  in  many  of  the  principal  cities  of  the  United  States. 
:periments  have  been  made  in  New  York  City  and  elsewhere  in  this  cotmtry 
tn  varying  degrees  of  success,  but  it  can  be  stated  that,  generally,  the 
nd  is  toward  some  more  permanent  form  of  construction.  This  is  the 
«  also  in  many  of  our  western  cities,  even  those  of  the  Northwest  where 
ibcr  is  very  plentiful  but  where  the  wood  block  is  being  supplanted  by 
halt,  brick  and  Belgian  block  pavements.  In  section,  the  blocks  may  be 
variotis  shapes,  rotmd,  square,  rectangular,  etc.,  but  the  rectangular 
tion  is  perhaps  the  most  common.  The  blocks  should  be  laid  with  the 
TS  or  grain  vertical  and  with  close  ioints.  In  the  cheaper  construction, 
ome  parts  of  the  West,  they  are  laid  on  a  bed  of  sand  resting  on  a  gravel 
adation.  or  on  planking  oi  single  or  double  thickness,  and  with  joints 
ked  with  sand.  In  the  better  construction,  they  are  laid  on  a  bed  of 
-tar  spread  on  a  concrete  fotmdation,  with  joints  smeared  with  tar, 
lalt  or  cement,  and  expansion  joints  provided  at  intervals  and  along 
curb.  Many  engineers  prefer  to  lay  the  blocks  so  the  course  of  joints 
be  diagonal  to  direction  of  traffic.  If  laid  square  they  are  more  easily 
ened  by  the  corks  of  the  horses'  shoes.  A  common  objection  to  wooden 
k  pavement  is  made  on  the  grotmd  of  cleanliness  or  sanitation.  The 
ks  shotild  be  treated  with  some  preservative,  as  creosote,  but  this  is  not 
ys  done.  Blocks  so  treated  expand  much  less  after  being  laid,  and 
provision  need  be  made  therefor;   but  if  laid  untreated  they  will  swell 

the  absorotion  of  moist  tire,  and  careful  provision  must  be  made  for 
nsion,  at  frequent  intervals.  The  writer  has  seen' 'blisters"  raised  on 
urface  because  of  lack  of  provision  in  this  respect.  The  harder  woods, 
k,  are  not  generally  used  m  this  cotmtry,  as  Uiey  wear  too  slippery. 

obblestone  Pavement  consists  of  cobblestones  from  4'  to  6'  in  longest 
Bter,  set  vertically,  with  the  fattest  end  up,  in  a  bed  of  gravel,  thoroughly 
led,  and  with  jomts  filled  with  gravel.  This  pavement  is  but  a  make- 
for  roadways,  and  is  bein^  supplanted  by  Belgian  blocks  or  other 
nent  of  better  qtiality.    It  is  frequently  used  for  gutters. 


1100  dO.—HIGHWAYS, 

B«ifiao  Block  Pavement  consists  of  hard  trap  or  basalt  blocks  of  stone 
laid  in  parallel  courses  and  rammed  into  a  bed  of  sand,  with  sand  joints. 
The  blocks  are  tisually  about  7  ins.  high  and  6  or  6  ins.  square. 

Qninite  Bh>ck  Pavement  is  supplanting  the  Belgian  blocks  as  the  latter 
did  the  cobblestones,  and  it  is  now  considered  the  beatpavement  for  heavy 
traflfic.  The  blocks  may  be,  say  7"  deep,  y  wide  and  1  Oblong,  laid  with  ccm- 
tinuous  parallel  joints  or  courses  at  right  angle  to  the  direction  of  traffic 
on  a  concrete  foundation  not  less  than  A'  thick;  6*  to  8*  is  better  for  un- 
usually heavy  traffic.  They  are  laid  directly  on  a  thin  layer  of  sand,  weH 
rammed  to  a  firm  bed.  and  the  joints  filled  with  bituminous  cement. 

Brick  Pavement  has  become  quite  popular  in  recent  years  in  certaia 
sections  of  the  country  where  a  moderately  durable  pavement  is  required 
for  all-around  traffic  at  not  too  great  expense.  The  brick  should  be  uni- 
formly hard-biimed  and  tough,  and  subjected  to  rigid  inspection  before  being 
laid.  They  should  be  laid  on  edge  in  parallel  courses  (with  broken  joints' 
at  right  angle  with  the  direction  of  traffic,  on  Portland  cement  concrete  4 
or  more  in  thickness,  with  a  cushion  layer  of  sand,  and  with  small  joints  so 
the  sand  will  work  up  into  the  joints  during  rolling.  The  bricks  may  be  of 
the  ordinary  size,  or  vitrified  blocks  mav  be  used. 
At  street  intersections,  the  courses  may  be  diagonal 
with  either  street.  There  is  no  advantage  in  laying 
bricks  herring-bone  fashion   as  in   Pig.    2,   except 

Serhaps  to  please  the  eye,  as  in  sidewalk  fancies, 
traight,  transverse  courses  give  a  better  foothold  Pig.  2. 

for  the  horses.  Bituminotis  cement,  or,  better,  Portland  cement  ^rout 
should  be  used  in  filling  the  joints  after  the  bricks  are  laid.  Sazid  is  far 
inferior  and  should  never  be  used. 

Asphalt  Pavement  takes  first  rank  for  combined  general  serviceabilit)*. 
low  tractive  resistance,  cleanliness  and  hygienic  properties.  It  consists,  is 
general,  of  about  a  4'  base  of  hydraulic  cement  concrete  or  bituminous  con- 
crete, for  a  foundation.  On  this  base  is  laid  a  J'  (finished)  cushion  coat  or 
binder  which  contains  about  3%  more  asphalt  cement  than  the  surface 
coat.  The  surface  or  wearing  coat  is  laid  with  a  finished  thickness  of  aboat 
2*.  It  is  composed  of  asphaltic  cement  (85  parts  pure  asphalt  and  15  parts 
heavy  petroleum  oil)  15%,  sand  and  stone  dust  80%,  and  crushed  carbonate 
of  lime  6%,  more  or  less;  the  proportions  often  being  varied.  A  bituminous 
base  is  composed  of  broken  stone  coated  or  mixed  with  coal-tar  cement. 
It  usually  calls  for  a  slightly  thicker  cushion  coat  than  the  above,  say  1^  to 
li",  and  also  a  1}'  wearing  coat. 

Asphalt  Paving  Blocks  are  made  in  a  variety  of  shapes,  and  laid  on 
sand,  gravel,  or  concrete  foundation. 

Bitnmlnous-Rock    Pavement  is  made  from  bituminous  sandstone  or 

limestone,  of  which  extensive  quarries  are"  worked  in  California,  Kentudn*, 
and  elsewhere.  The  quarried  rock  is  broken  up,  melted,  and  rolled  whue 
hot.  A  proper  amotmt  of  asphalt  is  added  if  necessary  to  give  the  required 
proportions.  The  product  is  commonly  called  rock  asphalt.  This  is  heated 
to  about  200^  P.  and  spread  in  a  finished  layer,  after  rolling,  of  about  St' 
in  thickness. 


d  by  Google 


PAVEMENTS.    ROAD  SPECIFICATIONS.  1101 

C— PAVEMENT  SPECIFICATIONS. 

ALLEGHENY  COUNTY  (PA.)  ROAD  SPECIFICATIONS. 

(Geo.  T.  Bomsley,  Chf .  Rd.  Engr.) 

Work  by  Contractor. — Do  clearing,  grubbing,  leveling,  grading,  surfac- 
ing; make  excavations,  embankments,  ditches,  drains,  gutters;  construct 
masonry,  stonework;  build  fences  and  protection  railings  required.  In  fact, 
complete  road  and  stnictures.  Excavation. — Straight  classiftcation,  and  in- 
cludes trees  and  clearing.  Embankments  rolled  in  layers  not  over  12*  thick. 
Earthwork  measured  and  paid  for  by  cu.  yd.  in  excav.  When  required,  top 
soil  to  be  removed  from  road  surface  and  deposited  as  directed.  May 
require  clay  and  spongy  materialto  be  removed  to  any  depth  and  replaced 
with  gravel  or  coarse  stone.  Where  possible,  embankment  slopes  to  be 
covered  with  3*  of  surface  loam.  No  work  on  covered  drains,  paved  gutters 
3r  foundations  to  be  paid  for  in  excavation.  Ordinarily,  no  allowance  for 
excavation  beyond  lines  of  cross-section.  Clearing. — Trees,  stumps,  bushes, 
X)ots,  etc.,  to  be  removed:  and  no  perishable  matter  allowed  imder  em- 
)ankmcnts.  Drainage. — Where  reouired,  a  trench  12*  wide  at  bottom  and 
15'  wide  at  top  to  be  excavated  at  least  Zff  below  sub-grade;  at  least  3*  of 
rravel  to  be  pLaced  in  the  bottom,  and  on  this  lay  salt-^Tazed  vitrified  drain- 
»ipc  as  directed,  with  bell  and  spigot  joints,  laid  with  open  joints,  ordi- 
arily:  then  fill  to  0*  above  pipe  with  gravel  between  1'  and  J*  screening; 
hen  fill  to  top  of  trench  with  stone  between  ST  and  2*  screening.  Open 
itches  paid  tor  as  excavation;  covered  drains,  bjr  the  lin.  ft.,  price  to 
iclude  all  expenses  of  trenching,  furnishing  and  laying  pipe,  refilhng,  etc. 
Hy  RabUe. — ^For  small  culverts,  ordinarily,  and  for  retaining  walls.  Spalls 
sed  only  where  needed  for  leveling  or  pinning;  lar^e  stones  for  fotmdation 
>urses,  and  for  heads  and  faces  of  culverts.  Covenng-stones  of  culverts  to 
;  not  less  than  12^  thick,  laid  close  together,  and  cracks  closed  with  pin- 
»^.  All  walls  to  be  of  coursed  rubble,  laid  with  best  bed  down;  breaking 
ints  at  least  1  ft,,  and  to  have  no  pinners  on  the  face;  joints  not  over  1  . 
id  walls  of  culverts,  and  all  retaining  walls,  to  be  capped  with  roughly- 
abbled  coping  stones  16'  thick,  at  least  24'  wide,  and  as  long  as  possible, 
its  masonry  paid  for  by  cu.  yd.,  actual  measurement.    Fencing. — -Posts  to 

straight  locust,  not  less  than  6*  dia.,  with  knots  hewn  down  to  face; 
aced  8  ft.  apart  and  set  3  ft.  in  ground,  with  3i  ft.  above  surface.  Top 
1  4'  sq.  ana  notched  into  top  of  post  so  all  surfaces  will  incline  45®;  in 
dition  to  spiking,  it  shall  be  held  with  a  ^*  by  II'  iron  strap  ZV  long, 
urely  nailed.  Side  rail.  2'  by  6'.  notched  mto  mside  of  posts  and  spiked, 
id  for  by  lin.  ft.  in  place.  Shaping  Sul>-Krades. — Before  the  foundation  is 
i.  the  roadbed  shall  be  shaped  and  rolled  with  a  steam  roller  of  at  least 
tons,  all  resulting  depressions  filled,  and  the  surface  again  rolled. 
indaljoas. — Upon  the  sub-grade  so  prepared,  a  foundation  to  be  laid 
Drding  to  method  a,  b,  or  c:  (a)  For  clay  or  wet  soil,  a  Telford  founda- 
I,  witn  stones  (y  to  8'  deep,  not  over  4'  wide  on  top,  and  6*  to  16'  long; 

by  hand  with  the  broadest,  edges  down  and  longest  side  across  the 
1,  on  the  sub-grade.  Not  over  10%  to  be  less  than  7'  deep.  Stones  to 
ik  jointa;  projecting  points  to  be  broken  off  with  hammer;  wedging 
es  to  be  driven  untO  foundation  is  to  grade  and  8'  thick.  Foundation 
I  to  be  rolled  with  not  less  than  10-ton  roller,  (b)  For  soil  of  medium 
tance,  spread  evenly  to  finished  depth  of  8'  broken  stone  between  3i' 

2^'  ring  dia.;  roll  this  with  roller  of  not  less  than  10  tons  imtil  the 
ie  mass  is  firmly  imbedded  into  the  earth  sub-way  and  the  top  is  4' 
V  finished  grade,  (c)  Where  nature  of  soil  will  permit,  spread  oroken 
>  6'  finished  depth,  and  roll  as  in  b.  Surfacing. — Upon  the  fotmdation 
ired  according  to  a,  b  or  c,  spread  two  layers  of  broken,  close-grained, 
rock,  granite,  ligonier  or  limestone,  free  from  dirt  or  dust,  and  broken 
irly  uniform  or  regular  cubes,  and  comparatively  free  from  fiakes  or 
^rs;  crushing  strength  of  not  less  than  20000  lbs.  per  sq.  in.  Con- 
>r  required  to  furnish  certified  copies  of  railroad  weights  for  macadam 
•ial  snipped  and  placed,  or  cu.  yds.  of  same  when  furnished  by  local 
ST.  The  first  layer  to  consist  ol  2^  to  2i'  broken  stone  and  to  be  2* 
w^hen  consolidated;  rolled  with  at  least  a  10- ton  roller,  all  depressions 
virith  stone  of  same  quality,  and  again  rolled  to  finished  surface  2' 

finished  grade.  The  second  layer  to  consist  of  2^  in  consolidated 
ess  of  5^*  to  IH'  broken  stone  to  which  may  be  added  a  proportionate 
it  of  i^^to^' screenings,  free  from  dust;  the  whole  surface  then  to  bo 


1102  90.'"HIGHWAYS. 

rolled  to  finished  ^rade.  If  ordered,  dtist  from  the  crusher  shall  be  laid  on  as 
a  binding  course,  just  sufficient  to  bond  the  top  and  make  the  surface  smooth, 
and  in  no  case  thicker  than  i';  then  sprinkled  and  the  whole  rolled  until 
mud  flushes  to  the  surface,  and  until  roller  causes  no  wave  in  surface. 
Engineer  may  vary  macadam  surfacing  from  6'  for  heavy  traffic,  to  4*  for 
light  traffic;  and  increase  width  of  macadam  from  14  ft.  to  22  ft..  or  decrease 
it  to  10  ft.  Mile  Stones. — Cut  granite.  10*  sq.  at  top  and  12*  sq.  at  bottom; 
5i  ft.  long,  3  ft.  above  groimd. 

BOSTON  (MASS.)  PAVEMENT  SPECIFICATIONS. 

(William  Jackson,  City  Engineer.) 
Granitb  Block  Pavbmbnt — Brick  Sidbwalk. 
Covws,  ^c— City  to  reset  and  repair  catch-basin  and  manhole  covets 
and  other  structures  to  be  left  in  street.  Preparing  Site. — Ground  to  be 
brought  to  proper  sub-grades;  bottom  of  excavation  for  sidewalks  and 
edgestones  to  be  rammed  and  rolled,  and  bottom  for  roadway  to  be  watered 
thoroughly,  made  solid  and  of  even  surface,  with  heavy  steam  road  roller, 
places  not  accessible  to  be  tamped  with  hand  rammers;  unsuitable  bottoms 
to  be  excavated  and  refilled.  Edgestones. — (a)  New  edgestones.  including 
circulars  and  comers,  to  be  of  Quincy,  Cape  Ann,  or  other  equally  good 
granite,  all  of  same  color,  cut  in  lengths  not  less  than  6  ft.,  free  from  Inindies 
and  depressions,  and  have  horizontal  beds;  ends  to  entire  depth  to  be  square 
with  top,  and  set  with  mortar  joints  not  over  f;  to  be  out  of  wind;  ham- 
mered surfaces  to  be  full  to  line;  to  be  7*  wide  on  top  and  20*  deep:  to  be 
hammered  on  top,  fine  pointed  3*  down  on  the  back,  squared  with  the  top. 
and  fine  pointed  10*  down  on  the  face;  remainder  of  face  to  be  straiglit  spHt; 


face  to  be  cut  square  with  top.    (b)  Excavation  to  be  18*  wide,  andits  bot- 

it  the  sub-grade  of  24'  below  top  of  finished  edgestone.     (c)  Upoo 

this  bottom,  the  foundation  to  consist  of  clean  coarse  gravel  4'  thick  when 


torn  to  be  at  t 


rammed;  then  more  gravel  to  be  spread,  the  edgestone  laid  thereon,  with 
closed  joints,  spaces  under  stone  thoroughly  filled  with  gravel  and  tamped 
firmly  to  grade,  (d)  Excavation  on  each  side  of  edgestone  then  filled  to  the 
sub-^rade  of  roadway  and  sidewalk,  respectively,  with  clean  gravel.  laid  in 
4'  layers,  each  rammed  and  tamped  tmder  and  around  the  edgestone,  and 
joints  carefully  pointed,  top,  front  and  back,  with  mortar,  oT equal  ports 
Natural  hydraulic  cement  and  clean,  sharp  sand,  (e)  Good  clean  gravel  then 
to  be  laid,  without  ramming,  against  and  up  to  top  of  edgestone  on  side- 
walk side;  after  which  the  roadway  paving  is  to  be  laid  and  rammed,  care 
being  taken  not  to  disturb  the  grade  of  stone;  and  thereafter  all  gravel  and 
other  material  on  the  sidewalk  side  to  be  excavated  to  depth  of  12*  bek>« 
top  of  edgestone,  and  replaced  by  gravel  in  4'  layers,  rammed,  to  sub-erade 
of  sidewalk.  Roadway. — (Either  gravel  base  or  concrete  base.)  Qmvcl  Base. 
— Sub-grade  to  be  12*  below  finished  surface  of  roadway;  and  on  this  tay 
gravel  base,  consisting  of  coarse-screened  paving  gravel,  not  larger  than  |  . 
thoroughly  rammed  into  a  solid  layer,  4*  thick  when  completed.  Concrete 
B«8C.--Sub-grade  to  be  16'  below  finished  surface  of  roadway;  and  on  this 
lay  concrete  base,  consisting  of  1  part  Portland  cement.  3  parts  screened 
coarse  sharp  sand,  and  7  parts  broken  stone,  not  larger  than  2 J'  and  very 
few  smaller  than  i',  and  evenly  graded  between  these  sizes,  (b)  Templates 
and  other  forms  used  to  hold  concrete  in  place,  to  be  set  true  to  lines  and 
grades,  and  secured  firmly,  (c)  Oment  and  sand,  just  before  concrete  is  to 
be  used,  to  be  mixed  dry.  then  add  only  enough  water  to  make  a  paste, 
thoroughly  worked  with  noes  or  other  tools;  broken  stone  is  then  wet, 
after  whidi  the  materials  are  handled  rapidly  to  the  end;  paste  is  spre^ 
evenly  over  pile  of  stones,  on  platform,  and  the  whole  turned  over  at  lasa 
twice,  thoroughly  mixed,  put  in  place  at  once,  and  thoroughly  rammed  so 
that  interstices  between  stones  are  filled  with  mortar  and  water  flushes  to 
surface,  made  true  and  parallel  with  finished  roadway,  (d)  After  ramming, 
concrete  allowed  to  set;  defects  remedied  with  |['x>d  concrete,  (e)  Wheo 
Portland  cement  is  specified  it  is  to  be  DykerhoflF,  Star  Stettin,  Alsni,  Alpihjk 
Lehigh,  Vulcanite  or  Atlas;  when  Natural  cement  is  specified  it  is  to  be 
Natural  hydraulic  cement,  equal  to  best  Rosendale;  other  brands  can  only 
be  substituted  when  approved.  No  cement  will  be  tested  in  cars,  or  in 
TOuras  of  transportation,  or  on  the  street.  QranHe  Block  Pavins. — (a 
Standard  granite  blocks,  SJ'  to  4'  wide,  7i'  to  8*  deep,  and  9*  to  14*  Vms 
(average  not  less  than  IIH:  edges  to  be  sharp  and  straight,  right  aiwlr 
Doth  horizontally  and  vertically,  faces  to  be  straight-split,  free  from  bunches 


PAVEMENT-GRANITE.  WOOD.    BRICK  WALK.  llOa 

and  depressions  exceeding  K,  and  carefully  piled,     (b)  Unon  the  gravel  or 

concrete  base,  spread  a  layer  of  clean,  coarse-screened  oedding  sand,  on 

which  lay  the  blocks  in  cotirses  of  uniform  depth,  at  ri^ht  angle  with  street 

line  (ordinarily),  with  close  joints,  the  longitudinal  joints  broken  by  lap  of 

at  least  2*,  sumcient  sand  being  used  to  bring  blocks  to  grade,  after  thor- 

ough  ramming;  then  covered,  and  covering  raxed  and  swept  until  joints  are 

filkd,    blocks  then  thoroughly  rammed  to  unyielding  bed,  with  surface 

parallel  with  grade  and  crown  required ;  then  again  covert  and  raked  and 

swept  as  before;  blocks  again  rammed  until  solid  and  secure  at  grade  and 

crown  of  finished  roadway;  no  ramming  done  within  15  ft.  of  paving  being 

laid;  one  rammer  to  each  paver,    (c)  If  blocks  are  laid  with  Gravel  Joints, 

cover  blocks  (after  being  rammed)  with  clean,  coarse-screened  sand,  dried 

by  artificial  heat  if  necessary,  and  rake  and  sweep  imtil  joints  are  filled; 

entire  area  covered  with  l"  layer,    (d)  If  blocks  are  laid  with  Pitch  Joints. 

lav  as  above,  but  the  covering  is  to  be  washed  pebbles,  equal  to  best  Long 

Island  white  pebbles,  y  to  f',   thoroughly  heated  and  raked  or  swept, 

filling  joints  to  within  I*  of  surface;  joints  then  filled  with  paving  cement  of 

proper  consistency,  flush  to  grade  and  crown  of  finished  roadway;    the 

cement  left  upon  top  of  blocks  to  be  covered  with  dry  sand,  sufiScient  to 

absorb  the  cement  if  reouired.    The  paving  cement  to  be  obtained  by  the 

direct  distillation  of  coal  tar,  and  kept  at  a  temperature  of  300°  P.  while 

being  used.    Flagging  Crosswalks. — (a)  Granite  flagging  stone,  each  exactly 

2  ft.  wide,  not  less  than  4  ft.  long,  of  same  thickness  as  the  others,  not  less 

than  6*  nor  more  than  7*,  of  best  grade  and  quality,  uniform  color,  top 

rough  pointed,  and  ends  jointed  and  square-cut  to  full  depth  of  stone. 

(b)  Upon  the  gravel  or  concrete  base,  spread  a  layer  of  clean,  coarse-screened 

bedding  sand,  in  which  lay  the  flagging  crosswalks;    to  oe  rammed  and 

tamped  to  a  solid  and  unyielding  bed,  sufficient  saad  being  used  to  bring 

surface  of  flagging  to  grade  and  crown  of  finished  roadway,  after  ramming. 

fc)  If  crosswalks  are  to  be  laid  with  Gravel  Joints,  fill  joints  with  sand  as  for 

i)Iock  paving  with  ^rravel  joints,    (d)  If  crosswalks  are  to  be  laid  with  Pitch 

foints,  fill  joints  with  paving  cement  as  for  block  paving  with  pitch  joints. 

srlck  Sidewalks. — (a)  Bricks  to  be  burned  hard  entirely  through,  straight- 

^ged,  of  compact  texture,  regular  and  tmiform  in  shape  and  size;   bricks 

vhich  after  being  thoroughly  dried  and  then  immersed  m  water  for  24  hrs. 

ibsorb  more  than  16%  of  their  volume,  may  be  rejected;   any  edge  of  a 

irick  sidewalk  not  against  a  curb  or  buildings  is  to  be  supported  by  a  con- 

inuous  spruce  plank,  2*  by  8*.  held  by  2^  by  4'  spruce  stakes  driven  in  the 

round,    (b)  Excavation  for  sidewalk  is  to  have  its  bottom  brought  to  sub- 

rade  8^  below  finished  surface  of  walk,  and  on  this  lay  foundation  consisting 

f  coarse-screened  paving  gravel,  not  larger  than  f,  rolled  and  rammed  so  as 

>  be  4'  thick  when  completed,     (c)  Gn  this  foundation,  spread  a  l^yer  at 

ast  2^  thick  of  clean,  sharp  sand,  parallel  with  finished  grade  of  walk:  on 

lis,  the  bricks  are  to  be  laid  on  tneir  widest  side,  in  courses  of  imiform 

idth  and  depth,  at  right  an^le  with  street,  or  in  herring-bone  fashion,  with 

ose  joints,  all  longitudinal  joints  broken  by  at  least  2rl  the  bricks  then  to 

•  covered  with  clean,  fine,  dry  sand,  using  screen  of  20  meshes  to  an  inch: 

id  upon  the  bricks,  a  plank,  covering  several  courses,  is  to  be  placed  and 

mmed  carefully  with  a  heavy  hammer  to  a  firm  bed,  with  surface  to  proper 

ade;    then  spread  fine  sand  over  surf§ce  and  sweep  or  rake  so  as  to  fill 

ints. 

Wood  Block  Pavbmbnt — Brick  Siobwalk. 
Coven,  etc. — (Same  as  for  granite  block  pavement.)  Preparing  Site, — 
ixne  as  tor  granite  block  pavement.)  Edgestones. — (Same  as  for  granite 
►ck  pavement.)  Roadway. — (Either  gravel  base  or  concrete  base.)  Qravel 
%€.--— (Same  as  for  granite  block  pavement.)  Concrete  Base. — (Same  as  for 
inite  Diock  pavement,  except  that  sub-grade  is  to  be  lOJ*  below  finished 
face  of  roadway  for  wood  block  pavement.)  Flagging  Crosswalks. — (Same 
for  sranite  block  pavement.)  Wood  Block  Pavement. — (a)  Southern  long- 
f  yeUow  pine,  not  less  than  90%  of  heart,  texture  permitting  satisfactory 
itznent;  sticks  inspected  at  works  before  being  sawed  into  blocks. 
Blocks  to  be  of  sound  timber,  free  from  bark,  loose  or  rotten  knots,  or 
cr  defects  which  would  be  detrimental  to  life  of  block  or  interfere  with 
tns:  no  second  growth  timber  allowed,  (c)  Blocks  to  be  well  made, 
.ajiffular  and  of  tmiform  size:  depth  (parallel  to  fiber)  4';  length  not  less 
n  8*;  width  not  less  than  4';  depth  and  width  to  be  exact,  (d)  The 
hod  of  Treatment  to  conform  to  the  best  and  most  advanced  knowledge 
he  art,  the  purpose  being  to  allow  contractors  to  manufacture  block  by 


1104  eo.— HIGHWAYS. 

following  any  preferred  detail  and  by  use  of  any  process  which  may  properiy 
be  adapted  to  secure  the  results  demanded,  namely,  that  all  parts  of  each 
block  snail  be  thoroughly  impregnated  with  *he  preservative  (an  antiseptic 
and  water-proofing  oil),  not  less  than  20  lbs.  per  cu.  iU  of  wood;  the  block 
not  to  split  or  warp,  and  to  have  a  specific  gravity  greater  than  that  of 
water,  (e)  The  preservative  to  have  a  specific  gravity  not  less  than  1. 12  at 
68°  F.  When  distilled  in  a  retort,  with  the  thermometer  suspended  not  less 
than  1"  above  the  oil,  it  is  to  lose  not  more  than  36%  up  to  315**  C.  and  not 
more  than  50%  up  to  370**  C.  Oil  to  be  free  from  adulteration  or  foreign 
material,  (f)  After  treatment  the  blocks  are  to  show  such  waterproof 
qualities  that,  after  being  dried  in  an  oven  at  a  temperature  of  100**  for  a 
period  of  24  hours,  weighed,  and  then  immersed  in  clear  water  for  a  period 
of  24  hours  and  weighed,  the  gain  in  weight  is  not  to  be  greater  than  3%. 
(g)  Material  and  blocks  may  be  rejected  if  not  satisfactory,  (h)  Upon  the 
surface  of  the  concrete  foundation  is  to  be  spread  a  b^  of  cement  nuntar 
i'  thick,  the  surface  to  be  composed  of  slow-setting  Portland  cement  and 
clean,  sharp  sand,  free  from  pebbles  over  i"  diameter,  1  part  cement  to  4 
parts  sand ;  this  mortar  top  to  be  thoroughly  rammed  into  place  with  con- 
crete rammers  until  all  unevenness  in  the  concrete  is  taken  up,  and  is  then 
to  be  "struck"  to  a  true  surface  parallel  to  top  of  finished  pavement,  (i)  On 
this  mortar  stirface,  lay  the  blocks  with  the  grain  vertical  and  at  such  an 
angle  with  the  ctirb  as  may  be  directed;  to  be  laid  in  parallel  courses  with 
tight  joints,  firmly  imbedded  in  the  mortar  bed  so  as  to  form  a  true  and  even 
surface,  (j)  Joints  then  to  be  filled  with  cement  grout,  2  parts  clean  sand 
and  1  part  Portland  cement,  mixed  to  a  liquid  form,  and  the  surface  of  the 
block  slushed  with  same  and  the  joints  swept  until  completely  filled;  ex- 
pansion joints,  filled  with  a  paving  cement  of  proper  consistency,  to  be 
made  next  the  edgestones.  Stirfacc  then  covered  with  i'  of  screened  sand, 
(k)  Where  grade  of  street  is  more  than  8%,  the  blocks  are  to  be  not  less 
than  8'  nor  more  than  10"  long,  and  the  upper  edge  of  each  block  is  to  be  cut 
away  for  a  width  of  i',  and  a  depth  of  1  ,  to  provide  a  transverse  groove 
between  each  course  of  blocks  when  laid  in  place:  or  such  other  construction 
is  to  be  used  as  will  provide  an  equally  good  foothold  for  horaes.  Brkk 
Sidewalks. — (Same  as  granite  block  pavement.) 

Asphalt  Pavement. 

Bituminous  Concrete  Binder. — (a)  On  the  concrete  base,  covered  with 

Trinidad  asphalt,  lay  the  binder,  (b)  In  making,  use  15  gallons  Trinidad 
asphaltic  cement  and  1  cu.  yd.  of  crushed  stone,  not  over  f,  heated  and 
thoroughly  mixed,  (c)  In  using,  this  binder,  while  hot  and  plastic,  is  to  be 
evenly  spread  and  thoroughly  rolled  until  the  roller  ceases  to  make  any 
impression,  the  compressed  binder  to  be  at  least  IJ*  thick,  on  which  aa 
asphalt  wearing  surface  is  to  be  laid.  Trinidad  Wearinf  Surface. — ^For 
Trinidad  asphalt  pavement,  the  wearing  surface  is  to  be  composed  of  (I) 
Trinidad  Lake  asphalt,  specially  refined  and  brought  to  a  uniform  standard 
of  purity  and  gravity;  (2)  heavy  petroleum  oil,  freed  from  all  impurities 
ana  brought  to  a  specific  gravity  of  18**  to  22**  Baum^,  and  a  fire  test  of 
250**  P.;  (3)  sand  entirely  tree  from  clay  or  other  objectionable  material,  of 
such  size  that  none  of  it  will  oass  through  a  No.  80  screen,  and  all  Uirough  a 
No.  10  screen;  (4i  powderea  carbonate  of  lime  of  such  degree  of  fineness 
that  15%  by  weight  will  pass  through  a  No.  100  screen,  and  all  through  a 
No.  26  screen,  (b)  In  making,  100  parts  of  the  asphalt  and  15  to  20  parts 
of  the  petroleum  oil  are  to  be  made  into  an  asphaltic  cement,  which  is  to 
have  nre  test  of  250**  P.,  and  a  temperature  of  60^  F.  is  to  have  a 
specific  gravity  of  1.19;  this  cement  and  the  sand  are  to  be  kept  heated 
separately  to  about  300**  P.,  and  the  carbonate  of  lime  is  to  be  kept 
cold;  70  to  83%  of  the  sand  so  heated  and  5  to  15%  of  the  lime  while  cold 
are  to  be  thoroughly  mixed  together,  but  the  lime  may  be  reduced  or 
omitted  if  the  sana  is  satisfactory  in  quality  and  qtiantity;  to  this  mixture, 
while  so  heated,  is  to  be  added  12  to  15%  of  asphaltic  cement  at  a  tempera- 
ture of  about  300**  P.,  kept  at  that  temperature,  and  thoroughly  mixed  in 
a  suitable  apparatus,  (c)  In  using,  spread  the  above  mixture,  at  about 
250**  P.,  evenly  on  the  concrete  binder  by  hot  iron  rakes,  to  produce  a  xini- 
form  surface;  then  compress  with  tamping  irons  and  hand  rollers  and  sweep 
a  small  amount  of  dry  hydraulic  cement  over  H;  then  thoroughly  compact 
by  st^m  roller,  not  less  than  5  tons,  until  roller  fails  to  make  any  mipr^skm 
w  -"Ji  *^  c*  *ii®  finished  wearing  surface  not  to  be  less  than  1  J'  thick.  Siciliaa 
wearing  Surface. — (a)  For  Sicilian  asphalt  pavement,  the  wearing  aorface  is 


PAVEMENT— ASPHALT,  BITUUTHIC,  MACADAM.      UOfi 

to  be  oompoeed  o£  (1)  natural  bituminotis  limestone  rock,  mined  by  the 
"United  Lunmer  &  Verwohle  Rock  Asphalt  Co.,  Limit^,"  at  Raigusa, 
Sicily;  (2)  limestone  rock  mixed  by  said  company  at  Vorwohle,  Germany. 
(b)  m  making,  8  or  4  parts  of  the  Ragusa  rock  are  to  be  thorotighly  mixed 
with  1  part  of  the  Verwohle  rock,  and  this  mixture  to  be  crushed,  pulver- 
ized to  a  powder  and  passed  through  a  fine  sieve,  nothing  being  added  or 
taken  from  the  powder,  (c)  In  using,  spread  the  above  mixtxire,  at  about 
160^  P.,  evenly  upon  the  concrete  base,  and  compress  evenlv  by  heated  hand 
rollers  and  rammers,  smooth  by  heated  smoothers  and  roll  for  2  or  8  days 
with  a  heavy  iron  roller  until  it  ceases  to  make  any  impression,  the  finished 
wearing  surface  not  to  be  less  than  2f  thick,  ^oal  Tar  Painting. — ^The  wearing 
surface,  to  a  width  of  24'  from  ctirb,  is  to  be  painted  with  coal  tar  distil- 
late and  ironed  with  hot  smoothing  irons,  to  make  a  continuous  layer  without 
holes. 

BiTULITHIC  PaVBMBNT. 

Sab-Qrade. — CT  below  finished  surface  of  roadwair.  Cnislied  Stone  Founda- 
tion.— Upon  the  sub-grade,  lay  a  foundation  consisting  of  a  layer  of  hard 
cmshed  stones  to  a  depth  of  0  ,  and  compress  with  heavy  steam  road-roller. 
L'pon  these  stones,  spread  a  thin  layer  of  Warren's  No.  1  Puritan  brand 
bituminous  semi-liquid  cement,  to  be  flexible  and  to  unite  freely  with  the 
:old  stones.  Upon  this  cement,  spread  a  heavy  coating  consisting  of  1  gallon 
>f  Warren's  No.  24  Piuitan  brand  hard  bittmiinous  cement  to  each  sq.  yd. 
)f  stirface.  the  wearing  sxirface  immediately  spread  thereon,  and  the  stones 
irmly  bound  together  and  with  the  wearing  surface  by  this  coating.  Wearing 
Surface. — Hard  crushed  trap  rock  to  be  heated  in  a  rotary  mechanical  dryer 

0  a  temperature  of  about  250°  P.  This  material  then  to  be  elevated,  passed 
hrough  a  rotary  screen  having  6  sections,  each  with  a  different  sized  opening, 
he  largest  1)'  and  the  smallest  i^'  diameter,  the  materials  to  be  separated 
•y  these  sections  into  6  lots,  each  lot  consisting  of  the  materials  passing 
hrough  one  of  the  sections  of  the  screen  into  a  separate  compartment  or 
in.  The  materials  in  each  lot  are  then  weighed  separately  and  mixed  with 
he  materials  of  each  of  the  other  lots  into  batches,  in  the  proportions  which 
lall  have  been  determined  by  laboratory  tests  to  give  the  best  results, 
lat  is,  the  most  dense  mixture  of  mineral  aggregate  having  inherent 
ability;  and  if  the  fine  crushed  rock  does  not  provide  the  best  proportion 
f  fine-grained  particles  there  must  be  supplied  not  more  than  15%  of  hy- 
raulic  cement,  ptilverixed  stone  or  very  fine  sand.  Each  batch  is  then 
issed  into  a  **Twin  Pu^"  or  other  approved  form  of  mixer,  and  then  mixed 
ith  a  sufl&cient  quantity  of  Warren's  No.  21  Puritan  brand  bituminous 
aterproof  cement  to  thoroughly  coat  all  the  materials  s^id  fill  all  voids;  the 
mcnt  when  tised  is  to  be  at  a  heat  between  200**  and  250*  P..  and  the 
nount  used  with  each  batch  is  to  be  accurately  weighed  and  used  in  such 
oportions  as  shall  have  been  determined  by  laboratory  tests  to  give  the 
St  results,  the  mixing  to  continue  imtil  mixture  is  a  uniform  bituminous 
ncrete,  thiat  will  when  cold  have  as  closely  as  practicable  the  solidity  and 
nsitv  of  solid  stone.  This  concrete  is  imm^iately  after  mixing  to  be 
uled  to  the  street,  spread  on  the  No.  24  cement,  and  compressed  with  a 
.am  road-roller  to  finished  thickness  of  2f.  Surface  Finbh. — On  the  wearing 
rface,  a  thin  coating  of  Warren's  quick-drying  bituminous  fiush-coat  com- 
sition  is  to  be  so  spread  over  the  surface  that  any  unevenness  or  honey- 
nbing  in  the  concrete  is  filled.  A  thin  layer  of  stone  chips  is  then  to  be 
led  into  the  «irface  so  it  will  be  gritty  and  not  slippery.  In  Qeneral. — 
ch  layer  of  the  work  to  be  kept  as  free  as  possible  from  dirt  so  that  the 
crs  will  unite.  Bituminous  cement  used  shall  be  free  from  water,  pctro- 
m  oil,  water  gas  or  process  tars,  and  all  light  oil,  naphthalin  and  other 
stalline  matter  susceptible  to  atmospheric  influences  removed  by  refining. 

Macadam  Roadway — Crush bd-Stons  Sidewalk. 

QrmnHe  Block  Paving. — ^To  be  used  for  gutters  and  brows  for  crosswalks; 
;k«  to  be  Si"  to  4 J'  wide,  7*  to  8*  deep,  and  T  to  12*  long  (average  not  less 

1  10^.  Sub-grade  12*  below  finished  surface;  on  this,  the  gravel  base 
hick  nvhen  completed.  On  this  foundation,  spread  a  layer  of  bedding 
1,  and  in  this  lay  the  blocks,  in  courses  of  uniform  width  and  depth  at 
t  ansle  with  street  line  (ordinarily),  with  close  joints,  longitudinal  joints 
ins  at  least  2^,  enough  sand  used  to  bring  blocks  tograde;  usual  spread- 
)f  gravel  on  surface,  sweeping  and  ramming.    Brick  Block  Paving. — ^To  be 

{€>r  gutters  and  crosswalks;  blocks  to  be  re-pressed,  hard,  tough,  com- 


1106  m.— HIGHWAYS. 


^^     -  -       .   .   average  U«- — 

weight  not  to  exceed  20% ,  and  no  one  brick  to  lose  more  than  24%.  Ab90TT>- 
tion  Test,  using  6  bricks  previously  subjected  to  rattler  test,  or  bncks  bxt^ces 
in  half;  bricks  to  be  dried  48  hrs.  at  230°  to  250°  F.,  then  weighed  and  im- 
mersed in  water  48  hrs.,  wiped  and  weighed,  increase  in  weight  not  to  exceed 
4%.  Sub-grade  for  brick  blocks  to  be  10*  below  finished  surface;  on  this, 
lay  4"  layer  of  paving  gravel.  On  this  foundation,  spread  a  layer  of  bedding 
sand,  and  in  tnis  lay  the  bricks,  in  courses  of  uniform  width  and  depth  at 
right  angle  with  street  line  (ord&arily),  with  close  joints,  longitudinal  joints 
lapping  at  least  2*.  enough  sand  used  to  bring  blocks  to  gz^de,  usual  spmKlicf 
of  gravel  on  surface,  sweeping  and  ramming.  Macadain  Surface. — Sub-grade 
0*  below  finished  surface;  on  this  lay  the  macadam  surface,  made  as  foUovs: 
Hard,  durable,  broken  stones,  either  of  the  best  quality  of  broken  trap  or 
Roxbiuy  conglomerate,  or  of  acceptable  field  stone,  2i'  to  1*  diameter  screen, 
free  from  round  or  other  ill-shaped  or  improper  stones,  to  be  spread  over  whole 
surface  of  base,  and  thoroughly  rolled  and  packed  with  15-ton  steam  road- 
roller,  tmtil  suriace  is  i'  below  finished  roadway:  spaces  between  stones  then 
to  be  filled  with  fine  screenings  or  binding  gravel  applied  in  at  least  3  layers. 
each  layer  thcrroughlv  worked  in  by  wetting  and  rolling  aforesaid  before  the 
next  layer  is  appliea,  and  dtiring  the  operation  the  surface  to  be  brought, 
with  the  broken  stone,  to  a  finished  grade.  Crushed-Stone  Sidewalk. — Sub- 
grade  5*  below  finished  surface  of  walk;  on  this,  spread  2}"  to  1'  broken 
stone,  making  a  3*  layer  after  rolling  and  ramming.  On  this,  a  layer  of  No.  2 
crushed  stone  to  be  spread  and  thoroughly  rolled  to  2*  thick.  On  this,  spread 
a  layer  of  fine  screenings,  trimmed,  watered  and  rolled  with  steam,  horse  or 
hand  rollers  so  as  to  make  a  hard ,  compact  sidewalk  at  required  grade.  Edges 
to  be  supported  by  spruce  plank  if  required. 

THE  PROPER  CONSTRUCTION  OF  BRICK  STREET  PAVEMENTS. 

(Will  P.  Blairt.) 

Sub"Qrade. — Must  be  drained,  graded,  compacted  and  parallel  with 
grade  of  finished  street;  not  essentially  different  than  required  for  other 
pavements.  A  depression  here  and  there,  a  spot  of  loose  earth,  a  lack  of 
thorough  compaction,  or  a  wet  condition  due  to  improper  drainage  wiH  be 
followed  by  disaster  to  the  street  as  a  whole.  Foundation. — (a)  Impos^hle 
to  define  the  proportions  of  cement,  sand,  broken  stone  or  gravel  that  shall 
compose  the  mix,  because  of  the  varied  qualities  of  these  materials;  but  in 
order  to  secure  maximum  strength  they  must  be  mixed  dry  in  the  first  in- 
stance, and  then  thoroughly  mixed  after  the  water  is  applied,  fb)  Either 
in  the  machine  or  hand  mixing,  an  intelligent  supervision  is  worth  while  at 
all  times.  The  value  of  the  concrete  is  often  reduced  at  least  60%  by  care- 
lessness, by  ignorance  or  indifference,  by  application  of  too -much  or  too 
little  water,  by  lack  of  proper  proportion  of  some  one  or  another  of  the 
other  ingredients  composing  the  lotmdation,  resulting  in  1,  2,  or  3  sq.  yds.  of 
the  concrete  foundation  being  of  no  more  value  than  merely  loose  pil«  of 
stone  or  gravel,  (c)  The  concrete  surface  as  it  is  put  in  place  must  have  a 
uniform  surface  witn  grade  of  finished  street,  and  the  sxirface  must  be  snoooth. 
This  cannot  be  accomplished  by  the  eye;  the  grade  stakes  should  be  set  at 
no  greater  distance  apart  than  4  or  6  ft.  If  any  stone  used  in  the  concret* 
exceeds  2*  in  largest  diameter  it  will  be  next  to  impossible  to  accomplish  the 
condition  desired.  Sufficient  water  should  be  used  in  the  mixing  ao  that  otw 
man  can  smooth  the  top  with  an  ordinary  dirt  shovel — never  should  it  be  so 
stiff  as  to  call  into  use  a  rammer.  When  we  say  "smooth  surface"  we  mean 
that  a  greater  variation  than  1'  shall  not  be  allowed.  Sand  Cushion. — Musi 
be  2"  thick;  if  less,  it  will  not  afford  a  sufficient  relief  from  the  vibratioo 
created  by  the  impact  of  travel;  if  more,  it  cannot  be  sufficiently  compacted 
to  afford  a  support  to  the  load  coming  upon  the  brick  street,  and  prevent 
cracking  and  crushing  of  the  joints  of  the  cement  filler  which  is  required  in 
fiinishing  the  street.  Thus,  this  cushion  must  be  of  such  a  thickness  ttiat 
will  afford  relief  from  the  impact  and  weight,  slight  though  it  be.  yet  axffi- 
rienthr  imyielding  to  furnish  the  support  for  the  load  it  must  bear.  Expui> 
sion  Cushion. — ^This  must  be  proviaed,  after  the  sand  cushion  is  spreaa.  by 

*  Sec  page  607. 

t  Secretary  National  Paving  Block  Manufacturers'  Association. 


PAVEMENT— BRICK  (STREET),  BOULDER.  1107 

idng  next  the  curb  a  board  of  sufficient  width  to  extend  above  the  height 
the  brick:  and  in  order  that  it  may  be  drawn  readily,  it  is  advisable  that 
tredge  be  dropped  at  intervals  of  3  or  4  ft.  behind  this  board  and  extending 
3ve  it  from  dr  to  4';  the  wedges  to  be  i'^  thick  at  top;  the  thickness  of 
ard  varying  with  width  of  street,  providing  sufficient  thickness  ranging  &x>m 
to  1^*.  Layinff. — ^The  brick  shotild  be  placed  in  the  street  with  the  best 
{e  up.  This  is  a  rule  tmiversally  required  of  brick  construction  in  masonry 
rk.  In  order  that  this  shall  be  done,  the  brick  should  be  delivered  to  the 
rson  who  drops  them  into  the  street  with  the  faceplaced  to  suit  the  hand 
sration  of  such  person,  called  the  brick  layer.  The  brick  shotild  not  be 
i  in  place  in  close  contact  with  one  another.  Such  practice  will  result  in 
:  bride  being  chipped,  and  it  will  be  impossible  to  put  in  the  cement  filler 
>perly  in  the  interstices.  Inspectloa. — ^After  the  bricks  are  placed,  thev 
>uld  be  inspected  before  being  rolled  so  that  as  few  bricks  as  possible  will 
disturbed  after  the  rollmg.  RoUlng. — ^The  roller  should  be  a  light  one, 
m  4  to  5  tons;  one  that  is  easily  handled,  and  can  move  rapidly  upon  the 
face  of  the  brick.  The  rolling  should  proceed  from  each  side  along  the 
b,  working  toward  the  center  of  the  street;  then  cross-rolling  at  angles 
45^;  again  rolling  longitudinally  and  cross-rolling  as  before,  continuing 
s  process  until  the  bricks  are  thoroughly  compacted  into  the  sand,  so  that 
grade  of  the  pavement  shall  be  as  intended  and  the  ineqxialities  of  the 
hion  ironed  out  by  the  sand  being  pushed  up  in  the  interstices  of  the 
:k,  a  condition  always  found  in  the  case  of  properly^  rolled  streets  by  an 
;vcn  amount  pressed  upwards  in  the  interstices  running  from  ^  to  Kand 
sibly  1'  in  some  cases.  (The  use  of  the  horse  roller  and  the  8  to  10-ton 
un  roller  should  be  prohibited) .  Wetting. — After  rolling,  the  bad  bricks 
uld  be  replaced  with  good  ones,  the  street  swept  clean,  and  then  sprinkled, 
the  use  of  a  nozzle  either  upon  a  sprinkling  can  or  a  hose  which  will 
mit  but  the  finest  spray  of  water  to  come  upon  the  street.  Cement  Filler. — 
;  sand  to  be  clean,  sharp  and  dry;  the  mixing,  not  over  ^  bu.  of  sand  and 
ic  amoimt  of  Portland  cement,  to  be  placed  in  box  and  mixed  dry  until 
»  is  of  even  shade;  water  then  addeo,  forming  mix.  like  thick  cream. 
;t  be  kept  in  constant  motion  from  time  of  mixing  until  floated  into 
13.  Mix.  to  be  removed  from  the  box  to  the  street  surface  with  a  scoop 
veil  box  to  be  3i  to  4  ft.  long,  27'  to  30"  wide  and  14*  deep,  with  one 
ler  low,  and  8*  to  10*  above  pavement.  The  mix.,  from  the  moment  it 
:hes  the  bricks,  shall  be  thoroughly  swept  into  the  Joints.  Two  boxes 
c  provided  where  street  is  tmder  20  ft.  wide;  over  20  ft.,  3  boxes.  This 
k  of  filling  should  be  carried  forward  in  line  until  an  advance  of  1 6  to  20 
Is  has  been  made,  when  the  same  force  diall  be  turned  back  and  cover 
same  space  in  like  manner,  except  that  the  proportions  for  the  second 
shall  be  |  Portland  cement  and  i  sand.  To  avoid  possibility  of  thickening 
ny  point,  there  should  be  a  man  with  a  sprinkling  can,  the  head  per- 
lea  with  small  holes,  sprinkling  gently  the  surface  ahead  of  the  sweepers, 
lin  i  to  I  hour  edter  the  second  coat  is  applied,  and  grout  between  joints 
fully  subsided,  and  initial  set  is  taking  place,  the  whole  surface  is  to  be 
tly  sprinkled  and  all  surplus  mixture  left  on  the  tops  of  the  bricks 
•t  into  the  Joints,  bringing  them  up  flush  and  full.  Then,  after  sufficient 
for  evaporation  has  taken  place,  a  i'  layer  of  sand  shall  be  spread  over 
whole  surface,  and  if  xmder  a  hot  summer  sun,  the  sand  should  be 
ikled  occasionally  for  a  few  days. 

CINCINNATI  (OHIO)  PAVEMENT  SPECIFICATIONS. 

BOULDBR  PaVEMBNT. 

ub-Qrade. — Brought  to  even  surface,  parallel  with  grade  proposed  for 
□aent,  making  necessary  excavation  and  embankment.  Soft  or  spongy 
,  etc.,  to  be  removed,  and  space  filled  with  broken  stone,  rammed  or 
I-  Sub-grade  surface  to  be  compacted  by  rolling  with  steam  roller 
ing  not  less  than  250  lbs.  per  lin.  in.  of  roller;  portions  not  accessible 
rammed.  Finished  sub-grade  to  be  14'  below  surface  of  pavement. 
datloo. — Upon  the  sub-grade  thus  prepared  the  entire  surface  of  the 
va,y  between  the  gutters  will  be  spread  evenly  with  a  layer  of  soimd, 
hill  limestone,  broken  into  fragments  as  nearly  regular  as  practicable, 
ver  2K  dia.;  the  layer  to  be  ot  such  thickness  that  when  thoroughly 

This  cushion  to  be  composed  of  pitch  or  asphaltum  composition, 
i  the  Allotted  snace-  the  remaininff  too  third  to  be  filled  with  sand. 


1108  tO.'-HIGHWAYS. 


roller^ 


compacted  its  surface  shall  be  ff  above  true  surface  of  sub-grade,  usins  roller 
above  described .  Where  additional  material  is  required,  after  rolling,  to  bri 
surface  to  proper  grade,  the  rolled  surface  must  be  loosened  to  depth  of  _ 
to  receive  the  new  material,  and  afterward  rerolled.  Qravd  Layer.— On  the 
broken-stone  fotmdation,  spread  a  layer  of  gravel,  loose,  and  of  sufficient 
depth  in  which  to  pave  the  boulders.  The  gravel  must  be  clean  and  fzee 
from  animal  or  vegetable  matter  or  refuse;  it  must  not  contain  more  than 
15%  of  clay  or  loam,  nor  pebbles  exceeding  1'  longest  diameter.  Pavlnc 
(Qeneral) . — In  paving,  the  foundation  work  ^all  be  kept  laid  to  proper  grade, 
rolled  or  rammed  into  proper  slope  or  shape  at  least  1 00  it.  ahead  of  paving;  be 
laid  in  sections  of  not  less  than  100  ft.  in  length,  entirely  free  from  gravel. 
rubbish,  etc.,  and  thoroughly  swept,  ready  for  inspection.  Bonlders. — The 
boulders  will  be  laid  down  between  the  gutter-flagging;  to  be  of  good  shape 
free  from  Haws  or  breaks,  of  hard,  imperishable  substance,  no  sandstone  or 
limestone  boulders  to  be  tised,  no  stone  to  measure  less  than  4'  nor  more 
than  V  in  longest  diameter;  the  stones  to  be  carefully  assorted  and  so  placed 
that  the  largest  shall  be  next  the  gutter-flagging  and  gradually  jliminish  in 
size  to  the  center.  Laying. — No  stone  when  set  in  an  upright  position,  to 
show  a  horizontal  diameter  of  less  than  3*  or  more  than  6'  in  anv  direction, 
and  they  must  be  set  firmly  on  the  fotmdation  in  a  perfectly  upri^t  position, 
with  small  ends  down,  and  as  closely  and  compactly  together  as  possible: 
none  to  be  laid  flat  or  on  side  edge.  When  boulders  have  been  set  for  a 
distance  of  60  ft.,  the  first  50  ft.  must  be  lightly  rammed,  after  which  a 
covering  of  gravel,  sufficient  only  to  fill  the  interstices,  will  be  spread  over 
the  surface  and  thorotighly  broomed  in,  when  the  whole  will  be  thoroughly 
rammed  with  not  less  than  40-lb.  rammers.  When  two  sections  (aggregat- 
ing 110  ft.)  have  been  treated,  the  first  100  ft.  will  be  again  covered  with 
gravel,  broomed,  rammed,  and  ready  for  inspection.  As  soon  as  eadi 
section  of  100  ft.  is  accepted,  a  final  covering  of  V  of  gravel  will  be  spnad 
over  the  entire  surface. 

DETROIT  (MICH.)  PAVEMENT  SPECIFICATIONS. 

Gbnbral. 

Old  Pavement  and  curbing  to  be  meas\ired  to  contractor  as  excavatkic; 
all  old  material  and  rubbish,  including  surface  dirt,  to  be  removed,  city 
reserving  curbing,  etc.  for  new  pavement,  same  to  be  delivered  free  by  con- 
tractor to  nearest  city  yard  or  for  distance  of  1  mUe,  if  reqxiired.    Contractor 
to  use  care  in  removal  of  old  cushion  sand  to  prevent  mixture  with  other 
material.    Grading. — ^After  excavation  to  sub-grade,  should  there  be  places 
in  street  which  are  not  firm,  the  earth  must  be  taken  out  and  the  space  re- 
filled with  crushed  stone  and  rolled.    Before  laying  the  concrete  foundatioc 
and  after  the  cxirbstone  has  been  set,  the  sub-grade  shall  be  rolled  with  7-toc 
roller  furnished  and  operated  by  City,  at  cost  to  contractor  of  Jc.  per  sq.  yd 
After  this  rolling,  high  places  shall  be  brought  to  sub-grade  and  depressiom 
filled  with  concrete  at  expense  of  contractor.     Sub-grade  to  be  properlr 
planked  before  teaming  is  allowed.    Curb  Trench. — Trench  to  be  excavated 
on  each  side  of  roadway  to  depth  sufficient  to  set  curb  on  concrete  base  6* 
deep  and  of  such  width  as  to  allow  concrete  backing  to  the  curb  of  AT  thkk- 
ness;  bottom  to  be  smoothly  trimmed  parallel  to  curb  grade.    Stone  CnrMi^ 
—Old  ciu-bing  taken  up  shall  be  rejointed.  edges  rounded,  retopped.  refaod 
and  reset  wherever  directed,  as  per  specifications  for  jointing,  facing  asd 
setting  new  curb.    New  curb  to  be  of  best  quality  of  granite,  Medina.  North 
River  Blue.  Elyria,  Bcrea,  or  other  curb  as  may  be  bid  upon  and  ordered. 
The  stone  shall  be  4'  thick  (ordinarily),  at  least  8  ft.  long,  and  18*  deep 
upper  comer  next  to  roadway  to  be  rounded  with  radius  of  IJ'.    Top  and 
face  of  above-named  stone  curb  to  be  dressed  to  what  is  known  as  4-^x 
work,  true  and  even,  and  the  softer  curb  to  be  crandall  dressed,  true  and 
smooth,  all  with  close  joints  at  the  ends  of  at  least  7*  below  top  of  crut  „ 
and  a  joint  of  not  to  exceed  i'  for  the  remaining  18"  depth  of  curb;  stonesu 
to  have  straight  and  even  face  on  gutter  side  to  deptii  of  V  below  topL«, 
Back  of  ctirb  to  be  dressed  3*  down  from  top.    Top  to  be  dressed  to  a  stra«^b4| 
line,  and  to  \'  bevel  in  5',  and  to  uniform  thickness  or  4*  (ordinar^> , 
Stones  to  be  taken  out  of  wind,  set  with  close  joints  to  street  line  and  giaae| 
on  concrete  bed  6'  deep,  and  to  full  width  of  trench,  and  backed  up  wtt^ 
^oncrete  to  within  4'  of  top  of  ctirb;   the  remaining  4*  behind  curb  to  b^ 
?  ?1  ^ith  suitable  earth  well  compacted.    The  crushed  stone  for  ooncreM 
to  be  i  to  1".    Concrete  Curbing. — Concrete  for  cement  curb,  plain  or  x«^ 


CURBING.    BRICK  PAVEMENT  ON  CONCRETE.         1100 

forced  with  metal,  shall  consist  of  not  more  than  4  parts  of  V  to  k'  broken 
stone  or  sla«.  2  parts  sharp  sand,  and  1  part  Portland  cement;  ciorbing  to 
be  of  approved  construction  and  finish.  Foundation. — When  the  roadbed 
has  been  prepared,  it  shall  be  covered  with  a  layer  of  concrete  not  less  than 
e*  thick,  and  rammed  until  the  surplus  cement  mortar  appears  on  the  sur- 
face, which  shall  be  smooth  and  parallel  to  roadbed.  No  teaming  allowed 
until  set  and  covered  with  plank;  defects  to  be  repaired  before  work  pro- 
ceeds. Concrete. — Broken  stone.  Tf  to  i",  may  be  from  boulders,  granite, 
syenite,  slag,  or  hard  limestone',  it  must  be  clean,  screened  if  necessary  to 
free  it  from  dirt  or  stone  refuse,  and  wetted  before  being  placed  on  mixing 
boards.  The  concrete  shall  consist  of  1  part  nattiral  cement,  2  parts  sand, 
and  4  parts  stone  or  slag;  or  1  part  Portland  cement,  3  parts  sand,  and  0 
parts  stone  or  slag;  depending  upon  which  cement  is  specified. 

Brick  Pavement  on  Concrete  Foundation. 

Cofhlon. — Coat  of  clean,  sharp,  bank,  lake  or  river  sand,  well  screened, 
to  be  spread  over  concrete  foundation  to  depth  of  14'  when  compacted. 
Brick  Paving. — Shall  consist  of  best  quality  of  sound,  hard,  burned  paving 
brick,  or  cement  brick,  made  especiallv  for  street  paving  ptuposes,  and  to 
stand  all  reasonable  tests  as  to  diuability  and  fitness,  to  which  paving 
material  is  usually  subjected.    Bricks  to  be  round  or  bevel-edged,  straight, 
free  from  cracks  and  other  defects,  of  uniform  size,  and  of  approved  quality, 
equal  to  approved  sample  in  office.  Handling  and  Piliof  Brick. — Brioc  to  be 
handled  with  brick  tongs,  carefully,  to  avoid  breakage  or  chipping,  and 
piled  on  street  in  rectangular  piles,  with  uniform  tiers  or  courses  to  aid 
irounting.    Manner  of  Laying. — ^pon  the  cushion;  the  pavement  to  be  laid 
Arith  a  single  laver  of  brick  on  edge,  end  to  end,  m  right  angle  or  diagonal 
:otu-ses  across  the  street,  as  may  be  directed,  except  at  street  intersections 
md  along  street  railway  tracks  where  the  courses  are  to  be  placed  at  such 
ingles  as  may  be  designated.    Bricks  to  be  set  in  straight  cotu^es,  with  body 
•f  bricks  close  together,  sides  and  ends  touching,  and  breaking  joints  at 
;ast  2*  with  the  bricks  in  adjoining  courses;   to  be  set  perpendicular  to 
fade  of  street,  and  to  height  o!  from  i'  to  I'j  or  as  may  be  directed,  above 
^e  true  grade  and  crown  of  street  when  finished,  to  allow  for  settlement 
1  pounding  and  rolling.    Whole  bricks  to  be  used,  except  in  starting  a 
>ur8e  or  in  making  a  closure,  when  not  less  than  half  bricks  may  be  used  in 
reaking  joints,  tight  and  close  at  ends.    Rolling  and  Tamping. — ^The  paving 
hen  laid,  and  before  filling  of  the  joints  and  top  dressing  is  put  on,  ^all  be 
lied  three  or  more  times  lengthwise  of  street,  with  not  less  than  7-ton 
llcr,  furnished  and  operated  by  City  at  \c.  per  sq.  yd.    Parts  which  cannot 
rolled  shall  be  rammed.    Tar  Filling. — Whenever  tar  filler  is  specified,  the 
ints  to  be  filled  to  the  bottom  with  paving  cement  obtained  from  the 
'ect  distillation  of  coal  tar,  and  shall  be  residuum  thereof,  such  as  is 
iinarily  numbered  5  and  6  at  the  manufactory,  or  any  other  approved 
31  position;    quality  and  temperature  to  be  approved.     Extra  material 
i  care  to  be  used  at  gutters,  catch-basins,  etc.,  to  prevent  lefUcage  of  water 
sub-roadway.    Oront  Filling. — A  joint,  Y  in  width,  next  to  and  parallel 
the  curbstone,  to  be  filled  to  top  with  a  composition  of  cofd  tar  cement, 
ced  with  at  least  10%  of  refined  asphalt,  and  the  whole  mixed  with 
icient  still  wax  to  prevent  softening  or  brittleness  in  hot  or  cold  weather, 
streets  with  car  tracks,  three  rows  of  brick  to  be  laid  along  outside  of 
s  in  form  of  stretchers,  with  broken  joints,  and  all  joints  filled  with 
ve  coxnposition.    Balance  of  pavement  to  be  filled  with  grout,  composed 
part  Portland  cement  and  1  part  sand.  The  grout  to  be  prepared  in  small 
ntities,  stirred  while  being  applied  to  pavement,  and  swept  into  joints 
I  pxx>per  brooms:   no  settlings  or  residue  to  be  xised.    Filling  to  be  done 
wo  or  more  applications  of  grout;  the  first  J' in  depth  from  the  bottom 
e  filled  with  grout  somewhat  thinner  than  required  for  the  remainder; 
balance  with  a  thicker  grout,  and  if  necessary  refilled;  brick  to  be  pre- 
sly  wet.     Teaming  and  traffic  prohibited  for  about  one  week.     Top 
sins* — Sixrface  of  paving  to  be  covered  with  K  top  dressing  of  sand. 
inins  Stone. — ^At  intersections  with  paved  streets  and  alleys  having  a 
-ent   surface,  the  pavement  shall  be  finished  up  to  a  Medina  stone 
ST  4*"  tliick,  not  less  than  16'  deep,  and  not  less  than  dXf  long,  to  be  set 
concrete  bed  fl*  deep,  8*  wide  and  backed  with  4'  of  concrete  to  withiu 
top.     Stones  to  be  dressed  on  top.  pointed  down  on  both  sides  to  bot- 
>f  STirfacing  material,  having  good  joint  for  depth  of  3*  from  top,  and 


1110  ^.—HIGHWAYS. 

Shbbt  Asphalt  Pavbmbnt  on  Concrbtb  Foundation. 

Binder. — Upon  the  concrete  bed  a  binder  cotirse  to  be  laid,  composed  of 
clean,  broken  stone,  varying  in  size  from  fine  to  coarse,  all  to  pass  a  If*  ring 
in  its  larger  dimensions.  Stone  after  being  heated  shall  not  contain  less 
than  5%  nor  more  than  15%  of  material  passing  a  No.  10  screen.  Stone  to 
be  heated  not  higher  than  350°  F.  in  suitable  appliances;  then  thorotu^y 
mixed  by  machinery  with  asphaltic  cement,  such  as  is  acceptable  for  siume 
cement;  penetration,  60  to  90,  at  77°  F.,  City  standard,  at  stich  tempen- 
tures  and  in  such  proportions  that  the  resulting  binder  will  have  life  and 
gloss  without  an  excess  of  cement.  Should  it  appear  dxill,  from  ovexlieatsng 
or  lack  of  cement,  it  will  be  rejected.  While  hot,  it  will  be  hauled  tip<Mi  the 
work  and  spread  upon  the  base,  so  'that  when  compacted  it  will  be  at  least 
H'  thick,  and  immediately  rammed  and  rolled  tmtil  it  is  cold.  Weuinf  Sur- 
face.— Upon  the  binder  course  will  be  laid  the  wearing  surface,  or  pavement 
proper,  the  binding  material  of  which  must  be  a  cement  prepared  fron: 
asphalt,  refined  until  free  from  water  and  volatile  oils.  This  surface  to  be 
composed  of  asphaltic  cement,  clean,  sharp-grained  sand  and  fine  absorbent 
mineral  dust.  The  Asphaltic  Cement  must  be  prepared  from  refined  asphah 
of  one  of  the  following  brands:  Trinidad,  Bermudez,  Obispo,  or  any  other 
equally  as  good.  The  refined  asphalt  shall  be  softened  into  a  proper  asphaltic 
cement  by  the  addition  of  a  suitable  flux.  The  flux  must  be  either  a  resi- 
duum from  eastern  petroleum  oil,  Texas  petroleum  oil,  or  a  maltha  fioin 
which  the  light  oils  and  water  have  been  removed  by  distillation.  The 
asphaltic  cement  to  be  satisfactory,  practically  free  from  water,  and  within 
the  range  of  40  and  70  penetration  (amount  of  penetration  to  be  fixed  by 
Department  of  Public  Works),  at  77°  F.,  City  standard.  The  Sand  to  be 
hard  grained  and  moderately  sharp.  On  sifting,  it  should  have  at  least  155* 
catight  on  a  40  mesh  to  the  inch  screen;  25%  pa^  an  80  mesh,  10%  c^ 
which  must  pass  a  100  mesh  screen.  If  the  sand  used  does  not  contain  the 
desired  fine  material,  mineral  dust  can  be  added  to  make  up  the  deficiency, 
and  in  any  case  at  least  5%  of  such  mineral  d\ist  shall  be  used.  The  Mineral 
Dust  shall  be  fine,  absorbent  inorganic  d\ist,  not  acted  upon  by  water,  the 
whole  of  which  shall  pass  a  30  mesh  screen,  and  at  least  75%  pass  a  100 
mesh  screen.  The  Asphalt  Paving  Mixture  to  be  composed  of  above  ma- 
terials mbced  in  proportions  by  weight,  depending  upon  their  character  and 
the  street  traffic  and  character  of  asphalt,  and  will  be  determined  by  the 
inspector;  but  the  per  cent  bitumen  in  any  mixture,  soluble  in  carbon 
di-sulphide,  shall  not  exceed  the  limits  9  to  13  per  cent.  Proportions  of 
mixture  must  not  be  varied  from  those  specified.  The  sand,  or  the  mixture 
of  sand  and  stone  dust,  and  the  asphaltic  cement,  shall  be  heated  sei>arately 
to  about  300°  F.  The  dust,  if  limestone,  will  be  mixed  while  cold  with  hot 
sand,  in  the  reqviired  proportions,  and  then  mixed  with  the  asphaltic  cement 
at  the  required  temperature  and  in  the  proper  proportion,  in  a  suitable  ap- 
paratus, so  as  to  effect  a  thoroughly  homogeneous  mixture.  The  mixture 
thus  prepared  will  be  brought  to  the  street  in  carts,  at  a  temperature  of  sc^ 
less  than  230°  nor  more  than  350°  F.,  depending  on  the  asphalt  in  use; 
canvas  covers  to  be  \ised  if  the  temperature  of  ue  air  is  less  than  00°  F. 
It  is  then  to  be  spread  to  a  thickness  of  at  least  3*  by  means  of  hot  rakes, 
to  a  tmiform  grade,  so  that  when  compressed  it  will  have  a  finished  thick- 
ness of  at  least  2^.  The  stirface  to  be  compressed  by  rolling,  after  which  a 
small  amotmt  of  hydraulic  cement  will  be  swept  over  it,  and  it  will  then  be 
thoroughly  compressed  by  a  steam  roller  weighing  not  leas  than  175  lbs. 
to  the  inch  nm,  the  rolling  being  continued  for  not  less  than  5  hours  for  each 
1000  yds.  of  surface.  Contractor  to  furnish  a  10-year  guarantee.  R«Uinim 
Stooe. — (Same  as  for  brick  pavement.) 

Cedar  Block  Pavbmbnt  on  Concrbtb  Foundation. 

Cushion. — (Same  as  for  brick  pavement.)    Cedar  Blocks  to  be  4*^ ! 

best  qixality  of  sound,  selected,  live  timber,  stripped  of  all  bark  and  free 

traces  of  rot  or  indications  of  decay,  and  not  less  than  4)*  nor  more  than  9* 
in  diameter  and  so  selected  in  size  as  to  make  a  close-iointed  pavemcDt. 
Filling. — Spaces  between  blocks  to  be  filled  with  screened  gravel  or  crushed 
granite  or  boulders  of  size  varying  from  i*  to  1"  diameter  and  free  from  dust. 
sand,  loam  or  thin  stone,  screened,  when  necessary,  through  a  wire  screen 
set  at  an  angle  of  60°,  with  meshes  of  not  less  than  8*  lengthwise  by  \'  xa 
^  11  'iiH^^P^  ^*^^  "^'^  tamping  bars  as  required,  and  then  the  surian 
well  rolled  by  City  roller  at  cost  to  contractor  of  Jc.  per  sq.  yd.    After  lolting 


ASPHALT,    WOOD.    MACADAM.    TELFORD.    CURB.      1111 

spaces  between  gravel  or  stone  filling  of  the  blocks  to  be  completely  filled 
from  bottom  to  top  with  paving  cement  obtained  from  the  direct  distillation 
of  coal  tar,  and  shall  be  the  residuum  thereof,  such  as  is  ordinarily  numbered 
5  or  6.  Qkiality  and  temperature  to  be  approved.  Extra  care  at  gutters, 
catch-basms,  etc.  Top  Dressing. — (Same  as  for  brick  pavement.)  Retaiidiic 
Plank.— Where  cedar  pavement  is  laid,  the  pavement  at  intersections  ot 
unpaved  streets  and  alleys  to  be  finished  up  to  a  piece  of  timber  3^  thidc 
and  12'deep,  set  on  O' of  concrete,  and  extending  across  the  proposed 
width  of  roaidwaY  of  such  street  or  alley.  For  all  other  kinds  of  pavement 
a  stone  header  will  be  used,  similar  to,  and  set  as  stated  for  retaimng  stone. 
Retaiolof  Stone. — (Same  as  for  brick  pavement.) 

EASTON  (PA.)  PAVEMENT  SPECIFICATIONS. 

(John  McNeal,  City  Engineer.) 
Macadam  and  Tblford  Roads. 
Work.— Done  by  City  force;  not  by  contract.  Qrading. — Completed 
fade  to  have  slope  of  from  J'  to  1'  per  ft.  from  center  to  sides,  according  to 
percentage  of  grade  of  street.  Roadbed. — Must  be  rolled  firm  with  steam 
oad  roller:  depressions  formed  by  rolling  to  be  filled  and  rolled  again  to 
nished  sub^rade.  Macadam  Foundation. — On  the  sub-grade,  place  3*  to 
'  crushed  stone,  spread  evenly,  and  roll  with  road  roller  until  none  of  the 
tones  move  under  the  roller;  all  material  to  be  added  dry,  but  water  added 
head  of  the  roller.  This  course  to  be  5'  thick.  Telford  Foundation. — On  the 
ib-^rade,  place  the  bottom  course  composed  of  stones  8*  to  12*  long,  dT  to 
'  wide,  and  fi*  deep,  vertically  by  hand  on  their  broadest  edges  and  pointed 
:  the  top;  stones  to  be  laid  m  lengthwise  courses  across  the  street,  and  all 
terstices  filled  with  broken  stone,  wedged  with  a  hammer;  projecting 
)ints  to  be  broken  off  to  surface  grade.  This  course  to  be  thoroughly  rolled 
itil  stones  do  not  rock  under  the  roller.  Clay  may  be  used  as  a  binder  on 
is  course  if  directed.  Second  Course. — (Same  for  either  macadam  or  tel- 
rd.)  On  the  foundation,  lay  a  3*  course  of  crushed  stone,  H'  to  1*.  and 
11  tmtil  firm  and  solid,  water  being  applied  ahead  of  the  roller.  Binder. — 
le  binder  for  the  bottom  and  second  course  shall  be  limestone  screenings, 
plying  water  ahead  of  the  roller  if  necessaiy.  Surface. — On  the  second 
irse,  a  coat  of  60%  of  \'  stone  and  60%  or  screenings,  properly  mixed, 
i  about  I''  thickness,  shall  be  applied  dry  and  rolled  once  before  wetting, 
n  alternate  watering  and  rolling  until  finally  completed,  when  the  sur- 
e  must  be  uniform  to  shape  and  grade.  (The  several  courses  of  material 
St  be  of  required  depth  alter  rolling,  allowance  for  compression  being  at 
(t  one-half.)  Rolling. — Each  course  to  be  rolled  with  the  utmost  thor- 
hness,  the  roller  starting  from  the  sides  and  working  toward  the  center. 

CoNCRBTB  Curbs,  Guttbrs  and  Sidewalks. 


Fig.  3. — Concrete  Curb,  Gutter  and  Sidewalk. 

t€ir  sidewalk  is  excavated  and  shaped  to  proper  depth  and  grade,  the 
t  curb,  gutter  and  sidewalk  shall  be  constructed  in  place,  upon  a  bed 
/el  or  cinders  8*  to  10"  deep,  well  consolidated  by  ramming  to  an  even 


1112  to.— HIGHWAYS. 

surface,  and  moistened  before  the  concrete  is  placed  thereon.  The  curb, 
gutter  and  sidewalk  to  be  composed  of  concrete  formed  by  mixing  dry, 
1  part  Portland  cement,  2  parts  coarse,  clean  sand  and  4  parts  clean  screened 
limestone  or  trap  rock,  cnished  to  pass  through  a  li'  mesh  screen,  to  whidi 
shall  be  added  s\ifficient  water  to  torm  a  concrete  that  when  placed  an  the 
templets  and  thoroughly  rammed,  free  mortar  will  appear  on  the  surface. 
The  ramming  of  the  concrete  in  the  forms  shall  be  done  with  the  proper 
tamping  bars  and  other  tools  to  insure  a  compact  mass  with  ftill  square 
comers.  All  exposed  surfaces  to  be  covered  with  a  finished  coat  V  thick, 
composed  of  1  part  cement.  1  part  clean,  fine  hard  stone  acreenings.  and  1 
part  clean .  coarse  sand ,  applied  before  concrete  has  hardened.  Top  facing  of 
curb,  gutter  and  sidewalk  to  be  thoroughly  troweled  to  insure  perfect  cos* 
tact;  when  sufficiently  hard  it  shall  be  troweled  and  floated  to  a  smooth 
true  surface.  Concrete  curb  to  be  6*  thick  at  top,  8*  at  base,  and  24'  deer, 
exclusive  of  foimdation.  Concrete  gutter  to  be  fi"  deep,  3  ft.  wide  on  all 
streets  more  than  20  ft.  wide,  and  2  ft.  wide  on  narrower  streets;  stirface  ot 
outside  edge  to  be  grooved  with  4^  squares  for  width  of  2  ft.  on  the  3-ft. 
gutters,  and  1  ft.  on  2-ft.  gutters,  to  prevent  slipping  of  horses.  Concrete 
sidewalk  to  be  at  least  5'  deep.  For  the  entire  depth  of  curb,  gutter  and 
sidewalk,  joints  to  be  made  with  tar  paper  or  by  means  of  removable  plates 
to  form  expansion  joints  or  planes  of  weakness;  joints  to  be  not  more  than 
10  ft.  apart. 

REINFORCED  CONCRETE  FOUNDATIONS. 

See  article  entitled  "Reinforced  Concrete  Foundations  over  Bxcavatioos 
on  Paved  Streets,"  in  Trans.  A.  S.  C.  E.,  Vol.  LX.  p.  217  (1908). 

EL  PASO  (TEX.)  PAVEMENT  SPECIFICATIONS. 

(F.  H.  Todd,  City  Engineer.) 

Pbtrohthic  Pavbmbnt. 

Preparing  Roadway. — ^The  roadway  shall  be  so  excavated  or  filled  that 
after  thorough  rolling,  or  tamping  with  hand  rammers  at  such  points  as  caa* 
not  be  well  done  witn  roller,  its  surface  shall  be  TT  below  and  approximatelT 
parallel  with  stirface  of  finished  street.  Soft  and  boggy  places  not  affocxlhi£ 
a  firm  foundation  shall  be  dug  out,  refilled  and  thoroughly  tamped  with  gotM 
sound  earth,  cinders,  gravel,  slag,  stone  or  concrete,  as  may  be  directec: 
the  contractor  to  be  paid  for  this  excavation  the  same  price  as  other  exca- 
vation, if  the  soft  ana  boggy  place  was  not  caused  by  him,  but  if  caused  by 
him,  then  at  his  own  proper  cost  and  expense.  The  entire  roadway  sha^I 
then  be  ploughed  to  a  depth  of  not  less  than  0*  nor  more  than  flr.  and 
thoroughly  pulverized  by  cultivating,  harrowing,  or  such  other  method  ai 
will  accomplish  the  result.  Foundation. — On  this  thoroughly  puIverizcU 
roadway,  including  the  intersections  of  all  streets  and  alleys  up  to  the  prof- 
erty  lines  of  the  street  being  improved,  the  roadway  shall  be  evenly  coated 
with  liquid  asphalt,  J  gal.  per  sq.  yd.  of  surface;  it  shall  then  be  tbon 
cultivated  to  a  depth  of  6*  until  the  liouid  asphalt  wlyich  has  been  a] 
is  thoroughly  mbccd  with  the  soil;    then  a  second  application  of 

asphalt,  i  gal.  per  sq.  yd.,  shall  be  made  and  the  area  a»un  well  and 

oughly  cultivated  to  a  depth  of  6*,  tmtil  the  liquid  asphalt  and  the  materjii 
comprising  the  surface  ot  the  street  are  well  and  thoroughly  mixed;  th^ 
the  third  application  of  liquid  asphalt,  i  gal.  per  sq.  yd.,  shall  be  evec^ 
spread  over  the  entire  roadway  and  the  area  for  a  third  time  well  and  thd 
oughly  cultivated  in  such  a  manner  that  the  liquid  asphalt  shall  becod 
thoroughly  mixed  with  the  street  surface  to  a  depth  of  vT.  The  street  s^ 
be  thoroughly  watered  after  each  application  ot  the  liquid  asphalt.  Tl 
surface  of  the  street  shall  then  be  brought  to  a  grade  approximately  paralll 
to  grade  of  finished  street.  Tamping. — ^The  street  shall  then  be  tampi 
with  a  petrolithic  rolling  tamper  until  it  is  solid  to  within  2*  of  the  8ur£a4 
When  the  tamping  of  the  road  with  the  rolling  tamper  is  begun,  the  rolhl 
tamper  shall  be  immediately  followed  by  a  cultivator  set  so  as  not  to  disttu 
the  sub-base  already  tamped;  said  cultivator  being  reset  as  the  tanapi 
progresses,  so  as  to  cultivate  to  shallower  depths.  The  cultivator  shaU 
used  continually  during  the  tamping,  the  purpose  bein^;  to  prevent  a  t 
rapid  solidification  whereby  the  roadway  would  be  solidified  without  bei 
compacted  from  the  bottom  up.  Upon  this  base  prepared  as  above  soecifii 
shall  be  applied  liquid  asphaltum,  \  gal.  per  sq.  yd.  ol  street  surface.  Weari 


PETROLITHIC  PAVEMENT.  1113 

Surface*— On  the  fotmdation,  shall  be  placed  a  layer  of  hard,  durable, 
crushed  stone,  2*  to  1'  screen,  spread  evenly  and  to  such  thickness  that 
after  it  has  been  thoroughly  sprinkled,  and  roiled  with  a  roller  weighing  ilot 
less  than  10  tons,  its  surface  shall  be  parallel  to  and  )'  below  surface  of 
finished  street.  Liquid  asphaltum  shall  then  be  applied,  }  gal.  per  sq.  yd.  of 
surface;  then  a  layer  of  crushed  rock,  IK  to  K  screen,  shall  be  spreaa  evenly 
to  depth  of  y',  then  the  surface  shall  be  thoroughly  watered  and  rolled, 
followed  by  a  coating  of  liauid  asphalttim  apnlied  at  rate  of  \  gal.  per  sq.  yd. 
then  a  light  coating  of  rock  screenings  y  and  under  in  size,  and  in  sufficient 
quantity  to  absorb  all  the  surface  liquid  asphaltum  and  produce  a  uniform 
surface.  The  pavement  shall  then  be  watered  and  rolled  until  it  becomes 
lard,  smooth,  true  to  grade  and  cross-section,  free  from  all  hollows  and 
)ther  irregularities,  until  but  slight  movement  takes  place  imder  the  action 
)f  the  roller.  In  streets  or  avenues  having  a  street-railway  track,  the  street  i 
hall  be  excavated  to  a  point  6'  below  the  ties  and  Q'  beyond  the  end  of  the  ' 
ies,  and  this  space  filled  with  broken  stone  or  slag  to  the  upper  surface  of  the 
ies;  this  filling  to  be  so  well  tamped  with  stones  of  assorted  sizes,  from  3*  in 
reatest-  to  K  in  least  dimension,  that  but  slight  movement  will  take  place 
nder  the  ties  during  the  passage  of  the  electric  car  The  space  between  the 
Ills  shall  then  be  filled  in  the  same  manner  as  is  provided  for  wearing  sur- 
icc  on  other  portions  of  the  street.  It  will  be  necessary,  however,  to  pro- 
ide  a  roller  so  formed  as  to  make  the  fiange-ways  similar  in  form  to  that 
jproved  by  the  City  Council,  Jan.  9,  1908.  With  this  roller,  the  surface  of 
le  street  between  the  rails  must  be  so  compressed  that  but  slight  move- 
ent  takes  place  under  a  10-ton  road  roller.  That  portion  of  the  roadway 
itside  of  the  rails,  shall  be  treated  in  a  manner  similar  to  the  wearing  surface 
r  the  remaining  portion  of  the  street.  In  case  rock  is  encountered  in  exca- 
ting,  it  will  be  necessary  to  remove  that  to  a  depth  of  at  least  3*  below 
ished  surface  of  street.  Liquid  Asphaltum. — ^The  liquid  asphaltum  used 
ill  contain  not  less  than  76%  of  asphaltum  at  80**  penetration  when  tested 
a  temperature  of  77°  F-  The  specific  gravity  shall  not  be  lower  than  10° 
r  higher  than  11**  Baume,  at  a  temperature  or  60°  F..  and  shall  not  contain 
re  than  2%  of  water  and  sediment.  In  all  cases  the  liauid  asphaltum  shall 
applied  at  a  temperature  between  200°  and  250°  F.    It  shall  be  applied  to 

roadway  by  an  approved  form  of  sprinkler,  such  as  will  give  a  uniform 
tribution  over  the  entire  surface  of  the  roadway  Concrete. — ^The  cement 
St  be  equal  in  quality  to  the  best  American  Portland  cement,  and  oppor- 
ity  shall  be  provided  to  test  it  for  30  days  before  it  is  used  in  the  work,  in 
sr  to  prove  its  strength  and  soundness.  The  Sand,  for  mortar,  must  be 
n,  sharp,  and  have  grains  of  different  sizes  so  proportioned  as  to  make  a 
se  aggregate.     The  Concrete,  for  pavement  foundation  or  street  rail- 

fotmdation,  must  be  made  from  1  part  by  measure  of  Portland  cement, 
xts  sand,  and  7  parts  clean,  sound,  hard,  broken  rock,  or  clean  gravel,  of 
ous  sizes  from  2^'  in  greatest-  to  y  in  least  dimension,  and  these  sizes  so 
)ortioned  as  to  give  the  greatest  density.  Meastiring  Boxes  shall  be  pro- 
d,  if  required.  After  the  cement,  sand  and  rock  or  gravel  have  been 
oxighly  mixed  dry,  either  by  hand  or  machinery,  it  shall  be  wet  in  such 
ner  as  not  to  wash  away  the  cement,  and  at  the  same  time  the  mixing 

be  done  so  that  the  wet  particles  of  cement  and  sand  are  thoroughly 
porated  as  mortar,  and  each  stone  covered  with  mortar,  the  whole  mass 
ig  in  it  just  enough  water  to  make  the  concrete,  when  in  place,  slightly 
•py."  From  the  time  water  is  first  applied  to  the  batch  until  the  con- 
is  thoroughly  rammed  in  place,  the  work  must  proceed  rapidly  and  the 
ling  must  be  so  well  done  that  no  voids  remain  in  the  concrete,  and  the 
*  flushes  to  the  surface.  Before  the  concrete  sets,  but  after  it  is  rammed 
ICC,  enough  hard,  clean,  broken  stone,  2§*  to  li',  to  about  cover  i  of 
u-face  shall  be  evenly  spread  on  it.  These  stones  shall  then  be  rammed 
icragh  into  the  concrete  to  hold  them  firmly  and  yet  leave  it  rough 
h  to  securely  hold  the  petrolithic  wearing  surface.  The  Concrete 
r  shall  be  composed  of  1  part  Portland  cement,  2^  parts  sand,  and 
s  clean,  hard,  durable  broken  stone,  i*  to  2*  in  greatest  dimension  and 
h  proportions  as  to  give  the  densest  mixture,  and  placed  in  the  same 
;r  as  si>ecxfied  for  concrete  foundation.  After  the  concrete  has  been 
jgrhly  rammed  in  the  gutter,  and  while  it  is  yet  soft,  1 K  of  mortar  com- 
3f  1  part  Portland  cement  and  2  parts  sand  and  as  much  fine  crushed 
;oTie  as  -will  make  the  densest  aggregate,  shall  be  placed  on  top  and  well 
d,  after  ^vhich  the  surface  shall  be  finished  with  the  proper  tools  to 
t  acctirately  conform  to  the  given  lines  and  grades.  Proper  forms 
c  provided  for  all  concrete  work.    Expansion  Joints  of  roonng  paoer 


1114  CO.— HIGHWAYS, 

and  bitumen,  or  of  bitumen  alone,  must  be  provided  and  placed  at  such  pa 
and  in  such  manner  in  the  concrete  as  may  be  reqtured,  but  not  c« 
together  than  20  ft.  All  concrete  work  shall  be  covered  with  earth  and  I 
after  it  has  set  and  shall  be  kept  wet  for  at  least  1  week  and  shall  be  prot4i 
from  injury  for  at  least  10  days  after  laying,  to  allow  it  to  set  propi 
Marginal  Curb. — Whenever  a  paved  street  is  joined  to  an  unpaved  oi 
marginal  curb  of  hard,  durable  stone  at  least  16*  deep,  6'  thick,  and  ; 
long  and  with  top  surface  broken  to  a  straight  line,  must  be  provided 
set,  if  required.  This  curb  shall  be  set  in  6'  of  the  same  class  of  concrd 
specified  for  fotmdation,  and  backed  up  with  the  same  to  within  G*  oC 
top.  The  upper  surface  must  conform  to  the  cross-section  of  the  sl^ 
General. — ^The  price  bid  per  sq.  yd.  for  complete  petrolithic  pavement  i 
include  the  excavation  or  filling  reqiiired  to  bring  the  street  to  its  establL^ 
grade  and  surface,  and  further,  must  include  the  furnishing,  placing  1 
manipulation  of  all  material  necessary  for  the  construction  of  this  pavema 
including  all  labor  arid  necessary  implements.  No  wearing  surface  shall  1 
laid  when  the  temperature  of  the  air  is  below  40°  F.,  and  preferably,  i 
asphaltum  for  the  foimdation  and  surface  shall  be  applied  during  waf 
dry  weather. 

LOS  ANOELES  (CAL.)  PAVEMENT  SPECIFICATIONS. 

(Homer  Hamlin,  City  Engineer.) 
Gravblbd  Strbbts. 
(OUe^.) 
Sub-Qrade. — For  the  roadway,  shall  be  i'  below  surface  of  finished  wo: 
unless  otherwise  indicated  or  directed.  Qradinf . — Shall  include  all  filac 
excavation,  shaping  and  trimmir^  required  to  bring  surface  of  street 
grade  and  cross-section.  Mud  and  other  soft  material,  to  a  depth  of  2  ti 
shall  be  taken  out  and  the  space  filled  with  good  earth  or  graveL  All  £Ui] 
to  be  with  good  sound  earth;  the  embankment  to  be  carried  up  of  full  wiii 
in  horizontal  layers,  not  over  1  ft.  thick,  the  teams  to  travel  as  evenly  i 
possible  over  the  whole  stuf ace  of  each  layer,  both  going  and  coming.  Aft 
the  street  has  been  brought  to  the  required  grade  and  cross-section,  the  surf&t 
shall  be  thoroughly  moistened  and  rolled  with  a  roller  weighing  not  less  th; 
250  lbs.  to  the  inch  width  of  tire,  tmtil  it  is  unyielding.  Depressions  made  : 
the  rolling  shall  be  leveled  up  with  good  earth  and  again  rolled.  Such  portiis 
of  the  street  as  cannot  be  reached  by  the  roller,  and  all  places  excavated  bel: 
grade  and  refilled,  and  all  pipe  trenches  and  other  places  that  cannot  1 
properly  compacted  by  the  roller,  shall  be  tamped  solid,  and  in  case  of  w 
weather  or  soft  or  muddy  ground,  making  the  use  of  the  roller  unsafe  i 
impracticable,  the  rolling  shall  not  be  tmoertaken  tintil  the  ground  has  b 
come  sufficiently  dry.  The  sub-grade  shall  then  be  tested  for  grade,  crci: 
section  and  condition.  Surfacinc  Roadway. — Upon  the  sub-grade,  spreai 
layer  of  good  gravel,  to  have  a  thickness  of  4  (ordinarily)  after  rollio 
The  surface  of  this  layer  for  a  depth  of  1'  is  to  be  raked  free  from  all  stoa 
larger  than  I'in  greatest  dimension.  If  no  gutters  are  provided^  the 
larger  stones  shall  be  raked  to  the  curb  and  distributed  over  a  strip  2  ft. 
width  next  to  the  curb;  if  gutters  are  provided,  the  stones  are  to  be  d 
tributed  on  a  strip  2  ft.  wide  next  to  the  gutter.  This  layer  of  gravel  is  to ' 
uniformly  spread  on  the  roadway,  and  well  moistened:  then  well  ramn* 
for  at  least  1  ft.  from  the  gutters,  should  these  be  paved;  or  if  not  pave 
then  1  ft.  from  the  curb.  The  remaining  portion  ot  the  roadway  shall  th> 
be  rolled  with  a  roller  weighing  not  less  than  250  lbs.  to  the  inch  width 
tire.  The  rolling  of  roadway  shall  commence  at  the  ranmied  portion.  / 
depressions  must  be  promptly  filled,  moistened,  and  again  rolled.  Tl 
sprinkling  and  rolling  must  continue  until  the  surface  is  iiniformly  har 
compact,  and  in  such  condition  that  it  will  not  yield  or  cut  up  xinder  ti 
wheels  of  a  heavily  loaded  wagon.  Oiling. — Oil  shall  then  be  distribut< 
evenly  over  the  entire  surface  of  roadway,  I  gal.  per  sq.  yd.  Coarse,  sha 
sand  shall  then  be  sprinkled  over  the  entu^  surface  of  roadway  imtil  no  tr 
oil  can  be  seen.  After  a  lapse  of  not  less  than  12  hrs.,  oil  shall  again  be  d 
tributed  over  entire  surface,  i  gal.  per  sq.  yd.  Entire  surface  of  road-^ 
shall  again  be  sprinkled  with  coarse,  sharp  sand  tmtil  the  oil  is  complete 
absorbed,  and  then  rolled  with  a  roller  weighing  not  less  than  250  lbs.  to  t 
>"ch  width  of  tire  until  the  siuf  ace  is  unyielding.  In  all  cases,  sxtfficient  sa 
slmll  be  used  to  prevent  the  oil  material  from  picking  up.  Total  amount 
oil  used  shall  not  be  less  than  1 J  gals,  per  sq.  yd.  ot  street  surface.    In  proo 


OILED  GRAVEL  ST,    BITUM. -BRICK  GUT RS.  1116 

9f  rolling,  care  must  be  taken  not  to  soil  the  curbs  or  walks.  After  the  oiling 
^  begun,  it  shall  be  carried  on  diligently  and  continually  to  its  completion. 
$and  used  in  covering  the  oil  must  be  distributed  in  piles  along  the  sides  of 
lie  street  before  the  oil  is  applied,  and  must  be  spread  quickly  and  in  suffi- 
aent  quantity  to  prevent  the  oiled  surface  from  picking  up.  Oil  shall  not  be 
ipplied  to  the  surface  of  a  street  while  in  a  wet  condition.  During  and  im- 
nediately  after  rolling,  the  surface  of  the  street  shall  be  gone  over  with 
)rooms  or  rakes  and  all  irregularities  removed. 

Oi/.— (a)  The  oil  used  shall  be  a  natural  oil  treated  to  remove  water  or 
ediment,  or  one  from  which  the  volatile  material  has  been  removed  by  dis- 
illation.  It  must  not  have  been  injured  by  over-heating,  and  it  must  not  be 
btained  by  adding  solid  asphalt  to  lighter  oils,  or  by  cutting  asphalt  with 
listillatcs.  (b)  Temperature.  All  oil  must  be  delivered  at  the  point  required 
3r  sprinkling,  at  a  temperature  not  less  than  150°  F.  (c)  Measurement.  In 
etermining  the  quantity  of  oil  delivered,  the  correction  for  expansion  by 
eat  shall  be  as  follows:  60°  F.  shall  be  considered  normal  temperature; 
ubtract  0.0004  of  measured  volume  for  each  °F.  above  60°  F.,  as  a  correc- 
ion  for  expansion  by  heat,  (d)  Volatility.  The  oil  shall  not  contain  more 
lan  8^  of  matter  volatile  when  said  oil  is  heated  slowly  to  220°  P.  and 
taintamed  at  that  temperature  for  15  minutes,  (e)  Asphalt.  After  being 
•eed  from  water  and  sediment,  the  oil  shall  contain  not  less  than  70%  of 
sphalt,  having  a  temperature  of  77°  F.,  a  penetration  of  80°,  District  of  Col- 
mbia  standard.  The  percentage  of  asphalt  shall  be  determined  by  heatinga 
eighed  amount  of  said  oil  in  an  evaporating  oven  to  a  temperature  of  400°  P. 
itil  it  has  reached  the  proper  consistency,  when  the  weight  of  the  residue 
lall  be  determined  and  the  per  cent  calculated.  (0  Water  and  Sediment, 
eduction  will  be  made  for  water  and  sediment  in  exact  proportion  to  the 
^rcentage  of  water  and  sediment  fotmd  therein,  which  must  not  exceed  2%. 
)  Tank  wagons.  All  tank  wagons  used  for  the  delivery  of  this  oil  must  first 
;  submitted  to  the  Department  of  Oil  Inspection,  which  will  gauge  and 
unp  into  the  steel  heads  of  said  tanks  the  capacity  in  gallons,  which  shall 

the  official  rating,  (h)  All  oil  used  shall  be  tested  by  the  Department  of 
I  Inspection. 

Surfacing  Sidtwalk  Areas. — In  cases  where  the  plans  provide  for  cement 
[ewaUcs  on  portions  of  the  street  to  be  improved,  and  do  not  provide  for 
:h  walks  over  its  entire  length,  then  there  shall  be  constructed  at  the 
:epted  places  gravel  walks  TT  deep  and  of  a  width  and  location  correspond- 
;  to  those  for  the  cement  walk  provided  for.  In  cases  where  the  plains  do 
t  provide  for  cement  walks  on  the  street  to  be  improved,  then  gravel  side- 
Iks  2^  deep  and  6  ft.  wide  shall  be  constructed,  except,  however,  in  cases 
ere  the  total  width  of  the  sidewalk  area  is  less  than  5  ft.,  in  which  event 

total  area  of  the  sidewalk  is  to  be  G^raveled.  In  the  construction  of  the 
vcled  walks,  the  same  quality  of  material  as  that  used  in  the  roadbed 
y  be  employed.  It  shiul  be  raked  free  from  large  stones,  sprinkled  and 
ed  until  firm. 

BiTUMiNizBD  Brick  Gutters. 
S«iid  Cushiofi. — ^Upon  the  concrete  base  (the  surface  of  which  is  6'  below 
ihed  grade,  and  thoroughly  watered  for  at  least  48  hours,  before  receiving 
lion  coat,  and  swept  free  from  all  dirt  and  rubbish)  shall  be  spread  a  layer 
and  2^  deep.  The  sand  need  not  necessarily  be  sharp,  but  it  must  be 
ened.  dry  and  free  from  more  than  3%  of  loamy  matter.  It  shall  be 
eui  by  the  aid  of  a  templet  and  made  to  conform  smoothly  to  the  true 
e  of  the  gutter.  There  shall  be  no  disturbance  of  the  surface  of  the 
ion  coat  previous  to  laying  the  bituminired  brick  thereon.  Laying 
minized  Brick. — Upon  the  cushion  coat  shall  be  laid  the  bituminized 
c.  vertically  on  edge,  and  in  close  contact  with  each  other.  Brick  in 
ining  rows  must  be  laid  so  as  to  break  joints  at  least  7f.  No  bats  or 
I  of  bricks  shall  be  used  except  for  the  purpose  of  closure  or  for  breaking 
s  in  starting  courses.  After  the  bricks  are  laid  they  shall  be  thoroughly 
•cted  and  all  warped,  spalled  and  chipped  brick  removed  and  replaced  by 
perfect  ones.  The  edge  of  the  gutter  next  the  curb  shall  then  be  care- 
taznped  by  hand  and  the  whole  gutter  shall  then  be  rolled  \mtil  all 
s  are  thoroughly  bedded  and  the  tops  lie  in  a  smooth  surface  conforming 
idc  and  cross-section  of  gutter.  Asphalt  of  a  composition  hereinafter 
ibed,  and  heated  to  a  temperature  of  300°  F.,  shall  then  be  poured  into 
rints  until  they  arc  fxill  and  remain  full  to  height  of  top  of  brick.  Surplus 
It  shall  then  be  removed,  before  it  has  become  stiff,  from  the  surface  of 


in«  fXi.^HlGHWAYS, 

the  gutter,  and  fine  sand  ihall  be  swept  over  tiie  top  until  all  stickiness  is 
removed.  Bitumiaized  Brick. — Shall  be  obtained  by  subjecting  ordimuT 
brick  of  the  quality  specified  hereinafter  to  a  bath  of  asphalt,  also  of  the 

Duality  hereinafter  described,  and  heated  to  a  temperature  of  from  300^  to 
25°  P.,  tmtil  at  least  80%  of  the  cross-section  of  the  brick  shall  have  become 
saturated  with  asphalt.  They  shall  be  free  from  warps,  cracks,  chips  or 
other  flaws,  and  the  surfaces  shall  be  free  from  superfluous  asf^ialt  and  in 
condition  to  lay  closely  together.  All  bittuninized  brick  will  be  subject  w 
the  following  Abrasion  Test. — ^This  test  shall  be  made  in  a  foimdry  rattkr 
whose  inside  diameter  is  28*  and  inside  length  is  20'.  Such  a  number  of 
whole,  dry  brick  that  their  total  volume  shall  eaual,  as  nearly  as  possible. 
8%  of  the  cubic  contents  of  the  rattler,  shall  be  placed  therein.  There  shall 
then  be  added  an  abrasive  charge  of  300  lbs.  of  cast  iron  blocks  as  follows: 
10  blocks  about  24*  square  and  4  J*  long,  with  edges  rounded  to  about  \* 
radius  and  weighing  7i  lbs.  each,  and  226  lbs.  of  cubical  blocks  about  1^  cti 
a  side  and  with  square  comers  and  edges.  The  rattler  shall  be  revolved  1800 
times  at  a  speed  of  from  28  to  30  rev.  per  min.  The  loss  by  abrasion  dtaring 
such  test  shall  not  exceed  20%  of  the  original  weight  of  the  brick.  Ordiaanr 
Brick. — Shall  be  whole,  sound  brick  with  smooth,  rectangular  surfaces  and 
straight  edges  and  must  give  a  clear  ringing  sound  when  struck  together. 
They  shall  be  uniform  in  quality,  free  from  laminations,  and  shall  run  in  sise 
from  8'  to  8 J'  long,  4'  wide  and  from  2*  to  2  J'  thick  and  burned  to  a  meditur 
degree  of  hardness.  All  brick  shall  be  culled  or  sorted  by  the  contractor 
before  being  treated  to  an  asphalt  bath,  and  will  be  subject  to  the  following 
test:  Three  or  more  bricks  shall  be  broken  across,  thoroujg^hly  dried,  weighed, 
then  immersed  in  water  for  24  hours  and  weighed  agam.  The  absorptios 
shall  be  determined  by  the  difference  between  the  two  weights,  and  it  sbaD  I 
not  exceed  16%  nor  be  less  than  12%  of  the  dry  weight  of  the  brick;  other- 
wise the  brick  from  which  the  tested  samples  were  selected,  shall  be  rejected 
Asphalt. — This  mxist  be  prepared  froqi  California  products.  It  shall  be  & 
mixture  of  refined  liquid  asphalt  with  a  refined  solid  asphalt  or  be  an  oiJ 
asphalt,  and  must  be  free  from  admixture  with  any  residues  obtained  by  the 
artiRcial  distillation  of  coal,  coal  tar  or  paraffine  oil.  The  asphalt  must  be 
homogeneous  and  its  consistency  at  the  time  of  its  use  in  the  bath  must  fall 
within  the  limits  of  60**  and  80°  penetration  by  the  District  of  Columbia 
standard.  It  must  be  adhesive  and  ductile  and  also  slightly  elastic  at  a  tem- 
perature of  32°  F.  When  20  grams  are  heated  to  a  temperature  of  800°  F. 
for  6  consecutive  hours  in  an  uncovered  cylindrical  dish  Z\  cm.  high  by  5i  cm- 
in  diameter,  it  must  not  lose  more  than  1%  in  weight,  and  itspenetratixi 
mxist  not  be  reduced,  as  a  result  of  such  heating,  more  than  60%.  It  must. 
when  ready  for  use,  contain  at  least  90%  of  bitumen  soluble  in  carbon  di- 
sulphide.  It  shall  be  soluble  in  cold  carbon  tetrachloride  to  the  extent  of 
at  least  97% .  Not  less  than  70%  shall  be  soluble  in  86° naphtha.  It  ^lallnot 
contain  more  than  16%  of  fixed  carbon  on  ignition.  When  the  asphah  is 
prepared  by  mixing  a  solid  oil  asphalt  with  a  liquid  asphalt,  the  solid  oi] 
asphalt  shall  be  prepared  by  distilling  the  crude  oil  tmtil  the  anihaltic 
residutun  has  a  penetration  not  less  than  60°  bv  the  District  of  Cohunbia 
standard,  and  shall  not  be  prepared  by  mixing  or  fluxing  a  more  solid  asphalt 
with  a  liquid  or  softer  asphalt.  The  refined  liqtiid  asphalt  used  in  aoftenisg 
a  solid  asphalt  must  be  a  stiff  residuimi  of  petroleum  oil  with  an  asphalt  tiase. 
It  must  be  free  from  water  and  from  light  oils  volatile  at  leas  than  260^  F. 
When  20  grams  are  heated  to  a  temperature  of  300°  F.  for  5  consecutrre 
hours  in  an  uncovered  cylindrical  dish  3i  cm.  high  by  6}  cm.  in  diameter,  i^ 
must  not  lose  more  than  6%  in  weight.  It  mtast  contain  not  less  than  99^ 
of  bitumen  soluble  in  carbon  disulphide. 

MARYLAND  STATE  HIGHWAY  SPECIFICATIONS. 

(Maryland  Geological  Sxirvey.) 

Macadam  Construction. 

Class  A,  B  and  C. — ^Thickness  after  rolling,  to  be  as  follows: 

Class  A.    1st  course,  3^; 2nd,  3*'; Srd.  as  described  later. 

Class  B.         ••  6\in21ayers;     "     3'; " 

Class  C.         "  6*.  gravel; "     3*,  stone;    " 

Roadbed. — Natvual  earth  bed  prepared  and  rolled  tmtil  firm  and  hard, 
a  small  amount  of  clay  to  be  added  it  sandy  or  other  soil  win  not  cocup«ac^ 
readUy  under  roller.   La  Cuts  and  Fills,  roadbed  is  to  be  graded  84  ft.  wide  I 


MACADAM  CONSTRUCTION,   CEMENT  WALK.         1117 

Rotdbed  prepftred  for  broken  stone  surface  to  be  14  ft.  wide*  and  rolled  firm 
and  hard;  depressions  filled  with  earth  and  rerolled.  Old  earth  roadbed, 
where  there  is  no  change  in  grade,  is  to  be  shaped  to  proper  cross-section,  ele- 
vations and  depressions  removed,  and  surface  rolled  hard  and  smooth.  The 
portion  of  the  roadbed  prepcu'ed  for  the  broken  stone,  is  to  be  below  the 
sides  by  an  amount  equal  to  thickness  of  1st  cotirse  of  stone,  to  prevent 
spr^ingat  sides.  Roaidbed  tohave  cross-slope  of  f  to  1  ft.  First  Course.-— 
Sotmd  broken  stone,  3*  to  2*,  known  as  "No.  1"  size.  If  approved  it  may  be 
gravel,  8*  to  1*.  with  not  more  than  26%  less  than  1*.  No  layer  of  crushed 
stone  to.be  spread  thicker  than  ^  before  being  thoroughly  rolled.  Broken 
stone  or  gravel  for  Ist  course  to  be  rolled  with  steam  roller  weighing  not  less 
than  10  tons,  tmtil  compacted  firm  and  smooth;  sprinkling  with  water  or 
lightly  spreading  with  sand  if  needed;  rolling  to  b^in  at  sides  and  work 
toward  center,  unevenness  or  depressions  to  be  remedied.  Shoolders. — 
After  1st  course  is  made,  construct  shoulders  along  each  side  for  width  of 
at  least  5  ft.;  against  these  shoulders,  spread  broken  stone  for  second  course; 
the  shoulders  with  the  14  ft.  of  broken  stone  will  make  a  total  width  of  24  ft., 
to  be  cross-sloped  I'  to  1  ft.  Second  Coorsa. — Same  width  as  first  course. 
Broken  stone  1'  to  2",  known  as  No.*'2"  size.  Unless  otherwise  specified  the 
stone  for  this  course  shall  be  trap  rock  with  a  "coefficient  of  wear"  as  deter- 
mined by  tests  made  at  the  laboratory  of  the  Hicfhway  Division  of  the  Mary- 
land Geological  Survev,  of  not  less  than  15,  or  Imiestone  with  a  "coefficient 
>f  wear"  of  not  less  than  10.  The  broken  stone  to  be  spread  upon  the  1st 
xmrse,  to  a  uniform  thickness,  and  rolled  with  not  less  than  a  1 0-ton  roUer, 
sprinkling  with  water  or  lightly  spreading  with  sand  or  other  material  if 
lecessary,  until  surface  is  hard  and  smooth;  cross-slope  of  surface,  K  to  1  ft. 
Jnevenness  and  depressions  to  be  remedied.  Third  Coarse. — ^Trap  rock 
creenings,  from  V  to  dust;  other  material  may  be  used  if  approved;  lime- 
tone  screenings  to  be  used  with  a  limestone  2nd  course.  Upon  it\A  2nd 
ourse,  and  in  quantity  just  enough  to  cover  it,  the  screenings  are  to  be 
pread  dry,  then  sprinkled  with  a  sprinkling  cart,  and  rolled  with  not  less 
dan  a  10-ton  roller,  beginning  at  the  sides.  If  after  rolling  the  screenings, 
le  No.  2  stone  ftpp«ars  at  the  surface,  use  additional  screenings.  Rolling 
nd  watering  to  continue  until  the  water  flushes  to  the  surface;  the  rolling 

>  extend  over  whole  width  or  road  and  shoulders.  Unevenness  and  depres- 
ons  to  be  remedied. 

NATIONAL  ASSOCIATION  OF  CEMENT  USERS. 

(Philadelphia,  Pa.) 
Portland  Cbmbnt  Sidewalk  SPBCiriCATioNs. 
(Adopted  January,  1908.) 
MfttOTiab. —  (1)  Cement  shall  meet  requirements  of  specification  for  Port- 
ad  cement  of  the  A.  S.  T.  M.,  and  adopted  by  this  association  (Spec.  No.  1), 
nuary,  1006.    (2)  Sand  shall  pass  a  No.  4  screen  and  be  free  from  foreign 
itter,  except  loam  and  clav  up  to  5%  when  not  occurring  as  a  coating  on 

>  sand  grains.  Not  more  tnan  40%  shall  be  retained  on  a  No.  10  sieve;  or 
Yo  pass  a  No.  10  and  be  retained  on  a  No.  20;  or  35%  pass  a  No.  20  and  be 
ained  on  a  No.  30;  or  35%  pass  a  No.  30  and  be  retained  on  a  No.  40:  or 
%  I>ass  a  No.  40  and  be  retamed  on  a  No.  50.  Not  more  than  20%  snail 
»  a  No.  50  sieve;  or  70%  pass  a  No.  10  and  be  retained  on  a  No.  40;  or 
Yo  pass  a  No.  20  and  be  retained  on  a  No.  50  sieve.  (3)  Stone  shall  be 
^ed  from  clean,  sound,  hard,  durable  nxJc,  be  screened  dry  through  a 
mesh,  and  be  retained  on  a  i'  mesh.  (4)  Screenings  from  the  crushed 
ne,  if  they  meet  Uie  requirements  for  sand,  may  be  tisedi  as  sand  if  approved. 
Gravel  uiall  be  clean,  hard,  and  vary  in  size  from  ^^  to  i'  screening;  im- 
sened  gravel  shall  be  clean,  hard,  and  contain  no  particles  larger  than  |', 

proportions  of  fine  and  coarse  to  be  determined  and  corrected  to  agree 
h  requirements  for  concrete.  (6)  Water  to  be  clean,  free  from  oil, 
>huric  add  and  strong  alkalies.    Forms. — (7)  Ltunber,  iree  from  warp, 

not  less  than  If*  thick;  all  mortar  and  dirt  to  be  removed  from  forms 
riously  used.  (8)  Setting. — ^The  forms  shall  be  well  staked  to  the  estab- 
id  lines  and  grades,  and  their  upper  edges  shall  conform  with  finished 

*  Mr.  B.  P.  Ruggles,  First  Assistant  Engineer,  writes  the  author  as  fol- 
;:  *  'As  a  rule,  otir  roads  are  built  with  a  width  of  1 2  ft.  for  the  macadam; 
Dush  "WC  have  built,  where  the  travel  requim  it,  a  good  deal  of  14-ft. 
adam." 


1118  90.—HIGHWA  YS. 

grade  of  sidewalk,  which  shall  have  sufficient  rise  from  curb  to  provide  prot>> 
cr  drainage;  this  rise  not  to  exceed  i'  per  ft.,  except  where  such  rise  ^idl 
parallel  length  to  walk.  (9)  Cross  Forms,  at  each  block  division,  shall  be 
put  in  the  fuil  width  of  walk  and  at  right  angle  to  side  forms.  (10)  Expan- 
sion Joints.  A  metal  parting  strip  J'  thick  shall  take  theplace  of  the  cross- 
forms  at  least  once  in  every  60  lin.  ft.  of  sidewalk.  When  sidewalk  has 
become  hard,  this  parting  strip  shall  be  removed  and  joint  filled  with  suit- 
able material  prior  to  opening  the  walk  to  traffic.  Similar  joints  ^aU  be 
provided  where  new  sidewalks  abut  curbing  or  other  artificial  stone  sidewalk. 
(11)  Wetting.  All  forms  to  be  thoroughly  wetted  before  any  material  is  de- 
posited against  them.  Size  and  Thickness  of  Blocks. — (12)  In  Business 
Districts,  blocks  shall  be  so  divided  that  no  dimension  shall  be  greater 
than  6  ft.;  thickness  of  sidewalk  shall  correspond  directly  with  the  greatest 
dimension  of  the  walks  as  follows:  6"  thick  for  block  6  by  6  ft.;  5^'  for 
block  6  by  5  ft.;  ST  for  block  4*  by  4i  ft.;  4'  for  block  4  by  4  ft.  (13)  In 
Residence  Districts,  thickness  of  sidewalk  shall  be  as  follows:  (ST  thick  for 
blockObyOft.;  8*  for  block  5  by  6ft.;  4' for  block  4  by  4ft.;  y  for  blodc 
3  by  9ft.:  it  being  permissible  to  lay  sidewalks  with  a  thickness  at  the 
edges  26%  less  than  at  center.  (14)  Minimum  Thickness  of  walk  to  be  3* 
in  any  case.  Sub-Base. — (16)  Preparation.  Sub-base  to  be  thoroughlv 
rammed,  and  all  soft  spots  removed  and  replaced  by  suitable  hard  material. 
(16)  Pills.  When  a  fill  exceeding  1  ft.  thick  is  required,  it  shall  be  thoroughly 
compacted  by  flooding  and  tamping  in  layers  not  over  6*  thick,  and  uiall 
have  a  slope  of  not  less  than  1  to  U.  The  top  of  all  fills  shall  extend  at  least 
12*  beyond  the  sidewalk.  (17)  Wetting.  While  compacting,  the  sub-base 
shall  be  thoroughly  wetted  and  shall  be  maintained  in  that  condition  until 
the  concrete  is  deposited.  Base. — (18)  Proportions.  The  concrete  for  the 
base  shall  be  so  proportioned  that  the  cement  shall  overfill  the  (19)  Voids* 
in  the  sand  by  at  least  6%,  and  the  mortar  shall  overfill  the  void^  in  the 
stone  by  at  least  10%.  The  proportions  shall  not  exceed  1  part  cement  to 
8  parts  of  the  other  materials.  When  the  voids  are  not  determined,  the 
concrete  shall  be:  1  part  cement.  3  parts  sand  or  screenings,  and  5  parts 
stone  or  gravel.  A  sack  of  cement  (94  lbs.)  shall  be  considered  to  have  a 
volume  of  1  cu.  ft.  (20a)  Hand  Mixing.  Spread  sand  evenly  on  level  water- 
tight platform:  spread  cement  upon  sand;  mix  thorotighly  dry  to  onifonn 
color;  add  water  in  a  spray,  and  turn  mass  imtil  homogeneous  mortar  of 
even  consistency  is  obtained;  to  this  mortar,  add  the  required  amount  <rf 
stone  or  gravel  previously  drenched,  and  mix  the  whole  tmtil  the  aggregate 
is  thorotighly  coated  with  mortar.  When  unscreened  gravel  is  used,  the 
cement  and  gravel  shall  be  thoroughly  mixed  dry  until  no  streaks  o£  cement 
are  visible ;  water  shall  be  added  with  a  spray  in  sufficient  quantity  to  render 
when  thoroughly  mixed,  a  concrete  equal  to  that  specified  above.  Water 
may  be  added  during  the  process  of  mixing,  but  the  concrete  ^lall  be  turned 
at  least  once  immediately  after  its  addition.  (20b)  Mechanical  Mixing.  Ma- 
chine mixing  will  be  acceptable  when  a  concrete  eoual  in  quality  to  that  speci- 
fied above  is  obtained ;  mixing  to  be  thorough.  (21)  Retempering  will  not  be 
permitted.  (22)  Depositing.  The  concrete  shall  be  deposited  within  1  hour 
after  being  mixed,  and  shall  be  transferred  to  the  forms  in  water-tisbt 
wheelbarrows;  the  barrows  not  to  be  filled  so  full  as  to  allow  mortar  to  uop 
out,  and  shall  not  be  run  over  freshly  laid  concrete.  The  concrete  to  be 
spread  evenly  and  tamped  imtil  water  flushes  to  the  top.  (23)  Separation  of 
Blocks  shall  be  done  with  a  tool  not  over  6*  wide  and  f*  thick,  and  to  insure 


*  To  determine  voids,  fill  a  vessel  with  sand  and  let  net  weight  of  sand 
equal  B.    Fill  same  vessel  with  water  and  let  net  weight  of  water  equal  A, 

Per   cent  voids  -  ^^^^^^^X  100. 

This  formula  may  also  be  used  in  determining  voids  in  crushed  stooe 
and  screenings  by  substituting  for  2.66  the  specific  gravity  of  the  stone. 

The  following  is  a  more  simple  method  of  determining  voids  in  coarse 
aggregate:  Pill  a  vessel  with  the  aggregate  and  let  net  weight  equal  B. 
Add  water  slowly  imtil  it  just  appears  on  the  suriace,  and  weigh.  Let  net 
weight  equal  A.    Pill  same  vessel  with  water  and  let  net  weight  equal  C. 

Per  cent  voids-  ^-^  X  100. 

Use  a  vessel  of  not  less  than  one-half  (i)  cubic  fooVcaoacitr^  The  larger 
the  vessel,  the  more  accurate  the  results  ogtized by\"iWnor(>         <=  **»w^ 


CEMENT  WALK.    GRANITE  BLOCK  PA\^EMENT.        1119 

complete  separation  the  groove  should  be  cut  through  into  the  sub-base. 
Pill  the  groove  with  dry  sand  before  the  top  coat  is  spread,  and  the  top  coat 
should  be  cut  through  to  the  sand  after  fleeting  and  troweling  and  a  jointer 
run  in  the  groove;  then  again  draw  a  trowel  through  the  groove,  so  as  to 
insure  a  complete  separation  of  the  block.  (24)  Protection.  Workmen  not 
permitted  to  walk  on  freshly  laid  concrete,  and  where  sand  or  dust  collects 
on  the  base  it  shall  be  carefully  removed  before  the  wearing  surface  is  applied. 
Wearing  Surface— (25)  Thickness.  }'.  (26)  Mixing.  The  mortar  to  be  mixed 
in  the  same  manner  as  the  mortar  for  the  base,  but  usin^  1  part  cement  to 
2  parts  of  sand  or  screenings,  and  it  shall  be  of  such  consistency  as  will  not 
require  tamping,  but  will  be  readily  floated  with  a  straightnedge.  (27)  De- 
positing. Spread  mortar  on  the  base  within  30  minutes  after  mixing,  and  in 
no  case  shall  more  than  50  minutes  elapse  between  the  time  that  the  concrete 
for  the  base  is  mixed  and  the  time  that  the  wearing  course  is  floated.  Ploat 
a  thin  coat  of  mortar  on  the  base  before  spreading  the  wearing  surface. 
( 28)  Marking.  After  being  worked  to  an  approximately  true  surface,  the  block 
markings  shall  be  made  directly  over  the  joints  in  the  base  with  a  tool  which 
shall  cut  clear  through  to  the  base  and  completely  separate  the  wearing 
courses  of  adjacent  blocks.  (29)  Edges.  All  surface  edges  of  blocks  to  be 
rounded  to  radius  of  not  less  than  i".  (30)  Troweling.  When  partially  set, 
the  siuface  shall  be  troweled  smooth.  (31)  Roughening  wearing  stzrface.  On 
grades  exceeding  5%.  the  surface  shall  be  roughened,  by  using  a  grooving 
tool,  toothed  roller,  brush,  wooden  float  or  other  suitable  tool,  or  by  working 
coane  sand  or  screenings  into  the  sxirface.  (32)  C^lor.  If  color  ut  desired, 
only  mineral  colors  shall  be  used,  which  shall  be  incorporated  with  the 
entire  working  surface.  Single  Coat  Work. — (23)  Proportions.  Single  coat 
woiic  shall  be  composed  of  1  part  cement,  2  parts  sand,  4  parts  gravel  or 
crushed  stone,  and  the  blocks  separated  as  provided  for  in  the  specifications 
for  two-coat  work.  (34)  Finishing.  The  concrete  shall  be  thoroughly  com- 
pacted by  tamping  and  evenly  struck  off  and  smoothed  to  the  top  of  mold. 
Then,  with  a  suitably  grooved  tool  the  coarser  particles  of  the  concrete 
tamped  to  the  necessary  depth  so  as  to  finish  the  same  as  two-coat  work. 
Protection  and  Qrading. — (35)  Protection.  When  completed,  the  sidewalk 
Uiall  be  kept  moist  and  protected  from  traffic  and  the  elements  for  at  least 
3  days;  the  forms  to  be  removed  with  great  care,  and  when  removed,  earth 
(half  be  banked  against  the  edges  of  the  walk.  (36)  Grading,  after  the 
valks  are  ready  for  use,  should  be  on  the  curb  side  of  the  sidewalk,  li' 
owcr  than  the  sidewalk,  and  not  less  than  i'  per  ft.  fall  toward  the  curb  or 
.^tter.  On  the  property  side  of  the  walk,  the  ground  should  be  graded 
>ack  at  least  2  ft.  and  not  lower  than  the  walk;  this  will  insure  the  frost 
browing  the  walk  alike  on  both  sides. 

MANHATTAN  (N.  Y.  CITY)  BOROUQH  PAVEMENT  SPECIFICATIONS. 

GRANrrB  Block  Pavembnt. 

Blodcs. — Shall  be  of  a  durable,  sound  and  uniform  quality  of  granite; 
•  to  12*  long,  34'  to  44'  wide,  and  7"  to  8'  deep;  same  quality  as  to  hard- 
ess,  color  and  grain.  No  outcrop,  soft,  brittle  or  laminated  stone  accepted. 
Hocks  to  be  rectangular  on  top  and  sides,  uniform  in  thickness,  to  lay  closely, 
nd  with  fair  and  free  surfaces,  free  from  bunches.  Other  dimensions  of 
locks  may  be  used  for  special  construction.  Stone  from  each  quarry  shall 
e  piled  and  laid  separately  in  different  sections  of  the  work;  no  mixing  of 
ones  from  different  quarries.  Sand  Cushion. — On  the  concrete  fotmdation 
previously  prepared  6'  thick)  place  a  layer  of  clean,  course,  dry  sand  to 
ich  a  depth  (not  less  than  1  i'O  as  may  be  necessary  to  brizig  the  surface 
pavement  when  thoroughly  rammed,  to  the  proper  grade.  Laying. — On 
lis  sand  bed,  and  to  grade  and  crown  specified,  lay  the  blocks  at  right 
iglc  to  line  of  street,  or  at  such  angle  as  may  be  directed;  each  course  to 
;  straight  and  regular,  with  the  end  joints  by  lap  of  at  least  3*;  stones  of 
fferent  width  not  to  be  laid  in  the  same  course,  except  on  curves;  joints  to 
i  close,  except  where  gravel  filling  is  used  the  joints  between  courses  shall 
►t  exceed  i'.  After  the  blocks  are  laid,  they  shall  be  covered  with  clean. 
ird  and  dry  gravel  (previously  heated  and  dried),  to  be  bnished  in  until 
I  the  joints  are  filled  therewith  to  within  3*  of  the  top;  the  gravel  to  be 
ished  white  quartz,  free  from  sand  or  dirt,  and  f  to  f*^  mesh  screenings. 
unmifiS. — Blocks  must  then  be  rammed  and  ramming  repeated  until  they 
s  brouc^ht  to  an  unyielding  bearing  with  a  uniform  surface,  true  to  even 
etde  and  crown;  no  ramming  to  be  done  within  20  ft.  of  face  of  work  being 


1 1 20  W.—HIGHWA  YS. 

laid.  Joints. — After  ramming,  the  pavement  cement  heated  to  SO<P  P.  shall 
then  be  poured  into  the  joints  until  same  are  full  and  remain  full  to  top  of 
gravel.  Hot  gravel  shall  then  be  poured  aloii^  the  Joints  flush  with  top  of 
blocks;  and  paving  cement  again  potired  in  jomts,  nllins  all  voids.  Pavte 
Cemeot. — Shall  be  composed  of  20  parts  of  refined  asphalt  and  3  parts  of 
residuum  oil,  mixed  with  100  parts  of  coal-tar  pitch  such  as  is  orainarily 
nimibered  4  at  the  manufactory,  the  proportions  to  be  determined  by 
weight. 

Wood  Block  Pavbmbnt. 

Fouiidatioo. — 0*  thick,  including  5i'  of  concrete  proper  and  i'  of  mortar 
top  surface,  ordinarily.     Blocks. — (a)  Either  of  southern  kmg-leaf  yeUow 

Sine,  southern  black  ^um,  Norway  pine  or  tamarack,  not  less  than  90%  of 
eart;  texttire  permitting  satisfactory  treatment:  inspection  at  worki,  in 
the  stick,  before  being  sawed  into  blocks,  (b)  All  blodcs  shall  be  of  sound 
timber,  free  from  bark,  loose  or  rotten  knots,  or  other  defects  detrimental 
to  life  of  blocks  or  to  laying;  no  second-growth  timber  allowed,  (c)  Blocks 
shall  be  well  made,  rectangular  and  of  uniform  dimensions:  Depth  (parallel 
to  fiber)  31*.  length  6*  to  10",  width  3*  to  4';  in  any  one  contract,  blocks  to 
be  of  same  timber,  and  depth  and  width  shall  not  vary  more  thsA  i'.  (d) 
Blocks  to  be  treated  with  an  antiseptic  and  waterproof  mixture,  not  more 
than  75%  per  cent  of  which  shall  be  creosote  or  heavv  oil  of  coal  tar,  and  at 
least  25%  of  which  shall  be  resin;  all  parts  of  each  block  to  be  thoroughly 
treated,  mjecting  not  less  than  20  lbs.  per  cu.  ft.  (e)  Treated  pine  blocks 
shall  weigh  as  much  as  water;  treated  gum  blocks,  at  least  59  lbs.  per  cu.  ft.; 
any  other  wood,  at  least  20  lbs.  per  cu.  ft.  more  than  its  recognised  weight 
untreated .  Blocks  cut  from  the  several  classes  of  timber  will  require  different 
treatment,  hence  the  exact  methods  of  applying  the  mixture  will  not  be 
specified,  but  must  conform  in  every  respect  to  the  beet  and  most  advanced 
knowledge  of  the  art.  (f)  The  creosote  oU  at  68**  P.  shall  have  a  specific  grav. 
of  not  less  than  1.12;  when  distilled  in  a  retort  with  the  thermometer  sus- 
pend^ not  less  than  1'  above  the  oil,  it  shall  lose  not  more  than  36%  up  to 
315**  C,  and  not  more  than  50%  up  to  370*  C.  Oil  to  be  free  from  adultera- 
tion or  foreign  material,  (g)  The  resin  to  be  solid  resin  obtained  from  pine: 
and  reduced  to  a  fine  dust  by  grinding  and  then  incorporated  with  the  hot 
creosote  oil  in  a  suitable  mixing  tank  until  the  proper  proportions  are  se- 
cured, (h)  After  treatment,  blocks  not  to  gain  more  than  8i%  in  wei^ 
after  being  oven-dried  at  100®  for  24  hours  and  then  immersed  in  water 
24  hours.  Analysis  off  Treated  Block. — Pine  turnings  from  the  block  AaU  be 
placed  in  an  extraction  apparatus  and  the  oil  completely  extracted  therdtitnn 
with  ether  or  carbon  bisulphide;  the  oil  then  placed  in  a  still  and  distiUed; 
the  portion  up  to  120*  C.  consisting  of  the  solvent,  is  to  be  collected  apart; 
the  oil  then  distilled  up  to  370*  C.  The  oil  thus  obtained  must  conform  in 
all  respects  to  the  requirements  of  (h),  above.  Mortar  Bed. — On  concrete 
fotmdation,  spread  |'  layer  of  mortar  composed  of  1  part  Portland  cement 
to  4  parts  clean,  sharp  sand,  free  from  pebbles  over  }'  diameter;  the  mortar 
top  to  be  "struck"  3)'  belQW  and  ^uallel  to  top  of  finished  pavement.  The 
mortar  bed  to  be  laid  as  follows:  On  surface  of  concrete  foundation,  before 
mortar  bed  is  laid,  set  strips  of  wood  4*  wide  by  4'  thick,  or  strips  of  steel  4* 
by  i'.  and  of  convenient  length;  these  strips  to  be  set  parallel  and  about  8 
to  10  ft.  apart,  running  from  curb  to  curb,  and  imbedded  in  mortar  so  that 
top  surface  shall  be  3 r  below  grade  of  finished  pavement;  the  space  between 
two  strips  having  been  filled  with  mortar,  a  true  and  even  top  surface  tiiall  be 
struck  by  using  an  iron-shod  straight-edge  on  the  strips  as  a  guide,  the  strips 
to  be  removed  and  the  places  filled  with  mortar  as  the  blocks  are  Iwd. 
Laying. — On  this  mortar  stirface  the  blocks  are  laid,  with  the  grain  vertical 
in  parallel  courses,  at  angles  as  directed,  tight  joints  as  possible,  each  blodc 
being  firmly  imbedded  in  the  mortar  bed  so  as  to  form  a  true  and  even 
surface.  Expansion  Joints,  i',  shall  be  used  along  each  curb,  and  across  the 
street  every  100  ft.  The  joints  shall  then  be  filled  with  cement  grout  (2  puts 
sand  and  1  part  Portland  cement,  mixed  to  a  perfectly  liquid  form)  and  the 
surface  of  the  blocks  shall  be  slushed  with  same  and  joints  swept  until  com> 
pletely  filled;  siu^ace  then  covered  with  \'  of  screened  sand.  Orooved 
Blocks.— Where  Rrade  exceeds  3%,  the  blocks  shall  be  between  O'and  l<f 
tongj  the  upper  edRc  of  each  block  to  be  cut  away  for  a  width  of  f*  and  depth 
ot  1  .  so  as  to  provide  transverse  grooves  between  each  course  (as  a  foothold 
tor  horses)  •  or  other  equally  good  construction.  Bk>cks  to  be  laid  (in  xisual 
manner),  i'  lap.  whole  blocks  used,  and  covered  with  sand  when  laid. 


PAVEMENT—WOOD,  IRON-SLAG,  BRICK.  1121 

RICHMOND  (N.Y.  CITY)  BOROUGH  PAVEMENT  SPEapiCATIONS. 

(Louis  L.  Tribus,  Commissioner.) 
Iron  Slag  Block  Pavbmbnt. 
Blocks.— Iron  tlag  blocks,  8*  to  9*  long.  31'  wide,  V  deep;  shall  be 
hard,  durable  and  pertect;  upper  edges  to  be  chamfered.  On  grades  of  6% 
or  over,  the  joints  between  blocks  are  to  be  left  open  to  receive  hot,  clean 
jravel,  with  paving  cement;  for  grades  below  8%,  the  joints  will  be  laid 
:]ose  without  gravel  but  filled  with  paving  cement.  Sand  Cushion. — On  the 
bundation  (concrete)  place  about  a  2*  layer  of  clean,  dry  sand  to  bring 
lurface  of  pavement,  when  rolled,  to  proper  grade;  sand  to  be  screened  imd 
ree  from  stones  and  rubbish;  cushion  to  be  brought  to  required  form  and 
rown  by  means  of  template  resting  on  ctirbs  and  drawn  forward  a  few  feet, 
head  of  laying.  Laying. — Blocks  laid  on  edge  at  right  angle  to  curb  line, 
xcept  at  street  intersections  where  they  shall  be  laid  as  required.  End 
)int8  to  be  broken  by  lap  of  half  length  of  bkx:k.  At  every  4th  course,  or 
s  often  as  directed,  blocks  shall  be  closed  up  by  hammering  and  the  course 
raightened.  End  joints  to  be  closed  by  means  of  crowbar  applied  at  ends 
;xt  the  curbs  before  the  closures  sue  made.  Whole  blocks  used  except  in 
;giiming  or  closing  a  course,  or  as  directed.  Rolling. — As  soon  as  street 
odk  has  been  laid,  the  pavement  shall  be  swept  clean  and  rolled  with  6-ton 
Her  until  all  blocks  are  thoroughly  imbedded  in  the  sand  cushion;  all  de- 
eased  surfaces  to  be  relaid ;  pavement  then  reroUed  tmtil  finished  surface 
smooth  and  even,  to  requirea  grade  and  crown.  Broken  or  chipped  blodcs 
*  to  be  replaced.  Expansion  Joints. — Before  laving  the  blocks,  laths  %' 
ick  shall  be  placed  next  each  curb.  The  spaces  thus  formed  shall  be  filial 
th  hot  paving  cement  composed  as  follows:  Paving  Cement. — Shall  be 
uminous  material  either  natural  or  artificial,  free  from  coal  tar  or  any 
tducts  of  coal  tar  distillation.  It  shall  be  waterproof,  free  from  water  or 
om  position  products,  remain  ductile  and  pliable  at  idl  climatic  tempera- 
es  to  which  it  may  be  subjected  in  actual  use,  and  shall  not  run  in  the 
Its  in  the  hottest  temperature  in  summer,  nor  become  hard  and  brittle 
jxigh  the  action  of  frost.  It  shall  conform  to  the  following  requirements: 
%  or  over  by  weight  shall  be  soluble  in  carbon  bisulphide;  specific  gravity 
\fy*  P.  to  be  not  less  than  1;  100  grams  of  this  cement  not  to  lose  more 
1  10%  weight  when  maintained  at  a  uniform  temperature  of  400^  P.  for 
)urs  in  a  cylindrical  vessel  ZY  diameter  and  1'  high;  amoimt  of  fixed 
<yn  not  to  be  more  than  12%  and  it  shall  show  a  flashing  point,  open  oil 
>r.  of  more  than  510<*  P.,  and  shall  not  contain  more  than  2\%  of  paraf- 
scale;  if  obtained  by  mix  of  bituminous  materials,  it  shall  be  homo- 
ous,  ft^ee  from  water  and  light  oils,  obtained  by  agitation  with  hot  air 
temperature  of  not  more  than  400**  until  all  the  mass  is  blended  com- 
ly.  and  shall  be  free  from  granular  accumulations.  Penetration  test: 
X**  P.  with  No.  2  needle  and  100  grams  weight  for  6  seconds,  shall  not  be 
ban  1  mDlimeter;  at  115^  P.,  No.  2  needle,  60  grams,  not  less  than  8 
lore  than  15  mm.;  \  gram  of  the  material  when  made  into  a  ball  shall 
lelt  and  drip  through  an  aperture  1  mm.  in  diameter  at  less  than  220^  P. 
>avizig  cement  shall. be  heated  on  the  work  to  a  temperature  between 
ind  460^  P..  in  quantities  to  allow  this  temperature  to  be  maintained  in 
^ttles  during  progress  of  pouring;  none  with  temperature  bek)w  400**  to 
d.  It  shall  then  be  put  m  a  conical  can  and  poured  in  the  interstices 
blocks  till  the  filler  is  flush  with  top  of  blocks;  repeating  filling  if 
ary.  All  joints  between  blocks  shall  be  filled  with  this  hot  paving 
t,  pouringfrom  center  to  sides,  but  no  flushing  of  the  pavement  will 
-nitted.  Where  girder  rails  are  used,  the  space  between  the  web  of  rail 
joimna,  blocks  shall  be  filled  with  mortar,  composed  of  Portland  cement 
1  4.  Underdraining. — Pipes  shall  be  vitrified,  salt-glazed  stoneware 
tted  -writh  proper  collars,  pipes  to  be  4'  inside  diameter  and  12^  to  24' 

ViTRiriBD  Brick  Pavbmbnt. 
zUm, — The  carriageway  to  be  paved  with  best  quality  of  repressed 
[  pavins  blocks  made  of  shale  or  clay,  and  with  jr  lugs  on  the  sides: 

m  Bixc,  color  and  quality  and  of  same  make;  blocks  to  be  from  2\* 
ide.  7^  to  iClong.  and  4'  to  4  J' deep,  exclusive  of  projection.  Select^ 

(34  blocks  of  average  quality  from  each  60000  or  less)  to  be  sub- 
>  the  following  tests:  Bricks  to  be  free  from  lime  and  magnesia  in 
I  of  pebbles  and  shall  show  no  signs  of  cracking  or  spawling  on  re- 

ixi  mr&ter  96  hours;   when  subjected  to  tesU  for  abrasion,  loss  in 


1122  Vi.— HIGHWAYS. 

weight  not  to  be  more  than  20% ;  shall  have  a  specific  gravity  of  not  kss 
than  2.3;  shall  not  absorb  more  than  3%  of  water  when  dried  at  212^  F.  for 
48  hours  and  afterward  immersed  for  48  hoxirs  in  water  (test  to  be  made  oc 
blocks  which  have  been  subjected  to  abrasion  test) ;  for  transverse  test,  thev 
shall  show  a  modulus  of  rupture  of  not  less  than  2000  lbs.  per  sq.  in.  whes 
tested  on  edge  as  laid  in  the  pavement,  the  modulus  to  be  computed  by  the 
formula  /?«  Uw-i-Tbd^.  in  which  R  is  the  modulus  of  rupture,  /  the  length 
between  supports  ( <=  6),  &  and  d  breadth  and  depth,  all  in  inches,  and  w  the 
load,  in  lbs.,  producing  rupture.  Sand  Cushion,  Laying,  Rolling,  Expwisioi 
Joints,  Paving  Cement,  Underdralning. — (Same  as  for  iron  slag  block  pave- 
ment.) 

Asphalt  Block  Pavbment. 

Blocks.— The  asphalt  blocks  shall  be  41'  to  bV  wide,  llf*  to  12i'  laag, 
and  2}'  to  3i'  deep;  and  composed  of  6  to  8  parts  asphaltic  cement,  86  to 
82  parts  crushed  trap  rock,  and  8  to  10  parts  inorganic  stone  dust.  The 
Asphaltic  (dement  shall  be  composed  of  refined  and  natural  asphalt,  or  as- 
phalttmi,  fiuxed  with  liquid  petroleum  residuum  or  refined  maltha  or  Uquid 
asphalt;  no  residuum  ot  petroleum  other  than  that  contained  in  the  flux,  to 
be  used;  the  refined  asphah  and  flux  shall  be  mixed  in  proper  and  approved 
proportions;  the  bituminous  flux  to  be  free  from  imptirities  and  brou^t  to 
a  specific  gravity  of  from  18**  to  22^  Beaume.  and  a  first  test  not  less  than  ^flff* 
P.,  and  shall  contain  no  appreciable  amount  of  light  oils,  or  matter  volatile 
under  260''  P.;  the  distillate  of  the  petroleum  oil,  if  used  at  400°  F.  for  30 
hours,  shall  not  exceed  10%.  The  Crushed  Trap  Rock  shall  not  exceed  i"; 
the  size  to  be  nearly  cubical  as  possible,  and  graded  from  maxim  am  siae  to 
dust,  so  as  to  give  the  mineral  aggregate  with  a  minimxim  percentage  of 
voids.  The  Inorganic  Dust  shall  be  pulverized  stone,  free  from  loam,  clay 
or  other  earthy  material ;  no  weathered  rock  or  dust  from  same  to  be  used. 
Blocks  when  laid  shall  have  a  specific  gravity  of  not  less  than  2.45,  and  when 
dried  for  1  day  at  a  temperature  of  150**  P.,  and  then  immersed  in  water 
7  days,  they  shall  not  absorb  more  than  1  %  water.  Laying. — On  the  concrete 
surface,  after  same  has  been  swept  and  wetted,  spread  a  laver  of  cement 
mortar  (composed  of  1  part  slow-setting  Portland  cement  and  4  parts  clean 
^arp  sand,  tree  from  gravel  over  \'  diameter)  to  such  thickness  that  when 
struck  to  a  surface  3^  below  and  parallel  to  the  grade  of  completed  pavement 
its  depth  ^all  be  nowhere  less  than  k"'*  the  spreading  and  surfacing  to  be  as 
follows:  On  the  suirface  of  the  concrete,  set  strips  of  wood  4'  wide  by  \' 
thick,  or  strips  of  steel  4^^  by  k",  and  of  greatest  convenient  length;  tnese 
strips  to  be  set  parallel  and  about  8  or  10  ft.  apart,  running  from  curb  to 
curb,  and  imbedded  in  mortar  throughout  their  length  so  top  surface  shall 
be  3*  below  and  parallel  to  grade  of  finished  pavement;  the  space  between 
two  strips  having  been  filled  with  mortar,  an  even  sxuface  shall  be  stnurk  by 
using  an  ironshod  straight-edge  on  the  strips  as  a  guide,  and  as  soon  as  ^^ 
bed  has  been  struck,  the  strip  which  would  interfere  with  laying  the  block 
shall  be  removed  and  its  place  filled  with  mortar  with  a  trowel.  On  this 
mortar  surface,  the  blocks  are  to  be  laid,  in  courses  at  right  angle  to  line  of 
street  (ordinarily),  each  course  to  be  of  uniform  width  and  depth,  laid  to 
proper  crown  and  grade,  with  close  joints,  and  end  joints  broken  by  a  lap 
of  at  least  4'.  The  stirface  shall  present  no  greater  variation  than  \'  between 
adjoining  blocks.  Blocks  fractured  or  broken  shall  be  replaced.  Sand  Jolnto 
and  Covering. — ^When  laid,  the  blocks  shall  be  covered  with  clean,  fine  sand. 


Pig  4. — Curb  on  Concrete  Fouodation. 
entirely  free  from  loam  or  earthy  matter,  perfectly  dry  and  screened  through 
5  **^**ulr*^*^  "°^  ^^^  than  20  meshes  per  lin.  in. ;  the  san'd  to  be  swept  and 
Dnished  into  the  joints  and  left  on  the  surface  until  such  time  when  the  pave- 
ment shall  be  swept  clean  for  final  inspectkm,  and  defects  remedied. 


ASPHALT  BLOCK.    STREET  CROWNS,    BRICK, 


1128 


RICHMOND  (IND.)  STREET  CROWNINa 

(H.  L.  Weber,  City  Engineer.) 


Crowning  is  parabolic:  ^  ""  -nT*.  fh= 


iJh^jH, 


Uvtf  of  Crown 


rowrt  ;i 


-  b ->fcf- c *k d J^ 

Half  Width  of  Street — •>j^ 


Fig.  5.— Diff .  between 

e 

andH 

- 

diff.  in 

elev.  bet.  curb  and  crown  levels. 

Width 

of 

a 

h 

c 

■d 

G 

g 

H 

/4 

Ai 

Street. 
Ft. 

Ft.   Ins. 

Ft.     Ins. 

Ft.  Ins. 

Ft.  Ins. 

Ins. 

Ins 

Ins. 

Ft. 

Ins. 

Ft. 

Ins. 

20 

2    4 

2    6 

2     6^ 

21 

.088 

1 

.021 

\ 

24 

2    4 

8    2 

3    2 

4. 

8 

.112 

^A 

.026 

A 

30 

2    4 

4    2 

4    2 

4 

.146 

If 

.036 

% 

30 

2    4 

4    2 

4    2 

2J 

.083 

1 

.021 

36 

2    4 

6    2 

6     2 

5 

.188 

2 

.047 

1  r 

40 

2    4 

5  10 

6  10 

5   11 

6 

.224 

2 

.062 

•45 

2     4) 

(6    9) 

7     6 

iiii 

(6) 

.288 

3fir 

.073 

t46 
^45 

(2     4) 
2     3 

7     6 
6     9 

.222 
.167 

2 

1 

.066 
.039 

IE 

48 

2     4 

7    2i 

7     2* 

7 

.260 

3i 

.062 

*  Crowning  is  calculated  for  H  »»  7|'  at  curb  line;  and  level  of  crown  is 
1 1*  above  level  of  curb. 

t  Half  width  of  street  to  be  used  on  side  next  to  stone  curb.  Crowning 
s  calculated  for  if  —  6*  at  curb  line;  and  crown  is  level  with  curb. 

/  Half  width  of  street  to  be  used  on  side  next  to  cement  curb;  and 
trown  is  level  with  curb. 


SYRACUSE  (N.  Y.)  PAVEMENT  SPECIFICATIONS. 

(H.  C.  Allen,  City  Engineer.) 
Genbral. 
Excavatioo. — Includes  earth,  rock  or  other  material  necessary  to  be 
txnovcd  from  work,  to  depth  required  to  reach  sub-grade,  and  work  con- 
noted vrith  adjusting  street  intersections  and  grading  slopes  back  of  curb 
^.  ^Excavations  below  sub-grade  shall  be  made  up  with  cement  concrete. 
xrplus  material  shall  be  deposited  within  an  average  distance  of  2000  ft.,  or 
;  cuaposed  of  by  contractor.  Embankment.— Shall  start  from  a  well-prepared 
lac,  mellowed  or  stepped  on  sloping  grotmd,  and  be  carried  up  in  horizontal 
ircrs  not  over  4'  thick,  each  layer  carefully  rammed  or  rolled,  and  well 
■.tered.  Rolling  and  Ramming. — After  the  sub-grade  has  been  brought  to 
es  prescribed,  it  shall  be  roll^  with  steam  roller  of  not  less  than  6  tons, 
til  surface  is  firm  and  compact.  Portions  inaccessible  to  roller  shall  be 
-Timed,  and  all  depressions,  defects,  etc.,  made  by  the  contractor,  and 
^in  rolled  and  rammed. 

ViTRiriBD  Brick  Pavbubnt. 
Concrete  Foandation. — Upon  the  sub-grade  thus  prepared,  lay  a  bed  of 
rtlAnd  cement  concrete  6*  deep,  of  1  part  cement,  8  parts  sand,  6  parts 
^Icen  stone.  Use  best  quality  of  Portland  cement;  sand  to  be  clean,  coarse 
1  sbarp.  fixse  from  foreign  matter;  broken  stone  to  consist  of  hard  durable 
ne,  varying  in  size  from  2i^  to  i'  in  diameter,  and  free  from  dust  or  dirt. 
^Iifoo. — Upon  the  concrete  foundation,  thoroughly  set  and  dry,  carefully 
r^sudi  i^  layer  of  clean,  coarse,  sharp  sand,  or  fine  screened  gravel,  free  from 
^,  dirt  or  vegetable  matter;  leaving  surface  true  and  even  and  parallel 
^raide.     Paving  Bricks.— Shall  be  made  and  burned  especially  for  street 


1 1 24  W.—HIGHWA  YS, 

paving  purposes,  and  shall  stand  all  reasonable  tests  as  to  durability  and 
ntness.  to  which  paving  material  is  usually  subjected;  the  material  to  be 
burned  in  down-draught  kilns  or  furnaces.  Bricks  to  be  square  and  straight, 
with  sharp  or  slightly  beveled  edges,  free  from  cracks  or  other  defects,  and 
of  uniform  size  and  pattern,  and  approved  quality,  equal  to  approved  sam- 

Sles;  specific  gravity  not  less  than  2.  Siae  mav  be:  l^igth  7K  to  8f*.  width 
i'  to  Zi",  depth  3r  to  4*.  The  absorption  of  water  by  any  one  brick  to  be 
not  greater  than  3% ;  average  absorption  of  all  bricks  tested  not  to  exceed 
2%  of  their  dry  weight;  tests  to  be  made  on  either  abraded  or  broken  bricks 
by  drying  them  for  12  hours  in  an  oven  and  then  soaking  them  12  hours  id 
water.  At  least  three  bricks  shall  be  used  for  this  test.  The  bricks  shall  also 
be  tested  in  the  standard  rattler*  and  by  the  method  of  the  National  Bric^ 
Manf .  Assn.  and  Am .  Soc.  of  Municipal  Improvements.  Sain|>le  Bricks. — Three 
or  more  bricks  of  the  kind  or  qiiality  to  be  used  on  the  paving  shall  be  fur- 
nished with  each  proposal ;  the  bricks  to  be  labeled  with  bidder's  and  maker's 
names  and  addresses.  Manner  of  Laying. — Upon  the  cushion,  the  pavement 
to  be  constructed  with  a  single  layer  of  bricks,  laid  on  edge,  end  to  end,  in 
courses  at  right  angles  with  the  curb  line,  except  at  street  intersections, 
where  courses  are  to  be  placed  at  such  angles  as  directed.  Bricks  to  be  set 
in  courses  across  the  street,  which  must  be  kept  true  and  parallel,  with  the 
body  of  the  bricks  close  together,  sides  and  ends  touching,  and  breaking 
joints  at  least  3*  with  bricks  in  adjoining  courses;  they  are  to  be  set  perpen- 
dicular to  grade  of  street,  and  to  a  height  of  from  i'  to  f  (ordinarily)  above 
the  true  |(rade  and  crown  of  street  when  finished,  to  provide  for  settlement 
in  poundmg.  Whole  bricks  to  be  used  except  in  startmg  and  closing  courses 
at  curbs,  catch-basins  and  street  structures,  when  not  less  than  half  brides 
may  be  used  in  breaking  Joints,  which  shall  be  tight  and  close  at  ends. 
Ramming  and  Tamping. — ^The  paving  when  laid,  and  either  before  or  after 
the  filling  of  the  joints  and  top  dressing  is  put  on,  as  may  be  directed,  shall 
be  thoroughly  rammed  not  less  than  three  times  with  a  paver's  rammer  of 
90-lb.  weight;  the  blows  of  the  rammer  must  not  be  made  directly  on  the 
bricks,  but  upon  a  2*  plank  not  less  than  10  ft.  long  and  12*  wide,  which  will 
be  laid  upon  the  surface  of  the  pavement,  which  must  conform  to  true  grade 
and  crown  of  street.  Qrout,  composed  of  equal  parts  Portland  cement  and 
sand,  with  proper  amoimt  of  water,  to  be  poured  upon  the  pavement  and 
swept  to  and  fro  until  every  joint  is  filled  flush  with  the  surface  of  the  pave- 
ment, and  continued  until  joints  are  entirely  filled.  Wet  sand  then  to  be 
spread  over  the  entire  pavement  k"  thick,  and  kept  wet  until  ordered  r^ 
moved. 

Sandstonb  Block  Pavbmbnt. 
Concrete  Foundation. — (Same  as  for  vitrified  brick  pavement.)  CuhkHi. 
— Upon  the  concrete  foundation,  thoroughly  set  hard,  carefully  spread  2* 
layer  of  clean,  coarse  sand,  free  from  loam,  dut  or  vegetable  matter:  leaving 
surface  true  and  even  and  parallel  to  grade.  Sandstone  Blocks. — Shall  be  of 
best  quality  of  Medina  or  Potsdam  sandstone,  not  less  than  3*  nor  more  thaa 
fl*  thick,  not  less  than  6*  nor  more  than  7*  deep,  and  from  7*  to  12*  kmg: 
must  be  sufficiently  dressed  to  present  rectangular  faces  with  straight  edgc^ 
on  top,  bottom  and  sides,  and  all  blocks  whose  faces  vaiy  more  than  Y  froze 
the  rectangular  shape  will  be  rejected.  The  sides  and  ends  of  the  bloda 
must  be  so  dressed  that  they  will  make  joints  not  to  exceed  4*  in  width.  If 
necessary  to  obtain  a  satisfactory  surface,  the  top  surf  ace  of  the  blocks  to 
be  cut  or  "axed"  off  smooth,  sides  and  ends  to  receive  similar  treatmoit 
when  necessary  to  secure  the  Y  joint.  The  stones  to  be  set  tight  together, 
perpendicular  to  grade,  so  as  to  break  joints  at  least  2*,  in  uniform  rows 
across  the  street  at  right  angles  to  line  of  curb,  except  at  street  intcrsectkos 
and  other  places  as  may  be  directed.  When  laid,  the  blocks  to  be  carefully 
rammed  as  may  be  directed,  with  a  paver's  rammer,  no  iron  bein^  allowed  on 
its  lower  surface  to  come  in  contact  with  the  pavement,  which  is  to  be  sur- 
faced by  using  a  long  straight-edge;  shall  conform  to  established  grade  az*d 
crown.  Qrout  Filling. — Pour  into  joints  a  Portland- cement  grout  composed 
of  2  parts  clean,  sharp  sand  to  1  part  Portland  cement,  of  approved  quality, 
together  with  enough  water  to  make  proper  grout,  whidi  will  be  poured  upon 
the  pi^ement  and  swept  to  and  fro  until  every  joint  is  filled  fiuJsh  with  sur- 
Mce  of  pavement,  operation  to  be  continued  imtil  joints  are  entirely  filled. 
Wet  sand  then  to  be  spread  over  entire  pavement  1*  thidc,  and  kept  wet  imiil 
ordered  removed. 

*  See  page  507.  Digitized  by  VjOOQIC 


PA  VEMENT— SANDSTONE  BLOCK,  ASPHA LT.         1 1 25 

Asphalt  Shbbt  Favbubnt. 

Upon  the  concrete  fotmdation,  thoroughly  set  and  hard,  shall  be  laid 
the  wearing  surface,  which  is  divided  into  two  classes  of  standard  gnule 
sheet  asphalt:  Refined  Asphalt  and  Rock  Asphalt.  It  is  intended  to  admit 
the  use  of  any  asphalt  of  reputation  which  can  be  made  into  a  suitable  paving 

fined  asphalt  (an 
or  organic  matter 
mt;  (3)  sand  and 
[ties  required  arc: 
chemically  stable 
e  the  asphalt  and 
it  volatilize  more 
nts  shall  be  taken 
refined  asphalt  is 
t.  to  be  tested  as 
water;  must  not 
F;  and  must  not 
'  hours  at  350**  P. 

^, -         --  Jitter  insoluble  in 

carbon  bi-sulphide,  and  must  not  show  more  than  15%  of  fixed  carbon,  and 
must  not  contain  more  than  3%  of  paraffine  scale.  The  test  for  consistency 
of  penetration  of  the  asphaltic  cement  shall  be  the  distance  expressed  in  'Aoo 
3f  a  centimeter  that  a  No.  2  needle  will  penetrate  into  it  at  25**  C.  (77*  F.) 
under  a  weight  of  100  grams  in  5  seconds  of  time,  the  needle  to  penetrate 
iirect  without  friction.  Sand. — Sand  used  for  body  of  wearing  surface  shall 
je  clean  and  sharp  and  composed  of  grains  not  easily  crushed.  Shall  be 
graded  in  size  of  grains  to  reduce  voids  to  a  minimum,  to  secure  which,  a 
jtiantity  of  powdered  carbonate  of  lime,  from  5  to  15%,  shall  be  added.  The 
and  grains  to  be  graded  in  size  about  as  follows:  Retained  on  10  mesh  per 
ineal  inch,  3% ;  on  20  mesh,  5% ;  40  mesh  25% :  60  mesh  25% ;  80  mesh  1 2% ; 
00  mesh  18%;  passed  100  mesh,  12%;  total  100%.  Mixing. — ^The wearing 
urface  of  gradea  aggregate  and  sufficient  asphaltic  cement  to  fill  the  voids 
rben  laid  shall  contain  no  trace  of  coal-tar,  water,  appreciable  amount  of 
ght  oils,  no  matter  volatile  at  a  temperature  of  250**  F.  It  shall  yield,  when 
ictracted  with  bisulphide  of  carbon  and  after  evaporation  of  the  solvent,  not 
S3  than  9^%  nor  more  than  13%  of  bitumen,  and  at  least  68%  of  the  ex- 
sucted  bitumen  shall  be  soluble  in  petroleum  naphtha.  The  sand  and  as- 
laltic  cement  to  be  heated  separately  to  about  300**  P.  The  pulverized 
trbonate  of  lime,  while  cold,  will  be  mixed  with  the  hot  sand  in  the  required 
oportion  and  then  mixed  with  the  asphaltic  cement  at  the  required  tem- 
rattire,  and  in  proper  proportion,  in  a  suitable  apparatus,  so  as  to  effect  a 
orou£rhl>r  homogeneous  mixture.  Sand  boxes  and  tar  and  asphalt  gauges 
jl  t>c  weighed  up  daily.  Laying. — Pavement  mixture  thus  prepared  will 
la.id  on  the  foundation  (same  as  for  vitrified  brick  pavement)  in  two  coats: 
le  first,  or  cushion  coat,  will  contain  2  to  4%  more  asphaltic  cement  than  is 
ixxircd  for  the  surface  mixture,  and  laid  so  as  to  give  a  thickness  of  J*  after 
xi^  consolidated  by  rollers.  The  second,  or  surface  coat,  prepared  as 
[uircd,  to  be  laid  on  the  cushion  coat;  it  will  be  brought  to  the  ground  in 
•ts  at  a  temperature  not  less  than  250**  nor  more  than  300**  P..  and  if  the 
ipcTSkture  oi  the  air  is  less  than  50**  the  contractor  must  provide  canvas 
ers  for  \ise  in  transit;  the  mixture  to  be  spread  with  hot  iron  rakes  to 
form  errade,  and  to  have  thickness  of  2*  after  ultimate  compression.  The 
faoe  to  be  compressed  by  a  hand  roller,  after  which  a  small  amount  of 
Ira^ulic  cement  will  be  swept  over  it,  then  thoroughly  compressed  with  a 
vry  steam  roller,  continued  as  long  as  it  makes  an  impression  on  the  sur- 
:,  at  least  5  hours  for  each  1000  sq.  yds.  of  suirface.  Qutters.— Strip  of 
etxient  12*'  wide  next  to  ciu-b,  to  be  coated  with  hot  pure  asphalt,  and 
o^lied  with  hot  smoothing  irons,  prioe  to  be  included  m  price  for  pave* 

j^ock  Asphalt  Pavement. — Shall  consist  of  one  or  more  natural  bituminous 
srtOTies  or  bituminous  sandstone  rocks.  If  necessary,  they  are  to  be  mixed 
tla.er  or  a  quantity  of  natural  asphalt  added  to  secure  proper  proportion 
itxxmcn,  between  9  and  10%.  A  bituminous  limestone  shall  be  coarse- 
led,  fits  nearly  as  possible  a  pure  carbonate  thoroughly  and  evenly  im- 
n,a.te<i  with  asphalt,  with  no  more  impurities  than  the  standard  German 
aJipliAlt  of  Limmer  or  Vorwohle.  Laying  Pavement. — (1)  The  lumps  of 
to  be  crushed  and  pulverized  and  the  powder  passed  through  a  fine 


1126  m.—HIGHWAYS. 

sieve.  (2)  This  powder  to  be  heated  in  a  suitable  apparatus  to  a  tempeiattire 
of  about  200^  P.,  and  brought  to  the  ground  at  such  temperature,  m  outs, 
and  spread  on  the  concrete  foundation  (same  as  for  vitrified  brick  pavement) 
previously  prepared.  (3)  Then  skillfully  compressed  by  heated  hand  rollers 
and  rammers  until  it  shall  have  required  thickness  of  2^.  (A)  Surface  thra 
made  even  by  heated  smoothers.  (5)  Finally,  after  completion,  to  be  roHel 
with  a  heavy  roller  at  least  5  hours  for  each  1000  sq.  yds.,  a  small  amount  c^ 
hydratdic  cement  to  be  swept  over  the  surface  during  rolling. 

Crbosotbd  Wood  Block  Pavement. 
Concrete  Foundation. — (Same  as  for  vitrified  brick  pavement.)  Mortar  Bed. 
— On  the  foundation,  spread  a  i*  bed  of  Portland  cement  mortar.  1  p*rt 
cement  and  2  parts  sand,  surfaced  true  and  smooth  and  parallel  to  fini^ied 
grade  and  cross-section.  Blocks. — Long-leaf  yellow  pine,  50%  heart,  treated 
as  described  below;  blocks  to  be  of  sound  timber,  free  from  bark,  sap  wood. 
loose  or  rotten  knots,  etc.;  no  second -growth  timber  to  be  allowed.  Bl^cs 
not  less  than  3*  wide,  6'  to  9*^  long  and  4'  deep,  tmiform  in  depth  and  thick- 
ness; to  be  treated  throughout  with  an  antiseptic  and  water-proofing  mixture 
as  follows.  Treatment  of  Blocks. — Mixture  shall  contain  60%  of  dead  oil  oi 
tar,  known  as  creosote  oil;  its  specific  gravity  shall  not  be  less  than  1.12  at 
68°  P.,  it  shall  lose  not  more  than  40%  when  distilled  in  a  flask  or  retort  for 
30  minutes  up  to  600**  P.  The  distillate  to  contain  4%  tar  acids  and  at  least 
12%  naphthalin.  Specific  gravity  of  residue  obtained  by  distilling  the  mix- 
ttire  up  to  600°  P.  must  be  at  least  1.15.  After  treatment,  specific  gravity  of 
block  shall  be  greater  than  that  of  water;  and  shall  show  such  waterproof 
qualities  that,  after  being  dried  in  an  oven  at  a  temperature  of  1 00*  for  24  hrs , 
weighed  and  then  immersed  in  water  for  24  hours,  the  gain  in  weight  not  to 
be  greater  than  3%.  Blocks  to  be  treated  as  follows:  Blocks  to  oe  placed 
in  an  air-tight  cylmder,  and  when  doors  are  closed  the  dry  heat  is  to  be  raised 
to  215°  P.  without  pressure,  for  1  hour,  to  get  rid  of  moisture.  Then  heat 
to  be  increased,  pressure  to  be  applied  and  both  are  to  be  raised  gradually  to 
avoid  injury  to  fiber,  for  2  hours,  imtil  heat  has  reached  about  285°  and 
pressure  about  90  lbs.,  and  both  are  to  be  held  there  for  1  hour.  The  heat  is 
then  to  be  shut  off  and  the  tanks  allowed  to  cool  gradvially  for  1  hotir;  then 
heat  reduced  to  250°  and  pressxu«  to  about  40  lbs.  Pressure  is  then  blown 
ofi  and  heat  still  further  reduced.  Vacuimi  is  then  applied  until  about  26*  is 
raised,  and  whUe  under  vacuum  the  creosote  mixture  (which  shall  contain 
no  tar,  petroleiun,  or  petroleimi  residue)  is  to  be  run  into  the  cylinders  at  a 
temperature  of  175°  to  200°,  and  hydraulic  pressure  is  to  be  applied,  reachicf 
200  lbs.  per  sq.  in.,  and  kept  at  this  point  until  20  lbs.  of  the  mixttire  per  cu. 
ft.  has  been  absorDed.  The  liquid  is  then  run  off,  and  the  wood  placed  in 
another  cylinder  and  milk  of  lime  at  a  temperature  of  about  150°  is  run  in  ar.d 
hydratUic  pressiu^e  of  about  200  lbs.  applied  for  from  J  to  1  hour.  The  anti- 
septic and  waterproof  mixture  shall  not  contain  more  than  2%  water  at  any 
time.  The  quantity  specified  for  each  tar  acid,  naphthalin  and  residue  is  the 
minimum  for  each.  Laying  Blocks. — Blocks  to  be  set  immediately  ujxm  the 
cement  mortar  bed,  before  it  has  set,  and  driven  together  as  closely  as  pos- 
sible. Pavement  to  be  constructed  with  a  single  layer  of  the  blocks  laid  oc 
edge,  with  grain  vertical,  end  to  end  in  courses  at  right  angle  with  the  cuit> 
line  except  at  street  intersections  where  the  courses  are  to  be  placed  as  di- 
rected. Blocks  to  be  set  in  coxu«es  across  the  street;  must  be  kept  true  ar«i 
parallel,  sides  and  ends  touching,  and  breaking  joints  at  least  8*  with  bkxks 
m  adjoining  courses.  Only  whole  blocks  to  be  used  except  in  starting  and 
closing  courses.  Expansion  Joints  of  bituminotis  cement  to  be  placed  at  ctcrt 
lines  and  across  the  street  at  intervals  of  50  ft.  Gutter  joints  to  be  1'  acd 
cross  joints  i".  To  make  these,  a  plank  shall  be  inserted  and  the  blocks  laid 
against  it;  the  plank  then  remov^,  and  the  crack  thus  left  filled  with  bitn- 
minous  cement  which  shall  have  a  temperattire  of  at  least  300^  P.  Pavemoit 
then  to  be  rolled  with  a  hand  roller  tintil  tops  of  blocks  are  even.  BitnmfaMWi 
Cement  used  shall  not  flow  at  120°  P.,  and  shall  not  become  brittle  at  0°  P.; 
^all  be  proof  against  street  liquids,  and  pliable  rather  than  r^skl.  FWaf 
Joints. — After  pavement  is  rolled,  bittuninous  cement  heated  to  at  least  ^0<^ 
P.  shall  be  poured  along,  filling  each  crack,  and  only  when  blocks  are  diy. 

BiTULITHIC  PaVBIIBNT. 

Poundation.— Bittmiinous,  or  concrete.  Bitimiiooiis  FoandstkHi.— On  tbi 

JU^^^wf Nation,  crushed  hard  limestone  which  will  pass  a  SJ'  ring,  to  be 
spread  to  a  depth  of  6*.  and  compressed  with  heavy  steam  road  soUer.    Ob 


CREOSOTED  WOOD  BUXK  P.    BITUUTHIC  P.  1127 

this,  after  rolUnff,  spread  a  heavy  coating  of  Puritan  brand  bittuninous 
cement,  to  make  foundation  unite  with  bituhtbic  wearinssurface:  One  gallon 
of  the  cement  to  each  sq.  yd.  of  fotmdation.  Coocreta  Fouiidatioo. — (Same 
as  for  vitrified  brick  pavement.)  Wearing  Surface. — On  the  foundation,  lay 
the  wearing  surface,  composed  of  carefully  selected,  sound,  hard,  crushed  trap 
or  syenite  rock,  mixed  with  bitiunen.  as  follows:  After  heating  stone  in  rotary 
mechanical  mixer  to  temperature  of  about  250^  P.,  it  is  elevated  and  passed 
through  a  rotary  screen,  having  sections  with  various  size  openings;  differ- 
ence in  width  of  openings  in  successive  sections  not  to  exceed  i"  in  sections 
with  openin^^s  less  than  §',  and  not  to  exceed  i"  in  sections  with  openings 
more  than  \  .  The  several  sizes  of  stone  thus  separated  by  the  screen  sections 
shall  pass  into  a  bin  with  sections  corresponding  to  screen  sections.  From 
these,  the  stone  is  drawn  into  a  weigh  box,  resting  on  a  scale  having  seven 
beams;  the  stone  to  be  weighed,  using  the  proportions  previously  determined 
by  laboratory  tests  to  give  the  best  results;  that  is,  the  most  dense  mixttire 
Dt  mineral  aggregate,  and  one  having  inherent  stability.  If  the  crushed 
stone  in  the  wearing  sxirface  does  not  provide  the  best  proportions  of  fine- 
grained particles,  such  deficiency  must  be  supplied  by  the  use  of  not  to  ex- 
:eed  25%  hydraulic  cement,  pulverized  stone,  or  very  fine  sand.  From  the 
xreigh-box  each  batch  of  mineral  aggregate,  of  different  sizes  weighed  as 
ibove,  shall  pass  into  a  "twin  pug.'  or  other  approved  form  of  mixer.  In 
:hi8  mixer  shall  be  added  a  sufficient  quantity  of  Puritan  brand  bituminous 
Kraterproof  cement,  to  coat  all  the  particles  of  stone  and  to  fill  all  voids  in 
he  mixture.  Before  mixing,  the  bituminous  cement  shall  be  heated  to 
>etween  200^  and  250°  P.,  and  the  amotmt  in  each  batch  shall  be  weighed 
tnd  used  in  such  proportions  as  have  been  determined.  Mixing  to  continue 
mtil  the  combination  is  a  imiform  bituminous  concrete.  In  this  condition  it 
s  to  be  hauled  to  the  street,  and  spread  on  the  prepared  foundation  to  such 
I  depth  that,  after  compression  with  a  steam  road  roller,  it  shall  have  a  thick- 
less  of  2r.  The  proportioning  shall  be  such  that  the  compressed  mixture 
hall  have  the  density  of  solid  stone,  as  nearly  as  practici&ble.  Surface  Finish. — 
Lfter  rolling  the  wearing  surface,  spread  over  it,  while  it  is  still  warm,  a  thin 
oating  of  qtiick-drying  bituminous  flush  coat  composition,  by  means  of  a 
uitabte  flush  coat  spreading  machine  provided  with  a  flexible  spreading 
and  and  adjustable  device  for  regulating  the  quantity  and  uniformity  of 
le  composition.  On  grades  of  over  4%  a  mineral  flush  coat  may  be  used  in 
lace  of  the  liquid  flush  coat.  While  the  flush  coat  is  still  warm,  spread  over 
.  in  at  least  two  coats,  fine  particles  of  hot  crushed  stone,  in  sufficient  quan- 
ty  to  cover  the  surface  of  the  pavement;  these  stone  chips  to  be  spread  by 
leans  of  a  suitable  stone  spreading  machine,  so  designed  as  to  provide  a 
^rage  receptacle  of  at  least  6  cu.  ft.  capacity  and  to  rapidly  and  imiformly 
>ver  the  stirface  of  the  pavement  properly.  The  hot  stone  chips  to  imme- 
iately  be  rolled  into  the  surface  tmtil  it  has  become  cool.  Patents. — Agree- 
icnt  of  Warren  Bros.  Co.,  on  file  with  City  Engineer,  to  license  all  contractors 
•siring  to  bid  for  the  work  to  lay  bitulithic  pavement  in  accordance  with 
i  patents. 

TORONTO  (ONT.)  PAVEMENT  SPECIFICATIONS. 

(C.  H.  Rust,  City  Engineer.) 
A. — Grading. 
Excavation. — Levels  and  cross-sections  may  be  varied  to  conform  to  sills 
buildings,  grades  of  intersecting  streets,  lanes,  carriage  ways,  etc.  Trenches, 
c. — ^Trenches  or  excavations  that  have  been  made  for  or  in  connection 
th  sewers,  private  drains,  gas  or  water  pipes,  telephone  or  electric  wires, 
pes  or  conduits,  street  or  other  railway  works,  or  any  other  lawful  purpose, 
d  which  are  not  thoroughly  settled,  shall  be  opened  out  and  re-filled  with 
ivcl,  well  pounded,  in  layers  of  not  over  4*;  no  extra  allowance  to  be  made 
contractor.  Defective  Places. — Soft,  boggy,  wet,  muddy  or  defective  places 
ist  be  wholly  removed  and  filled  with  gravel,  as  in  above  clause,  with  no 
tret  allowance.  Bonl<ters.  Trees,  Etc. — Boulders,  stones,  rocks,  stumps,  trees, 
>ts.  etc.,  to  be  removea  when  directed,  without  extra  pay.  Excavations 
low  Qnule. — ^Where  excavation  is  made  below  proper  level  of  sub-grade,  it 
ill  be  made  up  with  concrete  where  foundation  is  concrete,  or  with  gravel 
all  other  cases,  without  extra  pay.  Rollins,  Etc. — Sub-grade  to  be  rolled 
;h  steam  roller  ^ei^hing  not  less  than  . . .  tons ;  to  be  omitted  when  engineer 
ill  consent  in  writmg.  Portions  inaccessible  to  roller  shall  be  rammed. 
;tlexnents,  etc..  to  be  repaired,  and  again  rolled  or  rammed.     Engineer 


1128  Vi,— HIGHWAYS. 

reserves  privilege  of  testing  sub-mde  with  City  RoHer.  Slopes. — In  cuttings, 
excavation  to  be  made  for  a  stimcient  distance  above  ana  behind  curbing, 
to  form  a  slope  of  2  horizontal  to  1  vertical.  OH  Macadam. — ^Where  a  ma- 
cadam or  broken  stone  roadway  has  to  be  excavated,  the  old  material  mint 
be  picked  out  and  screened  separately,  and  the  stone  delivered  by  contractor 
where  directed,  within  1  mile,  without  pay;  extra  haul  at  \c.  per  cu.  yd.  per 
100  ft. 

B. — Cbdar  Block  Pavbmbnt. 
Character  of  Pavement. — ^When  gravel;  sand  or  broken  stone  is  used  for 
foundation.  it  must  be  watered,  rolled,  rarhpied  and  consolidated,  untfl 

Suite  hard  and  compact,  using  a  12}-ton  roller,  unless  a  lifter  one  is  allowed, 
locks.— Shall  be  of  first-growth,  sound  white  cedar,  stripped  of  bark.  No 
pin  hole  more  than  y  diameter,  and  not  more  than  3  pin  holes  allowed  on 
wearing  surface  of  block.  Blocks  from  5'  to  11'  in  diameter,  and  ^aU  not 
show  more  than  y  of  sap  wood  at  anv  part  of  outside  edge.  Laying. — After 
blocks  are  laid,  they  shall  be  fammed  with  a  pounder  of  80  lbs.  or  more,  12* 
diameter  and  flat  on  bottom.  The  whole  sxmace  then  rolled  with  a  roUer 
weighing  at  least  6  tons.  When  pavement  has  been  brought  to  surface,  it 
shall  (unless  other  filling  is  called  for)  be  covered  with  a  sufficient  quantity 
of  gravel  to  fill  all  joints,  being  worked  in  with  suitable  brooms.  Surphs 
material,  if  any,  then  to  be  swept  off.  and  pavement  to  be  rammed  as  before. 
To  be  repeated  if  necessary.  Finally,  pavement  to  be  covered  with  f  layo" 
of  good  clean  gravel.  Board  Bed. — Shall  be  laid  upon  the  fotmdation  bed  if 
required.  Shall  be  pine.  9^  to  12*  wide,  perfectly  sound,  etc.;  and  thor- 
oughly swabbed  on  both  sides  and  ends  with  aporoved  composition,  or 
dipped  in  same,  or  other  preservative  process.  Wnere  double  boards  are 
used,  the  lengthwise  boards  shall  be  12  and  16  ft.  in  length,  respectively, 
laid  so  as  to  break  joint.  Concrete  Bed. — When  a  concrete  bed  is  required  it 
shall  be  laid  as  specified  tmder  "C. — Concrete,"  below.  After  the  bed  has 
set  hard,  spread  a  layer  of  clean,  sharp  sand  so  that  it  will  be  \'  thick  after 
the  blocks  are  laid  upon  it  and  rammed.  Qrouting . — ^When  grout  fining  is 
required  between  the  blocking  it  shall  be  composed  of  1  part  Portland  cem.. 
3  parts  coarse,  sharp,  clean  sand,  thoroughly  mixed  and  flooded,  and  swept 
into  all  joints;  repeating  same  until  joints  are  full  and  flush  with  surface. 
Stuiace  then  to  be  covered  with  at  least  %"  layer  of  approved  gravel.  Tar 
Filling. — When  tar  composition  is  required  for  filling,  it  shall  be  composed  of 
1  part  coal-tar  to  2  parts  pitch,  boiled  and  freed  from  moisture,  and  applied 
at  a  temperature  of  250  to  275'*  P.,  filling  all  joints.  A  paving  pitch,  when 
approveo.  may  be  used  instead,  and  applied  similarly,  or  as  directed.  Clean 
gravel,  Y  to  Y,  dried  and  heated,  must  be  used  with  above  composition; 
the  gravel  to  be  swept  into  the  interstices  hot,  and  the  composition  appHed 
at  once,  completely  tilling  joints  and  flushing  to  surface.  Composition  and 
Qravel. — With  board  foundation,  use  not  less  than  2  gallons  (^imperial)  of 
composition  per  sq.  yd.  of  pavement;  without  board  fotmdation,  use  not 
less  than  3  gallons,  and  as  much  more  as  needed  to  fill  flush  to  top  of  pave- 
ment. After  ramming,  pavement  to  be  swept  clean,  and  covered  wita  hot 
composition,  upon  which  shall  immediately  be  spread  heated  gravel  or 
stone  chippings,  Y  to  J*,  at  least  Y  deep. 

C. — CONCRBTB. 

Proportions.— *-Upon  the  sub-grade,  lay  a  bed  of  concrete,  ....  ins.  thidc 
composed  of  1  part  best  Portland  cement,  8  parts  clean,  sharp  sand,  7  parts 
broken  stone  or  furnace  slag;  the  proportions  may  be  varied  to  1  part 
cement  and  10  parts  of  the  sand,  broken  stone  and  slag.  Gravel  may  be 
required  instead  of  broken  stone. 

D. — ^Asphalt  Pavbmbnt. 

Kinds  of  Asphalt. — Use  best  quality  of  following  asphalt:  Trinidad. 
Bermudez,  Venezuela,  Natiiral  Rock,  California,  or  other  equally  as  good, 
and  approved.  No  coal-tar.  or  any  other  product  thereof,  or  any  other  in- 
ferior products,  will  be  accepted.  Cushion  Coat. — ^When  lii^t  asphalt  is 
specified  no  binder  or  cushion  coat  will  be  required.  When  heavy  anphalt  is 
specified  a  binder  course  1'  thick  will  be  laid  directly  on  the  concrete  founda- 
tion, but  it  will  not  be  required  where  Natural  Rock  asphalt  is  used.  This 
underlayer  to  be  rolled  and  consolidated,  while  fresh  and  hot,  with  a  steam 
roller  weighing  not  less  than  6  tons,  to  a  finished  thickness  of  1'.  No  binder 
asphalt  to  be  laid  during  wet  weather.  Should  Rock  asphalt  be  used  it 
should  be  at  least  TT  thick.    Surface  Coat.— Shall  be  ^^^i^ftl^ter  ultimaU 

compression.  Digitized 


itm^^" 


CEDAR  BLOCK,  ASPHALT,  MACADAM,  ETC.  1129 

E. — Brick  Pavbubnt. 

Foundation. — ^A  base  of  Portland  cement  concrete  4'  or  6'  in  depth. 
Cushion. — Where  no  thickness  is  shown,  the  depth  of  sand  will  be  at  least  H'. 
Paving  Bricks.— Must  not  be  less  than  2]^  by  Sr  by  4'.  Pavinf  Blocks.— 
Must  not  be  less  than  3}'  by  8i*  by  4'.  Tests  shall  be  made  for  absorption 
and  abrasion.  Laying. — (Usual  manner.)  Ramming  and  Rolling. — First  with 
80-Ib.  rammer,  then  with  6-ton  roller.  Qrout  Filling. — Composed  of  equal 
parts  best  Portland  cement  and  sand,  mixed;  water  added,  stirred  and  mi- 
mediately  used,  filling  joints  to  no  more  than  half  their  depth.  Then  thicker 
grout,  2  cement  to  1  sand,  for  balance  of  joint.  Sand  Coating. — Not  less 
than  K- 

P. — Macadau  Roadway. 

Foandation  Coursa. — Upon  the  sub-grade,  lay  a  course  of  stone,  5'  in 
thickness;  stones  to  be  laid  by  hand,  largest  sides  down,  and  in  line  at  right 
angle  to  the  curb,  and  breaking  joint  as  much  as  practicable.  The  upper 
surface  of  stones  not  to  be  less  than  CT  nor  more  than  9*  in  width,  nor  less 
than  12"  nor  more  than  16^  in  length.  The  stones  to  be  set  close  together 
and  bound  by  wedging  in  small  stones  and  filling  the  interstices  with  stone 
chipping  so  as  to  form  a  compact  bed.  Stones  projecting  above  the  surface 
must  be  broken  off,  great  care  being  used  not  to  loosen  the  foundation.  No 
wedging  is  to  be  done  within  20  ft.  of  the  work  being  laid.  'Next,  spread 
evenly  over  this  course,  clean  gravel  to  fill  all  interstices,  and  then  roll  and 
re-roll  until  thoroughly  consolidated.  Intermediate  Course. — Upon  the 
foundation,  place  a  layer  of  broken  stone,  as  granite,  trap,  or  hard  limestone, 
3f  approved  quality.  Not  more  than  5%  of  the  stone  snail  be  less  than  1 }' 
md  no  particle  of  stone  shall  be  more  than  3"  in  breadth.  After  this  course 
ias  been  evenly  spread  over  the  street  (and  raked  if  necessary)  so  as  to 
present  a  uniform  surface,  a  layer  of  coarse,  clean  sand  is  to  be  spread  upon 
t,  sufficient  to  fill  voids,  and  the  surface  then  watered  (if  necessary)  and  rolled, 
Tiore  sand  and  stone  being  applied  where  and  as  required,  and  the  rolling 
ind  watering  continued  until  an  even,  hard  and  uniform  surface  is  obtained, 
ifter  which  the  sand  is  swept  up  and  removed  from  the  surface.  Top 
^urse.— Consists  o!  broken  stone. ....  ins.  in  depth,  as  uniform  in  size  as  possi- 
ble, no  particle  to  be  more  than  2}',  and  not  more  than  6%  to  be  less  thiui  l^'. 
n  length  or  breadth.  The  svirface  shall  be  raked  evenly,  watered,  rolled, 
epaired,  brought  fully  up  to  grade,  and  then  re-rolled  tintil  firm,  compact 
nd  true.  A  sufficient  layer  of  good,  coarse,  clean  sand  is  then  spread  over 
he  surface,  rolled,  and  flooded  with  water,  to  carry  the  sand  into  all  inter- 
tices'  more  sand  to  be  added  as  rolling  and  watering  progresses,  so  as  to 
Ave  finished  thickness  of  i'  to  }'. 

'K. — C^NCRBTB  Sidewalk. 

Foundation. — ^After  the  street  has  been  graded,  a  fotmdation  shall  be 
kid,  composed  of  coarse  gravel  or  suitable  soft  coal  cinders,  to  a  depth  of  4', 
fter  being  consolidated  by  pounding  or  rolling  with  a  suitable  and  approved 
>l]er.  weighing  at  least  1  ton,  and  the  whole  broxight  to  an  even  surface. 
iTliilst  potmding,  a  small  quantity  of  water  may  be  used  through  a  sprinkler, 
directed.  Templates. — When  required,  the  contractor  must  furnish 
ooden  templates,  cut  to  exact  form  and  slope  of  the  walk,  for  use  by  the 


Fig.  6. — Cross-section. 

spectors.  Concrete  Base. — Upon  this  fotmdation,  a  layer  of  concrete.  Si' 
lickT  aball  be  laid,  composed  of  1  part  Portland  cement  (of  approved  qtial- 
y)     2  ports  of  clean,  sharp,  coarse  sand,  and  6  parts  of  approved  furnace 


1130  m.—HlGHWAYS. 

slag,  broken  stone  or  screened  gravel,  thoroughly  free  from  stone  over  2* 
diameter,  and  free  from  clay,  loam,  dirt  or  other  impurities.  The  concrete 
thus  made  shall  be  rammed  with  iron  rammers  into  one  solid  mass,  and  until 
it  has  a  straight  and  even  surface.  Divisions. — ^Bvery  6  ft.  a  cut  shall  be 
made  completely  through  the  concrete  before  it  is  set.  with  an  iron  for  that 
purpose,  not  less  than  f'  in  width.  The  opening  shall  then  be  filled  in  with 
clean,  sharp  sand.  A  clear  soace  not  less  than  P  must  be  left  between  back 
of  curbing  and  abutting  ends  of  sidewalks  to  allow  room  for  expansion, 
excepting  where  the  wa^  and  curb  are  combined.  Heavy  Surface. — On  the 
concrete  base,  before  it  has  had  time  to  set,  lay  the  wearing  suirface.  \V 
thick,  composed  of  1  part  Portland  cement.  1  part  clean,  sharp,  coarse  sa^ 
and  3  parts  crushed  granite  or  quartzite.  Light  Surface. — On  the  concrete 
base,  before  it  has  had  time  to  set,  lay  the  wearing  surface  1'  thidc,  com- 
posed  of  1  part  Portland  cement,  1  part  clean,  sharp,  coarse  sand,  and  3 
parts  of  screened  pea  gravel,  crushed  granite,  quartzite  or  smtable  hard 
limestone.    (See  Pig.  0.) 


d  by  Google 


TARS  FOR  ROAD  SURFACES.  1131 

D.— CARE  OF  ROAD  SURFACES. 

DUST  PREVENTIVES.*, 

Classipication. 
Two  classes:  Ist.  water,  salt  solutions,  certain  light  oils  and  tars,  and 
oil  and  tar  smtilsions;  2nd.  the  heavier  oils,  tars,  senu-solid  and  solid  ma- 
terials. Salt  solutions  are  valuable  because  the  dissolved  salt  has  a  con- 
siderable affinity  fOr  water  and  keeps  the  road  moist  long  after  a  stirface 
treated  with  water  alone  would  have  become  dry.  The  light  oils  and  tars, 
ind  oil  and  tar  emulsions,  leave  upon  the  road  surface  a  comparatively 
unall  amount  of  true  binding  base  aiter  the  volatile  products  have  evapor- 
ited.  The  heavy  oils  and  tars  contain  a  greater  amount  of  binding  base, 
lence  more  lasting.  The  semi-solid  and  soUd  preparations  usually  contain  a 
(till  greater  amount  of  binder,  and  also  other  materials  of  a  solid  nature, 
luch  as  rocks,  sand  or  clay.  With  some  few  exceptions,  all  the  true  binders 
ire  bitumens,  either  natural  or  artificial. 

Tars.  Thbir  Manupacturb  and  Propsrtibs. 
Coal  Tars. — Coal  is  by  far  the  most  important  source  of  tar.  (a)  Tar 
rom  Coke  Ovens  is  made  as  follows:  The  coal  is  charged  into  long  narrow 
hambers  or  retorts  of  about  4  or  5  tons  capacity  and  heated  by  means  of 
lues  set  in  the  retort  walls;  volatile  matter  held  in  the  coal  passes  out 
brough  an  opening  in  the  top  and  is  conducted  through  a  series  of  washers 
nd  scrubbers,  as  in  gas  manufacture,  to  remove  the  tar  and  ammonia; 
be  purified  gas  is  then  allowed  to  pass  into  a  holder  from  which  it  is  drawn 
5  needed  for  burning  tinder  the  retorts,  (b)  Tar  from  Gas  Plants  is  tm- 
voidable  in  the  manufacture  of  illuminating  gas;  the  bittuninous  coal  is 
laced  in  fire-clay  retorts  about  8  ft.  lon^.  Ifir  high  and  18*  wide;  6  or  3 
storts  set  together  in  a  furnace  and  formmg  a  "boich;"  a  number  of  these 
snches  built  together  is  called  a  "stack;"  the  retorts  are  heated  by  means 
:  a  coke  fire  or  by  generator  gas.  The  tar  which  collects  in  the  hydraulic 
Ain.  the  condensers,  and  the  tar  towers,  is  run  into  large  wells  where  it  is 
lowed  to  settle;  the  accompanying  ammoniacal  liquor,  being  lighter  than 
le  tar,  rises  and  is  drawn  off;  the  crude  oil  tar  which  remains  is  a  black 
scid  fluid  with  peculiar  odor,  and  with  specific  gravity  from  1.1  to  1.2.  It 
presents  about  5%  of  weight  of  coal.  The  true  tany  products  are  artifi- 
£l  bitumens;  the  natiuul  bitumens  being  fotmd  in  various  mineral  oils  and 
phalts.  The  nature  and  value  of  tar  vary  with  the  coal  used,  and  with  the 
mperature  and  other  conditions  under  which  it  is  produced.  Free  carbon, 
iving  no  binding  value,  will  prove  detrimental,  (c)  Refined  Coal  Tar  is 
itained  by  fractional  distillation  for  the  separation  of  certain  constituents 
ed  in  the  arts;  the  residue  left  in  the  still  is  Known  as  coal-tar  pitch,  and  is  a 
ick  viacotis  material  while  hot.  It  represents  the  true  binding  base  of  the 
r,  and  if  the  tar  is  produced  at  comparatively  low  temperattuv  the  residue 
composed  mainly  of  bitumens.  After  cooling  for  a  few  hours  it  is  run  out 
the  still  and  isgraded  as  soft,  medium  or  hard,  according  to  its  condi- 
n  when  cold.  The  dead  oils,  or  heavier  distillation  products,  and  of  less 
lue  than  the  other  volatile  distillates,  are  often  run  back  into  the  still 
'ore  the  pitch  is  drawn  off,  in  which  case  the  pitch  is  liquid  when  cold. 
preparing  a  tar  for  dust  prevention,  most  of  the  valuable  products  are 
aoved  by  fractionation,  and  the  least  valuable — as  some  of  the  carbolic 
1  all  the  dead  oils — are  nm  back  into  the  pitch  until  it  reaches  about  the 
isistency  of  a  heavy  crude  tar,  sometimes  adding  dead  oils  from  previous 
filiation,  if  necessary.  These  oils  give  life  to  the  tar,  and  if  percentage  of 
zh  is  not  reduced  too  low  the  mixture  has  certain  advantages  over  the 
de  tar,  and  it  is  comparatively  free  from  naphthalin  and  anthracine  and 
tains  none  of  the  volatile  oils  and  ammoniacal  liquor  found  in  the  latter. 
Dehydrated  Tar  (crude)  is  sometimes  prepared  for  dust  prevention,  the 
i  being  to  remove  all  water,  ammonium  compoimds,  and  some  of  the 
t  oils.  The  absence  of  water  makes  it  easier  to  handle  when  applied  hot, 
probably  allows  of  a  better  absorption  of  the  tar  by  the  road  surface. 
ter  in  tar  hastens  disintegration  of  the  heavy  binding  materials;  the 
•noniacal  liquor  may  saponify  some  of  the  oily  products,  mix  with  the 
er  and  wash  out.  Dehydrate  tar  may  be  prepared  by  boiling  the  crude 
erial  in  open  kettles  until  its  boiling  point  lies  between  105**  and  110°  C. 


irotft 


IHcrest  of  Bulletin  No.  34,  Office  of  Public  Roads.  U.  S,  D^tx/of  Agric. 
itHubbard.  Assistant  Chemist.  tzecTbrVifOC 


1132 


90.^HIGHWAYS. 


Water-Gas  Tar  has  been  used  to  some  extent  as  a  dust  layer  and  road 
preservative.  It  is  first  obtained  by  admitting  steam  into  a  chamber  called 
a  generator  which  contains  coke  heated  to  incandescence;  .the  water  vapor 
reacts  with  this  coke  to  form  certain  products  and  the  mixture  of  gases  is 
led  into  another  chamber  called  the  carburetor,  where  it  meets  a  spray  of 
hot  oil,  which  is  thus  volatilized  and  carried  to  another  chamber  known  as 
the  superheater,  where  most  of  the  hydrocarbons  combine  to  form  a  per- 
manent gas.  The  gas  thus  produced  is  washed  with  water  and  passed 
through  extractors  and  scrubbers  in  much  the  same  manner  as  ordinary  coal 
gas,  in  order  to  remove  the  tarry  products.  The  product  is  entirely  different 
from  ordinary  coal-tar  and  contains  a  relatively  small  amount  of  heavy 
bitumens;  the  base  is  more  or  less  thin,  and  of  poorer  binding  quality  thaa 
that  of  good  coal  tar;  it  may  be  used  to  advantage  in  certain  instances, 
being  cheap  and  easily  handled.  It  compares  quite  favorably  wiUi  the 
lighter  oils,  and  oil  ana  tar  emulsions. 

Composition  of  Tars. — ^The  following  Table  shows  some  of  the  properties 
of  crude  coal  tar,  refined  coal  tar  and  water^as  tar,  previously  described. 
The  notes  to  the  table  refer  to  the  condition  of  distillates  and  residues  when 
cold: 

Spbcific  Gravity  and  Composition  of  Tar  Products. 


Kind  of  Tar. 

Specific 
Gravity. 

III 

Total 
Light  Oils 
to  170X. 

Total 
Dead  Oils 
170«-270^. 

Resklue 
(by  differ- 
ence). 

Water-gas  tar 

Crude  coal  tar 

Refined  coal  tar . . 

1.041 
1.210 
1.177 

Percent. 
2.4 
2.0 
0.0 

Per  cent. 
a21.6 
dl7.2 
&12.8 

Per  cent. 
652.0 
#26.0 
«47.0 

Percent. 
C24.0 
/54.8 
/30.e 

a  Distillate  mostly  liquid. 
b  Distillate  all  liquid. 
c  Pitch  very  brittle. 
d  Distillate  mostly  solid. 


e  Distillate  one-half  solid. 
/  Pitch  hard  and  brittle. 
g  Distillate  one-third  solid. 


Thb  Application  op  Tars. 

Application  to  finished  road  surfaces. — The  primitive  method  in  thas 
country  is;  Road  siirface  first  thoroughly  swept  to  remove  all  dust;  hot  tar 
then  spread  on  and  thoroughly  broomed  in;  road  then,  if  possible,  closed  to 
traffic  12  hours  to  allow  tar  to  soak  in;  at  end  of  that  time,  or  sooner,  a  coat 
of  clean  sand  or  stone  chips  applied  to  absorb  excess  of  tar,  and  surface  then 
rolled  several  times  to  bring  it  to  proper  condition  ouickly.  The  tar  is 
heated  in  an  open  kettle  preferably  motmted  on  wheels  and  fitted  with  a 
portable  fire-box.  It  is  usually  brought  to  its  boiling  point — ^about  \9ff  P- 
(If  temperature  of  crude  tar  is  raised  above  190**  F.  when  heated  it  is  very 
likely  to  foam  up,  boil  over  and  catch  fire.) — ^before  being  spread  upon  the  road, 
although  a  lower  temperature  is  sometimes  sufficient;  and  if  the  kettle  is  ot 
the  above  type  the  tar  may  be  run  out  upon  the  road  by  means  of  a  hose, 
the  kettle  bemg  kept  just  in  advance  of  the  work;  two  kettles  will  alb* 
continuous  working,  one  being  charged  and  heated  while  the  other  is  in  use: 
kettles  to  hold  easily  9  barrels  or  about  450  gallons.  Application  of  tar  by 
mechanical  means  is  also  being  used,  notably  in  England. 

Use  of  tar  in  road  construction. — ^When  a  New  Road  is  under  construc- 
tion, or  an  old  road  being  resurfaced,  the  road  should  first  be  shaped  and 
consolidated  as  well  as  possible  without  the  use  of  water.  The  voids  should 
be  filled  well  with  clean,  fine  stone  chips  free  from  dust,  but  an  excessive 
amovmt  of  rolling  should  be  avoided  because  if  the  roller  is  used  too  freely 
the  larger  stones  will  become  rounded  and  covered  with  dust,  thxis  meventxog 
the  tar  from  adhering  properly.  Hot  tar  may  be  applied  to  all  tne  couxsea 
if  desired,  but  sometimes  only  the  upper  coiu:se  is  so  treated.  After  the  tar 
has  been  applied,  a  dressing  of  fine  material  is  spread  on  and  the  whole  road 
well  rolled.  The  tar  may  be  spread  by  hand,  but  it  is  most  economical  to 
use  a  tar  spreader:  the  spraying  apparatus  is  motmted  on  wheels  and  is  so 
arranged  that  the  tar  is  forced  from  the  tank  in  which  it  is  heated,  into  an  air 
receiver  under  a  pressure  of  160  to  350  lbs.  per  sq.  in.;  the  necessary  powex 


TARS  AND  OILS  FOR  ROAD  SURFACES.  U3S 

for  pumping  the  air  and  the  liquid  into  the  receiver  being  obtained  by  means 
of  cnjdn  drive  from  the  road  wheel.  From  the  receiver  «ie  tar  is  distributed 
upon  the  road  by  means  of  specially  designed  spraying  nozzles. 

Amount  and  cost  of  materials. — ^According  to  conditions  and  methods 
of  application,  a  surface-treated  road  will  require  from  0.35  to  0.70  gallons  of 
tar  per  sq.  yd.  when  applied  by  hand;  and  as  small  as  0.21  gallon  has  been 
used  with  good  results  when  applied  by  machine,  for  first  treatment.  With 
dUier  method  the  application  of  tar  must  be  repeated  from  time  to  time, 
though  less  is  required  at  each  successive  application.  If  tar  is  applied  as 
road  is  built,  as  much  as  1.6  gallons  per  sq.  yd.  are  often  constmied  it  spread 
by  hand;  but  by  means  of  devices  like  the  pneimuitic  tar  sprayers,  it  is 
claimed  that  the  road  stones  to  a  depth  of  ZY  may  be  well  covered  with 
about  0. 6  gallon  per  sq.  yd .     Crude  coal  tar  can  ordinarily  be  purchased  from 

fis  or  coke  companies  at  from  3  to  5  cts.  per  gallon;  renned  tars  nm  from 
to  12  cts.  and  even  higher.  The  cost  of  treatment  in  France,  by  machine, 
will  average  about  3  cts.,  and  by  hand  5  cts.;  in  this  cotmtry,  where  it  is 
generally  applied  by  hand,  the  cost  ranges  from  about  0  to '12  cts.  or  more 
persq.  yd. 

Oils.  Tbbir  Classipication  and  Propbrtibs. 
Oil  fields. — ^There  are  seven  distinct  oil  fields  in  the  United  States:  1st 
the  Appalachian  (including  New  York,  Penn.,  W.  Va.,  southeastern  Ohio, 
and  parts  of  Kv.  and  Tenn.)  produces  oils  known  as  eastern  oils  or  paraffin 
petroleums,  and  which  are  therefore  of  use  only  as  temporary  binders  in  dust 
suppression;  2nd  the  Ohio- Indiana  field  produces  oils  much  like  those  of  the 
Appalachian  and  are  also  classed  as  paraffin  oils;    3rd  the  Colorado  field, 
sinular  to  above;   4th  the  Wyoming  field  with  oils  varying  from  the  lighter 
oils,  to  the  heavy  asphaltic  oils  which  are  found  principally  in  California; 
5th  the  California  field  produces  oils  of  the  most  varied  character,  consisting 
mainly  of  more  or  less  dense  asphaltic  hydrocarbons,  none  of  the  componmits 
being  of  the  paraffin  series,  the  percentage  of  asphaltic  residue  usually  high  and 
of  good  binding  character,  the  oils  being  considered  the  best  for  use  as  perma- 
nent binders;    6th  the  Texas  field  contains  oils  of  a  mixed  character,  with 
some  paraffin  as  well  as  a  greater  or  less  amoimt  of  asphaltic  residue,  some 
having  been  used  successfully  as  dust  preventives,  with  others  unfit  for  this 
purpose;    7th  the  Kansas  field  (including  Oklahoma)  produces  oils  quite 
similar  to  those  from  Texas.     The  same  is  true  of  Louisiana.     In  general. 
the  eastern  oils  are  of  the  paraffin  type  and  useless  as  permanent  binders; 
the  western  oils  are  of  asphaltic  character  and  of  great  value  as  permanent 
binders;  while  the  southern  oils  are  of  a  mixed  character,  their  value  as  dust 
preventives  lying  in  the  relative  amount  of  asphalt  base  contained. 

Rgfining. — Although  crude  oil  is  used  to  a  great  extent  in  the  West  as  a 
lust  preventive,  it  is  often  customary  in  the  East  to  partially  distill  oils 
ron taming  asphaltic  residues  before  using  them,  thus  recovering  many  of  the 
nore  valuable  constituents  and  producing  residual  oils  having  a  much  better 
>indins  quality  because  they  contain  a  larger  percentage  of  asphalt  base. 
*rude  petroleum  is  an  oily  liquid,  of  unpleasant  odor,  with  specific  gravity 
rom  0.73  to  0.97,  according  to  locality  from  which  it  is  derived;  color  from 
TcenvAi  brown  to  nearly  black,  often  reddish  brown  or  orange  when  viewed  by 
ran^mitted  light;  sometimes  fluorescent.  The  crude  petroleiun  is  refined 
y  means  of  fractional  distillation,  somewhat  similar  to  that  for  crude  coal 
%T.  The  most  valuable  products  are  the  kerosene,  or  burning  oils,  and  the 
letlxod  called  "cracking  is  employed  to  increase  their  yield:  this  consists 
I  modifyixig  the  fire,  during  process  of  distillation,  so  that  only  the  bottom 
'  the  still  is  intensely  heated,  while  top  and  sides,  being  exposed  to  the  air, 
-come  somewhat  cooled;  thus  the  heavy  oil  vapors  are  condensed  within 
.e  still  itself,  and  upon  dropping  back  into  the  residuum,  which  is  much  hotter 
£01  their  boiling  point,  break  up  into  lighter  oils  with  lower  boiling  points. 
itli  a  separation  at  the  same  time  of  free  carbon  or  coke,  which  is  deposited 
tlic  remduum.  The  paraffin  petroleuiii  residuums  contain  a  large  amount 
oaraffin  hydrocarbons  and  paraffin  scale  or  crude  paraffin,  and  are  tmsuit- 
icfoT  road  surface  treatment.  The  base  held  by  the  California  petroleums 
^^omposed  of  bitumens  resembling  asphalt;  the  residuum  contains  no  par- 
g.zi  and,  if  cracking  has  not  been  employed  in  its  preparation,  carries  but 
,l&  free  carbon;  both  the  crude  oil  and  the  residuums,  if  properly  prepared, 
r  excellent  binders  and  give  the  best  results  of  any  oils  which  have  been 
^  as  dust  preventives.  The  semi-asphaltic  oils,  as  from  Texas,  carry  an 
^ju^tic  base,  but  also  a  considerable  amount  of  paraffin  hydrocarbons  and 


1134 


ti.-^HIGHWAYS, 


1%  or  more  of  paraffin  scale;  are  somewhat  inferior  to  the  Calif orina  prod- 
ucts but  often  give  good  results. 

Comparisons  of  crude  oils  and  residuums. — ^The  two  following  Tables 
show  some  results  obtained  from  an  examination  of  various  crude  and 
refined  petroletuns  in  the  New  York  Testing  Laboratory. 

Results  op  Tbsts  op  Crudb  Pbtrolbums. 


Kind  of  Oil. 


Spec. 
Grav. 


Fla«h-| 

ing 
Point 


VolatilV 
at  llOX. 
7  hours. 


Volatil'y 
at  160X. 
7hoiu«. 


Volatil'y 
at  205*^. 
7  hours. 


Residue. 


Pennsylvania,  paraffin . 
Texas,  semi-asphaltic. 
California,  asphaltic. . . 


0.801 
.904 
.939 


(a) 
43 
26 


Percent. 
47.3 
20.0 


Per  cent. 
58.0 
27.0 


Percent 
68.0 
49.0 

d42.7 


Percent. 
e>33.0 
C51.0 
«57.3 


a  Ordinary  temperature. 

6  Soft. 

c  Quick  flow. 


d  Volatility  at  200*».  7  hours. 
e  Soft  maltha;  sticky. 


Rbsults  op  Tbsts  op  Pbtrolbum  Rbsiduums. 


Kind  of  Oil. 

Spec. 
Grav. 

Flash- 
point. 

VolatU'y 
at  200<^. 
7  hours. 

Residue. 

Solid 
Paraffin. 

Fixed 
Carbon. 

Pennsylvania,  paraffin. 
Texas,  semi-asphaltic. . 
California,  asphaltic. . . 

0.920 

.974 

1.006 

186 
214 
191 

Percent. 

14.2 

6.2 

17.3 

Per  cent. 
a85.8 
a93.8 
a82.7 

Percent. 

11.0 

1.7 

0.0 

Percent. 
3.0 
3.S 
6.0 

a  Soft. 

The  Application  op  the  Heavier  Oils. 

To  macadam  surfaces. — Holes  and  inequalities  should  be  repaired;  not 
necessary  to  remove  all  dust  as  in  case  of  tar.  but  sticks,  leaves,  etc.,  should 
be  removed;  crude  oil  either  hot  or  cold,  according  to  its  viscosity  and 
ability  to  penetrate  the  road  surface;  much  cheaper  applied  cold.  A  cover- 
ing of  sharp  sand  or  i"  stone  screenings  shoiild  be  applied  after  the  oil  has 
been  allowed  to  penetrate  as  much  as  possible,  in  order  to  take  up  aU  excess, 
and  the  surface  well  compacted  by  rolling,  additional  sand  or  screenings 
being  thrown  on  wherever  the  oil  ^ows  a  tendency  to  force  its  way  to  the 
siu^ace  and  produce  a  sticky  condition.  Sometimes  2  or  8  courses  of  oil  and 
screenings  are  applied. 

During  construction  of  macadam  road. — ^The  greatest  success  has  been  in 
California  where  the  heaviest  asphaltic  oils  are  fotmd;  and  the  residuums 
obtained  from  the  partial  distillation  of  these  oils  have,  so  far,  given  the 
best  results.  The  treatment  is  ^sentially  the  same  as  with  tar,  above  de- 
scribed. The  macadam  is  built  in  the  usual  mimner  and  each  course  thor- 
oughly rolled  tmtil  the  whole  road  is  consolidated.  A  road  constructed  in 
this  manner  will  require  from  }  to  li  gallons  of  oil  per  sq.  yd. 

To  gravel  roads. — A  gravel  road  is  oiled  in  much  the  same  way  whethcf 
it  is  an  old  road  or  one  under  construction,  as  only  the  upper  course  is  treated 
in  either  case.  Good  drainage  is  very  essential.  The  oil  may  be  apf^ied 
either  hot  or  cold,  according  to  its  viscosity,  by  any  method  previously  de- 
scribed. Where  the  treated  surface  is  loose  and  contains  a  considerable 
amount  of  clay,  the  oil  may  be  worked  into  the  upper  course  by  raking,  in- 
suring an  equal  distribution.  After  application  of  oil,  the  road  dunild  be 
rolled  vmtil  properly  compacted,  adding  fresh  material  as  the  oil  works  to 
the  surface.  Condensed  specifications  from  biennisd  report  (1906)  by  Com- 
mu«ioner  of  Department  of  Highways  of  California  are:  Sub-gnuie  to  he 
thoroughly  rolled;  then  2  layers  of  gravel,  bottom  layer  6*  and  top  layer  3" 
alter  bemg  rolled;   1st  layer  containing  not  larger  than  21'  stone;   gr&vel  to 


SPECIFICATIONS— FOR  COAL  TARS;  OILS,  1185 

be  evenly  spread,  well  moistened,  rammed  1  ft.  from  gutter  or  curb,  and 
remaining  portion  rolled:  depressions  filled,  moistened,  and  again  rolled  to 
tmyielding  surface;  on  this  surface  place  the  top  layer  of  gravel,  no  stones 
over  1*  diameter,  and  compacted  in  same  manner.  Oil  should  then  be  evenly 
distributed  over  the  entire  surface,  J  gallon  per  sq.  yd.,  and  covered  with 
clean,  sharp  sand  until  no  oil  can  be  seen;  after  12  hotus.  another  applica- 
tion of  oil  and  sand  in  same  manner,  and  rolled  to  unyielding  surface.  Use 
crude  oil  applied  at  temperature  between  160*  and  IW  F. 

To  earth  roads. — (a)  The  oil  is  simply  sprinkled  on  the  road,  laying  the 
dust  and  incidentally  hardening  the  surface.  Alkali  soils  disintegrate  the 
oil  and  destroy  its  binding  qualities.  A  sandy  loam  is  the  most  suitable  for 
treatment,  usually  giving  good  results  when  properly  treated  with  an  oil  of 
good  binding  quality.  Clay  is  probably  the  worst  of  all,  as  it  does  not 
absorb  the  oil  well  and  exhibits  a  tendency  to  ball  up  and  give  trouble;  sand 
should  therefore  be  added  to  the  clayey  surface.  Special  attention  should 
be  paid  to  drainage,  the  roadbed  to  be  dry  when  the  oil  is  applied,  (b)  An- 
other method:  The  road  is  first  plowed  to  depth  of  6'  and  properly  crowned: 
all  clods  and  lumps  broken  up  by  means  of  a  harrow,  and  roadway  well 
sprinkled  with  water;  a  specially  constructed  rolling  tamper  is  then  used  by 
which  the  lower  portion  ox  the  loose  earth  is  compacted  to  depth  of  about  2r, 
except  in  cases  where  sub-grade  is  tmusually  firm.  After  the  lower  portion  is 
made  firm,  a  heavy  asphaltic  oil  is  applied,  H  gallons  per  sq.  yd.,  and  a 
cultivator  passed  over  the  road  until  the  oil  and  earth  are  thoroughly  mixed. 
The  tamper  is  then  used  a^ain,  and  the  road  is  further  compacted  until  only 
1 K  of  loose  material  remam  on  top.  Oil  is  again  applied,  and  surface  rolled 
with  the  tamper  until  firm,  and  finally  it  is  ironed  down  with  an  ordinary 
roller,  additional  applications  of  earth  being  made  wherever  necessary  to 
take  up  any  excess  of  oil.  A  road  constructed  in  this  manner  will  require 
from  2t  to  3  gallons  of  oil  per  sq.  yd.  It  is  hard  and  dustless  and  resembles 
asphalt.  CaUfomia  oils  are  the  best.  Texas  and  Kentucky  oils  cost  from 
4  to  8  cts.  per  gallon.  The  residuums  and  special  preparations  vary  from 
2  to  12  cts. 

Spbcipications  for  Coal  Tars. 

I.  When  used  as  temporary  binder  it  is  usually  employed  in  form  of  an 
*mulsion;   specifications  difficult. 

II.  When  used  as  a  semi-permanent  binder  it  is  necessary  that  sufficient 
binding  base  be  present  to  last  through  dusty  season;  and  for  economy, 
naterial  to  be  sumciently  fluid  to  apply  cold;  hence — 

1.  Coal  tar  to  be  formed  at  low  temperature,  such  as  produced  from 
by-product  coke  ovens  or  by  gas  plants. 

2.  A  crude  tar  may  be  employed  because  of  cheapness. 

8.  If  not  sufficiently  fluid  to  apply  cold,  enough  water-gas  tar  may 
be  added  to  bring  it  to  proper  consistency,  but  proportion  of  latter  should 
not  exceed  60%  of  mix. 

III.  When  used  as  a  permanent  binder  for  surface  application,  either  a 
rude  or  a  refined  product  may  be  employed,  preferably  the  latter. 

1.  If  a  crude  tar,  it  should  have  the  following  properties: 

(a)  Same  as  II.  1. 

(b)  Its  specific  gravity  to  be  between  1.16  and  1.10. 

(c)  It  should  be  free  from  water-gas  tar  and  oil  tar. 

2.  If  a  refined  tar,  the  following  might  be  specified: 

(a)  Same  as  II,  1. 

(b)  Its  specific  gravity  to  be  between  1.17  and  1.20. 

(c)  No  water  nor  ammoniacal  liquor  to  be  present;  boiling  point 

above  1 10*  C.  (230*  F.). 

(d)  Upon  distillation,  at  least  40%  by  volume  of  pitch  should  re- 

main after  all  oils  have  been  driven  off  below  i70*  C.  (618*F.). 

IV.     When  used  as  a  permanent  binder  in  road  construction  it  is  ncces- 
ry  that  more  binding  base  be  present  than  is  usually  found  in  the  crude 


uae  m.'-HiGHWAYs. 

pfxxSuct.    A  refined  product  should  therefore  be  emp1o3^;  either  pmpanA 
from  a  crude  tar  by  the  contractor  or  a  special  preparation  ptirdiased. 

1.  In  the  former  case,  a  mixture  may  be  prepared  as  follows  from  a 
crude  tar,  which  meets  the  specifications  set  forth  in  III,  1: 

(a)  The  tar  should  be  heated  until  boiling  point  is  raised  to  at 

least  110«»C.  (230°F.). 

(b)  One-tenth  part  or  more  of  Rood  soft  pitch  should  then  be  dis- 

solved in  the  tar  while  hot;  the  quantity  added  should 
be  sufficient  to  produce  a  pitch  residue  of  at  least  50%  by 
volimie  after  all  oils  have  been  driven  off  under  270°  C. 
(618"  F.). 

2.  A  refined  tar  for  this  ptirpose  should  meet  the  requirements  as 
suggested  for  III,  2,  except  that  the  pitch  remaining  after  volatile  oils 
under  270"  C.  have  been  driven  off  should  amount  to  at  least  60%  by 
volume. 

In  some  cases,  especially  where  climate  is  warm  throughout  the  year,  a 
tar  considerably  thicker  in  pitch  may  be  preferred. 

Spbcipications  for  Mineral  Oils. 
(a)  The  oil  shall  have  a  specific  gravity  of  not  less  than  0.05.  (b)  Its 
flash  point  shall  not  be  lower  than  300"  F.  (c)  It  shall  be  free  from  water 
as  determined  by  the  gasoline  test,  (d)  When  heated  to  400**  F.  its  loss  in 
weight  should  not  be  over  35%.  The  character  of  the  residue  should  be 
smooth  and  nearly  solid  when  cold,  but  not  so  hard  that  it  may  not  be 
easily  dented  with  the  finger,  and  when  soft  it  should  pull  to  a  long,  thin 
thread,  (e)  The  oil  shall  be  soluble  in  carbon  disulphide  to  the  extent  of 
98%,  and  in  88"  naphtha  to  at  least  88%. 

EXPERIMENTS  WITH  DUST  PREVENTIVES. 

Note. — Following  is  from  circular  No.  89,  Office  of  Public  Roads,  U.  S. 
Dept.  of  Agric,  issued  April  20.  1908.  During  the  past  few  years  a  number 
of  preparations  for  laying  and  preventing  dust  have  appeared  on  the  market 
in  competition  with  crude  materials,  such  as  coal  tar  and  petroletim,  and  it 
was  therefore  decided  by  the  Office  of  Public  Roads  to  carry  on  a  aeries  of 
experiments  during  the  summer  of  1907  with  a  view  to  determining,  if  pos- 
sible, the  relative  value  of  these  preparations  and  crude  products  and  tlicir 
adaptability  to  different  conditions.  Experiments  were  conducted  at  Way- 
land,  Mass.,  Washington,  D.  C,  and  Bowling  Green,  Ky.  Following  are 
results: 

Experiments  at  Wayiand,  Mass. — The  water-gas  tar  was  obtained  fiom 
a  local  gas  company  at  $1.50  per  barrel  of  50  gallons,  delivered.  The  crude 
coal  tar.  in  50-gal.  bbls.  at  $2  per  bbl.,del.  It  had  been  produced  at  a  lov 
temperature  and  contained  a  good  pitch  base.  The  special  coal-tar  product 
was  supplied  free  in  50-gal.  bbls.,  the  Office  paying  the  freight  from  Boston 
to  Wayland.  It  contained  no  water,  was  free  from  the  extremely  volatile 
oils  present  in  the  crude  tar,  and  held  a  good  pitch  base.  The  other  proper- 
ties are  shown  in  comparison  with  the  water-gas  and  coal  tars  in  preced- 
ing Table.  Labor  cost  per  8-hour  day  was  as  follows:  Common  labor,  fl  .50  to 
$1.85;  single  teams,  $3;  double  teams,  $5;  foreman,  $3;  steam  rollerjjf  12. 
The  cost  of  repairs  per  sq.  yd.  of  road  surface  was  from  2.6  to  3.8  eta.  When 
gravel  was  used  it  was  obtained  from  pits  near  the  road,  costing  the  commis- 
sion $1.08  per  cu.  yd.  Clean  trap  screenings,  li',  or  pea  stone/however,  was 
used  whenever  it  could  be  obtained  and  was  furnished  at  |1 .10  per  ton  by  a  rode- 
crushing  plant  located  about  4  miles  from  nearest  section  of  work.  Thir- 
teen experiments  were  made  as  summarized  in  the  two  following  Tables. 


d  by  Google 


DUST  PREVENTIVES— TAR  EXPERIMENTS. 


1137 


Cost  Data  of  Tar  Bxpbrimbnts. 


Material  Supplied. 


Cost  of 

repairs 

per  square 

Irani. 


Cost  of 
application 

square  yard. 


n 


.8 
S 

3 


Water-gas  tar. 


10.022^.010^.04910 
"        "         049 


.010 


Coal  tar.. 


.018 
.018 


.006 

.006 


Water-gas   and    coal- 
"  tars 


.018 


.006 


Special  tar  mixture 
Special  tar  preparation 


.023 


.010 


.006 
.013 
.061 
.056 
.044 
.058 
.030 
.037 
.046 
.148 
.058 


02710 

.Oil 

.009 

.006 

.024 


.017 
.033 
.015 
.017 
.026 
.090 
.040 


008S0.013$0.129 
006^  .01^  .114 
.015 
.033 
.129 
.129 
.068 
.137 
.062 
.072 
.102 
.310 
.127 


.006 
.009 
.014 
.010 
.007 
.008 
.017 
.033 
.019 


.012 
.010 
.010 
.013 
.010 
.010 
.010 
.013 
.012 
.010 


^220.74 

19.03 

7.30 

6.60 

32.46 

129.14 

52.82 

57.49 

58.26 

119.89 

27.27 

31.64 

103.46 


Total.. 


72.28 


36.00382.07203.38 


82.26  90.10 866.09 


MiSCBLLANBOUS  DaTA  OP  TaR  BxPBRIMBNTS. 

d 

C 
< 

Material  Applied. 

Surface 
Apg«=a- 

1- 

in 

i'o'H. 

it 

1 

Water-gas  tar 

Gravel 

None..*;.*.' 
Gravel".  .* '. '. 

Pea  stone. 

Gravel 

Pea  stone. 

0.90 
.38 
.30 
.25 
.60 
.70 
.42 
.90 
.43 
.48 
.42 

1.50 
.67 

0.0079 
.0080 

0.009 
.009 

1.700 

2 

167 

3 

•• 

500 

1 

•« 

.6686 

.0080 
.0133 
.0096 
.0086 
.0072 
.0202 
.0400 
.0226 

.009 
.009 
.009 
.009 
.009 
.009 
.009 
.009 
.009 
.009 

200 

5 

Cool  tar 

250 

3 

1.000 

7 

•« 

600 

i 

Water-gas  and  coal  tars 

417 
933 

) 

•• 

1,667 

{ 

Special  tar  mixture 

Special  tar  preparation 

267 
100 
817 

Total 

^ 

11.118 

Digitized  by ' 

Pot 

1 1 88  W.^HIGHWA  YS, 

Experiments  at  Washington,  D.  C. — ^With  calcitun  chloride,  as  a  dust 
preventive:  tested  on  portion  of  macadam  driveway  in  Agricultural  Dept. 
groirnds,  Wa^ington.  D.  C.  The  roadway  is  built  of  trap  rock,  held  in  posi- 
tion by  a  soft  limestone  binder;  the  screenings  of  the  binder  pulverized 
rapidly  under  traffic,  forming  a  light  dust  continually  raised  by  passing 
vemcles.  and  carried  away  by  the  wind;  the  road  was  thus  becoming  stripped 
of  its  binding  material.  In  preparing  for  treatment,  all  dust  and  dirt  wen 
scraped  from  surface  of  roadway;  a  solution  was  prepared  by  mixing  300  lbs. 
of  commercial  calcium  chloride  (granular,  con  taming  76%  calcium  dikmde 
and  25%  moisture)  with  300  gallons  of  water  in  an  ordinary  street  sprinkler, 
agitating  the  liquid  thoroughly  before  applying.  It  was  then  applied  from 
one  sprinkling  head,  and  the  sprinkler  passed  slowly  back  and  forth  over  the 
road  to  facilitate  the  complete  absorption  of  the  solution;  each  application 
consisting  of  600  gallons  over  an  area  of  1582  sq.  vds.,  or  0.38  gallon  per 
sq.  yd.  The  first  application  was  made  Jxily  13,  1007,  followed  by  a  similai 
one  July  1 5,  to  increase  the  efficacy  of  the  treatment.  The  effect  was  marked. 
The  texture  of  the  road  surfac^ras  completely  changed:  before  treatment, 
raveling  was  excessive  in  spots  a^d  the  whole  surface  seemed  loosely  knit 
together;  after  treatment  of  July  15,  this  condition  changed  and  the  road 
surface  became  smooth,  compact  'and  resilient.  The  third  treatment. 
August  Srd,  was  given  because  certain  points  exposed  to  the  most  severe 
wear  were  showing  signs  of  raveling;  the  results  of  this  treatment,  and  of 
successive  ones,  were  most  satisfactory  and  not  unlike  those  attending  the 
first  two  treatments.  The  calcium  chloride  is  charged  at  rate  of  $16  per  toe, 
f.  o.  b.  cars  at  Baltimore;  freight  13  cts.  per  100  lbs.  Specific  gravity  of 
solutions,  1.058  to  1.060.    Following  is  Table  of  cost  of  applying: 

Cost  of  Applying  Calcium  Chloridb. 


Item. 


Cost. 


600  pounds  calcium  chloride,  at  $18.60  per  ton 

3  men  for  \\  hours,  at  15  cents  per  hour 

1 -horse  sprinkling  wagon  for  H  hours,  at  85  cents  per  hour. 

Total  cost  of  1,582  square  yards 

Cost  per  sqtiare  yard  at  this  rate 

Total  cost  of  five  applications. 


$5.58 

.675 

.525 

6.78 

.0043 

38.90 


C^t  per  square  yard  of  five  applications '       .0215  . 

Experiments  tA  Bowling  Qreen,  Ky. — Materials  used  were  Kentucky 
rock  asphalt  tested  for  its  fitness  as  a  binder  in  macadam  construction,  crude 
Kentucky  oil,  and  special  preparation  of  residutun  oils,  the  last  two  of  which 
were  used  as  dust  preventives. 

(a)  Rock  Asphalt  Exp^iment. — ^The  rock  asphalt  used  is  a  natural  product 
formed  in  the  Chester  group  of  subcarboniferousrocksoveracourseextendioc 
through  Breckenridge.  Grayson,  Edmonson,  Logan,  and  Warren  counties. 
marking  the  edge  of  the  coal  fields  lying  in  the  western  part  of  Kentucky. 
It  is  a  nne-grained  sandstone  impregnated  with  mineral  pitch  or  bitumen, 
the  latter  averaging  from  6  to  8%,  with  a  maximum  of  12%.  After  guarrj'- 
ing  and  crushing,  2^  size,  it  is  further  passed  between  steel  rollers,  the  miii^>ed 
product  being  a  mass  of  individual  grains  of  sand,  each  thoroxighly  coated 
with  a  film  of  mineral  pitch,  adhering  to  surrounding  grains  and  packing 
very  firmly  if  subjected  to  pressure;  with  a  rich  dark  brown  color  with  s 
slignt  luster  which  gradually  disappears  as  the  bitumen  hardens  and  dries^ 
If  chilled  when  compacted,  a  lump  becomes  very  hard  and  tough;  if  warmed 
in  the  hand,  the  bitumen  becomes  soft  and  semi-fitiid  and  the  individual 
grains  of  sand  fall  from  the  mass  of  their  own  weight.  The  test  was  made 
on  Cemetery  pike,  a  main  thoroughfare.  The  form  of  construction  originally 
adopted  was  a  20-ft.  Telford  road.  When  the  surface  had  been  worn  away 
exposing  the  foundation,  it  was  repaired  and  brought  to  i^rade  with  a  sharp 
gravel  containing  about  20%  sand  and  clay,  the  layer  being  about  8*  thick 
when  compacted.  Previous  to  the  experiment,  it  was  loosened  to  a  depth 
of  *j  by  means  of  a  spiked  roller  and  a  heavy  harrow,  and  shoveled  out  by 
hand.  The  sub-«rade  was  then  made  to  conform  to  crown  of  roadway. 
Planned  to  be  4r  in  0  ft.,  or  an  average  of  J'  per  ft.  After  roUins  the  aub- 
grade  the  wearing  course  of  stone  was  laid;  it  consisted  of  crushed  lunestone. 


EXPER.— CALCIUM  CHL.,  ROCK  ASPH.,  OIL. 


1139 


1*  toli'.  spread  in  a  4*  layer,  rolled  once  to  turn  down  the  sharp  edges  of 
the  stone  and  form  a  smooth,  even  surface.  The  rock  asphalt  was  then 
thrown  on  with  shovels  and  spread  to  a  depth  of  H',  care  being  taken  to 
break  all  lumps  and  to  work  all  the  asphalt  rock  possible  into  the  interstices 
of  the  stone  without  disturbing  the  latter.  As  the  work  progressed,  the 
roller  was  kept  moving  back  and  forth  parallel  to  axis  of  roadway,  working 
from  outer  edge  to  crown  as  in  ordinary  macadam  construction.  The  in- 
advisability  of  woxking  the  material  when  chilled  and  damp  was  apparent, 
for  the  portion  of  the  road  laid  at  a  temperature  of  66**  F.  failed  to  become 
hard  and  firm  for  several  hours  i^ter  subsequent  applications  had  compacted 
satisfactorily.  The  cost  of  the  work  is  shown  in  the  following  Table.  Labor 
ranged  from  $1.20  to  $1.25,  and  teams  cost  $3  per  day  of  ll)  hours;  roller 
was  loaned,  cost  of  operation  being  $2.50  per  day  for  engineer  plus  cost  of 
fuel;  stone  was  delivered  on  roadway  at  il.20  per  cu.  yd.  and  was  spread 
4'  thick  uncompacted,  making  cost  per  sq.  yd.  delivered  13  cts;  cost  of 
isphalt  charged  at  market  price  of  $5  per  ton  f.o.  b.  cars  at  Bowling  Green; 
t  was  spread  about  IK  thick,  or  at  rate  of  24.5  sq.  yds.  per  ton. 

Cost  Data  of  Rock  Asphalt  Bxpbrimbnt. 


Item. 


Cost 

per  square 

yard. 


Total  cost. 


Percentage 
of  total. 


ihaping  sub-grade, 
tone  on  work. . . . 
preading  stone . . 

Lolling  stone 

sphalt  on  work., 
preading  asphalt, 
oiling  asphalt... 

Total.. 


Ctnts. 

5.66 

18.71 

.78 

.00 

23.77 

1.44 

2.18 


Dollars. 

43.60 

105.60 

5.97 

.67 

183.10 

11.064 

16.78} 


Per  cent. 

11.8 

28.8 

1.7 

.3 

50.0 

3.1 

4.3 


47.63 


366.79 


100.0 


(b)  Oils. — In  connection  with  work  on  rock  asphalt,  experiments  were 
ade  to  determine  the  comp>arative  value  of  a  residuum  oil  preparation  and 
ude  oil,  as  dust  preventives.  The  oil  preparation  is  a  patented  mixture  of 
sidurnn  oils,  combined  with  a  view  to  obtaining  such  proportions  of  as- 
ia.ltic  and  lighter  oils  as  shall  be  best  fitted  for  immediate  dust  lading  and 
rtnanent  improvement  of  the  roadway.  The  tests  were  made  on  Cemetary 
Ice  beyond  the  point  where  the  rock  asphalt  work  ended.  The  general 
ndition  of  the  gravel  roadway  was  imsatisfactory  for  the  purposes  of  such 
test;  the  cross  section  of  the  roadway  was  quite  fiat,  the  crown  having 
eti  completely  worn  down,  so  that  lateral  drainage  was  defective;  also 
»ro  were  extensive  pockets  of  loose  material,  characteristic  of  roads  made 
grravel  containing  a  large  percentage  of  sand  and  clay.  Heavy  rains  had 
len  for  several  days  precedmg  the  application  of  the  oil,  and  although  the 
wi  surface  was  quite  dry  there  was  a  large  amount  of  moisture  in  the  road- 
1 ,  thus  prevening  the  rapid  absorption  of  the  oil  by  the  gravel  before  the 
tporation  of  the  lighter  oils  took  place.  The  oils  were  applied  over  a 
I  til  of  12  ft.  of  the  roadway  by  means  of  an  oil  sprinkler  adapted  to  the 
form  spreading  of  heavy  liquids.  A  tank  load  of  the  oil  preparation  was 
ead  over  an  area  of  841  sq.  yds.,  or  an  average  of  0.903  gallon  per  sq.  yd. ; 

temperature  of  the  oil  87®  F.  due  to  its  exposure  to  the  sim;  it  was  heavy 
[  -was  absorbed  very  slowly  bjr  the  gravel,  about  4  days  being  required  to 
sc  it  to  become  thoroughly  incorporated  into  the  surface  of  the  road; 

grravel  becoming  very  compact  and  showing  few  traces  of  wheel  marks 
ept  at  points  where  repairs  had  been  made,  in  which  cases  the  cementing 
cess  took  place  more  slowly.  In  the  case  of  the  crude  oil,  5  tank  wagons, 
t  total  of  3712  gallons,  were  applied  to  4416  yards  of  surface,  making  an 
rsLge  of  0.84  gallon  per  sq.  yd.  An  experiment  was  also  made  with  crude 
on  macadam  road ;  there  was  about  i'  of  diist  on  roadway  consisting 
ely  of  powdered  limestone*  the  roadway  was  given  an  application  of 
gallons  over  an  area  of  1462  sq.  yds.,  or  at  rate  of  0.52  gallon  per  sq.  yd. 

ioUavring  Table  gives  a  statement  of  the  cost  of  repairs,  materials,  and 
licatioii  of  the  oils. 


1140 


W.—HIGHWAYS, 


Cost  Data  op  Oil  Ezpbrimbnts. 


Experiment. 

Item. 

Cost  per 
square 
yard. 

Total 

cost. 

Repairs  and  ditching. . . 
Oil 

Cents. 

0.67 
.13 
.47 

DoUars. 

4.79 

110.00 

SpGciftl  oil  preparation 

Application 

8.93 

Total  cost 

1.17 

118.72 

Repairs  and  ditching. . . 
Oil 

.33 

4.46 

.16 

14.38 
196.94 

Crude  oil  on  gravel  road 

Application 

7.28 

Total  cost 

4.05 

218.60 

fOil 

2.76 
.11 

40.00 

Crude  oil  on  macadam  road . . . 

J  Application 

1.64 

[         Total  cost 

2.86 

41.64 

d  by  Google 


ASPHALT  AND  BITUMINOUS  ROCK  DEPOSITS. 


1141 


Bittunmous. . . 


EXCERPTS  AND  REFERENCES. 

The  Acphalt  and   Bituminous  Rock   Deposits  of  tlie  U.  S.  (By  G.  H. 

Eldridge;  U.  S.  Gcol.  Stirv.;   Eng.  News.  June  5,  1»02).— 

Tablb  I. — Classification  of  Natural  Hydrocarbons. 

G-~-» {^r.V^. 

Fluid f  Naphtha. 

\  Petrolciun. 
^Maltha. 

Mineral  tar. 

Brea. 

Chapapote. 

Elatente  (mineral  caoutchouc). 
^  Wurtzilite. 

Albcrtite. 

Impsonite. 

Orahamite. 

Nigrite. 

Uintaite  (gilsonite). 

Lignite. 

Bituminous  coal. 

Semi-bituminous  coal. 
.Anthracite  coal. 

Succinite  (amber). 

Ojpalite. 

Amberite,  etc. 

Ozocerite. 

Hatchetite.  etc. 

Pichtelite. 

Hartite,  etc. 

Tablb  II. — Grouping  of  Natural  and  Artificial  Bituiiinous 
Compounds. 

Mixed  with  limestone     fSeyssel.  Val  de  Travers.  Lobsan,  Illinois, 
(asphaltic  limestone)..!     Utah,  etc. 

"wT«ph!iSi? '".'' . .  }CBUfomi..  Kentucky.  UUh.  etc. 


tural. 


"S?1iSJIhkftk)'?!'."".':}Trimdad.  Cuba.  CalifomU.  Utah. 

Bituminous  ichisU /Canada.  California,  Kentucky.  Virginia. 

{    etc. 

pj^j  fThick  oils  from  distilled  petroleum, 

^^^ l    "residuum." 


ficial. 


Viscous. 


SoUd. 


/Gas  Ur. 
Pitch. 

Refined  Trinidad  asphaltic  earth. 
Mastic  of  asphaltite. 
Gritted  asphaltic  mastic. 
Paving  compounds. 


'he  Adjustment  of  Macadam  Road  Design  to  Various  Subgrade  Soils 
ort  of  Mass.  Highway  Commission;  Eng.  News,  Sept.  4,  1902). — Deals 
Sand  and  Gravel.  Clay,  and  Sandy  Loam. 

a  vine  a  Comtry  Road  With  Brick  (By  Sam.  Houston.  Paper, 
Soc.  C.  E.  8t  Surv.,  Jan.  20,  1902;  Eng.  News,  Sept.  25. 1902).— HTus- 
1  details  in  cross-section.  Specifications  and  discussion  under  the 
ring  licadings:  Underdrains;  Foundation  of  Broken  Vitrified  Pipe; 
ie<fClay  Curbing;   Crown  of  Pavement  and  Curve  of  Summer  Road; 

Pavement.  Cost  data  is  given  showing  that  6479  ft.  of  road  cost 
7.72:     the  total  width  of  road  between  ditches  is  26  ft.,  with  10.  ft. 

of  pavement  proper;  etc. 


1142  tXi.— HIGHWAYS. 

An  ExperimenUI  Steel  Trackway  In  N.  Y.  City  (Bng.  News.  Dec.  i 
1902). — Illustrated  cross-section  of  trackway,  and  details  of  rail  sectioc. 
used  in  Murray  St.  Rails  are  special  channel  section,  40  ft,  long,  and 
weigh  25  lbs.  per  lin.  ft.  Approximate  cost  of  trackway,  laid,  complete. 
$7,500  per  mile. 

The  Design  of  a  BHuminoas  Macadam  Road  for  Salem  Co-  N.J. 
(Eng.  News,  Sept.  24.  1903). — Illustrated  cross-section  of  30-ft.  road. 

Data  on  Roads  and  Pavements  in  Iowa  (By  A.  Marston.  Report 
Iowa  Eng.  Soc.;  Eng.  News,  Feb.  9,  1906). — Table  of  traction  tests  ca 
brick  and  asphalt  pavements  in  various  stages  of  condition.  Tractioa 
resistance:  Brick  pavement,  25.4  to  68  lbs.  per  ton.  Asphalt  pavemen*^ 
23.3  to  67.8  lbs.  per  ton. 

Experience  With  Various  Pavements  on  Streets  With  Heavy  Qiadtt 
(By  C.  G.  Anderson.  Paper.  111.  Soc.  of  Engrs.  and  Surv.,  Jan.,  1907. 
Eng.  News,  Mar.  14,  1907). — Illustrated  cross-sections  showing  dlffereai 
styles  of  paving  employed. 

Bituminized  Dirt  Roads  at  Santa  Monica,  Cat.  (Bng.  News.  May  li 
1907). — Illustration  of  latest  type  of  road-tamping  roller. 

Street  Railway  Track  and  Paving  at  Fort  Wayne,  Ind.  (Bng.  News 
June  20,  1907). — Illustrations  of  track  and  paved  streets,  nose  blo^  ios 
street  railway  track,  and  reinforced  concrete  poles. 

Notes  on  Tar  Macadam  (By  C.  P.  Wike,  England;  Eng.  Nevs. 
Aug.  8.  1907). — Initial  cost  of  tar  macadam  roads  in  England  is  abotxt  li 
to  60  cents  per  sq.  yd.,  exclusive  of  foundation:  and  the  annnflj  charge 
(including  initial  cost)  for  a  period  of  14  years  has  averaged  8  cents  pet 
sq.  yd.— down  to  5  cents. 

The  Use  of  T-Ralls  for  Street  Railway  Tracks  In  Cities  (By  C.  G 
Reel.  Paper,  Am.  St.  &  Int.  Ry.  Assn.,  Oct.,  1907;  Eng.  News.  (3ct.  31 
1907). — Illxistrations:  Standard  T-rail  construction  in  Milwaukee;  latest 
construction  in  Kingston,  N.  Y.,  showing  special  brick  outside  of  rail. 

Cost  of  Brick  Pavements  and  Cement  Mortar  Corbs  at  Centervilci* 
Iowa  (By  M.  G.  Hall.    Eng.  News.  April  2,  1908).— Tables  of  costs. 

Cost  of  Oillnf  Roads  in  N.  Y.  State  (Eng.  News,  May  14.  1908).- 
Table  showing  costs  of  experimental  road  oiling,  for  macadam  road,  sand 
road,  and  gravel  road. 

Concrete  Paving  for  Streets  (Eng.  News,  Aug.  20,  1908). — Costs. 
and  illustrated  sections  of  Streets.    Specifications. 

Specifications  and  Notes  on  Macadam  Road  Construction  (By  A.  N. 
Johnson.  Paper,  West.  Soc.  of  Engrs..  Oct.,  1908;  Eng.  News,  Nov.  5> 
1908). 

The  Use  of  Asphaltlc  Flux  for  Coating  Macadam  Roads  mi  Pab 
Alto,  Cal.  (By  J.  F.  Byxbee.  Eng.  News,  May.  13.  1909).— Spccificatkc 
and  description  of  method.  Total  cost  for  material  and  labor,  5i  ^nts  per 
sq.  yd. 

An  "Accelerated  Test**  of  Road  Wear  by  AutomoMle  Traffic  in  Qcrmaay 
(Eng.  News,  July  8,  1909). — Illustrated. 

Method  of  Keeping  Data  Relating  to  Street  Lines  and  Qnules,  In  Broak- 
line,  Mass.  (By  H.  A.  Vamey.  Eng.  News,  July  8.  1909). — Illustnted 
Sample  pages  of  data  sheets. 

Sampittic  Surfacing  (By  W.  W.  Crosby.  Trans.  A.  S.  C.  E.,  Vol.  LXIV.. 
Sept.    1909). — Specifications. 

inverted  Macadam  Road  Construction  (Eng.  Rec.,  Jan.  8.  1010).-- 
Inverted  macadam  road  construction  has  been  adopted  in  a  number  oC 
cases  by  Mr.  A.  N.  Johnson,  highway  engineer  of  Illinois,  as  a  roeans  of 
meeting  conditions  which  obtain  in  many  parts  of  the  State.  The  specifi- 
cations proposed  to  cover  this  method  of  construction  and  the  rcaaona  U^ 
placing  the  fine  material  on  the  bottom  and  the  large  pieces  of  stone  at  tb£ 
top  were  described  in  a  paper  Mr.  Johnson  presented  before  the  Westeit^ 
Soc.  of  Engrs.     This  paper  was  printed  in  the  Eng.  Rec  of  Nov.  7,  1908. 

Vitrified  Clay  Curbing  for  Streets  and  Roads  (En^.  News.  Jan.  1 3, 1 910)  .-^ 
Illustrated.  The  blocks  are  hollow  and  form  contmuous  drains,  ao  that  i^ 
usual  line  of  broken  stone  for  drainage  of  the  roadbed  is  not  required  what 
tms  form  of  curb  is  used.     Has  been  used  for  eight  years  on  the   countn^ 


CHICAGO-CEMENT  WALKS,  STREET  CROWNS.        1148 

road  between  Toledo  and  Calumet,  O.,  and  is  said  to  be*  in  excellent  con- 
dition, showing  practically  no  wear. 

Sidewalk  Practice  in  Chicago  (By  N.  E.  Murray.  Paper  111.  Soc.  Engrs. 
and  Survrs.,  Jan.  26,  28.  1910 j  Eng.  News,  Feb.  17,  idlO).— The  average 
cost  of  cement  walks  laid  in  Chicago  from  1901  to  1908,  inclusive,  based  on 
the  total  cost  ($8,918,278)  divided  by  the  total  mileage  (1802)  was  $4,787  per 
mile,  or  15. 1 1  cents  per  sq.  ft.  This  price  was  for  walks  complete,  includmg 
filling,  which  in  many  instances  was  from  2  ft.  to  6  ft.  in  depth  and  is  not  a 
fair  average  cost  for  the  ordinary  cement  walk.  Average  Chicago  prices 
for  labor  and  material,  give  following  average  cost  of  material  dehvezisd  on 
the  work:  Cinders,  60  cts.  per  cu.  vd.;  cement,  $1.20  per  bbl.  (3.8  cu.  ft.); 
sand,  $1.75  per  cu.  yd.;  gravel,  $1.60  per  cu.  yd.  An  ordinary  concrete 
sidewalk  gang  in  Chicago  is  usually  composed  of  six  men  paid  as  follows  (for 
8  hours):  1  finisher  at  65  cts.,  $6.20;  1  helper  at  47)  cts..  $3.80;  4  laborers  at 
37|  cts.,  $12;  total,  $21.  Assuming  that  this  ^:ang  of  six  men  can  construct 
600  square  feet  of  walk  per  day  (a  fair  assumption,  borne  out  by  experience), 
we  have,  as  total  cost,  13.61  cents  per  sq.  ft.;  thus: — 

Cinders  (20%  shrinkage),  20.83  cu.  yds.  at  60  cts $10.42 

Base.4iin8.  (l:2i:6): 

Cement,  9.77  bbls.  at  $1.20 $11.72 

Sand,  3.47  cu.  yds.  at  $1.76 6.07 

Grnvel.  6.86  cu.  yds.  at  $1.60 10 .  28  28 . 07 

Tleanng  coat,  f-in.  (2:8): 

Cement,  6.56  bbls.  at  $1.20 6.67 

Sand,       1.17  cu.  yds.  at  $1.76 2.04  8.71 

Vatcr,  1  mill  per  so.  ft .60 

^bor.  1  gang  one  day 21 .  00 

Ise  of  tools,  waste  of  material,  etc.,  at  2% 1 .  37 

upt.  and  office  expense,  at  6% 3.61 

'rofitatl0% 7.36 

Total  600  sq.  ft.  at  13.61  cts.  per  sq.  ft $81 .04 

Pavinff  Practice  in  Cliicago  (By  P.  E.  Green.  Trans.  A.  S.  C.  E.,  Vol. 
XVI..  Mar  1910). — Crown  of  roadway:  Chicago  ordinance  calls  for  arc  of 
role,  but  the  parabola  is  mostly  used  in  construction;  the  formula  is  y« 
^-i-a^t  in  which  6— depth  of  gutter  below  grade  of  center  or  roadway, 
■abalf  roadway,  ac— hor.  dist.  from  center  of  roadway,  and  v  — vert.  dist. 
ilovr  the  grade.  Above  formula  applies  to  roadways  up  to  lOO  ft.  and  to 
tvemcnts  having  a  rigid  wearing  surface;  for  wider  roadways,  and  with 
acadam  surfaces,  the  curve  should  approach  a  straight  line  from  center  of 
adway  to  gutters.    The  Rosewater  (Omaha)  formula  for  height  of  crown 

//=.  W'(  100- 4P) +6000,  in  which  H- height  of  crown,  VV"- width  of 
axiway,  and  P— percentage  of  grade;  this  formula  is  best  adapted  to  park 
axis  or  boulevards,  or  for  streets  having  stiff  grades  where  little  crown  is 
ressary.  For  residence  streets  a  good  formula  is  H^Q.02W.  Ulus- 
ktions  of  girder  rail  and  pavement. 

Two  Years'  Experience  in  Dust  Su|»pression  on  New  Jersey  Roads  (By 
mcs  Owen.     Paper  before  State  Sanitary  Assn.,  of  N.  T.;  Eng.  Rec,  Dec. 

1910). — ^Mr.  Owen  records  some  of  his  failures  in  road  construction,  and 
lws  certain  conclusions  as  the  results  of  his  experience:  "In  construction, 
;  no  penetration  of  heavy  oil,  but  construct  the  road  as  of  ordinary  mac- 
itn  and  provide  after  complete  consolidation  of  surface  a  coating  of  46% 

xMsins  about  one-half  gallon  per  sq.  yd.,  and  in  the  maintenance  contract 

tli«  yesLt  provide  for  two  applications  in  that  period.  With  this  practice 
ire  satisfaction  has  been  realized."  It  is  apparent  that  an  ordinary 
cadam  surface,  even  when  oiled,  is  not  satisfactory,  but  satisfaction  hais 
«  obtained  with  various  patent  pavements  as  Amiesite,  Filbertine, 
rrenite  and  what  is  known  as  roaa  asphalt.  These  all  use  the  broken 
ne  with  a  plastic  mixture  injected,  in  most  cases  asphalt.     Cost. — Before 

automobile  era,  the  cost  of  maintaining  a  good  stmace  upon  the  Essex 
I  nty  roads  was  3  cts.  per  sq.  yd.  per  annum.  This  was  increased  in  later 
rs  to  about  6  cts..  and  including  the  oiKng,  amounts  to  6  cts.  The 
:?nt  jjavements  alluded  to  cost  from  80  cts.  to  $1.20  per  sq.  yd.  It  is 
ions  that  those  pavements  must  last  15  to  20  years  to  be-on  theiMime 
jetary  basis  as  ordinary  repairs.  '^^^  by  ^^uuy  le 


1144 


9/i.-^HIGHWAYS. 


Tests  of  Various  Road  Sarfacinff  MateriaU  by  the  OUo  State  Highw^ 
Department  (Bulletin  No.  12.  O.  S.  H.  D.;  Ens.  News,  Nov.  10.  1910).— 
The  following  table  shows  the  wear  on  Nelson  Avenue  experimental  road, 
one  year  after  its  construction: 


Section. 


8  ft. 

4  ft. 

Center 

4  ft. 

East. 

East. 

line. 

West. 

.07  ft. 

.07  ft. 

.00  ft. 

.00  ft. 

.02  ft. 

.07  ft. 

.06  ft. 

.08  ft. 

.07  ft. 

.07  ft. 

.06  ft. 

.03  ft. 

.02  ft. 

.04  ft. 

.04  ft. 

.06  ft. 

.08  ft. 

.04  ft. 

.03  ft. 

.00  ft. 

.01  ft. 

.03  ft. 

.01  ft. 

.03  ft. 

.04  ft. 

.06  ft. 

.06  ft. 

.03  ft. 

.04  ft. 

.04  ft. 

.04  ft. 

.05  ft. 

.06  ft. 

.04  ft. 

.04  ft. 

.05  ft. 

.00  ft. 

.00  ft. 

.02  ft. 

.08  ft. 

.03  ft. 

.00  ft. 

.07  ft. 

.08  ft. 

.04  ft. 

.06  ft. 

.05  ft. 

.01  ft. 

.02  ft. 

.01  ft. 

.03  ft. 

.00  ft. 

.03  ft. 

.01  ft. 

.06  ft. 

.00  ft. 

.04  ft. 

.06  ft. 

.02  ft. 

.00  ft. 

.00  ft. 

.00  ft. 

.00  ft. 

.00  ft. 

.01  ft. 

.08  ft. 

.08  ft. 

.01  ft. 

8ft, 
West. 


1.  Glutin 

2.  Standard  Asphalt . . 

3.  Pioneer  Asphalt .... 

4.  Tarvia"X^' 

6.    Tarvia  "B" 

6.  Indian  Asphalt 

7.  Ugite 

8.  Fairfield  Asphalt . . . 

9.  Asphaltoilene 

10.  Rock  Asphalt 

11.  Carbo-Via 

12.  Concrete  Macadam. 

13.  Taroid 

14.  Petrolithic 

16.  Limestone  Concrete. 

1 6.  Gravel  Concrete 

17.  Water-bound  Mac- 

adam   


.00  ft, 
.09  ft. 
.08  ft 
.03  ft. 
.00  ft 
.02  ft 
.05  ft 
.00  ft 
.03  ft 
.04  ft 
.07  ft 
.00  ft 
.00  ft. 
.00  ft 
.00  ft 
.01  ft 

.01  ft 


Illustrations  and  Specifications. 
Description.  Eng.  New 

Specifications  for  bituminous  concrete  paving  Mar.  17.  'Id 

Specifications  for  sheet  asphalt  pavement  Mar.  17,  '18. 

Specifications  for  concrete  sidewalk,  curbs,  street  pavement       Mar.  17/lOL 
Suggestions  for  street  ijavement  crowns,  with  formulas  May     6,'I8. 

General  plans  for  location  of  street  conduits  and  pipes,  Seattle  May  12,  'Id 
Formulas  for  street  crowns — curbs  at  different  elevations  Jtme  30,  '10. 

Eng.  Rec 
Combined  concrete  and  gutter  in  Salt  Lake  City  Oct.    15,  '10. 

Typical  sections  of  covered  conduits  (10'  x  20')  at  Jones  Palls  Dec     3  '10. 


d  by  Google 


61  .—HYDROSTATICS. 

Hydrostatics,  in  its  brocidest  sense,  treats  of  the  conditions  of  equilibrium 
and  pressure  of  fluids*  at  rest.  As  the  term  "fluid"  comprehends  both 
liqudas  and  gases  our  discussion  will  be  confined  to  the  former,  and  especially 
to  water.  To  the  engineer.  Water  may  be  considered  as  practically  friction' 
less  and  incompressibla.  In  other  words,  we  assume  it  to  be  a  perfect  fluid 
possessing  no  statical  friction;  and  not  subject  to  increased  density  under 
pressure,  to  any  perceptible  degree. t  Prom  this  it  follows  (1)  that  the 
intensity  of  pressxire  (in  lbs.  per  sq.  in.,  or  lbs.  per  sq.  ft.)  at  any  given  point 
in  the  liquid  is  equal  m  all  directions;  (2)  that,  neglecting  the  weight  of  the 
atmosphere  above,  the  intensitv  of  pressure  is  directly  proportional  to 
the  depth  below  the  surface;  (3)  that  the  intensity  of  pressure  is  directly 
proportional  to  the  density  ( —  mass  of  a  unit  of  volume)  or  to  the  weight, 
of  a  unit  volume  of  the  liquid;  (4)  that  the  pressure  is  always  norm^  to 
any  plane,  pressed  siirface;  (5)  that  the  pressure  on  a  curved  surface  may 
be  resolved  into  one  or  more  resultant  pressures  each  acting  normal  to  a 
tangent  plane  projected  on  the  curved  portion. 

The  reader  is  referred  to  the  subject  of  Dams,  pages  846,  etc.,  for  many  of 
:he  elementary  principles  of  hydrostatics  which  bear  particularly  on  that 
nibject,  and  they  will  not  be  repeated  here. 

Atmospheric  Pressure  may  be  neglected  in  most  hydrostatic  calculations 
yec&ixae  its  effects  are  usually  balanced .  For  instance,  the  effect  of  the  atmos- 
)hcric  pressure  on  the  up-stream  water  surface  at  a  dam  exerts  so  much 
xlditional  force  tending  to  overturn  the  structure,  but  it  must  be  remem- 
•ered  that  an  equal  and  opposite  pressure  is  exerted  against  the  down- 
tream  face  of  the  dam,  tending  to  preserve  equilibritim,  and  hence  the 
fTect  is  neutralized!.  The  height  of  the  atmosphere  above  sea  level  is 
ariously  estimated  at  from  40  to  200  miles.  Whatever  the  height  may  be 
is  certain  that,  beginning  with  the  maximum  density  at  sea  level,  it  be- 
>mes  exceedingly  rarefied  above  an  elevation  of  30  to  40  miles.  A  column 
:  air  at  sea  level  will  balance  a  column  of  water  34  ft.  in  height  or  a  column 
'  mercury  2}  ft.  (30  ins.}  in  height,  each  column  exerting  a  pressure  of 
L  7  lbs.  per  sq.  in.  This  is  based  on  a  cubic  ft.  of  water  weighing  about 
1.6  lbs.,  and  the  specific  gravity  of  mercury  at  13.6. 

Atft.  dry.  at  atmospheric  pressure,  and  at  a  temperature  of  56**  P.. 
iighs  exactly  i^  of  a  pound  per  cubic  foot.  (See  Table  of  weight  of  air, 
Lge463.) 

Water  is  77  3  times  as  heavy  as  the  denser  air  at  0**  C.  A  column  of  water 
iq.  in.  in  section  and  1  ft.  high  weighs  about  0.434  lb.;  or.  in  other  words, 
't.  '*head"  corresponds  to  a  "pressure"  of  about  0.434  lb.  per  sq.  in. 
•noe  a  pressure  of  1  lb.  per  sq.  in.  corresponds  to  a  head  of  about  2.304  ft. 
ese  values  should  be  committed  to  memory.) |  Table  No.  1,  following. 
,en  used  decimally  will  give  corresponding  pressures  in  lbs.  per  sq.  in.  for 
y  given  heads  in  ft.,  and  vice  versa. 

*  "Incompressible**  fluids,  only,  are  included  in  the  modem  acceptation 
tlie  term  hydrostatics. 

t  Under  one  atmosphere  (14.7  lbs.  per  sq.  in.)  fresh  water  is  compressed 
0.99905  its  original  volume,  amoujiting  to  an  mcreased  density  of  0.0032 
per  cu.  ft.;  salt  water  to  0.999966  its  original  volume.  Sea  water  one 
e  in  depth  below  the  surface,  equal  to  166  additional  atmospheres  or 
2  lbs.  per  89.  in.,  is  compressed  only  to  0.99996666  its  original  voltime; 
ce  the  additional  166  atmospheres  increases  its  density  only  about  |  of  1% 
re  than  does  one  atmosphere. 

X  This  is  only  partly  true,  as  a  partial  vacuum  is  frequently  formed  at  the . 
rxi -stream  face  when  the  water  is  flowing  over  the  crest  of  the  dam. 
]|  The  refinement  sometimes  employed  by  using  about  62.424  to  62.428 
aa  the  -weight  of  a  cu.  ft.  of  water  at  its  maximum  density,  is  unnecessary 
ordinary  engineering  problems.  The  value  62.6,  used  above,  involves 
rror  of  only  0.6  lb.  pressure  per  sq.  in.  for  a  1000-ft.  head,  equivalent  to 
xZ  Vio  of  1  per  cent  on  the  side  of  safety.    But  see  Tables  3,  4  and  6, 

JJ^g  Digitized  by  VjOOQ  IC 


1146 


Bh— HYDROSTATICS. 


Hydrostatic  Pressure. — ^There  are  two  Pressure  Units  in  general  use  in 
the  United  States,  as  lollows: 

(a)  "Lbs.  per  sq.  in."  corresponding  to  head  in  ft.,  as  given  in  Tables  1,  3 

and  4,  is  used  in  the  design  of  water  pipes,  tanks,  sewers,  etc. 

(b)  "Lbs.  per  sq.  ft."  corresponding  to  head  in  ft.,  is  used  in  the  design  of 

dams.    See  Tables  2  and  5. 
Let  P  —total  pressure  in  lbs.  on  any  submerged  plane  surface: 
f/  —  pressure  in  lbs.  per  sq.  ft. ; 
*^— pressure  in  lbs.  per  sq.  in.; 
n  "=  height  of  column  of  water  or  "head,"  in  ft.; 
a' —area  of  submerged  surface  acted  upon,  in  ft.; 
a'  — area  of  submerged  surface  acted  upon,  in  ins.; 
ti/  — wt.  of  a  column  of  water  1  ft  high  and  1  ft.  sq  ,  in  lbs.  —  62.5  lbs.* 
fi/' — wt.  of  a  column  of  water  1  ft.  high  and  1  in.  sq..  in  lbs.  —  .434  lb. 
Then,  neglecting  atmospheric  pressure  (14.7  lbs.  per  sq  in  ).  we  have, 

p«,i/  a'  A  -  62.6  a'  h  (I) 

"w'  a'  A- .434  a' h       (2) 

f/ -w'  h"  62.6  h (3 

p'-tt/*  ;»- .434  h (4) 

A-^-.Oiep' (5) 

-^-2.304^ («) 

1. — Hbad  and  Prbssurb  Equivalents. — Lb.  per  Sq.  Ik. 
(Water  assumed  at  62.6  lbs.  per  cu.  ft.) 


Head. 

Pressure. 

Pressure. 

Head. 

Feet. 

Lbs.  per  Sq.  In. 

Lbs.  per  Sq.  In. 

Feet. 

1 

0.434 

1 

2.304 

2 

0.868 

2 

4.608 

1.302 

6  012 

1.736 

0.216 

2.170 

11  520 

2.604 

13.834 

3.038 

16.128 

3.472 

18.433 

3.906 

80.736 

10 

4.340 

10 

23  040 

Example. — What  pressure  in  lbs.  Solution.— 

?er  sq.  in.  corresponds  to  a  head  of      (From  above 
04.8  ft.?  table.) 


100-43.4 
4-    1.736 
.8-      .347 


Ans.  46.488  lbs. 

2. — Head  and  Pressure  Equivalents. — ^Lbs.  per  Sq.  Ft. 
(Water  assumed  at  62.6  lbs.  per  cu.  ft.) 


Head. 

Pressure. 

Pressure. 

Head. 

Feet. 

Lbs.  per  Sq.  Ft. 

Lbs.  per  Sq.  Ft. 

Feet. 

1 

62.5 

.016 

2 

126. 

.032 

3 

187.6 

048 

250. 

.064 

312.5 

.080 

376. 

.006 

437.5 

.113 

500. 

.128 

562.5 

.144 

10 

626. 

10 

.160 

Example  —Pressure  correspond- 
*"^i9J^2.4  ft.  hcad-5000+  125+  25 
=-5150lbs.  persq.  ft 


82.4  (. 


. Or.  -62. 5X 

•8°  X  82.4),  by  formula. 


Example. — ^Head  correspoodinjt 
to  pressure  of  1350  lbs.  per  sq.  ft.  " 
16+3.2+.8-20ft. 

Or.  -.016X  1350.  by  fonnula. 


PRESSURES  REDUCED  TO  HEADS.    H.  TO  P.  1147 

P.P. 

8. — Hbad  of  Watbr,  ih  Pb»t  j  ,^'^. 

^  J.      \.  fi    1     -231 

Corresponding  to  »J  2     .491 

GivBN  Prbssurbs  in  Lbs.  Pbr  Sq  In.  ^3    .992 

Note. — ^Weight  of  water  assumed  at  62.424  lbs.  per  cu.  ft.  2  5  l!  153 

ixnmX  point  may  be  moved  simultaneously  to  right  or  left  for  a  <^  1-384 

Pressure  and  Head.  g  J  1.616 

[Head  of  Water,  in  Feet.]  fl  \'^l 

'  t  Unite. 


d  by  Google 


1148  Qh-'HYDROSTATICS. 

P.P. 


4. — Prbssurbs  in  Lbs.  pbr  So.  In.  •*   -^^ 

Corresponding  to 


u 


.MS4 


GiVBN  Hbads  of  Watbr,  in  Pbbt.  ^  J  *1^ 

Note. — ^Weight  of  water  assumed  at  62.424  lbs.  per  cu.  ft.  5  5  !2is$ 

Decimal  point  may  be  moved  simultaneously  to  right  or  left  for  ^  6  .XOi 

Head  and  Pressure.  |  7  .mi 

[Pressiu^  in  Lbs.  per  Sq.  In.]  9  !3§^ 


d  by  Google 


HEADS  REDUCED  TO  PRESSURES.  1140 


6. — Prbssurbs  in  Lbs.  per  Sq.  Ft. 
Corresponding  to 
GiVBK  Heads  op  Watbr,  in  Feet. 
Note.— Weight  of  water  assumed  at  62.424  lbs.  per  cu.  ft. 
Decimal  point  may  be  moved  simultaneously  to  right  or  left  for 
Head  and  Pressure. 
[Pressure  in  Lbs.  per  Sq.  Ft.] 

Head.]  Units. 


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1160  %l.— HYDROSTATICS. 

The  Center  of  Pressure  on  any  submerged  plane  surface  is  the  point  of 
resultant  pressure  on  that  siu^ace.  We  have  explained,  under  Dams,  page 
846,  the  position  of  the  center  of  pressiu-e  on  rectangular  surfaces.  Wc  will 
now  present  a  general  formula  for  finding  the  center  of  pressure  on  any  place 
surface,  and  whether  vertical  or  inclined. 

Ixjt  tb.  Fig.   1,  represent   the   edge   of   a  sub- 
merged plane  figure  of  any  shape  (as  ui-*-.  r^n-^  » 
a  rectangle,  circle,  triangle,  etc.) ;              A      |HOTro«r7aat 
a,  the  angle  which  this  plane  makes  with    >\^\/r        jT 
the  water  siu^ace:                                       ^V* Vv  -     J  i 
Dx,  the  inclined  distance  (ft.)  from  A  to  the         "S  \     ^\u 

center  of  gravity,  or  to  the  horizon-  ^v\  i  •/%--/>/« 

tal  neutral  axis,  of  the  figure  t  b;  '^'\>^^Jf^    ^^ 

Do,  the  inclined  distance  to  the  center  of  ♦''x  j^f^^^ 

pressure;  ^^ 

hx,  the  head  in  feet  on  the  center  of  gravity;  Fig.  1. 

kn,  the  head  in  feet  on  the  center  of  pressure; 
a',  the  area  in  sq.  ft.  of  the  surface  t  b.     Also — 
Let     /x— the  moment  of  inertia  of  the  figure  t  b  about  a  horizontal  neutral 
axis  passing  through  its  center  of  gravity; 
/a -"the  moment  of  inertia  of  the  figure  tb  about  a  horizontal  axis 
passing  through  A, 
^Ix  +  afDx^\ 
5 —  the  statical  moment  about  ^4, 
"a'  Dx\ 

Then  Do -^-      a^D,       ^^ 

And    ho  "■  Do  sin  a  —  — — jy: — —  sin  a (8) 

O  Ux 

Having  obtained  ho  we  can  easily  find  the  total  pressiire  P  from  formulas 
(1)  and  (8);   thus,  making  h  —  ho, 

.(«) 

If  the  submerged  figure  tb'v&  rigid,  the  pressure  P  mav  be  considered  as  a 
resultant  pressure  acting  normal  to  the  surface  tb  9X  the  center  of  pressun 
distant  ho  ft.  vertically  (or  D©  ft.  inclined)  below  the  surface  of  the  water. 
Moreover,  if  the  figure  i  b  is  vertical,  a  —  90^  and  sin  a*"  1  in  equations  (S) 
and  (9);  hence,  Ao"»Do. 

The  practical  application  of  equations  (8)  and  (9)  consists  in  substituting 
the  proper  values  for  /x,  a',  Dx  and  sin  a  in  the  second  members  of  the 
equations.  The  angle  a,  the  distance  A  t,  and  the  shape  and  dimensions  of 
the  figure  t  b  will  usually  be  given;  then  find  1%  and  Dx—At,  from  the  tables 
in  Section  29,  page  524,  etc. 

Problem. — Let  t  b  represent  the  section  of  a  triangular  plane  of  altitude 
f  &  -B  1 2  ft.  and  horizontal  base  at  bottom  6  »  8  f t.  Let  it  be  submexKed  so 
that  At— 10 ft.,  and  a  — 60**.  Find  the  head  ko on  the  center  of  pressure? 
Find  the  total  pressure  P? 

Solution.— From  Table 6,  next  page,  we  deduce  /«-  8X  ^-~-  -  S84.  and 

3d 

Dx'=-10-»-iXl2-18.  Area  of  triangle  a* -12X4- 48;  sin  a- 0.866.  Then, 
(8).  Ao-^^^^^^Yp^X0.866-18ax0.866-15.973  ft.;  and  P-62.5X48X 

15.973-47,919  lbs.    Ans. 

Any  other  shaped  figure  may  be  treated  in  the  same  manner.  The 
center  of  pressure  will  always  be  found  below  the  center  of  gravity  of  the 
figure. 

If  the  figure  <  6  is  a  rectangle,  in  a  vertical  plane,  and  with  the  top  t  at  A. 
3«st  touching  the  surface  of  the  water,  then  Do— A©— I  ib  (Fig.  1). 

The  position  of  the  center  of  pressure  is  essential  in  designias  laxge 
hydraulic  gates,  valves,  etc. 


P-  62.5  a'  A  -62.5  a'  /to- 62.5  (^'^^^^'*)  ^  «• 


Digitized 


by  Google 


CENTER  OP  PRESSURE, 


115 


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5.^ 


20 


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^      ^      ^ 

by  Google 


1152 


61.— H  YDROSTA  TICS. 


Pretsure  in  Pipes,  Tanks,  etc. — In  Pig.  2,  let  A  be  the  total  head  in  ft, 

at  any  level,  on  each  diameter  d  of  sections 

i4,  B.  and  C.    A  is  a  water  pip«  leading 

from  the  water  tank  B,  which  in  turn  is 

connected  by  the  tube  t  with  the  tank  C 

through  the  vertical  tube  T.  Then  it  follows 

that  the  water  surfaces  in  B  and  T  must 

remain  at  the  same  level.    From  formulas 

(3)  and  (4)  we  have  for  either  section  A,  B 

or  C,  at  a  depth  h  below  the  surface: 

Pressing  in  lbs.  per  sq.  ft.    —   62.6  h\  _.     ^ 

Pressure  in  lbs.  per  sq.  in.   —    .434  h,  '*•  *• 

If  d'  — the  diameter  in  feet,  and  d'—the  diameter  in  inches,  then  A^  B 

and  C  will  each  have  to  resist  a  bursting  pressure  of  62.5  h  d'  lbs.  per  lin.  ft.. 

or  .434  h  ^  lbs.  per  lin.  in.  of  pipe  or  tank;   and  900!%  sid€  would  have  to 

resist  ang-half  that  pressure. 

The  combination  of  the  tube  T  inserted  in  the  tank  C  (with  t  omitted) 

illustrates  what  is  called  the  "hydrostatic  paradox."  The  unit  pressure  at  d 

due  to  the  head  h  remains  the  same  no  matter  what  the  diameter  of  T. 

Clearly,  the  diameter  of  T  does  not  affect  the  unit  pressure;   the  height  k 

does.    Thus,  a  heavy  cask,  as  C.  may  be  made  to  burst  if  even  a  small  tube, 

as  r,  is  filled  with  water  so  as  to  give  the  required  bursting  head. 

Flotation. — ^The  weight  of  a  substance  is  proportional  to  its  densitj: 
and  the  relative  density  of  a  substance,  referred  to  water,  is  called  itsspecinc 
gravity.*  Hence,  of  two  substances  of  equal  weight,  that  one  having  the 
least  volimie  has  the  greater  specific  gravity.  As  the  voltime  of  a  body  is 
affected  by  heat,  it  follows  that  the  specific  gravity  of  substances  decreases 
with  a  rise  in  temperature,  the  formation  of  ice  bein^  a  phenomenal 
exception  to  this  law.  Pure  water  at  4**  C.  its  maximum  density,  is 
assumed  to  have  a  specific  gravity  of  1;  and  all  other  substances,  at  (rC, 
are  referred  to  that  standard.  A  porous  substance  will  increase  in  density 
by  absorbing  water;  thus,  water-soaked  logs  is  an  instance  of  this  kind. 

Any  solid  with  specific  gravity  greater  than  tmity  will  sink;  if  less  than 
tmity  it  will  float.  Any  floating  body,  whether  solid  or  not,  will  displace  a 
volume  of  water  whose  weight  is  equal  to  the  weight  of  the  body;  if  the 
body  sinks,  the  weight  of  the  volume  of  water  displaced  wiU  be  less  than 
that  of  the  body. 

The  Depth  of  Flotation  depends  upon  the  specific  gravity  of  the  body,  if 
solid;  upon  the  av9Tag$  specific  gravity  of  the  volume,  if  hallow;  and  upon 


WatSL 


SUffKd, 


the  surface  form  of  the  body.     Assuming  the  average  specific  gravity  of 
volume  to  be  less  than  unity,  let  d —  depth  of  flotation. 

5 —  average  specific  gravity  of  volume  of 
body; 
then  for  any  rod.  bar.  tube,  cylinder,  etc.,  of  tmiform  cross-section  and  of 
length  i,  floating  vertically, 

d-sl (10) 

For  the  same,  if  lying  horisontal,  d  can  be  obtained  bv  fixing  the  water  sur- 
fac'e  on  the  end  section  at  such  elevation  (Fig.  3)  that 

^ shaded  area  below  water  surface  ^-jv 

total  area  of  the  section 

Buoyancy. — Let  Figs.  4,  6  and  6  represent  oval  sections,  and  Pig.  7  a 
circular  section,  of  any  body  floating  in  water,  with  the  surface  at  5; 
then — 

Stable  equilibrium  is  represented  by  Pig.  4, 

Unstable  equilibrium,  by  Fig.  6; 

Neutral  eqiiilibrium,  by  Fig.  7. 


*  For  discussion  of  Specific  Gravity,  see  page 


frzefSObogle 


PRESSURE.    FLOTATION.' BUOYANCY. 


1153 


The  position  in  Fig.  5  can  obtain  only  when  some  outside  force  is  applied, 
as  will  be  seen  from  the  following  discussion:  The  center  of  buoyancy  B  in 
each  figure  below  is  the  center  of  gravity  of  the  displaced  water;  and  G^is  the 


Pig.  4. 


Pig.  5. 


Eig.«. 


Pig.  7. 


center  of  gravity  of  the  body.  Then,  as  long  as  G  and  B  are  in  the  same 
vertical  line  there  is  some  kind  of  equilibrium,  as  stable,  unstable,  or  neutral, 
becMise  the  resultant  downward  weight  of  the  body,  acting  in  a  vertical 
line  pcusing  thxotigh  its  center  of  gravity  G,  must  be  equal  and  opposite  to 
the  resultant  upward  pressure  R  otthe  water  below  the  body.  Furthermore, 
the  upward  resultant  pressure  R  will  not  be  changed  in  position,  direction  or 
amount  if  we  imagine  the  bodv  to  be  removed  from  the  "depression"  in  the 
water  and  that  depression  refilled  with  the  displaced  water;  for  equilibrium 
would  be  maintained  by  the  equal  weight  of  the  displaced  water,  its  re- 
sultant passing  vertically  through  its  center  of  gravity  B.  Hence  if  /?, 
acting  vertically,  is  equal  and  opposite  to  the  resultant  weight  of  the  body 
and  also  to  the  displaced  water,  acting  through  their  respective  centers  of 
gravity  G  and  B.  then  it  follows  that  G  and  B  are  in  the  same  vertical  line 
when  the  body  is  in  equilibrium. 

The  equilibrium  of  a  floating  bodv  may  be  tested  by  noting  the  position 
of  the  *'mctacenter"  M  when  the  body  is  slightly  disturbed  in  any  direction 
from  a  position  of  rest.    (Af  is  the  intersection  of  the  "equilibrium  axis" 
a^a  with  a  vertical  through  B.): 
<a)     When  M  rises  above  G  it  indicates  that  the  body  was  in  stable  equili- 

britim. 
^)     When  Af  falls  below  G  it  indicates  that  the  body  was  in  unstable  equili- 
brium. 
'c)     When  Af  coincides  with  G  it  indicates  neutral  equilibrium. 

In  the  above.  Pig.  5  shows  that  Pi^.  4  is  in  stable  equilibrium.    In  the 
Azne  way  it  can  be  proved  that  Pig.  6  is  tmstable,  and  Pig.  7  neutral. 

The  tollowing  rules  apply  not  only  to  floating  bodies  but  to  supported 
Mxlie*  in  general. 
1)     A  body  is  im  stable  equilibrium  when  a  slight  change  tends  to  raise  its 

center  of  gravity; 
3)     A  body  is  in  unstable  equilibrium  when  a  slight  change  tends  to  lower 

its  center  of  gravity: 
Sy     A  body  is  in  neutral  equilibrium  when  a  slight  change  neither  raises  nor 
lowers  its  center  at  gravity. 


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62— HYDRAULICS. 

Hydraulics  embraces  the  application  of  the  principles  of  both  hydio- 
sUtics  and  hydrokinctics;*  for  a  fluid  at  rest,  as  treated  by  hydrostatics, 
is  but  the  lower  limit  of  a  condition  of  motion.  It  therefore  treats  of  the 
laws  governing  the  pressure,  flow  and  energy  of  water  (and  other  Uqoids) 
with  the  accompanying  phenomena.  These  laws,  however,  are  but  impo^ 
fectly  imderstood  and,  like  all  other  branches  of  enginecrmg.  hydraulics  a 
not  an  exact  science.  Theoretical  hydratilics  assumes  no  loss  of  energy 
during  the  flow,  a  condition  which  can  never  obtain  in  practice:  but  its 
great  value,  in  the  investigation  of  any  problem,  lies  m  fixing  the  upper 
limit  of  efficiency  which  can  ever  be  expected.  Practuxil  hydraxalics  is 
founded  on  theoretical  hydraulics,  but  takes  into  consideration  the  Josses  ot 
energy  during  the  flow.    These  losses  are  deduced  from  expemncnts. 

Theory  of  Flow. — Under  hydrostatics  we  have  discussed  the  relation 
between  the  static  head  h  and  the  pressure  p  of  stfll  water.  In  hvdiaulk 
computations  it  is  convenient  to  reduce  all  pressures,  velociti^  and  kMaes  of 
every  description  to  equivalent  heads  and  losses  of  head.  Moreover,  the 
unit  of  pressure  used  is.  m  English  units,  the  "lb.  per  sq.  in.  Thus,  reCerrxcE 
psirticularly  to  a  pipe  line,  we  have: 

p- pressure  in  lbs.  per  sq.  in.  -0.434  Ju;         ^  ^.  ^ 

H— hydrostatic  head,  or  simply  static  head ->  2.304  p; 

h,  -  entry  head,  or  loss  of  head  at  entry ; 
A -velocity  head,  or  head  due  to  velocity  at  given  section:     ^ 

*.  — "velocity  of  approach"  head,  or  gain  in  head  a  given  section  due  to 
velocity  of  approach  above  the  given  section; 

Af-frictionhead,  or  loss  of  head  due  to  friction;     .     ^     ^. 

A,  —  "suction"  head,  or  head  due  to  suction,  acting  m  the  direction  of  the 

h  -"curvature"  head,  or  loss  of  head  due  to  curves  or  bends; 
A- -pressure  head,  or  head  due  to  the  resultant  pressure  at  a  given  sec- 
tion (i.  e.,  piezometer  head);  .        t       .' 
h  .-"expansion  head,"  or  loss  of  head  due  to  expansion  of  section; 
Ak-  "contraction  head,"  or  loaa  of  head  due  to  contraction  of  section: 

A, -total  loss  of  head  above  a  given  section.  .  v    *i. ^ 

Then,  using  the  same  sub-notation  for  the  velocity,  we  have,  by  theory: 

V-theoretwvelocityduetoH.or  V«-2«H;  t».»-2f  A.; 

^.2^  A:  v.«-2«A.;  ^'I'-^i''^  K'^'i' 

tn«-  2g  Ai;  in  which  the  gravity  acceleration  ^-  32.16.  and  V2f-8ay  8.01 

Considering  the  gains  and  losses  in  the  pipe  line,  the  following  relatioas 

exist: 

Gains 


Pres.   Stat.   Appr.   Suet.     Veloc.    Entry     Fric.     Curv.     Expan.   Contr. 
A,  -  H   +  A.   +   A.  -     A     -    (A.  +    At    +     A,  +    A.    -I-    AO  ..a) 
V*       V«_^    t;.«       «.«       J?.    _  /E2!  +  Ei!    +    Hi!   +  ^    +  ?^  .    (2. 

t"  Tg^  Tg-^H-H     U^  2«  ^   a«  ^  Jte  ^  u)"'' 

If  we  neglect  the  velocity  of  approach  and  the  suction  haijd.  and  let  k 
represent  the  losses  in  head  (mostly  friction),  equations  (1)  and  (2)  reduce  to 

A,  -H  "h  -M (^ 

vl    V^  ^ii  _£»!         (4) 

2«"2«  2«  2g 

Combining  (3)  and  (4),  we  have  the  general  equation  (5).  followinjr. 

*  The  term  hydrodynamics  was  formerly  defined  as  the  science  whkh 
treats  of  the  motion  of  liquids  (now  included  under  hydrokinetics).  but  tt  now 
has  a  brx>ader  acceptation:  The  science  which  treats  erf  the  laws  of  forw  as 
applied  to  fluids.    Hence  it  comprises  hydrostatics  and  bydxokiiMtKS. 


1154 

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THEORETIC— FLOW \  VELOCITIES  FOR  HEADS  H.       1166 


loclty  and  Discharge. — ^The  velocity  of  dischai^e  v  at  any  section 

2  obtained  from  equation  (1),  by  substituting  r-  for  h^  and  trans- 
as  follows:  ^* 

»- n/2^  (//-Ap -Ai) (6) 

ressure  head  A,  equals  zero  for  any  given  section,  and  we  also  assume 
«  h,  then  

V''V2iH  -8.02V77 (6) 

following  is  a  table  of  theoretic  velocities  for  various  heads,  calcu- 
om  equation  (6).    See,  also,  table  on  page  283. 
'hborbtic  Vblocities  V  POR  Various  Heads  h.    (Equation  6.) 


Ill 

¥ 

1^1 

¥ 

1^ 

i'A 

1^ 

ih 

I' 

II* 

.57 

.37 

488 

.93 

7.73 

3.1 

14  1 

18.5 

34.6 

68 

66.1 

.80 

.38 

4.94 

.94 

7.78 

3.2 

14.3 

19.0 

35  0 

69 

66.6 

.98 

.39 

5.01 

.95 

7.82 

3.8 

14.6 

.5 

35.4 

70 

67.1 

1.13 

.40 

6.07 

.96 

7.86 

3.4 

14.8 

20.0 

36.9 

71 

67.6 

1.27 

.41 

6.14 

.97 

7.90 

3.5 

15.0 

.6 

86.3 

72 

68.0 

1.39 

.42 

6.20 

.98 

7.94 

3.6 

15.2 

21.0 

36.8 

73 

68.5 

1.50 

.43 

6.26 

.99 

7.98 

3.7 

15.4 

.5 

37.2 

74 

69.0 

1.60 

.44 

6.32 

1.00 

8.02 

3.8 

15.6 

22.0 

37.6 

75 

69.5 

1.70 

.45 

6.38 

1.02 

8.10 

3.9 

16.8 

.6 

38.0 

76 

69.9 

1.79 

.46 

6.44 

1.04 

8.18 

4.0 

16.0 

23.0 

38.5 

77 

70.4 

1.88 

.47 

5.60 

1.06 

8.26 

.2 

16.4 

.5 

38.9 

78 

70.8 

1.96 

.48 

5  56 

1.08 

8.33 

.4 

16.8 

24.0 

39.3 

79 

71.3 

2.04 

.49 

5.61 

1.10 

8.41 

.6 

17.2 

.6 

39.7 

80 

71.7 

2.12 

.50 

6.67 

1  12 

8.49 

.8 

17.6 

25 

40.1 

81 

72.2 

2.19 

.51 

5.73 

1.14 

8.56 

5.0 

17.9 

26 

40.9 

82 

72.6 

2.27 

.52 

5.78 

1.16 

8.64 

.2 

18.3 

27 

41.7 

83 

73.1 

2  34 

.53 

6.84 

1.18 

8.71 

.4 

18.6 

28 

42.4 

84 

73.6 

2.41 

.54 

6.89 

1.20 

8.79 

.6 

19.0 

29 

43.2 

85 

73.9 

2.47 

.65 

6.95 

1.22 

8.86 

.8 

19.3 

30 

43.9 

86 

74.4 

2.54 

.56 

6.00 

1.24 

8.93 

60 

19.6 

31 

44.7 

87 

74.8 

2.60 

.57 

6.06 

1.26 

9.00 

.2 

20.0 

32 

45.4 

88 

75.2 

2.6« 

.68 

6.11 

1.28 

9.07 

.4 

20.3 

33 

46.1 

89 

75.7 

3.72 

.69 

6.16 

1.30 

9.14 

.6 

20.6 

34 

46.8 

90 

76.1 

2.78 

.60 

6.21 

1.32 

9.21 

.8 

20.9 

35 

47.4 

91 

76.6 

3.84 

.61 

6.26 

1.34 

9.28 

7.0 

21.2 

36 

48.1 

92 

76.9 

2.89 

.62 
.63 
.64 

6.31 

1.36 

9.36 

.2 

21.5 

37 

48  8 

93 

77.3 

2.95 

6.37 

1.38 

9.42 

.4 

21.8 

38 

49.4 

94 

77.8 

3.00 

6.42 

1  40 

9.49 

.6 

22.1 

39 

50.1 

95 

78.2 

3.05 

.65 

6.47 

1.42 

9.56 

.8 

22.4 

40 

60.7 

96 

78.6 

3.11 

.66 

6.52 

1.44 

9.62 

8.0 

22.7 

41 

61.4 

97 

79.0 

3.16 

.67 

6.56 

1.46 

9.69 

.2 

23.0 

42 

62.0 

98 

79.4 

J.21 

.68 

6.61 

1.48 

9.76 

.4 

23.3 

43 

53.6 

99 

79.8 

).2« 

.69 

6.66 

1.50 

9.82 

.6 

23.5 

44 

53.2 

100 

80.2 

1.31 

.70 

6.71 

1.52 

9.89 

.8 

23.8 

45 

53.8 

110 

84.1 

»  35 

.71 

6.76 

1.54 

9.95 

9.0 

24.1 

46 

54.4 

120 

87.9 

1.40 

.72 

6.80 

1.56 

10.02 

.2 

24.3 

47 

55.0 

130 

91.4 

1.45 

.73 

6.85 

1.58 

10.08 

.4 

24.6 

48 

55.6 

140 

94.9 

50 

.74 

6.90 

1.60 

10-14 

.6 

24.8 

49 

66.1 

150 

98.2 

.54 

.75 

6.95 

1.65 

10.30 

.8 

25.1 

50 

56.7 

175 

106.1 

.5» 

.76 

6.99 

1.70 

10.46 

10.0 

25.4 

51 

67.3 

200 

113.4 

.68 

.77 

7.04 

1.75 

10.61 

.5 

26.0 

52 

57.8 

225 

120.3 

.76 

.78 

7.08 

1.80 

10.76 

11.0 

26.6 

53 

58.4 

250 

126.8 

.85 

.79 

7.13 

1.85 

10.91 

.5 

27.2 
27.8 

54 

58.9 

275 

133.0 

.93 

.80 

7.17 

1.90 

11.05 

12.0 

56 

69.5 

800 

138.9 

01 

.8! 

7.22 

1.95 

11.20 

.5 

28.4 

66 

60.0 

335 

144.6 

09 

.82 

7.26 

2.00 

11.34 

13.0 

28.9 

67 

60.6 

350 

150.0 

17 

.83 

7.31 

2.10 

11.63 

.5 

29.5 

58 

61.1 

375 

155.3 

24 

.84 

7.35 

2.20 

11.90 

14.0 

30.0 

59 

61.6 

400 

160.4 

33 

.85 

7.89 

2  30 

12.16 

.5 

30.5 

60 

62.1 

450 

170.1 

39 

.86 

7  44 

2.40 

12.43 

15.0 

31.1 

61 

62.6 

500 

179.3 

47 

.87 

7.48 

250 

12  68 

.5 

31.6 

62 

63.1 

550 

188.1 

54 

.88 

7.52 

2.60 

12.93 

16.0 

82.1 

63 

63.7 

600 

196.4 

61 

.89 

7.57 

2  70 

13.18 

.6 

32.6 

64 

64.2 

700 

212.2 

S9 

.90 

7.61 

2.80 

13  43 

17.0 

33.1 

65 

64.7 

800 

226.8 

A 

.91 

7  65 

2.90 

13.66 
13.89  1 

.6 

33.5 

66 

65. 2 

900 

240.6 

.93 

7.69 

3.00 

18.0 

34.0 

67 

65.6 

1000 

253.6 

1166  62.— HYD/MC/L/CS. 

The  theoretic  velocity,  therefore,  is  the  same  as  that  which  woold  be 
acquired  by  the  water  (or  any  other  body)  falling  freely  in  vacuo  through 
the  height  H.    Also,  from  equation  (6),  we  have 

//-.0l556i;» (7) 

The  Dischargg  through  a  pip€,  when  the  velocity  is  known,  is  obtaxned 
from  the  following  simple  formula: 

q^av (8) 

In  which  9« discharge  in  cu.  ft.  per  ♦sec.; 

a » area  of  cross-section  of  flowing  water,  in  sq.  ft.; 
v  —  mean  velocity  of  flow,  in  ft.  per  sec. 
Then,  from  (8)  and  (6)  we  have,  for  any  practical  case, 

q  =  8.02 a VH-h    -A, (§) 

which  takes  into  consideration  all  the  losses  of  head.  If  there  are  no  kisses 
in  head,  and  no  pressure  head  at  the  section  considered,  then  we  have  for 
the  theoretical  discharge,  since,  A,  ==  0,  Ai  —  0, 

(7- 8.02  a  VH (10) 

in  which  8.02  VH  is  the  theoretic  velocity  (equation  6)  whose  values  are 
given  in  Table  1,  preceding. 

tTable  2,  following,  gives  the  areas  of  pipes  in  square  feet  for  various 
diameters  in  feet  and  inches: 

Problem  1. — What  is  the  least  diameter  of  pipe  that  could  possibly  be 
used  for  discharging  300  cubic  ft.  per  sec.  tmder  a  14-ft.  head? 

Solution. — Neglecting  friction  and  other  losses  we  have  from  Table  1, 
page  1166,  that  the  theoretic  velocity  is  30  ft.  per  second.    Without  the  use 

of  any  formula t  we  know  that  the  area  of  pipe  required  ■»  -=■  —  10  sq.  ft.: 

and,  from  Table  2,  page  1157,  the  corresponding  diameter  is  3  ft.  61  ins. 
Hence,  we  know  that  the  diameter  would  have  to  be  larger  than  3  ft.  Of  ins. 
to  take  care  of  the  friction-  and  other  losses.  ■ 

In  practice,  after  a  pipe  has  been  properly  designed  to  meet  the  con- 
ditions of  the  problem  and  take  care  of  all  losses  of  head,  it  is  customary  to 
increase  the  diameter  of  the  pipe  somewhat:  (1)  to  provide  for  future  in- 
creased demands  on  the  supply,  and  (2)  to  anticipate  the  roughening  of  the 
inner  surface  of  the  pipes  irom  rust  or  vegetable  growth.  Sewer  pipes  axe 
increased  usually  about  2  ins.  in  dia.;  water  mains,  about  the  same;  and 
small  pipes,  10  to  60%  in  area. 


*  To  find  cubic  feet  per  minute,     multiply  a  by  60 

^'     hour,  ••        ^  8.600 

"     24  hours,         "         "  86,400 

••     30  days,  "         "        3.692.000 

"  366  days,  "        "       31,636,000 

I  <TOfi         Ji7A 

To  reduce  cubic  feet  to  gallons,  multiply  by  "oqT"*  7v  ii    ■"7. 48052- 
t  See,  also,  tables  of  circles,  pages  230-236. 
X  Or,  from  equation  (6),  9«a  v,  we  have  a--  —  — -jg-. 


d  by  Google 


PIPES^DISCHARGE;  DIAMETERS  TO  AREAS. 


1157 


2.~Arbas  of  Pipes  in  Sq.  Pt.  for  Diambtbrs  in  Pbbt  and  Inches. 


Diam- 
eter. 

Fraction  of  ao 

Inch. 

Ftlu 

i 

" 

i 

I 

0     0 

0 

.000085 

.00034 

.00077 

.00137 

.00213 

.00307 

.00418 

.00545 

.00690 

.00852 

.0103 

.0123 

.0144 

.0167 

.0192 

.0218 

.0246 

.0276 

.0308 

.0341 

.0376 

.0412 

.0451 

.0491 

.0533 

.0576 

.0621 

.0668 

.0717 

.0767 

.0819 

.0873 

.0928 

.0985 

.1044 

.1104 

.1167 

.1231 

.1296 

.1364 

.1433 

.1503 

.1575 

.1650 

.1726 

.1803 

.1883 

.1964 

.2046 

.2131 

.2217 

.2304 

.2394 

.2485 

.2578 

.2673 

.2769 

.2867 

J967 

.3068 

.3171 

.3276 

.3382 

.3491 

.3601 

.3712 

.3826 

.3941 

.4056 

.4176 

.4296 

.4418 

.4541 

.4667 

.4794 

.4922 

.5053 

.5185 

.5319 

.5454 

.5591 

.5730 

.5871 

.6013 

.61.57 

.6303 

.6450 

.6600 

.6750 

.6903 

.7057 

.7213 

.7371 

.7530 

.7691 

1     0 

.7854 

.8019 

.8185 

.8352 

.8522 

.8693 

.8866 

.9041 

.9218 

.9396 

.9575 

.9757 

.9940 

1.013 

1.031 

1.050 

1.069 

1.088 

1.108 

1.127 

1.147 

1.167 

1.187 

1.207 

1.227 

1.247 

1.268 

1.289 

1.310 

1.331 

1.353 

1.374 

1.396 

1.418 

1.440 

1.462 

1.485 

1.507 

1.530 

1.653 

1.576 

1.599 

1.623 

1.646 

1.670 

1.694 

1.718 

1.742 

1.767 

1.792 

1.817 

1.842 

1.867 

1.892 

1.917 

1.943 

1.969 

1.995 

2.021 

2.047 

2.074 

2.100 

2.127 

2.154 

2.182 

2.209 

2.237 

2.264 

2.292 

2.320 

2.348 

2.376 

2.405 

2.4.34 

2.463 

2.493 

2.521 

2.550 

2.580 

2.610 

2.640 

2.670 

2.700 

2.730 

2.761 

2.792 

2.823 

2.854 

2.885 

2.916 

2.948 

2.980 

3.012 

3.044 

3.076 

3.109 

2      0 

3.142 

3.174 

3.207 

3.240 

3.274 

3.307 

3.341 

3.375 

8  409 

3.443 

3.477 

3.512 

3.547 

3.581 

3.616 

3.651 

3.687 

3.722 

3.758 

3.794 

3.830 

3.866 

3.903 

3.939 

3.976 

4.013 

4.050 

4.087 

4.125 

4.162 

4.200 

4.238 

4.276 

4.314 

4.353 

4.391 

4.430 

4.469 

4.508 

4.547 

4.587 

4.626 

4.666 

4.706 

4.746 

4.786 

4.827 

4.868 

4  909 

4.950 

4.991 

5.032 

5.074 

6.115 

6.157 

5.199 

6.241 

5.283 

5.326 

5.369 

5.412 

5.455 

5.498 

5.541 

6.585 

5.629 

5.673 

6.717 

5.761 

5.805 

6.850 

5.895 

5.940 

5.985 

6.030 

6.075 

6.121 

6.167 

6.213 

6.259 

6.305 

6.351 

6.398 

6.445 

6.492 

6.539 

6.586 

6.633 

6.681 

6.729 

6.777 

6.825 

6.874 

6.922 

6.971 

7.020 

3      0 

7.069 

7.118 

7.167 

7.216 

7.266 

7.316 

7.. 366 

7.416 

7.467 

7.517 

7.568 

7.619 

7.670 

7.721 

7.773 

7.824 

7.876 

7.928 

7.980 

8.032 

8.084 

8.137 

8.190 

8.243 

8.296 

8.349 

8.403 

8.456 

8.510 

8. 564 

8.618 

8.672 

8.727 

8.781 

8.836 

8.891 

8.946 

9.001 

9.057 

9.112 

9.168 

9.224 

9.280 

9.336 

9.393 

9.450 

9.507 

9.664 

9.621 

9.678 

9.736 

9.794 

9.8.52 

9.910 

9.968 

10.026 

10  085 

10.144 

10  203 

10.262 

10.321 

10.380 

10.440 

10.499 

10.559 

10.619 

10.680 

10.740 

10.801 

10.862 

10.923 

10  984 

11.045 

11.106 

11.168 

11.229 

11.291 

11.3.53 

11.416 

11.478 

11.541 

11.604 

11.667 

11.730 

11  793 

11.856 

11.920 

11.984 

12.048 

12.112 

12.177 

12.241 

12.306 

12.371 

12.436 

12.501 

1       0 

12.566 

12.632 

12.698 

12.764 

12.830 

12.896 

12.962 

13.028 

13.096 

13.162 

13.229 

13.296 

13.364 

13.431 

13.499 

13.567 

13.636 

13.703 

13.772 

13.840 

13.909 

13.978 

14.047 

14.116 

14.186 

14.256 

14.326 

14.396 

14.466 

14.536 

14.606 

14.677 

14.748 

14.819 

14.890 

14.962 

15.033 

15.105 

15.176 

15.249 

15.331 

15. 393 

15.465 

15.538 

15.611 

15.684 

15.758 

15.831 

15.904 

15.978 

16.052 

16.126 

16.200 

16.274 

16.349 

16.424 

16.499 

16.574 

16.649 

16.724 

16.800 

16.876 

16.952 

17.028 

17.104 

17.181 

17.2.57 

17  .334 

17  411 

17.488 

17.565 

17.643 

17  721 

17.799 

17.876 

17.954 

18.033 

18.111 

18.190 

18.269 

10 

18  348 

18.427 

18  •■,06 

18  ^96 

18  665 

18  745 

18.826 

18.906 

" 

18.986 

19.067 

19.147 

19.228 

19.309 

19.390 

19.472 

19.553 

Note. — ^Areas  of  pipes  are  proportional  to  the  squares  of  their  diameters. 

CxAxnple. — ^The  area  of  pipe  2f  6'  in  dia.  =-  4.909  sq.  ft.  Then,  for  a  pipe 
(T'dia..  0-4.909x4;  for  7' 6' dia..  a  =  4.909X9;  for  lO' 0*  dia..  a -4.909 
lU:   etc.      See,  also,  Tables  13-15,  pages  230-236. 


1168  %2.—HYDRAUUCS. 

Velocity  inveriely  proportional  to  a  and  to  d*. — When  a  pipe  of  -variabk 
cross-section  is  discharging  a  constant,  ftill  volume  of  water,  as  per  Pig.  1« 
we  have, 

g«,at;  — Oi  Vi—aaVa^-aaVa,  etc (11) 

But  a  - -T- :  oi  - -4^  ;  aa--7^  :  etc.   Then^--^v--^Vi--^vj.etc.(12) 


Fig.  1. 

Whence  v-— ;  V|-  — ;         ©a-— ;etc (13) 

a  Oi  as 

O'-  «-^=    "'-^y-  "'-rl?:'*' (»«) 

In  which  q     —discharge  in  cubic  feet  per  second; 
d,  di,  ^2.  ''a       —diameter  of  pipe  in  feet  at  different  sections; 
o.  <3i.  ^Zt  ai^^area  of  pipe  in  sq.  ft.  at  sections  d,  di,  d2,  d^; 
V,  Vi.  Vs,  vs  —velocity  of  flow  in  ft.  per  sec.  at  sections  a,  Ot,  a^,  a^; 

X- 3.1416;  J-  0.7864. 

It  is  to  be  noted  that  the  above  formulas  represent  the  practical  rela- 
tions which  may  exist  in  any  pipe  line  regardless  of  friction  and  loss  of  head. 
These  formulas  may  be  transposed  in  various  ways.  If  it  is  desired  to 
substitute  the  "head"  of  water  in  place  of  the  velocity  we  must  be  careful 
to  use  the  velocity  head  k  and  not  the  static  head  H.  Thus,  from  (6),  (13) 
and  (14)  we  have 

qr-^X  8.02 Va"  -  6. 298908  d»  \/T (16) 

4   

whence  <i-2^/ ^-7^  -0.3984 -r^ (16) 

\  8.02  irVT  Vk 

and  if  all  friction  and  other  losses  are  neglected,  h'^H, 

and  d^2J ^-—r -0.3984^ (17) 

\8.02,rVH  Vh 

Hence  it  is  seen  that  the  diameter  of  the  pipe  is  directly  proportional 
to  the  square  root  of  the  discharge,  and  inversely  proportional  to  the  foxirth 
root  of  the  "head."     Solving    Problem  1    by    eqtiation  (14),  we    obtain 

rf- 0.3984^^^-3.67  ft. -3  ft.  6|  ins. 
</l4 
We  will  now  take  up  the  question  of  "losses"  of  energy,  head  and 
pressure,  which  occur  during  flow. 

Losses  During  Flow. — In  the  following  discussion  reference  is  made  to 
Fig.  2,  showing  water  discharging  from  the  upper  reservoir  U.  R.,  throogfa 
the  pipe  line  o  d,  into  the  lower  reservoir  L.  K. 

o  — orifice,  intake  or  inlet  end  of  pipe,  at  which  a  gate  is  placed; 
(i  — discharge  end,  or  outlet  of  pipe,  at  which  a  gate  is  placed; 
t  V  r— Venturi  water  meter,  inserted  in  the  pipe  line  for  measuring 
the  discharge; 
V  — Venturi  itself,  or  the  contracted  section  of  the  meter; 
t  or  c  — contracted  section  of  the  pipe  line; 
T  or  r— expanded  section  of  the  pipe  line; 
6  — bend  in  the  pipe  line. 
During  flow,  loss  of  head  will  occur  at  all  these  points;  and  throusbouC 
the  whole  line,  due  (1)  to  the  friction  of  the  water  along  the  sides  of  the 
pipe,  and  (2)  to  the  lateral  or  radial  forces*  set  up  by  the  impingement  o5 

•  Usually  termed  viscosity.  °  ^  '^^^  ^'  GoOglc  | 


FLOW  IN  PIPES-VELOCITIES  AND  LOSSES. 


1160 


tke  water  particles  against  each  other  in  oblique  directions  to  the  flow. 
But  (I)  ana  (2)  are  usually  grouped  together  under  the  symbol  Jn^  loss  of 
head  due  to  friction  (see  page  1160). 

There  are  two  other  losses  of  head  which  have  to  be  considered,  namely, 
(1)  loss  due  to  "dropping"  head  (decrease  of  H)  in  the  upper  reservoir, 
and  (2)  loss  due  to  "rising"  head,  above  d,  in  the  lower  reservoir  (decrease 
of  Ha);  the  static  head  /f  at  d.  is  Hi+hf  when  the  water  surface  in  L.  R.  it 
below  d\  and  Ht  when  above  d. 


\M^9C!^J!Pj^fi!Bf^??^^  L 


Fig.  2. — Pipe  Line  Between  Reservoirs. 

Ezpbnatlon  of  Figure  2. — A  hydraulic  grade  line  is  a  line  of  "no  pres- 
sure." That  is,  if  a  vertical  tube  or  piezometer  is  inserted  in  the  top  of  a 
pipe  line  at  any  point  it  will  be  found  that  the  water  will  rise  in  the  piezo- 
meter tube  to  the  hydraulic  grade  line  and  thus  indicate  the  pressure  head  ht 
at  that  point  of  the  line.  Hence,  a  H.  G.  L.  is  very  useful  in  the  study  of 
any  pipe  line  as  it  rives  directly  the  pressure  head  at  any  point.  The  above 
Figure  shows  five  H.  G.  L.'s,  (a),  (6),  (c),  (d)  and  (r),  which  will  be  explained: 
(a). — ^This  can  obtain  only  when  a  gate  is  closed  in  the  pipe  line  as  at  d, 
or  tome  other  point.  As  soon  as  the  gate  is  opened,  water  will  begin  to  dis- 
cbarge at  d  and  the  end  of  the  H.  G.  L.  at  L  will  drop. 

g). — This  condition  will  obtain  with  the  gate  at  d,  partly  open,  when 
the  H.  G.  L.  would  drop  to  M  and  the  pressure  head  h^  at  d  would  equal 
H^+hf-^Ht  if  the  surface  of  water  in  L.  R.  is  below  d;  or  Hz—H\  if  surface 
ofwateris  above  d.  The  total  loss  of  head  is  Hx'-h,  the  latter  being  the 
velocity  head.  Note  that  the  H.  G.  L.  S  Af  is  straight  only  when  the  loss  of 
head  is  uniform  or  proportional  to  the  length  of  the  line.  The  discharge  at 
d  will  issue  with  a  velocity  ♦v— 8.02  VF,  h  forming  a  fractional  part  of  Ht. 

{c). — This  is  the  usual  condition  for  a  pipe  line  of  uni- 
form cross-section  discharging  freely,  that  is,  all  gates  open, 
and  the  water-level  below  d  in  L.  R.  Note  that  there  is  no 
presstire  head  above  the  top  of  the  pipe  at  d  because  the  efflux 
do«6  not  quite  fill  the  discharge  end;  but  the  actual  mean 
ffressure  head  at  d  is  shown  in  Fig.  3,  by  A',  the  depth  below 
the  jEree  atirfcure,  and  the  velocity  ot  discharge  at  outlet  is 
»—  8,02y/J^-h velocity  of  approach. 

(dy. — ^The  hydraulic  grade  line  is  here  shown  as  a  very  broken  or  ir- 
resrular  line,  and  marks  the  elevation  at  which  the  water  would  rise  in  the  piez- 
:>meter  tube  if  inserted  in  the  pipe  line  at  any  point.  The  pipe  is  as  shown 
n  Fi^.  2,  and  not  uniform  in  section  as  was  assumed  with  (fr)  and  (c).  A 
sharp  drop  (to  the  ri^ht)  in  the  H.  G.  L.  indicates  a  greater  rate  of  loss  of 
leacf,  per  lin.  ft.  of  pipe,  than  one  of  flatter  slope.  Thus,  the  grade  drops 
ha.rply,  by  comparison,  at  c  and  *,  points  of  abrupt  change  in  diameter;  at 
7,  the  converging  tube  leading  to  the  venturi  V;  and  at  the  bend  b.  The 
urved  form  of  the  H.  G.  L.  at  section  A  is  due  to  a  loss  of  head  at  the 
ri6ce  o  forming  a  downward  (first)  part  of  curve;  while  the  upward  (second) 
art  of  the  curve  is  due  to  suction  by  vacuum  just  beyond  the  orifice.  A 
inil&r  suction  occurs  just  beyond  the  venturi  -V  causing  an  upward  H.  C>.  L. 
t  section  H.  Note  that  the  H.  G.  L.  at  section  D  is  sharper  than  at  sections 
,  jp,  /  and  K  because  the  area  of  the  pipe  is  less,  therefore  ^e  velocity, 
urtlon  and  rate  of  loss  of  head  are  greater.    The  conditions  at  the  outlet  d 

*  Xreated  as  a  weir  without  end  contraction;  see  Weirs,  page  1177,  etc. 


Fig.  3. 


1160  f^.'-HYDRAUUCS. 

are  the  same  as  described  in  (c).  This  case  (d)  represents  a  usual  oocorrence 
in  practice,  and  the  losses  are  described  in  detail  in  the  following  pages- 
It  may  be  remarked  here,  however,  that  the  pressure  head  hp  at  any  point 
in  the  pipe  line  is  the  vertical  distance  from  the  H.  G.  L.  to  the  center  of 
pressure  of  the  water  section  in  the  pipe.  The  center  of  pressure  is  usiaally 
aMumed  at  the  center  of  a  circular  pipe,  although  in  reality  it  is  a  Httle 
below  the  center. 

{e). — Here,  it  is  assumed  that  the  water  in  the  lower  reservoir  has  risen 
abcve  the  discharge  end  d  of  the  pipe,  to  the  elevation  of  ^.  The  theckretic 
head  is  therefore  Hz.  Now  we  know  that  the  total  loss  of  head  cannot  ex- 
ceed the  theoretic  head  //g.  therefore  the  H.  G.  L.  must  slope  to  some  pomt 
X,  above  or  at  sf.  Moreover,  we  know  that  x  must  be  above  j^  otherwise 
there  would  be  no  pressure  head  {x  sf)  to  cause  a  flow  into  L.  R.  We  can 
reasonably  assume  x  s'  to  be  less  than  hf  (say  about  half  the  diameter  of  the 
pipe)  and  to  diminish  as  s^  rises  in  elevation,  so  that  when  Hf^o,  xsf'^o 
also. 

Total  Head  is  usuallv  sub-divided  into  etUry  head,  velocity  head  and 
friction  head.  That  is,  the  force  exerted  bv  the  pressure  due  to  the  total 
head,  as  in  a  reservoir,  is  expended  partly  (1)  in  overcoming  the  resistance 
at  the  entrance  of  the  pipe;  (2)  in  producing  velocity  of  flow  or  discharge; 
(3)  in  producing  friction  (and  viscosity).  There  is  a  fourth  resistance  whurh 
has  to  be  overcome,  namely,  curvature  head*,  but  this  is  usually  included  in 
an  ordinary  pipe  line,  under  friction  head.  The  combined  entry  and  viilocity 
heads  seldom  exceed  one  foot  even  when  the  entrance  is  sharp-edged,  in 
which  case  they  are  about  equal.  The  entry  head  reduces  with  increased 
length  of  pipe  line,  becoming  inappreciable  when  the  length  exceeds  about 
1000  diameters.  Even  for  short  pipe  lines,  less  than  1000  diameters,  the 
entry  head  almost  entirely  disappears  with  the  use  of  the  bell-shap«i  or 
flaring  entrance.  It  is  thus  seen  that  the  main  considerations  in  any  ordi- 
nary pipe  line  are  velocity  head  and  friction  head.  Moreover,  one  is  a 
function  of  the  other  so  that,  for  a  given  smoothness  of  wetted  surface  and 
a  given  diameter  of  pipCj  they  both  increase  with  the  hydraulic  slope.  The 
relations  between  velocity  head  (or  rather  velocity  due  to  the  velocity 
head),  friction  head,  smoothness  of  wetted  surface,  and  hydraulic  slope,  ocm- 
stitute  the  laws  of  flow  and  when  thoroughly  known,  may  be  incorporated 
in  a  working  formula. 

Loss  of  Head  due  to  Friction. — In  long  pipe  lines  this  is  really  the  only 
loss  that  is  practicallv  considered,  or  at  least  other  incidental  losses  are 
included  in  "friction  losses.  The  "dropping"  head  as  in  emptying  a 
reservoir  may  be  reduced  to  "mean  average  '  head  or.  with  more  exactness 
to  several  mean  average  heads  at  successive  elevations  of  water  surface. 
The  loss  of  head  at  entrance  becomes  almost  a  negligible  quantity;  nK»e- 
over,  the  orifice  is  usually  a  converging  tube,  thereby  reducing  the  loss  to  a 
minimum.  Similarly,  converging  and  diverging  "reducers"  are  inserted  in  a 
line  joining  pipes  of  aifTercnt  diameters,  thereby  greatly  reducing  the  loss  of 
head  which  would  obtain  if  the  change  were  abrupt  as  at  c  and  e.  Fig.  2. 
Where  such  changes  of  section  occiu"  fre- 
quently, as  in  lap- join  ted  riveted  steel  r — f  \  innttf  I  c  f 
pipe  (Fig.  4),  it  is  customary  to  use  the    /      *'    •        .   '"^    »  I 

smaller  diameter  d  in  computing  the  flow     '      ^    t  8 ^  S      * 

The  losses  due  to  contraction  of  sections  at 

c,  and  the  expansion  at  e,  together  with  Fig  4. — ^Riveted  Pipe. 

the  loss  effect  due  to  rivet  heads  are  considerable,  and  it  is  a  qtiestiisi 
whether  a  uniform  pipe  of  diameter  d  would  not  show  the  greater  capac- 
ity. The  losses  due  to  bends  are  seldom  computed  unless  the  curvattue  is 
considerable.    Short  curves,  moderately  sharp,  are  the  best. 

Friction  losses  are  deduced  from  expenments  on  pipe  lines  actually 
constructed,  and  from  laboratory  experiments.    The  former  point  to  a  safe 

*  The  loss  of  head  due  to  ctirvature  of  pipe,  as  short  curves,  bends,  etc., 
is  but  imperfectly  understood.  Theoretical  formulas,  as  those  of  Weisbach. 
are  not  reliable.  Roughly  speaking,  the  loss  of  head  in  a  short  90*  bend 
may  be  assumed  at  3  to  5  times  what  it  would  be  in  the  same  length  of 
straight  pipe.  For  a  good  discussion  of  this  subject  see  Paper  No  911  ia 
Trans.  Am.  Soc.  C.  E..  for  April,  1902,  by  Gardner  S.  Williams,  Clarence  W. 
HubbeU  and  George  H.  FenfeU.  „g,,,,  ,^  GoOgle 


FLOW  IN  PIPES— LOSSES  OF  HEAD— FRICTION,        1161 

precedent  for  similar  designs,  while  the  latter  lead  to  the  establishtxig  of 
general  laws  of  flow,  in  a  relative  sense.  It  would  hardly  be  safe,  however, 
to  design  large  pipe  lines  based  on  formulas  derived  from  laboratory  experi- 
ments alone.  Many  physicists  have  attempted  to  formulate  laws  of  flow 
and  of  friction  based  almost  wholly  on  theory  without  considering  the 
viscosity  of  the  flowing  Uquid.  It  is  perhaps  needless  to  sa^  that  all  such 
formulas,  while  interesting,  are  practically  useless  to  the  engmeer,  and  they 
are  positively  dangerous  to  the  young  student.  The  class  offormulas  which 
the  hydraulic  en^eer  is  using  to-day,  and  will  contiune  to  use,  are  founded 
on  experimentation.    Experiments  reveal  to  us  that — 

(a)  Friction  F  of  water  in  pipes  is  proportional  to  some  variable  power  of 

the  velocity  v,  that  is,  jF  oc  v*.  In  pipes  of  commercial  size  the  values 
of  X  have  been  found  to  range  from  about  ;r  —  1. 76  to  x  —  2.  depending 
on  the  diameter  of  pipe  and  roughness  of  wetted  surface,  or  perimeter. 

(b)  Friction  is  proportional  to  the  length  of  the  pipe,  so  far  as  at  present 

known. 

(c)  Friction  is  less  in  curves  of  short  radius,  down  to  2}  diameters,  than  in 

curves  of  long  radius,  for  the  same  total  angle  of  deflection.  (See 
Trans.  Am.  Soc.  C.  E.,  Vol.  XLVII.  pages  183.  1»1.) 

(d)  Friction  is  inversely  proportional  to  some  power  of  the  diameter  of  the 

pipe  or  the  hydraulic  radius  r  of  the  conduit.  The  index  of  the, 
power  may  be  assvimed  as  1.2,  within  small  limits  of  error. 

(e)  Friction  increases  rapidly  with  the  rotighness  of  the  wetted  perimeter. 

A  newly  laid  conduit  with  a  smooth  surface  can  often  deteriorate  so 
that  the  velocity  of  discharge  will  decrease  from  2  to  5  per  cent 
per  annum  for  a  number  of  years. 

Author's  Hydraulic  Formula. — ^The  following  general  formula  is  based 
on  the  most  reliable  existing  experimental  data,  and  is  applicable  to  the 
flow  of  water  in  pipes,  sewers,  fltimes,  etc. 

Notation: 
a— area  of  cross-section  of  water  in  pipe,  flume,  etc.,  in  sq.  ft.; 
t)  — velocity  of  discharge  in  ft.  per  second  (»'"     )  I 

a-> discharge  in  cubic  ft.  per  second  (q^a  v); 
H  -  loss  of  head  in  friction,  etc.,  in  ft.  per  1000  ft.    (//  - 1000  5) ; 
5— hydraulic  slope  or  sine  of  angle  of  slope  (5».001  //); 
p— wetted  perimeter  of  cross-section  of  pipe,  etc.,  in  ft.; 

V— hydraulic  (mean)  radius  in  ft.——.    (For  drctilar  pipe  ''■■-7-)  ; 

d — diameter  of  circular  pipe  in  ft.    (rf — 4f ) : 
f— coefficient  of  smoothness  of  wetted  surface;  also  alinement; 
X  — index  of  the  power  of  the  velocity,  proportional  to  friction; 
yi  index  of  the  power  of  d  or  4f,  inversely  proportional  to  frictioii. 

*  As  the  velocity  of  discharge  v  increases  with       ^^^  t  / 
the  mean  radius  r,  it  is  desirable  to  desi^  the  section 
of  the  conduit  so  that  r  will  be  a  maximum  for  the 
area  a,  other  things  equal.    The  circular  section  is 

ideal  in  this  respect,  and  the  value  of  r  is  equal  to  -r- 

whether  the  circular  pipe  is  full,  as  in  Fig.  6,  or  only  • ^— 

half  full,  as  in  Pig.  6.     When  not  full,  but  more  than  Fig.  7. 

y^e^U  full,  ^ > T*  ^^  ^'3^^  (*t®  maximum  value)  when    _ 

the  depth  of  water  in  the  circular  pipe  is  0.8  Id.   When    lg<?'-  'jf^-'z^  ^ 

ihe  pipe  ia  less  than  half  full,  f<  J.  Fig.  7  shows  the 

lection  of  a  flume,  in  which  r  has  its  maximum  value  ^**  ^' 

vhen  ^  —  2d,.  Practical  considerations  however  usually  call  for  a  1ms  ijro- 
>ortioiiate  depth.  Pig.  8  is  a  section  of  a  trapezoidal  canal  in  which  r  is  a 
amximum  when  6j- 2T«-y),  or  62-  ^  (cosec  tf-cot  (f).  In  practiw,  canals 
^d  ditches  are  usually  designed  with  such  slopes  as  will  probably  be  mam- 
axned  without  wash  during  the  flow  of  water.  n^^r^n^o 

^^^^  Digitized  by  V^OOQIC 


1161  e2.—HYDRAUUCS. 

Formulas; 
Hyd.  Radius,  r.  Diameter,  d. 

0"-'=  »-7-U  "-7-^ « 

But  X  generally  varies  from  1.75  to  2.00  -•-  somewhat  nearer  the  former 
value;  ana  y  varies  usually  from  1.16  to  1.25.    Assuming  average  values  of 

«  and  y.  we  have.  «- 1.82;  ««-8.81  +  ;    —  -  0.55;   -^-8.0+;  y- 1.2. 

Hence.  H^-^-j^j^  "'T'JdT* »> 

Equation  (2)  is  the  author's  formula  for  loss  of  head  in  feet  per  1000  feet. 
The  various  values  of  c,  v,  r,  d,  and  H,  raised  to  the  proper  powers,  are  givtec 
in  the  subjoined  Tables  8,  4.  5,  0  and  7.  Other  forms  o£  (2)  which  are  usefol 
in  practice  are  the  following: 

Hydraulic  slope.  5-  .001  H C80 

Velocity.  »-  (8c)«-»»  //"•  (4f Jo  «      -  (8c)0-»  H»-»  </*•« (^ 

Diameter,  ^'"(i^JoS  *  H^i  '  •^'•"^ <« 

Hydraulic  radius,  '  ~  T (^ 

^Coefficient.  c^J^yTi  "  W^ ^ 

Note  that  H- hydraulic  slope  muH.  by  1000. 

*  Formula  (7)  is  used  in  determining  the  coefficient  c  of  smoothness  and 
alinement  in  pipe  lines  actually  built  and  tested.  The  values  given  in 
Table  8  are  close  averages  from  actual  experimenta- 


d  by  Google 


HYDRAUUC  FORMULAS. 


1163 


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1164 


G^-'HYDRAUUCS, 


4. — Valubs  of  »»•»  FOR  Various  Values  of  r 
In  Author's  Formula,  prbcboinq. 


Ve- 
loc- 
ity 

V 

Tenths. 

.0 

.1 

.2 

.3 

.4 

.5 

.6 

.7 

.8 

.9 

0.000 
1.00 
3.53 
7.39 
12.47 

0.015 
1.19 
3.86 
7.84 
13.04 

0.053 
1.39 
4.20 
8.31 
13.62 

0.112 
1  61 
4.55 
8.78 
14.22 

0.189 
1.84 
4.92 
9.27 
14.83 

0.283 
2.09 
5.30 
9.78 
15.45 

0.396 
2.35 
6.69 
10.29 
16.06 

0.523 
2.63 
6.10 
10.83 
16.72 

0.666 
2.91 
6.51 
11.36 
17.37 

o.ss 

3.22 
6.M 

11.91 
18.04 

8 
9 

18.71 
26.08 
34.52 
44.02 
54.54 

19.40 
26.87 
35.42 
45.02 
55.65 

20.10 
27.68 
36.34 
46.04 
56.77 

20.81 
28.50 
37.26 
47.07 
57.89 

21.63 
29.33 
38.19 
48.10 
69.03 

22.26 
30.16 
39.14 
49.15 
60.18 

23.00 
31.01 
40.09 
60.21 
61.34 

23.75 
81.87 
41.06 
51.28 
62.51 

24.  B2 
32.75 
42.03 
53.35 
63.69 

25. » 
33,€J 
43  03 
53-44 
04.0 

10 

66.07 

67.28 

68.50 

69.72 

70.96 

72.21 

73.46 

74.73 

76.01 

n.» 

Ex.--3.1»M  -  7.84;   6.3 »•«  -  28.50;   9»-»  -  M.M. 


5. — Values  of  V-*+  for  Various  Values  of  v 
In  Author's  Formula,  prbcbding. 


Ve- 
loc- 
ity 

Tenths. 

.0 

.1 

.2 

.3 

.4 

.6 

.6 

.7 

.8 

.9 

0.000 
1.00 
2.86 
5.29 
8.19 

0.030 
1.16 
3.08 
6.66 
8.60 

0.087 
1.32 
3.31 
6.84 
8.82 

0.161 
1.49 
3.54 
6.12 
9.14 

0.249 

1.67 

3.77 

6.40 

9.46 

0.350 

1.85 

4.01 

6.69 

9.79 

0.461 
2.04 
4.26 
6.98 
10.12 

0.682 
2.24 
4.61 
7.27 
10.46 

0.713 
2.44 

4.77 
7  67 
10.80 

o.n 

2.08 

ft.t3 
T.88 
U.14 

11.48 
15.14 
19.13 
23.43 
28.01 

11.83 
16.53 
19.55 
23.87 
28.48 

12.19 
15.92 
19.97 
24.32 
28.96 

12.56 
16.31 
20.39 
24.77 
29.43 

12.91 
16.70 
20.81 
25.22 
29.92 

13.27 
17.10 
21.24 
25.68 
80.40 

13.64 
17.50 
21.67 
26.14 
30.89 

14.01 
17.90 
22.11 
26.60 
31.88 

14.38 
18.31 
22.64 
27.07 
31.87 

14.T« 
18.72 
23.98 
S7.M 
33.96 

10 

32.86 

33.36 

33.87 

34.37 

34.87 

36.38 

36.90 

36.41 

36.93 

S7.45 

*1.60+  -  1.82-1-1.2. 


zed  by  Google 


HYDRAULIC  FORMULAS. 


1165 


6.— Values  of  (iOo^.d^*,  and  ^,  for  Various  Valubs  of  d 
In  Author's  Formula,  prbcbding. 


.25 

0208 

.0777 

104.11 

.378 

.0312 

.1015 

64.00 

.60 

.0417 

.1228 

45.32 

.«2S 

.0521 

.1422 

34.67 

.76 

.0625 

.1604 

27.86 

.878 

.0729 

.1776 

23.15 

1.00 

.0833 

.1940 

19.73 

1.25 

.1042 

.2348 

15.09 

1.378 

.1146 

.2393 

13.46 

1.50 

.1250 

.2535 

12.13 

1.75 

.1458 

.2806 

10.08 

2.00 

.1667 

.3065 

8.586 

2.25 

.1875 

.3305 

7.454 

2.50 

.2083 

.3551 

6.569 

2.75 

.2292 

.3782 

5.869 

3. 

.2500 

.4005 

6.278 

3.6 

.2017 

.4434 

4.387 

4. 

.3333 

.4843 

3.737 

5. 

.4167 

.6611 

2.859 

6. 

.5000 

.6329 

2.297 

7. 

.5833 

.7007 

1.909 

8. 

.6667 

.7652 

1.627 

9. 

.7500 

.8271 

1.412 

10. 

.8333 

.8866 

1.245 

11. 

.9167 

.9442 

1.110 

12. 

1.0000 

1.000 

1.000 

13. 

1.083 

1.054 

.908 

1.150 

1.097 

.846 

14. 

1.167 

1.107 

.831 

1.200 

1.128 

.803 

16. 

1.250 

1.159 

.766 

1.300 

1.189 

.730 

16. 

1.333 

1.209 

.708 

1.360 

1.219 

.698 

1.400 

1.249 

.668 

48 
54 
60 
66 
72 
78 
84 
90 
96 
102 
108 
114 
120 


1.45 

1.2''8 

.640 

10 

1.60 

1.307 

.615 

11 

1.60 

1.364 

.669 

12 

1.667 

1.401 

.543 

13 

1.70 

1.419 

.529 

14 

1.80 

1.474 

.494 

15 

1.90 

1.528 

.463 

16 

2.00 

1.580 

.435 

17 

2.10 

1.632 

.411 

18 

2.20 

1.683 

.388 

19 

2.30 

1.733 

.368 

20 

2.40 

1.782 

.350 

21  • 

2.50 

1.831 

.333 

22 

2.60 

1.879 

.3177 

23 

2.70 

1.926 

.3036 

24 

2.80 

1.973 

.2907 

25 

2.90 

2.019 

.2787 

26 

3.00 

2.065 

.2676 

27 

3.20 

2.155 

.2476 

28 

3.40 

2.243 

.2303 

29 

3.50 

2.286 

.2224 

30 

3.75 

2.393 

.2047 

35 

4.0 

2.497 

.1895 

40 

4.5 

2.698 

.1645 

45 

6.0 

2.893 

.1450 

50 

5.6 

3.081 

.1293 

55 

6.0 

3.263 

.1165 

60 

6.6 

3.440 

.1058 

65 

7.0 

3.612 

.0968 

70 

7.5 

3.780 

.0891 

75 

8.0 

3.945 

.0825 

80 

8.5 

4.106 

.0770 

85 

9.0 

4.264 

.0716 

90 

9.6 

4.419 

.0674 

95 

10.0 

4.571 

.0631 

100 

4.671 

.0631 

4.868 

.0563 

6.156 

.0507 

5.435 

.0461 

5.708 

.0421 

6.973 

.0388 

6.233 

.0359 

6.488 

.0334 

6.737 

.0312 

6.982 

.0292 

7.222 

.02746 

7.459 

.02591 

7.691 

.02450 

7.920 

.02322 

8.146 

.02207 

8.368 

.02101 

8.588 

.02007 

8.804 

.01916 

9.018 

.01834 

9.230 

.01758 

9.438 

.01688 

10.45 

.01403 

11.41 

.01195 

12.33 

.01038 

13.22 

.00915 

14.08 

.00816 

14.91 

.00735 

15.72 

.00668 

16.51 

.00611 

17.28 

.00562 

18.03 

.00620 

18.77 

.00484 

19.49 

.00452 

20.20 

.00423 

20.89 

.00398 

Ex.— For  a  pipe  l^dia.,  d-1.6.  f-1.6-*-4.  (f>«- 1.307,  1 -*-</»•«- 0.616. 


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1166 


e2,—HYDRAUUCS. 


7. VaLUBS  of  //"•*»  AND 


HOA 


:  FOR  Various  Valubs  of  H 


In  Author's  Formula,  prbcbdino. 


mh 

isroM 

1 

.1^ 

H9M 

'  1 

,1. 

aoM 

1 
tf6.tt+ 

H^tM 

IrOPf 

.000 

.000 

00 

.10 

.282 

6.81 

1.0 

1. 000 

1.000 

3.55 

.147 

.002 

.033 

177.5 

.11 

.297 

6.29 

1.1 

1.054 

0.824 

3.74 

.I3« 

.004 

.048 

99.6 

.12 

.312 

6.88 

1.2 

1.105 

.869 

3.  S3 

.116 

.006 

.060 

71.0 

.13 

.326 

6.48 

1.3 

1.166 

.804 

4.10 

.118 

.008 

.070 

65.9 

.14 

.339 

6.15 

1.4 

1.203 

.765 

4.27 

.111 

.010 

.079 

46.4 

.15 

.352 

4.86 

1.6 

1.250 

.713 

4.44 

.Its 

.012 

.088 

39.9 

.16 

.365 

4.60 

1.6 

1.295 

.676 

4.69 

.0999 

.014 

.096 

35.1 

.17 

.877 

4.38! 

17 

1.339 

.643 

4.76 

.0M3 

.016 

.103 

31.4 

.18 

.389 

4.17 

1.8 

1.382 

.613 

4.90 

.08S9 

.018 

.110 

28.4 

.19 

.401 

3.99 

1.9 

1.423 

.586 

5.05 

.Qe«o 

:SS 

.116 

26.05 

.20 

.413 

8.82 

2.0 

1.464 

.561 

20 

6.19 

.0634 

.123 

24.06 

.22 

.435 

3.53 

2.2 

1.643 

.518 

22 

6.48 

.0760 

.024 

.129 

22.38 

.24 

.456 

3.28 

2.4 

1.619 

.482 

24 

5.74 

.OTOt 

.026 

.134 

20.93 

.26 

.477 

8.07 

2.6 

1.691 

.461 

2< 

6.00 

.060 

.028 

.140 

19.68 

.28 

.497 

2.89 

2.8 

1.762 

.424 

28 

6.25 

.0«22 

.030 

.145 

18.58 

.30 

.616 

2.73 

3.0 

1.830 

.400 

30 

6.49 

.asm 

.032 

.161 

17.62 

.32 

.534 

2.58 

3.2 

1.806 

.379 

32 

6.73 

.0557 

.034 

.156 

16.74 

.34 

.652 

2.46 

3.4 

1.960 

.361 

34 

6.96 

.0939 

.036 

.161 

15.96 

.36 

.670 

2.34 

3.6 

2.023 

.344 

36 

7.18 

.0505 

.038 

.166 

15.26 

.38 

.687 

2.24 

3.8 

2.084 

.339 

38 

7.39 

.0483 

.040 

.170 

14.62 

.40 

.604 

2.16 

4.0 

2.144 

.315 

40 

7.61 

.•4C3 

.042 

.175 

14.04 

.43 

.621 

2.06 

4.2 

2.202 

.301 

42 

7.81 

.•«t4 

.044 

.179 

13.50 

.44 

.637 

1.98 

4.4 

2.259 

.291 

44 

8.02 

.042? 

.046 

.184 

13.01 

.46 

.652 

1.91 

4.6 

2.315 

.280 

46 

8.21 

•412 

.048 

.188 

12.56 

.48 

.668 

1.84 

4.8 

2.370 

.271 

48 

8.41 

.•sm 

.050 

.193 

12.14 

.60 

.683 

1.78 

6.0 

2.42 

.262 

50 

8.60 

.nm 

.065 

.203 

11.21 

.55 

.720 

1.66 

6.6 

2.66 

.242 

56 

9.06 

.uit 

.060 

.213 

10.43 

.60 

.755 

1.53 

6.0 

2.68 

.225 

60 

9.61 

.1391 

.065 

.222 

9.76 

.66 

.789 

1.43 

6.5 

2.80 

.210 

66 

9.93 

.03*6 

.070 

.232 

9.17 

.70 

.822 

1.35 

7.0 

2.02 

.198 

70 

10.36 

.0391 

.075 

.241 

8.66 

.76 

.854 

1.27 

7.6 

3.03 

.187 

T5 

40.76 

,mi 

.080 

.249 

8.20 

.80 

.885 

1.20 

8.0 

8.14 

.177 

80 

11.14 

.099 

.085 

.258 

7.80 

.85 

.914 

1.16 

8.5 

3.25 

.168 

86 

11.51 

.094? 

.090 

.266 

7.44 

.90 

.944 

1.09 

9.0 

3.35 

.160 

•0 

11.88 

.0236 

.095 

.274 

7.11 

.96 

.972 

1.04 

9.5 

3.45 

.163 

» 

12.24 

.9US 

.100 

.m 

6.81 

1.00 

1.000 

1.00 

10.0 

3.65 

.147 

100 

12.60 

.ttis 

Ex.— For  hydrauHc  slope  «-  .004.  H  -  4.0.  &••«-  2.144.  «nd  t^  -  .S15l 


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CHBZyS  FORMULA,    KUTTERS  FORMULA,  11«7 

PrcbUms  in  Us9  of  Author* s  Hydraulic  Formula, 
(See  page  1161,  etc.) 

pT^oblem  1. — ^What  loss  of  head  per  1000  ft.  would  occur  in  an  ordinary 
.  ixx>n  pipe  line  20  ins.  in  diameter,  if  the  velocity  is  3  ft.  per  second? 

Solution.— Use  formula  (2);  then  — .  from  Table  8,  -1.60;  »»*«,  from 

c  \ 

lo  4.  -7.80:  4?.  from  Table  6.  -0.542;  hence,  if- 1.50X7. 80X|X 
i2  —  2.00  ft.  per  1000  ft.    Ans. 

Problem  2. — What  velocity  of  discharge  "would  be  expected  in  an  un- 
n.  efi^-shaped,  brick  sewer,  whose  hydraulic  radius  is  0.75.  and  hydxaul^ 
»e  OMl25r 

Solution.— Use  formula  (4);  then  from  the  Tables.  (8c)»*»-1.2«; 
»^1.25^»-*1.13:  (4r)««-(P«-3P«- 2.066;  hence, v- 1.20X1.13X2.07 
.02  ft.  per  sec.    Ans. 

"Problem  8. — What  diameter  of  riveted-steel  pipe  would  be  required  to 
.IxskTSe  2.4  cu.  ft.  per  second,  after  it  has  been  in  use  about  12  years,  if 
liycmiulic  slope  is  0.01226? 

Solution. — Use  formula  (4)  by  trial  method — assuming  d,  obtaining  v, 
I  tben  a  (— a  v  —  2.4).  First,  assume  pipe  to  be  12  ins.  in  diameter;  then 
1.  V- 1.20X8.97X1-5.12;  g-av- 0.7864X5.04-4.02;  hence,  as  4.02 
.  4.  a  1 2-in.  pipe  is  too  large.  Second,  assume  pipe  to  be  10  ins.  in  diameter; 
n  d-0.838:  v- 1.20X3.07X0.887-4.54;  9-av-0.6464x  4.64-2.48. 
required  discharge  being  2.4;  hence  a  10-in.  pipe  is  required.    Ans. 

Problem  4. — A  conduit  whose  hydraulic  radius  is  0.875,  and  whose 
lra.ulic  slope  is  .001375  has  a  velocity  of  discharge  of  4.5  ft.  per  second, 
lat  is  the  coefficient  c  of  smoothness  and  alinement  of  the  conduit? 

Solution. — Use  formula  (7).  in  which  v— 4.5,  H— 1.375.  and  4r— 8.5; 

•      'T  1.,  15.46X0.2224     ^  ^^      v  ,.     t 

n  by  use  of  accompanymg  Tables,  c—  — ^    .  ^. —  —0.83,  which  places 

inder  Class  C  in  Table  8. 

Choy's  Hydraulic  Formula  assumes  the  velocity  to  be  proportional  to 
.  square  root  of  both  the  hydraulic  radius  and  the  hydrauhc  slope;   or 

vcy/rs    (1) 

which  c  is  a  coefficient  to  be  determined  by  experiment.  (See  Kutter's 
mula,  following.) 

Kifttcr*!  Formala,  so-called,  is  really  the  Chezy  formula  (preceding),  but 
th  values  of  the  coefficient  c  supplied  so  as  to  give  it  a  general  application. 
ese  values  of  c  were  deduced  trom  experiments  made  by  GanguiUet  and 
itter,  and  were  primarily  intended  to  apply  to  the  flow  of  water  in  streams 
d  canals.  They  have,  however,  received  general  application,  to  a  greater 
less  extent,  in  the  design  of  water  mains,  sewers,  fltmies,  ditches,  etc. 
te  value  of  the  coefficient  in  English*  measure  is  as  follows: 

'"-Vt  («•-¥•) '" 

whx^  f  and  s  are  the  mean  radius  and  the  slope,  respectively,  as  explained 


*  In  metric  measure, 

(J) 


1 + ^  (28+ -55^)  ■  ;;;';;;,Googie 


U08  62.— HYDRAULICS. 

on  paffe  1101;  and  m  is  a  coefficient  depending  upon  the  ronghneas  of  tfce 
wetted  surface  of  the  conduit,  sewer,  canal,  or  stream.    Thus. 
na.009  for  well-planned  timber,  perfectly  aligned.* 
"■.010  for  neat  (pure)  cement;    glazed  or  enameled  surfaces  generally; 

smooth  cast  uon  or  iron  pipes;  planed  timber.* 
■■.Oil  for  cement  with  one-third  sand,  in  good  condition;   well-jointed 

pipes  of  ixxmt.  cement,  and  terra  cotta. 
"-.012  for  unplaned  timber  in  good  alinement,  as  flumes. 
"■.013  for  ashlar  and  brickwork,  well  laid;   ordinary  metal;    earthen-, 

cement-,  stoneware-  and  terra  cotta  pipd  not  well  pointed  nor  in 

first-class  ozder;   cement  plaster  and  planed  timber  m  second-class 

condition:   generally,  the  materials  for  n-".010  when  imperfect  in 

quality  or  condition. 
"-.015  for  imclean  surfaces  in  pipes  and  sewers;  second-class  or  rough 

brickwork;  stonework,  well  dressed;  iron-,  stoneware- and  terracotta 

pipes  with  imperfect  joints  and  in  bad  condition. 

—  .017  for  rubble  masonry  in  good  order;    brickwork,  stoneware  and 

ashlar  in  poor  condition;   generally,  the  materials  for  m». 01 3  when 
imperfect  in  quality  or  condition;  tuberculated  iron  pipe? 

—  .020  for  canals  in  very  firm  gravel,  and  carefully  trimmed;    infenctf* 

rubble  in  cement;  coarse,  dry  rubble. 

—  .0225  for  coarse,  dry  rubble  in  bad  condition. 

—  .025  for  canals  and  rivers  free  from  stones  and  weeds,  and  in  good 

order, 
-s  .030  for  canals  and  rivers  having  some  stones  and  weeds. 

—  .035  for  canals  and  rivers  in  bad  order,  with  great  quantities  of  stones 

and  weeds. 

—  .040  for  rivers  in  extremely  bad  condition. 

These  values  of  n  are  to  be  inserted  in  equation  (2)  for  finding  the  value 
of  c  used  in  equation  (1).  The  correct  use  of  Kutter's  (or  Chezy  s)  formula 
depends  upon  theproper  selection  of  the  values  of  n  for  the  roughness  of  the 
wetted  surface.  The  values  n  —  .010  to  n  —  .016  will  cover  all  conditkms  for 
good  water  mains — the  lower  values  for  the  smooth  pipes,  and  Uie  higher 
values  for  the  pipes  with  rough  surfaces.     (See,  also,  page  1188.) 

In  order  to  simplify  the  calctilations  of  the  coefficients  e  in  Kutter's 
formula,  equations  (1)  and  (2),  the  following  reductions  of  form  of  equation 
( 2)  are  given  for  various  values  of  roughness  n.  It  remains  only  to  substitute 
the  proper  values  of — 

f,  the  hydraulic  radixis  of  the  pipe,  sewer  or  canal,  in  ft.; 
d,  the  diameter  of  the  circular  pipe,  in  ft.; 
St  the  average  slope  of  the  pipe,  or  rate  of  fall  of  the  hydraulic  grade  line. 

Using  Hyd .  Rad  r.  Using  Diameter  d. 

»  AAA  \/7(242.872  5+.00281)  's/7(242. 872 s+. 00281)  ,., 

For  n— .009,   c  — ■— —  — ~ .(4) 

5(vT+.3748S)+.0000263     j(>/7  +  .74»7)  +  .0000500 

„  ^..  >/7(222.765+. 00281)  >/J(222.755  +  .00281)    ,., 

Forn-.OIO,    C  — y=r — ;r=:^ ^.(5) 

s(y/r  +.4165) +  .0000281      ^(Vd  +  .883) +  .0000662 

Forn-.0105,.-     ^^(^1^  13.  +  .00281L„     Vd(214.13x+.00281) 

5  (vT  +  . 437325) +  .000295     5  (>/d+. 87465) +.000059 

For «- Oil     c~     ^^(2062g^  +  »00281)     ^     >/d  (206.29  5+.  00281)    ^^ 

"  *(vT+.45815)+.0000809"5(>/d+.9163)+.0000618* 

,.*,'^«  values  n».010  and  n-.0105  are  often  used  for  wood-«tave  pipe 
well  Ifiud,  with  dressed  timber. 
•     J  i**®.  "^*'"«^s  n'-.OH  and  m°-. 01 6  are  often  used  for  lap-joinud  steel- 
nveted  pipe.    For  foul  and  tuberculated  iron  pipe,  use  M-.016+. 


KUTTERS  FORMULA— VALUES  OF  N.  1160 

Using  Hyd.  Rad  r.  Using  Diameter  d. 

-012  v^(192.57j-f  .00281)    ^     V^(192.g75-f  .00281) 

\/7(180.965->- .00281)  >/J(180.»6^+. 00281)    ,«, 

Pom-.OU,  c  —  — ;= — -= ^.(9) 

*(>/7+.54146)+.0000366     j(>/dr+1.0829) +.0000730 

p„,..OH.   ,,     v^(171.01  .+  .00281)    ,     V7(171.01. 4-00281) 

«(VT+. 6831) +  .0000898     5(V7+1.16«2) +  .0000786 

«»  A1IC  V7'(162. 385+. 00281)  n/7(162.385+. 00281)  ,... 

5(VT+.62476)+.0000422     5  (V7+ 1.2495) +.0000844 

For  »- 017  v^(H8. 18 j+. 00281)    ^     >/7(148.185+ .00281) 

or»-.      .  ^"^(vT+.70806)+.0000478"r(>/d'+1.4161)+.0000966 

Porn- 020.   ,,     ^^(132.20.  +  . 00281)    ^     v^Jc  132. 20. +  .00281) 

J  (>/7+. 833) +  .0000662       .(>/d+ 1.666) +.0001 124 

Porn-.0226..-     ^(^22.14.+  . 00281)     ,     v/7(  122. 14  .+.00281) 

.(Vr+.93713)+.000068a     5(V^+ 1.87426) +.0001264 

VT(114.09.+  .00281)     ^     V7(114.095+. 00281)  „_ 

5(V7+1.04126)+.0O0O703     .(>/J+2.0826)+. 0001 406 

_  rt-^  VT(102.025+. 00281)  n/J(  102.02.+  . 00281)  .,.. 

Jfor  H^.UoUt    C  ■■  ;:!::  ^ 7=r — -  (10) 

5(Vf+ 1.2496) +  .0000843  .(\/7+ 2.499) +.0001686 
Par«-.086.  „     v;7(93.39.+  . 00281) v^(93. 89. +  .00281) 

.(\/7+1.46776)+.0000984  .(v^+2.9166)+. 0001 968 
For  ••-.040,   J,.      v^(86.926.+  00281)    ^^     \/J(86.926  .+.00281) 

*(VT+ 1.666)  +  .0001124  "^CVd  +  3.382) +.0002248 


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1170  eSi^—HYDRAUUCS. 

Coefficients  c  in  Kutter's  fonnnla,  for  various  valaes  of  roughneas  s. 

mean  radius  r,  and  slope  s,  are  given  in  Table  8.  following.  Intermediate 
values  of  c,  for  values  ot  n,  r  and  s  not  given  in  the  Table,  may  be  obtained 
by  interpolation,  by  simple  proportion.  In  cases  where  the  slope  ^  is  grctLter 
than  ^-".01,  section  7,  the  values  of  c  as  deduced  from  section  7  may  be 
considered  sufficiently  accurate — a  little  too  laxge  for  values  of  r  greater  than 
8.28  (1  meter),  and  a  little  too  small  for  values  of  r  less  than  8.2&  Note 
that  the  value  of  c  is  independent  of  the  slope  « in  all  cases  where  the  mean 
radius  r—  3.28  (1  meter):  and  for  this  reason  the  "one  meter"  line  is  shown 
in  Italics  in  each  of  the  7  sections.  Above  the  one-meter  line  the  valxies  o£  e 
increase  with  the  slope  s:  below,  they  decrease. 

For  explanation  of  the  use  of  Kutter's  formula  and  Table  8,  see  Practical 
Examples  following  the  table. 


8. — COBFFICIBNTS  C  IN  KUTTBR*8   PORMXTLA,  V  — cVfJ,    BnOLXSR   MbaSUXB 

For  various  values  op  s,  r  and  n. 


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KUTTERS  FORMULA—VALUES  OF  C.  1171 

8.-<CoBvricxBNT8  c  IN  Kuttbr's  FORMULA.  Emolish  Mbasurb — Cont'd. 
S?:l  Coeffldenti  n  of  RoughneBS. 


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1171  G2.—HYDRAUUCS, 

8.— CoBPFiciBNTS  e  IN  Kutter's  Formula.  Emolish  Mbasurb. — Concl'd- 


Hyd. 
Iliul.r 


Ooefflcieats  n  of  Roughneas. 


Ft.      0091  .0101.01051  .on  I  .0121  .0131  .0141  .0151  .017  |  .0201.02251 .0251  .030|  .O35|.0«t 


115 
18.0 

n.i 
a.  5 

[7.2 
M.O 
2.3 
«.6 
9.7 
4  3 
i.3 
7.5 
2.» 
6.1 
7.4 
•.3 
2.1 
4.2 
7.7 

4.4 
t.2 


3.S 

».i 
1-5 
3.i 
t.i 
}.Z 

9.9 

L3 
i.i 
r.4 

l.S 
L7 

r.o 

S.S 

1.5 
L4 
L8 

J.5 

1.1 
L7 


Practical  Examples  in  Use  op  Kutter's  Formula  ahd  Tablb  8. 

(1)  Given,  the  average  or  mean  cross-section  of  a  stream;    to  find  the 
mean  radius  r  ? 

Calculate  or  scale  the  area  a  in  sq.  ft.  of  the  section  of  flowing  water; 
also,  the  wetted  perimeter  p  in  ft.,  or  transverse  length  of  (sectional)  contact 

of  flowing  water  with  the  stream  bed.    Then,  r— -— . 

(2)  Given,  a  stream,  canal,  or  pipe  line,  etc.,  of  average  tiniform  section; 
to  find  the  hydraulic  slope  5? 

j=-the  average  fall  in  ft.  of  the  stream  or  canal,  per  foot  of  length;   or 
the  fall  in  ft.  of  any  hydraulic  grade  line,  per  ft.  of  length. 

(3)  Given,  the  character  of  a  stream,  canal,  or  pipe  line;    to  fiiKi  the 
roughness  n? 

Con.sult  the  tabular  values,  page  1168. 

(4)  Given,  the  co-efficient  c,  mean  radius  f.  and  slope  si    to  find  ti^ 
velocity  v?  n  ] 

Digitized  by  VjOOQ IC 


KUTTEKS  FORMULA.    THE  VENTURI  METER.         1173 

Prom  Chezy's  formula.  «=»(rVf5.  Note  that  the  rooghness  n  is  not  con- 
sidered directly  because  c  and  n  are  functions  of  each  other;  but  as  r  is  given. 
n  can  be  obtained  if  desired.  (The  dischaige  in  cu.  ft.  per  sec.>»(7«»a  v,  in 
which  a"  the  area  of  cross-section  of  the  discharging  volume,  in  sq.  ft.) 

(5)  Given,  roughness  tf.Oli,  mean  radius  r— 18,  slope  5-».0003;  to 
find  velocity  v? 

First,  find  c  from  sections  4  and  6  of  Table  8:  c  i(154.9-i- 157.64- 152.1 
+  154.5)  =  154.8.    Then  t;-cV;j-164.8X4.243X. 01732- 11.38  ft.  per  sec 

(6)  Given,  velocity  v-»  1.2  ft.  per  sec.,  mean  radius  r— 1.5,  slope  5—  .0004; 
to  find  »? 

V  12 

First  find  c,  —  — ;=r  —   ' —  49.0.    Then  from  section  5  of  pre- 

y/Ts        1.2247X.02 
ceding  Table, on  line  with  r-»  1.5,  we  find  that  a  coefficient  c  of  49.7  corres- 
ponds to  n-.030; .'.  use  n»-.030. 

(7)  Given,  roughness  »  — .017,  slope  5  —  .001,  velocity  t;  — 2.2  ft.  per  sec.; 
to  find  the  mean  radius  r? 

1       t;' 
Use  "cut  and  try"  method:    assume  r  in  the  equation,  r— —  •  — j  — 

1000  ^-  1st,  let  r- 1,  then  from  section  6  of  Table  8, ;-1000  X  if— { 

C*  5        C*  .    (80)' 

1      i;»  (2  2)* 

-0.65;   2nd,letf-0.8,  thenj--^-1000X^~-,-0.72;   3rxi,  let  r- 0.76, 

then    7  •■^-1000X^—^,-0.75.       .•.r-0.76.        Checking,  v-cV^ - 

80.45X0.866X0.031 62=- 2.2,  the  given  velocity. 

(8)  Given,  mean  radius  r— 6,  roughness  n  — .020,  and  required  velocity 
t;»  3;   to  find  the  slope  5? 

Use  "cut  and  hy"  method:  assume  s  in  the  equation  j—  —  •  "^"Tf  *  — j- 

\      tA      \  9 

1st.  let  5-. 0001,  then  from  section  6  of  Table  8, -^--a'  TTTi^iT,- 

f        C*       O      (lOi.l)* 

000144;  2nd.  let  5-.00015.  then—    -^-X- TTAT-sr.-  00015.  .'.5-. 00015. 
r       C*      O      (101.3)' 

:hecking,    ©-cVrJ- 101. 3X2.45X. 01225- 3.04.      If  greater  accuracy   is 

cqtxired,  assume  a  new  slope  slightly  less  than  s-»  .00015  and  try  again. 

The  Vcfitnri  Meter. — ^This  is  an  apparatus  for  determining  the  rate  of 
ischarse  of  water  through  pipes,  by  inserting  the  meter  in  the  pipe  line 


\fet)fmMefer7ade 
i-^  <  t  i 

Fig.  9. — Venturi  Meter. 

\  connecting  it,  by  pressure  pipes,  to  a  register.  The  principle  on  which  it 
>Ased  "V^as  discovered  by  J.  B.  Venturi.  and  his  experiments  were  followed 

0o68ut,  Castel,  Herschel  and  others.  The  apparatus  is  illustrated  in 
9.  and  consists  of  a  short  pipe  V,  of  comparatively  small  diameter,  called 

•v^tUMTi^  joining  a  convergmg  frustum  of  a  cone  or  mouthpiece  Af ,  with  a 
srgrog  conical  frustum  D:   these  three  pipes  beinff  inserted  in  the  pipe 

^I^,  "With  the  water  flowing  in  the  direction  indicated  by  the  arrows. 
rounding  the  imtturi  V.  is  an  air  chamber,  the  cast-iron  shell  separating 
air  cliamber  from  the  venturi  being  pierced  with  a  few  small  holes,  care- 
/■  drilled,  living  ^arp,  square  edges  on  the  inside  face  of  the  venturu 


1174 


^.—HYDRAUUCS, 


Venturi  discovered  that  when  water  flows  through  such  a  oonvetgicA 
mouthpiece  and  a  narrow  throat,  V,  and  then  expands  into  a  diveism^  tube 
or  bell.  D,  there  is  a  decided  decrease  of  water  pressure  against  the  inside 
of  the  conduit  from  the  beginning  of  the  mouthpiece  to  the  vetUuri,  at  which 
point  it  is  a  minimum,  and  then  a  decided  increase  in  pressure  from  the 
venturi  to  the  end  of  the  diverging  tube  D.  He  correctly  interpreted  the 
cause  of  this  reduction  of  pressure  at  V  as  due  to  a  partial  vacuum  at  o, 
just  beyond  the  venturi,  caused  by  the  jet  of  water  expanding  from  the 
throat  along  the  tube  D.  In  fact,  not  only  is  the  pressure  at  the  venitm 
greatly  reduced,  as  in  Pig.  11.  but  with  high  velocity  of  discharge  the  pres- 
sure changes,  sometimes,  from  positive  to  negative,  actually  causang  a 
suction  in  the  air  chamber  at  the  venturi. 

Mr.  Herschel  has  clearly  demonstrated  that  the  differences  in  pressure  at 
the  beginning  of  the  mouthpiece  and  at  the  venturi  increases  with  the  velocity 
of  flow,  and  has  established,  by  numerous  experiments,  a  relation  or  rela- 
tions between  the  two  so  that,  knowing  the  difference  in  pres- 
stu-es  at  the  two  points,  for  a  given  meter,  the  discharge  can  be 
determined. 

The  Meter  Register,  indicated  in  Pig.  9,  automatically  .records 
the  discharge  directly,  in  gallons,  cubic  feet  or  poxmds — per 
second,  minute,  hour  or  day.  The  register  is  controlled  by  the 
pressures,  or  dinerence  of  pressures,  in  the  pressure  pipes  leading 
trom  the  meter. 

The  Manometer  (Pig.  10)  is  a  cheap  device  and  not  auto- 
matic as  a  constant  recorder.  It  is  a  portable  instrument  that 
can  be  attached  to  any  meter  tubes  on  the  pipe  line  and  the  rate 
of  flow  determined  by  reading  the  gauge,  which  has  been  gradu- 
ated to  "cubic  feet  per  second,"  or  "gallons  per  day,  *  etc.,  ^ 
based  on  difference  of  pressure  in  tne  connecting  pre^ure  PigTlOi 
tubes.                                                                                                    Manometer. 

Piesometer  tubes  form  a  very  simple  device  for  measuring  the  pztsssure 
and  flow  in  pipe  lines  and  venturi  meters.  These  arc  glass  and  iron  tubes 
inserted  at  the  required  points  along  the  line  by  "tapping"  the  pipe  so  that 
water  will  rise  in  the  piezometers  to  the  hydraulic  gradient,  or  line  of  no 

Pressure.    Let  PM,  PV  and  PD  be  glass  piezometers  inserted  at  points  M, 
\  and  D,  Figs.  11  and  12.    Each  figure  shows  the  hydraulic  grade  line  (1) 


2S£Sffift5?_^-?%o. 


'^'^iSS^SIi^S^'Sf!:!^ 


Pig.  11. 

Pressiire  at  the  venturi. 


Fig.  12. 
Suction  at  the  ventteri. 


for  a  uniform  section  of  pipe,  and  (2)  with  the  venturi  meter  inserted  in  tt^ 
pipe  line.  If  there  is  n6  meter  in  the  pipe  line,  that  is,  no  contraction  of  area, 
the  H.  G.  L.  will  be  a  straight  line  on  a  falling  grade  in  the  direction  of  the 
flow,  but  may  be  considered  as  "level"  for  such  a  small  distance  as  the 
length  of  the  meter  would  occupy,  as  far  as  the  present  discussion  is  cor- 
cemcd;  in  other  words,  the  loss  of  head  for  this  distance  would  be  practically 
zero.  If  now  the  meter  is  inserted  in  the  pipe  line,  the  H.  G.  L.  win  drop 
with  a  descending  grade  from  Af  to  V,  and  with  an  ascending  grade  from  V 
to  D\  but  it  will  be  noticed  that  it  does  not  rise  to  its  former  level  at  D, 
there  being  a  loss  of  head  L  in  the  flow  through  the  meter  ixxsm  M  to  D.  As 
the  areas  of  the  pipe  at  the  piezometer  PM  and  PD  are  equal,  the  vekxaties 
at  these  points  are  equal,  hence  the  loss  of  pressure  head  L  represents  a  total 
loss  of  head  between  those  points,  no  part  of  it  beins  compensated  for  by  aa 
increase  in  velocity.  On  the  other  hand,  the  loss  of  preituie  head  betweeo 
-g  and  V,  represented  by  the  difference  in  water  levels  in  the  picsometei^ 
PM  and  P  V,  is  nearly  all  compensated  for  by  the  increased  velocity  <rf  fio* 


VENTURl  METER,   ORIFICES.  JETS,  ETC.  U75 

at  Vover  that  at  Af,  or  in  other  words  by  the  increased  velocity  head  h,.  Pig. 
11.  Experiments  on  standard  meters  show  that  this  velocity  head  represents 
about  9»  per  cent  of  the  lost  pressure  head  shown  by  the  piezometers,  the 
other  2  per  cent  being  a  total  loss. 

Where  there  is  negative  pressure  or  suction  at  the  vtnturi  (Pig.  12)  the 
piezometer  tube  is  bent  in  the  form  of  a  siphon  and  the  amount  of  negative 
pressure  head  is  measured  by  the  height  n.  of  the  colimin  of  water  m  the 
tube.  This  distance  is  laid  off  btlcw  the  center  of  the  twff/«rf,  as  fixing  the 
lowest  point  of  depression  in  the  hydraulic  grade  line.  The  velocity  head  is 
determined  by  the  total  change  of  pressure  head  as  in  the  preceding  descrip- 
tion, taking  into  account  of  course  the  snfall  percentage  of  actual  loss. 

Fig.  13  shows  the  standard  dimensions  of  the  vttUHri  meter  in  terms  of 
the  length  of  the  tmnturi  V,  assumed  as  unity;  and  it  is  claimed  that,  based 


Fig.  18. — Standard  Proportions  of  Venturi  Meter. 

on  these  proportions,  for  such  a  meter,  with  the  diameter  of  the  pipe  ranpring 
from  one  to  nine  feet,  and  with  a  velocity  through  the  pipe  ranging  from 
one-half  to  six  feet  per  second,  the  total  loss  of  head  in  the  mouthpiece  will 
be  about  2  per  cent  of  the  difference  in  pressure  at  these  points.  That  is  to 
say,  the  coefficient  of  velocity  at  the  venturi  closely  approxmates  98  per  cent. 
The  standard  meter  is  proportioned  with  one  main  pomt  in  view,  namely,  to 
produce  a  marked  increase  in  velocity  at  the  venturi,  with  as  little  total  loss 
as  possible  in  the  whole  meter.  In  principle,  it  shows  that  if  a  pipe  line  is 
contracted  at  an)^  point,  the  pressure  head  is  reduced  at  that  point,  being 
partly  converted  into  velocity  head:  and  conversely,  if  it  is  expanded  there 
is  a  tendency  toward  reconversion  oi  velocity  head  into  pressure  head. 

Leaving  out  the  velocity  of  approach,  the  makers  use  the  following 
formula  for  discharge: 

q^caVil.02±)fu (1) 

In  which    9 —discharge  in  cu.  ft.  per  sec.,  or  any  other  tmits; 

c  —  a  constant  or  coefficient  of  velocity,  determined  by  experiment; 
a  — area  of  cross-section  of  venturi  V,  in  so.  ft.; 
( 1. 02 d:)/k— difference  in  height  of  piezometers  PM  and  PV,  in  ft.; 
/k  — increase  in  velocity  head  at  V  over  that  at  M. 
Note  that  (1.02  ±)/k  is  us^  for  simplicity  of  illustration  in  keeping 
learly  in  mind  the  relative  value  of  the  difference  of  velocity  heads  h,.     It 
i  to  be  noted  also  that  the  actual  velocity  at  the  throat  or  venturi,  Vu 
■VTgA-Kthe  velocity  of  approach,  and  not  simply  V2gh. 

OritictSf  Tubes,  Noizles  and  Jets. — ^The  theoretic  discharge  from  an 
rifice  is  obtained  by  integrating  or  taking  the  summation  of  the  discharge 
r  each  infinitesimal  layer  of  water  of  transverse  length  x,  thickness  dy,  and 
2£Ld,  y  between  the  proper  limiting  values  of  the  head.  Thus,  in  computing 
able  9.  following,  we  have — 

J*y-// 
*  dy\/2  gy (2) 
y-A 
which  *— 6;  hence,  theoretically, 

9-16  vTr(H*-A*) ..(3) 

vc  rectangular  weirs,  the  upper  head  h^O,  H'^d,  bd^a;  .'.  q^  la  'n/2  g  d. 
Other  forms  of  orifices  are  calculated  in  the  same  manner.   The  actuai 
icHaj-ge  and  velocity  are  closely  approximated  by  using  coefficients  of  area 
•  contraction,  velocity  and  discharge.    Let — 

c— coefficient  of  contraction  of  jet;  ^^  , 

c-coefficient  of  velocity  of  jet;  Digitized  by  LjOOQIc 

c% — coefficient  of  discharge .  ^ 


1176 


02.— HYDRAULICS. 


Then,  Actual  area  of  issuing  jet  at  its  smallest  section  -CiO; (t 

Actual  veloc.  of  issuing  jet  at  its  smallest  section  —  c.  v— 8.02  c,VS;(I 

Actual  discharge  of  issuing  jet  — f,fl— 8.02  car,  VA©; (I 

Coefficient  of  discharge  — c,—c.<:» t" 

The  values  of  c,  c,  and  d,  for  the  variotis  shapes  and  conditions  of  on- 
fices,  nozzles,  jets,  etc.,  are  determined  by  experiment.  The  coefficient  d 
contraction  of  area,  c^  for  small  standard  orifices  may  be  a^umed  at  aboui 
0.63;  the  coefficient  of  velocity,  c»,  at  about  0.98;  and  the  coefficient  oc 
discharge  c, — r.  c.  —  0. 63  X  0. 98  -  0. 62.  These  values  of  the  coefficients  sub- 
stituted in  equations  (4),  (6)  and  (6)  will  give,  approximately,  the  results 
which  may  be  expected  in  practice. 

Table  9,  following,  shows  the  discharge,  q,  from  rectangular,  trianguhr 
and  circular  orifices: 

0. — ^Tablb  op  Discharges  Pfom  Oripicbs. 
(a)    Orifices  Submerged. 


Function. 


(1) 


Area.. 


Discharge. 


1^ 


Fig.  14. 
(2) 


hd 


c^lbVTgiH^-hh 


m 

Fig.  16. 
(8) 


bd 
2 

Not  important 


TT — JC~ 


Pig.  16. 
(4) 


4 


6r* 
'1024H* 


105H 
'65536//«' 


And  when  the  tops  of  the  orifices  touch  the  surface  of  the  water,  *  be- 
comes zero  and  we  have,  in  each  case,  the  following  values: 

(6)    Water  Surface  at  Tops  of  Orifices. 


Discharge 


<:,  I  a  y/2g  d 


c,  A6  d  y/Wdl  <:,  ^r«v'2g7(0.96) 


Hi  d^    //-*  d«    H-l  d*    H-i  d» 


6  82  80       /  • 

Comparison  op  Oripicbs  and  Tubes. 
The  standard  orifice  (Fig.  17)  has  sharp,  vertical  edges.    From  data  abow 
c.  -  0.626;  <r,  =  0.98;  c,- 0.6 126.     The  discharge  can  be  increased  by  insert- 
ing the  standard  tube. 

The  standard  tube  (Fig.  18)  is  made  just  long  enough  ao  the  expanding 


Fig.  17.  Fig.  18.  Fig.  19.  Fig.  20.  Fig.Stt. 

jet  completely  fills  its  extremity.  Around  the  contracted  portion  of  the  ie< 
there  is  a  partial  vacuum,  which  may  be 'tested  by  tapping  the  tube  and 
mserting  a  glass  piezometer,  P,  with  its  lower  end  immersed  in  a  basis  erf 
^atcr.  The  water  will  rise  in  the  piezometer,  indicating  suctioo.  Ttx 
vacuum  is  produced  by  the  particles  of  water  or  spray  of  the  jet  forcing  tttf 


DISCHARGE  FROM  ORIFICES,  ETC.    WEIRS. 


1177 


air  out  of  the  tube.  The  effect  is  to  increase  the  velocity  and  dischane 
over  that  of  the  standard  orifice.  The  values  of  c^  and  c,  are  about  0  81  or 
0.82,  average. 

The  conical  noMMU  (Fig.  19)  is  designed  to  increase  the  ene«ry  of  the  jet. 
The  aMie  of  divergence  of  the  sides  of  the  cone  is  about  13®  or  14*  for  maxi- 
mum discharge,  when  c,-0.»6.  nearly.  Sometimes  the  outer  end  of  the 
cone  is  provided  with  a  short  straight  tube.  The  coefficient  of  velocity 
increases  with  the  angle  of  the  cone. 

The  Vtnturi  meUr  is  simply  a  compound  tube  (Fig.  20)  and  is  explained 
on  page  1173,  etc. 

The  flaring  orMl^shaf^  mouthpiece  (Fig.  21)  decreases  the  loss  of  head 
at  entrance,  usually  called  Entry  Head  (see  page  1160)  and  is  recommended 
for  use  at  the  intake  end  of  pipe  lines. 

Wdft.— The  weir  is  simply  a  water  meter.  Next  to  the  Venturi  meter 
(sec  paffc  1173)  the  standard  wen*  is  probably  the  most  accurate  device  for 
measuring  the  flow  of  water.  It  is  practically  adapted  to  gaging  the  flow  of 
small  streams,  creeks,  canals,  ditches,  and  the  discharge  from  pipe  lines  and 
sewers^ 

The  standard  weir  is  a  rectangular,  vertical  opening  through  which  the 
surface  water  is  allowed  to  discharge.     The  edges  of  the 
opening  should  be  chisel-edged,   the   "crest"    perfectly 
level,  and  the  sides  perfectly  plumb.   Fig.  22  represents  a 
section  of  a  standard  weir 
with  the  water  flowing  over       |;  Jjfve/ 

the  crest.  Note  that  the  sur-       ^  —— »- 

face  of  the  discharging  vol-         i 

ume  describes  a  curve  from         •  rs      ^ 

a  point  of  tangency  T,  d  istant  •*k.  JT'^^^  Atg/fi 

D  from  the  crest  of  the  dam,   "^      ^^  ^^  •«-'«-»p- 

the  drop  at  the  crest  being  s. 

Pig.  23  is  a  plan  of  the  weir 

showing  the  length  of  crest/, 

and  the  side  contractions  e 

and  e'  of  the  flow,  for  the 

"end  contractions"  Hand  E\ 

The  standard  weir  is  a  weir  „.     o«      e  ^-       i  t>i 

with  end   contractions;    the  P«-  22.— Sectional  Elevation. 

weir   without   end   contractions   is  called  the  "suppressed' 

the  end  contractions  are  suppressed. 

The  theoretic  discharge  through  a  rectangular  weir,  neglecting  velocity 
of  approach,  is  obtained  Irom  the  equations  on  pages  1175  and  1176,  reduc- 
ixig  to—  ^ 

<7-  ILvilp //■  (no  velocity  of  approach) (8) 

in  which    9— discharge  in  cu.  ft.  per  second; 
L- length  of  weir,  in  feet  (Fig.  23); 

//  —  "surface  level"  head  on  crest,  in  feet  (Fig.  22).         

If  it  is  desired  to  include  velocity  of  approach,*  v,  (-V2«/».).  this 
value  must  be  inserted  inequation  (2).  page  1176.  before  integrating;  thus, 

J*y  — //        , 
X dy  V2gy  +  vJ (9) 
yh 

whence  9-i  L\/2iff(H +*.)•-  (A+A.)^  (including  velocity  of  approach)  .(10) 
in  which  *•  — velocity  head  of  approach;  and  A  =  0. 

It  is  to  be  noted  that  these  formulas,  (8)  and  (10),  are  purely  theoretical, 
and  that  little  or  no  importance  can  be  attached  to  them  as  they  stand. 
But  like  all  theoretic  expressions,  each  forms  a  skeleton  or  groundwork 
upKjn  which  to  build  the  more  or  less  "emperical"  formulas  which  are  used 
in  practice.  The  practical  formulas  are  deduced  from  the  above  by  supply- 
ing the  proper  coefficients,  which  are  determined  by  experiments. 

•The  velocity  of  approach  should  be  measured  at  the  point  T,  Fig.  22. 
[t  should  comprise  generally  the  average  velocity  for  some  depth  below  the 
norface  and  not  the  "surface"  velocity,  which  is  often  used;  the  latter  may 
>e  close  enough,  however,  in  many  instances.  The  surface  velocity  may  be 
>btamed  by  the  surface-float  method  (Fig.  29);  the  average  velocity,  by  the 
nten^ttng  float  rod  (page  1183),  or  by  the  current  meter  (page  1 186),  or  by 
h*rpitot  tube  (oaae  1183). 


1178  e2.'-HYDRAUUCS, 

(a)    Francis*  Wbir  Formulas. 
General  formula  applicable  to  any  sharp-crested,  surface  wrir: 

9- 3,33  (L-0.1 » /f)  [(H+hnfi-hJ^ (11) 

in  which    o  — discharge  in  cu.  ft.  per  second; 
/-  —  length  of  weir  in  feet; 
M  — number  of  end  contractions,  as  0,  1  or  2; 
H  — "surface  level"  head  on  crest,  in  feet; 

*.-veIocity  head  in  feet  - ''"""^^  "^^^P"*"^ '-. 

Formula  (11)  may  be  simplified  to  meet  the  following  special  cases: 
With  velocity  of  approach — 

Contracted  1^°^  ^''^'   «" 3.33  (L-0.2H)  [(H+h.)^-0] (12) 

[One  end:      <7-3.33  (L-O.IH)  [(H+k)^-kJ] (13) 

Suppressed;  <7-8.33L[(//+A0*-A.*] (14) 

Without  velocity  of  approach  (i.  e.,  Ao  —  O) — 

Contracted  }»<^^^"^'^-   «"  3.38  (L- 0.2  H)  «« (15) 

tone  end:       q^ 3.33  iL-0.lH)H* (1«) 

Suppressed:  9-3.38//* (17) 

The  above  formulas  are  veay  extensively  used  in  the  United  States. 
They  were  deduced  by  Mr.  J.  B.  Francis,  in  1854,  from  very  elaborate  expen- 
ments  which  he  conducted  at  Lowell,  Mass..  on  large  weirs  about  10  feet  long. 
The  heads  ranged  usually  from  0.4  to  1.6  feet.  The  formulas  are  simple, 
logical  and  fairly  reliable  within  the  range  of  the  experiments.  The  h^ids 
H  were  measured  6  ft  back  from  the  crest  (Fig.  22). 

(jb)    Bazin's  Wbir  Formula. 
General  formula  applicable  to  sharp-crested,  suppressed,  surface  weirs  is 

.,.  (0.405+":^)  [l+0.6«(^)']  tHVj^ (.8, 

in  which  p  — height  of  crest  above  the  bottom  (Fig.  22)  and  the  other 
notation  as  per  Francis'  formulas,  preceding.  This  formula  (16)  takes  into 
consideration  the  velocity  of  approach  in  the  height  of  crest  p,  hence  the 
former  does  not  require  any  special  treatment  when  p  is  known.  It  should 
be  remarked  that  the  formula  was  deduced  from  very  careful  experiments 
with  standard  weirs  from  0.656  ft.  (0.2  meter)  to  6.56  ft.  (2  meters)  in  length 
and  with  heads  ranging  from  2.50  to  1.00  ft.,  the  lower  heads  for  the  kmscr 
weirs.  C^are  should  be  used  in  extending  the  use  of  the  formula  beyond  the 
above  range  for  length  L  and  head  H.  It  should  be  noted  that  Basm 
measured  the  head  If  at  points  distant  D  — 16.4  ft.  back  from  the  crest.  (See 
Fig.  22.) 

The  above  general  formula  (18)  can  be  simplified  for  practical  use  by 
letting 

hence         <7-m  L  H  \/2e  H-'tnVTg  L  H  VH (!•) 

Either  of  these  two  forms  (19)  may  be  used  in  connection  with  the  fol- 
lowing table  which  gives  the  values  of  m  (and  of  mV^ )  for  given  values  of 
p  and  H. 

The  second  form,  q  -  (my/2g)  L  H  VH  will  probably  be  found  more 
convenient  as  the  table  gives  average  values  of  {m\/2g)  for  each  five  successive 
values  of  H,  and  intermediate  values  may  be  interpolated.  If  extreme 
accuracy  is  required  the  first  form  is  preferred,  remembering  that  V2jfi/«» 
8.02\/]tf.    Note  that  the  last  column  in  Table  10  gives  the  limiting  vahie  of 

(0  00984\ 
0.405+    •  j.  the  first  part  of  the  coefficient. 

as  the  latter  part  reduces  to  unity.  Hence  this  value  of  m  may  be  used 
^hen  there  is  no  velocity  of  approach,  that  is,  when  p  is  very  large. 

*  The  standard  weir  provides  for  free  admission  of  air  under  the  CalUng 
sheet  of  water. 


WEIR  FORMULAS— FRANCIS,  BAZIN, 


1179 


10.--VALUB8  OF  THB  COBrFICIBNT   m    IN   THB  FORMULA  q^mLH  V2gH, 

FOR  A  Sharp-Crbsted  Wbir  without  Lateral  Contraction. 
THB  Air  being  Aduittbd  Prbelt  Bbnbath 
THE  Overflowing  Sheet  of  Nappe. 


m 

Ott- 

weir  above  the  bottom  of  the  channel. 

Iff 

lit- 

(I) 

(2) 

(3) 

(4) 

(8) 

(6) 

(7) 

(8) 

W 

(10) 

(II) 

Value 
jfp.ln 
Feet. 

0.656 

0.964 

1.312 

1.640 

1.968 

2.624 

3.280 

4.920 

6.660 

GO 

0.164 
0.197 
0.230 
0.262 
0.295 

0.458 
0.456 
0.455 
0.456 
0.467 

0.453 
0.450 
0.448 
0.447 
0.447 

0.451 
0.447 
0.445 
0.443 
0.442 

0.450 
0.445 
0.443 
0.441 
0.440 

0.449 
0.445 
0.442 
0.440 
0.438 

0.449 
0.444 
0.441 
0.438 
0.436 

0.449 
0.443 
0.440 
0.438 
0.436 

0.448 
0.443 
0.440 
0  437 
0.435 

0.448 
0  443 
0.439 
0.437 
0.434 

0.4481 
0.4427 
0.4391 
0.4363 
0.4340 

4eans 

0.456 
3.66 

0.449 
3.60 

0.446 
3.58 

0.444 
3.66 

0443 

3.56 

0.442 
3.54 

0.441 
3.54 

0.441 
3.53 

0.440 
3.53 

0.4400 
3.53 

0.328 
0.394 
0.459 
0.525 
0.591 

0.459 
0.462 
0.466 
0.471 
0.475 

0.447 
0.448 
0.450 
0.453 
0.456 

0.442 
0.442 
0.443 
0.444 
0.445 

0.439 
0.438 
0.438 
0.438 
0.439 

0.437 
0.436 
0.435 
0.435 
0.435 

0.435 
0.433 
0.432 
0.431 
0.431 

0.434 
0.432 
0.430 
0.429 
0.428 

0.433 
0.430 
0.428 
0.427 
0.426 

0.433 
0.430 
0.428 
0.426 
0.425 

0.4322 
0.4291 
0.4267 
0.4246 
0.4229 

leans 

0.467 
3.74 

0.451 
3.62 

0.443 
3.56 

0.438 
3.52 

0.436 
3.60 

0.432 
3.47 

0.431 
3.46 

0.429 
3.44 

0.428 
3.44 

0.4271 
3.43 

D.656 
».72a 
).787 
).853 
).919 

0.480 
0.484 
0.488 
0.492 
0.496 

0.459 
0.462 
0.465 
0.468 
0.472 

0.447 
0.449 
0.452 
0.455 
0.457 

0.440 
0  442 
0.444 
0  446 
0.448 

0.436 
0.437 
0.438 
0.440 
0.441 

0.431 
0.431 
0.432 
0.432 
0.433 

0.428 
0428 
0.428 
0.429 
0.429 

0.426 
0.424 
0.424 
0.424 
0.424 

0.423 
0.423 
0.422 
0.422 
0.422 

0.4215 
0.4203 
0.4194 
0.4187 
0.4181 

[eans 
^V2^ 

0.488 
3.92 

0.465 
3.73 

0.452 
3.63 

0.444 
3.56 

0.438 
3.52 

0.432 
3.46 

0.428 
3.44 

0.424 
3.40 

0.422 
3.39 

0.4196 
3.37 

L984 
060 
.116 
.181 
.247 

0.500 
0.500 
0.500 
0.500 
0.500 

0.476 
0.478 
0.481 
0.483 
0.486 

0.460 
0.462 
0.464 
0.467 
0.469 

0.460 
0.452 
0.454 
0.456 
0.458 

0.443 
0.444 
0.446 
0.448 
0.449 

0.434 
0.436 
0.437 
0.438 
0.439 

0.430 
0.430 
0.431 
0.432 
0.432 

0.424 
0.424 
0.424 
0.424 
0.424 

0.421 
0.421 
0.421 
0.421 
0.421 

0.4147 
0.4168 
0  4162 
0.4156 
0.4150 

eanfl 

0.500 
4.01 

0.481 
3.86 

0.464 
3.73 

0.454 
3.64 

0.446 
3.58 

0.437 
3.50 

0.431 
3.46 

0.424 
3.40 

0.421 
3.38 

0.4162 
3.34 

.312 
.378 
.444 
.909 
.575 

0.500 
0.500 
0.600 
0.500 
0.500 

0.489 
0.491 
0.494 
0.496 
0.496 

0.472 
0.474 
0.476 
0.478 
0.480 

0.459 
0.461 
0.463 
0.465 
0.467 

0.451 
0.452 
0.454 
0.456 
0.457 

0.440 
0.441 
0.442 
0.443 
0.444 

0.433 
0.434 
0.435 
0.435 
0.436 

0.424 
0.425 
0.425 
0.425 
0.425 

0.421 
0.421 
0.421 
0.421 
0.421 

0.4144 
0.4139 
0.4134 
0.4128 
0.4122 

eaiiB 
v/2? 

0.500 
4.01 

0.493 
3.96 

0.476 
3.82 

0.463 
3.72 

0.454 
3.64 

0.442 
3.55 

0.435 
3.49 

0.425 
3.41 

0.421 
3.38 

0.4133 
3.32 

.640 
.706 
.772 
.837 
903 
969 

0.600 
0.500 
0.600 
0.600 
0.600 
0.600 

0.496 
0.496 
0.496 
0.496 
0.496 
0.496 

0.482 
0.483 
0.485 
0.487 
0.489 
0.490 

0.468 
0.470 
0.472 
0.473 
0.475 
0.476 

0.459 
0.460 
0.461 
0.463 
0.464 
0.466 

0.445 
0.446 
0.447 
0.448 
0.449 
0.451 

0.437 
0.438 
0.438 
0.439 
0.440 
0.441 

0.426 
0.426 
0.426 
0.427 
0.427 
0.427 

0.421 
0.421 
0.421 
0.421 
0.421 
0.421 

0.4118 
0.4112 
0.4107 
0.4101 
0.4096 
0.4093 

0.600 
4.01 

0.496 
3.98 

0.486 
3.90 

0.472 
3.79 

0.462 
3.71 

0.448 
3.60 

0.436 
3.50 

0  427 
3.42 

0.421 
3.38 

0.4104 
3.29 

c 

^ 

1180 


e2.^HYDRAULlCS. 


i 


No  velocity  of  approach . . .  (SO) 


CM) 


Problem. — ^What  is  the  diacharse  through  a  weir  whoae  crest  is  7  ft.  loog 
and  2.6  ft.  above  the  bottom;  the  measured  head.  H,  being  0.75  ft.  ? 

Solution. — ^The  value  of  m  in  the  preceding  table  for  ^ — 2.6  and  ^  —  0, 76. 
is  0.438;  then  from  first  equation  (10).  <7--0.433X 8.02X7X0.76 X 0.866* 
16.8  cu.  ft.  per  second.    Ans. 

(c)    Ptblby  and  Stearns'  Wbir  Pormitlas. 
General  formula  for  sharp-crested,  suppressed,  surface  weirs,  m 
<?=.  0.4126  L // V^il/+0.007i 
-8.31  Li/ V77+0.007L 
and.  if  there  is  velocity  of  approach, 

, ( Including  ve-  ] 

<7-3.31L(/f+1.6A.)  V/f+1.6A.+  0.007L^     locity  ofj 

(    approach,    j 

Use  notation  for  Prands'  formula,  page  1 1 78.  The  above  formulas  were 
deduced  from  experiments  which  they  made  in  Boston,  Mass.,  1877-0.  with 
weirs  6  to  10  ft.  long  and  tmder  heads  ranging  from  0.066  up  to  1.6  feet. 
The  heads  H  were  measured  6  ft.  back  from  the  crest. 

(d)  *Parmlbt*s  Wbir  PoRittTLA. 
General  formula  for  sharp-crested,  surface  weirs,  either  contracted  or 
suppressed,  taking  into  account  velocity  of  approach,  if  any: 

<7-CkiC[L-0.1»i/]H* (22) 

in  which    o— discharge  in  cu.  ft.  per  second; 

£■» length  of  weir,  in  ft.; 

n— number  of  end  contractions,  as  0,  1  or  2; 
//  —  "surface  level"  head  on  crest,  in  ft.; 
C— constant  for  given  valtie  of  H,  ifrom  Table  11; 

/^—constant  for  given  value  of  -r,  from  Table  12; 

a—  (L—  0.1  n  H)  /7— contracted  area  of  discharge; 
A  —area  of  water  section  in  channel  of  approach. 

11. — Valubs  of  Cobppicibnt  C  FOR  GivBN  Valubs  o»  H. 
(Equation  22.) 


H 

C 

H 

c  i 

a 

C 

a 

C 

H 

C 

Ft. 

Ft. 

Ft. 

Ft. 

Ft. 

0.10 

3.680 

0.40 

3.385 

OJO 

3.351 

1.00 

8.834 

l.M 

3.301 

0.15 

8.520 

0.45 

8.376 

0.75 

3.349 

1.10 

3.329 

1.70 

3.2M 

0.20 

8.478 

0.50 

3.368 

0.80 

3.346 

1.20 

8.324 

1.80 

3.1ft 

0.25 

3.444 

0.65 

3.362 

0.85 

8.348 

1.10 

8.819 

1.90 

a.  281 

0.30 

3.420 
3.400 

0.60 

3.358 

0.90 

3.340 

1.40 

3.813 

2.00 

xtm 

0.35 

0.65 

3.354 

0.95 

8.837 

1.60 

3.307 

12. — Valubs  of  Cobfficibnt  K  for  Givbn  Valubs  of  //. 
(Equation  22.) 


a 

K 

a 

K 

— r 

a 

K 

a 

K 

a 

K 

A 

A 

A 

A 

A 

0.01 

1.0001 

0.13 

1.0093 

0.25 

1.0344 

0.37 

1.0753 

0.49 

1.1321 

0.02 

1.0002 

0.14 

1.0108 

0.26 

1.0872 

0.38 

1.07M 

0.50 

1.137S 

0.03 

1.0005 

0.15 

1.0124 

0.27 

1.0401 

0.39 

1.0837 

0.61 

1.14S1 

0.04 

1.0009 

0.16 

1.0141 

0.28 

1.1431 

0.40 

1.06B0 

0.52 

I.14C7 

0.05 

1.0014 

0.17 

1.0159 

0.29 

1.0463 

0.41 

1.0925 

0.53 

l.I6« 

0.06 

1.0020 

0.18 

1.0178 

0.30 

1.0495 

0.48 

l.OWO 

0.54 

1.I494 

0.07 

1.0027 

0.19 

1.0198 

0.31 

1.0529 

0.43 

1.1017 

0.56 

1.I6S4 

0.08 

1.0035 

0.20 

1.0220 

0.32 

1.0563 

0.44 

1.1065 

0.56 

i.im 

0.09 

1.0044 

0.21 

1.0243 

0.33 

1.0599 

0.45 

l.UU 

0.67 

I.I7II 

0.10 

1.0055 

0.22 

1.0266 

0.34 

1.0636 

0.46 

1.1164 

0.8B 

cat 

0.00 

I.IM 

0.11 

1.0066 

0.23 

1.0291 

0.35 

1.0674 

0.47 

1.1216 

Litis 

0.12 

1.0079 

0.24 

1.0317 

0.36 

1.0713 

0.48 

1.1267 

I.IM 

*  Discussion  by  W.  C.  Parmley,  Trans.  Am.Soc.C.E.,  Vol.JCLIV.  p.  J5L 

Digitized  by  VjOOQ  IC 


WEIRS—SURFACE  AND  SUBMERGED— FORMULAS.     1181 

Pannley's  formula  (22])  was  not  deduced  from  any  particular  set  of 
experiments,  but  is  based  on  the  experiments  and  formulas  of  Bazin, 
Francis,  and  Fteley  and  Steams.  The  result  obtained  is  a  formula  com- 
prehensive in  character  and  giving  average  values.  Bazin's  experiments 
were  made  very  carefully  under  ideal  conditions  in  a  long,  smooth  canal 
lined  with  cement,  while  those  of  Francis  and  Fteley  and  Steams  were  con- 
ducted under  conditions  more  nearly  approaching  those  to  be  fotmd  in 
practice.  The  roughness  of  the  stream  or  canal  must  necessarily  produce 
an  appreciable  effect  on  the  flow. 

Triangular  and  trapewoidal  weirs  have  been  proposed  in  place  of  the 
standard,  rectangular  section,  on  account  of  the  very  slight  variation  of  the 
coefficient  of  discharge  for  different  heads  if.  But  they  have  not  yet  come 
into  practical  use. 

The  Submerged  Weir,  so-called  because  the  water  level  below  the  weir 
rises  higher  than  the  crest,  is  shown  in  fig*  24. 


Fig.  24. — Submerged  Weir. 

(a)  Fteley  and  Steams'  formula*  for  submerged  weirs,  without  end  con- 
tractions is, 

«-mL(//+Y)(H-A)* (23) 

in  which    o— discharge  in  cu.  ft.  per  second; 
//  —  up-stream  head  on  crest,  in  feet; 
A —down  stream  head  on  crest,  in  feet; 
L"- length  of  weir,  in  feet; 

k 
m-»  coefficient  for  given  values  of  ^,  as  in  the  following  Table. 


13. — Values  of  Cobppicibnt  m  for  Givbn  Values  of 


(Equation  23., 

m        1       * 

m 

h 
H 

m 

h 

m 

If 

m 

0.00 
0.04 
0.08 

3.33         0.12 
8.35        0.16 
3.37         0.20 

3.35 
3.32 
3.28 

0.30 
0.40 
0.50 

3.21 
3.15 
3.11 

0.60 
0.70 
080 

3.09 
3.09 
3.12 

0.90 
1.00 

3.19 
3.33 

(6)    Herschel's  formulat  for  submerged  weirs,    based  on  experiments 
ide  by  Francis  and  by  Fteley  and  Steams,  is  as  follows: 

«-  3.83  L  (c  //)* (24) 

•which     c  — coefficient  for  given  values  of  tt  in  the  following  Table,  the 

axice  of  the  notation  same  as  for  the  Fteley  and  Stearps'  formula,  preced- 


♦  Trans.  Am.  Soc.  C.  E.,  Vol.  XII.  page  103.  ^^  .    „^ 

t  Discussion  by  Clemens   Herschel,  Trans.  Am.  S«)|JtizC3.b^«i0^gl3trv. 


1182 


e2,— HYDRAULICS. 


14. — COBFPICIBNTS  C  FOR  GiVBN  VALUES  OF  ^7.      (Fig.  24.) 


(Eqtiation  24.) 


h 

h 

h 

h 

h 

If 

c 

If 

c 

-w 

c 

-H 

c 

H 

e 

0.00 

1.000 

0.18 

0.989 

0.38 

0.935 

0.58 

0.856 

0.78 

0.721 

.01 

1.004 

.20 

0.985 

.40 

0.929 

.60 

0.846 

.80 

0,703 

.02 

1.006 

.22 

0.980 

.42 

0.922 

.62 

0.836 

.82 

0.6a 

04 

1.007 

.24 

0.975 

.44 

0.915 

.64 

0.824 

.84 

0,659 

.06 

1.007 

.26 

0.970 

.46 

0.908 

.66 

0.813 

.86 

0.634 

.08 

1.006 

.28 

0.964 

.48 

0.900 

.68 

0.799 

.88 

0.60C 

.10 

1.005 

.30 

0.959 

.60 

0  892 

.70 

0.787 

.90 

0.5.-4 

.12 

1.002 

.32 

0.953 

.52 

0.884 

.72 

0.771 

.93 

0.54 

.14 

0.998 

.34 

0.947 

.54 

0.875 

.74 

0.755 

.96 

0.45 

.16 

0.994 

.36 

0.941 

.56 

0.866 

.76 

0  738 

1.00 

0.000 

Hydraulic   Measurements.  —  Measurements    of    flowing 
water  may  be  made  by  several  methods,  depending  upon  the 
circumstances  and  requirements  of  the  particular  case: 
f  1)    By  tank  measurement; 

(2)  By  venturi  meter; 

(3)  By  weir  measurement; 

(4)  By  pitot-tube  meter; 
(fi)    By  floats: 

(6)    By  current  meters. 

These  are  discussed  in  the  order  named. 

Tank  measttrtment. — ^This  method  is  the  most  exact  and 
can  be  used  where  the  discharge  is  small.  The  discharge 
from  a  pressure-pipe  line  leading  to  a  high  service  resci^ 
voir  may  be  measured  by  using  the  latter  as  a  tank  and 
shutting  off  the  outlet  while  it  is  being  filled.  The  capacity 
of  the  reservoir  must  be  determined  accurately,  or  it  may 
be  calibrated  to  gauge  readings  above  the  bottom. 

Venturi  meter. — ^This  is  described  fully  on  page  1173,  etc. 
This  meter  is  particularly  adapted  to  measuring  the  dis- 
charge in  pipes,  and  can  be  had  in  sizes  up  to  6  ft.  or  more 
in  diameter.  Results  can  be  obtained  usually  within  2  or 
3  per  cent  of  the  actual  discharge.  In  ordering,  it  is  neces- 
sary to  state  the  diameter  of  the  pipe  and  the  a\'erage 
velocity  of  discharge  so  that  the  cones  and  venturi  may  be 
proportioned  correctly,  for  accurate  results.  The  velocity 
through  the  venturi  must  be  accelerated  sufficiently  to  cause 
a  marked  decrease  in  pressure,  and  this  is  done  by  giving  the 
diameter  of  the  venturi  the  proper  ratio  to  that  of  the  main 
pipe.  It  should  be  large  for  high  velocities  and  small  for 
low  velocities.    A  register  should   accompany  each  meter. 

Weir  measurement. — Weir  formulas  are  discussed  on  page 
1177,  etc.  In  constructing  a  standard  weir  it  is  necessaryto 
have  the  crest  perfectly  level  and  the  sides  vertical.  The 
inner  edges  of  the  opening  should  be  sharp  and  chisel-edged 
or  square  cornered .  If  square  cornered  the  boards  or  parti- 
tion should  be  thin  or  they  may  be  beveled  on  the  down- 
stream side,  thus,  ■.    The  crest  is  often  formed  of  a  thin 

sheet  of  metal  fastened  on  the  inside  of  the  wooden  parti- 
tion. Special  care  must  be  taken  to  insure  free  access  of 
air  under  the  falling  sheet  of  water  below  (down  stream 
from)  the  crest,  otherwise  a  partial  vacuum  will  form  there, 
draw  the  sheet  inward  toward  the  weir,  and  aflfcct  the  dis- 
charge. In  measuring  the  head  H  on  the  crest,  it  is  neces- 
sary to  take  the  elevation  of  the  water-surface  at  a  suffi- 
cient distance  D  (Fig.  22)  above  the  weir  to  reach  the  still- 
water  level,  or  practically  so.    Frands  used  D-6  ft.,  while 


t 


zs. 


HOOK  GAGE,    PITOT  TUBE  METER,   FLOATS', 


1183 


Baan  used  D»  16.4  ft.  Hence  the  distance  D  may  depend  somewhat  on 
the  formula  to  be  used  (see  pages  1177  and  1178).  There  are  three  methods 
in  use  for  determining  the  head  H.  One  is  by  setting  a  reading  gage  in  the 
stream,  using  the  elevation  of  crest  as  the  datum  plane.  The  second  method 
consists  in  suspending  a  plumbbob  on  the  end  of  a  steel  tape  supported 
from  some  point  E,  Pig.  22.  at  a  known  elevation  h  above  the  crest,  and 
measuring  the  vertical  distance  d  to  the  water  surface.  Then  the  required 
head  H^h—d.  In  order  to  get  the  measiu^ment  d  accurately,  the  plumb- 
bob  may  be  allowed  to  swim;  gently,  and  raised  until  it  just  ceases  to  cause 
a  ripple  on  the  water  surface.  The  third  method  is  by  the  Hook  Gage, 
shown  in  Pig.  25.  The  point  of  the  hook  at  the  bottom  of  the  rod  (the  hook 
may  be  attached  to  a  leveling  rod,  reading  to  thousandths  of  a  ft.)  is  raised 
until  it  pierces  the  "skin"  of  the  surface,  raising  a  slight  pimple.  The  hook 
is  then  lowered  tmtil  the  pimple  "just"  disappears.  The  elevation  is  read 
by  the  vernier,  which  should  be  set  at  zero  when  the  end  of  the  hook  is 
at  the  elevation  of  the  crest  of  the  weir. 

Pitot  tube  meUr. — ^The  Pitot  tube,- in  its  primitive  conception,  consists 
essentially  of  a  bent  tube  (of  glass)  inserted  in  a  cur- 
rent of  water.  Fi^f.  26,  with  the  open  end  of  the  lower 
arm  squarely  fadng  the  cxirrent.   Then,  theoretically, 

will  the  water  rise  in  the  tube  toa  height^—  ^.  in 

which  r— velocity  at  that  particular  point  In  ft.  per 
second: 

and  A,  ■•  velocity  head  in  ft.  due  to  v.  Pig.  26. 

Hence,  by  measuring  the  height  A,  of  the  column  of  water  in  the  tube,  the 
vekxnty  v(— V2«A.)  is  obtained. 

Por  measuring  the  velocity  of  flow  under  pressure,  as  in  pipes,  the  Pitot 
tube,  complete,  comprises  two  pipes,  crudely 
shown  in  Fig.  27.  One  of  these  pipes  termi- 
nates as  in  Fig.  26,  and  records  the  velocity 
head  A,+ the  pressure  head  Ap.  The  other  ter- 
minates as  a  piezometer  tube  in  an  orifice  at 
right  angle  to  the  direction  of  flow,  and 
records  the  pressure  head  A,,  alone.  It  is 
clearly  evident,  then,  that  the  difference  in 
elevation  of  the  water  levels  in  the  tubes  is 
the  velocity  head  h,  and  that,  theoretically, 
the  velocity  »— V2gA»  as  above. 

Pig.  28  shows  one  of  the  forms  of  Pitot 
tubes  used  in  the  Detroit  experiments,*  to  receive  the  velocity  and  pressure 
heads.  Por  accurate  readiii,  the  tops  of  both  of  the  tubes  (Fig.  27)  are 
connected  by  pipes  to  a  differential  gauge  consisting  of  two  parallel  glass 
tubes  with  a  sliding  scale  between.  The  difference  m  elevation  is  reduced 
to  /(t  as  above,  or  to  any  other  equi  valent  expression .  Mercurial  or  oil  gauges 
may  be  used.    (See  Trans.  Am.  Soc.  C.  E.,  Vol.  XLVII.  pp.  72-3). 

Floats. — These  are  classed  as  surface  floats^  sub-surface  floats  and  rod 
floats. 

Surface  floats  (Pig.  29)  are  the  least  accurate.  Prof.  Dwight  Porter 
of  the  Mass.  Inst.  Tech.  says:  'These  are  of  little  value  when  run  alone, 
since  they  are  easily  affected  by  wind,  and  the  relation  between  surface  and 
mean  velocity  is  uncertain.  As  a  rough  approximation,  the  mean  velocity 
in  a  vertical  may  be  assumed  as  from  0.9  to  1.0  times  the  surface  velocity 
in  a  vertical,  and  the  mean  velocity  for  the  entire  cross-section  of  the 
stream  as  about  0.8  times  the  maximum  surface  velocity." 

Sub-surface  floats  consist  of  small  cylindrical  boxes,  say  8  or  9  ins.  in 
diameter,  and  weighted  at  the  bottom  section  with  a  small  cube  of  lead. 
These  are  suspended  from  small  surface  floats  to  any  depth  at  which  it  is 
required  to  measure  the  velocity. 

Rod  floats  are  the  most  exact.  They  are  particularly  adapted  to  measur- 
ing  the  flow  in  canals  or  in  streams  where  the  depth  of  water  is  fairly  con- 
stant. The  length  of  rod  should  be  equal  to  nearly  the  depth  of  the  water, 
should  project  slightly  above  the  surface  and  reach  nearly  to  the  bottom. 
Fhcy  are  used  frequently  in  depths  exceeding  even  30  feet.  The  advantage 
3f  the  road  float  is  that  the  mean  velocity  in  the  vertical  is  obtained  directly 

*See  Trans.  Am.  Soc.  C.  E.,  Vol.  XLVII,  p.  12.  DgtizedbyGoOglc 


Fig.  27. 


1184 


eL—HYDRAUUCS. 


i 


f--. 


^— 


I— 


"?? 


:s'-  Brass  TtdxHlhskkDkm. 


Section. 


-  idermanSihtr  Tubes 
i' Inside  Gisrm. 


yir^ 


2-i' 


mi' 


iOermcmSlfyeri 
Fig.  28.~Pitot  Tube  Meter.    (See  page  U880 


PITOT  TUBE,  FLOATS,  CURRENT  METERS, 


1186 


for  any  vertical  section  of  the  stream  or  canal  in  which  it  is  allowed  to  float 

at  a  "timed"  rate  between  two  cross-sections  of  the  stream  at  a  given  dis- 

Uuice  apart.   The  floats  may  be  made  of  long,  tin 

:ylinderB  about  2  to  2i  ins.  in  diameter,  loaded  at  the 

bottom  with  lead,  accurately  weighted  or  adjusted 

vith  pebbles,  and  closed  at  the  top  with  corK.     In 

measuring  the  discharge  in  a  canal,  the  cross-section 

jf  the  latter  is  divided  into  vertical  strips  of  p:iven 

irea,  the  mean  velocity  for  each  of  these  strips  is 

letermined  by  the  rod  float,  which  velocity  multiplied 

3y  its  area  gives  the  discharge  for  that  strip.    The 

:otal  discharge  divided  by  the  total  area  of  cross- 

;ection  gives  the  mean  velocity.    The  rods  are  floated 

through  the  middle  of  the  strips  at  the  dotted  lines 

;hown  in  Pig.  80,  which  represents  a  section  of  the 


Cufftnt  mgters. — Current  meters  may  be  exisected 
x>  give  results  with  error  ranging  from  3  to  10  per 
:ent.  The  greatest  accuracy  will  be  obtained  in 
anals  with  a  moderately  high  velocity  of  flow;  the 
east  accuracy  in  turbulent  streams  with  cross  cur- 
%nts,  also  when  the  velocity  of  the  water  is  very 
;Iight,  or  when  it  contains  suspended  matter,  as  in 
ewers. 

There  are  two  principal  types  of  current 
neters,  namely,  the  cup-wheel  meter  and 
he   propeller-wheel   meter.    Pig.  81  illus- 
rates  the  fbrmer  type  and  Fig.  33  the  lat- 
er.   The  turns  of  the  wheel  which  indicate 
he  velocity  of  the  water  are  registered  by 
Lo  electric  meter  similar  to  that  shown  in 
^ig.  83.    All   meters  should    be  tested  or 
ated    before     being 
ised.   as    they    are 
ometimes  subject  to 
luctuations   which 
lay  seriously  aflfect 
he  result.     The  me- 
er  is  rated  by  moving 
I  through  still  water 
t  given  speeds,  plot- 
leg   the    results  on 
ro6S- section  paper, 
^ith  "revolutions  per 
linute"  as  abscissa, 
nd  'Velocity  in  feet 
er  second"  as  ordi- 
ates.    The   curve 
rawn  through    the 
lotted  points  is  the 
rating  line"  for  the 
teter  for  imimdiate 


TopVtWM 

Pig.  20. 


Pig.  80. 


Pig.  81. — Brice  Meter. 


Pig.  32.— Haskell  Meter.      Digitized  by  GoOglc 


1186  n.—HYDRAULlCS. 

The  carrnit  meter  may  be  oaed  in  two  ways,  namely.  W  *0 
method  and  by  the  vertical  "integration"  method.  Th«  (oitoatf^ 
because  more  accurate,  and  consists  in  holding  the  meter  in  aP^P~ 
or  point  ot  the  cross-section  of  the  stream,  that  is,  the  center  dtP^ 
for  a  definite  length  of  time  and  noting  the  register  of  the  meter  lor 
interval.  The  Telocity  per  second  and  the  dischar^  for  ^^JZ 
obuined .  and  likewise  for  the  other  areas.  The  total  disduuse.a  uf ' 
divided  by  the  total  area  of  cross-section  sives  the  mean  ^'^^"'^'llf. 
intagratioii  method  is  quicker  but  somewhat  less  accurste  mkay^^ 


Pig.  8S.— Meter  Register. 

fully  done.    It  consisto  in  lowering  r^tad^ 

to  the  bottom  and  then  back  sgain  1  ^tST^vv^ 
given  vertical  strip  as  shown  by  thi  *^  befw '-" 

must  be  slow  and  constant  and  the  m- Taoescfi"^ 

actual  time  consumed,  bormning  ax  «!watr  tf^  ^* 

meter  well  under  the  surface.    The  VaM  ic  ^ 

charge  for  that  particular  vertical  si  *  "^^ 
same  manner,  and  the  resulting  me< 


d  by  Google 


CURRENT  METER  REGISTER.    MISCELLANY.  1187 

EXCERPTS  AND  REFERENCES. 

Iniinictioiis  for  InfUlUng  Weirt,  Measuriag-Plitiiict  and  Water 
R«fMen  (By  C.  T.  Johnston,  and  Elwood  Mead.  Paper.  U.  S.  Dept.  of 
Affnculttira,  and  Btilletin  86.  Irrigation  Investigations;  £ng.  News,  Atsg.  20, 
1901). — Slustrations:  Pig.  1,  arrangement  of  Cippoletti  weir;  Pig.  2,  meas- 
uring flume  and  register;  Pigs.  3  and  4,  arrangement  of  pulleys  to  magnify 
the  record  of  water  registers;  Pigs.  3a  and  4a,  arrangement  of  pulleys  to 
reduce  record  of  water  registers;  Pig.  5.  the  Mead  stream  heights  or  water 
register;  Pig.  6,  the  Priez  stream  heights  or  water  register;  Pig.  7.  the 
Leitz  stream  heights  or  water  register;  Pig.  8,  the  standard  stream  heights 
or  water  register.    Descriptions  and  discussions. 

of  the  Flow  of  Water  fai  the  Sodboy  and  Cochitiiate 

(By  W.  W.  Patch.    Eng.  News,  June  12,  1»02).— Illustration  of 
current  meter  apparatus;  also  diagrams. 

Current  Meter  and  Weir  Discharge  ComiMrisoas  (By  B.  C.  Murphy. 
Trans.  A.  S.-C.  E.,  Vol.  XLVII). 

The  Effect  of  Long  Lengths  of  Hose  on  Fbe  Streams  (By  S.  A.  Charles. 
Paper.  Am.  W.  W.  Assn.,  June  12,  1»02;  Eng.  News,  July  3,  1002).— Dia- 
gram showing  heights,  volumes  and  velocities  of  fire  streams  for  various 
lengths  of  hose,  size  of  nozzle  and  pounds  of  hydrant  or  steamer  and  nozzle 
pressure — ^from  experiments  by^  S.  A.  Charles,  combined  with  those  of 
J.  R.  Preeman.  See  discussions  in  Eng.  News  of  July  17  and  81.  and  Dec.  8, 
1902. 

The  Flow  of  Water  fai  Wood  Pipes  (By  Thcron  A.  Noble.  Trans. 
A.  S.  C.  E.,  Vol.  XLDC). 

Methods  of  Measuring  the  Flow  of  Streams  (By  J.  C.  Hovt.  Eng. 
News,  Jan.  14, 1004).— Interesting  diagram  showing  vertical  velocity  ctirves 
for  Susquehaxina  River;  also  table  of  velocity  determinations.  See.  also, 
Eng.  News,  of  Aug.  4,  1004. 

Notee  on  the  Computation  of  Stream  Oagings  (By  O.  V.  P.  Stout. 
Paper,  Sec.  of  Eng.  and  Mech.,  12th  Natl.  Irrig.  Cong.,  Nov.  15  to  18, 1004; 
Eng.  News,  Dec.  8,  1004). — ^Pormulas  and  diagrams. 

The  Hydraulic  Plant  of  the  Pucet  Sound  Power  Company  (By  E.  H. 
Warner.  Trans.  A.  S.  C.  E.,  Vol.  LV).— Table  1,  Make-up  of -steel  pipe; 
Table  3.  Experiments  on  the  hydraulics  of  the  timber  flume. 

Depth  of  Thread  of  Mean  Velocity  in  Rivers  (By  P.  W.  Hanna.  Eng. 
News,  Jan.  11,  1006). — In  the  measxirement  of  the  flow  of  rivers  it  is  often 
assumed  that  the  thread  of  mean  velocity  lies  at  approximately  0.6  of  the 
total  depth  from  the  suriace,  varying  for  extreme  cases  between  the  limits 
of  0.5  arid  0.7.  There  seems  to  be  a  general  imoression  that  this  assumption 
is  not  capable  of  theoretical  demonstration.  Mr.  Hanna  proceeds  to  demon- 
strate "rationally"  that  these  values  are  correct,  from  the  assumption  that 
the  vertical  velocity  curve  is  sensibly  a  parabola. 

An  Experiment  to  Determine  **N*'  in  Kutter's  Formula  (By  C.  W. 
Babb.  Eng.  News,  Peb.  1,  1006). — In  connection  with  the  work  of  the 
Reclamation  Service  of  the  St.  Mary  project  in  Montana,  the  values  of  **n** 
n  earth  canal  were  found  to  be:  .027,  .024,  .023,  .023,  .021;  average  .0230, 
>r  practically  .026. 

Sone  Experiments  on  the  Frictionless  Orifice  (By  Horace  Judd  and 
i.  S.  King.  Paper.  Am.  Assn.  for  the  Advan.  of  Science.  July,  1006;  Eng. 
4eW8,  Sept.  27.  1006). — Diagrams  and  tables. 

Additional  Information  on  the  Durability  of  Wooden  Stave  Pipe 
By  A.  L.  Adams.  Trans.  A.  S.  C.  E.,  Vol.  LVIID- — Refers  to  the  7i  miles 
f  wood-etave  pipe  laid  for  the  Astoria  city  water  works  ten  years  previously. 
IS  a  result  of  examination  of  the  pipe  line,  the  following  conclusions  are 
rawn:  (1)  Staves  which  are  constantly  subject  to  water  pressure  from 
rithin  and  are  buried  in  the  ground,  may  be  very  short-lived.  (2)  The 
lagnitude  of  the  water  pressure,  beyond  a  moderate  head,  has  but  little 
r  no  influence  in  preserving  the  timber.  (3)  The  pipe  laid  above  ground 
as  not  deteriorated  to  any  considerable  extent,  nor  has  the  pipe  laid  in 
le  trenches  leading  from  the  distributing  reservoir.  (4)  Where  biuied,  its 
orabilityhas  depended  upon  the  soil  conditions  ana  the  depth  of  back- 
II.  (5)  When  the  depth  ot  backfill  has  exceeded  2  ft.  above  the  pipe,  and 
le  material  has  been  free  from  vegetable  matter,  and  has  been  of  a  fine 


1188  m.-'HYDRAULICS. 

and  impervious  character,  much  less  deterioration  has  taken  place.  (6) 
Whenever  the  staves  have  been  in  contact  with  loamy  earth  or  earth  ooc- 
tainina  vegetable  matter,  or  wherever  they  have  been  covered  with  porous 
material,  or  to  a  depth  less  than  2  ft.,  rapid  decay  has  resulted.  (7)  De- 
cayed staves  have  been  fotmd  all  around  the  pipe.  (8)  Soimd  staves  have 
been  frequently  found  contiguous  to  badly  decayed  staves.  (9)  The  char- 
acter of  the  grain,  whether  slash  or  gram  edge,  has  not  influenced  the 
durability.  (10)  The  bruising  of  the  staves  during  the  process  of  erecting 
seems  to  have  been  one  of  the  chief  agencies  in  hastening  decay.  (11)  De- 
cay has  not  been  confined  to  the  outside  of  the  pipe.  (12)  The  pipe  has  not 
usually  shown  leakage  as  long  as  sotmd  wood  has  remained  in  excess  of  \* 
in  thickness.  (13)  The  malleable  cast  band  fastenings  have  been  found  to 
be  in  good  condition.  _  (14)  The  bands.  ^  in  size,  have  been  conaiderably 
corroded  save  where  secured  by  the  nut.  but  all  have  been  used  again  \^ 
placing  the  nut  in  its  original  position.  (15)  'The  pipe  in  the  2nd  and  drtl 
Sections,  2^  miles,  is  nearly;  sill  buried  in  nne-grained  sand,  and  will  last 
perhaps  10  years  more  by  giving  it  a  general  repairing,  say  6  years  hence. 
but  the  greater  part  of  the  1st  and  4th  Sections  will  have  to  be  replaced 
in  about  4  years. — Superintendent."  For  Mr.  Adam's  original  paper,  see 
Trans.  A.  S.  C.  E.,  Vol.  XXXVI;   see  also  Trans.,  Vol.  XLI. 

The  Kinetic  Enersy  of  Flowing  Water  (By  L.  P.  Harza.  Eng.  News, 
Mar.  7,  1907). — ^Formulas  for  the  energy  in  rivers,  streams,  pipes,  etc. 

OlMervations  to  Determine  Values  of  "C"  and  **N"  as  Used  in 
Kutter's  Formula  (By  T.  B.  Lippincott). — Eight  experiments  described: 
Exper.  No.  1 . — ^Timnel  440  ft.  long,  floor  grade  0.00096,  rectangular  section 
41'  wide  X  4'  deep  with  semi-circular  arch  and  finished  with  a  1:3  cement 
mortar  plaster.  Exper.  No.  i. — ^Tunnel  318  ft.  long,  floor  grade  0.00O95, 
section  and  finish  same  as  No.  1.  Exfer.  No.  5.— -Canal,  800-ft.  len^h, 
trapezoidal  section  with  slopes  1:1  ana  bottom  width  11.6  ft.,  concrete 
lined  with  1:3  mortar  plaster,  bottom  filled  up  with  1.5  to  2.5  ft.  of  fine 
sand.  Exper,  No.  4- — Canal,  600-ft.  length,  trapezoidal  section  with  side 
slopes  2  on  1  and  bottom  width  8  ft.,  concrete  lined  with  1:8  mortar  spread 
roughly,  partially  cleaned  before  measurements  were  made.  Exper.  Nos.  S 
and  6. — (^ondmt,  700-ft.  length,  concrete  lined  with  1:3  cement  naortar  in 
smooth  condition,  grade  of  floor  same  as  water  suriace.  Exper.  No.  7. — 
CsLna,\,  1000-ft.  tangent,  lining  of  concrete  without  plaster,  bottom  free  froa 
ssciiid  and  j?ravel,  sides  and  bottom  covered  with  thin  coat  of  moss.  Exper. 
No.  8. — Conduit,  1000-ft.  length,  lining  of  concrete  tamped  in  behind  boards 
and  not  plastered,  several  inches  of  sand  and  gravel  on  bottom,  some  n»oss 
and  grass  on  sides. 

Tabular  Results  op  Expbrimbnts: 


The  use  of  the  following  coefficients  in  Kutter's  formula  was  suggested 
by  the  board  of  consulting  engineers,  consisting  of  John  R.  Freeman. 
Frederic  P.  Steams  and  Jas.  D.  Schuyler:  (1)  For  open  masonry  conduits 
of  cement  or  smoothly  plastered  masonry,  n  — 0.018;  (2)  for  concrete-lined 
tunnels,  or  covered  masonry  conduits,  n<" 0.014;  (3)  tor  steel  pipe  with 
nvet  heads  and  seams  projecting  on  the  interior,  ««=  0.016;  (4)  for  earth 
canals  with  bottom  left  by  dredging,  »=«0.0275.— (Eng.  News,  June  6,  HOT) 

Flo  J^'m  ^S*^r  **/,  Changes   in    Canal   Cro«».Soctioni    Upon  the  Rate  of 
Flow  (By  F.  W.  Hanna.    Eng.  News,  June  6,  1907).— In  the  constroctioa 


MISCELLANEOUS  DATA.  1189 

of  a  canal  it  is  usually  necessary  to  imvide  for  carrying  its  waters  through 
culverts,  flumes,  siphons  and  other  important  changes  of  cross-section  of 
waterway;  and  in  order  to  compute  properly  its  capacity,  some  estimate 
of  the  effects  of  such  changes  on  the  flow  must  be  made,  'nie  mathematical 
I     discussion  in  this  article  deals  with  this  problem. 

A  Sdntioa  of  the  Probtem  of  DetenninioK  the  Economic  Size  of 
Pipe  for  HJcb-Preasiire  Water^Power  Installatioa  (By  A.  L.  Adams.  Trans. 
A.  S.  C.  E.,  Vol.  LIX). — Rule:  'That  pipe  fulfills  the  requirements  of 
greatest  economy  wherein  the  value  of  the  energy  annually  lost  in  frictional 
resistance  equals  four-tenths  (0.4)  of  the  anntial  cost  of  the  pipe  line." 
'    Discussed  by  formulas.  ^ 

The  Flow  of  Water  Through  Sabmerged  Tubes;  Results  of  Experi- 
ments at  the  University  of  Wisconsin  (By  C.  B.  Stewart.  Bulletin.  Univ.  of 
Wisconsin.  Eng.  News,  Jan.  9,  1908). — Very  extensive  article  with  illus- 
trations and  diagrams. 

A  Logaritliniic  Diagram  for  the  Flow  of  Water  in  Open  Channels 
(By  G.  T.  Prince.    Eng.  News,  Feb.  6.  1908). 

Coefficient  of  Discharge  through  Circular  Orifices  (Eng.  News, 
July  9,  1908). — ^Tables  of  coefificients;  also  seven  concliisions  stated  by  the 
writer,  Mr.  H.  J.  Bilton. 

Bazin's  Hydraulic  Formula  (*'AnnaIes  des  Fonts  et  Chaussees"  for 
the  fourth  quarter  of  1897;  Eng.  News.  Aug.  13,  1908). — Given  in  metric 
measure,  as  follows: — w—  87%/f5-i-(l+m-i- V  s),  the  value  of  m  varying  with 
the  surface  of  the  channel  as  follows:  (1)  Very  smooth  (cement,  planed 
wood,  etc.),  m»0.06;  (2)  smooth  (plank,  brick,  cut  stone,  etc.).  m  — 0.16; 
(3)  rough  masonry,  m  —  0.46;  (3a)  mixed,  or  mterraediate.  very  regular 
earth  excavation,  paved  slopes,  etc..  m-'0.86:  (4)  ordinary  earth  channels, 
m  — 1.30;   (5)  eartn  channels  in  bad  condition,  m— 1.76. 

A  diagram  for  Bazin's  formula  for  flow  in  open  channels,  prepared  by 
O.  von  Voigtlander,  is  published  in  Eng.  News  of  April  15,  1909. 

A  Collection  of  Formulas  for  Water-Pressure  and  Moments  In  Sub- 
merged Beams  (By  D.  N.  Showalter.  Eng.  News,  Iday  27,  1909).— Formu- 
las, illustrations  and  tables. 

Ratings  of  a  Pttot  Tube  (B^  £.  C.  Murphy.  Eng.  News.  Aug.  12, 1909.)— 
lUustrated.     Rating  curve  diagrams. 

Huge  (625  Cu.  Ft  per  Sec.)  Venturi  Meters,  India  (Eng.  News,  Nov.  25. 
1 009) . — Dlustrated. 

The  Vwt  and  Care  of  the  Current  Meter,  as  Practised  by  the  U.  S.  Qeol. 
Survey  (By  J.  C.  Hoyt.  Trans.  A.  S.  C.  E..  Vol.  LXVI.,  Mar.,  1910).— 
Illustrations  and  descriptions  of  various  types  of  meters  and  recording 
devices,  rating  of  meters,  and  methods  of  making  hydraulic  measurements. 
Friction  of  Air  fai  Small  Pipes  (By  E.  G.  Harris.  Univ.  of  Missouri 
Bulletin;  Eng.  Rec..  Dec.  3  1910). — ^Experiments  to  determine  the  value 
>f  the  coefficient  c  in  the  formula: 

n  which  /—loss  of  pressure  in  lbs.  per  sq.  in.;  /-length  o£  pipe  in  ft.;  V— 
he  cti.  ft.  of  free  air  passing  per  second;  o—diam.  of  pipe  in  ins.;  r— ratio 
.f  compression  to  atmospheres;  c— the  e^^rimental  coefficient.  The 
estilt  of  the  experiments  indicated  that  for  pipes  of  i'  to  12*  in  diameter 
he  vahie  of  f ->  0.070—  0.00188(i.  so  that  the  above  formula  would  reduce  to: 

/-(0.076-0.00188d)^. 


d  by  Google 


63.— WATER  SUPPLY. 

Source  and  Distribution. — Water  supply  is  derived  primarily  from  rain, 
snow,  hail,  sleet  and  dew.  generally  termed  rainfall  or  precipitation.  The 
amount  of  rainfall  in  any  locality  is  the  depth  of  the  precipitation  in  inches. 
when  melted.  In  some  localities  dew  forms  no  inconsiderable  proportiqp  of 
the  total.  The  "dew-point"  is  that  temperature  at  which  the  air  begins  to 
deposit  (more)  moisture  (than  it  takes  up).  It  is  not  a  fixed  temperattxre. 

The  iHsiributum  of  Rainfall  and  Source  of  Water  Supply  may  be  grouped 
as  follows:  ^Rainfall — 

if  Streams. 
Surface  Water  I  ii„,^i„     |Na*g™l^). 

Evaporation. 

G™undW.ter{V««^^^_ 


Seepage 


Underground 
Water 


Galleries. 
Springs. 

f  Shallow, 
Wells 


I  Deep  driven  {Aj^* 


-    Use  in  Various  Branches  of  Engineering. — ^The  consideration  of  irater 
supply  is  pertinent  to  the  sections  which  follow,  namely, 

64.  Water  Works page  1202. 

65.  Sanitation page  1295. 

66.  Irrigation page  1813. 

67.  Waterways page  1320. 

68.  Water  Power page  1832. 

70.    Electric  Power  and  Lighting page  1379. 

RainfaU. — ^Engineers  are  concerned  mainly  with  (1)  the  average  montUf 
precipitation,  (2)  the  monthly  rainfall  for  the  driest  years,  and  (3)  the  * 


mum  rates  of  rainfall  which  may  be  expected,  in  any  given  locality.     The 
first  two  are  for  the  consideration  of  Supply;  the  last,  for  Dischaive. 

*Mr.  Myron  L.  Fuller,  Geologist  in  Charge  of  Underground  Water 
Supplies,  U,  S.  Geol.  Surv.  (Water  Supply  &  Irrigation  Paper  No,  leW). 
states  that  there  is  much  looseness  in  tne  tise  of  the  word  "artesian/*  acHi 
great  variation  of  its  use  in  different  parts  of  the  cotmtry.  After  a  carefd 
canvass  of  the  leading  geologists  of  the  country  engaged  in  hydraulic 
studies,  he  has  proposed  the  following  definitions  of  terms: 

Artesian  Prtnctple. — ^The  hydrostatic  principle  in  virtue  o£  whi^  water 
confined  in  the  materials  of  the  earth's  crust  tends  to  rise  to  the  level  oC  the 
water  surface  at'  the  highest  point  from  which  water  is  transmitted.  Gas 
as  an  agent  in  causing  the  water  to  rise  is  expressly  excluded  fxom,  this 
definition. 

Artesian  Pressure. — The  pressure  exhibited  by  water  confined  In  the 
earth's  crust  at  a  level  lower  than  its  static  head. 

Artesian  Water. — ^That  portion  of  the  underground  water  which  is  voider 
artesian  pressure  and  will  riSfe  if  encoxmtered  by  a  well  or  other  passage 
affording  an  outlet. 

Artesian  System. — ^Any  combination  of  geologic  strocturet,  sa^  as 
basins,  planes,  joints,  faults,  etc.,  in  which  waters  are  confined  under 
artesian  pressure. 

ArUsian  Basin. — A  basin  of  porous  bedded  rock  in  wfaick,  as  a  vseolt  of 
the  svnclinal  structure,  the  water  is  confined  under  artesian  pressore. 

Artesian  Slope. — ^A  monoclinal  slope  of  bedded  rocks  in  which  water  if 
confined  beneath  relatively  impervious  covers  owing  to  the  obstractkxi  tc 
its  downward  passage  by  the  pinching  out  of  the  porous  bed^  by  their 
flange  from  a  pervious  to  an  impervious  character,  by  internal  nictkiQ,  or 
by  dvkes  or  other  obstructions. 

Artesian  Area. — An  area  imderlain  by  water  under  artesian  precscae. 

Artesuxn  Well. — Any  well  in  which  the  water  rises  under  artesian  pressoit 
when  encountered.  „g,,,,  ,^ GoOglc 


RAINFALL.    ARTESIAN  NOMENCLATURE.  1191 

1.— AvBRAGB  Monthly  Precipitation  in  thb  U.  S..  in  Inchbs. 
From  Time  of  Establishment  of  Station  to  End  of  1904. 


♦  Figures  enclosed  in  parentheses  are  totals  in  inches  for  the  12  months, 
and  indicate  average  yearly  precipitation  for  the  period  of  years  stated  in  the 
last  column. 

Note. — *T"  means  trace — too  small  to  measure.  ^  j 

Digitized  by  VjOOQ IC 


1102  93.— WATER  SUPPLY, 

1. — Atbragb  Monthly  Prbcipxtation  in  thb  U.  S..  in  Inchss. — 

Continued. 


*  Figures  enclosed  in  parentheses  are  totals  in  inches  for  the  12  months. 
and  indicate  average  yearly  precipitation  for  the  period  of  yean  stated  in  the 
«wt  column. 


d  by  Google 


AVERAGE  MONTHLY  PRECIPITATION.  IIOS 

l,_AvBRAGB  Monthly  Precipitation  in  thb  U.  S.,  in  Inches. — 
Continued. 


*  FigrtuxJS  enclosed  in  parentheses  are  totals  in  inches  for  the  12  months, 
&nd  indicate  average  yearly  precipitation  for  the  period  of  years  stated  in  the 
ast  column. 


Digitized 


by  Google 


1104  ^— WATER  SUPPLY, 

1. — AvBRAGB  Monthly  Prbcipitation  in  thb  U.  S.,  in  Inchks. — 
Concluded. 


*  Figures  enclosed  in  parentheses  are  totals  in  inches  for  the  12  months, 
and  indicate  average  yearly  precipitation  for  the  period  of  years  stated  in  the 
last  column. 

In  connection  with  the  preceding  table,  the  following  Table.  No.  2,  shows 
in  respective  order  the  percentages  of  rainfall  to  average  rainfall:  Ftrsi.  for 
the  driest  year;  Second,  for  the  two  driest  years;  Thdrd,  for  the  three  driest 
years;  closing  with  1896. 

Ex. — For  Pittsburg,  the  average  rainfall,  from  Table  1,  is  36.50  ins. 
Then,  using  the  percentages  in  Table  2,  following,  we  have:  First,  for  the 
driest  year,  36.50x0.70—25.61  ins.;  Second,  for  the  two  driest  years.  S6.5f 
X  0. 78  -  28.54  ins. ;  Third,  for  the  three  driest  years.  36. 50  X  0. 85  -  31 .  10  ins. 


d  by  Google 


RAINFALL— MONTHLY:  HIGH  INTENSITIES.  1195 

2. — *Pbrcbntaob  of  Rainfall  to  Avbragb  Rainfall. 

(To  be  used  in  connection  with  preceding  table.   See  Example,  p.  1194.) 

Non  York,  62. 

Soul  Augusta, 

Gftlf  70.  80.  83; 

M,  05.  72; 

Okie  apolis,  59. 

Lakt  »d.  71,  74, 

Upp  6.  68.  73: 

9.  58.  08; 

r/w  Platte.  66, 

Thg  [A,  79.  80; 

ty.  55.  64. 

Pact  nd.  67.  76. 

ncisco.  51. 
:>iego,    30. 

Hif h  Intensities  of  Rainfall. — Flood  discharges  in  rivers,  creeks,  sewers, 
etc..  naturally  occur  at  times  of  high  intensities  of  rainfall,  and  hence  it  is 
important  to  know,  for  particular  localities,  the  maximum  rates  of  down- 
pour which  have  been  recorded,  and  which  are  liable  to  take  place  in  the 
future.  Considerable  confusion  has  arisen  as  to  the  meaning  of  the  various 
terms  "intensity  of  rainfall,"  "maximum  rate  of  rainfall,"  etc.:  for  even  a 
single  shower  has  various  intensities  of  downpour,  while  the  recorded 
"intensity"  often  comprises  the  ratio  of  the  total  downpour  to  the  total 
time,  omitting,  perhaps,  the  critical  data  most  desired  for  the  design  of  the 
sewer,  namely,  a  higher  intensity  of  downpour  for  a  shorter  period  of  time, 
during  the  shower.    In  order  to  clarify  this  subject,  the  following  notation  is 

Let  d"the  depth  of  rainfall  in  ins.,  for  any  given  time  T  in  hrs.; 

7*— time  in  hours  corresponding  to  depth  of  precipitation  d  in  ins.; 
T"  average  rate  of  downpour  m  inches  per  hour  during  the  whole 

xfcoiwrf — -=.  designating  the  length  of  time  by  a  sub- numeral 

in  the  denomination  of  hours,  thus — 

r4  —  -=;  —  say-v-  —average  rate  of  downpour  diuing  the  whole 

4  hours  of  the  shower; 
i'' maximum  average  rate  of  downpour  in  inches  per  hour 

during  a  protracted  period  of  highest  intensity  —  -=  , 

designating  the  length  of  time  by  a  sub-numeral  in 
th6  denonunation  of  hours,  thus — 

t|.5—-=7  — say  r-r  — maximum  average  rate  for  1.5  hours; 

i  1.0 

I '^maximum  maximorum  rate  of  downpour  in  inches  per 

hour  during  the  short  time  or  greatest  intensity  —  y, 

designating  the  length  of  time  by  a  sub-niuneral  in 
the  denommation  ol  hours,  thus — 

lo.u^-j^'^sa.y'-^'^higktst  intensity,  for  i  hour. 


*  Abstract  from  Table  No.  6.  "Public  Water  Supplies"  by  Tumeaureand 
Russell:  John  Wiley  &  Sons,  1901.  Although  not  strictlv  applicable  to  pre- 
cedins  table  closing  with  1904,  these  percentages  may  be  used  with  fairly 
good  results.    Published  by  permission. 


UM  ^—WATER  SUPPLY, 

Thus,  from  the  above,  say  for  any  given  shower,  we  have  the  complete 
data:  r4  » 1,  «i.5—  2,  /o-af  3.  This  means  that  it  rained  4  ins.  in  4  hours.,  or 
at  the  average  rate  of  1  m.  per  hour;  2  ins.  per  hour  for  1.5  hours  of  greatest 
downpour;  and  0.75  in.  in  15  nunutcs,  or  at  the  rate  of  3  ins.  per  hour  for 
the  short  period  of  greatest  intensity.  In  current  literature  it  is  often  proUe- 
matical  whether  r,  i  or  /  is  intended  as  the  rate  of  downpour. 

Formulas  for  Maximum  Intensity  op  Downpour,  i. 
Notation. 
t*  average  rate  of  downpour  in  ins.  per  hotir  for  the  time  i  in  mxBS.; 
f  —  time  or  duration  of  downpour  in  minutes. 
Formulas. 
A.  N.  Talbot's  "Maximum    formula  for  Eastern  U.  S*. 

*-rr3o ^^^ 

A.  N.  Talbot's  ".Ordinary"  formula  for  Eastern  U.  S*. 

105  ^ 

"JTTs c« 

E.  Kushling's  formula  for  New  Yoric  City  and  vicinity: 
120 

'^JTTo ' ^« 

tC.  W.  Sherman's  formula  for  Eastern  U.  S.,  when  « 180: 

••-.-Ho ^« 

But  when  <>  180  the  value  of  i  is  too  small. 
tC.  W.  Sherman  s  "Maximum"  formula  for  Boston: 
38.64 

♦-Tois- C«) 

tC.  W.  Sherman's  "Ordinary"  formula  for  Boston: 
■      25.12 
♦-lolw   ^« 

E.  S.  Dorr's  "Ordinary"  formula  for  Boston: 

*'JTTo ^^ 

Standard  Rain  Qage. — For  a  complete  description  of  the  measurement 
of  precipitation,  see  Weather  Bureau  Paper  "W.  B.,  No.  286"  U.  S.  Dept. 
of  Agriculture,  by  C.  F.  Marvin,  1903. 
from  which  the  following  cut  (standard 
8-in.  gage)    is  reproduced.    A  is  the 
receiver;   B  the  overflow  attachment; 
C  the  measuring  tube;    D  the  meas- 
uring stick.     The  diameter  of  the  re-    . 
ceivingtube  a  is  ^ust  8  ins.  (8*-=  64)    ' 
and  of  the  measunng  tube  C  is  2.53 
ins.   (2.53*-=  6.4);    hence    the   rainfall 
is    magniified    in   the  latter  10  times, 
which  facilitates    accurate    measure- 
ment.    The  measuring  stick  D  is  a 
strip  of  straight-grained  cedar  0.08  in. 
thick,  0  5  in    wide,  and  24  ins.  long. 
When  the  tube  C  is  full  it  overflows 
at  d  into  B,  and  is  later  poured  into  C 

and  measured.     If  the  precipitation  is  l«t 

snow  or  hail  it  is  melted  before  meas- 
uring. Snow  will  occupy  from  7  to 
84  tunes  its  depth  melted.  Fig.  1. — Rain  Gage. 

*  Territory  east  of  the  Rocky  Motmtains.  ^r^nin]r> 

t  See  Trans  A.  S.  C.  E.,  Vol.  LIV.  pp.  178  and  212.  -^*-'^8^^ 


RAINFALL  FORMULAS.    RAIN  GAGE.    RUNOFF. 


11»7 


3. — ^Maximum  Ratbs  of  Rainfall  by  Prbcbdino  Formulas.  • 

For  periods  of  time  ranging  from  5  minutes  to  3  hoxirs. 

plates  of  downpour  in  inches  per  hour  for  time  /.] 


Formula. 

Duration 

or  time  of  Downpour. 

«-5m. 

r-iom. 

f»30m. 

f»60m. 

/-I80m. 

.,..360       I^lbot's  maximum; 
^^       t+iO'    tor  Eastern  U.S. 

r2W-^°5       Talbot's  ordinary; 
^^'  *    1+15*     tor  Eastern  U.S. 

,-,   .      120       Kushltag's;  tor  N.  Y. 
^^^  *    1+20"    aty  and  vicinity. 

iA\  4—Jl^      Shermans;  Xor  Eastern 
^*^  ^    iTtb'    U.  8.,  when  K 180. 

.»   .    38.84     Sherman's  maximum: 
<*'  *"  fi.va  •  tor  Boston. 

iK\   <-25.l2     Sherman's  ordtaary; 
<•>   »"7mS'    tor  Boston. 

,„    f      160       Dorr's  ordinary; 
*''        1+30*     tor  Boston. 

8.67 
5.25 
4.80 
12.00 
12.79 
8.31 
4.29 

7.50 
4.20 
4.00 
10.50 
7.94 
5.16 
3.76 

5.00 
2.33 
2.40 
7.00 
8.73 
2.43 
2.60 

3.33 
1.40 
1.60 
4.67 
2.32 
1.51 
1.67 

1.43 
0.54 
0.60 
2.00 
1.09 
0.71 
0.71 

Note. — ^To  obtain  the  total  depth  of  rainfall  for  the  duration  of  time  t 

given:  Multiply  the  rates  or  intensities  ♦  given  in  the  table,  by  zr  (=»  T,  the 

time  in  hours^ ;  thus,  from  formula  (3)  the  total  rainfalls  which  it  is  possible 
to  expect  in  0-,  10-,  30-,  60-  and  180  minutes  of  downpour  are,  respectively, 

4.80X^-0.4in.,4.00X^-0.67in.,  2.40X^-1.20 in.,  1.60X^-1.60 in., 

180 
and  0.60  X-^  — 1.80  in.     In  calctilating  the  maximum  rate  of  discharge 

from  a  catchment  area  into  a  stream  or  sewer,  it  is  necessary  to  estinoate  the 
time  required  for  the  rain  to  reach  such  outlet,  say  30  minutes,  more  or  less, 
for  sewers,  and  a  longer  time  for  streams,  generally.    See  Run-off,  below. 

Ran-off. — ^Thc  term  "run-off"  is  rather  indefinite,  but  in  general  ij  may 
be  defined  as  the  surface  discharge  from  a  catchment  area  or  basin.  Each 
stream  has  its  catchment  area.  The  discharge  from  a  stream  may  be 
estimated  in  three  ways: 

1st.      By  Kutter's  formula  (p.  1167),  with  sectional  area,  mean  radius 

and  hydraulic  slope  known; 
2nd.    By  actually  gaging  the  stream  (see  page  1182,  etc.); 
8rd.     By  estimating  the  percentage  of  run-off  to  total  rainfall. 
All  three  methods  should  be  used  if  possible,  for  checking. 
Foranulas  for  nm-off  are  founded  on  actual  stream  gagings,  but  must  be 
used  with  care  for  the  following  reasons: 

(a) .  Each  stream,  strictly  spreaking,  should  have  its  own  run-off  formula 
(or  tomiulas — see  b,  c  and  a). 

(b).  The  nm-off  increases  with  the  amount  and  intensity  of  rainfall. 
(c).   It  is  greater  in  the  spring,  when  the  ground  is  frozen  and  the  snows 
are  melting,  than  during  the  stmmier. 

(d) .  It  may  vary  considerably  at  different  points  in  the  same  stream,  the 
variation  being  due  almost  wholly  to  seepage  discharge  or  influx  from  springs. 
(e).  The  run-off  varies  generally  with  the  compactness  of  the  soil  and 
:ub-«oil,  being  very  slight  in  sand. 

Of).  It  is  influenced  more  or  less  by  the  slope  of  the  catchment  basin 
^contrary  to  some  authorities).  .  «    zr  _* 

In  addition  to  the  above,  it  is  to  be  noted  that  the  ttme  of  run-off  affects 
arsely  any  water  proposition.    If  the  run-off  is  immediate  the  waters  usually 


1108  t3,'-'WATER  SUPPLY. 

haw  to  be  stored  unless  the  supply  is  very  much  in  excess  of  the  deznaivL 
Storage  may  obtain  in  several  ways,  namely,  (1)  by  high  altitude  of  the 
catchment  basin,  delaying  the  melting  of  the  snow;  (2)  by  forest  growth  is 
the  catchment  basin,  decreasing  evaporation:  (3)  by  natural  lakes  in  the 
catchment  area;  (4)  by  artificial  storage  reservoirs:  (5)  by  sub-aoil  storage. 
Sub-surface  flow  accompanies  every  stream  and  may  be  considered  part 
of  the  nm-off,  imder  certain  circumstances,  if  readily  available.  It  is  not 
included  in  ozdinary  stream  measurements,  but  may  be  detected  in  "dry'* 
streams  by  digging  test  pits.  It  may  be  brought  to  the  surface  and  yi^-^f^tn^ 
available  by  tne  construction  of  tight  coffer-dams  extending  to  bed  rock,  or 
by  the  construction  of  ordinary  dams  with  tight  foundation.  liCany  credcs 
apparently  "dry"  in  summer  may  thus  be  made  to  jrield  a  considerable  dis- 
charge. 

Formulas  for  Run-off. — ^The  following  notation  is  for  the  subjoizwd 
formulas: 

a  "-area  of  catchment  basin,  in  acres; 
A  »  area  of  catchment  basin,  in  square  miles; 
d  — precipitation  on  catchment  per  month,  in  inches; 
I?  » total  precipitation  for  any  period,  in  inches; 
<r— coefficient  of  discharge: 
4 "discharge  in  cu.  ft.  per  second  per  square  mile  of  catchment  for 

frecipitation  d. 
_  discharge  in  cu.  ft.  per  acrt  of  catchment  for  precipitatioa  D. 

Then  for  total  nm-off  per  acre  of  catchment. 

(?  =  <r-^  •  43660a  -  3630 cD  a (1) 

in  which  c  may  vary  from  0  to  100;  almost  always  between  0.05  and  0.7$; 
generally  between  0.20  and  0.60:  rough  average  0.40.  (But  see  page  1197.) 
The  value  of  c  in  formula  (1)  can  usually  be  derived  from  the  coefficient  for 
some  other  catchment,  near  the  locality,  for  which  the  run-off  has  beoi 

gauged.    Then,  by  transposition,  c  =  ^a^in    *   '^®  accuracy  of  this  method 

is  enhanced  more  or  less  if  the  two  catchments  are  very  dissimilar  in  character 
of  soil,  geology,  topography,  area,  etc.  It  is  far  superior  however  to  any 
blind  assumption  of  percentage  based  on  averages  in  distant  localities. 

The  monthly  discharge  may  be  obtained  by  substituting  d  for  D  m 
formula  (1). 

Dicken's  formula  assumes  the  maximum  discharge  9.m  in  cubic  feet  per 
second  to  be  proportional  to  "^A;  thus, 

^„=-<:' VJ (J) 

in  which  c'  is  a  coefficient  depending  upon  rainfall,  character  of  soil,  topo- 
graphy,  geology,  etc.  The  value  of  c'  in  formula  (2)  may  often  be  obtained 
From  similar  catchments  in  the  same  locality,  in  about  the  same  manner  as 
described  for  c  in  formula  i\).  When  c'  is  known  this  formula  is  useful  in 
approximating  the  flood  discharge  from  a  catchment  for  the  design  of 
wasteways  for  dams. 

The  writer  has  seen  it  stated  repeatedly  that  run-off  is  independent  of 
the  degree  of  slope  of  the  catchment  area.  But  his  experience  and  investi- 
gations are  to  the  contrary.  Both  the  declivity  of  the  ground  surface  and 
Its  geological  formation  have  considerable  effect  on  the  time  and  amount  of 
run-off.  especially  if  measured  near  the  headwaters  of  the  effluent  stream. 

Run-off  formulas  must  be  used  with  great  caution  and  only  in  connectkm 
with  gagings  of  streams,  luiless  the  merest  approximation  is  desired.  Even 
then  the  gagings  should  cover  a  long  period,  by  months,  for  a  number  of 
years,  as  the  precipitation  varies  from  year  to  year  in  both  amoxmt  and 
mtensity,  greatly  affecting  the  nm-off.  In  general,  the  records  of  iO  years 
are  desirable  if  the  demands  approach  closely  the  minimtun  annual  scmply. 
The  minimum  as  well  as  the  average  discharge  should  be  sought,  ilxsctk 
valuable  data  relating  to  discharge  of  streams  may  be  obtained  from  the 
Water  Supply  Papers  issued  by  the  U.  S.  Geological  Survey,  Dept.  of  the 
Interior.  ■ 

For  a  good  discussion  of  an  additive  method  of  computing  mn-off  to  I 
MWCTs.  see  article  in  Eng,  News  of  March  11.  1909,  from  Paper  by  Carl  H.  j 


RUNOFF  FORMULAS,    EVAPORATION, 


1109 


Evaporatioii* — Evmporation  is  a  physical  change  from  a  solid  or  liquid 
to  a  vaporous  or  gaseous  state.  It  is  primarily  due  to  heat.  All  substances 
emit  vapors  to  a  greater  or  less  extent,  depending  largely  upon  the  tempera- 
ture and  also  upon  many  other  conditions,  including  htunidity. 

Evaporation  from  Ice  and  Snow  takes  place  at  all  umptraturgs.  The 
mean  evaporation  from  the  sxirface  of  ice  may  be  assumed  at  about  0.04  in., 
and  from  snow  at  about  0.02  in.,  per  day  of  24  hours. 

Evaporation  from  Water  surface  goes  on  continually  day  and  night,  at 
all  temperatures.  But  when  the  temperature  is  below  the  dew-point  the  ad- 
ditional moisture  from  condensation  may  more  than  offset  the  loss  due  to 
evaporation.    The  rate  of  evaporation  increases  with — 

(1)  Temperature  of  water  surface; 

(2)  Dryness  of  air  at  water  stu^ace; 

(8)     Velocity  of  the  wind  at  water  surface. 

The  maximum  evaporation  from  surface  of  running  water  exposed  to 
hot  sun  and  dry.  hot  wind  in  the  tropics  may  reach  0.50  inch  per  day  of 
24  hours.  But  m  the  southern  part  of  the  united  States  it  will  rarely  if 
ever  exceed  0.40  inch  per  day.  The  average  rate  of  evaporation  from  water 
surface  of  reservoirs  during  the  summer  months  may  be  asstuned  safely  not 
to  exceed  0.35  inch  per  day  in  the  south  and  southwest,  and  0. 18  inch  in  the 
northern  states,  unless  the  reservoirs  ar^  unusually  exposed  or  shallow.  The 
average  rate  ptr  day  for  the  year  may  be  asstmied  at  about  one-half  these 
figures,  that  is.  0.18  and  0.00  inches  respectively.  Running  water  evapor- 
ates more  rapidly  than  still  water:  and  water  in  a  shallow  pan,  exposed  to 
the  sun,  will  evaporate  more  rapidly  than  in  a  reservoir. 

In  a  catchment  basin  the  evaporation  from  the  land  stuface  continues 
only  for  a  definite  period  after  each  dbower  until  the  land  dries,  unless  there 
is  vegetation  in  which  case  it  continues  at  a  greater  or  less  rate.  Evapora- 
tion from  a  meadow  of  luxuriant  grass  has  been  found  to  be  two  or  three 
times  as  rapid  as  from  a  still  water  surface. 


4. — Monthly  Evapokation  in  Inchbs  in  tbb  United  States 
Prom  Water  Surfaces  (Approximate). 


Locality. 

3 

i 

t 

•< 

i 

'i 

3 

i 

< 

t 

1 

i 

k 

An. 
nual. 

North  AUantIc  Coast 

To 

1.3 

1.7 

2.5 

2.5 

3.4 

3.4 

3.4 

2.9 

2.5 

2.0 

~~ir 

Middle  AtianUo  CX>a8t 

1.7 

1.8 

2.3 

3.8 

3  8 

5.0 

4.8 

4.5 

3.7 

35 

3.0 

40 

south  AtlanUo  Coast 

2.5 

2.6 

3.3 

4.3 

4.1 

4.8 

4.4 

4.3 

4.1 

3.7 

3.3 

44 

Quif  Coast 

2.3 

2.7 

3.7' 

4.5 

4.6 

4.5 

4.9 

5.0 

5.0 

4.6 

3.9 

48 

Ohio  VaUey 

1.8 

2.2 

2.8 

5.1 

4  7 

5.3 

6.0 

6.0 

5.5 

4.2 

3.4 

49 

Qrsat  Lakes  Regkm 

0.7 

1.0 

1.2 

2.3 

3.1 

4.1 

4.8 

4.7 

3.3 

2.7 

1.9 

31 

Upper  MiMMppI  Valley. . . 
Hld^e  MUBlMlppl  VaUey. . 

0.6 

l.O 

1.7 

3.2 

3.5 

4.5 

6.2 

5.4 

3.8 

3.1 

2.1 

36 

1.2 

1.6 

2.5 

5.3 

4.6 

4.7 

6.4 

7.0 

5.2 

4.3 

3.5 

48 

MlMOurlVaUey 

0.8 

1.3 

1.5 

4.0 

3.8 

4.6 

6.2 

4.4 

4.0 

3  5 

2.7 

38 

Northern  Rocky  1ft.  Slope. 
Middle  Rocky  Mt.  Slope. . . 

1.1 

2.3 

1.8 

5.0 

5.0 

6.0 

7.2 

6.1 

5.4 

3.6 

2.9 

48 

2.0 

2.6 

2.8 

5.1 

4.6 

6.3 

6.7 

6.3 

5.2 

4  4 

3.8 

52 

Southern  Rocky  Mt.  Slope. 

3.2 

3.6 

4.4 

6.0 

7.5 

8.3 

8.8 

8.^ 

5  3 

4.7 

4.2 

68 

Northern  Plateau 

1. 1 

2.4 

3.8 

5.6 

6.5 

6.0 

9.2 

8.0 

5.6 

3.7 

2.2 

66 

MMdIe  Plateau 

1.4 

2.1^ 

3.6 

t.i 

6.5 

8.1 

9.2 

9.2 

7.4 

5.5 

3.9 

66 

Soothem  Plateau 

3.4 

4.0 

5.2 

7.8 

9.2 

n.7 

9.8 

9.4 

7.1 

6.7 

5.2 

83 

North  PadOe  Coast 

l.I 

1.2 

2.2 

2.5 

3.4 

3.0 

3.2 

3.0 

2.6 

2.0 

1.6 

\.2 

27 

Middle  PadOe  Coast. 

2.6 

3.5 

4.3 

4.5 

4.7 

5.4 

6.4 

6.3 

6.6 

7.6 

4.2 

3.0 

59 

South  Padfio  Coast 

S.3 

2.5 

2.8 

3.9 

4.1 

4.5 

5.4 

5.7 

4.5 

5.0 

3.3 

3.0 

48 

Not*  that  the  above  table  shows  incrgasing  evaporation  toward  the 
South  ioT  any  section  where  conditions  other  than  temperature  are  about 
eqtial.  Evaporation  is  less  in  regions  adjacent  to  large  bodies  of  water  (as 
the  Atlantic,  Pacific  and  Great  Lakes  regions)  for  the  same  latitude,  because 
there  is  greater  humidity  in  the  atmosphere.  Conversely,  it  is  to  be  noted 
that  the  great  dry  plateau  r^on  in  the  West  furnishes  the  greatest  evapora- 
tion. Evaporation  on  the  North  Pacific  Coast  is  low  because  of  the  almtwt 
incessaxit  rains  for  six  months  of  the  year.  But  south  of  Oregon  the  Pacific 
ZotkSt  shows  greater  evaporation  than  the  Atlantic  Coast  of  the  same  lati- 
tude, because  of  dryness  of  the  atmosphere  and  higher  mean  temperature. 


1200  93.— WATER  SUPPLY, 

8MfNig». — ^The  seepace  In  a  catchment  arM  It  aqtuJ  to  tbe  total  tBin- 
fall  minus  the  run-off  and  evaporation.  When  the  siotmd  is  troten  the 
seepage  is  practicaUy  naught,  while  in  deep,  sandy  soif  it  may  e<iual  nearly 
the  total  precipitation.  It  is  usual  to  estimate  the  seepage  and  evapofatioo 
together  as  the  total  loss  in  a  catchment,  reservoir,  stream  or  canal.  If  the 
latter  has  locks  or  gates,  leakage  is  also  included.  The  loss  due  to  seepage 
and  evaporation  combined,  for  a  canal  in  an  earthen  bed.  will  vary  genera^ 
from  li  to  2i  inches  per  day,  depending  upon  size  of  canal,  character  ci 
soil.  etc.  The  rate  of  seepage  often  decreases  with  the  age  of  the  canal,  as 
the  fine  particles  pack  into  the  soil  bed  and  decrease  the  voids.  Experimoits 
with  models  have  shown  that  the  ratio  of  annual  seepage  to  annual  evapoca- 
tion  for  total  rainfall  (with  no  run-off)  •  in  temperate  climates  is,  for  earth 
bed,  about  1  :  2.4;  and  for  sandy  bed,  about  5  :  1.  These  figures,  however. 
cannot  apply  to  reservoirs  and  canals  where  the  process  otevaporation  is 
continuous,  which  was  not  the  case  with  the  experiments.  Roui^xly  speak- 
ing, the  comparative  rates  of  seepage  in  various  soils  is  about  as  foUows, 
assuming  that  for  sandy  soil  to  be  xmity:  Minute  gravel,  100;  coarse  sand, 
10;  fine  sand,  2-  sandy  soil,  1*  sandy  clay.  0.6;  clay,  0.25  to  0.00. 

Mr.  Elwood  Mead  states*  that  the  loss  from  seepage  and  evaporation  as 
determined  from  a  large  number  of  measurements  made  by  the  U.  S.  Dept. 
of  Agriculture,  was  2.47  per  cent  per  mile  in  1000,  and  1.45  per  cent  per 
mile  in  1001-rgrouped  as  follow: 

Loss  per  mile. 
Capacity  of  Canals.  Per  cent. 

[a}.  Canals  carrying  100  cubic  ft.  per  second  or  more 0 .08 

Ccmals  carrying  between  60  and  100  cu.  ft.  per  second 2  «67 

Canals  carrying  between  26  and  60  cu.  ft.  per  second 5 .  13 

.  Canals  carrying  less  than  26  cubic  feet  per  second 7 .48 

It  is  interestmg  to  note  here  that  the  above  table  may  be  generalized  by 
the  following  law:  The  total  loss  per  mile  for  canals  carrying  from  26  to  200 
cubic  feet  per  second  was,  in  1900  and  1901,  from  1.9  to  2.0  cubic  feet  per 
second. 

From  evaporation  alone  it  is  probable  that  the  loss  rarely  exceeds  1  per 
cent  per  mile  in  irrigation  canals,  when  the  velocity  is  24  to  3  feet  per  second. 
Reservoir  losses  from  the  same  cause  may  vary  from  2  to  7|  feet  in  depth, 
annually;  generally  from  8  to  6ft.:  rough  average.  4  ft.  (see  Table  4,  pre- 
ceding page). 

*  "Irrigation  Institutions,"  pp.  12S-4. 


I 


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SEEPAGE  AND  EVAPORATION,    MISCELLANY,  1201 


EXCERPTS  AND  REFERENCES. 


0  Runoff  in  California  (Bv  J.  B.  Lippincott  and 
«,  June  5,  1902). — ^The  following  basma  are  dis- 
r  Basin,  San  Matea  Creek,  Salt  Springs  Valley 


ReUtkm  of  RainfaU  to  Runoff 

S.  G.  Bennett.    Eng.  News,  ' 

cusaed:    Sacramento  River  ]  ^ ,_    

Watershed,  Stanislaus  River  Basin,  Tuolumne  River  Basin^  San  Joaquin 
and  Kings  River  Basin,  Mojave  River,  Cuyamaca  Reservoir  Watershed, 
Sweetwater  Reservoir  Basins.  A  diagram  shows  the  annual  and  mean  run- 
off  from  the  above  watersheds.  A  table  gives  the  number  of  "acrc-ft.  per 
so.  mile"  for  "depth  of  runoff  in  ins."  for  depths  advancing  by  hundredths 
of  an  inch  up  to  one  inch.  The  table  is  basied  on  1'  depth  of  runoff-" fi3| 
acre-ft.  per  square  mile  — MO -i- 12. 

Formulas  for  Computing  the  Cost  of  Impure  Water  Supplies  (Eng. 
News,  Nov.  15.  1906). 

Works  for  the  Purifkatton  of  the  Water  Supply  of  Washington,  D.  C. 
(By  AUen  Hazen  and  E.  D.  Hardy.    Trans.  A.  S.  C.  E..  Vol.  LVII). 

Railways  and  Water  Pollutk>n,  With  Special  Refermice  to  the  Water 
Svpp^of  Seattle  (Eng.  News.  Dec.  27,  1906). 

Report  of  the  Proposed  226-Mile  Aqueduct  for  the  Water  Supply  of 
Los  Angeles,  Cal.  (Eng.  News,  Jan.  24,  1907).— Board  composed  of  T.  R. 
Freeman,  P.  P.  Steams,  J.  D.  Schuyler.  Total  estimated  cost,  $24,485,000. 
Length  of  Time  Required  to  Determine  Rainfall  or  Stream  Flow  Within 
a  Qiven  Percentage  of  Error  (By  J.  C.  Stevens.  Eng.  News.  Sept.  17,  1908). 
— Diagram. 

A  New  Water  Supply  for  the  Citv  of  Vancouver,  B.  C.  (By  H.  M. 
Burwell.  Eng.  News,  April  1,  1909).— <>ost  data  on  wood-stave  pipe  and 
steel  pipe. 

.   The  Purification  of  Qround  Waters  Containing  Iron  and  Manfaneie 
(By  R.  S.  Weston.    Trans.  A.  S.  C.  E..  Vol.  LXIV). 
lUttstfations  of  Water  Supply  Works  ^— 

Description.  Eng.  News. 

Crofls-eection  of  concrete  water  supply  conduit.  Los  Angeles  Am.  27,  1903. 
The  California  or  "stovepipe"  method  of  well  construction  Nov.  12,  '03. 
Brick  and  cast-iron  infiltration  conduits,  Columbus,  O.  Feb.  11,  '04. 

Water-filter  plant  at  Danville,  111.;   11  illustrations  Aug.  28.  '04. 

Settling  tank,  and  sinking  shoe  for  pump  well.  Ithaca  April  20.  '06. 

Plans  and  details  of  sedimentation  basin,  Charlestown,  W.  Va.  June  7.  '05. 
Cross-sections  of  new  conduit  for  Vienna  water  supply  Oct.    11,  '06. 

Cross-section  of  reinforced-concrcte  pressure  conduit  that  fail'd  Oct.  29,  '08. 
Aqueduct,  7  z  40  ft.;  steel  frame,  rein.-conc.  lining  Feb.  24,  '10. 

Eng.  Rec. 
Proposed  inclined  wells  at  shore  of  Lake  Superior  June  19,  *09. 

Catskill  Aqueduct,  cut-and-cover  construction  Jan.      8, '10. 

I^ross-section  of  5i-ft.  rein.-conc.  pressiu^  pipe  line  Feb.   19,  '10. 

Details  of  anchorage  for  42-in.  pipe  line  Feb.   19.  '10. 

Section  (14'  2*  dia.)  Moodna  cone,  pressore  tunnel  June    4.  '10. 

Rein.-conc.  siphon  for  66-ft.  head,  Los  Angeles  Aqueduct  July     9,  '10. 

r-ft.  dia.  rein.-conc.  oonduit  under  12  to  Id-ft.  head  July  28.  '10. 


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64.— WATER  WORKS. 

This  subject  is  treated  under  five  main  headings,  as  follows: 

A. — Consumption  of  Water Page  1202. 

B.— Purification  of  Water Page  1204. 

C. — Reservoirs Page  1205. 

D.— Conduits Page  1207. 

E. — Distributing  System Page  1280. 

A.— CONSUMPTION  OF  WATER. 

The  "consumption"  of  water  in  cities  and  towns  is  measured  in  gaUoos 
per  capita  per  day,  of  population  supplied.*  and  includes  the  total  amouat 
of  water  "used"  and  unxsled.  The  amount  of  water  actually  needed  for 
domestic  supply  could  undoubtedly  be  restricted  to  20  gallons  per  capita 
per  day,  but  there  is  a  great  deal  of  careless  and  wanton  waste,  as  wtH 
as  use  for  fire  protection,  manufacturing  purposes,  etc.  Roughly  spreaking, 
it  is  customary  to.  estimate  the  probable  consumption  at  50,  oO  or  80  gallons 
for  small  cities  aiid  towns  about  to  be  supplied,  and  based  on  a  populatioo 
20  years  in  the  future.     For  large  cities,  see  Tablet  1  and  2  following. 

Water  meters  are  most  frequently  used  in  connection  with  manufacturing 
plants;  and  where  water  is  not  plentiful  thev  are  useful  in  restricting  undue 
waste  in  domestic  supply,  otherwise  they  should  be  omitted,  as  a  free  toe 
of  water  promotes  cleanliness. 

1. — Population  in  Thousands  of  Pbrsons  in  Various  Cmxs 
OF  THB  U.  S. 
(To  accompany  Table  2,  following.) 


*  A  source  of  error  in  gathering  statistics  on  consumption  of  water  is  to 
include  the  total  population  of  a  town  as  being  served  from  a  certain  supply. 
whereas  a  portion  of  the  population,  sometimes  large,  may  be  served  from 
some  other  supply,  often  Irom  wells. 

t  Boston,  Somervillc,  Chelsea  and  Everett. 

♦  Metropolitan  Water  Works  (Boston  only). 


1202  Digitized  by  Google 


CONSUMPTION  OF  WATER. 


1908 


2. — ♦Daily  Avbraob  Consumption  of  Watbr  in  Gallons  pbr 

Capita  per  Day  in  Various  Cities  of  the  U.  S. 

(See  Population  Statics,  Table  1,  preceding.) 


Boston. 

1 

1 

ear 

i| 

d 

1 

\                                                           9 

\ 

ll 

^ 
a 

t                                  3 

I 

1 

i 

i 

(1) 

(2) 

.1    II    1    1    II 

(12) 

(13) 

(") 

"      ,    , 

150 

42 

20 

55 
«0 

165 

70 

1 

64 

97 

25 
30 
29 

14' 
22 

'44' 
52 
55 

27* 

'43* 

42 

36* 
50 

.... 

29 

.... 

18 

M 

44 

73 

55 

47 

. . .. 

48 

31 

64 

"** 

23 

44 

31 

«0 

56 

72 

55 

47 

.... 

53 

36 

76 

21 

43 

38 

2 
3 

63 
73 
72 
69 

70 
77 
78 
86 

74 
88 
96 
100 

54 
56 

58 
69 

63 
59 
54 
59 

■45" 
51 
55 
61 

54 
60 
55 
60 

40 
43 
45 
44 

88 
98 
97 
120 

'29' 

22 
22 
24 
24 

38 
48 
50 
67 

45 

41 
42 
40 

55 

4 

"\2 
18 

51 

175 

'24' 

6 

71 

80 

103 

57 

62 

68 

49 

111 

45 

27 

29 

25 

51 

32 

M 

7 

72 

75 

"m 

59 

66 

64 

56 

111 

69 

29 

'24' 

30 

26 

53 

32 

58 

8 

80 

76 

123" 

64 

58 

87 

66 

51 

110 

85 

30 

26 

32 

25 

45 

32 

53 

9 

87 

88 

66 

60 

72 

68 

63 

125 

96 

33 

30 

35 

27 

47 

34 

65 

C80 

87 

87 

112' 

68 

54 

72 

76 

65 

130 

106 

42 

34 

38 

28 

46 

32 

55 

1 

04 

80 

71 

56 

76 

87 

77 

145 

109 

56 

35 

40 

30 

46 

32 

86 

59 

2 

05 

73 

iio' 

76 

58 

v8 

69 

68 

132 

114 

47 

33 

43 

36 

45 

37 

82 

63 

3 

97 

74 

78 

58 

75 

66 

76 

1«6 

108 

52 

37 

46 

31 

47 

36 

78 

61 

4 

73 

65 

iii' 

74 

61 

63 

74 

83 

169 

101 

56 

34 

48 

26 

46 

39 

72 

60 

»5 

73 

68 

116 

72 

64 

67 

64 

93 

176 

105 

62 

37 

56 

26 

51 

42 

85 

62 

6 

74 

72 

118 

80 

65 

73 

74 

91 

178 

110 

65 

37 

59 

27 

56 

44 

86 

64 

7 

80 

72 

120 

89 

65 

73 

88 

96 

197 

117 

84 

37 

62 

25 

60 

48 

85 

77 

8 

87 

75 

119 

100 

67 

74 

99 

95 

204 

105 

62 

40 

69 

28 

63 

45 

88 

71 

» 

81 

69 

123 

110 

67 

73 

99 

99 

172 

116 

67 

41 

62 

27 

82 

43 

89 

68 

(90 

83 

71 

136 

132 

68 

78 

111 

106 

181 

109 

100 

48 

69 

29 

62 

45 

98 

69 

1 

90 

76 

133 

140 

70 

77 

138 

111 

156 

112 

98 

60 

74 

31 

60 

49 

92 

87 

a 

96 

79 

135 

143 

79 

83 

123 

118 

154 

101 

103 

55 

73 

28 

66 

53 

88 

81 

3 

107 

86 

167 

150 

86 

83 

124 

130 

165 

108 

104 

60 

79 

27 

75 

54 

99 

66 

4 

101 

89 

152 

159 

85 

129 

113 

156 

108 

97 

64 

75 

27 

69 

81 

85 

67 

195 

104 

83 

158 

162 

84 

*84' 

135 

137 

163 

101 

115 

57 

81 

36 

72 

68 

84 

62 

6 

117 

88 

157 

168 

86 

86 

no 

129 

141 

96 

101 

56 

82 

36 

76 

68 

89 

66 

7 

118 

88 

153 

185 

90 

85 

108 

136 

134 

89 

102 

52 

78 

36 

76 

70 

95 

64 

8 

ik 

147 

196 

84 

85 

95 

138 

143 

85 

100 

54 

78 

32 

86 

70 

102 

65 

• 

156 

199 

85 

98 

153 

159 

86 

100 

63 

81 

35 

87 

79 

107 

70 

•00 

|l 

161 

221 

86 

106 

116 

169 

162 

83 

92 

54 

83 

35 

79 

65 

101 

75 

1 

ih 

192 

211 

83 

.... 

121 

169 

163 

80 

102 

55 

74 

34 

81 

62 

91 

78 

2 

194 

232 

83 

Ill 

125 

168 

162 

81 

98 

58 

57 

40 

85 

62 

91 

83 

8 

4 

n 

196 

237 

84 

123 

130 

142 

157 

80 

103 

65 

55 

38 

90 

63 

96 

86 

140 

149 

203 

234 

88 

131 

137 

139 

179 

84 

101 

67 

53 

36 

90 

64 

96 

85 

105 

140 

151 

200 

227 

91 

101 

124 

131 

168 

86 

103 

68 

58 

41 

93 

59 

95 

88 

6 

160 

♦  Data  in  Tables  1  and  2  up  to  the  year  1890  are  from  Paper  No.  768  of 
ran*.  A.  S.  C.  E.,  Vol.  XXXIV,  entitled  "Consumption  and  Waste  of 
iTater"  by  Dexter  Brackett.  Prom  1890.  the  data  have  bee^^  gathered  by 
le  writer,  from  official  sources.  Digitized  by  GoOglc 


12Qi  QL'-WATER  WORKS, 

B.— PURIFICATION  OF  WATER. 

The  purification  of  water  for  domestic  use  has  received  considerable 
attention  in  the  United  States  during  the  past  15  or  20  years,  and  in  Europe 
for  a  much  longer  period.  Speaking  generally,  there  are  three  main  steps 
in  the  purification  of  surface  water,  from  streams  or  reservoirs,  naxnelyi  (D 
screenmg;  (2)  sedimentation;  (3)  filtration.  The  last  named  is  often 
omitted.* 

Screeninf . — At  the  approach  to  the  intake  end  of  the  pipe  there  shook! 
be  placed  a  grating  composed  of  vertical  bars  of  wood,  iron  or  steel  to 
screen  out  the  leaves  and  prevent  the  drift  p^enerally  from  entering  the  pipe. 
These  bars  are  placed  eogewise  to  the  du^ection  of  flow  and  are  stayed 
laterally  by  small  rods  and  fillers. 

Sedimentation. — ^The  screened  water  is  next  allowed  to  pass  into  a  settling 
basin  of  greater  or  less  capacity  to  deposit,  while  at  rest,  the  sedinaentary 
matter  which  it  held  in  suspension  while  in  an  agitated  state.  Turbid  watess. 
those  suspending  sand,  silt  and  clay,  should  necessarily  thus  be  treated.  If 
the  particles  of  clay  are  minute,  that  is,  as  fine  or  finer  than  bacteria,  it 
becomes  necessary  to  add  a  coagulant  to  the  water  before  it  enters  the 
basin.  Various  conipounds  of  alum,  lime  and  iron  are  used  as  coagulants. 
Perhaps  sulphate  of  altmiina  is  the  most  common.  If  a  fair  amount  of 
coagulant  is  used,  the  time  required  for  sedimentation  will  be  about  24 
hoiu^,  depending  upon  various  conditions.  It  is  to  be  noted  that  sedimenta- 
tion with  coagulation  may  be  efficient  in  removing  not  only  the  fine  partides 
of  suspended  matter  above  referred  to,  but  a  large  percentage  of  bacteria 
as  well. 

Settling  basins  may  be  single  or  multiple  and  provided  for  contintious 
or  intermittent  flow. 

"Slow"  Sand  Filtration.— Tliis  is  essentially  the  so-called  English  aystein. 
having  been  employed  almost  exclusively  in  England  since  the  early  part 
of  the  Nineteenth  Century.  The  filter  t>eds  consist  of  one  or  more  water- 
tight reservoirs  each  with  an  area  of  10,000  to  80,000  square  feet.  On  the 
bottom  of  each  reservoir  is  laid  a  system  of  drains  for  carrying  off  the 
filtered  water.  The  materials  composing  the  beds  proper  are  broken  stone, 
gravel  and  sand,  placed  in  successive  layers  and  grad\iated  to  size,  with  the 
coarser  material  at  the  bottom.  The  top  bed  of  sand  usually  varies  from 
24  to  60  inches  in  thickness  and  should  be  composed  of  fine  grams  of  uniform 
size. 

The  rate  of  filtration  usually  averages  from  6  to  9  feet  of  water  column 
per  day  of  24  hours  with  good  results.  Care  must  be  used  to  see  that  the 
drains  carry  off  the  filtered  water  freely.  The  water  may  be  ddivered  to 
the  filter  beds  by  gravity  or  by  pumping.  If  it  contains  much  sediment  it 
should  first  be  passed  througn  the  settling  basin  as  previously  described 
tmder  Sedimentation.  Two  systems  are  employed — the  continuous  and  the 
intermittent. 

The  result  of  sand  filtration  when  highly  efficient  is  to  remove  from  the 
water  its  impurities  and  render  it  potable.  These  impurities  are  injurious 
bacteria,  vegetable  organic  compounds  (sometimes  coloring  the  water 
highly)  and  animal  pollution,  as  sewage.  The  last  named  is  the  nK>st  Mtsaly 
removed.  A  good  sand  filter  usually  removes  from  98.6  to  99.5  per  cent  o* 
bacteria.  To  eliminate  vegetable  organic  coloring  effectively,  coagulants 
are  employed — compoimds  of  lime,  altma,  iron.  etc. 

During  filtration  a  thin  film  forms  on  the  svuiace  of  the  sand  axid  acts 
as  a  fine  strainer,  collecting  mc«t  of  the  bacteria  and  other  impurities. 
Althoiigh  the  process  is  (purely  ?)  mechanical  in  theory  yet  it  is  a  fact  that 
water  is  often  rendered  pvwer  chenttcaUy  by  having  passed  through  the  filter. 
The  oxygen  of  the  air  (and  of  the  water)  is  the  great  purifier. 

"Rapid"  Sand  Filtration. — ^This  system  is  distinctly  American  and  is 

generally  termed  "mechanical"  filtration.     Mechanical  niters  are  patented 

*Another  process,  the  Copper  Stdphate  treatment,  is  being  used  con- 
siderably where  algae  is  present  in  the  water.  Many  articles  descriptive  of 
copper  sulphate  as  an  algaecide,  for  reservoir  treatment,  etc.,  have  appeared 
m  current  technical  literature  during  the  past  ton  yean;  also,  of  svupbate 
of  alumina,  hypochlorite  of  lime,  etc. 


PURIFICATION  OF  WATER.    RESERVOIRS.  1205 

devices  for  increasing  the  rate  of  filtration,  by  agitating  the  sand  mechanic- 
ally or  by  compressed  air,  and  by  the  use  ot  coagulants.  They  have  generally 
given  satisfaction  and  bid  fair  tmder  many  conditions  to  compete  with 
ordinarv  sand  filters  in  beds.  The  first  cost  of  mechanical  filters  is  less  than 
for  sand  filters,  but  the  cost  of  operation  is  greater. 

C— RESERVOIRS. 

Reservoirs  may  be  classed  as  follows: 

(a)  Storage  Reservoirs,  comprising  large  natural  basins  with  dam   (see 

Dams,  page  844),  and  wasteway  constructed  at  outlet. 

(b)  Distributing  Reservoirs  (artificial)  constructed  in  earth  by  excavation 

and  embankment,  with  paved  inner  slopes: 
High-service  rescrvou^; 
Low-service  reservoirs. 

(c)  Stand-Pipes  or  water  towers  of  steel,  reinforccd-concrete  or  wood. 

(«)  Storage  Reservoirs*  of  greater  or  less  extent  are  commonly  to  be 
had  on  most  nmning  streams,  generally  near  the  source.  At  the  lower  end 
of  the  natural  basin  and  at  a  contracted  F>oint  of  the  out-flowing  stream,  as 
in  a  canon,  the  dam  is  constructed  of  sufficient  heu^ht  to  guarantee  a  storage 
supply  sufficient  for  the  dry  or  summer  months.  IT  the  supply  is  for  domestic 
use  the  storage  will  be  estimated  in  millions  of  gallons;  if  for  irrigation  it 
will  be  estimated  in  acre  ft.  (one  acre-foot  —  43,560  cubic  feet);  if  for 
water  power  it  will  be  estimated  in  cubic  feet  or  millions  of  cubic  xeet. 

(b)  Distributiiic  Reservoir  sites  should  be  selected  with  great  care.  A 
ride-hill  location  should  be  examined  very  carefully  for  any  indications  of 
tliding  land,  a  serious  condition  for  reservoir  construction.  A  slide  usually 
-eveals  a  wet  or  marshy  spot  at  its  upper  end.  The  water  collects  there, 
liters  to  an  inclined  sub-stratum  (generally  clay)  and  by  moistening  or 
ubricating  it  the  coefiicient  of  friction  is  reduced  to  such  an  extent  that 
liding  takes  place.  If,  unfortunately,  it  is  discovered  that  a  reservoir  has 
)een  constructed  on  such  a  slide,  the  hill-side  above  and  around  the  reser- 
voir should  be  sub-drained  thoroughly  at  the  sliding  plane  to  keep  it  as  dry  as 
ossible.f  This  sub-drainage  may  be  accomplished  by  driving  small  tun- 
lels.  with  branches,  and  laying  drain  tile  to  carry  away  the  water. 

Distributing  Reservoirs  situated  immediately  at  the  townsite  are  con- 
cnient  and  economical.  Incidentally  they  serve  as  secondary  settling 
asins,  and  hence  provision  should  be  made  for  "blowing"  them  out  when- 
ver  the  bottoms  accumulate  much  sediment.  The  waste  pipe  leads  from  a 
epression  in  the  bottom  of  the  reservoir,  and  small  water  pipes  are  laid  for 
:;casional  washing  and  cleansing.  Economically,  distributing  reservoirs 
trve  to  lower  the  static  head  on  the  distributing  system  of  pipes  through 
le  town,  by  receiving  the  supply  direct,  through  the  pressure-pipe  line, 
om  the  storage  reservoir  or  headworks.  By  this  means  the  pressure  on  the 
'Stem  may  often  be  reduced  several  hundred  feet.  If,  however,  the  storage 
scrvoir  is  not  at  too  high  an  altitude  the  pressure-pipe  line  may  be  con- 
;cted  directly  with  the  mains  and  allowed  to  discharge  into  tnem,  but 
ually  only  in  case  of  fire  when  high  pressure  is  needed.  The  high-service 
,d  low  service  reservoirs  are  primwily  designed  to  supply  the  high  and  the 
)v  sections  of  the  town,  respectively,  each  coimected  with  its  own  distribut- 
i  system. 

It  is  to  be  noted  that  considerable  pow^r  for  lighting  and  pumping  can 
;en  be  developed  at  the  distributing  reservoirs  by  utilizing  the  available 
ad  from  the  source  above.  By  this  means  water  may  be  pumped  to  a 
.nd-pipc  for  supplying  an  isloated  section  of  the  town  at  considerable 
vation  and  distance. 

The  outlet  pipe  from  a  reservoir  should  be  so  arranged  that  water  may 
taken  at  different  elevations  above  the  bottom  of  the  reservoir,  in  order 
avoid  suspended  matter  and  sediment. 

*  See  Paper  entitled  "Lake  Cheesman  Dam  and  Reservoir**  by  Messrs. 
prison  and  Woodard,  in  Trans.  Am.  Soc.  C.  E.,  Vol.  LIII  (Dec..  1904) 
:e  89.  for  a  very  complete  description  of  a  typical  storage  reservoir,  with 
strttction  of  dam,  wasteway,  outlet,  etc.  ^.    , 

t  See  Paper  entitled  "A  Phenomenal  Land  Slide*'  by  p.(D^(Jlarke,  in 
as.  Am.  B&c.  C.  E..  Vol.  LIII  (Dec..  1904).  page  322. ^^^  ^^^  ^^^ 


1206  ^— WATER  WORKS, 


Rgserooir  Linings. — ^The  bottom  may  be  lined  with  6  inches  or  moie  o( 
concrete  laid  with  expansion  joints;  on  this,  from  I  to  |  inch  of  cement 
mortar*  next,  a  coat  of  liquid  asphalt;  and  filially,  a  narder  coat  of  aK)halt 
The  side  slopes  may  be  lined  with  6  inches  or  more  of  concrete  laid  inth  I 
expansion  joints;  a  coat  of  asphalt;  a  layer  of  brick  dipped  in  hot  asphalt 
and  laid  flat;  and  then  a  finishing  coat  of  asphalt,  filling  up  all  the  joints. 
Instead  of  the  brick  lining,  a  coatmg  of  asphalt  or  asphalt  cement  is  some- 
times employed.  Expansion  joints  are  spaced  from  10  to  20  feet,  depending 
upon  the  climate. 

It  is  generally  advisable  to  discharge  the  water  into  the  reservoir  thitni^ 
an  aerating  fountain. 

(c)  Stand-Pipes  are  simply  upright  riveted  steel  pipes  with  the  lower 
end  capped,  resting  on  a  foundation  usuallv  of  concrete,  and  tboxough^y 
anchored.  The  plates,  joints  and  rivets  will  have  to  resist  various  oooa- 
plicated  stresses  if  the  stand-pipe  is  in  a  freezing  climate: 

(a)  For  static  pressure,   <«=  — — ^ —    [See  notation  below.] (Ij 

(b)  If  the  water  at  surface  of  tank  is  frozen  and  pumps  are  acting  to 

force  water  into  the  tank  there  is  an  added  presswv  which  would 
have  to  be  reduced  to  equivalent  head. 

(c)  Or,  if  the  water  subsides  from  the  ice  there  is  a  mtnux  prrssMrv  pn>- 

duced  by  the  resulting  vacuum,  which  may  tend  to  collapse  the 
tank. 

(d)  The  wind  pressure  is  a  very  considerable  item  which  has  to  he 

reckonea  within  the  design  of  large  stand-pipes.  The  resisting 
moment  Mb'  in  inch-lbs.,  for  a  cylindrical  section  of  stand-pipe, 
due  to  bending,  is 

M»'-^-/irr«<* (Si 

where  /—allowable  fiber  stress  in  lbs.  per  sq.  in.; 

/  —  moment  of  inertia  of  cross-section,  in  ins.; 
y—r«radius  of  pipe  or  tank,  in  ins.; 
)r- 3.1410; 

<= thickness  of  metal  shell,  in  ins.* 
#— efficiency  of  riveted  joint,  say  0.50  to  0.80. 
But  the  bending  moment  Af  b'  in  ft.-lbs.,  is 

,-  ,      6P    dh*  ^ 

where  P— wind  pressure  in  lbs.  per  sq.  ft  for  flat  surfaces; 

6P 

Tjr  —wind  pressure  in  lbs.  per  sq.  ft  for  cylindrical  diame* 
10  ters; 

d  — diameter  of  tank,  in  feet; 

^n depth  of  section  considered,  in  feet,  below  top  oT  fc»TiV 
Bquatin^  the  resisting  moment  (2)  with  the  bending  moment  (S), 
multiplymg  the  latter  by  12  to  reduce  to  inch-lbs.,  we  have 

fxr*te^Z.6Pdh* (1 

,     3.6  Pdk*     A.6Ph* 

whence  f—T^Te dTT «^ 

and  if  P  is  taken  at  50  lbs.  per  sq.  ft.,  we  have 
X     230  M 

^--jjr <^ 

J  .     230  A«  _ 

"^  '"-dTT ^' 

(e)  In  order  to  provide  for  possible  corrosion,  the  calculated  thkkxaess 

of  ^ell  may  be  increased  by  say  ^  m.,  as  with  riveted  sted 

water  Dipe.    It  should  be  noted  that  the  thicknefis  of  sheU  at  top 

of  tanlc  should  not  be  less  than  i  inch. 

A  common  method  employed  in  the  design  of  stand-pipes  is  to  caknUate 

for  static  pressure  (a) ,  wind  pressure  (rf) ,  and  allow  for  corrosion  (•).    If  sort 

steel  is  used,  with  an  ultimate  strength  of  00.000  lbs..  /  may  be      ' 


RESERVOIRS  AND  STANDPIPES,    CONDUITS  1207 

15,000  lbs.  where  no  freezing  it  expected.  But  otherwise  this  should  be 
reduced  to  12,000  or  10.000  lbs.,  depending  upon  the  climate.  The  tank 
should  be  well  stiffened  against  collapse. 

An  Elevated  Tank  is  a  tank  supported  at  an  elevation,  usually  on  tower 
posts,  hence  the  name  water-tower.  The  whole  structure  is  sometimes 
enclosed  in  a  drctilar  masonry  shell. 

Stand-pipes  and  elevated  tanks  are  more  economical  in  certain  localities 
than  are  ordinary  reservoirs.  They  are  useful  in  furnishing  a  supply  to 
districts  where  the  population  is  small  or  isolated;  or  to  sections  above  the 
altitude  of  the  mam  reservoirs.  They  are  often  used  in  towns  equipp^ 
with  the  direct  pumping  system,  to  provide  safe  pressure  in  case  of  nre; 
and  are  connected  with  the  main  line,  as  close  to  the  pumping  station  as 
possible. 

D.— CONDUITS. 

After  the  water  has  been  purified  to  a  greater  or  less  degree  at  the 
Headworks  by  stdtm^nUUion  and  perhaps  by  filtration,  it  is  delivered  by 
the  conduit  to  the  high-  or  low-service  reservoirs  or  to  stand-pipes, 
situated  as  near  the  town  as  proper  altitude  and  selection  of  site  will  permit. 

Conduits  (or  aqueducts)  may  be  classified  as  follows: 
U       Open  conduits,  or  those  which  follow  the  hydraulic  grade  line. 


JgCaniU.. 


,  ,   Plumes. 
//.     Closed  conduits  which  follow  relatively  the  hydraulic  grade  line. 

Bored  wooden  pipe,  not  banded. 

Salt  glazed  vitrined  pipe. 
,,    Masonry  aqueducts,  mcluding  cement  pipe. 
///.   PrMSure  pipe  lines. 

{a)  Bored  wooden  pipe,  banded. 

Wood  stave  pipe  (banded). 

Cast  iron  pipe. 

Wrought  iron  pipe. 

Steel  pipe. 

Attachments. 

Specials. 

la.— CANALS. 

Where  the  topography  will  admit,  considerable  saving  of  cost  may  often 
be  made  by  emplojring  open  channel  construction  from  the  headgate  to 
the  settling  basin  instead  of  the  more  expensive  pipe-line  construction 
usually  adopted.  But  the  sanitation  must  also  be  considered,  as  well  as 
the  poetibihty  of  freezing. 

lb.— FLUMES. 

Wooden  flumes  may  be  substituted  for  canals  (above)  for  small  towns 
where  a  cheap  construction  is  desired,  as  in  the  West.  Plumes  may  be 
V-shaped,  rectangular,  or  semi-circular  (see  Irrigation,  page  1317).  It  is  to 
be  noted  that  no  op€n  conduit  construction  is  to  be  allowed  below  the 
point  where  the  water  is  purified.    Steel  flumes  are  usually  semicircular. 

Ila.— BORED  WOODEN  PIPE. 

Bored  Wooden  Pipe  has  been  used  to  a  small  extent  in  the  West  in 
certain  localities  where  timber  is  cheap.  Its  use,  however,  has  been  con- 
Rned  mainly  to  the  smaller  sizes,  say  6  mches  or  less  in  internal  diameter. 
Jointa  are  made  by  using  wooden  or  cast  iron  hubs  to  couple  the  connecting 
?nda.  When  not  banded  they  are  seldom  subjected  to  very  much 
static  pressure.  The  writer  has  seen  specimens  of  bored  pipe  6  inches  in 
iiameter  whidi  had  been  removed  after  being  in  service  about  40  years. 

lib— SALT  OLAZED  PIPE. 
Salt  Glazed  Vitrified  Pipe  is  specially  adapted  to  economic  «on- 
Etruction  on  small  work  where  the  topography  of  the  grotmd  will  admit  of 
he  pipe  line  being  laid  fairly  close  to  the  hydraulic  grade  line,  and  where 
he  static  pressure  is  inconsiderable.  It  has  been  used  successfully  up  to 
\0  inches  in  diameter.* 


*  Sea  paper  read  before  Am.  W.  W.  Ass'n  at  Cleveland,  O^^ApnI^.J888, 
.y  Mr.  StcphSi  E.  Babcock.  ^^^^  by V^CTOg-ie 


1208 


^—WATER  WORKS. 


I 


lie— JHASONRY  AQUEDUCTS. 

Masonry  Aqueducts  are  particularly  economical  in  oonveyin^r  large 
supplies  of  water  under  little  or  no  pressure.  Various  shapes  of  section  are 
usea,  as  circular,  egg  shape,  rectangular  with  arch,  and  tunnel  shape.  The 
first  and  last  named  are  typical  of  the  New  Croton  ac^ueduct,  the  cixrular 
section  being  14  feet  in  diameter.  The  ordinarv  section  is  shaped  like  s 
horse-shoe  resting  on  an  inverted  arch.  Rubble  masonry,  concrete  and 
brick  are  variously  employed,  the  first  named  being  connned  to  the  side 
walls,  and  the  last  named  to  the  lining.  The  brick  lining  is  laid  generalljr  in 
one,  two  or  three  layers.  Concrete  may  replace  the  rubble  and  brick  to  s 
greater  or  less  extent.   Reinforced  concrete  is  used  for  high  pressures. 


Fig.  1. — Reinforced  Concrete  Aqueduct. 
Fig.  1  is  a  section  of  reinforced  concrete  aqueduct  for  the  City  of  Mexko 
J.  D.  Schuyler,  consulting. engineer  (sec  Eng.  News,  April  10,  1006). 

Ilia.— BORED  WOODEN  PIPE.  BANDED. 

Bored  Wooden  Pipe  (Ila)  if  Banded  may  be  used  imder  pressure,  bat 
it  should  be  avoided  generally  for  better  construction.     The  cheaper  form 
>iral  M 


of  banding  is  by  spin 


wound  wiring. 

Illb.— WOOD  STAVE  PIPE. 


Wood  Stave  Pipe   has  had  a  variable  reputation  and  has  been  the 
subject  of  much  discussion  among  engineers.    The  writer  has  laid  a  great 

.Band 


Pig.  2.  Fig.  2a. 

many  miles  of  this  pipe  and  can  recommend  it  for  cheapness  of  first  cost 
and  for  carrying  capacity.    But  it  yet  remains  to  be  demonstrated  to  what 


MASONRY  AQUEDUCTS.    WOOD  STAVE  PIPE. 


1309 


tent  it  will  compare  in  economy  with  other  kinds  of  pipe  when  its  lasting 
alities  are  better  known. 

Pig.  2  shows  a  half -section  of  stave  pipe  with  staves,  tongues,  band 
ith  head,  nut  and  washer)  and  shoe.  Fig.  2a  is  a  view  of  an  ordinary 
ve  showing  the  saw-kerf  at  one  end,  and  the  metallic  tongue 
erted  at  the  other.  On  the  nearest  edge  is  shown  a  beaded  projection 
t  by  the  planer  on  the  finished  stave  to  insure  water-tightness,  but  as  this 
id  IS  subpect  to  injury  it  is  often  omitted.  Note  that  the  tongue  projects 
newhat  beyond  either  edge  of  the  stave  and  is  embedded  m  adjoining 
ves  when  the  pipe  is  cinched  tifi[htly.  The  metallic  tongues  are  usually, 
t  not  always,  galvanized  before  being  placed  in  the  pipe.    Pig.  3  is  a  plan 


2-£i 


Fig.  8. 

i-indi  band  (upset)  with  head,  nut  and  washer.  Note  that  the  upset  is 
y  long  to  allow  for  proper  cinching,  and  that  the  length  is  "under  head." 
tids  should  be  protected  from  rust  before  the  pipe  is  back-filled.  A 
imon  method  m  the  West  is  to  dip  them  in  hot  asphalt  after  bending. 
2  bending  and  dipping  plants  may  be  erected  on  the  ground  where  the 
e  is  laid  if  the  wort  is  ot  considerable  magnitude;  otherwise  they  should 
(re  the  mill  ready  for  laying.  Pig.  4  illustrates  the  ordinary  malleable 
1  shoe  or  coupling  for  the  bands,  and  explains  itself. 


Section  A-B. 


Pig.  4. 

Table  8.  following,  was  prepared  by  the  writer  some  years  ago,  and 
be  found  useful  to  those  who  desire  to  make  estimates  on  wood  stave 
•  construction. 


d  by  Google 


1210 


^^WATER  WORKS. 


3. — Wood  Stavb  Pipb  and  Dbtails — 


Internal  dl&meter  of  pipe,  ins 

♦ThlckneaB  I  ot  etovefl. .     ?< IV J . . . 

Finished  width  W,  ins.  .•t"+-^5HBrt559»>l  •  •  •  • 
Partial  depth  iV,  Ins...  V^^^^^^^^   ■- 
Partial  depth  O.  Uis. . .  ^--^     *^-*«<i^ 
Finished  width  te,  Ins.. .       K  —  ^  — -H   . . . 

Size  of  rough  stave.  Ins. 

No.  of  staves  to  the  clrde 

Ft.  B.  M.  of  rough  lumber  per  100'  of  pipe 

sue  of  tongue — width  and  B.  W.  Q 

No.  of  tongues  per  lOO'  of  pipe  (average) 

Wt.  of  tongues  per  100'  of  pipe,  lbs 

Slac  of  band.  Ins. 

Length  ot  band  (under  head),  ft.  and  Ins 

Wt.  of  band  and  upset,  nut  and  head,  lbs. 

Value  of  s  In  lbs.  for  band  section,  factor  of  4. 

Allowables  In  lbs.  to  avoid  crushing  staves 

aosest  band  spacing  practicable.  Ins 

Band  spacing  for  lOO'  head.  Ins. 

No.  of  bands  per  lOO'  of  pipe  for  lOO'  head  . . . 
Wt.  of  bands  per  lOO'  of  pipe  for  100'  hd..  lbs. 

Wt.  of  one  shoe.  lbs. 

Wt.  of  shoes  per  lOO'  of  pipe  for  lOO'hd..  lbs. 

Wt.  of  washers  per  100'  of  pipe  for  100'  hd., 
lbs. 

sue  of  band.  ins. 

Length  of  band  (under  head),  ft.  and  Ins 

Wt.  of  band  and  upset,  nut  and  head.  lbs. 

Value  of  s  In  lbs.  for  band  section,  factor  of  4. 

Allowables  in  lbs.  toavoid  crushing  staves 

aosest  band  spacing  practicable,  Ins. 

Band  spacing  for  100'  head,  ins 

No.  of  bands  per  100'  of  pipe  for  100'  head 

Wt.  of  bands  per  100'  of  pipe  for  100'  hd..  lbs. 

Wt.  of  one  shoe,  lbs. 

Wt.  of  shoes  per  100'  of  pipe  for  100'  hd..  lbs.  . . . 

Wt.  of  washers  per  100'  of  pipe  for  100'  hd.. 

lbs 

Area  of  pipe.  sq.  ft  »=  cu.  ft. per  ft.  of  length 

Qallons  of  water  per  Un.  ft.  of  pipe 

Velocltyi»lnft.per8ecforn=.0l05;*— .0001 

"     "  "  "        «=.001 

"     "  "  "        »=.01 

Discharge  In  million  gals.  pcr24hrB.;s-. 0001 

"       ••        "  "         «=-.001 

• "  "         »-.01 


10- 


12* 


14- 


If 


lix4 
9 
450 

l'x#16|l 
45 
3 


i 
1 

1*X4 
11 
550 
x/16 
55 
4 


3H 
I 

^^ 
3iV 
1*X4 
13 
GOO 
x#16 
60 
4 


iA 

31 

H 

lix4 
14 

00 

l's#16 
"0 
5 


I 

11 
f«#iiii 

4 


A'xA"ovml. 


2-1 1{ 
1.19 


1.40 


4-1* 
1.60 


4-7} 

l.SO 


5-H 
1.99 


1611 

1035 

1255 

1475 

1611 

1611 

H 

1* 

1* 

li 

li 

*A+ 

41+ 

4iV- 

4i- 

31+ 

277 

274 

271 

284 

318 

330 

384 

434 

511 

633 

i 

i 

i 

i 

t 

139 

137 

136 

142 

239 

21 

21 

21 

22 

24 

i'  round. 


1.23 


2-1  li  8-6| 


1.44 


4-li 
1.65 


4-7i 

1.86 


2.« 


700 

409 

503 

i 

205 

31 


34907 
2.611 
.355 
1.30 
4.20 
.08 
.29 
.95 


1146 
li 
3 

399 

742 
i 

200 

31 


54542(.  78540  1 .  0690 1 .  »«3  M 

4.080  5.875  7.99ri0.44 

420  .490  .530     .6i: 

1.54  1.77  1.96    2,19 

4.97  5.70  6.37     6.99 

15  .25  .38      .&S 

.54  .90  1.37     1.98 

76  2.88  4.40    6  36 


1291 
li 
3 
396 
816 
f 


•Finished  thickness  /  of  staves,  in  inches. 


d  by  Google 


WOOD  STAVE  PIPE  AND  DETAILS, 


1211 


—  Poi 

1  PiPB  DiAlCBTBSS  8 

TO  88  Inchbs 

* 

22' 

24- 

26- 

28' 

so- 

32' 

34" 

36- 

88* 

1 

11 

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11 

5? 

li 

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ift 

ift- 

4 

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5 

5 

5* 

5 

6ft 

5ft+ 

5ft 

5 

3x6 

2x6 

3x6 

3x6 

2x6 

2x6 

3x6 

2x6 

3x6 

6 

14 

15 

16 

17 

18 

20 

31 

33 

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7 

1400 

1500 

1600 

1700 

1800 

2000 

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2200 

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86 

90 

100 

105 

110 

115 

10 

12 

18 

14 

15 

19 

20 

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23 

33 

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f  round 

A*  round. 

wot 

7-4i 

7-lOf 

»-H 

8-1* 

9-71 

10-11 

10-8i 

11-2* 

12 

3.68 

3.88 

3.07 

8.28 

4.84 

6.11 

5.38 

5.64 

5.93 

13 

1666 

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1656 

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308 

332 

355 

881 

399 

423 

445 

470 

493 

21 

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34 

36 

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31 

32 

34 

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k'  round. 

6-llf 

7-H 

8-0 

8-61 

9-1* 

9-7f 

10-2 

ia-8f 

11-3 

23 

8.74 

4.01 

4.28 

4.56 

6.39 

6.74 

7.09 

7.48 

7.81 

34 

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2803 

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2199 

2254 

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2944 

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If 

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m 

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358 

357 

330 

329 

341 

359 

381 

29 

1343 

1436 

1528 

1701 

3109 

2217 

2418 

2678 

2976 

30 

1 

1 

1 

1 

1* 

1* 

li 

It 

li 

31 

859 

358 

357 

373 

413 

411 

427 

449 

476 

33 

28 

27 

37 

39 

33 

33 

34 

36 

38 

33 

7     3.6398 

3.1416 

3.6870 

4.2761 

4.9087 

5.5851 

6.8050 

7.0686 

7.8758 

34 

19.75 

33.50 

27.58 

81.99 

36.72 

41.78 

47.16 

52.88 

58.92 

35 

.785 

.850 

.913 

.947 

.996 

1.05 

1.09 

1.13 

1.18 

36 

3.74 

3.93 

8.07 

3.26 

3.40 

3.56 

3.73 

3.86 

4.00 

37 

8.80 

9  84 

9.96 

10.39 

10.83 

11.35 

11.87 

12.30 

12.73 

38 

1  34 

1.73 

3.18 

2.62 

3.16 

3.79 

4.43 

5.16 

6.02 

39 

4.67 

5.95 

7.33 

9.00 

10.8 

12.8 

15.2 

17.6 

20.4 

40 

15.0 

19.0 

23.8 

28.7 

34.3 

40.9 

48.3 

66.5 

64.8 

41 

he  first  five  items  are  dimensions  of  finished  staves  (see  Fig.). 


d  by  Google 


1212 


M.— WATER  WORKS. 


8. — Wood  Stavb  Pipb  and  Details  (Concladed)- 

- 

f 

Intemai  diameter  of  pipe.  Ins 

40» 

42' 

44* 

46* 

48* 

W 

1 

3 
3 

4 
5 
6 

*ThlckneflB  1  of  itavei                               J 
Flntehedwldth  W,  loi                              Tfl 
Partial  depth  N,  Ina.                              5>s 
Partial  depth  O.  ln&.                             ^ 
Finlahed  width  v.  iiu                              « 
sizA  of  rough  Rtave,  ins. 

5f- 
2x6 
24 
2400 

82 

11           If 

t   t 

2x6        2x6 
25          26 
2500       2600 
If  •«#12  If  •«#12 
125        130 
33          35 

If 

2x6 
27 

2700 

lf»#12 

135 

36 

1« 
H 

■t- 

2x6 

28 

4 

23$ 
2S 

7 

No.  of  staves  to  the  circle 

8 
9 
10 
11 

Ft.  B.  M.  of  rough  lumber  per  I OO'  of  pipe 

Size  of  tongue— width  and  B.  W.  O 

No.  of  tongues  per  100'  of  pipe  (average) . . 
Wt.  of  tongues  per  lOO'  of  pipe.  Ibe. 

^180  '  29® 

If-«*12H-^'J 

140         U! 

38          44 

Size  of  l>and,  ins. 

f  round. 

- 

12 
13 

Length  of  band  (under  head),  ft.  and  ins. 
Wt.  of  band  and  upset*  nut  and  head.  lbs. 

Value  of  « In  lbs.  forband  section,  factor  of  4 

aosest  band  spacing  pracUcable.  ln& 

Band  spacing  for  IOC  head.  Ins 

No.  of  bands  per  100'  of  pipe  for  100'  head 
Wt.  of  bands  per  100' of  pipe  for  100' hd..lb«. 
Wt.  of  one  shoe.  lbs.  (x2 — 2  shoes  per  band) . 
Wt.  of  shoes  per  100' of  pipe  for  100' hd..lbs. 
Wt.  of  washers  per  100'  of  pipe  for  100'  hd.. 
lbs. .... 

11-9* 
8.16 

12-4 
8.58 

12-lOi 
8.88 

13-4» 
9.23 

13-IlJ 
9.59 

l*-3i 
9» 

14 

2944 

15 
16 
17 
18 
19 
20 
21 
22 

2944 
If 

lU 

9223 

If 
494 

39 

2944 
If 

m 

4  3 

3523 
If 
516 

41 

2944 

itt 

432 

3836 
If 
540 

43 

3944 

§ 

4154 
If 
562 

45 

2944 

470 
4807 
If 
S88 

47 

2S44 

li  : 
HI 

m 
«5 

Size  of  band,  ins.  . .    . 

4'  round. 

23 
24 

Length  of  band  (under  head),  ft.  and  ins. . 
Wt.  of  band  and  upset,  nut  and  head.  lbs. 

Value  of  9  In  lbs.  for  band  section,  factorof  4 

Allowable  » In  lbs.  to  avoid  crushing  staves, 
aosest  band  spacing  practicable,  1ns. ... . 

11-91 
12.96 

12-4i 
13.54 

f 
12-lOi 
14.08 

13-4f 
14.63 

13-1  li 

15.21 

15.  n 

25 

4602 

26 
27 
28 

4312 

1 

3499 
If 
405 

32 

4525 

1 

8656 
If 
405 

32 

4603 
If 

3900 
If 
416 

31 

4602 

1 

4213 
If 
433 

34 

4603 
If 

4 

800 

4563 

If 

450 

85 

II 

11 

29 
30 
31 
82 
33 

No.  of  bands  per  100'  of  pipe  for  100'  head 
Wt.  of  bands  per  100' of  pipe  for  100*  hd..  lbs. 
Wt.  of  one  shoe.  lbs.  (x2- 2  shoes  per  band) 
Wt.  of  shoes  per  100'  of  pipe  for  100'  hd..  lbs. 
Wt.  of  washers  per  iw/ot  pipe  for  100'  hd.. 
lbs 

34 

86 
36 
37 
88 
89 
40 
41 

Area  of  pipe.  sq.  ft. =cu.  ft.  per  f  i.  of  length 

GaUons  of  water  per  lin.  ft.  of  pipe 

Velocltyt>lnft.per8eaforn».0l05;»-.0001 

"         »-.0l01 

"        «-.01.. 

Discharge  in  million  gals,  per  24  hrs.  vs  -  .0001 
"      "      ••     *-.001. 
"     •'     "    »-.oi.. 

8.7267 
65.28 
1.23 
4.16 
13.24 
6.95 
23.6 
74.7 

9.6211 
71.97 
1.27 
4.29 
18.66 
7.88 
26.6 
84.2 

10.5SS 

78.99 
1.31 
4.42 

14.08 
8.93 

30.1 

96.0 

11.541 

86.33 

1.38 

4.55 

14.49 
10.1 
33.9 
108.0 

12.564 

94.00 

1.40 

4.68 

14.90 
11.4 
38-0 
121.0 

16:: 

IB 

r3< 

UT 
42.3 

i;4.ft 

*  Finished  thickness  t  of  staves,  in  ir 

ches. 

Di 

gitized  by 

Goo^ 

gle 

WOOD  STAVE  PIPE  AND  DETAILS, 


1218 


■  For  Pipe  Diameters  40  to  72  Inches. 

» 

M' 

56* 

58- 

60* 

62' 

64' 

66' 

68* 

70* 

72* 

3 

7  - 

^. 

21 

H 

H 

24 

2X 

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2» 

1 

7A 

7» 

7I-. 

7f+ 

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7 

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2 

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24- 

24- 

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8 

4 

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7i 

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7A 

74 

7  - 

7i?r 

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3x8 

3x8 

8x8 

3x8 

3x8 

3x8 

8x8 

6 

24 

25 

26 

26 

27 

28 

29 

30 

31 

32 

7 

4O00 

4167 

4333 

5200 

5400 

5600 

5800 

6000 

6200 

6400 

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9 

120 

125 

130 

130 

135 

140 

145 

150 

155 

160 

10 

61 

63 

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70 

73 

75 

76 

95 

97 

11 

ound. 

f  rotind. 

r  round. 

is-n 

Ifr-H 

16-91 

17-1  If 

18-51 

19-^ 

19-7i 

20-lf 

20-71 

81-21 

18 

10.79 

17.63 

18.17 

20.02 

20.57 

21.12 

31.31 

32.09 

82.89 

88.72 

18 

(»44 

4602 

6627 

14 

2944 

4602 

4602 

4602 

4602 

4602 

6627 

6627 

6627 

6627 

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1* 

11 

11 

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11 

2 

2 

2 

3 

16 

21 
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814 

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18 

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8084 

8654 

9080 

9531 

10031 

10588 

19 

14 

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li 

Ux3 

lfx2 

Hx2 

2x2 

2x2 

2x2 

2x2 

70 

668 

630 

546 

1337 

1375 

1417 

1160 

1188 

1220 

1413 

21 

58 

41 

42 

45 

46 

47 

47 

48 

49 

51 

22 

[Hind. 

rroond. 

J' round. 

I5-9J 

16-8f 

16-10 

17-111 

l8-6i 

19-0* 

19-71 

20-11 

20-84 

21-2t 

23 

17.09 

25.44 

26.22 

28.90 

29.68 

30.61 

42.69 

43.76 

44.82 

45.95 

24 

602 

6627 

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25 

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6627 

6627 

6627 

6627 

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24 

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51 

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28 

M8 

245 

253 

265 

273 

281 

213 

217 

224 

231 

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6288 

6634 

7659 

8103 

8601 

9093 

9496 

10040 

10614 

30 

It. 

If 

If 

2x2 

2x2 

2x2 

HS2 

2ix2 

3ix2 

2ix2 

31 

518 

429 

443 

1060 

1092 

1124 

958 

976 

1008 

1040 

82 

40 

40 

41 

43 

44 

45 

53 

54 

56 

68 

88 

ft 

15.904 

17.104 

18.348 

19.635 

20.966 

22.340 

23.758 

25.220 

26.725 

28.274 

34 

119.0 

127.9 

137  8 

146.9 

156.8 

167.1 

177.7 

188.7 

199.9 

211.5 

85 

1.S2 

1  56 

1.59 

1.64 

1.67 

1.71 

1.75 

1.79 

1.88 

1.86 

86 

5.08 

5.16 

5.28 

5.41 

5.50 

5.62 

5.75 

5.87 

5.96 

6.08 

V 

10.02 

16.42 

16.82 

17.23 

17.60 

17.90 

18.29 

18.57 

18.96 

19.85 

88 

16.6 

17.2 

18.9 

20.8 

22.5 

24.7 

26.8 

29.2 

81.2 

83.8 

89 

51.7 

57.0 

62.6 

68.5 

74.0 

81.2 

68.0 

95.5 

103.0 

111.0 

40 

165.0 

181.0 

199.0 

218.0 

235.0 

259.P 

280.0 

300.0 

325.0 

350.0 

41 

rhe  first  five  iterai  are  dimensions  of  finished  staves  (see  Fig.). 


d  by  Google 


1214 


tL— WATER  WORKS. 


NOTBS  ON  TaBLB   3.  PRBCBDING. 

Thickness  of  staves  given  is  the  maximum.    Some  engineers  limit  the  tfcddt- 

ness  to  2  ins.  even  for  the  large  sizes  of  pipe. 
Staves  can  be  planed  readily  by  grinding  the  blades  of  the  sticker  to  the 

proper  shapes. 
Sizes  of  rough  staves  are  merchantable.     The  lumber  most  be  clear  and 

seasoned  without  checking,  and  before  planing,  otherwise  the  subsequent 

shrinkage  will  greatly  affect  the  finished  diameter  of  pipe. 
The  metal  tongues  should  be  ^vanized  smoothly  and  evenly  to  pcevent 

leaky  pipes*  but  are  sometmies  left  plain.   • 
Length  of  band  may  be  obtained  from  following  formulas: 


For  angle  shoes,  Lt  > 


.  K  (D  4- 2/ + -S-)  4- d + upset  length  -  J. 


For  double  shoes.  Lj  -  it  (D  +  2/ + y)  +  2(d + upset  length  -  J) . 

in  which  Li  ~  length  of  single  band  under  head,  in  ins. 

Ls«  total  length  of  double  band  under  head,  in  ins., 

n  -3.1416. 

D  —internal  diameter  of  pipe  in  ins., 
t  —thickness  of  stave  in  ins., 

d  —diameter  of  band  in  ins., 
Care  must  be  used  in  ordering  bands.  It  is  better  to  have  them  a  little 
long  than  short.  Wood  stave  pipe  is  apt  to  form  up  with  a  diameter 
from  i'  to  i'  too  large,  which  mxist  be  taken  into  consideration  when 
ordering  hands. 
Bands  are  proportioned  to  not  exceed  a  hydrostatic-pressure  stress  of  ISjOOl 
lbs.  per  sq.  in.  Small  bands,  especially  on  pipes  of  small  diameter, 
are  apt  to  crush  the  wood,  hence  a  lower  stress  than  15.000  is  assumed 
to  meet  this  contingency,  in  necessary  cases,  as  ^lown  by  the  preceding 
table. 

4. DiSCHARGB   IN  MILLION  GALLONS  PBR  24  HoURS  THROUGH   WoOD 

Stavb  Pipb.    Nbw,  Clban  and  in  First-Class  CoNDmoN. 

(Value  of  roughness  n  — .010) 

[Million  Gallons  per  24  Hours.] 


Grade 
or  Slope 

Diameter  of  Pipe. 

in  Inches. 

». 

12 

18 

20 

24 

30 

36 

48 

$0 

n 

.0001 

0.28 

0.60 

1.09 

1.78 

3.33 

5.48 

11.9 

21.8 

ssTT" 

.00015 

0.80 

0.74 

1.38 

2.27 

4.16 

6.85 

14.9 

37.0 

4S.8 

.0003 

0.60 

1.11 

2.05 

8.35 

6.12 

9.96 

21.6 

38.9 

63.0 

.0005 

0.67 

1.47 

2.69 

4.40 

8.03 

13.10 

28.2 

50.« 

82.0 

.0008 

0.85 

1.86 

3.40 

5.68 

10.20 

16.50 

35.6 

64.6 

104.0 

.001 

0.95 

2.07 

3.81 

6.25 

11.40 

18.50 

39.8 

72.2 

117.0 

.003 

1.88 

8.65 

6.68 

10.90 

19.90 

33.40 

69.5 

126.0 

aaa.0 

.005 

2.17 

4.74 

8.70 

14.20 

25.70 

42.00 

90.2 

162.0 

3<a.o 

.008 

2.76 

6.00 

11.00 

18.00 

32.50 

63.10 

114.0 

206.0 

831.S 

.010 

3.07 

6.71 

12.30 

20.10 

36.30 

50.30 

ir.o 

330.0 

371.0 

.018 

3.88 

8.50 

15.50 

25.40 

46.00 

75.10 

181.0 

291.0 

409.0 

.020 

4.34 

9.49 

17.40 

28.40 

51.40 

83.90 

180.0 

335.0 

SU.0 

Note. — ^For  designing  ordinary  wood  stave  pipe  lines  it  is  safer  to  lae  a 
coefficient  of  roughness  n"-.0105  (Table  8)  rather  than  .010  as  above. 
Compare  discharges  in  Table  4  with  those  in  Table  3. 

lllc— CAST  IRON  PIPE* 
C^ast  Iron  Pi(>e  is  more  durable  than  wood-stave-,  wroog^it-insaa-, 
or  steel  pipe,  but  its  first  cost  is  greater  for  the  ordinary  sixes  required  in  a 
pressure-pipe  line  or  in  a  distributing  system.  It  especially  ooousMsids 
Itself  for  use  in  large  cities  where  the  increased  first  cost  can  be  boroe 
easily;  also  for  certain  portions  of  any  pipe  line  demanding  fairly  permao^: 
construction,  that  is,  where  cost  of  renewal  would  be  excessive;  and  saner- 
any  where  "specials"  are  required.    Before  deciding  on  the  kind  ol  pSpa  to 


WOOD  STAVE  PIPE.    CAST  IRON  PIPE.  1216 

use.  chemical  analyses  should  be  made  of  the  soil  and  the  water,  and  the 
Question  of  electrolysis  also  should  be  considered.  Cast  iron  pipe  should  be 
dipped  in  hot  coal  tar  or  asphalt  or  a  mixture  of  the  two  before  being  laid 
in  the  ground. 

FormuUu  for  I>MiKning  Cast  Iron  Pi^  are  numerous,  but  they  all  agree 
in  taking  into  consideration  (1)  the  static  pressure,  (2)  water  ram,  and  (3) 
liability  to  breakage  from  rough  handling  before  and  during  the  laying. 
Notation. 
t-»  thickness  of  pipe  shell,  in  inches; 
</-■  inside  diameter  of  pipe,  in  inches; 
A— pressure  head  in  feet  f  — 2.304  p); 
^—pressure  of  water,  in  lbs.  i>er  square  inch  (— 0.434A); 
^* allowance  for  water  ram,  in  lbs.  per  square  inch; 
f —internal  radius  of  pipe,  in  ins.; 
5— allowable  tensile  stress,  in  lbs.  per  square  inch; 
Based  on  a  factor  of  safety  of  6,  ^  is  assumed  at  3,200  to  3,600  lbs. 
For  static  presstire  alone,  we  have, 

.     pd       0.217  A  J  ... 

25    "         5        ^^ 

Practical  working  formulas  are  as  follows: 

Formula  used  by  Metropolitan  Water-works,  of  Boston: — 

.    ,.<P±p  +  o.25.15:«^i^±£^  +  0.26 (2, 

assuming  s  »  3300.    Allowances  for  water  ram  are— 
#/- 120  lbs.  (277  ft.  hd. )  forrf-   3  to  10  ins.; 

"" "  '    "  d=-12or  Hins.; 

d=»16or  18  ins.; 
d- 20  ins.; 
d-'24  ins.; 
d«=30ins.; 
d-=36ins.; 
<i»42to  60  ins. 
Formula  recommended  by  R.  D.  Wood  &  Co.,  Philadelphia: — 

,.(£^^0.333(:-X) ,3, 

Here.  5—3600  (or  25-7200);  //is  assumed  at  the  constant  value  100;  and 
the  added  thickness  to  allow  for  rough  handling  is  represented  by  the  last 
term,  a  variable  dependent  on  the  diameter.    But  formula  (3)  easily  reduces 

,_l£+^+0.333 (4) 

which  is  readily  comparable  with  (2). 

Kinds  of  Pipe  Joints. — Cast  iron  pipe  3  ins.  or  more  in  diameter  comes 
in  a  standard  laving  length  of  12  feet.  There  are  four  principal  types  of 
joints,  namely,  (1)  bell  and  spigot;  (2)  turned,  page  1235;  (3)  flanged,  page 
1235;  and  (4)  flexible  joint,  page  1238.    These  are  discussed  as  follows. 

(1)  Befl  and  Spigot  Joint  Pipe  (see  p.  1220)  is  the  most  common,  being 
almost  universally  employed  when  cast  iron  pipe  is  to  be  laid  in  trenches 
and  back-filled.  In  laying  the  pipe  it  is  customary  to  begin  with  some 
"special"  as  a  gate  or  tee,  etc.,  thrusting  the  spigot  end  of  each  pipe  into  the 
bell  of  the  piece  previously  placed,  "bell  holes"  having  been  dug  in  the 
trench  where  each  joint  is  to  come.  When  blocked  or  tamped  to  proper  line 
stnd  grade  the  joints  are  caulked  at  the  inner  or  spigot  end  with  oakum,  jute 
>r  hemp,  and  then  the  balance  of  the  joint  is  run  with  hot  lead,  and  caulked 
;i^htly.  In  order  to  confine  the  molten  lead  so  it  will  fill  the  joint  flush 
iVith  the  end  of  the  bell,  a  gasket  is  clamped  around  the  entering  pipe 
;ifirhtly  against  the  bell  of  the  other,  leaving  an  opening  at  the  top  for  pour- 
Tig.  Improvised  gaskets  may  be  made  wholly  out  of  clay,  but  manufac- 
. tired  gaskets  composed  of  layers  of  rubber  and  hemp  cloth,  and  backed  by 
t;eel  springs  are  imiversally  employed.  The  ends  are  clamped  nearly 
c^ether,  a  pouring  hole  is  made  with  clay,  and  the  metal  poured.  (See 
»a£:e  1219  for  notes  on  pipe  laying;  page  1280  for  lead-melting  furnace.) 


-110  " 

(254 

-100  '• 

(231 

-   90  " 

(208 

-   86  " 

(106 

-   80  •• 

(186 

-   76  •• 

(173 

-   70  •• 

(162 

'I 


1M6 


U.— WATER  WORKS. 


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C.  I.  PIPE— WEIGHT.  DISCHARGE,  LEAD.  HEMP. 


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Digitized  by  VjOOQ IC 


d  by  Google 


C.  I.  PIPE— DISCHARGE,  LA  YING,  WEIGHTS.  1219 

EXAlfPLBS  IN  USB  OP  TaBLB  6.  P&BCBDINO. 

(1)  Ths  maximum  discharging  capacity,  for  instance,  of  8500  ft.  of  0* 
straight  cast  iron  pipe,  under  a  head  of  196  ft.,  may  be  found  as  follows: 
First  ascertain  the  frictional  head  for  1000  ft.,  thus:  195  ft. -►  8.5-  22.94  as 
the  fric.  head  in  ft.  per  1000  ft.  By  referring  to  the  table.  1000  ft,  of  0* 
pipe  under  23.01  ft.  n«ftd  will  dischajnge  500  galls,  per  min. 

(2)  To  find  the  diam.  of  pipe  for  a  given  discharge. — To  deliver,  say, 
4.250.000  galls,  per  24  hrs.,  the  dist.  being  20.000  ft.  and  the  head  130  ft. 
The  trie,  head  per  1000  ft.  is  130-!- 20- 6.5  ft.,  and  the  table  shows  that 
under  6.19  ft.  head  per  1000  ft.  a  10*  pipe  will  discharge  4.320.000  galls. 

(Z)  To  ascertain  the  pressure  at  any  point  in  a  line  of  water  main,  given 
its  diam..  rate  of  disch.  and  static  head  against  which  the  water  is  forced. 
Assume  uiat  500  galls,  of  water  are  to  be  forced  per  minute,  through  5000  ft. 
of  df  cast  iron  pipe,  laid  on  an  incline  to  a  height  of  75  ft*  what  would  be 
the  varying  presswe  at  each  1000  ft.  from  the  pumps?  The  table  shows  a 
fric.  head  of  5.64  ft.  per  1000  ft.  of  8^  pipe,  discharging  500,  galls,  per  min. 
If  the  dist.  is  5000  ft.,  the  pressure  requwed  to  overcome  fric.  is  5  X  5.64-" 
28.20  ft.  head,  and  the  total  resistance  head  at  pumps  is  28.2-1-  75  ft. » 103.2 
ft.,  and  for  every  1000  ft.  from  the  pumps,  this  head  is  diminished  5.64  ft.  + 
the  vert,  ascent;  that  is,  at  3000  ft.  from  the  pumps  the  resistance  head  is 
61.92  ft.    Resistance  head  in  ft.  ■•-  2.3— pres.  in  lbs.  per  sq.  in. 

(4)  The  volume  of  water  flowing  in  a  pipe  may  be  found  by  ascertaining 
the  loss  of  pressure  or  fric.  resistance  per  1000  ft.  of  pipe.  To  this  end,  u 
two  accurate  gages,  entirely  similar  in  all  respects,  and  placed  1000  ft.  apart 
on  a  line  of  level  12*  pipe,  show  a  loss  of  0.5  lb.,  the  nearest  figures  indicate 
a  flow  of  600  galls,  per  min.;  if  the  loss  is  2\  lbs.,  a  flow  of  1400  galls,  per 
min.,  etc.  Due  allowance  should  be  made  for  difif.  in  elev.  of  points  of 
observation. 

M     Pipb-Laying  Notbs. 

The  following  Notes  on  Pipe-Laying  relate  to  the  re-construction  of  the 
distributing  system  at  The  Dalles,  Oregon,  in  the  winter  of  1898-9,  and  are 
taken  from  the  writer's  note  book: 

1  yamer  can  yam  1000 1.  f.  of  0*  to  10*  C.  I.  pipe  per  day. 

2  caulkers  can  caulk  1000 1.  f.  of  6*  to  10*  C.  I.  pipe  per  day. 
Gang  laid  700  1.  f .  8*^  pipe  on  4th  Street  one  day  -  lie.  per  1.  f . 

!  for  $60.00.  at  rate  of  i^c.  per  1.  f. 
12*  pipe- 6c,  9c.  12c,  16c,  18c. 
'  10*  with  derrick  unless  ground  is  sandy 
f  pipe  with  rope  at  each  end. 
trench  if  soft;  otherwise  by  hand, 
'o  men  can  carry  on  shoulders, 
ree  men  can  carry  with  two  bars  ( 1  behind.) 
nr  men  can  carry  with  two  bars. 
c  men  can  carry  with  three  bars, 
fht  men  can  carry  with  four  bars. 
tie  men  can  carry  with  five  bars  (1  behind) . 
(3466#).     7-8^(3780#),     A-1&  (3120#), 
I  per  load,  two  horses,  two  men  to  unload, 
ing  lOOOf  lead  (forlOOO  ft.  8*  pipe), 
ting  250  ft.  of  laid,  8'  pipe  for  taking  up. 
„ I  the  joints  and  fires  kmdled. 

Weiffhts  uid  Dimensions  of  Cast  Iron  Pipe  and  Specials. — ^The  following 
a'bles  are  mainly  from  a  pamphlet  issued  by  the  Engmeering  Department  of 
txe  Metropolitan  Water  Board  of  Boston.  The  weight  of  castings  is  based 
a  one  cuSic  inch  of  cast  iron  weighing  0.2604  lb.  These  tables  are  selected 
ecause  thev  are  based  on  methods  and  details  quite  generally  approved 
ot  only  in  New  England  but  elsewhere.  Various  fotmdries  furnish  details 
ifTering  more  or  less  from  these  and  from  each  other,  and  hence  the  sub- 
»ined  data  of  weights,  etc..  must  necessarily  be  approximate.  Five  classes 
'  pipe  are  recognized  as  standards:  Class  A  for  heads  up  to  1 15  ft.  (50  lbs.) ; 
a^s  B  for  heads  up  to  150  ft.  (65  lbs.) ;  class  C  for  heads  up  to  200  ft.  (87  lbs) ; 
mas  D  for  heads  up  to  250  ft.  (109  lbs.) ;  and  class  E  for  heads  up  tOrSOO  ft. 
.  30  Iba.  per  sq.  inch) .    (See  formula  (2) .  page  1216.)      ized  by  CiOOg IC 


1220 


6i.--WATER  WORKS, 


7. — Straight  Cast-Iron  Pipes  with  Bbll  and  Spigot.* 
(Met.  Water  Works.) 


cief 


J 

Dimensions  tn  Inches. 

Weight  in  PoQKk. 

II 

i 

0 

§a 

Per 
Length. 

PbtFuoI 

ft 

b 

0 

d 

t 

J 

8ti»J6tt 
Pipe. 

4 

D 

1.50 

1.30 

0.65 

8.00 

0.40 

0.40 

230 

•17.3 

4 

£ 

0.45 

255 

19.7 

6 

D 

•  • 

1.40 

0.70 

0.46 

380 

293 

6 

E 

•• 

0.50 

415 

31.9 

8 

D 

•• 

1.60 

0.76 

3.50 

0.62 

665 

43.5 

8 

E       1      •• 
D       1      •• 

0.65 

600 

46.2 

10 

•• 

•  « 

0.60 

800 

62.4 

10 

E 

•• 

0.63 

840 

65.7 

12 

B 

1.60 

0.80 

0.67 

910 

70.3 

12 

C 

0.61 

970 

75.5 

12 

D 

•• 

«• 

0.65 

1030 

80.7 

12 

E 

•• 

«• 

0.69 

1096 

86.0 

14 

B 

1.70 

0.85 

0.61 

1180 

87.5 

14 

C 

•• 

•• 

0.65 

"       1      1200 

93.5 

14 

D 

•• 

•  • 

0.70 

1290 

161.6 

14 

E 

•  • 

•  • 

0.76 

•       1      1380 

108.6 

16 

B 

1.75 

1.80 

0.90 

4.00 

0.66 

0.50     !      1380 

106.2 

16 

C 

•  • 

0.70 

148S 

114.8 

16 

D 

•♦ 

♦• 

0.76 

1590 

123.3 

16 

E 

•• 

" 

0.81 

1715 

133.7 

20 

D 

2.00 

1.00 

0.73 

1930 

148.6 

20 

c     1     •• 

•• 

0.79 

2080 

161.2 

20 

D 

'• 

•• 

0.85 

2236 

174.6 

20 

E       1       " 

•• 

•• 

0.92 

2415 

18S.9 

24 

B 

2.00 

2.10 

1.05 

0.80 

2626 

194.8 

24 

C 

•• 

0.87 

2740 

213.4 

24 

D 

•• 

0.95 

2965 

232.7 

24 

E 

•• 

" 

" 

1.03 

8230 

253.1 

30 

B 

•• 

2.30 

1.15 

4.50 

0.92 

3625 

27»,2 

30 

C 

" 

1.00 

8S30 

SM.3 

30 

D 

•• 

2.50 

1.25 

1.10 

4235 

335.8 

30 

E 

•• 

1.20 

4720 

367.5 

36 

A 

" 

" 

•• 

0.93 

4400 

237.1 

36 

B 

" 

" 

" 

1.03 

4850 

274.4 

36 

C 

•• 

«' 

•• 

1.13 

5800 

411.9 

36 

D 

'• 

2.80 

1.40 

1.25 

5900 

457.1 

36 

E 

•• 

" 

•♦ 

1.36 

6400 

486.3 

42 

A 

•• 

•' 

•• 

5.00 

1.01 

5610 

426.4 

42 

B 

•  • 

" 

•' 

1.14 

6390 

4S2.S 

42 

c 

" 

1.27 

6975 

539.4 

43 

D 

" 

3  20 

1.60 

1.40 

7750 

996.5 

48 

A 

" 

3.00 

1.50 

1.16 

7270 

554.9 

48 

B 

•• 

•• 

•• 

1.26 

7870 

604.3 

48 

C 

•• 

•' 

•• 

1.40 

8760 

678.9 

48 

D 

2.25 

3.50 

1.75 

1.56 

9820 

763.9 

54 

A 

2.25 

3.10 

1.65 

6.50 

1.23 

sm 

666.9 

54 

B 

•' 

1.36 

9570 

723.5 

54 

c 

•• 

3.90 

1.95 

1.53 

11030 

834.0 

60 

A 

'• 

3.20 

1.60 

1.36 

10630 

S13.0 

60 

B 

•• 

1.50 

11750 

915.6 

60 

0 

4.20 

2.10 

1.70 

I3SI0 

lOJO-7 

*  See  also  Tal)Ies  26.  27.  28  and  29.  followingsd 


byGoogk 


dAST  IRON  PIPE  WITH  BELL  AND  SPIGOT. 


1221 


Special  Castings  are  Grouped  as  follows: 
I. — 16  ins.  and  smaller,  only  Class  E.  [Thickness  of  metal  (except 

11.-20  to  24  ins.,  inclusive.  Classes  C  and  E.  [°J  ^STcS^'of  t^" 
111.^48,  64  and  60  ins.,  Classes  B.  C  and  E.    [pipe.  Table  7. 


8. — Bblls  of  Special  Castings. 
(Met.  W.  W.) 


OiS^ 


l!    ^^i^4 


Fig.  8. 


Nominal 
I>lametei>- 

ClasB.      1 

Incliefl. 

a 

b 

0 

d 

J 

3 

E 

l.M 

1.20 

0.60 

4.00 

0.40 

4 

1.30 

0.65 

•• 

6 

1.40 

0.70 

•  • 

8 

1.50 

0.75 

•  • 

10 

'• 

4.60 

•• 

13 

1.60 

0.80 

•• 

14 

1.70 

0.85 

•• 

16 

1.75 

1.80 

0.90 

5.00 

0.50 

20 

C 

2.00 

1.00 

•• 

20 

E 

•• 

•• 

•• 

24 

C 

2.00 

2.10 

1.05 

•• 

24 

E 

•• 

•• 

•• 

30 

C 

2.30 

1.15 

•* 

30 

E 

2.50 

1.25 

•  • 

36 

c 

*• 

•  • 

36 

E 

2.80 

1.40 

•• 

42 

C 

•• 

•* 

•• 

42 

E 

3.20 

1.60 

•• 

48 

B 

3.00 

1.50 

•  4 

48 

C 

" 

•• 

•• 

48 

E 

2.25 

3.50 

1.75 

•• 

54 

B 

3.10 

1.55 

•• 

60 

B 

3.20 

1.60 

•  • 

d  by  Google 


1222 


^— WATER  WORKS, 


9. — Straight  Cast-Iron  Pipes,  Bbll  and  Spigot. 

(Met.  W.  W.) 

Standard,  Maximum  and  Minimum  Weights  per  Leoffth  and  per  Indxi 

Weight  of  Lead  Joints  and  GaskeU.     AH  Weights  in  Lbs. 


8fd  Wt.      1 

Max.  Wt. 

MIn.  Wt. 

Wt.  Of  Lead 

9s 

i 

i| 

per  Joint. 

Per 

Per 

Per 

Per 

Per 

Per 

c 

JO- 

1 

i 

lenffth 

of 
12  Feet. 

Inch 
ofStr. 
Pipe. 

II 

% 

12  Feet. 

Inch 
ofStr. 
Pipe. 

12  Feet. 

Inch 
OfStr. 
Pipe. 

With 
Gasket 

Solid 
L«^4 

D 

230 

1.4 

4. 

239 

1.5 

221 

1.4 

7 

9.25 

O.ll 

E 

25S 

1.6 

265 

1.7 

246 

1.6 

•• 

D 

880 

2.4 

395 

2.5 

365 

2.3 

9.75 

12.  T5 

0.15 

E 

415 

2.7 

432 

2.8 

398 

2.6 

•■ 

D 

665 

3.6 

688 

3.8 

642 

3.5 

12.5 

18.75 

0.25 

E 

600 

8.9 

624 

4.0 

676 

3.7 

•• 

" 

D 

800 

5.2 

832 

5.4 

768 

5.0 

16.25 

23  25 

<l» 

E 

840 

5.5 

874 

6.7 

806 

5.3 

• 

•• 

B 

910 

5.9 

946 

6.1 

874 

5.6 

17.75 

26.75 

085 

C 

970 

6.3 

1009 

6.5 

931 
989 

6.0 

D 

1030 

6.7 

1071 

7.0 

6.5 

18 

27.25 

■• 

E 

1095 

7.2 

1139 

7.5 

1051 

6.9 

•• 

B 

1130 

7.3 

1175 

7.6 

1086 

7.0 

20.5 

SI 

•.« 

C 

1200 

7.8 

1248 

8.1 

1152 

7.6 

•• 

•• 

D 

1290 

8.4 

1342 

8.8 

1238 

8.1 

20.75 

81.5 

•• 

E 

1380 

9.1 

" 

1435 

9.4 

1326 

8.7 

•  • 

•  • 

B 

1380 

8.9    1  "  II    1435 

9.2 

1326 

8.5 

81 

50 

*;f 

C 

1485 

9.6 

" 

1544 

10.0 

1426 

9.2 

31 

50  25 

D 

1590 

10.3 

•• 

1654 

10.7 

1626 

9.9 

81.25 

50.5 

•■ 

E 

1715 

11.1 

" 

1784 

11.6 

1646 

10.7 

81.5 

51 

•• 

20 

B 

1930 

12.4 

•• 

2007 

12.9 

1863 

11.9 

38 

61 

•  » 

20 

C 

2080 

13.4 

•• 

2163 

14.0 

1997 

12.9 

38  25 

61.5 

20 

D 

2235 

14.5 

•• 

2324 

15.1 

2146 

13  9 

38.5 

68 

•• 

20 

E 

2415 

15.7 

" 

25i2 

16.4 

2318 

16.1 

39 

62.5 

•* 

24 

B 

2525 

16.2 

3^ 

26 13 

16.8 

2437 

.  15.7 

45 

78 

o.e 

24 

C 

2740 

17.7 

2836 

18.3 

2644 

17.1 

45.25 

73.5 

24 

D 

2985 

19.4 

'• 

3089 

20.1 

2881 

18.7 

45.5 

74 

•• 

24 

E 

3230 

21.1 

33«3 

21.8 

3117 

20.4 

46 

74.5 

• 

30 

B 

3625 

23.3 

3 

3734 

24.0 

8516 

22.6 

56 

100.5 

1.55 

30 

C 

3930 

25.4 

4048 

26.1 

8818 

24.6 

56.25 

101 

30 

D 

4335 

28.0 

4465 

28.8 

4205 

r.i 

56.5 

101.  i 

•  ■ 

30 

E 

4720 

30.6 

4862 

81.5 

4578 

297 

67 

102 

•• 

36 

A 

4400 

28.1 

4532 

28.9 

4268 

27.2 

66.5 

120 

1.35 

36 

B 

4850 

31.2 

4995 

32.1 

4706 

30.2 

67 

120.5 

36 

C 

5300 

34.3 

5459 

85.4 

5141 

333 

67.5 

m 

•■ 

86 

D 

5900 

38.1 

6077 

39.2 

6728 

36.9 

68 

122 

•• 

36 

E 

6400 

41.6 

6592 

42.8 

6208 

40.3 

68.5 

122  5 

•• 

42 

A 

5610 

35.5 

5778 

36.6 

5442 

84.5 

77.5 

158 

2.C8 

42 

B 

6290 

40.2 

6479 

41.4 

6101 

39.0 

n.5 

154 

42 

C 

6975 

45.0 

7184 

46.3 

6766 

43.6 

78 

156 

•  • 

42 

D 

7750 

49.7 

7983 

51.2 

7518 

48.2 

78.5 

ISO 

•• 

48 

A 

7270 

46.2 

7488 

47.6 

7052 

44.9 

88 

175 

s.n 

48 

B 

7870 

50.4 

8106 

61.8 

7634 

48.8 

88.5 

170 

48 

C 

8760 

56.6 

9023 

68.3 

8497 

64.9 

89 

177 

•• 

48 

D 

9820 

62.8 

10115 

64.7 

9529 

61.0 

89.5 

178 

«• 

54 

A 

8770 

55.6 

9033 

67.2 

8507 

63.9 

99 

814.6 

!-» 

54 

B 

9570 

61.1 

9867 

63.0 

9288 

59.8 

99  5 

819 

64 

C 

11030 

69.5 

11361 

71.6 

10699 

67.4 

100 

819.9 

•■ 

60 

A 

10630 

67.8 

10949 

69.8 

10311 

66.7 

110 

8S8 

4.40 

60 

B 

11760 

76.5 

12103 

77.7 

11396 

78.8 

110.6 

sst 

60 

C 

13590 

85.8 

13999 

88.4 

13188 

83.2 

111 

841 

•  • 

d  by  Google 


C.  I,  PIPE  WITH  BELL  AND  SPIGOT,   BELL. 


VO. — Propbrtibs  of  Bblls  op 

Straight  Pipbs  and  of 

Spbcial  Castings. 


1328 


(Met.  W.  W.) 


Fig.  10. 


Bells  of  Straight  Pipes. 

BeUs  of  Speolal  Castings. 

Area 

Diam. 

Rad. 

of 
Bdl. 
Feet. 

Area 

Diam. 

(Shad- 

of Bell 

Wt. 
LhH. 

(Shad- 

Of Bdl 

Wt. 
Lbs. 

!_ 

1 

ed). 
Sq. 

t 

q 

Open- 
ings. 

ed). 
8q. 

8 

q 

Open- 
ings. 

w 

Ids. 

Ins. 

Ins. 

Ins. 

E 

3.90 

0.40 

1.50 

4.7 

15 

E 

I> 

"siei* 

O.'ifi' 

iiw 

"e.'eo 

"'lb' 

E 

•  • 

•• 

•  • 

5.70 

0.35 

20 

4.26 

0.44 

1.65 

5.7 

23 

E 

D 

8.92 

0.49 

1.65 

7.72 

31 

E 

•• 

'• 

" 

7.80 

0.44 

31 

4.62 

0.47 

1.65 

7.8 

36 

E 

D 

4.<5 

0.51 

1.76 

9.84 

0.54 

41 

E 

•• 

•• 

•• 

9.90 

•• 

42 

5.03 

0.50 

1.75 

9.9 

45 

E 

D 

•• 

" 

•• 

12.00 

0.63 

50 

E 

•• 

•• 

•• 

12.06 

50 

5.40 

0.49 

1.75 

12.1 

58 

E 

B 

6.02 

0.55 

1.85 

13.94 

0.71 

62 

C 

•• 

•• 

•« 

14.02 

0.72 

62 

I> 

•• 

•• 

•• 

14.10 

62 

E 

•• 

•• 

•' 

14.18 

•• 

63 

5.82 

0.63 

1.85 

M4.2 

73 

E 

B 

5.40 

0.59 

1.90 

16.02 

0.80 

76 

C 

•• 

•• 

•• 

16.10 

0.81 

76 

D 

•• 

" 

•• 

16.20 

0.82 

77 

E 

'• 

" 

•• 

16.30 

77 

6.25 

0.57 

1.90 

16.3 

89 

E 

B 

«.M 

0.61 

2.10 

18.30 

0.91 

105 

C 

•• 

•• 

18.40 

0.92 

106 

D 

" 

•• 

•• 

18.50 

106 

E 

•• 

•* 

•• 

18.62 

0.93 

107 

7.49 

0.59 

2.10 

18.6 

121 

E 

B 

7.43 

0.67 

2.30 

22.46 

1.10 

145 

C 

" 

•• 

" 

22.58 

1.11 

145 

8.43 

0.65 

2.30 

22.6 

165 

C 

D 

" 

'• 

•• 

22.70 

•• 

146 

E 

*• 

•• 

•• 

22.84 

1.13 

147 

8.43 

0.65 

2.80 

22.8 

187 

E 

B 

8.15 

0.74 

2.40 

26.60 

1.28 

187 

C 

" 

" 

26.74 

1.29 

188 

9.20 

0.72 

2.40 

26.8 

212 

C 

D 

•• 

•• 

•• 

26.90 

1.30 

189 

E 

•• 

•• 

•• 

27.06 

190 

'9.20 

0.72 

2.40 

26.9 

214 

E 

B 

9.65 

0.79 

2.55 

82.84 

1.56 

272 

C 

•• 

•• 

38.00 

1.57 

273 

10.23 

0.78 

2.56 

32.9 

289 

0 

D 

10.63 

0.85 

2.75 

33.20 

1.69 

304 

E 

•• 

33.40 

1.60 

305 

11.26 

0.84 

2.75 

33.2 

321 

E 

A 

10.60 

0.87 

•• 

38.86 

1.83 

852 

B 

" 

39.03 

1.84 

354 

C 

•' 

•• 

•• 

39.26 

•• 

356 

11.23 

0.86 

2.75 

39.1 

376 

0 

D 

12  09 

0.95 

3.00 

39.50 

1.88 

410 

E 

•• 

39.72 

1.89 

412 

12.79 

0.94 

3.00 

89.5 

433 

E 

A 

12.80 

•• 

•• 

45.02 

2.11 

491 

B 

" 

•• 

•• 

45.28 

2.12 

494 

C 

•• 

•• 

•* 

45.54 

2.13 

497 

12.80 

0.95 

3.00 

45.3 

494 

0 

D 

15.01 

1.07 

3.35 

45.80 

2.18 

589 

£ 

•• 

•• 

46.06 

592 

15.01 

1.07 

3.35 

45.8 

589 

E 

A 

13.93 

1.02 

3.15 

51.30 

2.89 

608 

B 

•• 

•• 

51.50 

2.40 

610 

13.93 

1.02 

3.15 

51.6 

610 

B 

C 

•• 

•• 

•• 

51.80 

2.41 

614 

•• 

•• 

•• 

61.8 

614 

C 

D 

17.13 

1.23 

3.60 

52.10 

2.46 

765 

E 

•• 

•• 

•• 

62.40 

769 

17.13 

1.28 

3.60 

62.4 

769 

B 

A 

15.62 

1.07 

3.25 

57.46 

2.65 

762 

B 

'• 

•« 

•• 

57.70 

2.66 

765 

15.62 

1.07 

3.25 

67.7 

765 

B 

C 

20.45 

1.34 

3  95 

58.06 

2.74 

1016 

A 

16.20 

1.13 

3.85 

63.70 

2.92 

874 

B 

" 

64.00 

2.93 

878 

16.20 

1.13 

3.35 

64.0 

878 

B 

C 

22.89 

1.43 

4.20 

64.40 

3.03 

1232 

1224 


H.— WATER  WORKS. 


11. — ^Propbrtibs  of  H  Curvbs.* 
(Met.  W.  W.) 


Diam- 
eter. 
Ins. 

aaaB. 

Welgiit. 
I.hft. 

o 

t 

r 

k 

8 

4 

0.45 

16 

22.6 

8 

E 

m 

6 
8 

0.50 

• 

t35 

0.55 

•• 

" 

10 

1» 

10 

12.1 

0.63 

•• 

12    . 

2S5 

12 

14.2 

0.69 

•• 

340 

14 

0.75 

18 

25.5 

4K 

16 

18.6 

0.81 

24 

34.0 

680 

20 

22.6 

0.79 

•• 

•• 

C 

835 

20 

22.8 

0.92 

•• 

•• 

E 

dSO 

24 

26.6 

0.87 

30 

42.4 

0 

i2m 

24 

26.9 

1  03 

* 

*' 

B 

]4«5 

*  See  also  Table  31,  following. 

11a. — Properties  of  H  CuRVBS.f      11b. — Propbrtibs  of  ^  CuRVBS-t 
(Met.  W.  W  )  (Met.  W.  W.) 


^ *" 


Fig.  I  la:  Fig.  lib 

NoTB.— Dimensions  are  in  inches;  weights,  in  lbs. 


fl.: 

H  Curves. 

1 

tV  Curres. 

Js 

aass. 

o 

t 

qa, 

r 

k 

s 

Weight 

r 

k 

We^t 

4 

E 

5.7 

0.45 

24 

18  4 

4 

60 

48 

18.7 

e 

6 

7.8 

0.50 

" 

•• 

•  1 

100 

•' 

85 

8 

9.9 

0.55 

•• 

•• 

" 

135 

•• 

190 

10 

12.1 

0.63 

'* 

*• 

" 

185 

•* 

1«5 

12 

14.2 

0.69 

" 

•* 

" 

240 

•• 

210 

14 

16.3 

0.76 

36 

27.6 

345           72 

28  1 

365 

16 

18.6 

0.81 

•• 

•• 

440 

440 

20 

C 

22.6 

0.79 

48 

36.7 

675          96 

37.5 

S75 

20 

E         22.8 
C         26.6 

0.92 

•• 

760 

*• 

• 

7«> 

24 

0.87 

60 

45.9 

1050 

120 

46  8 

itso 

24 

E 

26.9 

1.03 

1      •• 

*• 

1215 

• 

1215 

30 

c 

82.9 

1.00 

• 

•• 

1490    ^ 

" 

• 

1490 

30 

E 

33.2 

1.20 

•* 

" 

1780    1 

•* 

'• 

1780 

86 

c 

39.1 

1.18 

90 

68.9 

2810 

180 

70.2 

2810 

36 

E 

39.5 

1.36 

• 

3400 

" 

"• 

3400 

42 

c 

1    45.3 

1.27 

•• 

It 

3700 

" 

•« 

3rw 

43 

E 

1    45.8 

1.53 

*• 

«• 

4470 

<• 

44?0 

48 

B 

51.5 

1.26 

•• 

•• 

4200 

•• 

•• 

OM 

48 

C 

61.8 

1.40 

•* 

•• 

4650 

•• 

• 

46SI 

48 

E 

62.4 

1.70 

•• 

*• 

6700 

•• 

•• 

mo 

64 

B 

67.7 

1.35 

•• 

4t 

6100 

• 

BlOB 

60 

B 

64.0 

1.50 

1      *' 

•' 

6250 

'• 

•  • 

tSee 

alsoTal 

ble  32, 

[ollowin 

g. 

Di 

gitized  by  V 

;oog 

e 

CAST  IRON  PlPEr-CURVES  AND  BRANCHES. 


1225 


12. — Propbrtibs  of  Branchbs — ^L's,  T's  and  Crossbs.* 
(Met.  W.  W.) 


Fig.  12. 


Dimensions  In  Inches. 


— ■ 

— 

e 

»t 

1 

1 

4 

4 

11 

1 

6 

4 

11 

1 

6 

12 

• 

8 

4 

11 

1 

•• 

6 

12 

• 

•* 

8 

13 

• 

10 

4 

11 

1 

6 

12 

• 

•• 

8 

13 

• 

•  « 

10 

14 

« 

12 

4 

11 

1 

6 

12 

• 

•  • 

8 

13 

• 

•• 

10 

14 

' 

fiO 

•• 

12 

15 

•• 

27 

M 

4 

11 

18 

23 

6 

12 

24 

•  • 

8 

13 

•• 

25 

•• 

10 

14 

•• 

26 

•  • 

12 

15 

•• 

27 

•  • 

14 

16 

*• 

28 

16 

4 

11 

17 

23 

6 

12 

24 

•  • 

8 

13 

•• 

25 

•  • 

10 

14 

•• 

26 

•  • 

12 

15 

•• 

27 

•  • 

14 

16 

•• 

28 

•  • 

16 

17 

•• 

29 

20 

6 

12 

19 

24 

•  • 

8 

13 

•• 

25 

•• 

10 

14 

19 

26 

•  • 

12 

15 

•• 

27 

" 

14 

».?« 

•• 

28 

" 

16 

17 

•• 

29 

" 

20 

19 

,, 

31 

16.3 


22.6 
22.8 
22.6 
22.8 
22.6 
22.8 
22.6 
22.8 
22.6 
22.8 
22.6 
22.8 
22.6 
22.8 


14.2 

1.25 

1.62 

2.50 

5.7 

7.8 

9.9 

12.1 

14.2 

1.25 

1.62 

2.50 

16.3 

" 

'♦ 

5.7 

7.8 

9.9 

12.1 

14.2 

1.25 

1.62 

2..')0 

16.3 

•• 

•• 

18.6 

'• 

" 

•• 

7.8 

9.9 

12.1 

14.2 

1.25 

1.62 

2.50 

16.3 

18.6 

22.6 

.. 

22.8 

Weights 
y 

tInLt 

«. 

Four  Way 

2 

Branch. 

18 

3Bells 

4BeU8 

120 

125 

155 

160 

IGO 

166 

200 

206 

190 

195 

245 
250 

260 

215 

210 

245 

245 

240 

300 

295 

270 

265 

345 

340 

285 

275 

320 

310 

315 

305 

370 

360 

345 

335 

415 

405 

380 

370 

480 

470 

335 

340 

395 

380 

390 

375 

440 

425 

420 

405 

490 

475 

460 

445 

550 

536 

" 

525 

510 

665 

650 

E 

435 

415 

475 

465 

475 

455 

525 

505 

510 

490 

675 

565 

550 

530 

640 

620 

615 

695 

755 

735 

665 

645 

835 

815 

545 

530 

580 

566 

580 

565 

630 

615 

620 

605 

685 

670 

665 

650 

750 

735 

730 

715 

865 

850 

780 

765 

945 

930 

870 

855 

1100 

1085 

C 

710 

710 

760 

760 

E 

795 

770 

845 

820 

C 

750 

750 

820 

820 

E 

840 

815 

905 

880 

C 

800 

800 

890 

890 

E 

890 

865 

975 

950 

C 

870 

870 

1005 

1005 

E 

965 

940 

1095 

1070 

C 

925 

925 

1090 

1090 

E 

1025 

1000 

1180 

1155 

C 

1000 

1000 

1205 

1205 

E 

1120 

1095 

1335 

1310 

C 

1125 

1125 

1400 

1400 

E 

1 

1260 

1235 

1555 

1530 

♦  See  also  Table  35.  following. 


d  by  Google 


1S26 


ti.-^WATER  WORKS. 


12.- 

-Propbrtibs  of 

Brancrbs — ^L 

s,  T'8  AND  Grossbs. — ContinQed. 

Dlmenslona  In  InelMS. 

■ 

i 

0 

WelgbU.  In  Lbs. 

6 

I 

p 

8 

o. 

<y 

z 

y 

t 

3  Way  Bnuicb|4  Way  Bnocb 

2BeU^ 

3  Bella  3  BcUfl 

'4  Belt 

t4 

6 

12 

21 

24 

26  6 
26.9 

7.8 

0 
E 

916 
1035 

910 
995 

900 
1080 

955 

1049 

^8 

13 

25 

26.6 
26.9 

99 

0 
E 

960 
1090 

956 
1050 

1035 
1150 

1010 
1110 

10 

14 

26 

26.6 
26.9 

12  1 

g 

1020 
1150 

1015 
1110 

1105 
1830 

1101 
1199 

12 

15 

27 

26.6 

14.2 

1.2! 

1.62 

2.5C 

C 

1090 

1090 

1230 

1225 

• 

• 

26.9 

•• 

B 

1340 

1200 

1360 

1810 

14 

16 
•• 

28 

26.6 
26.9 

16.3 

.. 

C 
E 

1160 
1300 

1155 
1260 

1315 
14S0 

1316 
1410 

16 

17 

29 

26.6 
26.9 

18.6 

. 

0 
E 

1255 
1400 

1250 
1360 

1476 
1610 

1470 

isn 

24 

20 

19 

31 

26.6 
26.9 

22.6 
22.8 

1.25 

1.62 

8.10 

C 
E 

1875 
1560 

1370 
1520 

1640 
1830 

1C3S 
1T90 

24 

21 

83 

26.6 
26.9 

26.6 
26.9 

.. 

C 

E 

1520 
1730 

1515 
1690 

1866 
2080 

1855 

8040 

80 

12 

IS 

27 

32.9 
33.2 

14.2 

1.25 

1.62 

3  50 

C 
E 

1490 
1740 

1470 
1690 

1630 
1860 

1600 

1819 

14 

16 

•• 

28 

82.9 
33.8 

16.8 

.. 

C 
E 

1570 
1830 

1560 
1770 

1730 
1960 

1700 
1919 

16 

17 

29 

82.9 
33.2 

18  6 

.. 

C 
E 

1680 
1940 

1660 
1890 

1880 
3130 

I860 
8000 

20 

19 

34 

82.9 
83.2 

22.6 
22.8 

" 

C 
E 

1900 
2210 

1810 
2070 

3140 
8470 

8050 
2330 

24 

21 

36 

32.9 

26.6 

•• 

C 

2060 

1970 

2370 

2380 

•• 

• 

*• 

83.2 

26.9 

E 

2410 

2270 

2780 

2890 

30 

24 

41 

82.9 
33.2 

32  9 

33  2 

1  60 

2.00 

8.00 

C 
E 

2410 
2840 

2270 
2640 

2870 
3320 

37U 
3120 

86 

12 

15 

27 

39.1 
39  6 

14.2 

1.25 

1  62 

8  50 

C 
E 

1960 
8810 

1920 
2250 

3070 
2410 

2830 
2356 

14 

16 

28 

39.1 
39.5 

16.3 

.. 

C 
E 

2060 
2410 

3010 
2360 
2130 

2190 
2540 

2156 
2480 

16 

17 

29 

39.1 

18.6 

" 

C 

2170 

2380 

2280 

•• 

•• 

•• 

39.6 

•• 

'• 

E 

2550 

2490 

2720 

2680 

20 

19 

34 

39.1 
89.6 

22.6 
22.8 

.. 

C 
E 

2450 
8890 

2810 
2710 

2670 
3120 

2530 

2840 

24 

21 

36 

39.1 
39.5 

26.6 
26.9 

'* 

C 
E 

2640 
8110 

2500 

2930 
2830 

2920 
S«00 

2780 
8280 

30 

24 

41 

39.1 

32.9 

IK 

20( 

3.0C 

C 

3040 

3450 

3240 

•' 

•• 

•• 

39.5 

33.2 

•• 

E 

3610 

3340 

4080 

8889 

36 

27 

44 

39.1 
39.5 

89.1 
39.5 

.. 

C 
E 

3390 
4050 

3180 
3770 

3940 
4680 

3730 
44O0 

42 

12 

16 

27 

45.8 
45.8 

14.2 

1.25 

1.63 

2.50 

C 
E 

2520 
SOiO 

3470 
2950 

2630 
3110 

8$80 
30M 

14 

16 

28 

45.8 
45.8 

16.8 

" 

C 
E 

2630 
3140 

2580 
3080 

2760 
8250 

2710 
3190 

16 

17 

29 

45.8 
45.8 

18.6 

.. 

C 

E 

2780 
8390 

2730 
3230 

2960 
3400 

2910 
34i9 

20 

19 

34 

45.3 
45.8 

22.6 
22.8 

.. 

0 
E 

3120 
3720 

2940 
3490 

8330 
3930 

8180 
3700 

24 

?i 

36 

45.3 
46.8 

36.6 
26.9 

'* 

C 
E 

8380 
8990 

317Q 
3760 

3600 
4240 

8420 

4010 

30 

24 

41 

45.3 
45.8 

329 
88.2 

1.60 

2.00 

3.00 

C 
E 

3810 
4570 

3550 
4280 

4180 
4980 

8810 
4040 

36 

27 

44 

45.8 
45.8 

39.1 
39.5 

*' 

C 
E 

4210 
5040 

8940 
4700 

4680 
5S90 

4480 
I2M 

42 

30 

47 

45.8 
45.8 

45.3 

45.8 

" 

C 
E 

4700 
5680 

4480 
S810 

MIO 

5180 
•130 

48 

16 

17 

29 

51.5 
51.8 
52.4 

18.6 

1.25 

1.62 

2.50 

B 
C 
E 

8140 
8480 

4150 

8140 

8SS0 
4010 

•3310 

8000 
4800 

8380 
8S80 
4M0 

20 

19 

34 

51.5 

22.6 

B 

8S10 

8800 

8710 

8SiO 

•  •       «  1  <  < 

51.3 

• 

C 

9m 

SHO 

4M0 

-" 

..  ,  .. 

52.4 

22.8 

• 

E 

4m 

44M 

«M 

by  Google 


CAST  IRON  PIPE—BRANCHES, 


1287 


11— Propbrtibs  09 

Branchb 

8— L's,T 

'sane 

CR06SB8.— fimchided. 

i 

0 

Welghta.  In  Lbs. 

t 

]                                                                   I 

3  Way  Branch ||4  Way  Branch 

2  Bellies  BdlB 

j3  Bells  4  BeUf 

48 

24 

21 

83 

3« 

61.5 

28.6 

1.2d 

1.6^ 

2.50| 

B 

1790 

8600 

4000 

3860 

•• 

61.8 

•• 

•• 

C 

4110 

8870 

4350 

4110 

62.4 

26.9 

•• 

E 

4980 

4710 

6210 

4940 

•  « 

41 

61.5 
61.8 
52  4 

32.» 
33.2 

1 

50 

2.00 

3.00 

B 
C 

E 

4250 
4650 
5660 

4000 
4300 
5250 

4600 
6000 

6010 

4350 
4650 
6600 

36 

27 

44 

51  5 

39.1 

" 

B 

4650 

4400 

6080 

4830 

•• 

*• 

51  8 

" 

•• 

C 

5100 

4750 

6510 

5160 

•• 

52.4 

39.5 

•• 

E 

6200 

5790 

6660 

6250 

•  • 

42 

^ 

48 

51.5 
51.8 

45.3 

.. 

B 
C 

5200 
5680 

4900 
5280 

6800 
6300 

5500 
5900 

" 

52.4 

46.8 

•• 

E 

6900 

6420 

7600 

7120 

48 

50 

51.5 

51.5 

" 

B 

5620 

5370 

6400 

6150 

51.8 

51.8 

" 

C 

6150 

6800 

6950 

6600 

•  • 

52.4 

52.4 

E 

7520 

7110 

8490 

8080 

13. — Properties  of  Y  Branches.* 
(R.  D.  Wood  &  Co.) 


Fig.  13. 


Dimensions  In  Inches. 

Approximate 
Weight 

in 
Pounds. 

A 

B 

c 

D 

3 

3 

9 

12 

80 

4 

3 

10 

13 

105 

5 

3 

12 

15 

140 

3.5 

13.5 

17 

180 

4 

16 

20 

2W) 

4  5 

18.5 

23 

360 

5 

21 

26 

495 

5.5 

24.6 

30 

700 

6.5 

27.5 

34 

905 

7 

30 

37 

1090 

20 

7.5 

32.5 

40 

1310 

Z4 

8.5 

37.5 

46 

1920 

Google 


^  3ee  also  Table  37,  following. 


1228 


tL— WATER  WORKS. 


1 


14.~>Propbrtib8  of  Y  Branches.* 
(Met.  W.  W.) 


Pig.  14. 


DlmenBions  In  Inches. 


il 

17« 
IM 

mo 

2S» 

3390 

r« 
stx 

431« 
«4» 


13.5 


38 


18.0 
21.0 
25.0 
21.0 

26.0 

28.0 


1.26 
1.45 
1.26 
r.45 
1.35 
1.60 
1.35 
1.60 
1.65 
1.90 
1.55 
1.90 
1.80 
2.15 
1.55 
1.90 
1.80 
2.15 
1.95 
2.46 
1.55 
1.80 
2.16 
1.76 
1.96 
2.46 
1.96 
2.20 
2.78 
1.95 


22.6 
22.8 
22.6 
22.8 
26.6 
26.9 
26.6 
26.9 
32.9 
33.2 
32.9 
33.2 
39.1 
39.5 
32.0 
33.2 
39.1 
39.5 
43.6 
45.8 


39.5 
45.3 

46.8 
61.6 
61.8 
62.4 
61.6 


0.79 
0.92 
0.87 
1.03 
0.87 
1.03 
1.00 
1.20 
1.00 
1.20 
1.13 
1.36 
1.13 
1.36 
1.27 
1.53 
1  27 
1.53 
1.27 
1.53 
1.25 
1.40 
1.70 
1.25 
1.40 
1.70 
1.25 
1.40 
1.70 
1.50 


1.15 
1.35 
1.15 
1.35 
1.26 
1.50 
1.26 
1.60 
1.46 
1.75 
1.46 
1.75 
1.66 
2  00 
1.45 
1.76 
1.66 
2.00 
1.80 
2.25 
1.45 
1.65 
2.00 
1.60 
1.80 
2.25 
1.80 
2.05 
2.51 
1.80 


0.79 
0.92 
0.79 
0.92 
0.87 
1.03 
0.87 
1.03 
1.00 
1.20 
1.00 
1.20 
1.13 
1.36 
1.00 
1.20 
1.13 
1.36 
1.27 
1.53 
1.03 
1.13 
1.36 
1.14 

i.n 

1.53 
1.25 
1.40 
1.70 
l.U 


1.25 1.25 1.622.5a 


1.50 
1.25 
1.50 


C 
E 
C 

E 
C 

B 
C 
E 
l.50l2.0O3.00|c 
K 
C 
E 
C 


C 
E 
C 
E 
C 
E 
B 
C 
E 
B 
C 
E 
B 

cliMte 


4390 

S2« 

C34e 
Tsoe 

9i3e 

45« 

9041 
5ffl? 
€^ 
7236 
8796 


ITM 


*  See  also  Table  36.  following. 


d  by  Google 


C.  /.  PIPE^Y  BRANCHES:  HYDRANT  BRANCHES.     1220 


16. — Propbrtibs  op  Hydrant  Branches. 
(R.  D.  Wood  &  Co.) 


Fig.  16. 


Dimensions  in  Inches. 

Approximate 
Weight. 

A 

B 

C 

D 

E 

L 

R 

Lbs. 

8 

12 

24 

8 

36 

240 

10 

12 

24 

36 

315 

13 

12 

24 

36 

385 

14 

12 

24 

36 

490 

1$ 

12 

24 

36 

580 

18 

12 

24 

36 

670 

20 

12 

24 

36 

770 

34 

12 

24 

36 

1000 

d  by  Google 


1280 


tL—WATER  WORKS, 


16. — Propbrtibs  of  Blow-off  Branchbs.* 
(Met.  W.  W.) 


Fig 

.16. 

^ 

ft. 

Dlmenslona  In  InchM. 

Oaas. 

S[1S? 

e 

«  1  • 

P 

o. 

Of 

ti 

ta 

X 

y 

8 

8 

4 

10 

7 
8 

9.9 
12.1 

5.7 

0.55 
0.63 

0.45 

E 

I9f 

10 

25S 

12 

•• 

10 

14.2 

0.69 

•• 

•  • 

I2» 

u 

•• 

" 

11 

16.3 

0.75 

•• 

•  « 

tm 

16 

■• 

•• 

12 

18.6 

0.81 

•• 

•  • 

NO 

20 

6 

12 

14 

22.6 
22.8 

7.8 

0.79 
0.92 

0.50 

C 
E 

?M 

Ttt 

24 

.. 

.. 

16 

26.6 
26.9 

0.87 
1.03 

.. 

C 
E 

910 
1000 

80 

12 

13 

20.5 

32.9 

14.2 

1.00 

0.69 

1.25 

1.62 

2.50 

C 

1380 

" 

" 

" 

33.2 

1.20 

•* 

E 

1580 

86 

.. 

w 

23.5 

39.1 
39.5 

1.13 
1.36 

.. 

C 

E 

18M 
2101 

42 

.. 

15 

26.1 

45.3 
45.8 

1.27 
1.53 

.. 

C 
E 

Sit 
1911 

48 

12 

17 

29.5 

61.5 
51.8 
52.4 

1.25 
1.40 
1.70 

0.69 

1 

25 

1.63 

2.50 

B 
C 
E 

4om 

«. 

16 

;; 

" 

51.5 
51.8 

18.6 

1.25 
1.40 

0.81 

B 
C 

3180 
84M 

52.4 

1.70 

E 

41St 

*  See  also  Table  38,  following. 


d  by  Google 


C,  r,  PIPE— BLOW-OFF  BRANCHES,  WITH  M.  H. 


1281 


17. — Propbrtibs  of  Blow-off  Brancrbs* 

WITH  Manholes. 

(Met.  W.  W.) 


Fig.  17. 


DlmeoBlona  In  Inches. 

i 

0 

• 

1 1 

P 

0. 

Or 

ti 

t? 

T 

V 

ff 

V 

20 

n 

ta 

m 

u 

k 

s 

BolU. 
No.loia 

toi 

M 

217 
6" 

20.6 
23.6 
26.5 
29.5 

32.9 
33.2 
39.1 
39.5 
45.3 
45.8 
51.6 
51.8 
52.4 
51.6 
51.8 
52.4 

14.2 
18.6 

1.00 
1.20 
1.13 
1.36 
1.27 
1.53 
1.25 
1.40 
1.70 
1.25 
1.40 
1.70 

0.69 
0.81 

1.25 

1.62 

2.50 

21 

27 
30 

1.25 

1.75 

1.7 

25.5 

20 

154 

c 

E 
C 
E 
C 
E 
B 
C 
E 
B 
C 
E 

?030 
2250 
?500 
2840 
3110 
3590 
3520 
3740 

3600 
.1803 
4510 

*  See  alao  Table  89.  following. 


d  by  Google 


IMS 


^-^WATBR  WORKS. 


18. — PaopBRTiBS  OF  Makholb  Pip»s/ 
(Met.  W.  W.) 


Pig.  18. 


DUnensloQS  In  Inobes. 

i 

r? 

^ 

Bolta. 

|i 

6 

0 

T 

1 

• 

n 

t| 

ta 

m 

k 

u 

B 

^ 

No.;OI&^  ^ 

30 

S2  9 

20 

17 

29 

21 

1.00 

1.25 

1.75 

1.0 

l.f 

25.5 

20     1  •*  C 

ISM 

la  2 

•• 

1.20 

*• 

•      E 

2131 

M 

39.1 
39.  ft 

" 

24 

1.13 
1.36 

.. 

C 

E 

42 

45.3 

45.8 

27 

1.27 
1.53 

.. 

C 

E 

2M 

48 

51.5 
51.8 
52  4 

:: 

SO 

1.25 
1.40 
1.70 

,, 

::  :: 

B 

301 

60 

64.0 

18 

37 

1.50 

■TT- 

" 

tsa 

*  See  also  Table  40.  following. 


19. PrOPBRTIBS  op  SLREVBS.t 

(R.  D.  Wood  &  Co.) 


Fig.  19. 
NoTB.— Dimensions  are  in  inches;  weights  in Tfe. 


§1 

8 

c 

Dlmenslona  In  Inches. 

1 

If 

i 

DlmenflloQs  in  lockes. 

1 

0^ 

a 

o' 

t 

a 

b 

1    i    o- 

t 

3 

E 

1.50 

1.20 

10 

4.8 

0.60 

35 

36 

c 

2.00 

2.50 

15 

39.7 

L2^     » 

4 

•• 

1.30 

*• 

5.8 

0.65 

45 

** 

E 

•• 

1541  }t< 

6 

•• 

1.40 

'• 

8.0 

0.70 

67 

42 

o 

2.» 

•• 

45.5 

1«    I» 

8 

•• 

1.50 

12 

10.1 

0.75 

100 

•• 

•* 

7r\ 

';r 

f9) 

10 

•• 

•* 

12.2 

•• 

120 

*• 

E 

•  • 

15 

460    1  &S 

Il» 

12 

•• 

1.60 

14 

14.3 

0.80 

170 

•' 

•  • 

?0 

•• 

14B 

14 

•' 

1.70 

15 

16.4 

0.85 

220 

48 

B 

3.00 

15 

51  7 

i»'iS« 

16 

1.75 

1.80 

•• 

18.7 

0.90 

275 

" 

'• 

?() 

'••  m 

20 

C 

2.00 

•• 

23.0 

1. 00 

370 

•* 

C 

•• 

IS 

52.6 

i.»  i» 

" 

E 

" 

•  * 

• ' 

" 

1.05 

385      •• 

•* 

•  • 

?0 

••     K3 

24 

C 
E 

2.00 

2.10 

.. 

27.0 

1.15 

470      " 
495      •• 

E 

I! 

15 
20 

B,( 

'•.?i,'n 

ao 

C 

•* 

2.30 

" 

33.4 

•• 

630      60 

B 

2.25 

3.20 

IS 

64.2 

I.S6   l** 



E, 

1.30 

690      *• 

^ 

20 

••    fi» 

tSe 

«  alsc 

>  Tab] 

e4: 

{.  foll< 

awing 

Digitized 

OgJ 

C.  /.  PIPE— MANHOLE:  SLEEVES,  REDUCERS. 


1238 


20. — ^Propbrtibs  op  Rbducbrs — ^Typb  1.* 
(R.  D.  Wood  &  Co.) 


Pig.  20. 


Dlmenslona  In  Inches. 

Approximate  Weight, 
In  Pounds. 

A 

B 

L 

No.  1. 

4 

20 

65 

5 

21 

65 

« 

23 

75 

8 

23 

110 

10 

30 

155 

10 

28.6 

180 

12 

32 

185 

12 

30.6 

210 

12 

10 

28.8 

240 

*  See  also  Table  41.  following. 


21. — Propbrtibs  of  Rbducbrs — ^Typb  2.t 
(Met.  W.  W.) 


Pig.  21. 


■■   ■                      1 
Dimensions  In  Inches. 

8 

Dimensions  In  Inches. 

i 

0 

N 

e 

t 

V 

.|.. 

t2 

e 

f  1    V  !   s   I    ti 

ta 

14 

10 

20 

8 

0.75 

0.63 

E 

260     1 

36 

30 

32  i     8 

1.13 

1.00 

c 

1440 

16 

0.81 

•• 

•« 

300    l' 

•• 

•• 

1.36 

1.20 

E 

1740 

12 

•• 

0.69 

•• 

330 

42 

•• 

•• 

1.27 

1.00 

C 

1690 

20 

26 

0.79 

•• 

C 

435    1 

•• 

•• 

1.53 

1.20 

K 

2040 

•• 

0.92 

•• 

E 

480     1 

36 

•• 

1.27 

1.13 

C 

1920 

'  • 

16 

•• 

0.79 

0.70 

C 

485     : 

" 

•• 

1.53 

1.36 

E 

2320 

•  • 

•• 

•• 

•• 

0.92 

0.81 

E 

565 

•• 

66 

1.27 

1.13 

C 

3280 

24 

•• 

•• 

0.87 

C 

610 

'* 

" 

1.53 

1.36 

E 

3970 

•• 

•• 

1.03 

•• 

E 

675    1 

•' 

32 

1.25 

1.03 

B 

1970 

«« 

20 

" 

0.87 

0.79 

C 

655 

1.40 

1.13 

C 

3200 

•  • 

•• 

1.03 

0.92 

E 

775    1 

" 

" 

1.70 

1.36 

E 

2660 

JO 

" 

1.00 

0.79 

c 

810    , 

42 

1.25 

1.14 

B 

2200 

" 

1.20 

0.92 

E 

970    ' 

" 

" 

1.40 

1.27 

C 

2460 

•  • 

24 

" 

1.00 

0.87 

C 

905    1 

*• 

1.70 

1.53 

E 

3CC0 

•  « 

•• 

•• 

1.20 

1.03 

E 

1090 

36 

132 

1.25 

1.03 

B 

60C0 

M 

•  • 

32 

1.13 

0.87 

C 

1240 

1.40 

1.13 

C 

67C0 

•  • 

" 

1.36 

1.03 

E 

U«,|| 

1.70 

1.36 

E 

8130 

t  See  also  Table  42.  following. 


byGoogk 


1234 


^— WATER  WORKS, 


22. — ^Propbrtibs  op  Caps.* 
(Met.  W.  W.) 
A  \tAi  A 


Pf^^      ^ /%»     '  Section  e/^A^ 

/4indt  9nd  Smatke  iOinch  and  Uyer. 

Pig.  22. 
Note.— Dimensions  are  in  inches;  weights  in  lbs. 


1 

Dimensions  In  Inches. 

1 

i 

a 

b 

0 

o' 

h 

t 

m 

k 

I 

r 

R 

X 

y 

1 

4 

E 

1.50 

1.3 

0.65 

3.0 

5.8 

3.60 

0.60 

3i 

6 

•• 

1.4 

0.7C 

*• 

8.C 

3.6J 

0.6S 

41 

i 

•• 

1.5 

0.75 

8.5 

10.1 

4.25 

O.7S 

61 

IC 

•• 

•• 

•• 

12.2 

*• 

«• 

1.5C 

0.7S 

86 

12 

•• 

1.6 

0.80 

•• 

14.2 

" 

•• 

1.75 

*• 

106 

14 

'• 

1.7 

0.85 

•' 

16.4 

4.4( 

O.W 

1.9( 

" 

149 

1( 

1.7B 

1.8 

O.M 

4.0 

18.7 

5.0C 

1.0( 

2.0( 

•• 

2.5C 

1.2s 

1,62 

2« 

2C 

2.0 

1.00 

23.  C 

5.2! 

2.5( 

l.OC 

1.78 

22.85 

380 

24 

2.00 

2. 1 

1.05 

4.5 

27. C 

6.0( 

l.Ot 

3.0( 

•• 

1.8C 

28.62 

•• 

•• 

•• 

480 

8C 

•' 

2.3 

1.15 

•• 

33.4 

" 

1.15 

2.8S 

•• 

2.0c 

44. 6( 

3.0Q 

l.BC 

1.00 

CIO 

36 

•• 

2.5 

1.25 

•• 

39.7 

•• 

1.21 

4.0( 

1.25 

44.5: 

•• 

970 

42 

C 

E 

:; 

2.8 

r.^40 

5.0 

45.5 
46.0 

7.00 

1.50 
1.60 

3.90 

1.50 

2.25 

63.28 

.. 

•* 

*' 

1110 
1579 

48 
«• 

B 
C 

E 

•• 

3.0 

1.60 

B.26 

51.7 

8.00 

1.75 
1.90 
2.00 

4.0c 
3.85 
3.76 

- 

3.00 
3.15 
3.45 

90.0 

•• 

•• 

;; 

3130 
2100 
2289 

*  See  also  Table  44.  following. 


23. — Propbrtibs  of  Pluos.! 
(R.  D.  Wood  &  Oo.) 


Fig.  23. 
NoTB.— Dimensions  are  in  inches. 


Diameter  of  Pipe. 

A 

D 

Approximate  Welffct 
taPooDds. 

3- 

S.S* 

5.6» 

4 

4.9 

€ 

6.0 

8 

7.0 

10 

8.1 

IS 

10 

11.2 

28 

12 

13.2 

38 

t  See  also  Table  45,  following, 


d  by  Google 


C.  1,  PIPE'-CAPS,  PLUGS,  OFFSETS, 


1236 


24. — ^Propbrtibs  of  Opfsbts.* 
(R.  D.  Wood  &  Co.) 


Fig.  24. 


Pipe 

Dlmeoaloiu  In  Inchea 

Approx. 

DUtm. 

Weight  In 

Ids. 

R 

A 

B 

C 

L 

T 

Poandfl. 

8 

4.6 

13.86 

10 

0.40 

66 

14 

4.6 

24.26 

10 

0.40 

75 

8 

6.8 

13.86 

10 

0.45 

90 

14 

5.8 

24.25 

10 

0.45 

110 

8 

6.8 

13.88 

10 

0.48 

115 

14 

6.8 

24.25 

10 

0.48 

140 

8 

7.8 

13.86 

10 

0.50 

140 

14 

7.8 

24.25 

10 

0.50 

175 

10 

9.9 

17.32 

10 

0.55 

215 

15 

9.9 

25.98 

10 

0.55 

255 

12 

12.0 

20.78 

10 

0.60 

310 

18 

12.0 

31.18 

10 

0.60 

375 

14 

14.1 

24.25 

10 

0.65 

430 

20 

14.1 

34.61 

10 

0.65 

510 

*  See  also  Table  34,  following. 

(2)  Turned  and  Bored  Joint  Pipe  (see  page  1215)  is  rarely  used  in  the 
United  States.  During  extremely  cold  weather  the  joints  are  liable  to  pull 
apart.  If  there  is  no  danger  from  this  cause,  this  kind  of  pipe  will  perhaps 
be  economical  if  the  cost  of  boring  the  bell  end  and  turning  the  spigot  end 
does  not  exceed  the  cost  of  lead  joint  for  the  ordinary  bell  and  spigot  pipe. 

(3)  Flanged  Joint  Pipe  (see  page  682)  or  simply  flange  pipe  is  used  for 
special  connections  and  open  work.jrenerally  at  the  ends  of  pipe  lines,  as  in 
pump'houfles,  gate  chambers,  etc.  The  pipes  come  in  12-ft.  lengths,  and  the 
Banses  are  bolted  together,  with  rubber  or  other  packing  between.  The 
following  represents  the  practice  of  R.  D.  Wood  &  O).,  of  Philadelphia, 
Adopting  the  standard  of  National  Ass'n  of  Master  Steam  and  Hot  Water 
Fitters  and  the  Am.  Soc.  of  Mechanical  Engineers,  in  flange  diameters  and 
drilling: 

Note. — Flexible  Joint  Pipe  b  described  on  page  1238. 


d  by  Google 


U96 


9L— WATER  WORKS. 


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1288  U,— WATER  WORKS. 

(4)  HexiUe  Joint  Pipe  (page  1215)  is  particularly  advantageous  and  eco- 
nomical when  it  is  necessary  to  carry  the  pipe  line  across  a  stream  of  any 
considerable  size.  If  the  stream  is  navigable  and  vessels  are  liable  to 
anchor,  the  bed  of  the  stream  must  be  dredged  on  the  line  of  the  pipe,  aiKi 
a  line  of  guide  piles  is  often  driven  for  this  purpose.  These  piles  lUso  serve 
later  in  laying  the  pipe  in  the  dredged  trench.  The  process  of  laying  the 
pipe  is  comparatively  simple.  Beginning  at  one  shore,  connection  is  made 
with  the  line  laid  up  to  that  point  (in  a  gradually  doBendin^  deep  txtock 
toward  the  stream).  An  improvised  scow  with  a  run-way  or  mcliiw  is  wdl 
suited  to  the  purpose.  The  pipes  are  laid  successively  on  the  run-way.  the 
joints  are  leaded,  and  the  scow  pulled  ahead,  allowing  the  pripe  to  gradoallT 
settle  to  the  bottom  of  the  trench  without  straining  the  joints  excessively. 


Pig.  25. 

In  pouring  the  lead  for  any  joints  the  two  adjacent  pipes  must  be  in  a 
straight  line.  Sometimes  trestle  work  is  employed,  in  shallow  water,  and 
the  pipes  are  lowered  into  place  bv  block  and  tackle.  The  method  of  assem- 
bling the  pipe  on  the  bank,  and  tnen  dragging  the  whole  connected  line  into 
the  stream  is  very  liable  to  strain  the  jomts  and  even  pull  them  apart,  as 
sometimes  happens. 

Flexible  jomt  pipe  is  manufactured  in  pipe  length,  including  pipe  and 
joint,  with  bell-end  machined  inside;  or  the  cast  knuckle  joints  with  Baagt 
ends  or  bell  and  spigot  ends  may  be  ordered  separately  for  connectii^  witk 
ordinary  pipe. 

Flexible  joints  are  used  not  only  with  cast  iron  pipe  but  with  wrought 
iron  and  steel  pipe  as  well.* 


*  For  design  of  flexible  joint  in  connection  with  52-in.  riveted  steel  pipe, 
see  Trans.  Am.  Soc.  C.  E..  Vol.  XXXIV,  p.  23. 


d  by  Google 


FLEX.  JOINT  PIPE.    C.  I.  PIPE  SPECIFICATIONS.      1289 

Ambrtcan  Watbr  Works  Association 

*  STANDARD  SPECIRCATIONS 

FOR 

CAST  IRON  PIPE  AND  SPEQAL  CASTINGS 

With  Tables  op  Diubnsions, 

Thicknesses  and  Weights. 

Adopted  May  12,  1908. 

STANDARD  SPECIFICATIONS. 
Description  op  Pipes. 
Stction  li  The  pipes  shall  be  made  with  hub  and  spigot  joints,  and  shall 
conform  accurately  to  the  dimensions  given  in  Tables  26  and  27.  They  shall 
be  straight  and  shall  be  true  circles  in  section,  with  their  inner  and  outer 
surfaces  concentric,  and  shall  be  of  the  specified  dimensions  in  outside 
diameter*   They  shall  be  at  least  12  feet  in  length,  exclusive  of  socket. 

Pipes  with  thickness  and  weight  intermediate  between  the  classes  in 
Table  27  shall  be  made  of  the  same  outside  diameter  as  the  next  heavier 
class  Pipes  with  thickness  and  weight  less  than  shown  by  Table  27  shall  be 
made  of  the  same  outside  diameter  as  the  Class  A  pipe;  and  pipes  with 
thickness  and  weight  more  than  shown  by  Table  27  shall  be  maae  of  the 
same  outside  diameter  as  the  Class  D  pipe. 

All  pipes  having  the  same  outside  diameter  shall  have  the  same  inside 
diameter  at  both  ends.  The  inner  diameter  of  the  lighter  pipes  of  each 
standard  outside  diameter  shall  be  gradually  increased  for  a  distance  of 
about  6  inches  from  each  end  of  the  pipe  so  as  to  obtain  the  required  standard 
thickness  and  weight  for  each  size  and  class  of  pipe. 

For  pipes  of  each  size  from  4-inch  to  24-inch  inclusive,  there  shall  be 
two  standards  of  outside  diameter,  and  for  pipes  from  30-inch  to  60-inch 
inclusive,  there  shall  be  four  standards  of  outside  diameter,  as  shown  by 
Table  26. 

For  pipes  4^mch  to  12-inch  inclusive,  one  class  of  special  castings  shall 
be  furnished,  made  from  Class  D  pattern*  Those  having  spigot  ends  shall 
have  outside  diameten  of  spigot  ends  midway  between  the  two  standards  of 
outside  diameter  as  shown  by  .Table  26,  and  shall  be  tapered  back  for  a 
distance  of  6  indies. 

For  pipes  from  1 4-inch  to  24-inch  inclusive,  two  classes  of  special  castings 
shall  be  furnished;  Class  B  special  castings  with  Classes  A  and  B  pipes, 
and  Class  D  special  castings  with  Classes  C  and  D  pipes;  the  former  ui^ll 
have  cast  on  them  the  letters  "AB'  and  the  latter  "CD."  For  pipes  30-inch 
to  60-inch  inclusive,  four  classes  of  special  castings  shall  be  furnished,  one 
for  each  class  of  pipe,  and  shall  have  cast  on  them  the  letter  of  the  class  to 
which  they  belong. 

Allowable  Variation  in  Diameter  op  Pipes  and  Sockets. 
Section  2.  Special  care  shall  be  taken  to  have  the  sockets  of  the  re- 
qtiired  size.  The  sockets  and  spigots  will  be  tested  by  circular  gages,  and 
no  pipe  will  be  received  which  is  defective  in  ioint  room  from  any  cause. 
The  oiameters  of  the  sockets  and  the  outside  diameters  of  the  spigot  ends 
of  the  pipes  shall  not  vary  from  the  standard  dimensions  by  more  than  0.06 
of  an  inch  fot  pipes  16  inches  ot  less  in  diameter*  0.08  of  an  inch  for  18-inch. 
20-icch  and  24-inch  pipes,  0.10  of  an  inch  for  30-inch,  36-inch  and  42-inch 
pipes;  0.12  of  an  inch  for  48-inch,  and  0.16  of  an  inch  for  64-inch  and  60-inch 
pipes* 

Allowable  Variation  in  Thickness. 

Section  8.  For  pipes  whose  standard  thickness  is  less  than  1  inch,  the 
flii^VriAfM  of  metal  in  the  bodv  of  the  pipe  shall  not  be  more  than  0.08  of  an 
inch  less  than  the  standard  thickness,  and  for  pipes  whose  standard  thick- 
ness is  1  inch  or  more,  the  variation  shall  not  exceed  0.10  of  an  inch,  except 

•  Mr.  J,  M.  Diven,  Sec'y  Am.  W.  W.  Ass'n,  writes  the  author  as  follows, 
under  date  of  Sept.  3,  1908:  "The  specifications  are  not  absolutely  perfect 
yet,  nor  has  there  been  any  agreement  between  the  various  associations  as 
to  a  universal  standard.  This  is  something  greatly  to  be  desired,  and  which 
I  trust  will  be  brought  about  in  the  next  two  or  three  years." 


1240  M.— WATER  WORKS. 

that  for  spaceo  not  exceeding  8  inches  in  length  in  any  direction,  variatiaQs 
from  the  standard  thickness  of  0.02  of  an  inch  in  excess  of  the  aUowsoce 
above  given  shall  be  permitted. 

For  special  castings  of  standard  patterns  a  variation  of  50  p^  cent 
gxeater  than  allowed  for  straight  pipes  shall  be  permitted. 

Dbfbctive  Spigots  Mat  bb  Cut. 

Section  4.  Defective  spigot  ends  on  pipes  12  inches  or  more  in  diameter 
may  be  cut  off  in  a  lathe  and  a  half-roimd  wrought*iron  band  shrunk  into  a 
groove  cut  in  the  end  of  the  pipe.  Not  more  than  12  per  cent  of  the  total 
number  of  accepted  pii>es  of  each  size  shall  be  cut  and  banded,  and  no  pipe 
shall  be  banded  which  is  less  than  11  feet  in  length,  exclusive  of  the  sodcet. 

In  case  the  length  of  pipe  differs  from  12  feet,  the  standard  weight  of 
the  pipe  given  in  Table  27  shall  be  modified  in  accordance  therewith. 

Spbcial  Castings. 

Section  5.  All  special  castings  shall  be  made  in  accordance  with  the 
cuts  and  dimensions  given  in  the  tables  forming  a  part  of  these  specifications. 

The  diameters  of  the  sockets  and  the  extenial  diameters  of  the  spigot 
ends  of  the  special  castings  shall  not  varv  from  the  standard  dimensions  by 
more  than  0.1 2  of  an  inch  for  castings  lo  inches  or  less  in  diameter;  0.15  oiE 
an  inch  for  18-inch,  20-inch  and  24-inch:  0.20  of  an  inch  for  30-inch,  35-tnch 
and  42-inch,  and  0.24  of  an  inch  for  48-inch,  64-inch  and  60-inch.  These 
variations  apply  only  to  special  castings  made  from  standard  patterns. 

The  flanges  on  all  manhole  castings  and  manhole  covers  shall  be  faced 
true  and  smooth,  and  drilled  to  receive  bolts  of  the  sizes  given  in  the  tables. 
The  manufacturer  shall  furnish  and  deliver  all  bolts  for  bolting-on  the  man- 
hole covers,  the  bolts  to  be  of  the  sizes  shown  on  plans  and  made  of  the  best 
qualitv  of  mild  8teel»  with  hexagonal  heads  and  nuts  and  sound  well-fittiag 
threads. 

Marking. 

Section  6.  Every  pipe  and  special  casting  shall  have  distinctly  cast  upon 
it  the  initials  of  the  maker's  name.  When  cast  especially  to  order,  each 
pipe  larger  than  4-inch  may  also  have  cast  upon  it  figures  lowing  the  year 
m  which  it  was  cast  and  a  number  signifying  the  order  in  point  of  time  in 
which  it  was  cast,  the  figtires  denoting  the  year  being  above  and  the  number 
below,  thtis: 

1908  1008  1008 

12  8 

etc.,  also  any  initials,  not  exceeding  four,  which  may  be  required  by  the 
purchaser.  The  letters  and  figures  shall  be  cast  on  the  outside  and  shall  not 
be  less  than  2  inches  in  length  and  H  of  an  inch  in  relief  for  pipes  8  inches 
in  diameter  and  larger.  For  smaller  sizes  of  pipes  the  letters  may  be  1  inch 
in  length.  The  weight  and  the  class  letter  shall  be  painted  conspicuously  in 
white  on  the  inside  of  each  pipe  and  special  castmg  after  the  coating  oss 
become  hard. 

Allow ablb  Pbrcbntaob  op  Variation  in  Wbiobt. 

Section  7.  No  pipes  shall  be  accepted  the  weight  of  which  shall  be  less 
than  the  standard  weight  by  more  than  5  per  cent  for  pipes  16  inches  or 
less  in  diameter,  and  4  per  cent  for  pipes  more  than  16  inches  in  diameter, 
and  no  excess  above  the  standard  weight  of  more  than  the  given  percent- 
age for  the  several  sizes  shall  be  paid  for.  The  total  weight  to  be  paid  for 
shall  not  exceed  for  each  size  and  class  of  pipe  received  the  sum  of  the 
standard  weights  of  the  same  number  of  pieces  of  the  given  sise  and  clau 
by  more  than  2  per  cent. 

No  special  casting  shall  be  accepted  the  weight  of  which  shall  be  less 
than  the  standard  weight  by  more  than  10  per  cent  for  pipes  12  inches  or 
less  in  diameter,  and  8  per  cent  for  larger  sizes  except  that  ctirves,  Y-piece« 
and  breeches  pipe  may  be  12  per  cent  below  the  standard  weight,  and  no 
excess  above  the  standard  weight  of  more  than  the  above  percentages  for 
the  several  sizes  will  be  paid  for.  These  variations  apply  only  to  castings 
made  from  the  standard  patterns. 

Quality  of  Iron. 

^Sertww  8.    All  pipes  and  special  castings  shall  be  made  of  cast  iron  oi 

good  quality,  and  of  such  character  as  shall  make  the  metal  of  the  castingi 


CAST  IRON  PIPE  SPECIFICATIONS.  1341 

strong,  touffh  and  of  even  grain,  and  soft  enough  to  satisfactorily  admit  of 
drilling  and  cutting  The  metal  shall  be  made  without  any  admixture  of 
cinder  iron  or  other  inferior  metal,  and  shall  be  remelted  in  a  cupola  or  air 
furnace. 

The  contractor  shall  have  the  right  to  make  and  break  three  bars  from 
each  heat  or  run  of  metal,  and  the  test  shall  be  based  upon  the  average 
results  of  the  three  bars.  Should  the  dimensions  of  the  three  bars  differ 
from  those  given  below,  a  proper  allowance  therefor  shall  be  made  in  the 
results  of  the  tests. 

Tests  op  Material. 
^Sectum  9.  Specimen  bars  of  the  metal  used,  each  being  twenty-six  inches 
long  by  two  inches  wide  and  one  inch  thick,  shall  be  made  without  charge 
as  often  as  the  engineer  may  direct,  and  in  default  of  definite  instructions 
the  contractor  sh^l  make  and  test  at  least  one  bar  from  each  heat  or  run 
of  metal.  The  bars  when  placed  flatwise  upon  supports  twenty-four  inches 
apart,  and  loaded  in  the  center,  shall  support  a  load  of  2,000  potmds.  and 
show  a  deflection  of  not  less  than  0.30  of  an  inch  before  breaking;  or  if 
preferred,  tensile  bars  shall  be  made  which  will  show  a  breaking  point  of 
not  less  than  20.000  poimds  per  square  inch. 

Casting  op  Pipe. 

Section  10.  The  straight  pipes  shall  be  cast  in  drv  sand  molds  in  a  vertical 
position.  Pipes  16  inches  or  less  in  diameter  shall  be  cast  with  the  hub  end 
up  or  down,  as  specified  in  the  proposals.  Pipes  18  inches  or  more  in  dia- 
meter shall  be  cast  with  the  hub  end  down. 

The  pipes  shall  not  be  stripped  or  taken  from  the  pit  while  showing  color 
of  heat,  but  shall  be  left  in  the  flasks  for  a  sufficient  length  of  time  to  prevent 
unequal  contraction  by  subsequent  exposure. 

Oualitt  op  Castings. 
Section  11.   The  pipes  and  special  castings  shall  be  smooth,  free  from 
scales,  lumps,  blisters,  sand  holes  and  defects  of  every  nattu«  which  tmfit 
them  foi  the  tise  for  which  they  are  intended.    No  plugging  or  filling  will  be 
allowed. 

Cleaning  and  Inspection. 
Station  12.    All  pipes  and  special  castings  shall  be  thoroughly  cleaned 
and  subjected  to  a  careful  hammer  inspection.    No  casting  shall  be  coated 
unless  entirely  clean  and  free  from  rust,  and  approved  in  these  respects  by 
the  engineer  mmiediately  before  being  dipped. 
Coating. 
Section  13    Every  pipe  and  special  casting  shall  be  coated  inside  and 
out  with  coal-tar  pitch  varnish.    The  varnish  shall  be  made  from  coal  tar.    ' 
To  this  material  sufficient  oil  shall  be  added  to  make  a  smooth  coating, 
tou^h  and  tenacious  when  cold,  and  not  brittle  nor  with  any  tendency  to 
scale  off. 

Each  casting  shall  be  heated  to  a  temperature  of  300  degrees  Fahrenheit 
immediately  before  it  is  dipped,  and  shall  not  possess  less  than  this  tempera- 
ture at  the  time  it  is  put  m  the  vat.  The  ovens  in  which  the  pipes  are 
heated  shall  be  so  arranged  that  all  portions  of  the  pipe  shall  be  heated  to 
an  even  temperature.  Bach  casting  shall  remain  in  the  bath  at  least  five 
minutes. 

The  varnish  shall  be  heated  to  a  temperature  of  300  degrees  Fahrenheit 
(or  less  if  the  engineer  shall  so  order),  and  shall  be  maintained  at  this  tem- 
perature during  the  time  the  casting  is  immersed. 

Fresh  pitch  and  oil  shall  be  added  when  necessary  to  keep  the  mixture 
at  the  proper  consistency  and  the  vat  shall  be  emptied  of  its  contents  and 
refilled  with  fresh  pitch  when  deemed  necessary  by  the  engineer.  After 
t>ein£r  coated  the  pipe  shall  be  carefully  drained  of  the  stuplus  varnish.  Any 
pipe  ot  special  casting  that  is  to  be  recoated  shall  first  be  thoroughly 
Bcraped  and  cleaned. 

Hydrostatic  Test. 
Section  14    When  the  coating  has  become  hard,  the  straight  pipes  shall 
be  st^jected  to  a  proof  by  hydrostatic  pressure,  and,  if  requirea  by  the 
^o^ineer,  they  shall  also  be  subjected  to  a  hammer  test  under  this  pressure. 

♦  Pipe  may  be  made  under  higher  metal  tests  when  desired.  Stock 
>ipe  may  be  made  under  metal  tests  as  low  as  1,800  poimds. 


1243 


M.—WATER  WORKS. 


The  pressures  to  which  the  different  sizes  and  classes  of  pipes  shall  be 
subjected  are  as  follows: 


20-Inch  Diameter 

Less  than  20-Inch 

and  Larger. 

Diameter. 

Pounds  per 

Potmds  per 

Square  Inch. 

Square  inch. 

150 

300 

200 

300 

250 

300 

300 

300 

Class  A  Pipe 
Class  B  Pipe 
Class  C  Pipe 
Class  D  Pipe 


Wbighinq. 
Section  15.  The  pipes  and  special  castings  shall  be  weighed  for  payment 
tmder  the  supervision  of  the  engineer  after  the  application  of  the  ooal-tar 
pitch  varnish.  If  desired  by  the  engineer,  the  pipes  and  special  castings 
shall  be  weighed  after  the  delivery,  and  the  weights  so  ascertained  shaU  be 
tised  in  the  nnal  settlement,  provided  such  weighing  is  done  by  a  lesaHzed 
weighraaster.  Bids  shall  be  submitted  and  a  final  settlement  made  upon 
the  basis  6f  a  ton  of  2,000  pounds. 

Contractor  to  Furnish  Men  and  Materials. 

Section  16.  The  contractor  shall  provide  all  tools,  testing  machines. 
materials  and  men  necessary  for  the  required  testing,  inspection  and  weigh- 
ing at  the  foundry,  of  the  pipe  and  special  castings;  and  should  the  pttrchaser 
have  no  inspector  at  the  works,  the  contractor  shall,  if  required  by  the  engi- 
neer, furnish  a  sworn  statement  that  all  of  the  tests  have  been  made  as 
specified,  this  statement  to  contain  the  results  of  the  tests  upon  the  test 
bJEirs. 

Power  op  Engineer  to  Inspect. 

Section  17.  The  engineer  shall  be  at  liberty  at  all  times  to  inspect  Uie 
material  at  the  foundry  .and  the  molding,  casting  and  coating  of  the  pipes 
and  special  castings.  The  forms,  sizes,  uniformity  and  condition  of  all 
pipes  and  other  castings  herein  refered  to  shall  be  subject  to  his  insp»ectioQ 
and  approval,  and  he  may  reject,  without  proving,  any  pipe  or  other  casting 
which  IS  not  in  conformity  with  the  specifications  or  drawings 

Inspector  to  Report 

Section  18.  The  inspector  at  the  foxmdry  shall  report  daily  to  the 
foundry  office  all  pipes  and  special  castings  rejected,  with  the  causes  for 
rejection. 

Castings  to  be  Delivered  Sound  and  Pbrpbct. 

Section  19.  All  the  pipes  and  other  castings  must  be  delivered  in  all 
respects  sound  and  conformable  to  these  specifications.  The  inspvectson 
shall  not  relieve  the  contractor  of  any  of  his  obligations  in  this  respect,  and 
any  defective  pipes  or  other  castings  which  may  have  passed  the  engineer 
at  the  works  or  elsewhere  shall  be  at  all  times  liable  to  rejection  when  dis- 
covered, until  the  final  coihpletion  and  adjustment  of  the  contract;  pro- 
vided, however,  that  the  contractor  shall  not  be  held  liable  for  pipes  or 
special  castings  found  to  be  cracked  after  they  have  been  accepted  at  the 
agreed  point  of  delivery.  Care  shall  be  taken  in  handhng  the  pipes  not  to 
injure  the  coating,  and  no  pipes  or  other  material  of  any  kma  shall  be 
placed  in  the  pipes  during  transportation  or  at  any  time  after  thty  have 
received  the  coating. 

Definition  op  the  Word  "Engineer." 
Section  20.    Wherever  the  word  "engineer"  is  used  herein  it  shall  be 
understood  to  refer  to  the  engineer  or  inspector  acting  for  the  purchaser 
and  to  his  properly  authorized  agents,  limited   by   the  particular  duties 
intrusted  to  them. 


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CAST  IRON  PIPE  WITH  BELL  AND  SPIGOT. 


1248 


^-a-H 


20. — DiMBNsioNS  OP  Cast  Iron  Pipe. 
(A.  W.  W.  A.) 
Classes  A,  B.  C.  D. 


m^ 


S-CfL 


X  —  9i*  on  8*  to    ft*  inclusive. 
V-  A' on  rto    6* 
X-  1*  on  8*10  84' 
V- H' on  8*10  84' 


Fig.  26. 

Nom- 

Actual 

Dlam.  of  Sockets. 

Depth  Of  S'kets. 

inal 
Dlam 

dsases. 

Outside 
Diam. 

A 

B 

I^i^ 

Special 

Pipe. 
Inches. 

Special 

0 

Inches. 

Inches. 

Oast'gs. 
Inches. 

Oast'gs. 
Inches 

4 

A 

4.80 

5.60 

5.70 

8.50 

4.00 

1.5 

1.30 

.65 

4 

B-O-D 

6.00 

5.80 

5.70 

3.50 

400 

1.5 

1.30 

.65 

e 

A 

6.00 

7.70 

7.80 

3.50 

4.00 

1.5 

1  40 

70 

e 

B-O-D 

7.10 

7.90 

7.80 

3.50 

4.00 

1.6 

1.40 

.70 

8 

A-B 

005 

9.ffi 

10.00 

4.00 

4.00 

1.6 

1.50 

.75 

8 

C-D 

9.30 
11.10 

10.10 

10.00 

400 

4.00 

1.5 

1.50 

.76 

10 

A-B 

11.90 

12.10 

4  00 

4.00 

1.5 

1.50 

.75 

10 

0-D 

11.40 

12.20 

12.10 

4.00 

4.00 

1.5 

1.60 

.80 

12 

A-B 

13.20 

14.00 

14.20 

4.00 

4.00 

I.I 

1.60 

.80 

12 

C-D 

13.50 

14.30 

14.20 

400 

400 

1.70 

.85 

14 

A-B 

15.30 

16.10 

16.10 

400 

4.00 

15 

1.70 

.85 

14 

0-D 

15.85 

16.45 

16.45 

4.00 

4.00 

1  5 

1.80 

.90 

16 

A-B 

17.40 

18.40 

18.40 

400 

4.00 

1.75 

1.80 

.90 

18 

O-D 

17.80 

18.80 

18.80 

400 

4.00 

1.75 

1  90 

1.00 

18 

A-B 

19.60 

20.50 

20.50 

400 

4.00 

1.75 

1.90 

.95 

18 

0-D 

19.92 

20.92 

20.92 

4.00 

4.00 

1.75 

2  10 

1.05 

20 

A-B 

21.60 

22.60 

22.60 

4JOO 

4.00 

1.75 

2.00 

1.00 

20 

O-D 

22.06 

23.06 

23.06 

4.00 

4.00 

1.75 

2  30 

1.15 

24 

A-B 

25.80 

26.80 

26.80 

4.00 

4.00 

2.00 

2  10 

1.05 

24 

0-D 

26.32 

27  32 

27.32 

4.00 

4«00 

2.00 

2.50 

1.26 

80 

A 

81.74 

32  74 

32  74 

4.50 

4.50 

2.00 

2.30 

1.16 

30 

B 

82.00 

33.00 

33.00 

4.50 

4.60 

2  00 

2.30 

1.15 

30 

0 

32.40 

33.40 

33.40 

4  50 

4.50 

2.00 

2.60 

1.32 

80 

D 

82.74 

33.74 

33.74 

4.50 

4.50 

2.00 

3.00 

1.50 

80 

A 

87.96 

38-96 

38.96 

4.50 

4.50 

3.00 

2.50 

1.26 

80 

B 

38.30 

39.30 

39.30 

450 

4.50 

2.00 

2.80 

1.40 

88 

0 

38.70 

39.70 

39.70 

4.60 

4.50 

2.00 

3.10 

1.68 

88 

D 

39.16 

40.16 

40.16 

4.50 

4.50 

2.00 

340 

1.80 

42 

A 

44.20 

46.20 

45.20 

5.00 

6.00 

200 

2  80 

1.40 

42 

B 

44.50 

45.60 

45.50 

6.00 

6.00 

2.00 

3.00 

1.50 

42 

0 

45.10 

46.10 

46.10 

5.00 

5.00 

2.00 

3.40 

1.75 

42 

D 

45.58 

46.58 

46.68 

5.00 

5.00 

3.00 

3.80 

1.96 

48 

A 

50.50 

51.50 

51.50 

5.00 

600 

2.00 

3.00 

1.50 

48 

B 

50.80 

51.80 

51.80 

5  00 

5.00 

2.00 

3.30 

1.65 

48 

C 

51.40 

52.40 

52.40 

6.00 

5.00 

2.00 

3.80 

1.95 

48 

D 

51.98 

52.98 

52.98 

5.00 

5.00 

2.00 

4.20 

2.20 

M 

A 

56.66 

57.66 

57  66 

5.50 

650 

2.25 

3.20 

1.60 

54 

B 

67.10 

58.10 

58.10 

5.50 

5  60 

2.25 

3.60 

1.80 

54 

C 

67.80 

68.80 

68.80 

6.50 

6  SO 

2.25 

4.00 

2.15 

54« 

D 

68.40 

69.40 

69.40 

5.50 

5.50 

2.25 

4.40 

2.45 

60 

A 

62  80 

63.80 

63.80 

6.50 

6.60 

2.26 

3.40 

1.70 

60 

B 

63  40 

64.40 

64.40 

5.50 

5.50 

2.25 

3.70 

1.90 

60 

0 

64.20 

65.20 

65.20 

5.50 

6.50 

2.25 

4.20 

2.25 

60 

D 

64.82 

66.82 

66.83 

5.50 

5.50 

2.25 

4.70 

2.60 

72 

A 

75.34 

76.34 

76.34 

5.50 

5.50 

2.26 

3.80 

1.87 

72 

B 

76.00 

77.00 

77.00 

5  50 

5  50 

2.25 

4.20 

2.20 

72 

0 

76.88 

77.88 

77.88 

6.50 

5.50 

2.25 

4.60 

2.64 

84 

A 

87-64 

88-54 

88.54 

5.50 

5.50 

2.50 

4.10 

2.10 

84 

B 

88-54 

89.54 

89.54 

5.50 

5.50 

2.50 

4.50 

2.60 

1244 


6i.— WATER  WORKS. 


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Digitized  by  VjOOQ  IC 


Si 


CAST  IRON  PIPE  TABLE,   BELL  AND  SPIGOT. 


1246 


S8. — ^Ddibnsions  of  Pipb  for  High  Prbssurb  Sbrvicb. 
(A.  W.  W.  A.) 
Classes  B.  P.  G.  H. 


S'C-tL 


Pig.  28. 
NoTB.— Dimensions  are  in  inches. 


Noml- 

nal 
Dlam. 
loebee 

aasses. 

Aotoal 
Outside 
Diain* 

Dlam.  of 
Sockets. 

Depth  01 
Sockets. 

A 

B 

C 

R 

Nomi- 
nal 
Dlam. 

Inches 

Pipe  and 

Pipe  and 

Inches 

Specials. 

Specials 

6 

B-P 

7  22 

8.02 

4.00 

1.50 

1.75 

0.75 

1.10 

6 

6 

O-H 

7.88 

8.18 

4  00 

1.60 

1.85 

0.85 

1.10 

6 

8 

B-F 

9.42 

10.22 

4.00 

1.60 

1.85 

0.86 

1.10 
1.10 

8 

8 

O-H 

9.60 

10.40 

4.00 

1.50 

1.95 

0.95 

8 

10 

B-F 

11.60 

12.40 

4.50 

1^ 

1.99 

0.96 

1.10 

10 

10 

G-H 

11  84 

12.64 

4  50 

1  76 

8.05 

1.05 

1.10 

10 

IS 

B-F 

13.78 

14  58 

4.50 

1.75 

8.05 

1.05 

1.10 

12 

IS 

G-H 

14.08 

14  88 

4.50 

1.75 

8.20 

1.20 

1.10 

18 

U 

B-F 

16.08 

16  78 

4  50 

2.00 

2.15 

1.15 

1  10 

14 

14 

G-H 

16.32 

17.12 

4.50 

2.00 

2.36 

1  35 

1  10 

14 

16 

lEr-V 

18.16 

18.96 

4  50 

2.00 

2  30 

1.26 

1  15 

16 

16 

G-H 

18  54 

19  84 

4.50 

2.00 

2.55 

1  45 

1.15 

16 

18 

B-F 

20  34 

21.14 

4  50 

2.25 

2.45 

1.40 

1.15 

18 

18 

O-H 

20  78 

21  58 

4.50 

2.26 

2.76 

1.65 

1.15 

18 

20 

B-F 

22  64 

23  34 

4.60 

2.25 

2.55 

1.50 

1.15 

20 

20 

G-H 

23.02 

23.82 

4.50 

2  25 

2.85 

1.75 

1.20 

20 

24 

B-F 

26.90 

27.90 

5.00 

2  25 

2.85 

1.70 

1.20 

24 

20 

E 

33.10 

34.10 

600 

2.25 

8.25 

1  80 

1.50 

30 

SO 

P 

33.46 

34  46 

600 

2.26 

8.50 

2.00 

1.56 

30 

20 

E 

39.60 

40  60 

5.00 

2.25 

8  70 

2  05 

1.70 

36 

80 

F 

40.04 

41.04 

600 

2.25 

4.00 

2.30 

1.80 

36 

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1S46 


^—WATER  WORKS. 


^JS 


22    2S28    ;$8S 

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CAST  IRON  PIPE,  HIGH  PRESSURE.    LUGS. 


1247 


30. — Lugs. 

Number  and  Weights  of  Liigs  on  Outletfl  of  Different  ^ixes, 

(A.  W.  W.  A). 


4  Log*.  1S.14  iBcbM 
8  Lngi^  4940  iadiM 


Pig.  80a. 


•  Jjagp,  1646  lachM 


Pig.  30b. 


Nomloal 
Diameter 

Outlet. 

Incbet. 

Number 

of  Paire  of 

Luga. 

Approximate 

Weight  LURS 

on  One  Bell. 

Pounds. 

Nominal 
Diameter 

Outlet. 

Inches. 

Number 

of  Pairs  of 

Lugs. 

Approximate 

Weight  Lugs 

on  One  Bell, 

Pounds. 

12 
14 
16 
18 
20 
24 

32 
82 
56 
66 
66 
66 

30 
36 
42 
48 
54 
60 

6 
6 
8 

8 
8 
8 

80 
80 

in 

114 
134 
137 

Two  pairs  of  lugs  are  placed  on  the  vertical  axis  of  each  bell,  the  others 
jtt  equal  distances  around  circumference,    //  —  depth  of  bell  on  all  sizes. 

^—2.60  inches,  X— 1.25  inches.  y-«1.63  inches,  for  12  to  24  inches 
jncltisive. 

^.3.00  inches,  X-1.50  inches,  y-2.00  inches,  for  30  to  60  inches 
jncltisive. 


d  by  Google 


134B 


^—WATER  WORKS. 


81,  82. — Properties  of  Curves,  Bell  and  Spigot,  }i,  H.  A- 
3         (A.W.W.A.) 


Pig.  '6\. 
Table  81 


M  Corves. 

HCurvec 

i^Cnrroa. 

?o 

1 

DlmeniUons. 

ill 

11 

1 

DlmeosloDS. 

M«*^ 

DlmeiMioiiSwSti^ 

fi 

Inches. 

Inches. 

III 

Inches. 

aSi 

t 

r 

k 

t 

r 

k 

r 

k 

<^£ 

4 

D 

0.52 

16 

22.60 

82 

4 

D 

0  52 

24 

18.40 

66 

48 

18.70 

60 

6 

D 

0.55 

24 

18.40 

105 

48 

18.70 

lOi 

« 

D 

0.S5 

16 

22.60 

180       8 

D 

0.60 

24 

18.40 

150 

48 

18.70 

188 

MA       »0 

D 

0.68 

24 

18.40 

202 

48 

18.70 

M 

8 

D 

0.60 

16 

22.60 

200      ,2 

D 

0.75 

24 

18.40 

265 

48 

18.70 

861 

10 

D 

0.68 

16 

22.60 

278     1« 

B 

0.66 

86 

27.60 

359 

72 

88.10 

811 

14 

D 

0.82 

36 

87.60 

442 

72 

88. 10 

881 

12 

D 

0.75 

16 

22.60 

866 

16 

B 

0.70 

36 

27.60 

445 

72 

88.10 

888 

16 

D 

0.89 

36 

r.60 

658 

72 

28.10 

4M 

U 

B 

0  66 

18 

25.50 

406 

18 

B 

0.75 

86 

27.60 

533 

72 

28.10 

664 

14 

D 

0.82 

18 

25.50 

604 

18 

D 

0.96 

36 

27.60 

663 

72 

28.10 

574 

r«.       20 

B 

0.80 

48 

86.70 

758 

06 

87.80 

076 

16 

B 

0.70 

24 

84.00 

594      20 

D 

1.03 

48 

86.70 

964 

96 

37.50 

858 

16 

D 

0.89 

24 

34.00 

750      24 

B 

0.89 

60 

45.90 

1181 

120 

46.80 

ton 

24 

D 

1  16 

60 

45.90 

1515 

120 

40.80 

im 

18 

B 

0.76 

24 

34.00 

710     30 

A 

0.88 

60 

45.90 

1475 

120 

46.80 

1842 

30 

B 

1.03 

60 

45  90 

1684 

120 

46.80 

1128 

18 

D 

0.96 

24 

34.00 

888 

30 

C 

1.20 

60 

45.90 

1983 

120 

46.80 

1800 

30 

D 

1.37 

60 

46.90 

2291 

120 

46.80 

1060 

20 

B 

0.80 

24 

34.00 

840 

36 

A 

0  99 

90 

68.90 

2472 

180 

70.20 

2472 

20 

D 

1.03 

24 

34.00 

1070 

36 

B 

1.16 

90 

68.90 

2916 

180 

70.80  !  2916 

36 

C 

1.36 

90 

68.90 

8430 

180 

70.80     3430 

24 

B 

0.89 

30 

42  40 

1290 

36 

D 

1.58 

90 

68.90 

4012 

180 

70.80 

4012 

42 

A 

1.10 

90 

68.90 

3286 

180 

70.10 

3186 

24 

D 

1.16 

30 

42.40 

1656 

42 

B 

1.28 

90 

68.90 

3778 

180 

70.80 

8778 

42 

c 

1.54 

90 

68.90 

4600 

180 

70.20 

406 

80 

A 

0.88 

36 

50.90 

1814 

42 

D 

1.78 

90 

68.90 

6360 

180 

70.80 

5810 

80 

B 

1.03 

36 

50.90 

2082 

48 

A 

1.26 

90 

68.90 

4330 

180 

70.10 

4136 

48 

B 

1.42 

90 

68.90 

4830 

180 

70.10 

4820 

80 

C 

1.20 

36 

50.90 

2454 

48 

C 

1.71 

90 

68.90 

5796 

180 

70.20 

8796 

48 

D 

1.96 

90 

68.90 

6750 

180 

70.10 

6750 

80 

D 

1.87 

36 

50.90 

2836 

54 

A 

1.85 

90 

68.90 

5180 

180 

70.20 

8188 

86 

A 

0.99 

48 

67.90 

2964 

54 
54 

B 
C 

1.66 
1.90 

90 
90 

68.90 
68.90 

5990 
73)0 

180 
180 

70.28 
T0.20 

8098 

7388 

86 

B 

1.15 

48 

67.90 

3500 

54 

D 

2.23 

90 

68.90 

8680 

180 

70.10 

06» 

60 

A 

1.89 

90 

68.90 

5990 

180 

70.10 

8098 

86 

C 

1.36 

48 

67.90 

4120 

60 

B 

1.67 

90 

68.90 

7130 

180 

70.10 

7ia 

60 

C 

2.00 

90 

68.90 

8590 

180 

70.20 

8588 

86 

D 

1.58 

48 

67.90 

4820 

60 

D 

2.38 

90 

68.90 

10240 

180 

70.10 

10248 

5«>   8  inches  on  sizes  4  and  6  inches.        5«>  10  inches  on  sizes  8  tocfaes. 

o— 12  inches  on  sizes  10  to  30  inches. 

o  —  6  inches  on  %  Curves  on  sizes  4  to  30  inches  inclusive. 

o  —  <J  inches  on  A  Curves  on  sizes  4  to  12  inches  inclusi%»Jp 

AU  weights  are  approximate.  o 


C,  I.  PIPE— CURVES— BELL  AND  SPIGOT, 


1249 


83,  34. — Propbrtibs  op  Curvbs,  Bbll  and  Spigot. — Oppsbts. 
(A.  W.  W.  A.) 


Pig.  83b.  Pig.  34. 

All  dimensions  are  in  inches. 
Tablb  88.  Tablb  34. 


1 

.1 

A  curves. 

A  Curves.* 

onsets. 

i 

t 

r 

k 

r 

k 

is4  U 

i 

r 

■ 

g 

<? 

D 

0.52 

120 

23.53 

66 

4 

D 

8 

35.85 

91 

D 

0.55 

120 

33.52 

104 

D 

0.60 

120 

23.52 

150 

6 

D 

14 

46.26 

183 

D 

0.68 

120 

23.52 

192 

D 

0.75 

120 

23.62 

350 

8 

D 

15 

48.00 

280 

B 

0.66 

180 

35.28 

364 

D 

0.82 

180 

35.28 

450 

10 

D 

16 

49.70 

300 

B 

0.70 

180 

35.28 

453 

D 

0.89 

180 

35.28 

570 

12 

D 

17 

51.45 

530 

B 

0.75 

180 

35.28 

543 

D 

0.96 

180 

35.28 

674 

14 

B 

18 

63.70 

.  555 

B 

0.80 

240 

47.05 

808 

490 

47.10 

808 

D 

1.03 

240 

47.06 

1028 

480 

47.10 

1028 

14 

D 

18 

53.70 

695 

B 

0.89 

240 

47.05 

1080 

480 

47.10 

1080 

I> 

1.16 

240 

47.05 

1380 

480 

47.10 

1380 

16 

B 

19 

55.40 

708 

A 

0.88 

240 

47.05 

1350 

480 

47.10 

1850 

B 

1.03 

240 

47.05 

154U 

480 

47.10 

1540 

16 

D 

19 

56.40 

900 

C 
D 

1.20 
1.37 

240 
240 

47.05 
47.06 

18IU 
2090 

480 
480 

47.10 
47.10 

1810 
2090 

7i 

a  . 

""■" 

A 

0.99 

240 

47.05 

1790 

480 

47.10 

1790 

B 

1.15 

240 

47.05 

2100 

4S0 

47.10 

2100 

i§<  B 

t 

k 

8 

n 

o 

1.36 

240 

47.05 

3470 

480 

47.10 

2470 

ol 

a 

D 
A 

1.58 
1.10 

240 
240 

47.05 
47.05 

8880 
2380 

480 
480 

47.10 
47.10 

2880 
2380 

^0 

n_ 

I 

4 

D 

0.52 

13.85 

10.00 

2.00 

B 

1.28 

240 

47.05 

3720 

480 

47.10 

2720 

O 

1.54 

240 

47.06 

8310 

480 

47.10 

3310   e 

D 

0.55 

24.25 

10  00 

2.00 

D 

•1.78 

240 

47.05 

3850 

480 

47.10 

3850 

A 

1.26 

240 

47.05 

3150 

480 

47.10 

3150 

D 

0.60 

26.00 

10.00 

2.00 

B 

1.42 

240 

47.05 

3480  ' 

480 

47  lU 

3480 

C 

1.71 

240 

47.05 

4170  1 

48U 

47.10 

4170 

D 

0.68 

27.70 

10.00 

2.00 

D 

1.96 

240 

47.05 

4860 

480 

47.10 

4860 

A 

1.35 

240 

47.05 

3760 

480 

47.10 

3750 

D 

0.76 

29.45 

10.00 

2.00 

B 

1.56 

240 

47.05 

4330  I 

480 

47.10 

4330 

C 

1.90 

240 

47.05 

5290 

480 

47.10 

5290 

B 

0.66 

31  20 

10.00 

2.50 

D 

2.33 

340 

47.05 

6220 

480 

47.10 

6220 

A 

1.39 

240 

47.05 

4J40 

480 

47.10 

4340 

D 

0.82 

31.20 

10.00 

2.50 

B 

1.67 

240 

47.05 

5140 

480 

47.10 

6140 

C 

2.00 

240 

47.05 

62U0 

480 

47.10 

6200 

B 

0.70 

32.90 

10.00 

2.60 

D 

3.38 

240 

47.06 

7400 

480 

47.10 

7400 

D 

0.83 

33.90 

10  00 

2  50 

♦Plrit  three  columns,  for  20*  to  60"  diam.,  apply  also  to  ^  ctirvcs. 


1360 


^— WATER  WORKS, 

85. — ^Propbrtibs  of  Brancbbs. — 8-Way  and  4- Wat. 
(A.  W.  W.  A.) 


Fig.  36. 


Nominal  Dlam. 
Inclice. 

aafli. 

Approxlmat«  Weights.  Pounds 

A 

B 

H 

J 

I 

3- Way  Bnuiehee^  4- Way  Bnuwhn 

2  Bells. 

3  Bellt.    3  BeUs.  f  4  BeibL 

4 

8 

D 

11 

23 

11 

121 

120             1S3 

I5S 

4 

4 

D 

11 

23 

11 

125 

128            164 

166 

6 

8 

.  D 

12 

24 

12 

173 

170            JOT 

304 

« 

4 

D 

12 

24 

12 

185 

183            223 

231 

6 

6 

D 

12 

24 

la 

203 

200 

259 

257 

8 

4 

D 

13 

25 

13 

263 

255 

301 

^94 

8 

6 

D 

18 

25 

13 

278 

270 

833 

333 

8 

8 

D 

18 

25 

13 

301 

294 

878 

172 

10 

4 

D 

14 

26 

14 

356 

338 

895 

trt 

10 

6 

D 

14 

26 

14 

371 

351 

424 

4M 

10 

8 

D 

14 

26 

14 

389 

871 

461 

443 

10 

10 

D 

14 

26 

14 

414 

395 

511 

498 

12 

4 

D 

15 

27 

15 

478 

445 

514 

486 

la 

6 

D 

15 

r 

15 

486 

458 

MO 

512 

IS 

8 

D 

16 

27 

15 

502 

474 

573 

MS 

la 

10 

D 

15 

27 

15 

519 

491 

605 

677 

la 

12 

D 

If 

27 

15 

540 

512 

661 

683 

14 

4 

B 

16 

28 

16 

486 

480 

531 

530 

14 

4 

D 

16 

Z& 

16 

614 

588 

666 

641 

14 

6 

B 

16 

28 

16 

500 

495 

560 

655 

14 

6 

D 

16 

28 

16 

634 

608 

736 

7M 

14 

8 

B 

16 

28 

16 

515 

510            600 

616 

14 

8 

D 

16 

28 

16 

662 

636            787 

761 

14 

10 

B 

16 

28 

16 

535 

525 

635 

625 

14 

10 

D 

16 

28 

16 

679 

658 

822 

796 

14 

12 

B 

16 

28 

16 

560 

550 

680 

678 

14 

12 

D 

16 

28 

16 

698 

672 

860 

834 

14 

14 

B 

16 

28 

16 

575 

569 

733 

715 

14 

14 

D 

16 

28 

16 

750 

724 

938 

9a 

16 

4 

B 

17 

29 

17 

616 

610 

675 

679 

16 

4 

D 

17 

29 

17 

783 

760 

864 

841 

16 

6 

B 

17 

29 

17 

680 

625 

696 

696 

16 

6 

D 

17 

29 

17 

808 

779 

902 

879 

16 

8 

B 

17 

29 

17 

645 

640 

TSO 

725 

16 

8 

D 

17 

29- 

17 

881 

806 

961 

9n 

16 

10 

B 

17 

29 

17 

660 

655 

760 

765 

16 

10 

D 

17 

29 

17 

872 

849 

1043 

1019 

16 

12 

B 

17 

29 

IT 

685 

680 

80S 

8P8 

16 

12 

D 

17 

29 

17 

884 

861 

1066 

lOO 

16 

14 

B 

17 

29 

17 

695 

660 

825 

828 

CAST  IRON  PIPE— BRANCHES 


1261 


85. — Branchbs. — 3-Wat  and  4-Way. — Continued. 


1  Dlam. 
let. 

aaas. 

DlmenslonB.  Inches 

Approximate  Weights.  Pounds. 

B 

H 

J 

I 

3- Way  Branches 

4-way  Branches 

2  Bells 

3BeUs. 

3  Bells. 

4  Bells. 

M 

D 

17 

29 

17 

903 

880 

1104 

1082 

le 

B 

17 

29 

17 

729 

727 

904 

901 

16 

D 

17 

29 

17 

991 

969 

1282 

1259 

4 

B 

18 

30 

18 

756 

760 

820 

816 

4 

D 

18 

90 

18 

958 

927 

1046 

1020 

6 

B 

18 

30 

18 

766 

760 

840 

835 

« 

D 

18 

30 

18 

968 

942 

1075 

1049 

8 

B 

18 

30 

18 

780 

775 

870 

866 

8 

D 

18 

30 

18 

1000 

974 

1140 

1114 

10 

B 

18 

30 

18 

795 

790 

900 

895 

10 

D 

18 

30 

18 

1038 

1012 

1216 

1190 

12 

B 

18 

30 

18 

816 

810 

940 

935 

12 

D 

18 

30 

18 

1076 

1049 

1290 

1264 

14 

B 

18 

30 

18 

825 

820 

955 

950 

14 

D 

18 

30 

18 

1083 

1067 

1306 

1380 

16 

B 

18 

30 

18 

866 

850 

1020 

1015 

16 

D 

18 

30 

18 

1108 

1082 

1356 

1330 

18 

B 

18 

30 

18 

895 

889 

1101 

1096 

18 

D 

18 

30 

18 

1170 

1144 

1480 

1454 

4 

B 

19 

31 

19 

928 

916 

1006 

999 

4 

D 

19 

31 

19 

1172 

1148 

1273 

1248 

6 

B 

19 

31 

19 

930 

920 

1010 

1000 

6 

D 

19 

31 

19 

1188 

1164 

1304 

1280 

8 

B 

19 

31 

19 

946 

935 

1035 

1025 

8 

D 

19 

31 

19 

1212 

1188 

1352 

1838 

10 

B 

19 

31 

19 

966 

945 

1060 

1060 

10 

D 

19 

31 

19 

1262 

1227 

1431 

1407 

12 

B 

•  19 

31 

19 

976 

965 

1100 

1090 

12 

D 

19 

31 

19 

1288 

1263 

1502 

1479 

14 

B 

19 

31 

19 

980 

970 

1110 

1100 

14 

D 

19 

31 

19 

1342 

1818 

1618 

1588 

16 

B 

19 

31 

19 

1010 

1000 

1170 

1160 

16 

D 

19 

31 

19 

1347 

1323 

1622 

1597 

18 

B 

19 

31 

19 

1036 

1026 

1225 

1216 

18 

D 

19 

31 

19 

1366 

1341 

1658 

1634 

20 

B 

19 

31 

19 

1077 

1070 

1314 

1807 

20 

D 

19 

31 

19 

1462 

1438 

1852 

1828 

6 

B 

21 

33 

21 

1309 

1289 

1425 

1406 

6 

D 

21 

33 

21 

1670 

1637 

1809 

1776 

8 

B 

21 

33 

21 

1323 

1303 

1453 

1438 

8 

D 

21 

33 

21 

1697 

1664 

1863 

1830 

10 

B 

21 

33 

21 

1341 

1321 

1489 

1469 

10 

D 

21 

33 

21 

1732 

1699 

1933 

1900 

12 

B 

21 

33 

21 

1362 

1342 

1632 

1511 

12 

D 

21 

33 

21 

1768 

1785 

2006 

1978 

14 

B 

21 

33 

21 

1402 

1381 

1609 

1589 

14 

D 

21 

33 

21 

1810 

1777 

2088 

2058 

16 

B 

21 

33 

21 

1443 

1423 

1694 

1673 

16 

■D 

21 

33 

21 

1858 

1825 

2185 

2151 

18 

B 

21 

33 

21 

1460 

1440 

1727 

1706 

18 

D 

21 

33 

21 

1885 

1853 

2238 

2206 

20 

B 

21 

33 

21 

1474 

1454 

1756 

1736 

20 

D 

21 

33 

21 

2025 

1991 

2618 

2484 

lizyd  Uy  VJ 

UUyiL 

1253 


M.—WATER  WORKS. 


85. — Branchbs. — 8-Way  akd  4-Way. — Coatintied. 


NomloAl  Dlam. 
Indies. 

Dlmeoilona.  Tnohes 

ApprozlinAte  Weights.  PotiDd«. 

CI  MB. 

A 

B 

H 

J 

I 

3-WA7  Branches 

4-W»7  Branches 

2BHIB. 

8  Bens. 

3  BeUft. 

4  Bcils. 

24 

24 

B 

21 

33 

21 

1523 

1603 

1854 

1834 

24 

24 

D 

21 

33 

21 

2146 

2113 

2727 

26M 

80 

6 

A 

13 

25 

24 

1272 

1300 

1407 

14M 

80 

6 

B 

18 

26 

24 

14S3 

1417 

1680 

19«S 

30 

6 

C 

13 

25 

24 

1698 

1673 

1870 

18SD 

80 

6 

D 

13 

25 

24 

1984 

1930 

2118 

2099 

80 

8 

A 

14 

26 

24 

1318 

1346 

1463 

1481 

30 

8 

B 

14 

26 

24 

1482 

1466 

1624 

1€» 

30 

8 

C 

14 

26 

24 

1765 

1745 

1953 

1»4 

30 

8 

D 

14 

26 

24 

2004 

1990 

2182 

21C8 

80 

10 

A 

15 

27 

24 

1369 

1396 

1512 

1549 

30 

10 

B 

15 

27 

24 

1538 

1521 

1685 

1668 

30 

10 

C 

15 

27 

24 

1857 

1837 

2075 

20SC 

30 

10 

D 

16 

27 

24 

2108 

2094 

2319 

230S 

30 

12 

A 

15 

27 

24 

1896 

1420 

1555 

1589 

30 

12 

B 

15 

27 

24 

1555 

1640 

1715 

1709 

30 

12 

C 

15 

27 

24 

1911 

1891 

2184 

2164 

30 

12 

D 

15 

27 

24 

2154 

2140 

2411 

2398 

30 

14 

A 

18 

30 

26 

1547 

1575 

1737 

1764 

30 

14 

B 

18 

30 

26 

1805 

1789 

2086 

2069 

80 

U 

C 

18 

30 

26 

2159 

2140 

2497 

1477 

80 

14 

D 

18 

30 

26 

2567 

2553 

3026 

3018 

30 

16 

A 

19 

31 

26 

1648 

1675 

1805 

1832 

30 

16 

B 

19 

31 

26 

1899 

1883 

2200 

2184 

80 

16 

C 

19 

81 

26 

2272 

2253 

2662 

2648 

30 

16 

D 

19 

31 

26 

2692 

2678 

8306 

8191 

80 

18 

A 

20 

34 

26 

1757 

1741 

2024 

2387 

209T 

30 

18 

B 

20 

34 

26 

2044 

1976 

3318 

30 

18 

C 

20 

34 

26 

2434 

2353 

2862 

2781 

30 

18 

D 

20 

34 

26 

2805 

2791 

3361 

3348 

30 

20 

A 

21 

36 

26 

1857 

1818 

2157 

2118 

30 

20 

B 

21 

36 

26 

2182 

2088 

2584 

2499 

SO 

20 

C 

21 

36 

26 

2667 

2565 

3227 

8128 

30 

20 

D 

21 

36 

26 

3041 

2921 

3657 

3638 

30 

24 

A 

23 

38 

26 

1979 

1940 

2312 

2274 

30 

24 

B 

23 

38 

26 

2313 

2219 

2742 

Ka 

30 

24 

C 

23 

38 

26 

2847 

2736 

3474 

3363 

30 

24 

D 

23 

38 

26 

8290 

3170 

4014 

3896 

30 

30 

A 

26 

43 

26 

2212 

3129 

2602 

2520 

30 

30 

B 

26 

43 

26 

2599 

2453 

3106 

29(9 

30 

30 

C 

26 

43 

26 

3310 

8137 

4110 

39r 

30 

30 

D 

26 

43 

26 

3850 

3660 

4799 

4609 

36 

8 

A 

14 

26 

27 

1751 

1777 

1938 

1963 

36 

8 

B 

14 

26 

27  , 

2055 

2073 

2268 

2287 

3^ 

8 

C 

•14 

26 

27 

2421 

2433 

2679 

2(9t 

36 

8 

D 

14 

26 

27 

2780 

27W 

3038 

8039 

36 

10 

A 

15 

27 

27 

1810 

1833 

1996 

2021 

36 

10 

B 

15 

27 

27 

2128 

2147 

2345 

2364 

36 

10 

C 

15 

27 

27 

2534 

2546 

•  2«2 

2334 

36 

10 

D 

15 

27 

27 

2903 

2902 

3188 

2188 

36 

12 

A 

16 

28 

27 

1884 

1909 

2084 

2169 

36 

12 

B 

16 

28 

27 

2219 

2238 

2458 

24n 

86 

12 

C 

16 

28 

27 

2644 

2666 

2963 

29n 

CAST  IRON  PIPE— BRANCHES. 


1263 


86. — ^Branchbs. — 3-Wat  and  4-Way. — Contintied. 


Nominal  Dlam. 
InoHes 

Dlmenalona.  Inches 

Approximate  Weights.  Pounds. 

aaas 

A 

B 

H 

J 

I 

3-Way  Branches]  4-Way  Branches 

2BeU8. 

3  Bells.  3  Bella. 

4  Bells. 

36 

13 

D 

16 

28 

27 

3032 

3033 

3349 

3350 

96 

14 

A 

18 

30 

29 

2039 

2005 

3379 

3304 

96 

14 

B 

18 

80 

29 

2416 

2438 

ro9 

r28 

96 

14 

C 

18 

30 

29 

2872 

2883 

8251 

3263 

96 

14 

D 

18 

30 

29 

8470 

8470 

4033 

4033 

96 

16 

A 

19 

31 

29 

3135 

2100 

3410 

3436 

96 

10 

B 

19 

31 

29 

2521 

2540 

2853 

3873 

96 

16 

C 

19 

31 

29 

3003 

3014 

3431 

3443 

96 

16 

D 

19 

31 

29 

3018 

8017 

4331 

4230 

96 

18 

A 

20 

34 

29 

3279 

3240 

3581 

2548 

96 

18 

B 

20 

34 

29 

2701 

2050 

3073 

3023 

96 

18 

C 

20 

34 

29 

3206 

3180 

8073 

8604 

96 

18 

D 

20 

84 

29 

3852 

8756 

4500 

4409 

96 

30 

A 

•  21 

36 

29 

2409 

2340 

3753 

3689 

96 

30 

B 

21 

36 

29 

2885 

3800 

3336 

8261 

96 

30 

C 

31 

36 

29 

3537 

8430 

4213 

4101 

96 

30 

D 

21 

36 

29 

4050 

3905 

4757 

4613 

96 

24 

A 

23 

38 

29 

2451 

2513 

3844 

3907 

96 

34 

B 

23 

88 

29 

3099 

3014 

3624 

3539 

96 

24 

C 

23 

38 

29 

3800 

3095 

4585 

4474 

96 

24 

D 

23 

38 

29 

4511 

4300 

5307 

5161 

96 

30 

A 

26 

43 

29 

2830 

2708 

8242 

8120 

36 

30 

B 

26 

43 

29 

8594 

3438 

4335 

4179 

96 

30 

C 

26 

43 

29 

4248 

4055 

5140 

4947 

36 

90 

D 

26 

43 

29 

5100 

4918 

6192 
8539 

5950 

36 

36 

A 

29 

46 

29 

3007 

2940 

3418 

36 

86 

B 

29 

46 

29 

4040 

3891 

4956 

4800 

36 

36 

C 

29 

46 

29 

4788 

4595 

5867 

5673 

96 

36 

D 

29 

46 

29 

6810 

5507 

7099 

6857 

43 

13 

A 

16 

28 

30 

2507 

2577 

8467 

8537 

43 

13 

B 

16 

28 

30 

2070 

2889     3131 

3170 

43 

12 

C 

16 

28 

30 

3478 

8507     3830 

3860 

43 

13 

D 

16 

28 

30 

3971 

3989     4307 

4325 

43 

14 

A 

18 

30 

32 

2071 

2739     2942 

3010 

43 

14 

B 

18 

30 

32 

3075 

8114 

3400 

3440 

43 

14 

C 

18 

30 

33 

3747 

8770 

4147 

4177 

43 

14 

D 

18 

30 

32 

4590 

4609 

5288 

5306 

43 

.  1« 

A 

19 

31 

32 

2778 

2840 

8080 

3148 

43 

16 

B 

19 

31 

32 

3196 

3235     3552 

3592 

43 

16 

C 

19 

31 

32 

3891 

3920     4325 

4354 

43 

16 

D 

19 

31 

32 

4754 

4772     5487 

5506 

43 

18 

A 

20 

34 

33 

2950 

2941     3268 

3258 

43 

18 

B 

20 

34 

32 

3407 

8357     3794 

3744 

43 

18 

C 

20 

34 

32 

4393 

4312     5108 

5028 

43 

18 

D 

20 

34 

32 

5049 

4939    6819 

5709 

43 

20 

A 

21 

36 

32 

3104 

3050     3459 

8411 

43 

30 

B 

21 

30 

32 

3582 

3480     4009 

3913 

43 

20 

C 

21 

30 

32 

4016 

4479     5387 

6251 

43 

20 

D 

21 

30 

32 

5297 

6123  1   0122 

5948 

43 

34 

A 

23 

38 

32 

3314 

3200 

3724 

3676 

43 

34 

B 

23 

38 

83 

3853 

3750 

4370 

4274 

42 

24 

C 

23 

38 

33 

4906 

4829 

5806 

5730 

42 

34 

D 

23 

88 

33 

5709 

6535 

6579 

6405 

IC 

1264 


M.— WATER  WORKS. 


85. — Branchbs. — 3-Way  and  4-Way. — Concluded. 


Nominal  DlAin. 
Inches. 

Ai»proximate  Wolghta.  Poundiu 

aaas. 

3- Way  Branchea 

4-Wa7  Braaebes 

A 

B 

H 

J 

I 

2  Bells. 

SBeUs. 

3  Bells. 

4  Belta. 

42 

30 

A 

26 

43 

32 

3679 

3553 

4144 

4018 

42 

30 

B 

26 

43 

32 

4554 

4370 

5416 

S23t 

42 

30 

C 

26 

43 

32 

5649 

5402 

6675 

•^8 

42 

30 

D 

26 

43 

32 

6561 

6258 

7729 

7438 

42 

36 

A 

29 

46 

32 

4076 

3950 

4705 

4579 

42 

86 

B 

29 

46 

32 

4908 

4718 

5845 

5660 

42 

86 

C 

29 

46 

32 

6160 

5904 

7261 

7015 

42 

36 

D 

29 

46 

32 

7187 

6884 

8512 

8200 

42 

42 

A 

32 

49 

32 

4393 

4267 

5109 

4983 

42 

42 

B 

82 

49 

82 

5533 

5348 

6641 

6485 

42 

42 

C 

32 

49 

32 

7001 

6755 

8392 

8146 

42 

42 

D 

32 

49 

32 

8158 

7855 

9803 

9500 

48 

12 

A 

29 

33 

3266 

3319 

3853 

S70T 

48 

12 

B 

29 

33 

3758 

3804 

4107 

4160 

48 

12 

C 

29 

33 

4510 

4576 

4940 

6007 

48 

12 

D 

29 

33 

5564 

5624 

6376 

4436 

48 

14 

A 

30 

35 

3422 

3476 

3762 

3815 

48 

14 

B 

30 

35 

4173 

4226 

4836 

4880 

48 

14 

C 

30 

35 

4965 

5030 

5712 

B7T8 

48 

14 

D 

80 

35 

5754 

5815 

6596 

4650 

48 

16 

A 

31 

35 

3565 

3619 

3947 

4001 

48 

16 

B 

31 

35 

4046 

4098  ^ 

4466 

4519 

48 

16 

C 

31 

35 

5055 

5121 

5755 

S82I 

48 

16 

D 

31 

35 

5967 

6028 

6860 

4921 

48 

18 

A 

20 

34 

35 

3775 

3729 

4166 

4130 

48 

18 

B 

20 

34 

35 

4287 

4225 

4718 

4«5S 

48 

18 

C 

20 

34 

35 

5479 

5407 

6S28 

6256 

48 

18 

D 

20 

34 

35 

6328 

6327 

72M 

7188 

48 

20 

A 

21 

36 

35 

3956 

3860 

4378 

4283 

48 

20 

B 

21 

36 

35 

4500 

4380 

4973 

iSSZ 

48 

20 

C 

21 

36 

35 

5745 

5604 

6652 

65U 

48 

20 

D 

21 

36 

35 

6607 

6425 

7574 

7393 

48 

24 

A 

23 

38 

35 

4221 

4125 

4706 

4600 

48 

24 

B 

23 

38 

35 

5028 

4908 

5798 

5678 

48 

24 

C 

23 

38 

35 

6193 

6052 

7272 

7181 

48 

24 

D 

23 

38 

35 

7064 

6882 

7994 

7811 

48 

30 

A 

26 

43 

35 

4748 

4553 

6361 

5166 

48 

30 

B 

26 

43 

35 

5685 

6451 

6653 

6418 

48 

30 

C 

26 

43 

35 

7042 

6762 

8265 

70» 

48 

30 

D 

26 

43 

35 

8051 

7708 

9303 

8809 

48 

36 

A 

29 

46 

35 

5150 

4953 

5859 

S8C3 

48 

36 

B 

29 

46 

35 

6322 

6088 

78© 

7148 

48 

36 

C 

29 

46 

35 

7603 

7323 

8915 

8635 

48 

86 

D 

29 

46 

85 

8830 

8487 

10336 

9998 

48 

42 

A 

32 

49 

35 

5603 

5307 

6266 

ooot 

48 

42 

B 

32 

49 

35 

6881 

6587 

7973 

7739 

48 

42 

c 

32 

49 

35 

8278 

7999 

9760 

9470 

48 

42 

D 

32 

49 

35 

9644 

9301 

11367 

11024 

48 

48 

A 

35 

52 

35 

6043 

6846 

7043 

6846 

48 

48 

B 

35 

52 

35 

7659 

7424 

9076 

8841 

48 

48 

C 

35 

52 

35 

9229 

8960 

11006 

10731 

48 

48 

D 

35 

52 

35 

CAST  IRON  PIPE—BRANCHES, 


1255 


35. — ^Propbrtibs  of  Y 
Branchbs,  Typb  1. 

(A.  W.  W.  A.) 


f/M 




! 

» 

iK^.  36. 

Nominal 
DlaoLlDa. 

8 

P 

V 

w 

n 

r 

Thloknen,  Ins. 

^ii 

e 

f 

c 

ti 

t2 

t3 

12 

12 

D 

16  00 

21.50 

8.00 

9.79 

1.17 

30 

0.75 

1.08 

0.75 

687 

14 

14 

B 

16.00 

24.00 

3.00 

11.30 

1.08 

30 

0.66 

0.99 

0.66 

738 

14 

14 

D 

16.00 

24.00 

9.00 

11.30 

1.32 

30 

0.82 

1.22 

0.82 

894 

U 

16 

B 

17.00 

27.50 

10.50 

13.00 

1.12 

30 

0.70 

1.03 

0.70 

942 

If 

16 

D 

17  00 

27.50 

10.60 

13.00 

1.39 

30 

0.89 

1.29 

0.89 

1276 

18 

18 

B 

18.00 

30.00 

12.00 

14.70 

1.17 

30 

0.75 

1.08 

0.75 

1266 

18 

18 

D 

18.00 

30.00 

12.00 

14.70 

1.46 

30 

0.96 

1.36 

0.96 

1607 

20 

20 

B 

18.00 

34.00 

13.60 

16.40 

1.26 

30 

0.80 

1.16 

0.80 

1636 

20 

20 

D 

18.00 

34.00 

13.50 

16.40 

1.57 

30 

1.03 

1.46 

1.03 

2296 

24 

20 

B 

12.00 

34.00 

13.50 

16.40 

1.26 

30 

0.89 

1.16 

0.80 

1663 

24 

20 

D 

12.00 

34.00 

13.50 

16.40 

1.57 

30 

1.16 

1.46 

1.03 

2393 

24 

24 

B 

18.00 

38.00 

15.25 

19.30 

1.36 

30 

0.89 

1.26 

0.89 

2300 

24 

24 

D 

18.00 

38.00 

15.25 

19.30 

1.75 

30 

1.16 

1.63 

1.16 

2957 

30 

24 

A 

12  00 

38.00 

15.25 

19.30 

1.36 

30 

0.88 

1.26 

0.89 

2171 

80 

24 

B 

12.00 

38.00 

15.25 

19.30 

1.36 

30 

1.03 

1.26 

0.89 

2217 

30 

24 

C 

12.00 

38.00 

15.25 

19.30 

1.75 

30 

1.20 

1.63 

1.16 

2717 

30 

24 

D 

12.00 

38.00 

15.25 

19.30 

1.75 

30 

1.37 

1.63 

1.16 

2811 

80 

30 

A 

18.00 

48.00 

18.00 

23.70 

1.32 

30 

0.88 

1.22 

0.88 

3153 

30 

30 

B 

18.00 

48.00 

18.00 

23,70 

1.59 

30 

1.03 

1.47 

1.03 

3687 

30 

30 

0 

18.00 

48.00 

18.00 

23.70 

1.88 

30 

1.20 

1.74 

1.20 

4285 

30 

80 

D 

18.00 

48.00 

18.00 

23.70 

2.17 

30 

1.37 

2.01 

1.37 

4941 

36 

30 

A 

10.00 

48  00 

18.00 

23.70 

1.32 

30 

0.99 

1.22 

0.88 

3343 

30 

30 

B 

10.00 

48.00 

18.00 

23.70 

1.59 

30 

1.15 

1.47 

1.03 

3874 

36 

30 

0 

10.00 

48.00 

18.00 

23.70 

1.88 

30 

1.36 

1.74 

1.20 

4486 

36 

30 

D 

10.00 

48.00 

18.00 

23.70 

2.17 

30 

1.58 

2.01 

1.37 

5189 

36 

36 

A 

18.00 

56.00 

21.00 

28.20 

1.50 

24 

0.99 

1.39 

0.99 

4949 

36 

36 

B 

18.00 

56.00 

21.00 

28.20 

1.79 

24 

1.15 

1.66 

1.15 

5858 

36 

86 

0 

18.00 

56.00 

21.00 

28.20 

2.13 

24 

1.36 

1.98 

1.36 

6804 

36 

36 

D 

18.00 

56.00 

21.00 

28.20 

2  48 

24 

1.58 

2.31 

1.58 

8082 

42 

30 

A 

6.00 

48.00 

18.00 

23.70 

1.32 

30 

1.10 

1.22 

0.88 

3368 

42 

30 

B 

6.00 

48.00 

18.00 

23.70 

1.59 

30 

1.28 

1.47 

1.03 

3890 

42 

30 

C 

6.00 

48.00 

18.00 

23.70 

1.88 

30 

1.54 

1.74 

1.20 

4543 

42 

80 

D 

6.00 

48.00 

18.00 

23.70 

2.17 

30 

1.78 

2.01 

1.37 

5241 

42 

86 

A 

10.00 

56.00 

21  00 

28  20 

1.50 

24 

1.10 

1.39 

0.99 

4904 

42 

86 

B 

10  00 

56.00 

21.00 

28.20 

1.79 

24 

1.28 

1.66 

1.15 

5789 

42 

36 

C 

10.00 

56.00 

21.00 

28.20 

2.13 

24 

1.54 

1.98 

1.36 

6761 

42 

36 

D 

10.00 

56.00 

21  00 

28.20 

2.48 

24 

1.78 

2.31 

1.58 

8025 

42 

42 

A 

18.00 

66.00 

25.00 

33.10 

1.72 

24 

1.10 

1.60 

1.10 

7394 

42 

42 

B 

18.00 

66  00 

25.00 

33.10 

2.05 

24 

1.28 

1.90 

1.28 

8417 

42 

42 

C 

18.00 

66.00 

25.00 

33.10 

2.46 

24 

1.54 

2.28 

1.54 

10877 

42 

42 

D 

18  00 

66  00 

25.00 

33.10 

2.85 

24 

1.78 

2.64 

1.78 

12073 

48 

36 

A 

2.00 

56.00 

21.00 

28.20 

1.50 

24 

1.26 

1.39 

0.99 

4727 

48 

36 

B 

2.00 

56.00 

21  00 

28.20 

1.79 

24 

1.42 

1.66 

1.15 

5584 

48 

36 

C 

2.00 

56.00 

21.00     28.20 

2.13 

24 

1.71 

1.98 

1.36 

6494 

48 

36 

D 

2.00 

56.00 

21.00     28.20 

2.48 

24 

1.96 

2.31 

1.58 

7731 

48 

42 

A 

10.00 

66.00 

25.00     33.10 

1.72 

24 

1.26 

1.60 

I.IO 

7346 

48 

42 

B 

10.00 

66.00 

25.00     33.10 

2.05 

24 

1.42 

1.90 

1.28 

8338 

48 

42 

C 

10.00 

66.00 

25.00     33.10 

2.46 

24 

1.71 

2.28 

1.54 

10249 

48 

42 

D 

10.00 

66.00 

25.00     33.10 

2.8.-) 

24 

1.96 

2.64 

1  78 

11924 

48 

48 

A 

18.00 

76.00 

28.00     37.60 

1.99 

24 

1.26 

1.86 

1.26 

10200 

48 

48 

B 

18.00 

76.00 

28.00     37.60 

2.32 

24 

1.42 

2.15 

1.42 

12132 

48 

48 

C 

18.00 

76.00 

28.00     37.60 

2.78 

24 

1.71 

2.57 

1.71 

14716 

48 

48 

D 

18.00 

76.00 

28.00     37.60 

3.20 

24 

1.96 

2.95 

1.94 

16965 

NoTB. — All  dimez2sions  are  in  inches. 


ISM 


^-'WATER  WORKS. 


87. — PROraRTIBS  OF  \ 

Ttpb  J. 
(A.  W.  W.  . 


4to20lndm. 


»tt4$k 


Nominal 

DlMn.lD8. 


TlilckneeB. 
Indim. 


m 


4 
• 
8 
10 
11 

14 
14 
10 
16 
18 

18 
20 
20 
84 
24 

24 
24 

80 
80 
80 

80 
86 
86 
86 
86 

42 
42 
42 

42 

42 
42 

48 
48 

48 
48 
48 
48 


11.50 
13.00 
14  00 
15.50 
15.50 

16.00 
16.00 
17.50 

17.50 
18.00 

18.00 
18.75 
18.75 
18.75 
18.75 

19.75 
19.75 
17.00 
17.00 
22.75 

22.76 
19.75 
19.75 
24.00 
24.00 

16.75 
16.75 
21.00 
21.00 

25.25 
25.25 
18.00 
18.00 

22.25 
22.25 
26.50 
26.50 


10.50 
18.00 
16.00 
18.50 
21.60 

24.00 
24.00 
31.00 
81.00 
84.00 

34.00 
87.00 
37.00 
40.00 
40.00 

42.00 
42.00 
49.50 
49.50 
52.50 

52.50 
56.00 
56.00 
60.00 
60.00 

63.00 
63  00 
66.00 
66.00 

69.00 
69.00 
71.00 
71.00 

74.00 
74.00 
77.00 
77.00 


7.18 
9.27 
11.85 
13.94 
16.64 

18.62 
18.62 
25.80 
25.80 
28.00 

28.00 
30.75 
30.75 


6.64 
7.46 
8.80 
9.12 
9.98 

10.78 
10.76 
11.60 
11.60 
12.00 

12.00 

12.50 
12.50 


2.18 
3.27 
8.85 
4.94 
4.64 

4.62 
4.62 
6.70 
6.70 
f.OO 

6.00 
6.50 
6.50 


NoTB.-All  dimensions  are  in  inches. 


0.52 
0.55 
0.60 
0.68 
0.75 

0.6« 
0.82 
0.70 
0.88 
0.75 

0.96 
0.80 
1.03 
0.89 
1.16 

0.80 
1.16 
0.88 
1.03 
0.8S 

1  08 
0  99 
1.15 
0  99 
1.15 

1.10 
1.28 
1.10 
1.28 

1.10 
1.28 
1.20 
1.42 

1.28 
1.42 
1.28 
1.42 


0.64 

193 

0.67 

181 

0.72 

891 

0.88 

434 

0.93 

633 

0.84 

696 

l.OQ 

9S5 

1.03 
1.29 
l.U 

1.44 

1.20 

i.se 

0.88 
1.08 

0.89 
1.16 
0.89 
0.» 
0.88 

1.03 
0.8S 
1.93 
0.99 
1.15 

0.88 
1.03 
0.99 

1.15 

1.19 
1.28 
0.91 

1.15 

1.19 
1-28 
1.2< 
1.43 


by  Google 


1413 
138 

n» 

17» 
2199 
22B3 


1178 
36:4 

430 
4» 
4135 

IIH 


90 


Sf3 

!C9 


9lt« 


CAST  IROiW  PIPE—BRANCHES. 


1267 


3. — Properties  op  Blow-ofp  Branches. 
(A.  W.  W.  A.) 


Figs.  38. 


Nominal 
Diam. 
laOus. 

1 

I 

P 

ThlckneBB. 
Inohea. 

i 

Nominal 
Diam. 
Inches. 

i 

■ 

P 

Thickness. 
Inches. 

i 

e 

f 

U 

ta 

6 

t 

h 

ta 

8 

D 

12 

7 

0.60 

0.62 

227 

36 

12 

A 

18 

23 

0.99 

0.76 

1702 

10 

D 

12 

8 

0.68 

0.52 

286 

36 

12 

B 

13 

23 

1.15 

0.75 

1972 

10 

D 

12 

8 

0.68 

0.55 

300 

36 

12 

c 

13 

23 

1.36 

0.75 

2285 

12 

D 

12 

10 

0.75 

0.52 

365 

36 

12 

D 

13 

23  < 

1.68 

0.75 

2627 

13 

D 

12 

10 

0.75 

0.55 

379 

42 

12 

A 

16 

26 

1.10 

0.75 

3482 

14 

B 

12 

11 

0.66 

0.52 

400 

48 

12 

B 

16 

26 

1.28 

0.75 

r38 

U 

D 

12 

0.82 

0.52 

471 

42 

12 

C 

16 

26 

1.64 

0.75 

8271 

14 

B 

12 

11 

0.66 

0.55 

415 

42 

12 

D 

15 

26 

1.78 

0.75 

3768 

14 

D 

12 

11 

0.82 

0.55 

486 

42 

16 

A 

16 

26 

1.10 

0.70 

2489 

16 

B 

12 

12 

0.70 

0.52 

497 

42 

16 

B 

15 

26 

1.28 

0.70 

8786 

If 

D 

12 

12 

0.89 

0.52 

697 

42 

16 

C 

15 

26 

1.54 

0.89 

3366 

16 

B 

12 

12 

0.70 

0.55 

513 

42 

16 

D 

15 

26 

1.78 

0.89 

3862 

16 

D 

12 

12 

0.89 

0.55 

613 

48 

12 

A 

17 

30 

1.26 

0.76 

3274 

18 

B 

12 

13 

0.76 

0.52 

686 

48 

12 

B 

17 

80 

1.42 

0.76 

3699 

18 

D 

12 

13 

0.96 

0.52 

704 

48 

12 

C 

17 

30 

1.71 

0.75 

4417 

18 

B 

12 

13 

0.75 

0.55 

608 

48 

12 

D 

17 

80 

1.96 

0.75 

5107 

18 

D 

12 

13 

0  96 

0.55 

720 

48 

16 

A 

17 

80 

1.26 

0.70 

3337 

SO 

B 

12 

14 

0.80 

0.52 

687 

48 

16 

B 

17 

80 

1.42 

0.70 

3762 

20 

D 

12 

14 

1.03 

0.52 

850 

48 

16 

C 

17 

30 

1.71 

0.89 

4523 

20 

B 

12 

14 

0.80 

0.55 

705 

48 

16 

D 

17 

30 

1.96 

0.89 

5214 

20 

D 

12 

14 

1.03 

0.55 

867 

54 

12 

A 

19 

83 

1.35 

0.75 

4287 

24 

B 

12 

16 

0.89 

0.55 

916 

54 

12 

B 

19 

33 

1.55 

0.75 

4945 

24 

D 

12 

16 

1.16 

0.55 

1149 

54 

12 

C 

19 

83 

1.90 

0.75 

6981 

24 

B 

12 

16 

0.89 

0.60 

935 

54 

12 

D 

19 

33 

2.23 

0.75 

7002 

24 

D 

12 

16 

1.16 

0.60 

1170 

64 

16 

A 

19 

83 

1.35 

0.70 

4355 

ao 

A 

18 

20 

0.88 

0.60 

1269 

54 

16 

B 

19 

83 

1.55 

0.70 

6013 

30 

B 

13 

20 

1.03 

0.60 

1382 

54 

16 

C 

19 

33 

1.90 

0.89 

6096 

30 

C 

13 

20 

1.20 

0.60 

1616 

54 

16 

D 

19 

33 

2.23 

0.89 

7126 

30 

D 

»3, 

20 

1.37 

0.60 

1867 

60 

12 

A 

21 

36 

1.39 

0.75 

5263 

80 

13 

A 

13 

20 

0.88 

0.75 

1315 

60 

12 

B 

21 

86 

1.67 

0.75 

6159 

ao 

12 

B 

18 

20 

1.03 

0.75 

1426 

60 

12 

C 

21 

36 

2.00 

0.75 

7418 

30 

12 

0 

13 

20 

1.20 

0.75 

1658 

60 

12 

D 

21 

36 

2.38 

0.75 

8798 

30 

12 

D 

13 

20 

1.37 

0.75 

1913 

60 

16 

A 

21 

36 

1.39 

0.70 

6336 

80 

A 

13 

23 

0.99 

0.60 

1653 

60 

16 

B 

21 

36 

1.67 

0.70 

6233 

36 

B 

13 

28 

1.15 

060 

1922 

60 

16 

C 

21 

36 

2.00 

0.89 

7642 

36 

0 

13 

23 

1.36 

0.60 

2234 

60 

16 

D 

21 

36 

2.38 

0.89 

8927 

36 

D 

13 

23 

1.68 

0.60 

2576 

Note. — ^AU  dimensions  are  in  inches. 


d  by  Google 


135» 


^— WATER  WORKS. 


89. — PROPBRTIBS  or  BLOw-orp  Brakchbs  with  Mamholb. 
(A.  W.  W.  A.) 

Approximate  Weight  of  Cap,  200  Pounds. 


% 

Figs.  89. 

Nomln'l 
Diam. 
Inches. 

i 

■ 

P 

n 

Thickness. 
Inches. 

Nomim 
Dlam. 
Inches. 

i 

0 

I 

P 

n 

Thlcknev. 
Inches. 

e 

f 

t, 

t» 

^k 

e 

t 

ti 

U 

% 

80 

8 

A 

17 

lo" 

0.88 

0.60 

1628 

48 

12 

A 

17 

30 

80 

1.26 

0.75 

83>l 

to 

8 

B 

17 

20 

1.03 

0.60 

1758 

48 

12 

B 

17 

30 

80 

1.42 

0.7S 

8S08 

to 

8 

C 

17 

30 

1.20 

0.60 

2015 

48 

12 

C 

17 

80 

80 

1.71 

0.71 

449? 

to 

8 

D 

17 

20 

1.37 

0.60 

2290 

48 

12 

D 

17 

30 

80 

1.96 

0.7S 

51€7 

30 

12 

A 

17 

20 

0.88 

0.75 

1672 

48 

16 

A 

17 

30 

30 

1.26 

0.70 

3454 

80 

12 

B 

17 

20 

1.03 

0.76 

1803 

48 

16 

B 

17 

30 

80 

1.42 

on 

3866 

80 

12 

C 

17 

20 

1.20 

0.75 

2057 

48 

16 

C 

17 

30 

to 

1.71 

0.89 

4fM 

30 

12 

D 

17 

20 

1.37 

0.75 

2335 

48 

16 

D 

17 

to 

30 

1.96 

0.89 

5n4 

36 

8 

A 

17 

23 

0.99 

0.60 

2045 

54 

12 

A 

19 

33 

33 

1.35 

0.75 

4890 

30 

8 

B 

17 

23 

1.15 

0.60 

2351 

54 

12 

B 

19 

33 

33 

1.55 

0.T5  5«33 

36 

8 

C 

17 

23 

1.36 

0.60 

2690 

54 

12 

C 

19 

S3 

33 

1.90 

0.75i6«39 

36 

8 

D 

17 

23 

1.58 

0.60 

3071 

54 

12 

D 

19 

33 

33 

2.23 

0.75|  T1B3 
O.TO'  4458 

36 

12 

A 

17 

23 

0.99 

0.75 

2094 

54 

16 

A 

19 

33 

83 

1.S5 

36 

12 

B 

17 

23 

1.15 

0.75 

2395 

54 

16 

B 

19 

33 

33 

1.55 

0.7O  51M 

36 

12 

c 

17 

23 

1.36 

0.75 

2741 

54 

16 

0 

19 

33 

33 

1.90 

0.8»  6154 

36 

12 

D 

17 

23 

24 

1.58 

0.75 

3122 

54 

16 

D 

19 

33 

33 

2.23 

0.8»  7117 

42 

12 

A 

17 

26 

27 

1.10 

0.75 

2726 

60 

12 

A 

21 

86 

36 

1.89 

0.75!  5357 

42 

12 

B 

17 

26 

27 

1.28 

0.75 

3033 

60 

12 

B 

21 

36 

36 

1.67     0.75>  fX» 

42 

12 

c 

17 

26 

27 

1.54 

0.75 

3595 

60 

12 

C 

21 

36 

86 

2.00 

0.76  74Q 

42 

12 

D 

17 

26 

27 

1.78 

0.75 

4109 

60 

12 

D 

21 

36 

3^ 

2.38 

0.75  8Sie 

42 

16 

A 

17 

26 

27 

i.lO 

0.70 

2783 

60 

16 

A 

21 

36 

36 

1.39 

0.70   5429 

42 

16 

B 

17 

26 

27 

1.28 

0.70  3090 

60 

16 

B 

21 

36 

86 

1.67 

0.70  63»4 

42 

16 

C 

17 

26 

27 

1.54 

0.89  3689 

60 

16 

C 

21 

36 

36 

2.00 

0.8f  7587 

42 

16 

D 

17 

26 

27 

1.78 

0  89  4303 

60  1  16 

D 

21 

86 

86 

2.38  1  O.m  Mt9 

Note. — All  dimensions  are  in  inches. 


d  by  Google 


C.I.  BLOW-OFFS,  MANHOLE  P.,   REDUCERS. 


1250 


40. — Propbrtibs  of  Manhole  Pipe. 

(A.  W.  W.  A.) 
Note. — ^AU  dimensions  are  in  inches. 


Ill 

j 

n 

t 

M 

III 

i 

n 

t 

H 

0 

^2 

1     "^ 

b 

n 

30 

A 

21 

0.8S 

1536 

48 

A 

30 

1.26 

3194 

30 

B 

21 

1.03 

1711 

48 

B 

30 

1.42 

3610 

80 

C 

21 

1.20 

1973 

48 

C 

30 

1.71 

4292 

30 

D 

31 

1.37 

2245 

48 

D 

30 

1.96 

4968 

36 

A 

24 

0.99 

1953 

54 

A 

33 

1.35 

4006 

36 

B 

21 

1.15 

2260 

54 

B 

33 

1.55 

4598 

36 

c 

24 

1.36 

2614 

64 

c 

33 

1.9( 

5578 

36 

D 

24 

1.5^ 

3012 

M 

D 

33 

2.23 

6522 

43 

A 

27 

1.10  2535 

60 

A 

36 

1.39 

4750 

42 

B 

27 

l.^fi    2869 

60 

B 

36 

1.67 

5606 

42 

C 

27 

1.5^ 

3445 

60 

C 

38 

2.00 

6720 

42 

D 

27 

1.78|  3971 

60 

D 

36 

2.38 

7959 

Pig..  40 

Approximate  weight  of  cap, 
290  Pounds. 

/  >"  17  inches  on  30  inches  to  48  inches;   19  inches  on  54  inches;  21  inches 
a  60  inches  diameter. 


41. — Propbrtibs  op  Rbducbrs  and  Incrbasbrs.  Typb  No.  1. 
(A.  W.  W.  A.) 


Figs.  41. 
Note. — All  dimensions  are  in  inches. 


DlanL. 

[nohes. 

k 

m 

r 

Thickness, 
Inches. 

Weights.  Pounds. 

f 

ti 

ts 

Large 

Small 

End  Bell. 

End  BeU. 

« 

3.30 

14  70 

3 

0.65 

0.52 

99 

88 

8 

5.30 

12.70 

4 

0.60 

0.52 

131 

108 

8 

3.90 

14.10 

4 

0.60 

0.55 

149 

138 

10 

7  10 

10.90 

5 

0.68 

0.52 

164 

132 

10 

6.00 

12.00 

5 

0.68 

0.55 

181 

160 

10 

4.40 

13.60 

5 

0.68 

0.60 

205 

195 

IS 

7.90 

10.10 

6 

0  75 

0.55 

225 

191 

IS 

6.60 

11  40 

6 

0  75 

0.60 

246 

224 

12 

10 

4.80 

13.20 

6 

0.76 

0.68 

271 

260 

Class  D.    6x4  inches  to  12  x  10  inches.       On  all  8izcs^n-2 Jnchei 
On  all  sizes  /  -  30  inches  and  j  -  10  inches,  ^ouy  H^ 


1260 


M.— WATER  WORKS. 


42. — Propbrtibs  of  Rbducbrs  and  Incrbasbrs,  Ttpb  No.  2. 
(A.  W.  W.  A.) 


Fig.  42a. — 6  x  4  inches  to  60  x  54  inches. 


Nominal  Dlam 
Inches. 

Thickness.  Inches. 

Weights.  PouQda. 

V 

Ins. 

Class. 

e 

t 

ti 

ta 

!sr 

Lane 
End  Bell.] 

SmaU 
EndBcB. 

6 

4 

18 

0.55 

0.52 

D 

82 

104 

97 

8 
8 

4 

6 

18 
18 

0.60 
0.60 

0.52 
0.56 

D 
D 

104 

121 

132 
ISO 

119 
143 

10 
10 
10 

4 
• 
8 

18 
18 
18 

0.68 
0.68 
0.68 

0.62 
0.56 
0.60 

D 
D 
D 

131 
150 
170 

162 
180 
201 

146 
161 
198 

12 
12 
12 
12 

4 
6 
8 
10 

18 
18 
18 
18 

0.75 
0.76 
0.75 
0.75 

0.52 
0.55 
0.60 
0.68 

D 
D 
D 
D 

16S 
181 
202 
229 

201 
218 
240 
267 

179 
282 
231 
2«1 

U 
14 
14 
14 

6 
6 
8 
8 

20 
20 
20 
20 

0.66 
0.82 
0.66 
0.82 

0.66 
0.55 
0.60 
0.60 

B 
D 
B 
D 

194 
234 
220 
260 

249 
288 

275 
814 

31« 
2S« 
248 
288 

14 
14 
14 
14 

10 
10 
12 
12 

20 
20 
20 
20 

0.66 
0.82 
0.66 
0.82 

0.68 
0.68 
0,75 
0.76 

B 
D 
B 
D 

250 

290 
284 
324 

305 
844 

339 
878 

279 
S39 

S21    • 
860 

16 
16 
16 
16 

6 
6 
8 
8 

20 
20 
20 
20 

0.70 
0.89 
0.70 
0.89 

0.55 
0.65 
0.60 
0.60 

B 
D 
B 
D 

126 
278 
252 
804 

300 
355 
326 
381 

248 

300 
2» 
SI2 

16 
16 
16 
16 

10 
10 
12 
12 

20 
20 
20 
20 

0.70 
0.89 
0.70 
0.89 

0.68 
0.68 
0.76 
0.75 

.   B 
D 
B 
D 

282 
334 
317 
868 

356 
410 
391 
445 

312 
S«4 

406 

16 
16 

14 
14 

20 
20 

0.70 
0.89 

0.66 
0.82 

B 
D 

815 
407 

389 
484 

370 
461 

18 
18 
18 
18 

1 

10 
10 

20 
20 
20 
20 

0.75 
0.96 
0.76 
0.96 

0.60 
0.60 
0.68 
0.68 

B 
D 
B 
D 

287 
345 
317 
375 

374 
438 
404 
468 

SIS 
ST3 
347 

4C5 

18 
18 
18 
18 

12 
12 
14 
14 

20 
20  . 
20 
20 

0.75 
0.96 
0.76 
0.96 

0.76 
0.75 
0.66 
0.82 

B 
D 
B 
D 

352 
410 
360 
448 

438 

503 
437 
541 

S8 

446 
4tC 
603 

18 
18 

16 
16 

20 
20 

0.75 
0.96 

0.70 
0.89 

B 
D 

883 
492 

469 
589 

457 
609 

20 
_2q 

10 
10 

26 
26 

0.80 
1.03 

0.68 
0.68 

B 
D 

414 
499 

516 
615 

445 
639 

byGoogTe" 


CAST  IRON  PIPE— REDUCERS,  INCREASERS, 


1261 


42.— Rbducbrs  and  Incrbasbrs,  Typb  No.  2. — Continued. 
(See  Pig.  42a,  preceding  page.) 


iloAl  Diam. 
IncbM 

TblokneM.  IndieB. 

Welghtfl.  Poundo. 

▼ 
Ina. 

aaas. 

1 

ti 

ti 

«r^' 

Lartte 
End  Bell. 

SmaU 
BndBeU. 

12 
12 

26 
26 

080 
103 

0.76 
076 

B 
D 

455 
539 

556 
656 

491 
.     676 

14 
14 
1< 
16 

26 
26 
26 
26 

0.80 
1.03 
0.80 
1.03 

0.66 
0.82 
0.70 
0.89 

B 
D 
B 
D 

463 
683 
490 
635 

554 

700 
592 
751 

508 
638 
664 
711 

18 
18 

26 
26 

080 
1.03 

0.76 
0.96 

B 
D 

581 
683 

633 
800 

617 
776 

14 
14 
10 
16 

26 
26 
26 
26 

089 
1.16 
0.89 
1.16 

0.66 
0.82 
0.70 
0.89 

B 
D 
B 
D 

652 
710 
689 
762 

680 
866 
717 
917 

607 
764 
663 
838 

18 
18 
20 
20 

26 
26 
26 
26 

0.89 
1.16 
0.89 
1.16 

0.76 
0.96 
0.80 
1.03 

B 
D 
B 
D 

630 
810 
675 
871 

758 
965 
808 
1027 

717 
901 
776 
987 

18 
18 
18 
18 

26 
26 
26 
26 

0.88 
1.03 
1.20 
1.37 

0.75 
0.75 
0.96 
0.96 

A 

B 
C 
D 

710 
791 
956 
1054 

903 
969 
1166 
1305 

796 
878 
1048 
1146 

20 
20 
20* 

20 

26 
26 
26 
26 

0.88 
1.03 
1.20 
1.37 

0.80 
0.80 
1.03 
1.03 

A 

B 
C 
D 

754 
836 
1018 
1115 

947 
1014 
1227 
1366 

856  ' 

987 
1134 
1232 

20 
20 
20 
20 

66 

66 
66 
66 

0.88 
1.03 
1.20 
1.37 

9.80 
0.80 
1.03 
1.03 

A 

B 
C 
D 

1468 
1626 
1981 
2172 

1661 
1804 
2190 
2423 

1569 
1728 
2098 
2289 

24 
24 
24 

24 

26 
26 
26 
26 

0.88 
1.03 
1.20 
1.37 

0.89 
0.89 
1.16 
1.16 

A 

B 
C 
D 

854 
935 
1144 
1242 

1047 
1113 
1354 
149J 

981 
1063 
1300 
1398 

24 
24 
24 
24 

66 
66* 
66 

66 

0.88 
1  03 
1.20 
1.37 

0.89 
0.89 
1.16 
1.16 

A 

B 
C 
D 

1661 
1820 
222R 
2419 

1931 
1998 
2438 
2670 

1869 
1946 
2384 
2675 

20 
20 
20 
20 

82 
32 
32 
32 

0.99 
1.15 
1.36 
1.68 

0.80 
0.80 
1.03 
1.03 

A 

B 
C 
D 

1039 
1170 
1417 
1589 

1286 
1450 
1739 
1951 

1141 
1272 
1534 
1705 

20 
20 
30 
30 

66 
66 
66 
66 

0.99 
1.16 
1.36 
1.68 

0.80 
0.80 
1.08 
1.03 

A 
B 
O 
D 

1771 
1994 
2416 
2710 

2018 
2274 
2738 
8072 

1872 
2095 
2533 
2827 

24 
24 
24 
34 

82 
32 
32 
32 

0.99 
1.15 
1.36 
1.58 

0.89 
0.89 
1.16 
1.16 

A 
B 
0 
D 

1153 
1288 
1562 
1734 

1339 
1664 

1884 
2096 

1280 
1411 
1718 
1890 

all  sizes  5*8  inches. 


d  by  Google 


1262 


M.—WATER  WORKS. 


42. — ^Rbducbrs  and  Incrbasbrs.  Typb  No.  2. — Continoed. 
(See  Pig.  42a.  page  1260.) 


Nominal  Dlam. 
Inches. 

TtUckneas.  Inohes. 

aaas. 

Welghtf.  Pounds. 

e 

t 

V 

Ins. 

ti 

ti 

«^* 

Lazse 
BndBeU. 

BBiaU 
BndBdL 

86 

24 

66 

0.99 

0.89 

A 

1964 

2211 

2091 

86    . 

24 

66 

1.15 

0.89 

B 

2188 

2468 

2314 

36 

24 

66 

1.36 

1.16 

C 

2664 

2985 

8830 

86 

24 

66 

1.58 

1.16 

D 

2967 

3319 

3113 

86 

30 

32 

0.99 

0.88 

A 

1243 

1490 

1436 

36 

30 

32 

1.15 

1.03 

B 

1467 

1747 

1145 

86 

30 

82 

1.36 

1.30 

C 

1730 

2051 

1939 

86 

30 

32 

1.58 

1  37 

D 

3013 

2375 

3364 

86 

30 

66 

0.99 

0.89 

A 

2119 

2366 

2313 

86 

30 

66 

1.15 

1.08 

B 

2502 

3783 

3«e 

86 

30 

66 

1.36 

1.20 

C 

2950 

3271 

3159 

86 

30 

66 

1.58 

1.87 

D 

3434 

3796 

3884 

42 

20 

32 

1.10 

0.80 

A 

1262 

1602 

1364 

42 

20 

32 

1.28 

0.80 

B 

1413 

1768 

1513 

42 

20 

32 

1.54 

1.03 

C 

1753 

2168 

1869 

42 

20 

32 

1.78 

1.U3 

D 

1975 

2445 

3tSI 

42 

20 

66 

I.IO 

0.80 

A 

2152 

2491 

33M 

42 

20 

66 

1.28 

0.80 

B 

2410 

2764 

3511 

42 

20 

66 

1.54 

1.03 

C 

2989 

3405 

3105 

48 

20 

66 

1.78 

1.03 

D 

3869 

3839 

3481 

43 

24 

32 

1.10 

0.89 

A 

1576 

1715 

15M 

42 

24 

32 

1.28 

0.89 

B 

1627 

1881 

1654 

42 

24 

32 

1.54 

1.16 

C 

1898 

3313 

3053 

42 

24 

82 

1.78 

1.16 

D 

2120 

2590 

3S7C 

42 

24 

66 

1.10 

0.89 

A 

2346 

8685 

34n 

42 

24 

66 

1.28 

0.89 

B 

2603 

2958 

3738 

42 

24 

66 

1.54 

1.16 

C 

3237 

8653 

33Sa 

43 

24 

66 

1.78 

1.16 

D 

3616 

4066 

3773 

42 

30 

32 

1.10 

0.88 

A 

1467 

1806 

I6«i 

42 

30 

32 

1.28 

1.03 

B 

1711 

2065 

1889 

42 

30 

32 

1.54 

1.20 

C 

2065 

2480 

3375 

42 

30 

32 

1.78 

1.37 

D 

2399 

2869 

MOS 

42 

30 

66 

1.10 

0.88 

A 

2500 

2839 

3693 

42 

30 

66 

1.28 

1.03 

B 

2917 

3271 

9m 

42 

30 

66 

1.54 

1.20 

C 

8528 

3938 

3732 

42 

30 

66 

1.78 

1.37 

D 

4093 

4568 

4344 

42 

36 

82 

1.10 

0.99 

A 

1645 

1984 

1891 

42 

36 

32 

1.28 

1.15 

B 

1926 

2281 

3287 

On  all  sizes  5—8  inches* 


Pig.  42b. — Long  Increaser.    48  to  30  inches  x  132  inches  v. 


CAST  IRON  PIPE— REDUCERS,  INCREASERS, 


126a 


42. — Rbducbrs  and  Incrbasbrs,  Ttpb  No.  2. — Continued. 
(See  Pi8.  42a.  page  1260.) 


Nominal  Dlam. 
Inches. 

TbldcneeB.  Inches 

aaaa. 

Weights.  Poun<l8. 

e 

•f 

Ins. 

ti 

ts 

«£S.' 

Large 
EndBelL 

Small 
End  Ben 

42 
42 

34 
36 

32 
32 

1.54 
1.78 

1.36 
1.68 

C 
D 

2320 
2714 

2735 
8184 

2642 
8076 

42 
42 
42 
42 

34 
36 
36 
36 

66 
66 

66 
66 

l.IO 
1.28 
1.64 
1.78 

0.99 
1.16 
1.86 

1.58 

A 

B 

S 

2803 
3285 
3958 
4631 

8143 
8639 
4373 
6101 

3060 
3565 
4279 
4993 

48 
48 
48 
48 

30 
30 
30 
30 

66 
66 
66 

66 

1.26 
1.42 
1.71 
1.96 

0.88 
1.03 
1.20 
1.37 

A 
B 
C 
D 

2975 
8428 
4092 
4762 

3381 
8883 
4641 
6388 

8168 
3606 
4801 
6018 

48 
48 
48 
48 

SO 
30 
80 
30 

132 
132 
132 
132 

1.26 
1.42 
1.71 
1.96 

0.88 
1.03 
1.20 
1.87 

A 
B 
C 
D 

5363 
6180 
7379 
8588 

5769 
6635 
7928 
9214 

5556 
6359 
7588 
8839 

48 
48 
48 
48 

86 
86 
36 
36 

66 
66 

66 
66 

1.26 
1.42 
1.71 
1.96 

0.99 
1.15 
1.36 
1.58 

A 
B 
C 
D 

3278 
8796 
4527 
5300 

3684 
4252 
5076 
6925 

3526 
4077 
4849 
5662 

48 
48 
48 
48 

36 
86 
36 
36 

132 
132 
132 
132 

'  1.26 
1.42 
1.71 
1.96 

0.99 
1.15 
1.36 
1.58 

A 

B 
C 
D 

5909 
6844 
6164 
9558 

6316 
7299 
8713 
10184 

6156 
7125 
8486 
9920 

48 
48 
48 
48 

42 
42 
42 
42 

66 
66 
66 
66 

1.26 
1.42 
1.71 
1.96 

1.10 
1.28 
1.54 
1.78 

A 
B 
C 
D 

3659 
4212 
5100 
5959 

4066 
4667 
5649 
6585 

3998 
4664 
5516 
6429 

48 

48 
48 
48 

42 

42 
42 
42 

132 
132 
132 
132 

1.26 
1.42 
1.71 
1.96 

1.10 
1.28 
1.54 
1.78 

A 

B 
C 
D 

6597 
7594 
9197 
10747 

7003 
8049 
9746 
11378 

6986 
7948 
9612 
11217 

54 
54 
54 
54 

36 
86 
36 
36 

66 
66 
66 
66 

1.35 
1.55 
1.90 
2.23 

0.99 
1.16 
1.86 
1.58 

A 

B 
C 
D 

3722 
4330 
5259 
6181 

4228 
4925 
6953 
6996 

3969 
4610 
5580 
6548 

64 

54 
64 
64 

36 
36 
36 
36 

132 
132 
132 
132 

1.86 
1.55 
1.90 
2.23 

0.99 
1.15 
1.36 
1.58 

A 

B 
C 
D 

6710 
7806 
94S4 
11148 

7216 
8401 
10178 
11962 

6967 
8087 
9805 
11510 

On  all  sizes  f -*  8  inches. 


Fig.  42c.— Short  Increaser.    48  to  30  x  66  iftidlii 


tC^ogle 


1264 


H.'-WATER  WORKS, 


42. — Rbducbrs  and  Incrbasbrs,  Typb  No.  2. — Conduded. 
(See  Pig.  42a.  page  1260.) 


Nominal  Dlam. 
Inchea. 

Thickness,  Inches. 

Wdgbta.  Pounds. 

V 

Oaas. 

e 

f 

ti 

ts 

Sptfot 

Lai«» 

SmaU 

ID8. 

Ends. 

EndBelL 

EndBeU 

54 

42 

66 

1.36 

1.10 

A 

4103 

4609 

4442 

54 

43 

66 

1.66 

1.28 

B 

4745 

6340 

5U» 

54. 

42 

66 

1.90 

1.64 

0 

5832 

6526 

•247 

54 

42 

66 

2.23 

1.78 

D 

6841 

7655 

TUO 

54 

42 

182 

1.36 

1.10 

A 

7398 

7903 

T737 

54 

42 

132 

1.66 

1.28 

B 

8566 

9151 

8910 

54 

42 

132 

1.90 

1.64 

C 

10617 

11211 

loasx 

54 

42 

132 

2.23 

1.78 

D 

12338 

13151 

ism 

54 

48 

66 

1.35 

1.26 

A 

4878 

6083 

4»4 

54 

48 

66 

1.66 

1.42 

B 

5256 

6851 

5m 

54 

48 

66 

1.90 

1.71 

C 

6401 

7095 

6SiO 

54 

48 

66 

2.23 

1.96 

D 

7512 

8326 

iOf 

54 

48 

182 

1.35 

1.36 

A 

8253 

8759 

8tl0 

54 

48 

132 

1.66 

1.42 

B 

9478 

10073 

•9t3 

54 

48 

132 

1.90 

1.71 

C 

11544 

12239 

12093 

64 

48 

132 

2.23 

1.96 

D 

13680 

14364 

14175 

60 

36 

66 

1.89 

0.99 

A 

4096 

4711 

Ofi 

60 

36 

66 

1.67 

1.15 

B 

4906 

5576 

5186 

60 

36 

66 

2.00 

1.36 

0 

6867 

6692 

6189 

60 

36 

66 

2.38 

1.68 

D 

6960 

7934 

Tsa 

60 

36 

132 

1.39 

0.99 

A 

7384 

7999 

7631 

60 

36 

132 

1.67 

1.15 

B 

8846 

9616 

9I» 

60 

36 

132 

2.00 

1.36 

C 

10581 

11405 

10902 

60 

36 

132 

2.88 

1.58 

D 

12554 

13527 

12516 

60 

42 

66 

1.39 

1.10 

A 

4477 

5098 

4816 

00 

42 

66 

1.67 

1.28 

B 

5321 

6ni 

5876 

60 

42 

66 

2.00 

1.64 

C 

6440 

7264 

6855 

60 

42 

66 

2.38 

1.78 

D 

7619 

8693 

.8068 

60 

42 

132 

1.39 

1.10 

A 

8072 

8687 

8411 

60 

42 

132 

1.67 

1.28 

B 

9595 

10265 

60 

42 

132 

2.00 

1.54 

C 

11614 

12439 

12089 

60 

42 

132 

2.38 

1.78 

D 

13743 

14716 

14213 

60 

48 

66 

1.39 

1.26 

A 

4957 

6572 

S268 

60 

48 

66 

1.67 

1.42 

B 

6832 

6602 

6287 

60 

48 

66 

2.00 

1.71 

C 

7006 

7830 

75Si 

60 

48 

66 

2.38 

1.96 

D 

8385 

•850 

8918 

60 

48 

132 

1.89 

1.26 

A 

8938 

•652 

9844 

60 

48 

132 

1.67 

1.42 

B 

10517 

11187 

10«72 

60 

48 

132 

2.00 

1.71 

C 

12634 

13456 

13183 

60 

48 

132 

2.38 

1.96 

D 

14M3 

15117 

15868 

60 

54 

66 

1.39 

1.35 

A 

5404 

6019 

5810 

60 

54 

66 

1.67 

LS.*) 

B 

6348 

7018 

6961 

60 

54 

66 

2.00 

1.90 

C 

7760 

8674 

8444 

60 

54 

66 

2.88 

3.23 

D 

9178 

10152 

•992 

60 

64 

132 

1.89 

1.35 

A 

9745 

10360 

1Q2S1 

60 

54 

132 

1.67 

1.55 

B 

11462 

12132 

12875 

60 

54 

132 

2.00 

1.90 

c 

13979 

14803 

14673 

60 

64 

132 

2.38 

2.23 

D 

16657 

17530 

173T1 

On  all  sizes  *  =■  8  inches. 


d  by  Google 


CAST  IRON  PIPE—REDUCERS  AND  SLEEVES, 


1265 


48. — Properties  of  Sleeves. 
(A.  W.  W.  A.) 


Pig.  43. 
For  dimensions  a  and  b  see  Table  No.  26. 


Sq5 

i 

D 

Ins. 

L 

Ids. 

T 
Ins. 

i 

16 

3 

D 
Ins. 

L 
Ins. 

T 
Ins. 

ill 

4 

D 

5.80 

10 

0.65 

47 

36 

B 

39.40 

15 

1.40 

943 

4 

D 

5.80 

15 

0.65 

61 

36 

C 

39.80 

15 

1.60 

1077 

6 

D 

7.00 

10 

0.70 

68 

36 

D 

40.20 

15 

1.80 

1217 

• 

D 

7.00 

15 

0.70 

87 

36 

A 

39.00 

24 

1.25 

1202 

8 

D 

10.10 

12 

0.76 

104 

36 

B 

39.40 

24 

1.40 

1362 

8 

D 

10.10 

15 

0.75 

119 

36 

C 

89.80 

24 

1.60 

1563 

10 

D 

12.20 

12 

0.80 

123 

36 

D 

40.20 

24 

1.80 

1772 

10 

D 

12.20 

18 

0.80 

176 

42 

A 

45.30 

15 

1.40 

1097 

12 

D 

14.30 

14 

0.85 

174 

42 

B 

45.60 

15 

1.50 

1184 

12 

D 

14.80 

18 

0.85 

223 

42 

C 

46.20 

15 

1.75 

1381 

14 

B 

16.20 

15 

0.85 

220 

42 

D 

46.70 

15 

1.95 

1561 

14 

B 

16.20 

18 

0.85 

249 

42 

A 

45.30 

24 

1.40 

1577 

14 

D 

16.50 

15 

0.90 

240 

42 

B 

45.60 

24 

1.50 

1702 

14 

D 

16.50 

18 

0.90 

280 

42 

C 

46.20 

24 

1.75 

1997 

16 

B 

18.50 

15 

0.90 

274 

42 

D 

46.70 

24 

1.95 

2262 

16 

B 

18.50 

24 

0.90 

391 

48 

A 

51.60 

15 

1.50  . 

1337 

16 

D 

18.90 

15 

1.00 

305 

48 

B 

61.90 

15 

1.65 

1481 

16 

D 

18.90 

24 

1.00 

443 

48 

c 

52.50 

15 

1.95 

1752 

18 

B 

20.60 

15 

0.95 

321 

48 

D 

53.10 

15 

2.20 

1986 

18 

B 

20.60 

24 

0.95 

462 

48 

A 

61.60 

24 

1.50 

1922 

18 

D 

21.00 

15 

1.05 

360 

46 

B 

51.90 

24 

1.65 

2129 

18 

D 

21.00 

24 

1.05 

518 

48 

c 

52.50 

24 

1.95 

2532 

30 

B 

22.70 

15 

1.00 

374 

48 

D 

53.10 

24 

2.20 

2879 

20 

B 

22.70 

24 

1.00 

532 

54 

A 

57.70 

15 

1.60 

1612 

20 

D 

23.10 

15 

1.15 

440 

54 

B 

58.20 

15 

1.80 

1835 

20 

D 

23.10 

24 

1.15 

625 

54 

C 

58.90 

15 

2.15 

2156 

24 

B 

26.90 

15 

1.05 

477 

54 

D 

59.50 

15 

2.45 

5450 

24 

B 

26.90 

24 

1.05 

680 

54 

A 

57.70 

24 

1.60 

2316 

24 

D 

27.40 

15 

1.25 

583 

54 

B 

58.20 

24 

1.80 

2634 

24 

D 

27.40 

24 

1.25 

821 

54 

C 

58.90 

24 

2.15 

3126 

30 

A 

32.80 

15 

1.15 

648 

54 

D 

59.50 

24 

2.45 

3571 

30 

B 

33.10 

15 

1.15 

652 

60 

A 

63.90 

15 

1.70 

1906 

30 

C 

33.50 

15 

1.32 

760 

60 

B 

64.50 

15 

1.90 

2127 

30 

D 

33,80 

15 

1.50 

876 

60 

C 

66.30 

15 

2.25 

2491 

30 

A 

32.80 

24 

1.15 

943 

60 

D 

65.90 

15 

2.60 

2895 

30 

B 

33.10 

24 

1.15 

949 

60 

A 

63.90 

24 

1.70 

2731 

80 

C 

33.50 

24 

1.32 

1088 

60 

B 

64.50 

24 

1.90 

3058 

30 

D 

33.80 

24 

1.50 

1262 

60 

C 

65.30 

24 

2.25 

3601 

36 

A 

39.00 

15 

1.25 

«3 

60 

D 

65.90 

24 

2.60 

4231 

d  by  Google 


1266 


M.^WATER  WORKS. 


44. — PROPBRTIBS  OP  Caps. 
(A.  W.  W.  A.) 


VJ  y 

** 

Bosses  A  and  B'  cast 

on  only  when 

so  ordered. 

Nom'I 

^PSSS: 

Dlam. 

Class. 

d 

0 

1 

t 

m 

k 

r 

Inches. 

PoundL 

4 

D 
D 
D 
D 

4.00 
4.00 
4.00 
4.00 

6.70 
7.80 
10.00 
12.10 



0.60 
0.65 
0.76 
0.75 

M 

6 

40 

8 

19 

10 

L50 

10:75" 

16.20 

81 

12 

D 

4.00 

14.20 

0.75 

1.75 

0.75 

18.70 

IM 

14 

B 

4.00 

16.10 

0.90 

1.90 

0.75 

22.40 

140 

14 

D 

4.00 

16.45 

..'.'..... 

0.90 

1.90 

0.75 

22.40 

149 

16 

B 

4.00 

18.40 

1.00 

2.00 

0.75 

27.00 

16 

16 

D 

4.00 

18.80 

1.00 

2.00 

0.75 

27.00 

IK 

18 

B 

4.00 

20.50 

1.00 

2.00 

1.00 

82.00 

23« 

18 

D 

4.00 

20.92 

1.00 

2.00 

1.00 

82.90 

242 

20 

B 

4.00 

22.60 

1.00 

3.00 

1.00 

18.20 

278 

20 

D 

4.00 

23.06 

1.00 

3.00 

1.00 

18.20 

908 

24 

B 

4.00 

26.80 

"i'.JM" 

1.05 

3.50 

1.00 

23.50 

392 

24 

D 

4.00 

27.32 

2.50 

1.06 

3.50 

1.00 

23.50 

443 

30 

A 

4.50 

82.74 

2.62 

1.16 

3.50 

1.15 

34.80 

589 

30 

B 

4.50 

33.00 

2.62 

1.15 

3.50 

1.15 

34.80 

596 

30 

C 

4.50 

83.40 

2.62 

1.15 

3.50 

1.15 

34.80 

647 

30 

D 

4.50 

33.74 

2.62 

1.16 

3.50 

1.15 

34.80 

704 

36 

A 

4.50 

38.96 

3.12 

1.25 

4.00 

1.25 

44.00 

849 

36 

B 

4.50 

89.30 

3.12 

1.80 

3.95 

1.25 

44.00 

918 

36 

C 

4.50 

39.70 

3  12 

1.36 

3.90 

1.25 

44.00 

998 

36 

D 

4.50 

40.16 

3.12 

1.40 

3.85 

1.25 

44.00 

1084 

42 

A 

5.00 

45.20 

3.37 

1.40 

4.00 

1.40 

63.90 

13t0 

42 

B 

5.00 

45.50 

3.37 

1.50 

3.90 

1.40 

63.50 

1388 

42 

C 

5.00 

46.10 

3.37 

1.60 

3.80 

1.40 

63.50 

1539 

42 

D 

6.00 

46.58 

3.37 

1.70 

3.70 

1.40 

63.50 

1679 

48 

A 

6.00 

61.50 

3.62 

1.70 

4.00 

1.50 

76.50 

1773 

48 

B 

6.00 

61.80 

3.62 

1.90 

3.80 

1.50 

76.50 

1943 

48 

c 

5.00 

62.40 

3.62 

2.00 

3.70 

1.50 

76.50 

2144 

48 

D 

6.0O 

52.98 

8.62 

2.10 

3.60 

1.50 

76.50 

2341 

M 

A 

5.50 

67.66 

3.87 

1.90 

4.50 

1.50 

83.00 

2329 

54 

B 

6.50 

68.10 

3.87 

2.00 

4.40 

1.50 

82.00 

2619 

54 

C 

5.50 

58.80 

8.87 

2.10 

4.30 

1.50 

82.00 

2779 

54 

D 

6.50 

69  40 

3.87 

2.20 

4.20 

1.60 

82.00 

3009 

60 

A 

5.60 

63.80 

4.12 

2.00 

4.50 

1.50 

99  00 

2863 

60 

B 

5.50 

64.40 

4.12 

2.10 

4.40 

1.50 

99.00 

S0S3 

60 

C 

5.50 

65.20 

4.12 

2.20 

4.30 

1.50 

99.00 

3333 

60 

D 

_5.50_ 

65.82 

4.12 

2.30 

4.20 

i^ 

99.00 

9687 

No 

TB.—A 

1  dimcT 

isinns  nr 

«k  in  inr 

hntl 

Digitized 

byV^UV. 

CAST  IRON  PIPE— CAPS  AND  PLUGS. 


45. — Propbrtibs  op  Plugs. 
(A.  W.  W.  A.) 


1207 


20  ins. 


Pigs.  45. 
BoGses  a  and  h  cast  on  only  when  so  ordered. 


42  to  60  ins* 


Thickness. 
Inches. 


^11 


4.90 
7.00 
9.15 
11.20 
13.30 
15.30 
15.65 
17.40 
17.80 
19.50 
19.92 
21.60 
22.06 
25.92 
26.44 
31.86 
82.12 
32.62 
32.86 
38.08 
88.42 
38.82 
89.28 
44.33 
44.62 
45.22 
45.70 
50.62 
60.93 
61.62 
62.10 
56.78 
57.22 
67.92 
68.52 
62.92 
63.52 
64  32 
64.94 


5.28 
7.38 
9.65 
11.70 
13.80 
15.80 
16.15 
17.90 
18.30 
20.00 
20.42 
22,10 
22.56 
26.80 
26.88 
82.24 
32.50 
32.90 
33.24 
88.46 
38.80 
39.20 
39.66 
44.70 
45.00 
45.60 
46.08 
51.00 
61.30 
51.90 
52.48 
57.16 
57.60 
58.30 
58.90 
63.30 
63.90 
64.70 
65.  d2 


25.68 
26.20 
31.62 
31.88 
32.28 
32.62 
37.84 
38.18 
38.58 
39.04 
44.08 
44.38 
44.98 
45.46 
50.38 
50.68 
51.28 
51.86 
56.54 
56.98 
57.68 
58.28 
62.68 
63.28 
64.08 
64.70 


5.50 
5.60 
5.50 
6.00 
6.00 
6.00 
6.00 
6.50 
6.50 
6.50 
6.50 
6.50 
6.50 
8.00 
8.00 
8.00 
8.00 

8  00 
8.00 
8.00 
8.00 
8.00 
8.00 
9.00 
9.00 
9.00 
9.00 
9.00 
9.U0 
9.00 
9.00 
9.00 
9.00 
9.00 
9.00 
9.00 
9.00 
9.00 

9  0« 


2.00 
2.00 
2.00 
2.00 
2.00 
2.00 
2.00 
2.50 
2.50 
2.75 
2.75 


0.50 
0.60 
0.60 
0.70 
0.75 
0.70 
0.75 
0.70 
0.80 
0.75 
0.85 
0.85 
1.00 
0.89 
1.16 
0.88 
1.03 
1.20 
1.37 
0.99 
1.15 
1.36 
1.58 
1.10 
1.28 
1.54 
1.78 
1.26 
1.42 
1,71 
1.96 
1.85 
1.55 
1.90 
2.23 
1.39 
1.67 
2.00 
2.38 


0.40 
0.40 
0.40 
0.50 
0.50 
0.50 
0.50 
0.50 
0.60 
0.60 
0.60 
0.60 
0.60 


0.20 
0.20 
0.20 
0.20 
0.20 
0.20 
0.20 
0.30 
0.30 
0.30 
0.30 
0.30 
0.30 


yGo? 


8 

14 

24 

38 

50 

63 

65 

90 

96 

111 

121 

151 

156 

875 

472 

481 

556 

641 

723 

682 

786" 

914 

1050 

991 

1138 

1353 

1551 

1349 

1506 

1800 

2047 

1697 

1945 

2356 

2733 

2045 

2434 

2904 

3397 


^OTB. — All  dimensions  are  in  inches. 


1268  U.-'WATER  WORKS. 

Hid.— WROUGHT  IRON  PIPE. 

Wrought  Iron  Pipe  corrodes  more  rapidly  than  cast  iron,  and  less 
rapidly  than  steel.  Its  first  cost,  in  the  smaller  sixes,  is  less  than  the 
former;  and  in  all  sizes  it  is  greater  than  the  latter.  Between  cast  iron  on 
the  one  hand  and  the  steel  on  the  other  the  use  of  wrought  iron  in  pressure 
pipe  lines  has  become  limited,  but  it  yet  finds  a  demand  in  the  smaller  sixes 
of  pipe  for  distributing  systems.  It  remains  to  be  seen  whether  the  few 
remaming  manufacturers  of  wrought  iron  pipe  will  be  able  to  offer  cod  vine- 
ing  proofs  of  the  superior  merit  and  ultimate  economy  of  their  article,  as 
claimed.  More  attention  is  paid  now  to  suitable  coating  for  pipes  than 
formerly,  and  a  steel  pipe  well  coated  when  laid  shouJd  last  from  36  to  40 
years  in  ordinary  soil,  and  if  occasionally  cleaned  and  painted  it  will  last 
much  longer.  Wrought  iron  pipe  may  be  manufactured  in  the  same  forms 
as  steel  pipe  (Ille),  but  it  is  ustially  lap-welded,  seldom  riveted. 

Ule.— STEEL  PIPE. 

Steel  Pipe  is  tisually  designated  by  the  kind  of  "seam"  or  "joint." 
The  latter  term  is  generally  used  with  reference  to  the  (end)  connectioci 
between  two  pipes,  and  frequently  also  to  the  lon^tudinal  seam  at  the 
joining  of  plates  in  the  pipe  itself.  Seams  or  ioints  m  a  pipe  may  be  lap- 
welded,  spiral  riveted,  longitudinal  riveted,  or  locking-bar.  Riveted  (longi- 
ttidinal)  joints  may  oe  lap-  or  butt-,  and  be  (stngle-),  double-  or  triple- 
riveted,  with  (single  or)  double  straps.  Single  riveting  or  single  straps  are 
seldom  used  for  longitudinal  joints.    The  end  joints  for  pipes  may  be  f 


bell-and-spigot-  (rarely  used),  fiange-  (welded,  riveted,  or  screw),  single- 
riveted-,  patent-locking-,  etc.    A  few  of  these  will  be  described  as  follows: 

Riveted  Steel  Pipe  is  especially  economical  for  laige  diameters,  sub- 
jected to  pressure  head  of  300  ft.  or  more.  For  heads  between  200  and  MO 
ft.  riveted  steel  has  to  compete  with  cast  iron  pipe;  and  for  heads  under 
200  ft.  both  riveted  steel  and  cast  iron  pipe  have  to  compete  with  wood 
stave  pipe,  especially  in  the  West  where  lumber  is  plentiful. 

The  thickness  of  steel  plates  is  proportioned  by  the  formula — 

'-^1^- o> 

where    I —  thickness  of  steel  shell,  in  inches; 
d  — inside  diameter  of  pipe,  in  inches; 
^-pressure  head  in  ft.  (  —  2.304  p); 
p  — pressure  of  water  in  lbs.  per  square  inch  (•■0.434  h); 
p'  —allowance  for  water  ram,  in  lbs.  per  square  inch; 
j  — allowable  tensile  stress  of  steel,  in  lbs.  per  square  inch; 
#  — efficiency  of  riveted  joint,  say  0.60  to  0.80; 
c  — thickness  to  be  added  to  plate  for  corrosion,  etc. 
Based  on  a  safety  factor  of  4.  ^  is  assumed  at  16.000  (to  16.000)  lbs: 
and  c  may  be  assumed  at  sav  tV  in. 

The  practical  working  formula  will  result  as  follows,  assuming  p'at 
80  lbs.  (see  page  1215): 

'-looooT-"^^ aoooo;^ — ^^'^^^^ <^ 

If  A— the  static  head  in  feet,  we  have,  from  (2), 

H.m^'u-M-m.i2 ,B 

In  designing  the  riveting  of  longitudinal  scams,  we  have,  if  F— total 
tension  per  lin.  inch  of  seam,  due  to  p  and  p', 

F-y (p+  p')  - (/(0.217  A  +  40)  -  1500  ii-c)e (4) 

in  which  F  should  not  exceed  the  bearing-  nor  the  shearing  resistance  of  the 
rivets.  The  bearing  value  may  be  asstuned  at  16,000  lbs.  per  square  inch 
on  the  thickness  of  plate  /  —  c,  as  it  is  assximed  that  c  is  the  allowance  for 
corrosion;  while  the  shearing  value  may  be  assumed  at  say  10,000  lbs.  pe^ 
square  inch  of  rivet  section.  The  diameter  of  rivet  is  approximately  twice 
the  thickness  of  the  plate. 


WROUGHT  IRON  PIPE.    STEEL  PIPE, 


1260 


The  following  ia  a  table  of  pitches  and  dimensions  of  rivets  adopted  in 
the  manufacture  of  the  42-in.  pipe  for  the  Seattle  (Wash.)  Water-works, 
constructed  in  1900: 


Thickness  of  Steel,  in  inches 

A 

H 

A 

H 

A 

Diameter  of  rivets,  in  inches 

H 

A 

H 

H 

H 

Diameter  of  rivet  holes,  in  inches 

A 

H 

H 

H 

H 

Pitch  in  double  riveted  seams,  in  ins  . . 

1.76 

2.00 

2.26 

2.60 

2.60 

Pitch  in  single  riveted  seams,  in  ins . . . 

1.40 

1.60 

2.00 

2.26 

2.25 

Distance   between  rows  on   double 

1.60 

1.76 

2.00 

2.00 

2.00 

Lap  from  center  of  rivet  to  edge  of 
plate,  in  inches 

.760 

.876 

1.00 

1.00 

1  126 

The  edges  of  all  plates  are  bevel  sheared  for  caulking.  Shop-  riveting 
and  caulking  are  invariably  done  by  machine.  For  thick  plates  the  rivets 
may  be  countersunk  on  inside  of  pipe.  The  field-  riveting  and  caulking  are 
usiially  done  by  hand,  but  machine  riveters  and  caulkers  are  sometimes 
employed,  not  alwa3ra  to  advantage.  The  field  work  consists  in  joining  the 
pipes  together  in  the  trench  and  making  them  water-tight  under  pressure. 
If  the  end  joints  are  lap-riveted  there  must  necessarily  be  alternate  courses 
with  two  separate  diameters,  but  the  internal  diameters  of  the  smaller 
course  shall  be  "the  diameter"  of  the  pipe.  The  internal  diameter  of  the 
larger  course  must  equal  exactly  the  external  diameter  of  the  smaller  course. 
Pipes  of  ordinarily  large  diameter  usually  leave  the  shop  made  up  in  four 
courses,  and  in  length  from  20  to  30  ft.,  after  being  tested  to  a  sufficient 
hydrostatic  pressure,  and  suitably  coated  (see  page  ^.  etc.). 

In  shipment  it  is  well  to  bear  in  mind  that  a  "full"  carload  cannot 
always  be  made  up  with  pipes  of  the  sattu  diameter  if  large. 

When  laid  in  the  trench  the  longitudinal  seams  should  be  at  the  top  of 
the  pipe,  staggered  not  less  than  6  inches. 

*  Lockfaig-Bar  Joint  Pipe  is  designed  to  supplant  the  riveted  joint. 
Pig.  46  shows  a  transverse  section  of  the  (longi- 
tudinal) bar  and  joint  and  also  the  (end)  joint 
ring.  In  manufacture,  the  edges  of  the  plate 
are  upset  and  inserted  in  the  grooves  on  either 
side  of  the  locking  bar.  The  bar  is  then  sub- 
jected to  a  great  hydraulic  pressure,  tightly  lock- 
ing the  plates  in  a  hip^hiy  efficient  manner. 
No  riveted  longitudinal  joints  are  used.  Sleev^ 
or  joint  rings  are  used  for  end  joint  connections 
of  pipes  and  are  run  with  lead;  or  the  end  joints 
may  be  riveted. 

Lap-Weldad  Pipe  is  seldom  used  in  the  pressurepipe  line:  it  is  better 
adapted  to  use  in  the  distributing  system  (see  page  1280) .  The  tour  principal 
types  used  are  those  with  screw  ends  or  flange  ends  (Section  86),  Converse 
Jomt  (p.  1282),  and  Matheson  Joint  (p.  1281). 

Spiral  RhreCed  Pipe  (p.680)  is  used  largely  in  hydraulic  mining. 


Fig.  46. 


Illf.— PRESSURE  PIPE  ATTACHMENTS. 

Brief  mention  will  be  made  of  some  of  the  more  important  items  in 
connection  with  an  ordinary  pressure-pipe  line.  The  varying  conditions 
are  so  great  in  different  lines  that  the  merest  hints  only  will  be  given. 

*  This  form  of  joint  was  brought  prominently  to  the  attention  of  Amerir 
can  engineers  in  1896  by  an  article  published  in  Eng.  News.  Vol.  XXXIX, 
p.  373,  describing  its  use  in  connection  with  the  construction  of  a  large  pipe 
Biie  in  Australia. 


1270 


M.—WATER  WORKS, 


-ij,1 


Fig.  47  shows  a  SInice-Qate  for  the  inlet  end  of  the  pipe  at  the  head- 
works,  and  Fig.  48  shows  Stand  and  Wheel  for  operating  same.  Each  may 
be  fastened  to  either  masonry  (by  stone-bolts)  or  to  timber  (by  screw-bolts). 
This  pattern  is  suitable  for  large  inlets.  30  ins.  or  more  in  diameter.  The 
gear-wheel  is  often  horizontal  instead  of  vertical. 


Pig.  47. — Sluice<Gate  for  Headworks. 


Fig.  48.— Stand  and  Wheel  for 
Operating  Sluice-Gate. 


Air  Relief  Valves,  or  "Air  Valves."  are  placed  at  summiu  of  pipe  lines 
to  afford  relief  from  air  pressure  or  from  vacuum.  As  the  pipe  fills  with 
water  the  valve  operates  so  as  to  allow  the  air  to  escape,  but  closes  against 
the  outlet  of  the  water.  As  the  water  in  the  pipe  subsides,  the  valve  aUows 
the  air  to  enter  the  pipe  and  prevent  collapse  from  vacuum.    If  air  is  alk»wed 


Pig.  49. 


Pig.  50. 


to  collect  at  sunmiits  without  air  valves  it  is  clearly  seen  that  the  wattf 
area  of  the  pipe  at  those  points,  and  hence  the  flow,  will  be  decreased  ac» 
cordmgly :  and  also  that  the  pipe  is  more  liable  to  leak  and  burst  (fro«B  ub^ 


PRESSURE  PIPE  ATTACHMENTS.    VALVES. 


1271 


from  water  pressure).  Air  valves  may  be  single,  or  they  may  be 
tsed  in  cltisters  to  operate  consecutively.  There  is  an  advantage  in 
n«  a  stop- valve  between  the  air  valve  and  the  top  of  the  main  pipe,  so 
crater  can  be  shut  off  during  repairs.  Valves  should  be  protected  by 
i-  or  metal  casings  and  be  out  of  reach  of  the  frost. 
^i&'  49  illustrates  the  Ludlow  automatic  lever  and  float  air  valve,  and 
50  the  globe  air  valve. 
F^ig.  61  shows  section  and  plan  of  Metropolitan  Water  Works  air  valve, 

table  of  dimensions. 


Stctional   ilivation. 
Pig.  61. 


nm  n^    cf  Ccff  C 


46.— M.  W.  W.  Air  Valves.    (Fig.  61.) 
Dimensions  are  in  inches;  weights,  in  pounds. 


Staadpipet  (small)  are  sometimes  erected  at  the  summits  of  pipe  lines 
serve  both  as  air  valves,  and  also  as  piezometers  for  determining  the 

rdraulic  grade  line  (see  p.  1169).    They  are  often  preferred  to  air  valves 

oere  the  static  head  is  not  great. 

date  Valves,  stop  valves,  gates,  or  valves,  as  they  are  variously  termed 
e  of  numerous  designs,  suited  to  special  purposes.  The  best  manufac- 
irers  are  beginning  to  standardize  their  product  so  that  there  is  very  little 
Serence  in  quality  of  material  and  service.  But  there  is  a  vast  difference 
I  length  of  service  between  these  standard  makes  and  most  of  the  cheaper 
Uves  thrown  upon  the  market.  Waterworks  engineers,  generally,  fully 
aHse  the  importance  of  securing  at  all  times  the  best  article  even  at  the 
^ter  first  cost.  It  is  economy  in  the  end.  The  best  gates  are  bronxe- 
tounted. 


lira  tL-WATER  WORKS. 


Pis.  M,  pun  ISSft.  shows  a  section  of  the  Chapman  valve  with  ^md^\ 
shaped  gate,  rig-  62.  below,  shows  a  section  of  a  double  gate  valvrotta 
IxuUow  type;  and  Pig.  52.  views  of  the  gates  axul  wedgea.    The  pipe  oo» 


1 

90»W, 


Pig.  62.— Ludlow  Bronse  Mounted  Double  G&te  Valv« 
With  Bolted  Stuffing  Box. 


Fig.  6a— Style  of  Gates  and  Wedges  iorf^^eS^Vi 


Valves. 


GATE  VALVES--GEARED  AND  UNGEARED, 


1273 


ns  may  be  bell-  (as  shown  in  the  illustrations),  flange-  or  screw-,  as 
ed.  Gates  are  designed  for  either  vertical  or  horizontal  (the  larger 
p>osition,  and  for  operating  by  hand  or  "power,"  with  screw,  piston, 
or  gearing  (gates  iinder  16  ins.  in  size  are  seldom  geared).  They  are 
lanuf  act  urea  with  or  without  by-pass  relief.  The  by-pass  is  useful  in 
long  pipe  lines  without  impact,  and  in  equalizing  the  pressure  on  both 
of  a  gate  when  being  opened  or  closed. 

47.— M.  W.  W.  Gate  Valvbs. 
Principal  Dimensions,  in  Inches;  Weights,  in  Pounds. 


Using  gears.     With  wrench  on  main  stem,  67i  turns  will  open  the 
ch,  and  76J  turns  the  24-inch  valve.  

11 

ii 

ii 


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1274 


^,— WATER  WORKS. 


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55  : 


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ifedbyQoOgle 


ij 


DOUBLE  GATE  LUDLOW  VALVES, 


-2 


P 


O 


o 


d  by  Google 


1276  ^.— WATER  WORKS. 


49. — Wbiohts  of  Ludlow  Gates  and  Valvbs,  in  Lbs. 
(♦Abbreviations.) 


3:1 

13 
iB 
& 
IB 

.SB 


*  The  following  abbreviations  are  used  in  Table  4  9: 

For  connections,  etc.:  Sc.  Sot.  =  Screw  Socket;  F/^.  — Flanged;  Spig.'^ 
Spigot;  O.  S.  and  Y.,  #jif.« Outside  Screw  and  Yoke,  extra;  L.  F.,  *x.««* 
Loose  Flanges,  extra:  Sp.  Gr.,  *x. —Spur  Gear,  extra;  Bv.  Gr.,  ex, » 
Bevel  Gear,  extra;  By-Ps.,  ex. -By-Pass,  extra;  P.  F.,  R.  O.-Plai-: 
Frame,  round  opening;  P.  F.,  S.  O.  — Plain  Frame,  square  openin«;. 
R.  O.  with  Sftf.-Roimd  Opening  with  Spigot;  R.  O.  with  F.  cr  A*.- 
Rotmd  Opening  ^nth  Flange  and  Neck  Piece;  E.  F.,  R.  O. -> Bxtensior 
Frame,  roimd  opening;  E.F.,  S.  O.  —  Extension  Frame,  souare  openini^: 
S.  O.  with  F.  &  N.'^  Square  Opening  with  Flange  and  Neck  Piece, 

For  Test-  and  Working  Pressures:  T.  P.  W.  -Test  Pressure,  Water;  R.  W.  - 
Recommended  for  Water. — Working  prcssxires  not  to  exceed  the  nuxr.bci 
of  pounds  given  in  Table  headings;  K.  5.  —  Recommended  for  Stcsam— 
Working  Pressures  not  to  exceed  number  of  lbs.  given  in  Table  headn«$^ 


WEIGHTS  OF  LUDLOW  GATES  AND  VALVES. 


1277 


49. — ^Weights  op  Ludlow  Gatbs  and  Valves,  in  Lbs. — Continued, 
t;-+m«  k  ;6-in.andunder:r.P.ir.-=3501bs.:/?.PV.-2001bs.;/?.5.  =  1001b8. 
l-ist  wo.  5.  ^7.in.  and  above:  T.  P.  W^.-850  lbs.;i?.  W^.-200  lbs.;  R.S.^  85  lbs. 


List  No.  5H' 

T.P.W 

.»4001 

bs.; 

R. 

s.= 

>  150  lbs. 

Sizes. .   ... 

!«• 

2' 

2H' 

3' 

3Hi' 

4' 

*H' 

5- 

6' 

7' 

8' 

9- 

10' 

12* 

Flanged 

38 

70 
64 

75 

123 
107 

187 
185 

257 
237 

300 

379 
370 

648 

725 

Screwed 



f  20-inand  under:  T.  P.  W^.  =  300  \hs.'R,  W.^200  \hs.;R.  5.-=85Ibs. 
ListNo.6.j24-3e-ins.:    r.  P.  W^.=  300  lbs.;   R.  H^.- 160 lbs.; /?.  5.  =  75 lbs. 


L40-in.  and  above 

iT.P.W.^ 

300  lbs 

:/?. 

W.= 

a401bs.;. 

R.S 

.- 

56  lbs. 

sues..... 

14' 

15- 

16' 

17- 

18- 

20' 

22* 

24- 

30- 

with  Gearing. 

36* 

iO' 

42' 

48- 

50- 

54- 

60' 

72' 

jr|(f     

770 
705 

890 
820 

963 
875 

1260 
1203 

1650 
1585 

2580 
2461 

4260 
4425 

S600 
8500 

Vim 

11650 
12160 

18970 
18550 

Hub. 

arrfir 

8p.  Or.,  ex... 
Bv.  Or.,  ex.  . 
O  8.  &Y..ex. 

105 
114 

105 
114 

105 
114 

67 
68 

67 
68 

103 
1U4 

200 

188 

T    F..  ex 

By-P»..ex... 

Notes.— Ifi*.  Hub,  #6.  Bevel  Gear,  and  2^  By-Pass.  1230  lbs.;   30*.  Hub, 
46   Bevel  Gear,  and  6'  By-Pass.  DD  Stem,  5660  lbs.;    ""'   "  '     "" 
Gear,  and  By-Pass.  9500  lbs. 


&md^^ 


1278 


Qi.— WATER  WORKS. 


N  Lw/     ^Ot^tl 


49. — Wbiohts  of  Ludlow  Gatbs  and  Valves,  in  I  nft     iOfTnliniiir 
re-in.  and  under:  T.  P.  W. -  800  lbs.;  R.  W.  - 200  lbs.:    it.  ^ 
(3-in.)-1601bs. 
List  No.  7.      7-in.  and  above:   T,  P.  W.-  260  lbs.;  i?.  W.  -  126  lbs.:  J?.  "^ 
(3J-6-in.,inc.)-1251bs. 
7-12-in.,  inc.:  R.  S.  (7-12-in.,  inc.)  -86  lbs. 


List  No.  8. 

T.P. 

W. 

-16001b6.; 

R. 

W. 

-750  lbs. 

Sizes 

1* 

1^' 

2' 

2H' 

3- 

3«' 

4- 

Hi' 

5- 

6* 

T 

9^ 

f 

10-   12* 

Sc.Soc 

51 

101 

160 
1»8 
61 

405 
435 
95 

FlB 

i24    139 
14'    30 

815 

L.  F..  ex 



List  No.  9.      T.  P.  W.  -  2000  lbs. ;  /?.  W.  -=  2000  lbs. ;  /?.  5.  -  1 200  lbs. 


SlJsca. 

1' 

1«' 

2' 

2H' 

8- 

m' 

4* 

*«• 

5' 

6* 

7' 

8- 

9* 

10- 

IT 

Sc.  See 

123 

158 
206 

420 

FlK 

1062 
173 

L.  F..  ex 

1 

■■'Y" 

ListNo.lO.  Brass Hor.C'ks:  r.P.TV.-aOO  lbs.; /?.Vr.-lS01bs.: /?.S.-I00Ib«. 


Sixes 

*<• 

H' 

H' 

1' 

\H' 

i«' 

2* 

iH' 

3- 

3H- 

4- 

6- 

6- 

7' 

8-     9-  J  IP 

Sc.Soc 

» 

IM 

itt 

m 

3A 

6ft 

8ft 

Fig 

1        1    " 

Horizontal 
Check 
Valves. 


List  No.  11. 


List  No.  12. 


6-in.  and  under:    T.  P.  W.-300  lbs.;   R.  n\-=r 

160  lbs.;  i?.S.- 100  lbs. 
7-in.  and  above:    T.  P.  VT.-SOO  lbs.;   R.  IT.- 

-150  lbs.;  i?.  5. -85  lbs. 
20-in.  and  under:    T.  P.  H^.-300  lbs.;   R.  IV.- 

200  lbs.  i?.S.- 85  lbs. 
24-36-in.,  inc.:    T.  P.  H^.-300  lbs.;  R.  U'.-.  150 

lbs.;  /?.S.-751bs. 
40-in.  and  above:    T.  P.  W.^ZOO  lbs;.   R.  »^- 

140  lbs.;  /?.S.-651bs. 


SiKes 

2' 

2H' 

3' 

3^' 

4' 

4Hi- 

6- 

6' 

7' 

8* 

9' 

10- 

ir 

8c.  Sec 

45 
47 
65 

80 
92 
95 

120 
133 
150 

133 
150 
160 

tab 

225 

cso 

€30 
630 

Y\g 

490 
483 

Hub 

''°1;,- 

Sizes. 

14- 

15' 

16" 

18* 

20' 

22' 

24' 

28' 

30- 

36' 

40" 

42' 

44* 

43* 

50*   «• 

Fig 

880 
885 

960 
990 

1200 

1800 
1880 

2700 
2710 

7250 
7370 

Hub 

11360 

-J 

...,....|... 

WEIGHTS  OF  LUDLOW  GATES  AND  VALVES. 


1279 


i/      49. — Wbiohts  op  Ludlow  Gatbs  and  Valvbs,  in  Lbs. — Concluded. 
Vertical  Check  Valves.      List  No.  13.    T.  P.  IV- 300  lbs.;  R.  W.- 150  lbs. 


SIxea 

2» 

2H' 

8* 

SH- 

4' 

4H'' 

5* 

6* 

7* 

8* 

r 

IC 

12* 

8c.  See 

58 

113 
152 

155 

280 
287 

Fig 

36 

415 

Hub 

Sixes. 

14' 

15' 

16' 

IS" 

20' 

24' 

28' 

30* 

36' 

40* 

42' 

44- 

48' 

Hg 

685 

7080 

Hub 

Vertical  Foot  Valves.    List  No.  14.    T.  P. 

W.' 

-200  lbs. 

R. 

W.^ 

100  lbs. 

sues. 

2' 

2H' 

3' 

3«' 

4' 

4«' 

5' 

6» 

7' 

8' 

r 

10* 

12' 

8c.  See 

60 
58 

153 
160 
132 

Fig. 

105 

240 
275 

340 

Hub 

410 

SIMS. 

14' 

15' 

16' 

18' 

20* 

24' 

28' 

30' 

36' 

40' 

42' 

44' 

48* 

jTg 

519 
562 

660 

875 

3350 

Hub 

j 

Flume 
List  No 


Valves,  f  2*-i«- 
>-15-       l30-in. 


and  under:   T.  P.  W^.  -  40  lbs. ;  i?.  W. -=  30  lbs. 
and  above:   T.  P.  W.  -  30  lbs. ;  R.  W.  -  26  lbs. 


Sluice  Gates 

List  No. 

21. 

Slsea... 

10' 

12' 

u- 

15' 

16- 

18- 

20' 

24- 

28- 

30- 

36- 

40- 

42- 

44- 

48- 

Rem'kB 

I».  F..  R.  O.  . 
I>   F.,  8.  O.    . 

215 

320 

. .. . 

340 

435 

63U 

750 

1080 

1150 

1535 

2350 

2764 

s"^ 

R.O.  with 
Splg. 

i' 
h 

R.  O.  with 
F   AN 

E.  F..R.O... 
E    F.,  8.  O     . 

S.'  O.  with 
W,  4N 

-5 

d  by  Google 


1280  H,— WATER  WORKS. 

Blow-Offs  are  placed  on  the  bottom  of  pipes  at  depressions  in  the  pipe 
line  for  cleaning  out  or  emptyixig  the  conduit.  They  consist  essentially  ot 
a  small  pipe,  say  from  4  t^  16  inches  in  diameter,  leading  to  some  suitable 
point  where  the  waste  can  be  discharged.  A  gate  is  inserted  near  the  "wm 
pipe  line.    See  Tables  16,  17,  38  and  39,  preceding. 

Illg.— ••SPECIALS." 

"Specials"  are  usually  of  cast  iron  and  include  bends,  reducers,  tees, 
wyes,  and  in  fact  many  other  shapes  that  enter  also  into  the  distributing 
system  (see  preceding  and  following  tables).  Fig.  56  shows  the  methodo! 
connecting  wood-stave  pipe  with  a  cast  special.  The  socket  or  bell  of  the 
castiag  is  usually  about  6  inches  deep,  with  offset  equal  to  thickness  of 
staves.    Fig.  57  is  a  front  half  view  of  special  casting  for  connecting  a  small 


Fig.  66.  Pig.  67,  Fig.  68.  Fig*  59. 

branch  or  a  blow-off  with  a  wood  -stave  pipe.  Note  the  attached  lugs  (boGses) 
or  shoes  s  for  holding  the  ends  of  the  steel  bands  which  cinch  around  the 
opposite  side  of  the  pipe.  These  shoes  are  shown  in  side  view  by  Fig.  68, 
and  in  the  end  view  by  Pig.  69,  the  band  passing  between  the  prongs. 

E.— DISTRIBUTING  «vqtt7T^ 

Cast  Iron  Pipe  is  by  far  the  best  that 
can  be  used,  although  the  first  cost  is 
greater  than  that  of  lap-wielded  pipe. 
For  sizes,  details  and  weights  of  cast  iron 
pipe,  see  tables  under  IIIc.  page  1214  and 
lollowing. 

It  is  to  be  noted  especially  that  there 
should  be  no  "dead  ends"  in  a  distributing 
system,  i.  e.,  cross  connection  should  be 
made  at  terminal  points,  as  at  ends  of 
streets. 

Pig.  60  is  a   Portable  Lead-Melting 

Furnace  and  ladle  for  pouring  the  joints. 
(See  page  1216  for  description  and  use  of 
gasket.) 

Matheson  Patent  Lock  Joint  Pipe  (steel 
lap-welded)  is  manufactured  in  lengths 
up  to  about  20  feet  (average  about  1 7  to 
18  feet  over  all,  according  to  size)  and  is 
tested  to  500  lbs.  hydraulic  pressure  per 
square  inch. 
.     Tables  50-64,  on  following  page,  give 

sizes   and  weights  of  pipe  and  specials:  ^^  i 

also,  lead  required  per  Joint.  Digitized  by  UOOg IC 


BLOW-OFFS.  SPECIALS.    MATHESON  PIPE. 


1281 


50. — Matheson  Pipb. 


1 

Approximate 

p 

Weights. 

OQ 

K 

Lead 

Com- 

d. 

III 

Boi 

per 

pieto 

o 

?.o 

Joint. 

per  Foot 

s. 

Ins 

Lbe. 

Lbe. 

13 

Axli 

1.07 

1.93 

13 

A^   4 

1.77 

3.36 

11 

Hx  ! 

2.67 

4.94 

10 

MX  i 

3.50 

6.56 

10 

Axi 

4.87 

8.38 

9 

Xxl 

6.62 

10.32 

9 

TftXl 

6.90 

12.42 

HH 

Hxl 

8.38 

14.74 

8 

rt^l 

9.83 

17.26 

7 

\lxlH 

13.20 

23.26 

6HS 

5xlk 

15.30 

26.44 

6 

17.20 

30.07 

5« 

ISxm 

19.20 

33.81 

5 

^xl)<( 

21.80 

37.92 

4^ 

%xlM 

23.70 

42.45 

3\i 

<^xlM 

25.60 

47.23 

3 

Sxm 

28.80 

52.61 

2H 

«xl>i 

31.10 

58.34 

I 

^xm 

40.20 

70.86 

.330' 

H^i^i 

48.10 

84.88 

.362* 

HxW^ 

55.30 

100.69 

.396- 

ixm 

64.70 

119.02 

.432- 

ixl^ 

74.60 

138.85 

^Ximlshed  Asphalted  only,  and  Kala- 
iin  and  Asphalted. 


51. — Tbbs. 


Slie. 

Wt. 

'           Siie. 

Wt, 

Ins. 

Lbs. 

1           ins. 

Lbs. 

2x2x2 

11 

6x    6x 

96 

X3x3 

19 

6x    6x 

93 

Jx3x4 

35 

6x    4x 

100 

U4x4 

35 

6x    3x 

90 

X4x4 

39 

7x    7x 

tx4x3 

35 

7x    7x 

115 

4x4x3 

35 

8x    8x 

159 

*X4X2 

87 

8x    8x 

173 

4x4x3 

36 

8x    8x 

172 

4x4x1 

34 

8z   6x 

176 

\'^i^^ 

98 

9x    9x 

4x3x4 

35 

lOx  lOx  10 

2R6 

5X5X5 

41 

lOzlOz 

8 

270 

5X5X4 

58 

lOx  lOx 

6 

268 

5X5X4 

58 

lOx  lOx 

4 

285 

5x3x5 

56 

llx  llx 

1 

353 

«x6x« 

" 

12zl2x 

2 

Heftyy.ftu^  flmires  indicate  openings 
*PP0(1  tor  Standard  Pipe. 


Fig.  61. — Matheson  Joint. 
52. — Plugs. 


Ri»^. 

Wt., 

8i«e. 

Wt., 

SIse. 

Wt.. 

Ins. 

Lbs. 

Ins. 

Lbe. 

Ins. 

Lbs. 

2 

1 

6 

7 

10 

23 

3 

2 

7 

13 

12 

4 

3 

8 

15 

14 

58 

5 

5 

9 

16 

88 

53. — Crossbs. 


Sixe. 

Wt.. 

Blse. 

Wt., 

Ins. 

Lbs. 

Ins. 

Lbs. 

2x2x2x2 

13 

6x4   X    3x    3 

125 

3x3x3x3 

28 

7x7    X    7x    7 

135 

4x4x4x4 

42 

7x7    X    6x    6 

153 

4x4x4xd 

43 

8x8   X    8x    8 

200 

4x4x3x3 

46 

8x8    X    8x    4 

229 

4x4x2x2 

45 

8x8   X    8x    6 

230 

4x4x2x2 

43 

8x8    X    4x    4 

209 

4x3x3x3 

45 

8x8   Xl4xl6 

1190 

6x5x5x5 

66 

8x6    X    8x    6 

220 

5x5x5x4 

69 

8x6    z    8x    4 

236 

6x5x4x4 

74 

8x6   X    3x    3 

238 

5x4x5x5 

72 

8x4   Z    4x    4 

218 

6x6x6x6 

108 

9x9   x    9x    9 

6x6x4x4 

117 

10x10x10x10 

337 

6x6x4x3 

120 

lOxlOxlOx    8 

339 

6x4x4x4 

127 

12x12x12x12 

Heavy-faced  flguree  indicate  openings 
tapped  for  Standard  Pipe. 


54. — Rbducbrs. 


8i«o. 

Wt.. 

Slse. 

Wt., 

Siie. 

Wt., 

Ins. 

Lbs. 

Ins. 

Lbs. 

Ins. 

Lbs 

3x2 

6x4 

21 

9x8 

4x3 

6x3 

9x7 

.... 

4x3 

6x3 

26 

9x6 

.... 

4x2 

7x6 

10x9 

.... 

6x8 

7x6 

10x8 

60 

6x4 

8x7 

10x6 

46 

5x3 

8x6 

39 

10x4 

62 

6x5 

8X4 

43 

12X1C 

76 

6x4 

22 

Heavy-hkoed  flguree  indicate  openings 
tapped  for  Standard  Pipe. 


1282 


U.— WATER  WORKS. 


Converse  Patent  Lock  Joint  Pipe  (steel  lap-welded)  is  manufactured  in 
average  lengths  of  about  18  ft.  and  tested  to  500  lbs.  per  square  inch.  A 
hub  is  leaded  to  each  length  of  pipe  at  mill  to  receive  tne  spigot  end  of  the 
adjoining  pipe  when  laid. 

56. — CONVBRSB  PiPB. 


Slse. 

API 

^roxlnia 

te  Weight. 

1 

1 

1^ 

Si 

t 

Hub. 

If 

Ids. 

In. 

Lba. 

Lbs. 

Lba. 

Lba. 

.094 

1.91 

1.00 

.108 

3.33 

8!50 

2.15 

.118 

4.89 

12.50 

2.75 

.125 

6.51 

3.00 

.132 

8.27 

8.75 

.139 

10.20 

5.50 

12!26 

.146 

12.25 

6.50 

14.66 

.154 

14.55 

37!  50 

7.50 

17.03 

.162 

17.02 

7.75 

.171 

19.78 

8.60 

23!  00 

.181 

22.85 

9.50 

26.59 

.190 

26.00 

10.75 

30.21 

.200 

29.48 

12. 

34.16 

.210 

33.18 

16. 

38.68 

.221 

37.85 

17.5 

45.4? 

.233 

41.73 

23.75 

51.38 

.245 

46.46 

30. 

56. 3t 

.258 

51.65 

34. 

63.65 

.272 

57.32 

38. 

71.35 

.300 

69.53 

50. 

87.68 

.330 

83.43 

58.5 

105.46 

.862 

99.13 

70. 

123.88 

.396 

116.76 

85. 

145.09 

.432 

136.44 

100. 

168.07 

Fig.  52. — CoNVBRSB  Joint. 
(Cast  Hub.) 
For  details  of  specials  see  National 
Tube  Works  catalog. 


Furnished  Asphalted  Only,  and  Kalameln 
and  Asphalted. 


Pipe-Dipping  Tank. — ^The  writer  has  found  it  convenient  in  some  cases 
to  order  the  lap-welded  pipe  from  the  manufacttu^er  uncoated,  and  to  coat 
it  in  the  field  before  laying.  For  this  purpose  a  dipping  tank  is  used  as  shown 
in  Fig.  63.  The  tank  should  be  about  20  ft.  long,  2  ft.  wide  and  2  feet  deep. 
Such  a  tank  constructed  of  No.  12  gauge  steel  will  weight  about  700  Ibc. 
It  is  set  over  an  improvised  brick  furnace,  cheaply  constructed  and  pro- 
vided with  a  smoke  stack.    Hard  and  liquid  asphaltum  are  mixed  in  it  in 


Fig.  63.— Pipe-Dipping  Tank. 


the  proper  proportion  and  the  pipe  is  dipped  when  it  has  reached  the  pn>per 
*«™perature.  Approximately,  the  number  of  pounds  of  asphalt  required 
per  htmdred  feet  of  pipe  is  equal  to  5.5  X  diameter  of  pipe  in  mchea. 


CONVERSE  PIPE.    TANK.    TAPPING  MACHINE         1288 

Tap^nf  Machines  are  employed  for  tapping  mains  for  service  connec- 
ons.  *  There  are  many  styles,  moire  or  less  expensive.    The  Mueller  tap- 


Pig.  04. — Mueller  Tapping  Machine. 

Ing  machine  is  illustrated  in  Pig.  64.    Por  water  mains,  the  machine  oom- 
leta  includes: 

1  each,  Combined  Drill  and  Tap— J4  fi  H  and  1  inch. 

1  each.  Screw  or  Hexagon.  Plug — H.  H.  H  and  1  inch. 

4  Malleable  Iron  Saddles  j  any  size. 

1  Chain  for  any  size  of  Pipe. 


d  by  Google 


1284 


H.—WATER  WORKS. 


Black  or  (Ulvanised  Pipe  of  "standard"  weight  as  manufactured  by  iht 
National  Tube  Co.  is  shown  in  the  following  Table.  For  the  "extra  ftrang* 
pipe  the  1-in.  size  is  0.182  in.  thick,  and  12-in.  size  0.500  in.;  while  the"doubk 
extra"  is  0.364  in.  and  0.875  in.  thick,  respectively. 


56.— 

DlllBN 

SIGNS,  IN  InCHBS.  A1 

*D  WbIO 

ara  of  Black  Pipb  (Stand akd) 

1 
Nom. 

01 
E 

IT 

Nom. 

Foot, 
Pounds 

1^ 

M 

H 

0.405 

0.269 

0.068 

0.1288 

0.0568 

0.0720 

0.241 

27 

0  081 

0.540 

0.364 

0.088 

0.2290 

0.1041 

0.1249 

0.42 

18 

004t 

It 

0.676 

0.493 

0.091 

0.8578 

0.1909 

0.1669 

0078 

0.840 

0.623 

0.109 

0.5542 

0.3039 

0.2503 

0.IJ4 

9^ 

1.050 

0.824 

0.113 

0.8659 

0.5333 

0.3326 

DM 

I 

1.S16 

1.047 

0.134 

1.3581 

0.8609 

0.4972 

11  < 

l!S 

IH 

1.660 

1.880 

0.140 

2. 1642 

1.4957 

0.6685 

u2 

IH 

1.000 

1.610 

[).145 

2.8353 

2.0358 

0.7995 

11 2 

0.808 

2 

2.375 

2.067 

0.154 

4.4301 

3.3556 

1.074 

114 

l.M 

2H 

2.875 

2.467 

0.204 

6.4918 

4.7800 

1.712 

1.717 

3 

3.500 

3.066 

0.217 

9.6211 

7.3827 

2.238 

S.«2i 

3H 

4.000 

3.548 

0.226 

12.566 

9.886 

2.680 

4.088 

4 

4.500 

4.026 

0.237 

15.904 

12.730 

8.174 

4.  US 

4H 

5.000 

4.508 

0.246 

19.635 

15.960 

3.676 

It. mm 

4.87i 

6 

5.563 

5.046 

0.259 

24.306 

19965 

4.821 

14.502 

8.437 

6 

6.625 

6.065 

0.280 

34.472 

28.886 

5.586 

18.762 

10.828 

7 

7.625 

7.023 

0.301 

45.664 

18. 7a 

6.921 

28.271 

11.278 

8 

8.625 

7.981 

0  322 

68.426 

50.021 

8.405 

28.177 

15.158 

9 

0.625 

8.937 

0.344 

72.760 

62.722 

10.04 

33.701 

17.828 

10 

10.750 

10.018 

0.366 

90.763 

78.822 

11.94 

40.066 

27.708 

11 

11.750 

11.000 

0.375 

108.43 

95.034 

13.40 

48.95 

S1.2S8 

12 

12.760 

12.000 

0.375 

127.68 

113.09 

14.59 

48.985 

a.  187 

57. — DiSCHARGB    IN  GALLONS   PBR   MiNUTB  ThROUOH  Sm ALL  PiPBS. 

(Values  are  approximate.) 

//—head  in  ft.;  L  — length  of  pipe  in  ft.;  numbers  in  first  column  are 

values  ol  H'*-L. 

[Gallons  per  Minute.] 


Head 
H. 

Diameter  of  Pipe.  In  Inches. 

H 

% 

H 

1 

IM 

l« 

3 

2» 

3 

4 

5 

6 

O.IOOL 

2.0 

3.6 

11.2 

19.5 

30.8 

63.2 

110.4 

174.5 

358.1 

624.7 

98C  5 

O.lllL 

2.1 

3.6 

11.8 

20.6 

32  5 

66.fl 

116.4 

183.S 

377^ 

658.  S 

1038. 

0.1251, 

2.2 

3.9 

12.5 

21.8 

34.4 

70.7 

123.5 

195.1 

S99.( 

098.! 

1109. 

0.143L 

2.4 

4.1 

18.4 

23.3 

36.8 

75. « 

132.C 

208.5 

428.  ( 

746  7 

1178 

0.167L 

2.6 

4.4 

14.4 

25.2 

39.8 

81. C 

142.6 

225.2 

463.1 

806.9 

1272- 

0.200L 

2.8 

4.8 

16.8 

27.6 

43.9 

89.4 

156.2 

246.7 

506.5 

883.9 

13S4 

0.2501/ 

3.1 

6.6 

17.7 

80.9 

48.7 

lOO.C 

174.« 

275.  { 

566.2 

987.7 

1558 

0.3S3L 

3.6 

6.8 

20.4 

85.6 

56.2 

115.4 

201. « 

817. § 

653.S 

1141 

1799 

0.500L 

4  4 

7.7   12.2 

36.0 

43.7 

68.7 

141.4 

246.  S 

390.1 

8IW.8 

1394 

2204 

0.750L 

5.4 

9.5 

14.9 

80.6 

53.5 

84.3 

173.  l" 

302.4 

477.1 

979.3 

1711. 

2893 

L 

6.3 

10.9 

17.2 

36.3 

61.7 

97.4 

199.1 

349.2 

556.! 

1133. 

1976. 

3116. 

1.26L 

7.0 

12.2 

19.3 

89.5 

69.0 

108.9 

223.  { 

390.4 

615.S 

1264. 

2809. 

3484 

1.60L 

7.7 

11.4 

21.1 

48.2 

75.6 

119.3 

248.  { 

427.7 

674.  J 

1385. 

2420. 

3817. 

1.78L 

8.1 

14.4 

22.8 

46.8 

81.6 

128.8 

264.4 

462.  C 

728.! 

1496. 

2613. 

4121 

2L 

8.8 

15.4 

24.3 

60.0 

87.3 

137.7 

282.7 

493.  C 

780.  a 

1602. 

2791. 

4407. 

IL 

10.8 

18.9 

29.8 

61.2 

106.9 

168.7 

346.a 

804.1 

055.! 

1962. 

3406. 

5391. 

\L 

12.5 

21.8 

34.4 

70.7 

123.4 

194.8 

399.8 

698  E 

1103. 

8265. 

3951. 

6233. 

6L 

14.0 

24.4 

38.5 

79.0 

138.0 

217.7 

447. C 

780. t 

1234. 

2532. 

4417. 

69(8. 

6L 

15.3 

26.5 

42.2 

86.6 

161.2 

238.5 

488.1 

855,4 

1351. 

2774. 

4839 

7613. 

IL 

16.6 

28. 9 

46.6 

93.6 

163.3 

257  6 

528.  t 

024.C 

1460. 

2996. 

5227. 

8245. 

8L 

17.7 

30.1 

48.7 

100.0 

174.6 

275.4 

566.4 

987.J 

1560. 

3288. 

5588. 

8814. 

•L 

18.7 

12.7 

51.7 

106.0 

185.2 

292.1 

699.7 

1048. 

1651. 

3897 

5828. 

9349. 

lOL 

19.8 

84.6 

54.4 

111.8 

195.2 

306.0 

632.2 

1104. 

1745. 

8581. 

6347. 

9355. 

Ex. — ^What  is  the  capacity  of  a  pipe  IM  in.  dia..  and  150  ft.  long,  the  head 
being  50  ft.?    Solution— H ^  ^L" MZL\ 
discharge  is  35.6  gallons  per  min. 


Dte^'y(gbf)^lt*°-  P^P* 


the 


BLACK  OR  GALVANIZED  PIPE,   GATE   VALVES.        1286 

date  Valves  should  be  of  the  best  quality. 

Pig.  66  shows  a  section  of  standard  bronze  mounted  babbitt  seat  valve, 
ip  to  15  ins.,  as  mantifactured  by  the  Chapman  Valve  Co.  of  Indian 
>rchard,  Mass. 

Pig.  66  shows  a  section  of  the  Eddy  gate  valve. 

Notation  of  Parts:— 
A— Stem  Nut.         G— Body. 
—Stem.  H— Body  and  Cover  Bolts. 

—Follower.  I — Ball  and  Carrier. 

—Follower  Bolts.  J— Gate. 
—Stuffing  Box.    K— Gate  Ring. 
—Cover.  L — Case  Ring. 


Pig.  66.— Chapman.  Pig.  66.— Eddy. 


d  by  Google 


ISM 


U.—WATER  WORKS. 


-7—- — 


d  by  Google 


LUDLOW  GATE  VALVES,  SMALLER  SIZES.  1387 


•S 


c 

f 


5 


O 

Q 
I 


d  by  Google 


1283  M.—WATER  WORKS. 

59. — ^Wbiohts  of  Ludlow  Gatb-  or  Valvb  Boxbs. 
[Weight  in  Lbs.] 


Gate  Boxes,  Fig.  68,  are  telescopic  casings  of  cast  iron  to  place  over  the 
sate  valves  and  protect  them  from  surrounding  earth  or 
back-fill;  and  render  them  accessible  to  operate  from  the 
street  in  opening  and  closing.  The  cover  is  a  circular  cast 
plug  which  fits  m  the  bell  of  the  top  casting  or  telescope 
portion  of  the  box.  The  telescope  is  provided  with  a  flange, 
placed  at  the  middle  or  at  the  lower  end  to  hold  it  at  the 
proper  elevation  when  placed.  The  main  box  is  enlarged 
at  the  bottom  to  fit  over  the  body  of  the  gate.  Caution 
must  be  used  in  designing  gate  boxes  as  the  outside  dimgn- 
sions  of  gates  by  different  makers  vary  considerably. 
Thus,  a  gate  box  which  would  fit  a  12-in.  ffate  manufac- 
tured by  A,  wotild  perhaps  be  too  small  for  the  "same  size" 
gate  manutactured  by  a.    See  Table  60  for  weights. 

Check  Valves,  Pig.  60.  are  placed  in  pipe  lines  or  mains 
(either  in  a  vertical,  inclined  or  horizontal  position)  to 
prevent  back  flow  or  excessive  back  pressure.  They  are 
usually  located  at  or  near  the  pumping  station. 

Pressure  Relief  Valves  are  specially  designed  to  relieve 
excessive  pressure  within  a  mam  due  to  water  hammer. 
They  allow  some  of  the  water  to  escape,  and  operate  auto- 
matically. 

Hydrants  or  "fire  plugs"  are  designated  by  the  size 
of  valve  opening;  by  the  number  of  nozzles,  as  single-, 
double,- etc.;  and  ^  the  kind  of  discharge  nozzles,  as 
steamer-,  or  hose-.  The  4,  4i,  5  and  6-inch  (valve  opening;) 
fire  hydrants  are  the  most  common.    The  essential  principal  is 

that  the  valve  be  placed  below  the  reach  of  frost,  and  that  m ed 


Fig.  69.— Check  Valve. 
the  water  remaining  above  it  shall  be  allowed  to  "drip"  out  to  prevent  its 
freezing.    For  this  reason  the  hydrants  should  be  set  on  a  bed  of  firm,  loose  ' 
rock  to  provide  for  the  drip.    Figs.  70  and  71  show  sections  of  the  Chapmac  ( 
and  Ludlow  types,  respectively.    Figs.  72  and  73  show  sections  of  valves  I 
and  seats  for  the  Mathews'  patent  hydrant,  the  former  being  single-actiqg 
and  the  latter  double-acting.  Digitized  by  LiOOgle 


GATE  BOXES,  VALVES,  HYDRANTS.  1289 

Hydrants  are  connected  with  transverse  pipes  leading  from  the  street 
mains,  and  hence  it  will  be  seen  that  there  is  considerable  hydrostatic  pres- 
sure acting  horizontally  against  them  at  the  bottom.  This  should  be 
resisted  by  a  strong  stone  backing  when  the  hydrant  is  set. 

~  A— Hjrclnttt  BsmI  or 

mad  Pipe. 


I>-Top  Nut 


P— StufliAg  Box  NuL 
O— StdBqgDox. 
H— FoDowBr. 

I-DOOM. 

J— Doom  Bolt*. 
K-BraoMNosda. 

M-Uppw  Vaho 

Plato. 
llxVKlve. 


Va1v« 
PUto. 

^-Vlihro  Rubben. 


R— BrauM  NuL 

8— BraoM  Loek  Nut. 

T— BrooM  Comigided 
DnpPtm. 

V-Drip  Rubber. 

Z^Braoae  Dr^  Nut. 

T— BroBM  Drip  Cup. 


Pig.  70. 


Pig.  73. 


b igitized  by  NJ O OQIC 


1390 


^L--WATER  WORKS. 


50. — Wbioht  of  Ludlow  Hydrants,  ih  Lbs. 


Yard  Hydrants.  1  Test  Pressure 
List  No.  2  5.        J  Water-  1 00  lbs. 

Wash  Hydrants.  iTest  Pressure 
List  No.  25«.       /  Water-  1 00  lbs. 

Sizes  

H' 

H' 

!• 

sues 

H' 

H' 

1* 

6-f t.  Length. 

45 
8 

55 
5 

75 
6 

5-ft.  Length 

40 

S 

M 

6-ln.  Length,  extra. 

6-ln.  Leogth.  extra. . . . 

f 

Fire  Hydrants.   List  No.  76. 

Test  PresBore  Water-  300  Urn. 

Frost 

Stand 

Seat 

Pipe  Con- 

Number and 

Wt.8tandar<] 

Weight 

Oasefor 

^Sft 

Pipe. 

Ring. 

nection. 

SiseoC 

Length 

per  Ft. 

6-Ft. 

Nozsles. 

5  Feet. 

Length. 

Ins. 

Ins. 

Ins. 

Ins. 

Lbs. 

Lbs. 

Lbs. 

Lbs. 

3 

2  or  3 

one  8 

130 

12 

iH 

3  or  4 

one  tH 
one  2^ 

310to815 

26 

84 

21 

5H 

3  or  4 

365  to  370 

30 

96 

34 

f^H 

4or« 

two  2H 

375  to  380 

30 

06 

24 

eW 

\\i 

5  or  6 

two  2H 

437  to  442 

34 

106 

26 

•M 

5or« 

three  2H 

448  to  453 

34 

106 

26 

7 

5  or  6 

one  steamer 
and  two  2H 

475  to  486 

3< 

116 

29 

8 

6  or  8 

one  steamer  1 
and  two  2^  ] 

590  to  600 

40 

144 

2t 

10 

8orl0 

six  2H 

1200  to  1220 

73 

219 

.... 

Notes  on  List  No.  75:  Add  for  a  6-in.  Hub  or  Bell  over  Hydrant  wiA 
4-in.  Hub  or  Bell.  16  lbs.:  add  for  each  additional  2^-in.  Nozxle,  inchiding 
Cap  and  Chain,  11  lbs.:  add  for  each  additional  4-in.  Steamer  Noszle,  io^aa- 
ing  Cap  and  Chain,  25  lbs.  The  above  weights  are  based  on  a  length  of  5  £eei 
measuring  from  the  surface  of  ground  to  bottom  of  connecting  pipe. 

Hydrants  with  Crane  Attachment.    List  No.  76.    Test  Pressure  Water—  300  Ihs. 
Extra  to  add  to  weight  of  Hydrant:  300  lbs.  Cor  8  In.;  310  lbs.  tor  4-ln. 


Water  Cranes.  List  No.  77. 
3-ln.  Length,  5  feet,  587  lbs. 
4-ln.  Length.  5  feet.  600  lbs. 


Test  Pressure  Water—  300  lbs. 

Each  6-tn8.  Stand  Pipe  and  Box.  13  ibe. 

Eaoh  6-lns.  Stand  Pipe  and  Booe.  13  Iba. 


Flush  Hydrants.    List  No.  78.        Test  Pressure  Water—  300  lbs. 


Seat 
Ring. 

Stand 
Pipe. 

Pipe 
Connection. 

Nosales. 

Weight  5-rt. 
Length. 

S?^» 

Ins. 
2 
8 
4 

Ins. 

Ins. 

2 

3or4 

4or6 

Ins. 
one  2 

Lbs. 

90 
290 
360 

Um. 
12 
26 

30 

d  by  Google 


HYDRANTS.    MISCELLANEOUS  DATA,  12«1 

EXCERPTS  AND  REFERENCES. 

The  New  Water-Works  Reservoir  at  Trenton,  N.  J.  (By  C.  A.  Hague. 
Eng.  News,  June  13,  1901). — Six  illustrations:  Section  of  reservoir,  cross- 
section  of  wall  and  embankment;  view  of  gate  house;  plans  and  sections  of 
outlet  pipe. 

Iron  or  Wooden  Lock  dates;  Cost  of  Construction  and  Maintenance 
(Eng.  News,  Oct.  9,  1902). 

A  Stress  Diagram  for  Water-Tank  Hoops  (By  Ballinger  &  Perrot. 
Eng.News.Mar.  5.  1903). 

Four  Systems  of  Softening  Water  for  Industrial  Purposes  (Eng.  News, 
July  2.  1903).— Described  and  illustrated. 

A  Proposed  High-Pressure  Water-Supply  System  for  Fire  Protection 
in  Cliicago  (Eng.  News.  Mar.  3.  1904). — Illustrations:  Main  conduit;  details 
of  steel  and  cast-iron  pipe:  details  of  fire-boat  connection;  section  of  main 
conduit  lateral;  maps  of  high-pressure  water  supply  systems  for  fire  pro- 
tection in  different  cities. 

Experience  in  Tbawlng  Water  Pipes  By  Electricity  (Eng.  News, 
Bfar.  17.  1904). 

The  Five  Dams  and  Wood-SUve  Conduit  of  the  ^uthem  California 
Mountain  Water  Co.  (Eng.  News,  April  7.  1904). — Fifteen  illustrations:  and 
18  tables,  including  cost  data. 

The  PhiUdelphia  Filtration  System  (Eng.  News,  Dec.  8.  1904).— 
Numerous  illustrations. 

Cost  of  Laying  a  i2-in.  Water  Pipe  Across  a  River  (Eng.  News, 
Mar.  2,  1906). — ^The  labor  cost  of  building  44  A-frames,  placing  and  caulking 
the  516-ft.  pipe  line,  was  $122. 

A  Diagram  for  Estimating  the  Yardage  of  a  Trench  (Eng.  News, 
July  6,  1905). — (Quantities  in  cu.  yds.  for  various  widths  in  ft.,  up  to  20  ft., 
and  various  depths  in  ft.,  up  to  30  ft. 

Purification  of  Water  by  Copper  Sulphate  (By  D.  D.  Jackson.  Eng. 
News.  Sept.  21,  1905). — For  other  papers  and  discussions,  see  Eng.  News 
of  Nov.  30.  1906. 

The  Balseleys,  Springfield,  Forest  Stream,  and  Hempstead,  Filter 
Plants,  Borough  of  Brooklyn,  New  York  (Eng.  News,  Aug.  23.  1906).— Table 
showing  the  net  amount  of  water  filtered  at  two  mechanical  and  at  two 
slow  sand  filter  plants,  during  the  year  1906;  following  totals  are  repro- 
duced: 

BaiselevB  (mechanical) 1.435.6  million  gals.  @  $6  53  p.  m.  g. 

Springfield  (mechanical) 694.6       9.68 

Hempstead  (slow  sand) 416.8       "         "      "     2.89 

Forest  Stream  (slow  sand) 1.075.3       "         "       **     2.28 

The  Cost  of  aearing  and  Qrubbinc  a  Reservoir  Site  (By  T.  Griggs. 
Paper,  A.  S  of  Mun.  Imp.,  Oct.,  1906;  Eng.  News.  Nov.  29.  1906). 

DUiointinc  Cast-iron  Water  Mahis  (Eng.  News.  Oct.  10,  1907).— 
Methods  used. 

Repairing  a  Remarkable  Leak  in  a  Reservoir  Embankment  at  Provi- 
dence, R.  i.lEng.  News,  Oct.  17.  1907.)— Described  and  illustrated. 

Diagrams  for  Computing  Thickness  of  Steel  Pipe  Shells  for  Different 
Joint  Efficiencies  (By  R  Muller  Eng.  News,  Apnl  2,  1908).— The  dia- 
grams are  based  on  the  following  assumptions:  Tensile  strength  of  plate, 
50  000  lbs  per  sq.  in  of  section;  factor  of  safety,  4.  Percentage  of  effi- 
ciency of  riveted  joints,  assumed  at:  single  riveted  joint,  56%;  double- 
riveted  joint,  69%;  triple  riveted-joint,  75%;  double-weld  butt  joint,  87%; 
quadruple-riveted  joint,  95% 

Method  and  Cost  of  Hauling  a  Water  Main  Across  Channel  at  Van* 
cower.  B.  C.  (Enyg.  News,  May  14,  1909). — Dlustrated:  method,  and  section 
through  fiexible-joint. 

Data  on  SUting  Up  of  Reservoh^  (By  R.  H.  Bolster.  Eng.  News, 
July  80.  1908). 

Repairs  to  a  72-in.  Relnforced-Concrete  Jacketed  Steel  Conduit 
Under  30-Ft.  of  Water  (By  A.  W.  Cuddeback.  Paper,  A^W.  W.  Assn., 
May.  1908;   Eng.  News,  Aug.  6.  1908).— Illustrated.    izedbyCjOOglC 


1292  ^-'WATER  WORKS, 

The  Deslm  of  Elevated  Tanks  and  Stand-Plpes  (By  C.  W.  Birch-NortL 
Trans.  A.  S.  C.  E..  Vol.  LXIV.,  Sept..  1»0»).— Speofications, 

Watcr-Works  Valnatton  (By  Leonard  Metcalf.  Trans.  A.  S.  C.  B..  Vol 
LXIV.,  Sept.,  1909}. — Numerous  bond-,  compound-interest-,  and  srakxr^ 
fund  formulas,  a  bibliography  of  water-works  valuation;  variovis  kinds  of 
"values"  discussed. 

Cost  of  aearing  Water  in  Settlinff  Basins  (By  S.  Bent  Russell.  Pap«, 
Central  States  W.  W.  Assn.,  Columbus.  O..  Sept.  28,  1909.  Eng.  News, 
Oct.  14.  1909). — ^Tables  of  cost  of  reservoirs  and  settling  water. 

The  Purification  of  the  Water  Supply  of  Steeiton.  Pa.  (By  J.  H.  Puertca. 
Trans.  A.  S.  C.  E..  Vol.  LXVI..  Mar.,  1910).— Cost  data;  illustrations; 
discussions. 

The  Use  of  Sulphate  of  Alnmhia  and  Hypochlorite  of  Ume  hi  the  Storafe 
and  Distributing  Reservoir  of  the  Nashville  Water- Worics  (By  George  Reyer 
Eng.  News.  Apr.  7,  1910). — ^The  cost  of  sulphate  of  alumina  (the  ordinary 
is  used)  is  $1.07i  per  100  lbs.  and  of  the  hypochlorite  of  lime  (it  contafais 
about  36%  of  chlorine)  is  $1.50  per  100  lbs.  The  cost  per  l.OOO.OOO  gab.  of 
water  treated  is  about  $1.75  for  sulphate  of  alumina  and  $1.05  for  cost  c^ 
hypochlorite  of  lime,  making  the  combined  cost  of  chemicals  $2.80.  The 
water  comsumption  for  the  year  1909  averaged  about  14,000,000  gals,,  or 
some  107  gals,  per  capita. 

This  article  is  followed  by  five  others,  namely:  A  20,000,000-Gal.  Hypo> 
chlorite  Water-Disinfecting  Plant  at  Minneapolis,  Minn.  (By  J.  A.  Tensen). 
The  Use  of  Hypochlorite  ofLime  to  Disinfect  the  Water-Supply  of  Moatreaj. 
P.  0.  (Geo.  Janin,  C.  E.).  The  Use  of  Hypochlorite  of  Lime  in  Connectioo 
with  the  Mechanical-Filtration  Plant  of  Iiarrisbura,  Pa.  (G.  C.  Kennedy, 
Supt.).  Hypochlorite  of  Lime  as  an  Adjunct  to  Mechanical  Water  Filtra- 
tion at  Quincy.  DI,  (By  W.  R.  Gelston.  Paper,  Dl.  Water  Supply  Assn.. 
Mar.  8,  »,  1910). — Experiments  with  Hypochlorite  of  Lime  as  a  Water 
Disinfectant  at  Hartford.  Conn.  (By  Ermon  M.  Peck,  Engr.). 

The  Groined  Arch  in  Filter  and  Covered  Reservoh-  Constmctloo  (By 
Thomas  H.  Wiggin.  Paper,  Nat'l  Assn.  Cement  Users.  Feb.  21-26,  1910: 
Eng.  News,  Apnl  7,  1910). — Discussions  of:  Volumes  of  elliptical  groined 
arch  units;  Methods  of  design;  Computation  of  groined  arch  as  cantilever; 
Effect  of  steel  in  groin  arch;  Shrinkage  and  temperature  changes;  Aid  given 
by  earth  covering;  Omstruction  stresses;  Floors  of  filters  and  reservoirs; 
Side  walls  and  division  walls;  Comparison  of  groined  arch  roof  with  rein- 
forced-concrete  slab  and  beam  construction.  Dlustrations.  TaUe  oaa> 
taining  data  on  groined  arch  roofs  for  filters  and  reservoirs. 

The  Improved  Water  and  Sewerage  Works  of  Columbus,  O.  (By  J.  H. 
Gregory,  Trans.  A.  S.  C.  E..  Vol.  LXVIl..  June.  1910).— Illu8tratio«; 
Scioto  river  storage  dam;  pumping  station:  offices  and  laboratories;  settlix^ 
basins;  details  of  filter  gallery:  details  of  filters;  details  of  filterted-waSer 
reservoirs,  etc. 

Determinatkm  of  the  Resuttant  Angle  hi  Layhig  Out  Combined  Beodi 
for  Pipe  Lines  (By  C.  A.  Jackson.  Eng.  News.  Aug.  11.  1910). — Graphical 
and  analytical  methods.     Example  given. 

Concrete  Tower  Enclosing  a  Water-Worics  Tank  at  Gary,  End.  (Eng. 
News,  Oct.  20,  1910). — ^Tower  is  octagonal  in  plan,  34  ft.  diam..  inside  the 
faces,  and  133  ft.  high  from  the  grade  Tine.     Pixlly  described  and  illustrated. 

Steel  Pipes  for  WaterwWorks  (By  Emil  Kuichling.  Paper,  Tour.  Am. 
W.  W.  Assn..  presented  Sept.  21-23,  1910;  Eng.  News.  Oct.  21,  1910).— 
Discussion  of  wrought-iron  and  of  steel  water  mains  and  protective  coatinA 
strength  of  pipes,  vacuum  relief  valves,  capacity  of  pipe.  Cost  of  steel  and 
cast-iron  pipe. — "The  fact  that  lock-bar  and  welded  pipe  can  develop  the 
full  strength  of  the  plate,  while  a  riveted  seam  has  only  about  70%  efficiency. 
influences  the  comparative  costs.  This  difference  is  likely  to  be  made  up  by 
a  countervailing  difference  in  unit-prices,  however.  Empirical  formulas 
for  cost  of  steel  and  cast-iron  pipe  have  been  devised  by  the  author  (Mr. 
Kuichling)  "    *  "'  ^  .«.*  «         — . 

an  ( 

to  a    _      __.   ^_, ,    . 

iron  pipe  and  1-16*  for  steel  pipe.  Taking  d  as  the  nominal  dia.  of  pipe,  in 
ins.,  the  cost  in  cenU  per  lin.  ft.  is:  Cost  of  steel  pipe.  0.412W*;  cost  of  caat- 
iron  pipe,  19+d  (0.4845d— 0.861).  Subtracting  the  latter  from  the  former 
gives  the  saving  due  to  using  steel:  Steel  pipe  cheapw^ bK^{At(i  (0.072tf— 


MISCELLANEOUS  DATA,  1293 

0.851),  which  in  case  of  a  36-in.  pipe,  for  example,  amounts  to  81.7  cts.  per 
ft.  For  a  complete  comparison,  however,  the  shorter  life  of  the  steel  pipe 
must  be  taken  mto  account." 

Depreciation  in  Water-Worics  Operation  and  Accoimtiiif  (By  Leonard 
Metcalf .  Paper  read  before  the  N.  E.  W.  W.  Assn..  Sept.  22.  1»10;  Eng. 
News,  Nov.  3.  1010). — Contains  sinking-fund  and  depreciation  diaigramt 
and  tables. 

Pneumatic  Caulking  of  Mains  with  Lead  Wool  (By  C.  €.  Simpson,  Jr. 
Paper  read  before  the  Am.  Gas  Institute;  Eng.  Rec.,  Nov.  12,  1»10).— The 
Cons.  Gas  Co.  of  New  York,  in  an  effort  to  reduce  the  cost  of  caulking  mains 
by  hand,  carried  on  extensive  tests  with  pneumatic  tools  and  lead  wool, 
and  the  results  were  so  satisfactory  that  the  pneumatic  method  was  finally 
adopted  on  a  considerable  portion  of  its  work,  which  includes  lines  of  48,  36 
and  30-in.  mains.    The  suiicle  gives  detailed  costs. 

Forms  for  Concrete  (By  J.  D.  Stevenson.  Paper  before  Eng'rs  Soc.  of 
Western  Penn..  Sept.  20,  1010;  Eng.  Rec.,  Dec.  10,  1010). — ^Discussion  of 
experience  of  three  years  in  construction  of  the  Pittsburg  filtration  works 
(pmcing  abf^ut  334,000  cu.  yds.  of  concrete)  under  the  followinjK  heads:— 
Material.  /Resign  of  forms,  support  of  forms,  buoyancy  of  forms,  joints,  care 
while  filling,  and  removing  forms.  For  labor  costs  on  fonns,  see  Eng.  Rec. 
of  Dec.  17.  1910. 

Waterproofing  the  New  Ufan  (Minn.)  Reservoir  (By  H.  F.  Blomguist. 
Eng.  Rec.,  Dec.  17,  1910). — Reservoir  is  75  ft.  in  diam.,  30  ft.  deep,  capacity 
1.000,000  gals.,  built  of  reinforced  concrete,  with  a  conical  reinforced 
concrete  roof.  Hard  clay,  well  drained  naturally,  upon  which  a  12-in. 
layer  of  stone  having  the  voids  filled  with  a  wet  fine-grained  concrete  formed 
the  fotindation  for  the  10-in.  floor  slab  proper,  which  was  reinforced  near 
the  sixrface  with  10-gauge,  3-in.  mesh  expanded  metal.  To  insure  water 
tightness,  special  care  was  taken  during  construction  to  grade  the  concrete 
aggregate.  Pebbles  varying  in  size  from  J  to  2i  in.,  screened  from  a  gravel 
bank,  were  used  in  the  upper  floor  and  walls,  as  experiments  had  shown 
that  these  pebbles  made  a  denser  concrete  than  broken  stone.  To  reduce 
the  permcaDility  of  the  concrete  to  a  minimum  20  lbs.  of  hydrated  lime  was 
usea  to  every  barrel  of  cement,  and  after  the  forms  were  removed  the  walls 
were  brushea  and  cleaned  with  steel  brushes,  and  two  coats  of  1  :  2  cement 
plastering  about  i  in.  thick  were  applied.  The  mortar  for  the  plastering 
contained  the  waterproofing  compotmd  to  the  extent  of  10%  of  the  cement 
xised.  A  ^ush  coat  of  1 :  2  cement  mortar  was  floated  over  the  surface  of 
the  concrete  floor  at  the  time  it  was  laid  and  a  brush  coat  of  cement  grout 
applied  to  the  slushed  surface  after  it  had  set.  After  water  was  let  in.  some 
leakage  took  place  and  cracks  developed.  The  reservoir  then  received 
further  treatment,  and  was  rendered  watertight. 
IBustnitkms  of  Important  Woiks: — 

Description.  Eng.  News. 

Intake  caisson  for  Cincinnati  Water  works,  showing  break  May  30,  1901. 
Intake  timnel  of  Cleveland  water  works,  showing  accident  Aug.  29,  '01. 
Water  tank  at  Fairhaven,  Mass.,  showing  failure  Nov.  21.  '01. 

An  8*  gate  valve  for  River  Rogue,  Michigan  April  17,  '02. 

Ccmcrete-Hned  reservoir  with  concave  slopes,  Aurora,  HI.  May  22.  '02. 

Slow  sand  filters  of  Hudson,  N.  Y..  water  works  Aug.  14,  '02. 

Cross-section  of  a  fire  hydrant  with  a  balanced  valve  Nov.  20,'  02. 

Water  tank  with  hemispherical  bottom,  Chicago  Dec.  26,  '02. 

Plan  of  Klein's  classifier  for  fine  material  Jan.     8.  '03. 

Intake  timnel  for  the  C^hampion  Mill  on  Lake  Superior  Oct.     1.  '03. 

Plan  of  scow  for  submarine  pipe-laying  Dec.  24,  '03. 

New  type  of  water  tower,  Victoria  railways^  Australia  Dec.  31,  '03. 

A  tool  for  removing  broken  taps  in  water  pipes,  etc.  Jan.     7,  '04. 

Cast-iron  pipe.  48*  dia..  flattened  imder  back-fill  Dec.  15,  '04. 

Rfiinforcca-concrete  waterworks  standpipe  81'  high  Feb.  25,  '04. 

Sectioaial  plan  of  30*  "Premier"  water  meter  May  19,  '04. 

Failure  of  a  water  tank  designed  by  an  architect  May   19,  '04. 

Sections  of  core  walls  for  reservoir  embankments  June  30,  '04. 

Laying  submerged  pipe  at  N.  Tonawanda,  N.  Y.  Aug.    4,  '04. 

Details  of  coagulating  plant,  St.  Louis  settling  basins  Oct.   27,  |04. 

New  water  tank  and  tower,  E.  Providence,  R.  L  Nov.  10,  '04. 

Small  brick  reservoir,  showing  failure  ^  Nov.  17,  04. 

Digitized  by  VjOOQ  IC 


1294  H,— WATER  WORKS. 

Automatic  regulating  valve  for  reservoirs  and  standpipes  Mar.     Ol  '81 

The  water  softening  plant  at  Oberlin.  O.  Sept.  21,  *63. 

A  75  000-gal.  rein.-conc.  cistern  for  fire  protection  Sept.  28.  '#& 

Details  of  elevated  water  tank  and  supporting  tower  Oct.   26,  *0&. 

Plans  of  rein.-conc.  reservoir  at  Ft.  Meade.  So.  Dak.  Dec.  28,  '05. 

Steel  pipe  line  supported  across  gulch  by  arched  girder  Feb.     8,  *06. 

Reinforced-concrcte  filter-bed  walls  and  roofs  April  20,  *0t 

Plans  of  water  purification  plant,  Paris,  Ky.  May     3,  'Ot. 

Plans  of  a  slow  sand  water  niter  for  the  home  Aug.     y.  *0«. 

Reinforccd-concrete  mechanical  filter  plant,  Germany  Sept.    6w  'ift. 

Details  of  novel  reinforced -concrete  conduit,  42*  dia.  Oct.      4,  'OBi. 

Apparatus  for  regulating  discharge  from  reservoir  Oct.  25.  '06L 

Plans  of  slow  sand  filtration  plant,  Wash.  D.  C.  Nov.    8,  '06. 

Steel  water  tank  (ISC  dia.  x  2(y  high),  vertical  bracing  Nov.  15.  'Oi. 

Sand  chutes  for  canal  of  Bijou  Irrigation  District  Jan.     3,  '07. 

Reinforccd-concrete  standpipe,  Attleboro,  Mass.  Feb.  21,  '07. 

A  new  design  for  balanced  gate  valve  Oct.   17.  '07. 

Forbes  water-sterilizing  apparatus  Oct.   81.  '07. 

Plan  and  section  of  gate  house,  reservoir,  Portland.  Ore.  Feb.     6.  '07. 

Automatic  controlling  valve  for  reservoirs,  tanks,  etc.  Mar.  12,  '08. 

Experimental  water-filter  plant,  Oakkmd,  Cal.  May  21.  '08. 

Remforced -concrete  reservoir,  Indianapolis,  Ind;  Oct.    15,  'OS. 

Reinforced-concrete  tank  supported  by  hollow  shaft  Tan.  7,  '09. 
Alternate  designs  of  hand-  and  mach.  washed  slow  sand  filters  May  20.  '00. 

Fire-proof  temporary  crib,  water  tunnel,  Chicago  June  17,  '09. 

Design  of  an  8-mile  head  h>'drauUc  conduit  Aug.    5,  '09. 

Steel  penstocks — expansion  joints,  elbow,  saddle  Feb.   10,  *10. 

Brick  water  tower,  133  ft.  high,  28  ft.  diam.  Mar.  24,  '10. 

Forms  for  concrete  vaulted  roofs,  water  filters  Apr.   14,  '10, 

10, 000, 000-gal.  pressure  mechanical  filter  plant  Apr.  14.  '10. 

Sliding  sluice-gates,  Charles  River  Basin,  Boston  May  26i»  '10. 
Rein.-conc.  pumping  cistern,  42'  high  x  W  dia.,  sunk  in 

ground  Aug.  25^  '10. 

A  new  filter-sand  washing  machine,  in  France  Oct.    IS.  '10. 

Rein.-conc.  water  tank  with  dome-shaped  bottom  Dec.   15.  *10. 

Large  (102-in.)  venturi  meter  for  Montreal  W.  W.  Dec   15.  'la 

New  filtration  plant  at  Portsmouth.  Eng.  Dec.   15,  '10. 

Ens.  Rec 

An  endless  screen  for  a  water-woiks  intake  Ifay  29,  *09. 

Rate  controller  and  valve  for  Cincinnati  filters  June  19,  'OO. 

Plan  of  aerator,  settling  basin,  filter,  inlet,  Dover,  N.  H.  June  19,  'Of. 

Details  pipe  line  construction.  Canyon  City  water  supply  Dec.  4,  '09. 
Collapsible  form  for  concrete  conduit,  Los  Angeles  aqueduct     Jan.      1,  '10. 

10. 500, 000-gal.  covered,  rein.-conc.  reservoir.  Mexico  Aug.     0,  'lO. 

Reinforced  concrete  water  tower,  Wcsteriy,  R.  L  Sept.  24,  *  10. 

Details  of  concrete  lining,  Seattle  reservous  Sept.  24.  '10. 

Ultra-violet  ray  sterilizer  for  sterilizing  water;  cost  Dec.   10, '10. 

Illustrated  details  of  the  Toledo  (O.)  filtration  plant  Nov.  26,  '10. 
Tall  rein.-conc.  block  water  tower  (28,250  cu.  ft.  capac.)  near 

Brussels  Dec  10. 'lOi 


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65.— SANITATION. 


Dry  Refuse  , 


Garbage. 


The  DItpOMi  of  ReffnM  from  btiildings  in  cities  and  towns  may  be 
classified  as  follows: 

Dor^*  /  ^^  lAi^e  cities,  waste  paper  is  collected  and  sold 
rapcr.  j  ^  pj^p^  jjjjjlg 

A^^     f  Ashes  are  collected  and  used  in  extensive  filling 
^^     \  operations. 

Dumoed  I  ^^•^'    Very  objectionable — not  sanitary, 
x^rumpea  ^  ^^  ^^^^     Expensive;  not  always  sanitary. 

Crematory  plants.    Sometimes  self-supporting  by  reason 
of  the  residues  of  oil  and  grease. 

Cesspools.    Economical  for  isolated  buildings,  as  factories, 
and  fpr  suburban  districts. 

Farm  irrigation;  largely  employed  in  Prance. 

Septic  tanks;  for  inland  towns. 

Chemical  process — sludge . 

Rivers.     Raw  sewage  emptying  into  streams 

is  becoming  prohibitive. 
Ocean.    Boston  sewage  reaches  Moon  Island 

by  submarine  tunnel  where  it  is  pumped 

into  the  Bay. 

Storm  water  also  becomes  sewage  when  mixed  with  the  latter. 

House  Drainage  is  effected  by — 
TXToa^A  P5tw»*    i  Which  receive  and  convey  the  waste  water  from  baths, 
wasie  r-ipcB   ^     basins,  sinks,  wash  tubs,  etc.,  but  no  human  excreta. 

Which  receive  and  convey  the  human  excreta,  faeces  (solid 
Soil  Pipes  matter)  and  urine,  from  closets  and  urinals;  also,  general 

[        waste. 
Drain  pipes  connect  with  the  waste-  and  soil  pipes  at  the  building  line,  and 

convey  the  waste  and  soil  to  the  cesspool  or  sewer. 

Generally  speaking,  the  waste-  and  soil  pipes  are.  in  the  main,  vtrtical^ 
extending  from  top  to  bottom  insids  of  the  building,  and  connected  by 
branch  pipes  with  the  various  discharge  fixttires;  while  the  drain  pipes  are 


Sewage 
(House-drainage) 


Sewers 


Venf 


::^ 


Fig.  1. 


Fig.  2. 


Fig.  3. 


practically  horitontal  and  outside  of  the  building.  Soil-  and  waste  pipes 
should  be  ^tended  vertically  up  through  the  roof  of  the  building  as  shown 
in  Fig.  1,  to  provide  for  the  escape  of  sewer  gas.  In  order  to  prevent  the 
latter  from  finding  its  way  into  the  rooms,  a  trap   is   placed  on  each 

Digitized  by  VjOOQ IC 


12M  9^— SANITATION. 

pipe  leading  from  the  fixture  to  the  soil-  or  waste  pipe.  These  trape  an 
designated  by  various  letters  of  the  alphabet,  but  the  S-trap  (Pig.  2)  ii 
perhaps  the  most  common.  Their  efficiency  is  reduced  when  the  wat& 
evaporates  or  becomes  siphoned  out  <^  the  trap.  Pig.  3  shows  a  sectiiBi 
of  Waring's  check  valve,  which  remains  efficient  unless  foreign  matte- 
lodges  between  the  valve  and  its  seat,  or  the  bearings  become  too  mudi 
worn. 

Cesspoolt  are  excusable  in  sandy  or  gravelly  soil  in  new  additions  to 
townsites  where  the  water  supply  is  not  derived  m>m  weUs  in  the  immediatf 
locality;  or  for  isolated  building  where  cost  of  sewer  would  be  exceoave. 
A  notable  example  of  the  latter  is  the  cesspool  recently  constructed  for  the 
discharge  of  soil  and  waste  from  the  new  boathouse  pavilion  in  Prospect 
Park.  Brooklpm.  It  is  a  large  cylindrical  well  with  a  sand  bottom  and  with 
sides  lined  with  concrete. 

Sewers.— Pigs.  4  to  8,  in  Tables  4  to  8,  illustrate  five  standard  sectoral 
of  sewers,  namely,  Circular.  Catenary.  Basket-Handle,  Gothic,  and  Egg  or 
Egg-shape.  The  proportional  dimensions  are  based  on  the  diametrical 
height  oi  unity,  in  each  case. 

Por  the  Circular  section,  Pig.  4,  there  are  annexed  diagrams  of  relative 
area  a,  velocity  v,  and  discharge  q,  for  relative  depths  of  flow.  Thus,  if  the 
conduit  or  sewer  is  full,  a,  v  and  a  are  assumed  to  be  unity;  if  the  depth  is 
0.8.  a  =  0.86,t;=  1.14,  «-0.98;  if  half  full,  a- 0.6.  v- 1.0,  <?- 0.6.  etc.  Note 
that  V  and  ^  are  based  on  the  velocity  v  being  proportional  to  v/rT  in  wludi 
r  — hydraulic  radius  in  feet  (see  Hydraulics,  page  1161).  Similar  diagrams 
of  area,  velocity  and  discharge  may  be  drawn  for  the  other  sections — 
Catenary  (Fig.  5).  Basket-Handle  (Fig.  6),  Gothic  (Pig.  7),  and  Egg  (Pig.  8). 
The  Circle,  and  the  Horseshoe  with  invert,  are  the  most  common  forms  for 
tunnel  construction. 

The  Egg-shape  (Pig.  8)  possesses  the  merit  of  maintaining  a  compara- 
tively high  value  of  r  (and  hence  v)  for  small  depths  of  flow;  and  it  u  to 
be  noted  that  when  flowing  }  full  depth,  r  (and  v)  are  greater  than  when 
flowing  full.    (See  Table  8.) 

Table  1,  following,  gives  the  value  of  r,  N/Tand  a^/rior  Circular  sections, 
advancing  by  inches  up  to  20  ft.  11  ins.  dia.  These  properties  are  useful  in 
designing,  i.  e.,  in  connection  with  the  use  of  Kutter  s  formula,  being  inde- 
pendent of  the  grade  or  slope  s. 

Table  2,  used  in  connection  with  Table  1,  enables  us  to  find  the  values 
of  f ,  >/r  and  avTfor  the  Catenary.  Basket-Handle,  Gothic  and  Egg  sections. 

Table  3  gives  the  velocities  in  Circular  bnck  sewers,  tmclean,  using 
value  of  roughness  n  —  0.015. 

Tables  4,  6,  6,  7  and  8  show  properties  of  Circular.  Catenary,  Basket^ 
Handle.  Gothic,  and  Egg  sections  respectively,  with  relative  diameters, 
both  vert,  and  hor.,  for  equivalent  areas.  These  tables  will  be  found  useful 
for  comparison  of  the  different  sections  in  designing. 

Table  9  gives  the  velocities  in  Egg-shaped  sew^s  which  have  become 
somewhat  fouled,  using  value  of  roughness  n»  0.016. 

Size  and  Grade  of  Sewers. — ^The  design  of  sewers  may  be  by  either  of 
three  methods,  namely,  (1)  by  formulas;  (2)  by  tables;  (3)  by  diagrams. 
For  discussion  of  formulas,  see  Hydraulics,  page  1167.  In  usin^  Kutter's 
formula  the  value  of  c  may  be  determined  from  n=»  0.013*  for  ordmarv  brick 
sewers,  and  n«  0.015  for  large  sewers  with  unclean  surfaces.  As  there  is 
more  or  less  sand  or  scouring  matter,  the  velocity  of  flow  should  generally 
be  not  greater  than  6  or  6  ft.  per  sec. 

*For  ordinary  brick  sewers,  new  and  well  laid;  but  it  is  safer  to  use 
»»0.014.    See.  also,  pages  1168  and  1188. 


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CIRCULAR  SEWERS— VELOCITY,  DISCHARGE.         12«7 

LUBS  OF  r,  \/r  AND  aVT  FOR  *ClRCULAR-  CONDUITS  OR  SbWBRS. 

lulas: 

aulic  radius  r>-diam.  in  ft.-«-4. 

ity  t;  (in  ft.  per  sec.)-  T  J  (1)     r         in  Feet.     T 

cV^-cV;^  V7.      Values  of  \  (2)^^     «»  Feet. 
.arge  «  (in  cu.  ft.  per  sec.)  -  I                      i  (3)aVr     in  Feet.     J 
fWggVr  Vs       ** ^ 

Decimals  of  a  Foot. 

00  1.083  1.167   1.250  1.333  1.417   1.500  | .  583  |.fl67  1.750  | .  833  |.917 
Inches. 


Digitized  by  VjOOQ  IC 


1298 


95.— SANITATION. 


2. — UsB  OF  Table  1,  prbcbdino,  por  Othbr  Sbctions  than  CmcuiAR. 
(See  also  Tables  4.  5,  6.  7  and  8.) 


_ 

_                 ^ 

To 

SecUon. 

Relation  of 
Diameters. 

Find 
Value 
of— 

Mult.  Value  of— 

Multi- 
plier. 

Ittua. 

Vert.  dla.=.dla.  circle. 

r 

r    In  Table  i  by 

0.92688 

9.967  02SS 

Catenary. 
Flowlnn 
Full  Depth. 

"       ■■ 

VT 

y/F     '• 

0.96275 

9.983  511; 

"      -      " 

as/r 

aVT    •* 

0.86146 

9.935  339« 

Hor.  dla.  -      " 

r 

r         "    .      " 

1.0427 

0.0181766 

vr 

x/F     " 

1.0211 

0.009  0890 

— 

ov/F 

ay/r      " 

1.1564 

0.068  1169 

Vert.<lla.=      " 

r 

r         "          " 

0.98572 

9.993  T634 

BaBket-handle. 
Flowing 
Full  Depth. 

ay/r 

y/F     " 
ay/r     " 

0.99283  9.996  8?6« 
0.99386  9.997  S1S5 

Hor.  dla. «      '' 

r 

T            " 

1.0442 

0.018  7Blf 

vr 

y/F      " 

1.0219 

0.009  39M 

"       •=•      " 

ay/r   o^T      '* 

1.1479 

0.069  895$ 

Vert.  dla.-= 

r         T         "          " 

0.90760  9.957  SMS 

Oothlc 
Flowing 
FuU  Depth. 

••            a>           " 

vr  v^  " 

0.95368  9.978  9472 

"            M           " 

ay/F  ay/T     " 

0.79487  9.900  2971 

Hor.  dla.  -      " 

r 

r         "          '* 

1.0948 

0.039  8409 

\/F 

y/F      " 

1.0463 

0.019679Q 

" 

avr 

a-s/r     " 

1.2703  .0.103  9112 

Vert,  dla.-      ;; 

T 

y         ..          .. 

0.77253^9.887  1172 

Egg-ahape. 

\/F 

y/F     •' 

0.87894  9.943  9586 

..      "      .. 

ay/F 

avr  " 

0.57125  9.756  83«5 

Flowing 
PuU  Depth. 

Hor.  dla.  = 

r 

r         "          " 

1.1588    0.064  008S 

VT 

y/F     " 

1.0765    0.032  0042 

— 

a\/F 

ay/r      " 

1.5742    0.197  0547 

Vert.dla.=      ;; 

r 

T             "              " 

0.84187  9.926  3433 

y/F 

y/F     •* 

0.91753  9.963  63H 

Egg-shape, 

•«       =■       " 

ay/r 

aX/F    " 

0.39244  9.693  779S 

Flowing 

Hor.  dla.  — 

T 

r         "          " 

1.2628    0.1013344 

i  Full  Depth. 

\/r 

y/F     " 

1.1237    0  0M6473 

L                               ^" 

as/T 

ay/F     ' 

1.0814    0.033  9986 

Vert,  dla.-      •• 

T 

T            "              " 

0.55093  9.7410996 

\/y 

y/F     " 

0.74225  9.879  5496 

Egg-ehape. 

*•           cs           " 

a\/r 

a\/r     " 

0.11929  9.076  5963 

Flowing 

Hor.  dla.  — 

r 

r         "          " 

0.82640  9.917  1903 

}  FuU  Depth. 

VT 

s/T    •• 

0.90907  9.958  5951 

••       «      " 

ay/r  ^y/r      "          " 

0.32872)9.616  8338 

Examples  in  Use  of  Table  2,  above. 

£x  1  — From  Tables  2  and  1,  find  the  hydraulic  roditis  r,  s/r,  and  oVr 
(a  =  area  of  section  considered)  for  the  Catenary.  (1)  whose  vertical  diaxneter 
is  8  ft.  3  ins.,  and  (2)  whose  horizontal  diameter  is  7  ft  4  ms.r 

Solution.— ¥oT  (1).  vert.  dia.  of  8  ft.  3  ins.,  we  have,  r-2  063X.9269- 
1.912.  \/r-1.436X.9628-1.383»  a\/r-7e.77X.8ei6-6«.14;  and  for  (1). 
hor.  dia.  of  7  ft.  4  ins.,  we  have,  r-  1.833X  1.048- 1.912.  V7-  1.854X  1.0211 
"1.383.  av7-57.19Xl.l664  =  66.13+.^       .    ^        ^  ,      .      ._ 

Comparing  the  above  results  it  is  found  that  they  are  equal,  suni^ 
because  7  ft.  I  ins.  ( =  88  ins.)  is  the  hor.  dia.  of  a  catenary  whose  vert.  dia. 
is  8  ft.  3  ins.  (-99  ins.);  i.e.,  the  hor.  dia.  of  catenary -8  vert,  dia.  See 
Table  6  following.  >-     >- 

Ex.  2.— In  Kutter's  formula.  i»-cVVl-cvV  V5.  it  is  re<^uired  to  find 
the  velocity  v  of  flow  in  an  Egg-shaped  sewer  Tirtiosc  nor.  dia,  is  4  ft.  6  xns^ 
flowing  I  full  depth,  and  on  a  grade  of  5 -.0004,  aswiming  the  vahie  ot 
coefficient  c- 100  f 

Solution.— Vrom  Tables  1  and  2,  preceding,  the  value  of  >/7— l.OftlX 
1.1237-1.192;  hence  the  velocity  of  flow  is  i;-100>(ei.lttaXi.02-2.384  ft. 
per  sec.  Digitized  by  VjOO^ It: 


VELOCITIES  IN  CIRCULAR  BRICK  SEWERS, 


1390 


Ex.  3. — In  Kuttcr's  formula,  o—av— c  .  a\/7 ,  VT,  it  is  required  to  find 
the  discharge  from  a  Basket-Handle  conduit  whose  vert.  dia.  is  8  ft.,  flowing 
full,  and  on  a  grade  of  .000225,  assuming  the  value  of  roughness  n— .016. 

5o/i</«(m.—j-. 000225.  and  >/J-.015.  Prom  Tables  1  and  2,  r-2X 
•9857- 1.9714,  and  avT-  71.09X  .9939-  70.66.  The  value  of  c  is  obtained 
from  Table  8,  page  1171.  and- 111.  Hence,  the  discharge  «-  lllX 70.d6X 
.015— 117.6  cu.  ft.  per  sec 

8. — ^Vblocxtibs  in  Pbbt  psr  Sscond  in  Circular  Brick  Sbwbrs.* 
By  Kutter's  Formula,  using  n— 0.015. 
(Slope  5— value  in  first  coltmm-**  100.) 


FaUln 
Ft.  per 

Diameter  of  Pipe  or  Sewer.  In  Feet. 

100  Ft. 

v^r 

(100  f) 

0.5 

1 

3 

3 

4 

5 

6 

7 

8 

10 

12 

.002 

0.09 

0.16 

0.27 

0.36 

0.44 

0.52 

0.69 

0.66 

0.71 

0.82 

0.92 

.00447 

.004 

0.13 
0.16 

0.22 

0.38 
0.47 

0.51 
0.63 

0.63 
0.77 

0.73 
0.90 

0.83 
1.02 

0.92 
1.13 

1.00 
1.23 

1.16 
1.42 

1.31 
1.60 

.00632 

.006 

0.27 

.00775 

.006 

0.18 

0.32 

0.64 

0.72 

0.89 

1.03 

1.17 

1.30 

1.42 

1.64 

1.85 

.00894 

.01 

0.20 

0.35 
0.43 

0.60 
0.74 

0.81 
0.99 

0.99 
1.21 

1.16 
1.42 

1.31 
1.60 

1.45 

1.78 

1.69 
1.94 

1.84 
2.25 

2.06 
2.63 

.01 

.015 

0.25 

.01225 

.03 

0.29 

0.60 

0.85 

1.14 

1.40 

1.64 

1.85 

2.05 

2.24 

3.60 

2.02 

.01414 

.016 

0.32 

0.56 

0.96 

1.28 

1.67 

1.83 

2.07 

2.30 

2.61 

2.90 

3.26 

.01581 

.03 

0.35 

0.61 

1.04 

1.40 

1.72 

3.00 

2.27 

2.52 

2.75 

3.18 

3.58 

.01732 

.085 

0.38 

0.66 

1.12 

1.51 

1.85 

2.16 

2.45 

2.72 

2.97 

3.44 

3.86 

.01871 

.04 

0.40 

0.71 

1.20 

1.62 

1.98 

2.31 

2.62 

2.91 

3.17 

3.67 

4.13 

.02 

.045 

0.43 

0.75 

1.27 

1.71 

2.10 

2.45 

2.78 

3.08 

3.37 

3.90 

4.38 

.02121 

.06 

0.45 

0.79 

1.34 

1.81 

2.22 

2.69 

2.93 

3.25 

3  54 

4.11 

4.62 

.02236 

.06 

0.50 

0.87 

1.47 

1.98 

2.43 

2.83 

3.21 

3.56 

3.89 

4.50 

5.06 

.02449 

.07 

0.58 

0.94 

1.59 

2.14 

3.62 

3.06 

3.47 

3.84 

4.20 

4.86 

6.46 

.02646 

.06 

0.67 

1.00 

1.70 

2.28 

2.80 

3.27 

3.70 

4.11 

4.49 

6.20 

6.84 

.02838 

.00 

0.61 

1.06 

1.80 

2.42 

2.97 

3.47 

3.93 

4.36 

4.76 

5.51 

6.19 

.03 

.10 

0.64 

1.12 

1.90 

2.55 

3.13 

3.66 

4.14 

4.59 

5.02 

6.81 

6.53 

.03162 

.13 

0.70 

K23 

2.08 

2.80 

3.43 

4.01 

4.54 

5.03 

5.50 

6.36 

7.15 

.03464 

.14 

0.76 

1.32 

2.25 

3.02 

3.71 

4.33 

4.90 

5.43 

5.94 

6.87 

7.73 

.03742 

.16 

0.81 

1.42 

2.40 

3.23 

3.96 

4.63 

5.24 

5.81 

6.35 

7.35 

8.36 

.04 

.18 

0.86 

1.50 

2.55 

3.43 

4.20 

4  91 

6.56 

6.17 

6.73 

7.79 

8.76 

.04243 

.20 

0.90 

1.58 

2.69 

3.61 

4.43 

5.17 

6.86 

6.50 

7.10 

8.22 

9.23 

.04472 

.        .26 

l.Oi 

1.77 

3.00 

4.04 

4.96 

5.79 

6.55 

7.27 

7.94 

9.19 

10.3 

.05 

.80 

1.11 

1.94 

3.29 

4.42 

5.43 

6.34 

7.17 

7.96 

8.69 

10.1 

11.3 

.05477 

.85 

1.20 

2.09 

3.55 

4.78 

5.86 

6.84 

7.75 

8.60 

9.39 

10.9 

12.2 

.05916 

.40 

1.28 

2.24 

3.80 

5.11 

6.27 

7.32 

8.29 

9.19 

10.0 

11.6 

13.1 

.06325 

.50 

1.43 

2.60 

4.25 

5.71 

7.01 

8,18 

9.26 

10.3 

11.2 

13.0 

14.6 

.07071 

.60 

1.67 

2.74 

4.65 

6.26 

7.68 

8!96 

10.1 

11.3 

12.3 

14.2 

16.0 

.07746 

70 

i.69 

2.96 

5.03 

6.76 

8.29 

9.68 

11.0 

12.2 

13.3 

15.4 

17.3 

.08367 

.80 

1.81 

3.17 

5.37 

7.22 

8.86 

10.3 

11.7 

13.0 

14.2 

16.4 

18.5 

.08944 

.90 

1.92 

8.36 

5.70 

7.66 

9.40 

11.0 

12.4 

13.8 

15.1 

17.4 

19.6 

.09487 

1.00 

3.03 

3.64 

6.00 

8.08 

9.91 

11.6 

13.1 

14.5 

15.9 

18.4 

20.6 

.1 

1.20 

2.2! 

388 

6.58 

8.85 

10.9 

12.7 

14.4 

15.9 

17.4 

20.1 

22.6 

.10955 

1.40 

2.39 

4.19 

7.11 

9.56 

11.7 

13.7 

15.5 

17.2 

18.8 

21.7 

24.4 

11832 

1.60 

3.56 

4.48 

7.60 

10.2 

12.5 

14.6 

16.6 

18.4 

20.1 

23.2 

26.1 

.12649 

1.80 

2.71 

4.75 

8.06 

10.9 

13.3 

15.5 

17.6 

19.5 

21.3 

24.6 

27.7 

.13416 

3.00 

2.86 

5.01 

8.50 

11.4 

14.0 

16.4 

18.5 

20.5 

22.4 

26.0 

29.2 

.14142 

fa 

0.196 

0.785 

3.142 

7.068 

12.566 

19.635 

28.274 

38.485 

50.266 

78.540 

113.10 
3.000 

r 

0.125 

0.250 

0.600 

0.750 

1.000 

1.250 

1.500 

1.750 

2.000 

2.500 

<vE 

20.21 

35.40 

60.08 

80.77 

99.10 

115.7 

131.0 

145.3 

158.7 

183.7 

206.5 

at^r 

3.9604 

27.803 

188.77 

570.90 

1245  3 

2272.7 

3702.3 

5591.6 

7978.3 

14426 

23352 

♦For  second-class  brick,  dressed  stone,  or  tuberculated  iron.  (See  Table  9.) 
Note. — ^Velocities  in  table  are  eqiml  to  cVrxVJ;  o/r  is  in  the  next 
line  to  bottom  for  the  particular  diameter  of  pipe,  and  VJ  is  foxmd  in  the 
last  column. 

fa— area  of  section  in  sq.  ft.;  r— hydraulic  radius  in  ft.;  c— coefficient  in 
Kuttcr's  formula,  using  mean  value  of  5  —  .001.  Velocity  in  ft.  per  sec.  —  »— 
^VfJ— cVT  v'jI    Discharge  in  cu.  ft.  per  sec.  — ^—ov-acVrs-ocVrV^. 


laoo 


^SANITATION. 


4. — Propbrtiss  of  Circular-  Conduits  or  Sbwbrs. 


(a)  General. 
When  flowing  full: 

-0.7854d>. 

-3.1416d. 
d 

When  flowing  }  full: 
-0.3927d«. 
=  1.570M. 


Fig.  4. — Ratios  of  a,  u,  and  q  for  Pilled 
Segments, 
(a,  V  or  4 ■"Unity  when  section  is  fulL) 


In  which 

a  — area  in  sq.  ft. 
p=- wetted  perimeter  in  ft. 
r-=  hydraulic  radius  in  ft. 
Log  i;  -  0.4971490. 

Log  J-  9.8950899. 


(6)  Comparison  of  Circle  with  Other  Stciions  of  Equal  Ar^a. 
(See  also  Tables  5.  6,  7  and  8.) 
dia.  of  Circle  in  ft.  Logarithm. 


—  0 .  9407  X  vert.  dia.  of  Catenary  of  equiv. 
-=1.0683Xhor.      " 

BasketHandle 


-» 1.001  Xvcrt. 
-1.060  Xhor. 
-0. 9046  X  vert. 
-1.091  Xhor. 
-0. 8062  X  vert. 
-1.2093Xhor. 


Gothic 
Egg-shape. 


.9.973  4M7 
.0.024  619S 
.0.000  4M6 
.0.025  4625 
.0.056  4020 
.0.087  8475 
.9.900  4M0 
.0.082  5253 


d  by  Google 


SEWERS— CIRCULAR  AND  CATENARY  SECTIONS.      1801 


5. — Propbrtibs  of  Catbnart-  Conduits  or  Sbwbrs. 


(o)  G^nsral. 

a  -  area  in  sq.  ft.                Logarithm. 

-0.70277  £M                     9.846  8132 

-0.88044  dk«                     9.949  1182 

p- wetted  perimeter  in  ft. 

-  3.03284  <!,                      0.481  8497 

-3.4110!»(ih                      0.533  0022 

f— hydraulic  radixas  in  ft. 

-0. 23172  li,                      9.304  9635 

-0.260685<ik                   9.416  1160 

Where  d,-vert.  dia.  in  ft. 

dk-hor.  dia.  in  ft. 

Fig. 

5. — Catenary. 

.  (6)  Comparison  of  CaUnary  with  Other  Sections  of  Equal  Area. 

(See  also  Tables  4.  6.  7  and  8.) 

d.  —  vert.  dia.  of  Catenary  in  ft. 

Logarithm. 

—  1 .  063  X  dia.  of  Circle  of  equivalent  area 

0.026  5333 

—  1 .  125   Xhor.  dia.  of  Catenary       of  equiv.  area. 
-1. 0641 X  vert.     "        Basket-Handle      " 

0.051  1525 

0.026  9678 

-1.1272  Xhor.      *' 

0.0519958 

-0. 9615  X  vert.     "        Gothic 

9.982  9353 

-1.1598Xhor.      " 

0.064  3808 

-0. 8570  X  vert.     "        Egg-shape 

9.932  0673 

-1.2855  Xhor.      " 

0.109  0580 

Jt.  — hor.  dia.  of  Catenary  in  ft. 

—  0 .  9449  X  dia.  of  Circle  of  equivalent  area 

...      .9.975  3808 

—  0 .  8889  X  vert.  dia.  of  Catenary       of  eqxiiv.  area 
-0. 9458  X  vert.     "        Basket-Handle      " 

9.948  8475 

9.975  8153 

-1.0019  Xhor.      *• 

0.000  8433 

-0. 8546  X  vert.     "        Gothic 

9.931  7828 

-1.0309  Xhor.      " 

......0.013  2283 

-0. 7618  X  vert.     "       Egg-shape 
-1.1426Xhor.      "                  "                  "        " 

......9.881  8148 

0.057  9061 

d  by  Google 


1802  e^^SANITATION, 


0. — Propbrtibs  of  Baskbt-Handlb-  Conduits  or  Sbwb&s. 


(a)  General, 
a  »  area  in  sq.  ft.  Logarithm. 

-0.78621  d.>  9.895  6386 

-0.88226  (iK>  9.945  5946 

p«=  wetted  perimeter  in  ft. 
-3. 19040  (i,  0.503  8450 

-3. 37966^1,  0.528  8730 

r= hydraulic  radius  in  ft. 
-0.24643  d,  9.391  6936 

-0.26105dk  9.416  7216 

Where  d.  —  vert.  dia.  in  ft. 
db— hor.  dia.  in  ft. 

Pig.  6.— Basket-Handle. 

(b)  Comparison  of  Basket-Handle  with  Other  Sections  of  Equal  Area, 
(See  also  Tables  4.  5.  7  and  8.) 
(f,»vert.  dia.  of  Basket-Handle  in  ft.  Logarithm. 

—  0 .  999   X  dia.  of  Circle  of  equivalent  area 9 .  999  5655 

-  0 .  9398  X  vert.  dia.  of  Catenary       of  equiv.  area 9.973  0323 

=  1.0573Xhor.      "  "  "         "     0.024  1847 

-1.059   X    "         "        Basket-Handle     "         "     0.025  0280 

-0.9036Xvert.     "        Gothic  "         "     9.955  9675 

=  1.0900Xhor.      "  "  "        "     0.037  4130 

-0.8054Xvert.     "        Egg-shape  "        "     9.905  9996 

-1.208lXhor.      "  "  "        "     0.082  0908 

dh=hor.  dia.  of  Basket-Handle  in  ft. 

—  0.943   Xdia.  of  Circle  of  equivalent  area 9.974  6375 

-  0 .  8872  X  vert.  dia.  of  Catenary       of  equiv.  area 9 .  948  0042 

-0.998lXhor.      "  "  "         "     9.999  1567 

-0.944   Xvert.     "        Basket-Handle     "         "     9.974  9720 

-0.8630X   "        "        Gothic  "        "     9.930  9375 

-1.0289Xhor.      "  '*  "        "     0.012  3850 

-0.7603Xvert.    "        Egg-shape  "        "     9.880  9715 

-1.1404Xhor.      "  "  -        «     0.067  0«28 


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SEWERS—BASKET'HANDLE  AND  GOTHIC  SECTIONS.  1303 


7. — Propbrtibs  of  Gothic-  Conduits  or  Sbwbrs. 


(a)  General, 
a— area  in  sq.ft. 
-0.6563  d* 
-0.9636  d.s 
^—wetted  perimeter  in  ft. 
-2.8881  d, 
-3.4838  dk 
r— hydraulic  radius  in  ft. 
-0.2269  d, 
-0.2737  dk 
Where  (f,  — vert.  dia.  in  ft. 
dk— hor.  dia.  in  ft. 


Logarithm. 
9.816  4402 
9.979  3312 


0.460  6057 
0.542  0512 


9.365  8346 
9.437  2800 


Fig.  7.— Gothic. 
(6)  Comparison  of  Gothic  with  Other  Sections  of  Equal  Area, 
(See  also  Tables  4.  5.  6  and  8.) 
d,— vert.  dia.  of  Gothic  in  ft .  Logarithm. 

-  1 .  1056  X  dia.  of  Circle  of  equivalent  area 0 .  043  5980 

—  1 .0401 X  vert.  dia.  of  Catenary       of  equiv.  area 0.017  0647 


Basket- Handle 

Gothic 
Egg-shape 


-1.170lXhor. 
-1. 1067  X  vert. 
-1.1724Xhor. 
-1.2063X  " 
-0.8913Xvert. 
-1.8370Xhor. 
Jk— hor.  dia.  of  Gothic  in  ft. 

—  0.91 65 X dia.  of  Circle  of  equivalent 

—  0 .  8622  X  vert.  dia.  of  Catenary 
-0.9700Xhor.      " 

Basket-Handle 


0.068  2172 
0.044  0325 
0.069  0605 
0.081  4455 
9.950  0320 
0.126  1233 

.9.962  1525 


-0.9175Xvert. 
-0.9719Xhor. 
-0. 8290  X  vert. 
-0.7389X   " 
-1.1084Xhor. 


Gothic 
Egg-shape 


of  equiv.  area 9.935  6192 

••  9.986  7717 

"  9.962  5870 

"  9.987  6150 

"  9.918  5645 

*•  9.868  5865 

"  0.044  6778 


d  by  Google 


1104 


i^.SANITATION. 


8. — ^I^ROPBRTIBS  OF  EOO  (-ShAPBD)-     CoNDUITS  OR  SbWBRS. 

(a)  G€n$ral. 


Wetted 
Section. 


Flowing 
Full  Depth. 


Area  a.. 


Log  — 

Area  a 

Log- 
Perimeter  p 

Log- 
Perimeter  p 

Log- 

Hyd.  rad.  r 
Log- 

Hyd.  rad.  r 
Log  — 


Flowing  f 
Full  Depth 


0.510465(i.> 
9.707  9678 

1.148525db> 
0.060  1404 

6438d, 
0.422  1409 

'3.9640(ik 
0.598  2322 

0.19313J. 
9.285  8572 

0.2897(fh 
9.461  9485 


0. 335922  (^,t 
9.520  2386 


Flowing  i 
Full  Depth. 


0.120222<i.> 
9.101  1857 


0.755825(iL 
9.878  4212 

1.59607<f. 
0.203  0510 

2.3941dk 
0.370  1423 

0.21047d, 
9.323  1833 

0.3157d 
9.499  2746 


"0 


284dk> 
9.458  8183 

0.91647^. 
9.062  1166 

1.8747dk 
0.138  2079 

0.13778d 
9.139  0300 

0.2066(ik 
9.315  1308 


0   OJ  02  Q3  0b4 
Fag.  8.— BsB 


Where  d.—  vert.  dia.  in  ft. 
ih—  hor.  dia.  in  ft. 
(6)  Comparison  of  Egg-Shape  with  Other  Sections  of  Equal  Area, 
(See  also  Tables  4.  5,  6  and  7.) 
<i.— vert.  dia.  of  Egg-shape  in  ft.  Logarithm. 

—  1 .2404Xdia.  of  Circle  of  equivalent  area 0.098  6660 

—  1 .  1669X  vert.  dia.  of  Catenary      of  equiv.  area 0.067  0327 

-1.3128Xhor.       *  "  "         "     0.118  1853 

-1.2417Xvert.     "        Basket-Handle     "        "     0.094  0005 

-1.3158Xhor.      "  "  "        "     0.119  0285 

-1.1219Xvert.     "        Gothic  "        "     0.040  9680 

-1.3634Xhor.      '*  "  "         "     0.1314135 

-1.5000Xhor.      "        Egg-shape  "        "     0.176  0913 

Jb— hor.  dia.  of  Egg-shape  in  ft. 

-0.8269Xdia.  of  Circle  of  equivalent  area 9.917  4747 


-  0 .  7779  X  vert.  dia.  of  Catenary 

-  0. 8752  X  hor. 
-0.8278Xvert. 

-  0. 8769  X  hor. 
-0. 7480  X  vert. 

-  0. 9022  X  hor. 
-0. 6667  X  vert. 


of  equiv. 


Basket-Handle 

Gothic 

Egg-fihape 


9.890  9414 
9.942  0939 
9.917  9002 
9.942  9372 
9.878  8767 
9.966  3323 
9.828  9087 


d  by  Google 


EGG-SHAPED  SEWERS. 


1805 


9. — Vblocitibs  in  Pbbt  per  Second  in  Ego-srapbd  Sbwbrs. 

By  Kutter's  Formula,  using  n  — 0.016. 

(Slope  J --value  in  first  column  ••- 100.) 

[Velocities,  v,  in  Peet  per  Second.] 


Fall! 

1( 

in  Ft.  per 
10  FL 

100  f) 

QreateM  Transvene  or  Horlsontal  Diameter  d^  In  Feet. 

( 

1 

2 

8 

4 

6 

6 

7 

8 

10 

12 

n/T 

.01 

0.40 

0.67 

0.90 

1.10 

1.28 

1.45 

1.60 

1.75 

2.02 

2.27 

.01 

.02 

0.56 

0.95 

1.27 

1.55 

1.81 

2.04 

2.27 

2.47 

2.85 

3.21 

.01414  J 

.04 

0.79 

1.34 

1.79 

2.20 

2.56 

2.89 

3.20 

8.50 

4.04 

4.54 

.02  y 

1 

.06 

0.97 

1.64 

2.20 

2.69 

3.13 

3.54 

3.92 

4.28 

4.95 

5.56 

.02449 

.10 

1.25 

2.12 

2.84 

3.48 

4.05 

4.57 

5.07 

6.53 

6.38 

7.17 

.03162 

.14 

1.48 

2.50 

3.36 

4.11 

4.79 

5.41 

5.99 

6.54 

7.56 

8.49 

.03742 

.20 

1.77 

2.99 

4.01 

4.91 

5.72 

6.47 

7.16 

7.82 

9.03 

10.1 

.04472 

g 

.40 

2.51 

4.23 

5.67 

6.95 

8.10 

9.15 

10.1 

11.1 

12.8 

14.8 

.06325 

.60 

3.07 

6.18 

6.95 

8.51 

9.91 

11.2 

12.4 

13.5 

15.6 

17.6 

.07746 

1 

.80 

3.54 

6.99 

8.02 

9.83 

11.4 

12.9 

14.3 

15.6 

18.1 

20.3 

.08944 

1.00 

3.96 

6.69 

8.97 

11.0 

12.8 

14.5 

16.0 

17.6 

20.2 

22.7 

.1 

1.40 

4.68 

7.92 

10.6 

13.0 

15.1 

17.1 

19.0 

20.7 

23.9 

26.8 

.11832 

c 

2.00 

6.60 

9.46 

12.7 

15.5 

18.1 

20.4 

22.7 

24.7 

28.5 

82.1 

.14142 

a 

1.148 

4.594 

10.337 

18.376  28.713 

41.347 

56.278 

73.506 

114.85 

165.39 

r 

.2897 

.5794 

.8691 

1.159 

1.449 

1.738 

2.028 

2.318 

2.897 

3.476 

.     cy/r 

39.62 

66.93 

89.70 

109.9 

128.0 

144.6 

160.2 

174.8 

201.9 

226.8 

.01 

0.42 

0.71 

0.95 

1.16 

1.35 

1.53 

1.70 

1.86 

2.13 

2.39 

.01 

.02 

0.60 

1.01 

1.35 

1.65 

1.92 

2.16 

2.40 

2.61 

3.02 

3.39 

.01414 

.04 

0.85 

1.43 

1.91 

2.33 

2.71 

3.06 

3.39 

8.70 

4.27 

4.79 

.02 

^ 

.06 

1.04 

1.75 

2.34 

2.85 

3.32 

3.75 

4.16 

4.53 

5.23 

5.86 

.02449 

.10 

1.34 

2.26 

3.01 

3.68 

4.28 

4.84 

5.36 

5.85 

6.74 

7.57 

.03162 

■s 

.14 

1.59 

2.67 

3.57 

4.36 

5.07 

6.73 

6.35 

6.92 

7.98 

8.96 

.03742 

.20 

1.90 

3.19 

4.26 

5.21 

6.06 

6.85 

7.58 

8.27 

9.54 

10.7 

.04472 

i 

.40 

2.68 

4.52 

6.03 

7.37 

8.57 

9.68 

10.7 

11.7 

13.5 

15.1 

.06325 

.60 

3.28 

6.53 

7.38 

9.02 

10.5 

11.9 

13.1 

14.3 

16.5 

18.5 

.07746 

••• 

.80 

3.79 

6.39 

8.53 

10.4 

12.1 

13.7 

15.2 

16.6 

19.1 

21.4 

.08944 

1 

1.00 

4.24 

7.14 

9.53 

11.6 

13.5 

15.3 

17.0 

18.5 

21.3 

23.9 

.1 

1.40 

5.02 

8.45 

11.3 

13.8 

16.0 

18.1 

20.1 

21.9 

25.2 

28.8 

.11832 

2.00 

6.00 

10.1 

13.5 

16.5 

19.2 

21.6 

24.0 

26.1 

30.2 

83.9 

.14142 

a 

0.756 

3.023 

6.802 

12.093 

18.895 

27.210 

37.035 

48.873 

75.583 

108.84 

f 

0.316 

0.631 

0.947 

1.263 

1.579 

1.894 

2.210 

2.526 

3.157 

3.788 

<Vr 

42.40 

71.42 

95.33 

116.5 

135.5 

163.1 

169.6 

184.9 

213.3 

239.4 

.01 

0.30 

0.52 

0.70 

0.87 

1.01 

1.15 

1.28 

1.40 

1.62 

1.83 

.01 

.02 

0.43 

0.74 

1.00 

1.22 

1.43 

1.63 

1.81 

1.98 

2.29 

2.59 

.01414 

.04 

0.61 

1.04 

1.41 

1.73 

2.03 

2.30 

2.56 

2.80 

3.24 

3.66 

.02 

1 

.06 

0.74 

1.28 

1.73 

2  12 

2.48 

2.82 

3.13 

3.43 

3.97 

4.48 

.02449 

.10 

0.96 

1.65 

2.23 

2.74 

3.20 

3.64 

4.04 

4.42 

5.13 

5.79 

.03162 

.14 

1.14 

1.95 

2.64 

3.24 

3.79 

4.30 

4.79 

5.24 

6.07 

6.85 

.03742 

.20 

1.36 

2.33 

3.15 

3.87 

4.53 

5.14 

5.72 

6.26 

7.25 

8.19 

.04472 

1 

.40 

1.92 

3.29 

4.46 

5.48 

6.41 

7.27 

8.09 

8.85 

10.3 

11.6 

.06325 

.60 

2.36 

4.03 

6.46 

6.71 

7.85 

8.91 

9.91 

10.8 

12.6 

14.2 

.07746 

••" 

.80 

2.72 

4.66 

6.30 

7.75 

9.06 

10.3 

11.4 

12.6 

14.5 

16.4 

08944 

1 

1.00 

3.04 

5.21 

7.05 

8.66 

10.1 

11.5 

12.8 

14.0 

16.2 

18.3 

!l 

1.40 

3.60 

6.16 

8.34 

10.2 

12.0 

13.6 

15.1 

16.6 

19.2 

21.7 

.11832 

2.00 

4.30 

7.37 

9.97 

12.2 

14.3 

16.3 

18.1 

19.8 

22.9 

25.9 

.14142 

a 

0.284 

1.136 

2.556 

4.544 

7.100 

10.224 

13.916 

18.176 

28.400 

40.892 

r 

0.207 

0.413 

0.620 

0.826 

1.033 

1.240 

1.446 

1.653 

2.066 

2.479 

es/7 

30.41 

52.09 

70.48 

86.61 

101.3 

115.0 

127.9 

139.9 

162.1 

183.1 

Notation. — a— sectional  area  of  wetted  section  of  sewer,  in  square  feet; 
r" hydraulic  mean  radius;  <:  — coefficient  in  Kutter's  formula,  using  mean 
value  of  5 «-  .001.  Velocity  »— cVr  X  v7  for  the  particular  diameter  d\  and 
the  particular  grade  or  slope  s. 


Digitized 


by  Google 


J 


1806  n.— SANITATION. 

Example  tn  Use  of  Table  0.  preceding. 

Example. — ^What  size  of  egg-shaped  sewer,  running  two-thirda  ivSi  defvth, 
on  grade  of  one-tenth  of  one  per  cent.,  will  carry  16  cu.  ft.  per  seoood. 
assuming  n  — 0.016? 

Solution. — Prom  the  preceding  table,for  "Plowing  two-thirds  ftill  defyth" 
we  select,  if  possible,  the  width  Oh  whose  velocity  multiplied  by  the  cmiea 

fending  area  a  will  give  the  dischaxve  9  ( ^av)  — 16.  for  a  grade  of  0.1  ft.  per 
00  ft.  Now  for  dh-2  ft.,  9- 8.023X2.26"  6.83  cu.  ft.  per  sec.;  and  1^ 
dh  —  8  ft.,  9—6.802  X  3.01  -  20.47  cu.  ft.  per  sec.  Hence,  by  proportion,  f(» 
a- 16,  dh  -  2.67  ft.  or,  say,  2  ft.  8  in8.<  and  the  height  d.  —  ifdh  »  4  ft.  (See 
Table  8.)  In  practice  it  is  customary  to  increase  the  calctuated  eMmmii^tM*^ 
by  about  2  ins.,  more  or  less. 

Thickness  of  Brick  Sewer  Walls. — ^No  fixed  rule  can  be  tised,  but  for  brkJc 
sewers  tmder  30  ins.  in  diameter  a  single  4-in.  ring  will  generally  suffice. 
Two  rings  (2X4  ins.)  of  brick  are  required  for  diameters  from  2^  to  6  ft.: 
and  three  rings  from  about  6  to  10  ft.  Above  10  ft.  diameter  treat  aewer 
above  spring  line  as  a  masonry  arch,  and  keep  the  line  of  resultant  preamxn 
well  within  the  middle  third.  Baldwin  T««tham  gives  the  following  tonnola 
for  thickness: 

"m "> 

where   t » thickness  of  brick  wall,  in  feet ; 
d-" depth  of  excavation,  in  feet; 
f— radius  of  sewer,  in  feet. 

It  is  essential  that  sewer  linings  be  water  tight. 

Sewer  Foundations. — Many  sewers  are  rendered  leaky  and  tmaaaitary  by 
reason  of  their  having  been  constructed  on  improper  foundations.  Ac 
economical  foundation  for  sewers  projected  throtight  soft,  marshy  ground 
consists  of  two-pile  bents  driven  say  4  or  5  feet  apart,  capped  with  suitable 
cross  timbers,  on  top  of  which  are  laid  the  thick  longitudinal  fioor  planking, 
forming  a  platform  for  the  sewer  proper.  Sometimes  the  piling  supporting 
the  platform  is  omitted.  Timber  foundations  should  always  be  befow  the 
ground-water  level  to  prevent  decay. 

10. — SOMB  RbPBRBNCBS  to   IlLUSTRATBD  SbWBR  CONSTRUCTIOir 

IN  "Enginbbrino  Nbws." 
June  6, 1901.   Cast  iron  pipe  outfall  seWer,  with  frost  casing,  pile  foundatkm, 

etc. 
Oct.  10.  1001.    Sewers  in  Brooklyn;  circular.  IS'  0*  dia.  with  KT  brick  ait:fa; 

deep  maxUiole  construction. 
Jan.  1,  1903.    Sewer  construction  in  Platbush.  Brooklyn,  showxncr  vmrioias 

types,  with  foundations. 
Nov.  19,  1903.    Method  and  cost  of  constructing  a  30*  concrete  aewar  with 

brick  arch,  at  Medford,  Mass.;  illustrated,  with  fonns. 
Dec.  17,  1903.    Pear-shaped  concrete  sewer  with  brick  arch  12*  thick;  y^rt. 

dia.-72',  hor.dia.-72'. 
Peb.  4,  1904.    Wear  and  repairs  of  inverts  in  St.  Louis  sewers;  with  diasxanx 

of  sewer;  vert.  dia=>  16^  hor.  dia.  —  20^;  arch  ring  of  cut  stone. 
Peb.  18(1 904.     A  novel  form  of  centering  for  5-ft.  egg-shaped  aewer  at 

Washington,  D.  C. 
Oct.  20,  1904.    A  steel  center  or  form  for  constructing  concrete  sewers. 
Jan.  6,  1906.    A  new  form  of  reinforced  concrete-block  sewer  oonstructioo: 

illustration  of  sewer  42"  dia.  with  A"  thickne»  of  shell. 
Sept.  26,  1907.    A  36*  steel  lap-welded  pipe,  f  metal,  IS'  lengths,  used  for 

extending  sewer  outfalls  at  Blackpool,  England. 
Nov.  11.  1907.    A  new  concrete-pipe  joint;  hot  asphalt  poured  into  gwwves 

at  ends  of  abutting  cast  concrete  pipes. 
Mar.  26,  1908.    Intercepting  and  outfall  sewer  at  Watcrbury;  vert.  dia.  4*5', 

nor.  dia.  4'  6",  crown  thickness  6';  reinfordbd  concrete. 
July  30.  1908.    Sewers  at  St.  Louis,  constructed  with  collapsible  steel  center- 
ing:  (1)  vert.  dia.  18*  6',  hor.  dia.  29'  0*,  crown  thickness  about  IIT; 

'2)  vert.  dia.  about  17'  0".  hor.  dia.  20'  0*.  crown  thickoess  about 
3*;  reinforced  concrete. 


^ 


SEWER-WALLS,  -FOUNDATIONS.  -PIPE. 


1307 


S4wtr  Pipe. — Vitrified    clay   pipe   is  admirably  adapted    for  sewers. 
It  comes  in  lengths  of   2  ft.  6  ins.  for  the  smaller  sizes  (8  to  18  ins.), 


Pig.  9. 

while   the  large   diameters   are    made   in  3-ft.  lengths.     The  joints   are 
cemented  in  place.     Fig.  9  shows  a  section  of  three  lengths. 

11. — Standard  Salt-Glazbd  Vitrified  Pipb. 
(Mantxfactured  by  Blackmer  &  Post  Pipe  Co.,  St.  Louis.) 


Inside 
Dia- 
meter. 

Thlck- 
nesBof 
Shell. 

Depth  of 
Socket. 

Annular 
Space. 

Length 

of 
Sections. 

Weight 
per 
Foot. 

Car  Load 
14  Tons. 

Price 
Foot. 

Branches 

Curves, 

etc. 

Each. 

Ins. 

Ins 

Ids. 

In, 

Ft. 

Lbs. 

Ft. 

27 

2H 

S 

215 

129 

$3.36 

$16.25 

28 

2  3-32 

230 

120 

3.60 

17.60 

30 

2^ 

i 

270 

108 

4.00 

20.00 

33 

29l 

*H 

1 

320 

90 

6.00 

25.00 

36 

tH 

1 

365 

81 

6.00 

30.00 

The  above  price  list  is  subject  to  large  discounts. 

12. — Extra  Hbavy  Sbwbr  and  Culvert  Pipb. 
(Manufactured  by  Evans  &  Howard.  St.  Louis.) 


Diameter  of  Pipe  In  Inches. 


12 


30       36 


Weight,  per  foot 

Thickness  In  Inches , 

Depth  of  Socket  In  inches 

Na  of  feet  In  carload  of  1 5  tons. . 
Prloe.  per  foot. , 


52 

m 

3 

577 
$0.75 


76 

400 
$1.00 


291 
$1.50 


220 
$2.00 


170 
2 
4 

181 
$2.50i$3.26|$4.00 


305 

2H 
iH 
98 


77 
$6.00 


Sizes  18-in.  and  under  in  2Moot  lengths,  sizes  21-in.  and  over  in  3-foot 
lengths,  improved  corrugated  deep  sockets  and  comigated  ends. 
Discount  on  application. 

Kinds  of  Sewers. — Sewers  may  be  classified  according  to  the  special 
purposes  for  which  they  are  designed  or  according  to  the  material  entering 
Into  their  construction.  Thus  we  have  branch  sewers,  main-line  sewers, 
intercepting  sewers,  trunk  -line  sewers,  and  outfall  sewers.  Trunk-line 
■ewers  are  often  projected  through  several  towns,  the  expense  being  borne 
proportionately.  An  outfall  sewer  is  the  main  stem  of  discharge  to  the 
outlet.  Small  sewers  are  built  of  terra  cotta  pipe,  cast  iron  pipe,  concrete 
pipe,  etc.;  the  larger  sewers  are  constructed  ot  brick,  concrete,  reinforced 
concrete,  etc.  Wood-stave  pipe  enters  into  the  design  of  the  outfall  sewer 
of  the  Citv  of  Los  Angeles,  projected  as  follows:  2400  ft.  of  52- in .  circular 
brick  conduit;  4,400  ft.  of  40-in.  circular  brick  conduit:  16,000  ft.  of  in- 
verted syphon  of  38-in.  wood-stave  pipe;  1,900  ft.  of    4()-in.  circular  brick 


1308 


fi5.^^ANITATI0N, 


conduit;  5,800  ft.  of  6-ft.  oval  brick  and  concrete  tunnel;  800  ft.  of  40-m. 
circular  brick  conduit:  19.100  ft.  of  inverted  syphon  of  36-in.  wood-sta^ 
pipe;  12,100  ft.  of  4(J-in.  circular  brick  conduit;  000  ft.  of  d-ft.  oval  brick 
and  concrete  tunnel;  600  ft.  of  40-in.  circular  brick  conduit;  1.800  ft.  of  ft-ft. 
oval  brick  and  concrete  tunnel;  1.100  ft.  of  24-in.  cast  iron  pipe,  to  outlet 
in  Pacific  Ocean. 

Location  of  Sttotrs. — Sewers  are  most  oommonly  located  under  the 
centers  of  streets,  or  on  either  side  of  broad  avenues.    Some  cities  however 

E refer  to  build  only  one  sewer  near  one  curb,  in  streets  of  ordinary  width. 
a  cities  where  alleys  exist,  the  latter  are  often  selected  for  the  sewer  hnes. 
Manholes  are  street  openings  to  sewers;  they  are  built  for  inspect  ion 
and  cleaning  of  sewers,  and  for  ventilation.  Those  systems  of  sewers  whidi 
have  been  built  without  manholes  are  certainly  at  a  disadvantage.  For 
large  sewers  the  manholes  are  built  tangent  to  one  side  of  sewer,  in  the  form 
of  a  conic  frustum;  or.  an  entrance  to  side  of  sewer  may  be  made  by  a 
slanting  shaft  with  steps  for  descent,  with  a  manhole  entrance  at  top  of 
steps.  Manholes  should  be  situated  at  bends  of  both  alinement  and  grade 
of  the  sewer,  so  that  a  clean  si^ht  may  be  had  through  the  sewer  from  one 
manhole  to  another.  If  this  is  impracticable  by  reason  of  the  ezi>enae, 
lamp-hoUi  may  be  substituted  for  them 
occasionally.  These  latter  consist  of 
a  small  circular  shaft  from  the  street 
to  the  top  of  sewer  through  which  a  lamp 
may  be  suspended  to  be  mghted  at  from 
the  nearest  manhole  in  either  direction. 
Fig.  10  shows  a  section  of  a  circular  man- 

hole  frame  and  cover,  to  be  set  flush  with  „.     «a      \m     -u  % 

the  street  surface.  ^«- 10.— Manhole. 

Catch  Basins  are  placed  along  the  gutters  at  the  sides  of  streets,  ax»d 
especially  at  street  comers,  to  act  as  settling  basins  for  surface  waters  con- 
taining sand  and  dirt.  The  outlet  from  the  catch  basin  to  the  sewer  is  near 
the  top  of  the  basin.  They  should  be  cleaned  out  before  the  dep5»it  becomes 
too  great.    The  styles  used  are  innumerable.    That  shown  an  Pig.  11  is 


1 


Fig.  11.— Catch  Basin. 

manufactured  by  James  B.  Clow  &  Sons,  of  Chicago,  and  is  designed  for 
street  corners. 


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MANHOLES,  CATCH  BASINS.    MISCELLANY. 


1309 


EXCERPTS  AND  REFERENCES. 

The    Sanitary    Protectloo    of    the    Water   Supply  of  Baltimoro,  Md. 

(Eng.  News,  Dec.  5,  1901). — Illustrations:  Standard  designs  for  cesspools, 
privies  and  catchbasins  in  the  drainage  area  of  the  Baltimore  water  supply. 

Electric  Sewage  Pumps,  Septic  Tanks  and  Contact  Beds  at  Pond  du  Lac, 
Wis.  (By  G.  S.  Pierson.  Eng.  News,  May  22,  1902}. — Illustrations:  General 
view  of  works; nearer  view  of  pump  house  and  mam  carrier:  geneitd  plan  of 
sewajTC  disposal  works  and  sections  of  contact  filter  beos*.  storm  water 
overflows  in  intercepting  sewers;  grit  and  screen  chamber  near  sewage 
pumping  station;  plan  and  section  of  pumping  station;  sewage  distribute 
ing  and  effluent  receiving  chamber  for  contact  beds. 

Treatment   of   Sewage   in   a   Large  Open  Septic  Tank  at  WoKester, 

Mass.  (Eng.  News,  May  29.  1902).— Table. 

The  Chkuigo  Intercepting  Sewer  System   (Eng.  News,  May  28.  1903). 

— Illustrations:  Map  of  the  system;  driving  sheet  piling  for  trench  of  16-ft. 
sewer;  swinging-derrick  with  orange-peel  bucket ;  bricklaying  in  1 6-ft.  sewer; 
trenching  machine  on  intercepting  sewer:  train  of  dump  cars,  on  sewer 
work;  dueld  and  details  of  shield  for  20-ft.  sewer;  plan  of  int^e  and 
pumping  station;  sectionsof  channels  at  pumping  station;  details  of  screen 
chamber  or  sand  catcher  at  intake. 


Disposal    of    Munk:ipal    Refuse   (Trans.  A.  S.  C.  E.. 


The    Sanitary 
Vol.  L). 

Sewage  Disposal  for  Country  Residences  (Eng.  News.  Jtily  2,  1903). 
—Illustration  of  septic  tank,  the  estimated  cost  of  which  is:  3  casks  at 
75  cents  each -$2.25;  sewage  siphon,  $14.00;  100  ft.  of  farm  tile.  $1.00; 
pipe  and  plank,  $2.60;  labor  and  cement,  $6.00;  total,  $25.75. 

The  Northwestern  Ave.  Sewer  at  Indianapolis,  Ind.  (By  W.  Buehler. 
Paper.  Ind.  Eng.  Soc.;  Eng.  News,  July  16,  1903). — Illustrations:  Map; 
overflow  section  and  jxmction  with  main  sewer;  dam  in  combined  sewer  for 
diverting  sewage  flow  into  sepcuate  sewer;  construction  of  concrete  floor 
and  sides  of  bnck  and  concrete  overflow  sewer;  forms  and  I-beams  in  place 
for  roof  of  concrete  and  steel  rectangular  sewer. 

A  TaUe  Qiving  Quantities  of  Cement  and  Sand  and  of  Cement  Mortar 
for  Sewer  Pipe  Joints  (By  J.  N.  Hazlehurst.    Eng.  News,  Feb.  25,  1904).— 


QUANTITIBS  OP  CbMBNT.  SaND   AND   OF  CbMBNT   MoRTAR  FOR  SbWBR 

PiPB  Joints. 
For  Each  100  ft.  of  Sewer  (With  Portland  Cement  375  lbs. 
net  per  bbl.) 


Mortar 

Proportions:    1  Cement  to 

Size 

of 

Pipe. 

L-jth. 

ISand. 

2  Sand. 

yds. 

No. 

No. 

Cement, 

Sand. 

ft.  to 

Cement, 

Sand. 

ft.  to 

bbls. 

cu.  yd. 

bbl. 
Cemt 

bbls. 

cu.  yd. 

bbl. 
Cemt 

6-in 

2 

0.003 

0.01248 

0.00201 

803 

0.00855 

0.00252 

1.168 

8-in 

2 

O.OSfi 

0.15808 

0.02546 

633 

0.10830 

0.03192 

923 

10-in 

2 

0.058 

0.24128 

0.03886 

410 

0.16630 

0.04872 

605 

12-in 

2 

0.089 

0.37024 

0.05963 

270 

0.25365 

0.07476 

394 

l!^-in 

2 

0.12S 

0.51268 

0.08241 

195 

0 . 35055 

0.10332 

285 

18-in 

2 

0.167 

0.69472 

0.11189 

144 

0.47595 

0.14018 

210 

20-xn 

2 

0.237 

0.98592 

0.15879 

101 

0.67546 

0.19908 

148 

24-in 

2 

0.2M 

1.24384 

0.20033 

80 

0.85215 

0.25116 

117 

27-in 

3 

0.492 

2.04672 

0.32964 

49 

1.40220 

0.41328 

71 

80-in 

8 

0.548 

2.27968 

0.36716 

44 

1.56180 

0.46032 

04 

3e-in 

3 

0.849 

3.53184 

0.56883 

29 

2.41965 

0.71316 

41 

\^rM^n[f> 

1810 


eS.SANITATION. 


The  Wear  of  Sewer  Inverts  (By  E.  A.  Hermann.  Bng.  News.  Feb.  i 
1004). — ^The  materials  most  commonly  used  for  sewer  constructioa  an 
vitrined  clay  pipe,  vitrified  brick,  common  building  brick  Cmore  or  les 
unbumed),  and  concrete.  In  the  sewers  of  St.  Louis,  whick  are  on  tlie 
combined  system,  the  grades  range  from  0.2%  to  2%,  average  about  O.S% 
for  sewers  more  than  5  ft.  in  diameter  and  about  1%  for  the  amaller  seweis. 
The  vitrified  clay  pipes  show  no  appreciable  wear  after  about  86  years'  use; 
these  sewers  are  mostly  laterals,  and  have,  of  course,  the  smallest  discham, 
though  some  of  those  in  the  business  and  mantifacturing  sections  of  the 
city  carry  a  constant  stream  from  1  to  8  ins.  deep,  containing  more  or  less 
acids,  scalding  hot  water  and  steam.  The  pipes  vary  from  12  to  24  ins.  in 
dia.,  except  a  few  lines,  which  are  30  to  36  ins.  in  dia.  The  vitrified  brick 
(in  use  about  12  years)  also  shows  no  appreciable  wear.  The  inverts  of 
sewers  built  of  common  brick  begin  to  show  some  wear  after  about  3  years 
of  service,  and  after  about  30  years'  use  the  first  ring  of  brick  is  worn  away 
from  2  ins.  to  nearly  its  whole  depth  of  4  ins.  This  wear  varies  greatly  in 
sewers  of  different  size,  grade,  quantity  and  quality  of  sewage,  and  hard* 
ness  of  brick;  the  average  life  of  such  brick  appears  to  be  about  40  jrears. 
Illustrations:  Method  employed  in  repairing  badly  worn  sewer  inverts; 
section  of  large  sewer  at  St.  Louis,  Mo. 


A  New  Jointing  Material— Sulphur  and  Sand— for  Sew«r  Pfpei 


imbr- 


Alex.  Potter.    Eng.  News,  Mar.  10,  1»04).— The  following  table  gives  i 
mation  coi;iceming  the  cost  and  amotmt  of  material  in  making  smphur^and 
joints: 


Approximate  C^sts. 

Amt.  of 

Per  foot 

Size  of 

Mixture 

Mixture 

Gasket; 

Fuel. 

Labor. 

Total 

Lengths. 

Pipe. 

Lbs.  per 
Joint. 

3-Pt. 

2.Ft, 

24-in. 

10.0 

.125 

.02 

.02 

.18 

.206 

.10 

.16 

22-in. 

0.0 

.1125 

.02 

.02 

.13 

.282 

.006 

.14 

20-in. 

8.0 

.10 

.02 

.02 

.12 

.260 

.00 

.13 

18-in. 

7.0 

.087 

.02 

.02 

.11 

.247 

.08 

.12 

15-in. 

6.5 

.069 

.01 

.01 

.10 

.187 

.066 

.006 

12-in. 

4.2 

.052 

.01 

.01 

.00 

.162 

.066 

.08 

10-in. 

8.3 

.041 

.01 

.01 

.08 

.141 

.045 

.07 

8-in. 

2.5 

.031 

.01 

.01 

.07 

.121 

.04 

.06 

The  exclusion  of  ground  water  will  increase  the  capacity  of  the  sewer 
from  10%  to  100%  through  territory  subject  to  the  admission  of  grotmd 
water,  so  that  the  increase  in  cost  becomes  a  trifling  matter,  especiany 
when  it  is  considered  that  tree  roots  are  kept  out  of  the  sewer. 

Refuse  Destructor  Combined  With  Electric  Light  Plant  at  Wcot- 
moont,  P.  Q.  (Eng.  News,  May  24,  1906).— Table  of  estimated  costs. 

Specifications  for  Refuse  Destructor,  Borough  of  Richmond,  New 
York  City  (Eng.  News,  Dec.  6,  1906).— The  first  thorough-going,  if  not 
absolutely  the  first,  specifications  and  call  for  bids  for  a  refuse  destructor 
designed  to  produce  heat  for  lighting  or  power  purposes  in  the  U.  S. 

Cost  of  Shallow  and  Deep  Sewer  Trenches  (By  J.  G.  Palmer.  Bag. 
News,  June  25,  1908).— Cost-data  tables. 

Principles  of  Sewage  Purifkation  on  Land  (By  Rudolph  Bering. 
Eng.  News,  May  27  and  June  3.  1909). 

Rainfall,  and  Run-Off  in  Storm-Water  Sewers   (By  C.  C.  Gnaory. 

Trans.  A.  S.  C.  E.,  Vol.  LV III) .—Formulas,  diagrams  and  tables.    Tabte  1, 
Comparison  of  rainfall  and  discharge  from  the  6tn  Avenue  sewer.  N.  Y.  (^ty, 
the  drainage  area  of  which  is  221  acres;    Table  2,  Short«time  storms; 
Table  3,  Long-time  storms. 


Co^  of  a  66-Inch  Brick  Sewer  at  Qary,  Ind.  (By  E.  M.  Scfaefiow.     Bng. 

-.  of  sewer  per  lin.  ft.:  Excavation  by  machine; 

$1.25;  pumping,   11.61;  ahaetiniB.   90.80& 


S?*i'A  J*"-  2'  1909).— Total  cost  of  sewer  perlin.  f't.:'Excavation  by  marhine; 
•U.508;  excavation  by  hand,    "'  "'  "'  "'      *      "         '^  — 


MISCELLANEOUS  DATA,  «  1311 

laying,  11.82;  backfilling  by  omchine.  $0,406;  backfilling  bv  hand.  $0,136; 
hauling  material,  $0,607;  superintendence  and  generaC  $0.30;  materials, 
$1.81;  depreciation  of  machinery,  repairs  and  the  like  (estimated),  $1.50; 
total.  $10,122.  ^       — 

Louisville  Sewerage  Imi^royeinents  (By  R.  DeL.  French.  Eng.  News. 
Oct.  14,  1900). — Blustrated: — Standard  sections  of  circular  concrete 
sewers,  with  table  of  dimensions  and  Quantities,  for  hard  and  soft  ground* 
Tjrpical  horseshoe  section  of  rcinforced-concrete  sewer,  16  ft.  high;  Typical 
semi-elliptical  section  of  reinforced  concrete  sewer,  10  ft.  hign;  Typical 
junction  chamber,  reinforced-concrete  sewers;  Combined  sewer  and  drain. 

Aerial  Distribution  off  Sewage  over  Percolating  Filters  (By  Wm.  Gavin 
Taylor.  Eng.  News,  Nov.  11,  1900). — Illustrations  of  nozzle:  diagrams  of 
distribution  effected  by  same;  pressure  imdulating  valves,  described  and 
illustrated. 

The  Impreved  Water  and  Sewerage  Worics  of  Columbus,  O.  (By  J.  H. 

Gregory.  Trans.  A.  S.  C.  E.,  Vol.  LXVIL.  June.  1910).— Illustrations: 
Lfime  saturatois;  mixing  tanks;  sewage  pumping  station;  purification  works; 
septic  tanks;  gate  house;  etc. 

Modern  Procedura  in  District  Sewer  Design  (By  W.  W.  Homer.  Eng. 
News,  Sept.  29.  1910).-~Dia|:ranis:  (a)  Rainfall  curves  for  St.  Louis;  (b) 
Approximate  curves  for  designing  vitrified  pipe  and  circular  egg-shaped 
sewers  under  60  ins.  mean  diameter;  (c)  Approximate  curves  for  aesigning 
circular  sewers  4  to  24  ft.  in  diameter;  (d)  (/opacities  of  standard  horse- shoe 
sewer.    Illustrations :  Details  of  sewer  inlets.    Table :  Data  for  branch  sewer. 

The  Design  of  Storm-Water  Drains  (Eng.  Rec,  Oct.  29.  1910).— Tables 
of  heavy  precipitations,  and  discussion  of  typical  precipitation  curves. 

lUnstrations  of  Interesting  Designs: — 

Description.  Eng.  News. 

Adjustable  basin  and  manhole  covers  July  11,  1901. 

A  centrifugal  separator  for  shavings  and  dust  Sept.  26,  '01. 

Plan  of  small  sewer  system,  at  Lake  Bluff,  lU.  l^^    ^>  '^1* 

Deep  manhole.construction  on  60th  St.  sewer  tunnel,  B'klyn  Oct.    10.  '01. 

Septic  tank  and  double  contact  filter  beds,  Glencoe,  111.  Oct.   24,  '01. 

Proposed  light  refuse  crematory  on  dumping  pier,  N.  Y.  City  April  17.  '02. 

Steel  plate  mine  ventilating  fan,  Modoc  C.  &  M.  Co.,  Ohio  June  19,  '02. 

Plan  and  details  sewage  purification  works.  Depew.  N.  Y.  June  26,  '02. 
Sewage  disposal  wks.,  filter  beds  and  septic  tk..  Id.  Pk.  Resort  July  24,  '02. 

Method  of  anchoring  a  rein.-conc.  lining  for  septic  tank  Aug.  21,  '02. 

Couplings  for  rods  \ised  in  cleaning  sewers,  conduits,  etc.  Sept.    4.  '02. 

A  new  German  automatic  flush  tank  Nov.  27,  '02. 

The  64th  St.  sewer  tunnel  and  outlet  tunnel,  Brooklyn  Jan.  1,  '03. 
General  arrangement  of  sewage  sludge  treatment  apparatus, 

Cassel,  Germany  Jan.   15,  '03. 

Cross-section  of  72*  concrete  and  brick  sewer.  Coming,  N.  Y.  Dec.    17,  '03. 

A  novel  center  and  form  for  concrete  sewer  work  Feb.  18. '04. 

Oeitch  pit.  septic  tank  and  automatic  flush  tank  for  a  jail  Mar.     3.  '04. 

A  steel  form  for  concrete  sewers  Oct.    20,  '04. 

A  sewer  pipe  centering  device  Feb.  8  ,  '06. 

Sprinkler  motor  for  percolating  sewage  filter,  England  May     2,  '07. 

Rein.-conc.  intercepting  and  outfall  sewer,  Waterbury,  Conn.  Mar.  26, '08. 


Septic  tank  and  percolating  filters,  Univ.  of  Minn. 


une  26,  '08. 


Plans  of  Winston -Salem  interceptingsewer,  and  details  ,  ime  25,  '08. 

Septic  tanks  and  percolating  filters,  Washington,  Pa.  ,  uly   16.  '08. 

Steel  centering  for  Harlem  Creek  sewer  July  30.  '08. 

Adjustable  metal  forms  for  construction  of  large  sewer  Oct.      8,  '08. 

Septic  tank  and  filter  bed  for  residence.  Philippines  Oct.     8,  '08. 

A  Household  cesspool  and  overflow,  with  details  Dec.   17, '08. 

Reinforced-concrete  outlet  sewer.  10 J  ft.  dia.  Jan.    28,  '09. 

Details  of  5J  and  6-ft.  concrete-block  sewers,  Toledo,  O.  Feb.     4.    09. 
10-ft.  sewers,  rein.-conc,  pile  fotmd..  Kansas  City        .^  , bvGoi*?'    SI*  mo 

Plans  and  cross-section  of  Milwaukee  refuse  mcmcrator  July  ^i.   *"• 


1812  •  ei.—SANITATION. 

Descriptioiu  Bos.  Rec. 

Section  of  Stony  Brook  conduit,  and  cableway  carriage  Feb.      6.  "01 

Desi^  of  a  15-ft.  drop  in  a  larae  sewer  Feb.      ft,  *0t. 

Sections  of  rein. -cone,  sewers,  Louisville,  Ky.  May      1,  'OH 

Tvpical  manholes.  U.  S.  Military  Academy  May      8.  '09L 

13.12-ft.  dia.,  circular  rein.-conc.  conduit  drain.  Mexico  June     6. 'Bft. 

Ventilating  manhole  cover  with  dust -catching  box  Tune  36.  '(W. 

Molded  concrete  pipe  and  storm  drains.  Newark,  N.  J.  Nov.     (I,  'Oft. 

Storm  water  drain.  3  ft.  diam.,  with  cost  Dec.   18,  '09. 

Details,  septic  tanks  and  contact  beds,  Grand  Canyon  Tan.    2U,  *1Q. 

Cost  of  catch  basins  in  Boston;  illustrated  Mar.  12;  *10. 

Cross-section  rein.-conc.  stonr  sewer  (18x11  ft.),  on  piers  Mar.  19.  '10. 

Rein.-conc.  sewers  in  soft  ground.  Seattle,  Wash.  Oct.   2S,  '10. 
Sewer  sections,  canal  crossmg  and  siphon  shaft,  N.  trunk 

sewer.  Seattle,  Wash.  Dec.   10.  'lO. 

New  method  of  handling  sewage  sludge,  in  Germany  Dec.   10.  'II. 

Intercepting  sewer  and  outfall  at  New  Bedford  Dec.   17.  'II. 
Heavy  plain  concrete  sewers  i2H  ft.  rad.,  8*  ring)  at  Albany    Dec.  17,  '10. 


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66— IRRIGATION. 

Oeneral  Discnsslon* — ^Those  who  are  specially  interested  in  irrigation 
matters  will  find  much  valuable  information  in  the  Bulletins  issued  by  the 
U.  S.  Department  of  Agriculture,  and  in  the  Water-Supply  and  Irrigation 
Papers,  Annual  Reports,  etc.,  of  the  U.  S.  Geological  Survey.  Lists  of  the 
variotis  Documents  may  be  had  on  application,  and  the  papers  are  gen- 
erally for  free  distribution. 

The  Problems  of  Irrigation  are  broad  and  intricate,  the  local  conditions 
of  soil,  water,  climate,  crops,  etc.,  reouiring  much  study,  often  extending 
over  considerable  periods  oi  time.  The  amount  of  water  required  will 
depend  upon  the  kmd  of  crops,  as  well  as  upon  the  soil,  and  to  a  certain 
extent  upon  the  climate:  also  upon  the  amoimt  of  seepage  and  evaporation 
before  it  reaches  the  land  to  be  irrigated;  and  last  of  all  upon  the  method  of 
irrigation,  which  may  be  more  or  less  wasteful.  If  there  is  any  rainfall,  the 
records  of  monthly  precipitation,  extending  over  say  16  to  20  years,  should 
be  examined  for  one-,  two-  and  three-  year  periods  of  greatest  drought,  for 
a  possible  reduction  in  the  artificial  supply.    (See  Water  Supply,  page  1194.) 

The  Unit  off  Land  Area  in  irrigation  is  the  acre,  equal  to  48560  sq.  ft. 
A  square  1-acre  tract  is  208.71  ft.  square;  a  square  2-acre  tract  is  205.10 
ft.  square;  a  square  3-acre  tract  is  361.50  ft.  square;  a  square  4-acre  tract 
is  417.42  ft.  square;  a  square  5-acre  tract  is  466.60  ft.  sqiiare;  a  square 
10-acre  tract  is  660  ft.  square --i  mile  square;  a  square  20-acre  tract  is 
933.38  ft.  square;  a  square  40-acre  tract  is  1320  ft.  square —  i  mile  square: 
a  square  80-acre  tract  is  1866.76  ft.  square;  a  square  160-acre  tract  is  2640 
ft.  square—  i  mile  square. 

The  Units  of  Flow  of  water  are  the  *'inch"  (miner's  inch)  and  the  cubic 
foot  per  second. 

The  "Inch"  is  the  volume  of  water  (say  in  cubic  feet)  which  will  flow 
through  a  vertical  standard  orifice  one-inch  square  (say  in  one  minute) 
under  a  given  pressure  head  (say  6  to  6i  inches,  and  fixed  by  State  law). 
This  amoimts  to  about  1.6  cubic  feet  per  minute  (see  Table  1).  The  "inch" 
is  concenient  in  delivering  water  to  small  users  because  the  quantity  being 
delivered  is  apparent  at  a  glance.  Where  the  delivery  calls  for  more  than 
one  "inch"  a  box  is  constructed  with  a  long,  horizontal  slot  one  inch  or 
more  in  height  and  provided  with  a  slide  and  scale.*  By  manipulating  the 
slide,  the  slot  may  be  elongated  so  as  to  deliver  the  number  of  inches  re- 
quired; but  as  the  end  contractions  remain  constant  it  is  apparent  that 
tne  rate  of  discharge  increases  faster  than  the  scale  readings  indicate. 

Table  1  is  based  on  one  "inch"  discharging  1.6  cu.  ft.  per  min. 

1, — Equivalents  of  Discharob  of  1  "Inch,"  at  1.5  Cu.  Ft.  per  Min. 


Duration  of  Flow 

U.S. 
OaUons. 

Cubic 
Feet. 

Tons  of 
2000  Lbs. 

Acre-Ins. 

Acr&-Ft. 

I  Second. 

.187 
11.221 
673.25 
16157.9 
484738. 

0.025 
1.6 
90. 
2160. 
64800. 

.00078 
.0469 
2.8125 
67.5 
2025. 

.0000069 
.0004132 
.024793 
.59604 
17.861 

.00000057 

1  Minute. 

.00003444 

1  Hour 

.0020661 

1  24-Hour  Day 

.049587 

1- 30-Day  Month 

1.4876 

Note.— 1  cu.  ft. -7.48052  U.  S.  liquid  gallons -.03 125  tons  (at  62.5  lbs. 
per  cu.  ft) -.000  275  4821  acre-in.-.OOO  022  956  84  acre-ft. 

The  Cubic  Foot  per  Second  is  a  unit  rate  of  flow,  used  mainly  in  gaging 
streams  and  canals.  It  is  definite,  whereas  the  "Inch"  is  more  or  less 
indefinite.    Note  that  both  the  "Inch"  and  the  Ctu  Ft.  per  Sec.  are  rates  of 


*  See  Foot-note  on  following  page. 
1313 


d  by  Google 


1814 


96.— IRRIGATION. 


^ 


*flow,  and  that  where  definite  quantities  are  demanded  the  element  of  tim 
should  be  included,  as  10  "inches"  for  one  month,  or  0.25  cu.  ft.  per  sec  far 
one  month,  etc.  (See  Tables  1  and  2.)  Contracts  for  water  based  <»  asT 
fixed  number  of  cu.  ft.  per  sec.  throughout  the  season  are  unfair  to  the 
user,  or  wasteful,  or  both.  There  are  many  and  various  recording  instn- 
ments  on  the  market  for  determining  the  rates  of  discharge.  They  are  adf- 
registering  and  consist  usually  of  a  fluctuating  line  drawn  on  prc^e  paper 
wound  around  a  cylinder,  bv  a  pen-  or  pencil  i;>oxnt  traveling  longitudmaOy 
to  represent  the  time,  and  by  the  cylinder  oscillatin|r  as  the  water  rises  or 
falls  in  the  meastuing  chamber,  in  which  a  float  is  connected  with  the 
instrument. 

2. — Equivalents  op  Discharob  op  1  Cubic  Foot  pbr  Second. 
(1  cu.  ft.  per  sec. "-about  40  "inches.") 


Duration  of  Flow. 

u.  a 

Oallons. 

Cubic 
Feet. 

Tons  of 
2000  Lbs. 

Acre-Ins. 

Aore-Ft 

1  Second. 

7.48 
448.83 
26  929.9 
646  317. 
19  389  508. 

1 

60 

3  600 

86  400 

2  592  000 

.031 
1.875 
112.5 
2  700. 
81  000. 

.00028 
.01653 
.99173 
23.801 
714.05 

.000021 

1  Minute 

.001377 

1  Hour 

.08264 

1  24-Hour  Day 

1  30-Day  Moath 

1 . 98347 
59.504 

Note.— 1.  cu.  ft.-  7.48052  U.  S.  liquid  gallons- .03125  tons  (at  02,5  lbs. 
per  cu.  ft.)  -  .000  275  4821  acre-in.  -  .0000  229  5684  acre-f t. 

The  Units  of  Volume  of  water  are  the  Acre-Foot  and  the  Acre- Inch, 
the  latter  being  only  occasionasly  used,  and    A  of  the  former. 

The  Acre-Foot  is  the  volume  of  water  which  will  cover  an  acre  1  ft, 
deep  —  48560  cu.  ft.    Mr.  Elwood  Mead  says  of  this  unit: 

It  Is  a  convenient  unit  for  selling  stored  water,  since  the  capaelty  of  reaervotra 
can  be  measured  by  the  same  imlt.  Contracts  in  which  the  acre-foot  Is  used  pcwlde 
for  the  delivery  of  water  on  the  demand  of  the  IniKator.  or  at  Intovals  rather  tlMJi  In 
continuous  flow,  and  canal  companies  have  hesitated  about  adopting  this  xmtt 
because  of  a  fear  that  satisfactory  arrangements  for  delivery  could  not  l»e  made. 
but  that  more  water  would  be  called  for  at  some  time  than  the  canal  could  sanpiy. 
while  at  other  tJmes  the  entire  volume  would  run  to  waste.  Wherever  the  acre-loot 
has  been  adopted  It  has  proved  acceptable  to  IrrlgatOFS.  because  they  share  in  the 
benefit  reeultln|;  from  care  and  skill  In  distribution. 

Table  3  gives  the  rates  of  flow  equivalent  to  an  acre-ft.  in  a  24-hour 
day.  and  Table  4  gives  the  rates  of  flow  equivalent  to  an  acre-ft.  in  a  SO-day 
month. 

8. — Rates  op  Flow  por  Discrarob  op  1  Acrb-Foot  in  1  Dat 
(24  Hours). 
(For  1  acre-inch,  divide  by  12.) 


Flow — 

U.S. 
Qallons. 

Cubic 
Feet. 

Tons  Of 
2000  Lbs. 

Acre-Ins. 

Acre-Ft 

Per  Second 

3.77 
226.29 
13577   14 
325851.5 
9775544. 

.504 
30.25 
1815. 
43560. 
1306800. 

.0158 
.9458 
56.7188 
1361.25 
40837.5 

.000139 
.008333 
.5 
12. 
360. 

.OOOOllC 

"    Minute 

.0006944 

•'   Hour 

.04167 

"    24-Hour  Day 

"    30-Day  Month.... 

30.' 

*  Water  sold  by  the  inch  by  any  individual  or  corporation  shall  be 
measured  as  follows,  to  wit:  Every  mch  shall  be  considered  equal  to  an 
inch-square  orifice  under  a  five-inch  pressure,  and  a  five-inch  pressure 
shall  be  from  the  top  of  the  orifice  of  the  box  put  into  the  banks  of  the  ditdx 
to  the  surface  of  the  water.  Said  boxes  or  any  slot  or  aperture  through 
which  such  water  shall  be  measured  shall  in  all  cases  be  six  incdies  perpen- 
dicular, inside  measurement,  except  boxes  delivering  less  than  twelve  im^ies. 
which  may  be  square,  with  or  without  slides.  All  slides  for  the  same  diall 
mo>^  horizontally,  and  not  otherwise,  and  said  box  put  into  the  banks  of 
ditch  shall  have  a  descending  grade  from  the  water  in  ditch  of  not  less  thas 
one-eight  of  an  inch  to  the  foot.    (General  SUtutes  of  Colorado,  sec.  3471) 


UNITS  AND  DUTY  OF  WATER. 


1815 


4.— Ratbs  of  Flow  for  Dischargb  of  1  Acrb-Poot  im  1  Montr 
(30  Days). 
(Pot  1  acre-inch,  divide  by  12.) 


Flow— 

U.S. 
GallQoa. 

Cubic 
Feet. 

Tons  of 
8000  Lba. 

Acre-Ins. 

Acre-Ft. 

Per  Second. 

-    Minute. 

••    Hour 

.1257 
7.543 
452.57 
10861.7 
325851.5 

.0168 
1.0083 
60.5 
1452. 
43560. 

.000525 
.03151 
1.8906 
45.875 
1861.26 

.00000463 
.0002778 
.016667 
.4 
12. 

.000000386 
.00002815 
.0013889 
.033333 
1. 

-  24-Hour  Day. . . 

-  80-Day  Month. . 

3.4 


The  Doty  of  Water  is  the  amount  of  land  which  a  unit  volume  of  water, 
properly  applied,  can  irrigate;  or,  conversely,  it  is  measured  by  the  amount 
of  water  required  to  irrigate  one  acre  of  land.  This  amount  of  water  may 
l>©  measured  by  volume,  as  in  storage,  or  by  (average)  flow,  as  in  distribution. 

The  (miner's)  "Inch"  is  often  cited  by  many  irrigators  as  the  amotmt 
required  for  one  acre,  and  by  others  as  the  amount  required  for  two.  or 
even  three,  acres  of  land.  By  referring  to  Table  1,  perceding,  it  can  readily 
be  seen  that  a  flow  of  1  "inch"  is  equal  to  about  1.6  acre-ft.  per  month. 
If  flowing  constantly  this  would  amotmt  to  about  6  acre-ft.  for  an  irrigation 
period  of  4  months  (say  from  May  16  to  September  16),  and  about  7.6 
acre-ft.  for  an  irrigation  period  of  6  months  (say  from  May  1  to  October  1). 
For  shorter  periods  it  would  be  proportionately  less.  In  the  Rocky  Mountain 
regions  the  irrigation  season  ranges  from  100  to  160  days;  m  parts  of 
Southern  California  it  is  used  throughout  the  year:  while  in  the  colder 
climates,  as  in  some  parts  of  Montana,  the  period  is  often  shortened  to  two 
months. 

Assuming  that  a  continuous  (average)  flow  of  one  "inch,"  throtighout 
the  irrigation  season,  will  irrigate  If  acres,  then  from  Table  1  this  is  equiva- 
lent to  1  cu.  ft.  per  sec.  for  (if X  •025")  ^®  •*^"*  °^  ^*^^-  ^^  ^®  length 
of  irrigation  season  is  120  days,  this  would  amount  to  ( — '—=^ —  j 

acre-ft.  per  acre.    Similarly,  the  equivalents  in  cu.  ft.  per  sec.  and  in  acre-ft. 
can  be  found  for  any  other  asstmied  duty  in  acreage  per  "inch." 

The  Cu.  Pt.  per  Sec.  is  another  unit  of  flow  in  measuring  the  duty  of 
water.  Assuming  1  cu.  ft.  per  sec.  will  irrigate  60  acres,  we  see  by  Table  2 
that  this  is  equivalent  to  o9.6  acre-ft.  per  month,  or  about  1  acre-ft.  per 
acre  per  month,  or  4  acre-ft.  per  acre  for  4-months  period  of  irrigation. 

Again,  assuming  1  cu.  ft.  per  sec.  for  80  acres,  we  would  require  — ^ —  or 

about  H  acre-ft.  per  acre  per  month,  or  3  acre-ft.  per  acre  for  4-months 
period  of  irrigation. 

The  Acre-Poot  is  now  generally  conceded  to  be  the  best  duty  unit  by 
most  experts  in  irrigation,  but  it  must  be  admitted  that  the  "Inch  and  the 
Cu.  Pt.  per  Sec.  have  some  merits  as  supplementary  factors.  The  acre-ft.  is 
a  definite  quantity  both  in  volume  (43660  cu.  ft.)  and  in  depth  of  equivalent 
precipitation  (12  ins.);  and  by  the  use  of  the  preceding  tables,  it  is  easily 
converted  into  other  units.  It  is  well  to  remember  that  1  cu.  ft.  per  sec.— 
ahout  40  "inches"— about  2  acre-ft.  per  24-hour  day— about  60  acre-ft.  per 
month.  One  great  advantage  of  the  acre-ft.  is  that  it  is  convenient  to  apply 
in  meastuing  the  storage  or  source  of  water  supply,  as  well  as  the  direct 
quantity  required  in  irrigation,  the  contents  of  reservoirs  being  stated  usually 
in  acre-ft.  — total  storage  capcaity  in  cu.  ft.  divided  by  43660. 

Tables  6,  6^  7  and  8,  following,  are  from  Experiment  Stations  Bulletin  86, 
XJ.  S.  Dept.  of  Agriculture.  The  first  three  tables  show  the  duty  of  water 
under  varjring  conditions,  while  Table  8  shows  the  length  of  the  irrigation 


d  by  Google 


1816 


^.—IRRIGATION. 


6. — ^DuTT  OF  Watbr  whbrb  ICbasurbmbnts  Wbbb  ICadb  on  Small 
Canals  or  Latbrals. 


LooaUon. 


Acre-Ft. 


LocatlOQ. 


Acce-FL 


CroaquJst  (arm.  Utah. 1.60 

Long  tann.  Idaho 2.40 

Qage  Canal.  Oal 2.24 

Canal  No.  2.  Wva 2.53 

Vanoe  lann.  Axil 2.82 


BUea  Lateral.  Colo i .  gf* 

Middle  Cr.  Ditch.  Mont 2.  it 

Daggett  lann.  Nebr 2  47 

Mean  of  all  above 2.J7 


*  Low  duty  due  in  part  to  scanty  supply  of  water. 


0. — DuTT  OF  Watbr  whbrb  Mbasurbmbkts  Wbrb  Madb  at  Karght 

OF  FiBLDS. 


Location.  Acre-Ft. 

J  lateral.  Wyoming,  oats. 1 .  &5 

J  lateral.  Wyoming,  com 70 

Farm.  Edgar  WUson.  Idaho 1.48 

Lowest  division.  Gage  Canal 1.78 

Mean  of  measurements  at  B<»eman.  Monu.  Exp.  Sta 1.20 


7. — Duty  of  Water  whbrb  Lossbs  in  Main  Canal  Arb  Includbo. 


Name  of  Canal. 


Acre-Ft. 


Name  of  Canal. 


Aere-FL 


Pecos  Canal.  New  Mexico «.  61 

Mesa  Canal.  Art* 3.81 

Butler  Ditch.  Utah. 6. 24 

Brown  and  Sandtord  Ditch. 

Utah 5.32 


Upper  canal.  Utah. 6-30 

Amity  canal.  Colo 4.  M 

Rust  Lateral.  Idaho. h.H 

Average. i.  47 


8. — Duration  of  Irrigation  Pbriod  on  Somb  Main  Canals. 


State. 

Canal. 

Days. 

Bute. 

Oaoal.                  Days. 

Cal    . 

.  Gage  Canal 365 

.  Mesa  Canal 365 

..  Pecos  Canal 175 

..  Brown  A  Sanford  Ditch  175 
. .   Butler  Ditch .. . 175 

Utah.. 
Idaho. 
Colo... 
Utah.. 
Nebr.. 
Mont.. 
Wyo.. 

...  LowcrOanal 160 

Arix 

N.  Mez.. 
Utah.... 
Utah.... 

. . .  Boise  A  Nampa  Canal .  .  165 

...  AmltyOanal 140 

..  Logan  A  Rlehmood  Coital  125 
...  Ootbenbuif  OanaL 120 

Utah. . . . 
Utah.... 

. .  Big  Ditch 

165 

166 

...  Middle  Q«ek  Ditch OS 

. . .  Canal  No. 2.  Wheattand. .     10 

Utah.... 

. .  Oreen  Ditch. 

165 

D,q,tized  by  Google 

DUTY  OF  WATER,    CANALS.    CONDUITS. 


1317 


Table  0,  following,  is  from  King's  "Inlgation  and  Drainage,"  the 
second  column  having  been  adopted  by  King  from  Wilson's  "M^ual  of 
Irrigation  Engineering."  and  includes  all  losses  from  the  head  of  the  canals: 

9. — ^DuTY  OF  1  Cu.  Ft.  per  Sec,  and  No.  op  "Inches"  in  10  Days, 
In  Various  Countries. 


Name  of  Country. 


No.  of  Acres 
per  SeooDd-Foot. 


No.  of  Inches 
per  10  Days. 


Northern  India 

Italy 

Colorado. 

Utah. 

Montana. 

Wyoming 

Idaho 

New  Mexico. 

Southern  Arlsona. . . 
San  Joaquin  Valley. . 
•Southern  Osllfomla 


60  to  150 

65  to    70 

80  to  120 

60  to  120 

80  to  100 

70  to    90 

60  to    80 

60  to    80 

100  to  ISO 

100  to  ISO 

150  to  300 


3.  967  to  1.587 
3.661  to  3.4 

2.  975  to  1.988 

3.  967  to  1.983 
2.975to2.38 
3.4  to  2.644 
3.  967  to  2. 976 
3. 967  to  2. 975 
2.38  to  1.587 
2.38  to  1.587 
1.587  to  0.793 


*  The  comporitively  high  duty  of  water  in  California  is  due  to  the  extra 
care  taken  in  construction  of  conduits  to  prevent  losses,  and  to  economy  of 
distribution. 

Canals. — Canals  in  earth  are  usually  made  wide  and  shallow  with  side 
slopes  varying  from  i  to  2  horizontal  on  1  vertical.  It  is  best  to  select  such 
side  slopes,  depending  on  the  earthy  material,  as  will  be  maintained  during 
flow.  The  cross-section  of  a  canal  is  determined  often  by  the  allowable 
velocity  which  may  not  exceed,  ordinarily,  about  2f  feet  per  second  in  ordi- 
nary s(nls.  If  the  soil  is  light  2  ft.  is  about  the  maximum,  while  if  hard  and 
gravelly  3  or  4  feet  may  be  exceeded.  The  velocity  of  flow  in  a  canal  is 
dependent  on  the  hydraulic  radius,  the  grade  or  slope,  and  the  roughness  n 
of  wetted  surfaces  (see  Kutter's  formula,  page  1167).  Canals  with  rubble-, 
concrete-  or  cement  lining  are  often  used  where  water  is  scarce  and  valuable. 

In  estimating  the  flow  by  Kutter's  formula,  use  m  — .0225  for  ordinary 
earthen  canal  with  clean  bed.  and  n  —  .035  for  bed  in  bad  order  having  stones 
and  weeds  in  great  quantities.    (See  page  1168.) 

Wilson,  in  his  Manual  of  Irrigation  Engineering,  gives  the  following  data 
relative  to  some  great  perennial  canals: 


10. — Data  on  Some  Great  Perennial  Canals. 
(See  Wilson's  Manual  of  Irrigation  for  full  and  extended  data.) 


Name  of  Canal. 


Locality 


L'ngtb 
Miles. 


Capacity 
Sec-Ft. 


Bed- 
Width; 
Feet. 


•%?•' 


Bear  River  Canal 

Idaho  Mln.  A  Irrig.  Co.  Canal.. . 

Pecos  Canal 

TufiookOanal , 

KlniTs  R.  A  San  Joaquin  Canal  , 

Calloway  Canal 

Arlsona  Canal 

Hlghline  Canal 

Del  Monte  Canal 


Utah 
Idaho 
N.  Mex. 
Cal. 


Arts. 
Colo. 


150 
70 
75 
93 
67 
32 
41 
70 
60 


1000 
2585 
1100 
1500 
600 
700 
1000 
1184 
2400 


1  In  5280 
1  "  2640 
1  "  6707 
•  "  6280 
1  "  5280 
1  "  6600 
1  "  2640 
I  "  3000 
1  "  2112 


60 
40 
45 
70 
32 
80 
36 
40 
65 


7 

10 
6 

7.6 
4.6 
3.6 
7.63 
7 
5.6 


Conduits  and  Flumes  frequently  take  the  place  of  canals  even  in  locali* 
ties  other  than  at  crossing  of  streams.  The  flumes  are  usually  constructed 
of  wood  (sometimes  of  steel),  generally  rectangular  in  cross-section,  and 
supported  on  trestle  work  of  the  same  material  as  the  flume.  The  V-shaped 
fltmie  is  seldom  used  in  connection  with  large  irrigation  projects,  unless 
combined  with  logging.  The  semi-circular  flume,  of  wood-stave  P»P«  «»: 
■trwctkm.  or  of  steel,  has  the  merit  of  giving  the  maximum  velocity  oi 


1818  e^.—IRRIGATION. 


1 


flow  for  a  given  area  of  wetted  cro8S-«ection.  Pipe  lines  of  wooden  ataTes 
or  of  «(eel  are  frequently  used  as  inverted  syphons  for  oonvejrine  watc; 
across  valleys  where  cost  of  flumes  on  high  trestles  would  be  vexy  expensive. 
Wooden  flumes  may  be  made  tight  (1)  by  tangential  compressive  tarces  as 
with  adjustable  rods  or  wedges;  (2)  by  caulking  and  taning  the  joints; 
(3)  by  using  two  thicknesses  of  siding  and. bottom  plank  with  tarrod  paper 
between.    Steel  flumes  are  caulked  similarly  to  riveted  steel  pipe. 

EXCERPTS  AND  REFERENCES. 

Noteworthy  Water  Storage  and  Irrigation  Works  of  SontlMm  CeB- 
fomia  (By  R  Fletcher.  Eng.  News,  Aug.  22.  IMl). — Descriptions  of  the 
following:  System  of  the  San  Dieeo  Land  and  Town  Co.;  Southern  Cali- 
fornia Mountain  Water  Co.;  The  Morena  Dam  and  Reservoir;  The  Barrett 
Dam  and  Reservoir;  The  Lower  Otay  Dam  and  Reservoir;  The  Upper 
Otay  Dam  and  Reservoir. 

Irrigation  System  of  the  Arkansas  Valley  Stuaa  Beet  &  Irricalad 
Land  Co.,  Colo.  (By  W.  P.  Hardesty.    Eng.  News.  Nov.  13,  1«02).-— De- 

'ating 

atava 
...  .    Pawnee 

Canal;  Amity  Canal  System  (canal,  dam.  head-gate,  secondary  head-gate); 
Buffalo  (^nal.    Ten  illustrations  ot  structures. 

EstaMlshlng  Irrigation  Canal  Tangents  So  Cut  and  Fill  Will  Balaace 

(Eng.  News  Aug.  10.  Sept.  21.  1896).— Illustrated. 

A  Diafram  to  Aid  the  Location  of  Small  Irrinitlon  Canals  (By  P.  Mc- 

Oeehan.  Eng.  News,  Feb.  1.  1906). — ^Also  table  lor  laying  grade  line  on 
small  irrigation  canals. 

An  Underflow  Canal  Used  for  Irrigation  at  Ogalalla,  Nebr.  (By  S.  C. 

Slichter     Eng.  News,  July  6,  1906).— Map.    Table  of  flow. 

The  Truckee-Carson   Project   of   the   U.  S.  RecUmatkM  Sarvke  (By 

W.  P.  Hardesty.  Eng.  News.  Oct.  18,  1906).— Illustrations:  Details  of 
diversion  dam  and  head -gates;  lining  in  rock  cut;  jtmction  of  earth  and 
concrete-lined  tunnel;  method  of  lining  tunnel;  details  of  waterway,  with 
Taintor  gates  and  mechanism  for  operation ;  a  simple  form  of  fall  or  drop 
in  canal;  details  of  head  works  of  distributing  system;  details  of  combined 
fall  and  waterway.    Tables  of  cost  data. 

Effect  of  Changes  in  Canal  Onukt  on  Rate  of  Flow  (By  P.  W.  Hanna. 
Eng.  News.  Nov.  21,  1907). 

Lining  Ditches  and  Reservoirs  to  Prevent  Seepage  Losses  (Eng.  News. 
Dec.  6,  1907). — Illustrated  methods  of  lining. 

Cost  of  Canal  Work  on  the  Lower  Yellowstoae  Project  (Eng.  News. 
July  16,  1908). 

Depth  of  Water  in  Irrigatk>n  Canals  (By  C.  B.  Grunsky.  Eng. 
News,  Sept,  10.  1908). — ^Table  1:  Effect  of  water  depth  upon  required 
amount  of  excavation  for  irrigation  canals.  Table  2:  Required  fall  for 
canals  of  varying  capacity. 

Cost  Date  of  the  Cold  Springs  Reservoir  Constmctkm,  Oregoo,  U.  S. 
Red.  Serv.  (Eng.  News.  Nov.  12,  1908). 

Earthwork  Diagrams  for  Estimating  Quantities  In  SmaO  Irrigation 
Canals  in  Level  Sections  (Eng.  News,  June  10.  1909). 

Cost  of  a  Large  Irrieation  Canal  (Eng.  Rec..  Tan.  2.  1909). — ^Table  of 
unit  costs  on  about  4.400  ft.  of  the  south  canal  of  the  Uncompahgre  Proiect 
of  the  U.  S.  Reel.  Serv.  The  canal  has  a  bottom  width  of  40  ft.,  aide  slopes 
of  2  to  1.  and  a  depth  of  water  of  8.3  ft. 

_    Field  Work  in  Locating  Irrigation  Ditch  and  Canal  Unas  (By  A.  B. 

Bartlett.  Eng.  News.  May  26  1910).— Small  Ditches:  Ditcfaea  denned  to 
uriratc  100  to  200  acres  may  be  laid  out  by  setting  stakes  on  the  lower  side 
ot  the  ditch,  determined  by  the  level  only.     Ditches  6  to  10  ft.  on  tlie  bottom 


MISCELLANEOUS  DATA.  1810 

and  1  to  8  ft.  deep  require  more  care:  the  slope  stakes  on  the  lower  side  of 
the  ditch  are  set  first  for  about  l.ftOO  ft.,  after  which  they  are  lined  up  by  eye 
to  tangents  and  curves  nearly  conforming  to  the  contour  which  tne  slope 
stake  on  the  lower  side  of  the  ditch  would  naturally  follow,  but  improving 
on  this  alinement  by  increasing  or  decreasing  the  cut  in  order  to  have  good 
curves  and  tangents,  etc.  Ditches  over  10  to  12  ft.  on  the  bottom  generally 
require  the  methods  of  railway  location  and  cross-sectioning.  Sid»  Slooes. 
Lower  side  of  ditch,  from  1  on  H  to  1  on  3  in  excavation,  and  from  1  on  2  to 
1  on  4  for  fill  on  lower  bank.  On  side-hill  work,  cut  on  upper  side  of  ditch 
is  made  from  1  on  1  to  1  on  2.  for  earth.  Greatest  velocities,  in  feet  per 
second,  permissible  in  difTerent  classes  of  material  are  as  follows:  Sandv  soil, 
1.3;  loose  gravelly  soil.  2.6;  firm  soil  and  firm  sandy  loam,  3.0;  gravel,  3.6; 
firm  gravelly  soil,  5.3;  loose  rock  and  shale,  6.0  to  7.0;  solid  rock.  7.0  to  15.0. 
Kutter's  formula:  Use  n  ■<"  0.03  or  0.025  for  clean  ditches  in  ordinary  earth. 

Drainafe  of  Irrigated  Lands  with  Special  Reference  to  Experiments  io 
Utah  (By  C.  F.  Brown.  Farmers'  Bulletin  No.  371,  U.  S.  Dept.  or  Agric, 
Oct.  2,  1900;  Eng.  News,  Oct.  18,  1010).— Dlustrations:  (1)  Method  of 
grading  drainage  trench:  (2)  Plan  of  drainage;  (3)  Box  drains  with  and 
•without  bottoms;  (4>  Relief  well  and  methoa  of  laying  box  drain  through 
soft  ground.  The  tract  drained  consisted  of  31.5  acres.  Cost. — ^Tile  (lOOiy 
of  10*  @  lO.lSi-  $182.50. 1012^  of  S'  @  $0.12-1121.14,  330^  of  6*  ((4  $0.06- 
$19.80.  650'  of  5*  @  $0,058  =  $37.70,  2  O'  on  8^  wyes  @  $0.7i-$1.44) 
$362.88:  Hauling  (30  tons  li  miles  @  $0.30  per  ton-mile)  $13.50;  Digging 
(134  rods  @  $0r52-$69.68.  and  42  rods  @  $0.40-$16.80)  $86.48;  Laying 
tile,  $18.75;  Filling  trench,  $10.00.  Total  cost,  $401.61 -$15.60  per  acre. 
I«abor,  $2  per  10  hours;  tile  layers,  $2.50;  man  with  team,  $8  per  oay. 

lUustratkMU  of  Irrigation  Stmctnres: — 

Description.  Eng.  News. 

Automatic  drop  shutters  for  irrigation  dam.  India  June  4,  1003. 

Details  of  masonry  and  steel  head-^te  for  irrigation  canal  Aug.  13,  '03. 

Reinforced-concrete  siphon  on  an  irrififation  canal,  Spain  Aug.    1,  '07. 

Pumping  plant  of  the  Htmtley  irrigation  project  Sept.    8,  '08. 

Eng.  Rec. 

Construction  of  *'cut-and-cover"  canal,  Mojavo  desert  Apr.     8,  '00. 

Bconomic  sections  for  earth  canals  July  81,  '00* 


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67.— WATERWAYS.* 

The  Sttei  Canal,  coimectiog  the  Mediterranean  and  Red  Seas,  was  begm 
in  1850  and  completed  in  1860.  Its  total  length  is  90  miles,  of  which  abo>at 
two-thirds  is  throtigh  shallow  lakes.  The  material  excavated  was  usually 
sand,  though  in  some  cases  strata  of  solid  rock  from  2  to  3  feet  in  thickness 
were  encountered.  The  total  excavation  was  about  80,000.000  cubic  yards 
under  the  original  plan,  which  gave  a  depth  of  26  feet.  In  1895  the  canal 
was  so  enlarged  as  to  give  a  depth  of  31  teet,  a  width  at  bottom  of  108  feet 
and  at  the  surface  of  420  feet.  The  original  cost  was  $96,000,000.  and  for 
the  canal  in  its  present  form  slightly  in  excess  of  $100,000,000.  The  canal 
is  without  locks,  bein^  at  the  sea  level  the  entire  distance.  The  length  of 
time  occupied  in  passing  through  the  canal  averages  about  18  hours.  By 
the  use  of  electric  lights  throughout  the  entire  length  of  the  canal,  passages 
are  made  at  night  with  nearly  equal  facility  to  that  of  the  day.  The  toUs 
charged  are  8.50  francs  per  ton  net  register.  "Danube  measurement,"  which 
amovmts  to  about  $2  per  ton  United  States  measurement.  Steam  vessels 
passing  through  the  canal  are  propelled  by  their  own  power.  Since  Jan.  1, 
1902,  the  minimum  draft  of  water  has  been  raised  to  20'  3*  (8  meters). 

Table  1.  next  page,  shows  the  number  and  tonnage  of  vessels  whi^ 
passed  through  the  Suez  Canal,  together  with  the  transit  receipts  for  same, 
and  also  the  number  of  passengers  carried,  from  its  opening  until  1903. 

The  Crofistadt  and  Sf .  Petersburg  Canal,  connecting  the  bay  of  Cronstadt 
with  St.  Petersburg,  is  a  work  of  great  strategic  and  commercial  importance 
to  Russia.  The  canal  and  sailing  course  in  the  bav  of  Cronstadt  are  about 
10  miles  long,  the  canal  proper  being  about  6  miles  and  the  bay  channel 
about  10  miles,  and  they  together  extend  from  Cronstadt,  on  the  Gulf  of 
Finland,  to  St.  Pertersburg.  The  canal  was  opened  in  1890  with  a  navigable 
depth  of  204  feet,  the  original  depth  having  been  about  9  feet.  The  width 
ranges  from  220  to  360  feet.  The  total  cost  is  estimated  at  about  $10,000,000. 
There  are  no  locks. 

The  Corinth  Canal,  connecting  the  Gulf  of  Corinth  with  the  Gulf  of 
.^ina.  reduces  the  distance  from  Adriatic  ports  about  176  miles  and  from 
Mediterranean  ports  about  100  miles.  Its  length  is  about  4  miles,  a  part  of 
which  was  cut  through  g^ranitic  soft  rock  and  the  remainder  through  soil. 
There  are  no  locks,  as  is  also  the  case  in  both  the  Suez  and  Cronstadt  ^-^^^K 
described  above.  The  width  of  the  canal  is  72  feet  at  bottom  and  the  depth 
261  feet.  The  work  was  begun  in  1884  and  completed  in  1893,  at  a  cost 
of  about  $6,000,000.  The  average  tolls  are  18  cents  per  ton  and  20  cents 
per  passenger. 

The  Manchester  Ship  Canal,  connecting  Manchester,  England,  with  the 
Mersey  River,  Liverpool,  and  the  Atlantic  Ocean,  was  opened  for  traffic 
January  1,  1894.  The  length  of  the  canal  is  36)  miles,  the  total  rise  from 
the  water  level  to  Manchester  being  00  feet,  which  is  divided  between  four 
sets  of  locks,  giving  an  average  to  each  of  16  feet.  The  minimum  width  is 
120  feet  at  the  bottom  and  averages  176  feet  at  the  water  level,  though  in 
places  the  width  is  extended  to  230  feet.  The  minimum  depth  is  30  feet, 
and  the  time  required  for  navigating  the  canal  from  6  to  8  hours.  The  total 
amount  of  excavation  in  the  canal  and  docks  was  about  46.000.000  cubic 
yards,  of  which  about  one-fourth  was  sandstone  rode.  The  lock  gates  are 
operated  by  hydraulic  power.  Railways  and  bridges  crossing  the  route  of 
the  canal  have  been  raised  to  give  a  height  of  76  feet  to  vessels  traversing 
the  canal,  and  an  ordinary  canal  whose  route  it  crosses  is  carried  across  by 
a  springing  aqueduct  composed  of  an  iron  caisson  resting  upon  a  pivot 
pier.    The  total  cost  of  the  canal  is  given  at  $76,000,000. 

*  Much  of  the  information  relating  to  large  ship  canals  is  from  Grma 
Canals  of  th€  World,  1906.  Department  of  Commerce  and  Labor,  Washington, 
D.  C.  Those  who  are  particularly  interested  in  this  subject  should  consult 
the  "List  of  Works  Relating  to  Deep  Waterways  from  the  Great  Lakes  to 
the  Atlantic  Ocean  with  some  other  related  works."  published  by  Supt.  of 
Documents,  Washington.  D.  C. 


1320 


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IMPORTANT  CANALS,  SUEZ  CANAL  DATA. 


1821 


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1322  ^.^WATERWAYS, 

The  Kaifcr  Withelm  Canal.  Two  canals  connect  the  Baltic  axMi  Nordi 
Seas  through  Germany;  the  first,  known  as  the  Kaiser  Wilhelm  Cacal 
having  been  begun  in  1887  and  completed  in  1895  and  constructed  lais^ 
for  military  and  naval  purposes,  but  proving  also  of  great  value  to  generaj 
mercantile  traffic.  The  length  of  the  canal  is  61  miles,  the  terminus  in  ti» 
Baltic  Sea  being  at  the  harbor  of  Kiel.  The  depth  is  29}  feet,  the  width  at 
the  bottom  72  Teet,  and  the  minimum  width  at  the  stirface  190  feet.  The 
route  lies  chiefly  through  marshes  and  shallow  lakes  and  among  river  val- 
leys.  The  total  excavation  amoimted  to  about  100.000.000  cubic  yards, 
and  the  cost  to  about  $40,000,000. 

The  Elbe  and  Trave  Canal,  the  second  canal  connecting  the  Baltic  and 
North  Seas  through  Germany,  is  smaller  than  the  Kaiser  Wilhelm  Caxud. 
It  was  opened  in  1900.  with  a  length  of  about  41  miles  and  a  depth  of  about 
10  feet.    It  is  described  in  the  International  Yearbook,  1900.  as  follows: 

"The  Elbe  and  Trave  Osnal.  In  Oermany.  was  opened  by  the  Emperor  of  Qermaay 
on  June  16.  1900.  It  baa  been  under  ooDstructlon  for  five  years,  and  has  cost  abovl 
$5,831,000.  of  which  Prussia  contributed  $1,785,000  and  the  old  Hanae  town  of 
Lubek  $4,046,000.  The  length  of  the  new  canal  is  about  41  miles,  and  Is  the  seooiMl 
to  Join  the  North  Sea  and  the  BalUc.  foUowlnir  the  Kaiser  WOhelm  Canal  (or  KW 
Canal),  built  about  five  years  ago  at  a  cost  of  $37,128,000.  The  breadth  of  tbe  new 
canal  Is  72  feet:  breadth  of  the  locks.  46  feet:  length  of  locks.  261  feet;  depth  oC 
locks.  8  feet  2  Inches.  It  Is  crossed  by  29  brtdces.  erected  at  a  cost  of  $l.000.00«. 
There  are  seven  locks,  five  being  between  Lubek  and  the  IfoUner  See  (the  sumiott 
point  of  the  canal)  and  two  between  Mollner  See  and  Fauenberg-oo-tbe-JSbe.  At 
this  point  It  may  be  noted  that  the  Germans  began  expertmenta  during  1 9M  wf tk 
dectrto  towing  on  the  Flnow  Canal  between  Berlin  and  Stettin.  A  track  of  lomefeer 
gauge  was  laid  along  the  bank  of  the  canal,  having  one  9-pound  and  one  IS-pound 
rail  laid  partly  op  cross  ties  and  partly  on  concrete  Mocks.  The  larger  raO  aenrvs 
tor  the  return  current,  and  has  bolted  to  It  a  rack  which  gears  with  a  spur  wbeel  on 
the  locomotive.  The  locomotive  ts  6  feet  10  Inches  by  4  feet  10  hichee.  mounted  oq 
four  wheels,  with  a  wheel  base  of  3  feet  6  Inches,  and  weighing  2  tons.  It  Is  fitted 
with  a  i2-horBepower  motor,  current  for  which  Is  furnished  by  a  9-kllowatt  dynaouw 
driven  by  a  1  vhorsepower  engine.  The  current  Is  500  volts,  and  Is  transmitted  by 
a  wire  carried  on  wooden  poles  23  feet  high  and  about  120  feet  apart.  The  boats  are 
about  132  feet  long  and  15  feet  6  Inches  beam,  and  carry  from  150  to  175  tons  on  a 
draft  of  4  feet  9  Inches.  During  1 900  the  Stettln-Swlnemund  Canal,  with  a  length  of 
35  miles,  has  been  dredged  throughout,  and  Is  now  open  to  steamers  drawing  22  feel 
of  water.  Swlnemund  Is  on  the  Baltic  Sea.  Among  the  various  projects  for  Eoropeaa 
canals  may  be  mentioned  one  connecting  the  Danube  a  little  bdow  Vienna,  AuMita. 
with  the  Adriatic  Sea  at  Trieste,  a  distance  of  about  319  mUes.  Herr  Wagentatarer. 
of  Vienna.  Is  said  to  have  the  concession  for  this  canal,  the  construction  of  wldoh 
will  cost  some  $  1 20.000.000.  Late  in  1 900  a  canal  from  Liege  to  Antwerp.  In  Belgtum. 
was  being  seriously  discuawd.  In  order  to  connect  the  prosperous  dty  of  Liege  wttk 
the  sea.  and  make  It.  like  the  dty  of  Manchester.  England,  a  seaport.  Hie  original 
promoter  of  the  scheme  was  Mr.  Joseph  Redontl.  who  Is  now  dead.  Mr.  Redonti'a 
plana  have  recently  been  put  In  practical  shape  by  Loxils  Hubln  and  Oaston  DdvUe, 
who  propose  a  canal  84  miles  long.  200  feet  wide,  and  23  feet  deep  from  Antwerp  to 
Jjlege.  with  locks  at  Liege.  Haaselt.  Herenthals.  and  Antwerp.  The  dUierenoe  In 
levd  to  be  overcome  by  locks  would  be  175  feet,  and  It  Is  thought  that  thirteen 
single  locks  and  one  double  lock  would  be  sufBdent.  The  total  estimated  coat  of 
the  work  Is  $25,200,000." 

The  Wetland  Canal  connects  Lake  Ontario  and  Lake  Brie  on  the  Cana- 
dian side  of  the  river.  It  was  constructed  in  1833  and  enlarged  in  1871  and 
again  in  1900.  The  length  of  the  canal  is  26f  miles,  the  ntmiber  of  locks  26. 
the  size  of  locks  270  by  45  feet,  the  total  rise  of  lockage  3261  feet,  and  the 
total  cost  about  $25,000,000.  The  annual  collection  of  tolls  on  freight, 
passengers,  and  vessels  averaged  about  $226,000  and  the  canal  is  open  on 
an  average  about  240  days  in  a  year.  By  order  in  council  dated  April  27. 
1903,  the  levy  of  tolls  for  passage  through  Dominion  canals  has  been 
abolished  for  a  period  of  two  seasons  of  navigation. 

The  Sault  Ste.  Marie  Canals,  at  Sault  Ste.  Marie,  Mich.,  and  Ontario 
are  located  adjacent  to  the  falls  of  the  St.  Marys  River,  which  connects 
Lake  Superior  with  hake  Huron,  and  lower  and  raise  vessels  from  one  level 
to  the  other,  a  height  of  17  to  20  feet. 

The  canal  belonging  to  the  United  States  was  begun  in  1858  by  the 
State  of  Michigan  and  opened  in  1856.  the  length  of  the  canal  being  5.674 
feet,  and  provided  with  two  tandem  locks,  each  being  360  feet  in  length 
and  70  feet  wide,  and  allowing  passage  of  vessels  drawing  12  feet,  the 
origmal  cost  being  $1,000,000.  The  United  States  Government,  by  consent 
of  the  State,  began  in  1870  to  enlarge  the  canal,  and  by  1881  had  increased 


IMPORTANT  CANALS,    CANADIAN  SYSTEMS. 


1328 


Its  length  to  1.0  miles,  its  width  to  an  average  of  160  feet,  and  its  depth  to 
16  feet;  also  had  built  a  single  lock  ftl5  feet  long  and  80  feet  wide,  with  a 
depth  of  17  feet  on  the  sills,  which  was  located  100  feet  south  of  the  State 
locks.  The  State  relinquished  all  control  of  the  canal  in  March^882. 
In  1887  the  State  locks  were  torn  down  and  replaced  by  a  single  lode  800  feet 
kmg,  100  feet  wide,  and  a  depth  of  22  feet  of  water  on  the  sills.  This  lock 
'wasjD'Ut  in  commission  in  1806.    The  canal  was  also  deepened  to  25  feet. 

The  canal  on  the  Canadian  side,  on  the  north  side  of  the  river,  is  1 
miles  kms,  150  feet  wide,  and  22  feet  deep,  with  lock  900  feet  long,  60  feet 
viride,  witn  22  feet  on  the  miter  sills,  and  was  built  during  the  years  1888  to 
1895. 

Canadian  Canal  Systemf.— The  canal  svstems  of  the  Dominion,  under 
Government  control,  in  connection  with  lakes  and  navigable  rivers,  are  as 
follows: 

First.   The  through  route  between  Montreal  and  the  head  of  Lcdce  Superior, 
14  feet  navigation: 


Name  of  Waterway. 

Canal. 

River. 

Remarks. 

1.  Lachlne  Canal 

Miles. 

m 

Mites. 

"ii" 
'"'ibii' 

694 

River  Rt.  Lawrence 

3.   Soulanges  Canal 

u 

River  St.  Lawrence 

8    Own^all  C»nfi^  

11 

River  St.  lAwreneer ...,,.....,,..,..,. 

Tbe  Farrans 

4.   Farraos  Point  Canal 

1 

Point.    Rapide 

River  St.  Lawrence 

Plat,  and  Ga- 

6.  Rapide  Plat  Canal 

m 

lops  canals  are 

"^Rlver  St.  Lawrence 

6    Qalops  Canal , . ,  t  .  t  . , 

7H 

known  as  the 

River  St.  Lawrence  and  Lake  Ontario 

Williamsburg 

7.   Welland  Canal 

26M 

canals. 

Lake  Erie,  Detroit  Rlvy.  Lake  St.  Qalr, 
and  St.  Marys  River 

a.   SAult  Ste.  Marie  Canal 

IH 

Tiake  Snp«*OT  to  Port  Arthur, 

Lake  Superior  to  Duluth.  390. 

Total 

7396 

1.165^ 

Second.     Ottawa  to   Lake   Cham  plain:    Greenville,   Carillon,    St.  Annes, 

Chambly,  St.  Ours  Canals. 
Third.    Ottawa  to  Kingston  (and  Perth):   Rideau  River  and  Canal.    (Con- 
nects with  Perth  by  Tay  Canal.) 
Fourth.    Lake  Ontario  at  Trenton  to  Lake  Huron  at  mouth  of  river  Severn: 

Trent  Canal  (not  completed). 
Fifth.    Ocean  to  the  Bras  d'Or  Lakes:   St.  Peters  C^nal. 

The  Lake  Borgue,  Louisiana,  Canal  was  formerly  opened  in  August, 
1901.  It  opens  continuous  water  communication  with  lakes  Maurepas, 
Ponchartrain,  and  Borgue,  the  Mississippi  Sound,  Mobile,  and  the  Alabama 
and  Warrior  Rivers,  and  the  entire  Mississippi  River  system,  and  has  an 
important  bearing  as  a  regulator  of  freight  rates  between  these  sections. 
The  effects  of  the  canals  may  be  briefly  summed  up  as:  Shortening  the  dis- 
tance between  New  Orleans  and  the  Gulf  points  east  of  the  Mississippi; 
bringing  shipments  from  the  Gulf  coast  direct  to  the  levees  at  New  Orleans; 
saving  the  transshipment  of  through  freights,  with  a  consequent  reduction 
in  freight  rates;  enabling  sea-going  vessels,  drawing  10  to  12  feet  of  water, 
to  come  within  20  miles  of  New  Orleans,  saving  all  such  craft  the  cost  of 
towage  and  shortening,  by  60  miles,  direct  water  communication  between 
New  Orleans  and  the  deep  water  of  the  Gulf.  In  addition  to  these  effects 
may  be  enumerated  the  cheapening  of  coal  for  consumption  at  New  Orleans. 
Coal  has  hitherto  been  floated  down  the  rivers  from  Pittsburg,  a  distance  of 
2100  miles.  The  canal  6pens  up  the  coal  fields  in  the  intenpr  of  Alabama 
for  New  Orleans  consxmiption  and  reduces  coal  prices  considerably,  giving 


1834  Vt.—WATERWAYS, 

aa  additional  advantage  to  domestic  industries  and  to  steamers  t 

bunker  coal.  The  canal  is  7  miles  kmg  and  from  150  to  200  feet  wide 
Bayou  Dupree  forms  a  portion  of  the  canal.  The  lode  chamber  is  200  feet 
long.  50  feet  wide  and  25  feet  deep,  and  connects  the  canal  with  the  MImji 
sippi  River. 

The  Chicago  Sanltafy  and  Ship  Caoal  connects  Lake  Michigan  at 
Chicago  with  we  Illinois  River  at  Lockport,  a  distance  of  84  miles.  Tlie 
canal  was  cut  for  the  purpose  of  giving  to  the  city  of  Chicago  proper  drainage 
facilities  by  reversing  the  movement  of  water,  which  formerly  flowed  into 
Lake  Michigan  through  the  Chicago  River,  and  turning  a  current  from  Lake 
Michigan  through  the  Chicago  River  to  the  Dlinois  River  at  Lockport,  and 
thence  down  the  Illinois  River  to  the  Mississippi.  The  minimum  depth  of 
the  cazial  is  22  feet.  iU  width  at  bottom  160  feet,  and  width  at  the  top 
from  162  to  290  feet,  according  to  the  class  of  material  through  which  it  is 
cut.  The  work  was  begun  September  8,  1802^and  completed  and  the  water 
turned  into  the  channel  January  2.  1900.  The  flow  of  water  from  Lake 
Michigan  toward  the  gtdf  is  now  at  the  rate  of  360.000  cubic  feet  per  minute, 
and  the  channel  is  estimated  to  be  capable  of  carrying  nearly  twice  that 
amount.  The  total  excavation  in  its  construction  mcludea  28,500.000 
cubic  yards  of  glacial  drift  and  12.910,000  cubic  yards  of  ioUd  rock,  an 
aggregate  of  41.410.000  cubic  yards.  In  addition  to  this  the  oonstructioo  of 
a  new  channel  for  the  Desplaines  River  became  necessary  in  order  to  permit 
the  canal  to  follow  the  bed  of  that  river,  and  the  material  excavated  in 
that  work  amounted  to  2,068,659  cubic  jrards,  making  a  grand  total  dis- 
placement in  the  work  of  43.478,659  cubic  yards  of  material  which,  accordine 
to  a  statement  issued  by  the  trustees  of  the  sanitary  district  of  Chicago. 
would,  if  deposited  in  Lake  Michigan  in  40  feet  of  water,  fonn  an  island 
1  mile  square  with  its  surface  12  feet  above  the  water  line. 

All  bridges  along  the  canal  are  movable  structures.  The  total  cost  o€ 
construction,  including  interest  accoimt,  aggregated  $34,000,000,  of  which 
$21,379,675  was  for  excavation  and  about  $3,000,000  for  righu  of  way 
and  $4,000,000  for  buildixig  railroad  and  highway  bridges  over  the  canal 
The  city  and  State  authorities  by  whom  the  canal  was  constructed  are  now 
proposing  to  Congress  to  make  this  canal  a  commercial  highway  in  caae 
Congress  will  increase  the  depth  of  the  Illinois  and  Mississippi  Rivers  to  a 
depth  of  14  feet,  with  locks  for  fleets  of  baiges  f^t>m  Lockport.  the  terminus 
of  the  drainage  canal,  to  St.  Louis.  This,  it  is  argued,  would  give  through 
water  transportation  from  Lake  Michigan  to  the  Gulf  by  way  of  the  drainage 
canal,  the  Illinois  River,  and  the  Mississippi  River,  and  would  enable  the 
Unitra  States  in  case  ot  war  to  quickly  transport  light-draft  war  vessels 
from  the  Gulf  to  the  lakes.  This  work  of  deepening  the  Illinois  River  wouU 
also  give  through  water  connection  from  Rock  Island,  on  the  Upper  Mis- 
sissippi River,  to  Lake  Michigan  via  the  lUinois  and  Mississippi  Canal, 
which  extends  from  Rock  Island,  on  the  Mississippi  River,  to  Hennepin. 
on  the  Illinois  River.  The  estimate  of  the  Chicago  sanitaiy  district  trustees 
of  the  cost  of  deepening  the  Illinois  and  Mississippi  Rivers  nom  the  terminus 
of  the  ship  canal  to  St.  Louis  to  a  depth  of  14  feet  is  $25,000,000,  inchidmg 
five  locks  and  dams. 

Proposed  American  Isthmian  Canal. — ^The  construction  of  a  waterway  to 
connect  the  Atlantic  and  Pacific  across  the  American  isthmus  has  been  a 
subject  of  consideration  for  nearly  400  years.  Vasoo  Nunes  de  Balboa, 
governor  of  a  province  in  Darien,  in  1513  crossed  the  isthmus  and  discovered 
the  Pacific^  and  from  that  time  forward  efforts  were  almost  constantly 
made  to  discover,  a  water  connection  between  the  oceans  at  this  point. 
which  it  was  hoped  nature  had  supplied.  When  this  hope  was  abandoned 
the  construction  of  an  artificial  water  route  was  immediately  proposed, 
and  Charles  V.  is  said  to  have  directed,  as  early  as  1520,  that  the  Isthmus 
of  Panama  be  surveyed  with  the  purpose  of  selecting  a  route  for  the  con- 
struction  of  an  artificial  waterway  to  connect  the  two  oceans.  Another 
decree  was  issued  in  1534,  authorizing  a  careful  examination  by  experienced 
men  for  this  purpose;  but  the  governor  having  reported  that  such  work  was 
impracticable,  and  that  no  king,  however  powerful,  was  capable  of  forming 
a  junction  of  the  two  seas,  and  the  suggestion  having  been  made  that  the 
opening  of  a  canal  through  the  isthmus  would  be  *'in  opposition  to  the  will 
of  the  Almighty,  who  had  placed  this  barrier  in  the  way  of  navigation 
between  the  two  oceans,"  theproject  was  temporarily  abcmdoned.  Ftutber 
exammations  were  made  in  1771  in  the  hope  of  finding  a  continuous  water- 


CHICAGO  CANAL.    ISTHMIAN  CANAL.  1826 

way,  as  statements  had  been  made  that  a  river  had  been  found  flowing 
from  ocean  to  ocean,  but  an  examination  proved  the  inaccuracy  of  this 
statement.  In  1779  a  survey  was  made  to  determine  the  practicability  of 
connectixig  the  oceans  by  way  of  LcUce  Nicaragua,  but  the  report  was  not 
encouraging.  Prom  that  date  forward,  however,  ntunerous  examinations 
and  surveys  of  the  isthmus  were  made  at  various  points,  the  latest  being 
that  of  the  American  Commission  appointed  in  1899,  and  which  has  recently 
presented  its  full  report  to  Congress.    That  report  concludes  as  follows: 

"The  investigations  of  this  Commission  have  shown  that  the  selection 
of  'the  most  feasible  and  practicable  route'  for  an  isthmian  canal  must  be 
made  between  the  Nicaragiia  and  Panama  locations.  Piirthermore,  the 
complete  problem  involves  both  the  sea-level  plan  of  canal  and  that  with 
locks.  The  Panama  route  alone  is  feasible  for  a  sea-level  canal,  although 
both  are  entirely  practicable  and  feasible  for  a  canal  with  locks.  The  time 
required  to  complete  a  sea-level  canal  on  the  Panama  route,  probably  more 
than  twice  that  needed  to  build  a  canal  with  locks,  excludes  it  from  favor- 
able consideration,  aside  from  other  serious  features  of  its  construction. 
It  is  the  conclusion  of  this  Commission,  therefore,  that  a  plan  of  canal  with 
locks  should  be  adopted. 

"A  comparison  of  the  principal  physical  features,  both  natural  and 
artificial,  of  the  two  routes  reveals  some  points  of  similarity.  Both  routes 
cross  the  continental  divide  less  than  ten  miles  from  the  Pacific  Ocean, 
the  Panama  stunmit  being  about  double  the  height  of  that  in  Nicaragua. 
For  more  than  half  its  length  the  location  of  each  route  on  the  AtUmtic 
side  is  governed  by  the  course  of  a  river,  the  flow  from  whose  drainage  basin 
is  the  only  source  of  water  supply  for  the  proposed  canal;  and  the  summit 
levels,  dinering  but  about  20  feet  in  elevation,  Panama  being  the  lower. 
are  formed  by  lakes,  natural  in  the  one  case  and  artificial  in  the  other, 
requiring  costly  dams  and  wasteways  for  their  regulation  and  for  the  im- 
pounding of  stuplus  waters  to  reduce  the  effect  of  floods  and  to  meet 
operating  demands  during  low-water  seasons. 

"The  investigations  made  in  connection  with  the  regulation  of  Lake 
Nicaragua  have  demonstrated  that  that  lake  affords  an  inexhaustible  water 
supply  for  the  canal  by  that  route.  The  initial  proposition,  on  the  other 
hand,  for  the  Panama  route  is  to  form  Lake  Bohio  so  as  to  yield  a  water 
supply  for  a  traffic  of  10^000.000  tons,  which  can  be  supplemented  when 
needed  by  an  amount  sufficient  for  more  than  four  times  that  traffic,  by 
means  of  the  Alhajuela  reservoir.  For  all  practical  purposes  this  may  be 
considered  an  unlimited  supply  for  the  Panama  route.  So  far  as  the  practical 
operation  of  a  ship  canal  is  concrened,  therefore,  the  water  supply  features 
on  both  lines  are  satisfactory. 

"The  difficulties  disclosed  and  likely  to  be  encountered  in  the  construc- 
tion of  the  dams  are  less  at  Conchuda  on  the  Nicaragua  line  than  at  Bohio 
on  the  Panama  route.  Both  dams,  however,  are  practicable,  but  the  cost 
of  that  at  Bohio  is  one-half  more  than  at  Conchuda.  A  less  expensive  dam 
at  Bohio  has  been  proposed,  but  throtigh  a  portion  of  its  length  it  would  be 
underlaid  by  a  deposit  of  sand  and  gravel  perviotis  to  water.  The  seepage 
might  not  prove  dangerous,  but  the  security  of  the  canal  is  directly  dependent 
upon  this  dam,  and  the  policy  of  this  Commission  has  been  to  select  the 
more  perfect  structure  even  at  a  somewhat  greater  cost.  The  wasteways  at 
both  locations  present  no  serious  difficulties.  The  advantages  in  the  design 
and  construction  of  the  dams  are  in  favor  of  the  Nicaragua  route. 

"The  system  of  regulation  at  Lake  Bohio  consists  only  of  the  discharge 
of  water  over  the  crest  of  a  weir,  as  the  lake  level  rises  under  the  influence 
of  floods  in  the  Chagres  River.  The  plan  of  regulating  the  level  of  Lake 
Nicaragua  is  less  simple,  though  perfectly  practicable.  It  involves  the 
operation  of  movable  gates  at  such  times  and  to  such  extent  as  the  rainfall 
on  the  lake  basin  may  require.  The  experience  and  judgment  of  the  operator 
are  essential  elements  in  the  effective  regulation  of  this  lake.  The  regula- 
tion of  Lake  Bohio  is  automatic. 

"The  only  means  of  transportation  now  found  on  the  Nicaragua  route 
are  the  narrow-gauge  Silico  Ltuce  Railroad,  about  6  miles  in  length,  and  the 
limited  navigation  of  the  San  Juan  River  and  the  lake,  but  the  Nicaragimn 
Government  is  now  building  a  railroad  along  the  beach  from  Greytown  to 
Monkey  Point,  about  45  miles  to  the  northward,  where  it  proposes  to  estab- 
lish a  commercial  port.  By  means  of  a  pier,  in  the  area  protected  bv  the 
point,  goods  and  material  for  canal  purposes  can  readily  be  landed  and 
transported  by  rail  to  Greytown.  Such  piers  are  in  constant  use  on  our 
Pacific  coast.    This  railroad  and  port  would  be  of  great  value  durmg  the 


1836  V!.—WA  TERWA  YS, 

period  of  preparation  and  harbor  construction,  and  should  material? 
shorten  that  period.  A  well-eqiupped  raflroad  b  in  operation  aloog  t^ 
entire  length  of  the  Panama  route,  and  existing  conditions  there  affocii 
immediate  accommodation  for  a  large  force  of  laborers. 

"The  Nicaragua  route  has  no  natural  harbor  at  either  end.  At  both  the 
Atlantic  and  Pacific  termini,  however,  satisfactory  harbors  may  be  created 
by  the  removal  of  material  at  low-imit  prices,  and  by  the  constructxm  ot 
protective  works  of  well-established  design.  An  excellent  roadstead, 
protected  bv  islands,  already  exist  at  Panama,  and  no  work  need  be  do« 
there  for  either  harbor  construction  or  maintenance.  At  Colon,  the  Atlantic 
terminus  of  the  Panama  route,  a  serviceable  harbor  already  exists.  It  has 
afforded  harbor  accommodations  for  many  years,  but  it  is  open  to  noirthers, 
which  a  few  times  in  each  year  are  liable  to  damage  ships  or  force  them  \a 
put  to  sea.  Considerable  work  must  be  done  there  to  create  a  staitable 
narbor  at  the  entrace  of  the  canal,  which  can  easily  be  entered,  and  viO 
give  complete  protection  to  shipping  lying  within  it.  The  compleivm  of 
the  harbors  as  planned  for  both  routes  would  yield  but  little  advantage  to 
either,  but  the  balance  of  advantages,  including  those  of  maintenance  and 
operation,  is  probably  in  favor  of  the  Panama  route. 

"The  existence  of  a  harbor  at  each  terminus  of  the  Panama  loute,  and 
a  line  of  railroad  across  the  Isthmus,  will  make  it  practicable  to  commeooe 
work  there,  after  the  concessions  are  acquired,  as  soon  as  the  necessarr 
cdant  can  be  collected  and  put  in  place,  and  the  worldxu:  force  ongaxdaed. 
This  period  of  preparation  is  estimated  at  one  year,  m  Nicaragua  this 
period  is  estimated  at  two  years,  so  as  to  include  also  the  construction  of 
working  harbors  and  terminal  and  railroad  facilities. 

"The  work  of  excavation  on  the  Nicaragua  route  is  distributed;  it  is 
heaviest  near  Conchuda,  at  Tamborcito,  and  in  the  divide  west  of  the  lake. 
On  the  Panama  route  it  is  largely  concentrated  in  the  Culebra  and  Emperador 
cuts,  which  are  practically  one.  As  a  rule  distributed  work  affords  a  greater 
number  of  available  points  of  attack,  contributing  to  a  quicker  oompletkxi; 
but  in  either  of  these  cases  such  difficulties  as  may  exist  can  be  successfuCy 
met  with  suitable  organization  and  efficient  aopliances. 

"The  time  required  for  constructing  the  Nicaragua  Canal  will  depend 
largely  on  the  promptness  with  which  the  reouisite  force  of  laborers  can  be 
brought  to  Nicaragua,  housed  and  organized  at  the  locations  of  heaviest 
work  along  the  route.  The  cut  through  the  divide  west  of  the  lake  will 
probably  require  the  longest  time  of  any  single  feature  of  constraction. 
It  contains  about  18,000.000  cubic  yards  of  earth  and  rock  excavation,  or 
a  Uttle  less  than  10  per  cent  of  the  total  material  of  all  classes  to  be  removed. 
With  adeqtiate  force  and  plant  this  Commission  estimates  that  it  can  be 
completed  in  four  years.  This  indicates,  under  reasonable  allowance  for 
ordinary  delays,  that  if  force  and  plant  enough  were  available  to  secure  a 
practically  concurrent  execution  of  all  portions  of  work  on  the  route,  the 
completion  of  the  entire  work  might  be  expected  within  six  years  after  its 
beginning,  exclusive  of  the  two  years  estimated  for  the  period  of  preparation. 

'*The  securing  and  organizing  of  the  great  force  of  laborers  needed, 
largely  foreigners,  so  as  to  adjust  the  execution  of  the  various  portions  oi 
the  work  to  such  a  definite  pro^^ramme  of  close-fitting  parts  in  a  practiadly 
unpopulated  tropical  country,  mvolves  unusual  diffictilties  and  would  pro- 
long the  time  required  for  completion. 

"The  greatest  single  feature  of  work  on  the  Panama  route  is  the  excava- 
tion in  the  Culebra  section,  amounting  to  about  48.000,000  cubic  yards  of 
hard  clay,  much  of  which  is  classed  as  soft  rock,  or  nearly  45  per  cent  of  all 
classes  of  material  to  be  removed.  It  is  estimated  that  this  cut  can  be 
completed  in  eight  years,  with  allowance  for  ordinary  delays,  but  exdusivt 
of  a  two-year  period  for  preparation  and  for  unforseen  delays,  and  that  the 
remainder  of  Uie  work  can  be  finished  within  the  same  period.  The  great 
concentration  of  work  on  this  route  and  its  less  amount  will  not  rrauire  so 
great  a  force  of  laborers  as  on  the  Nicaragua  route;  hence  the  difioculties 
and  delays  involved  in  securing  them  will  be  correspondingly  dinuxiished. 

"The  total  length  of  the  Nicaragua  route  from  sea  to  sea  is  183.66  milas, 
while  the  total  length  of  the  Panama  route  is  49.09  miles.  The  length  « 
standard  canal  section  and  in  harbors  and  entrances  is  73.78  nules  for  the 
Nicaragua  route  and  36.4 1  miles  for  the  Panama  route.  The  length  of  saaHas 
line  in  Lake  Nicaragua  is  70.51  miles,  while  that  in  Lake  B^iio  is  12.Ce 
miles.  That  portion  of  the  Nicaragxia  route  in  the  canaliaed  San  Juaa  is 
39.37  miles. 

"The  preceding  physical  features  of  the  two  lines  measure  the  magnitude 


PROPOSED  AMERICAN  ISTHMIAN  CANAL,  1827 

of  the  work  to  be  done  in  the  construction  o£  waterways  along  the  two 
routes.  The  estimated  cost  of  constructing  the  canal  on  the  Nicaragua 
route  is  $45,630,704  more  than  that  of  completii^  the  Panama  Canal, 
omitting  the  cost  of  acquiring  the  latter  property.  This  sum  measures  the 
difference  in  the  magnitude  of  the  obstacles  to  be  overcome  in  the  actual 
construction  of  the  two  canals  and  covers  all  physical  considerations,  such 
as  the  greater  or  less  height  of  dams,  the  greater  or  less  depth  of  cuts,  the 
presence  of  absence  of  natural  harbors,  the- presence  or  absence  of  a  railroad, 
and  the  amount  of  work  remaining  to  be  done. 

"The  estimated  annual  cost  of  maintaining  and  operating  the  Nicaragua 
Canal  is  $1,300,000  greater  than  the  corresponding  charges  Tor  the  Panama 
Canal. 

"The  Panama  route  would  be  134.57  miles  shorter  from  sea  to  sea  than 
the  Niouugua  route.  It  would  have  less  summit  elevation,  fewer  locks, 
1,668  degrees  and  26.44  miles  less  curvattire.  The  estimated  time  for  a 
deep-dratt  vessel  to  pass  through  is  about  12  hours  for  Panama  and  thirty- 
three  hours  for  Nicaragua.  These  periods  are  practically  the  measure  of 
the  relative  advantages  of  the  two  canals  as  waterways  connecting  the  two 
oceans,  but  not  entirely,  because  the  risks  to  vessels  and  the  dangers  of  de- 
lay are  greater  in  a  canal  than  in  the  open  sea. 

"Except  for  the  items  of  risks  and  delays,  the  time  required  to  pass 
through  the  canals  need  be  taken  into  account  only  as  an  element  in  the 
time  required  by  vessels  to  make  their  voyages  between  terminal  ports. 
ComF>ared  on  this  basis,  the  Nicaragua  route  is  the  more  advantageous  for 
all  transisthmian  commerce  except  that  originating  or  ending  on  the  west 
coast  of  South  America.  For  the  commerce  in  which  the  United  States  is 
most  interested,  that  between  our  Pacific  ports  and  Atlantic  ports,  European 
and  American,  the  Nicaragua  route  is  shorter  by  about  1  day.  The  same 
advantage  exists  between  our  Atlantic  ports  and  the  Orient.  For  our  Gulf 
ports  the  advantage  of  the  Nicaragua  route  is  nearly  two  days.  For  com- 
merce between  North  Atlantic  ports  and  the  west  coast  of  South  America 
the  Panama  route  is  shorter  by  about  two  days.  Between  Gulf  ports  and 
the  west  coast  of  South  America  the  saving  is  about  one  day. 

"The  Nicaragua  route  would  be  the  more  favorable  one  for  sailing  ves- 
sels because  of  the  tmcertain  winds  in  the  Bay  of  Panama.  This  is  not, 
however,  a  material  matter,  as  sailing  ships  are  being  rapidly  displaced  by 
steamships. 

"A  canal  by  the  Panama  route  will  be  simply  a  means  of  commimication 
between  the  two  oceans.  That  route  has  been  a  highway  of  commerce  for 
more  than  three  hundred  years,  and  a  railroad  has  been  in  operation  there 
for  nearly  fifty  years,  but  this  has  effected  industrial  changes  of  but  little 
consequence,  and  the  natural  features  of  the  country  through  which  the 
route  passes  are  such  that  no  considerable  development  is  likely  to  occur  as 
a  result  of  the  construction  and  operation  of  a  canal. 

"In  addition  to  its  use  as  a  means  of  communication  between  the  two 
oceans,  a  canal  by  the  Nicaragua  route  would  bring  Nicaragua  and  a  large 
portion  of  Costa  Bica  and  other  Central  American  States  into  close  and 
easy  commimication  with  the  United  States  and  with  Europ>e.  The  intimate 
business  relations  that  would  be  established  with  the  people  of  the  United 
States  during  the  period  of  construction  by  the  expenditure  of  vast  sums 
of  money  in  these  States  and  the  use  of  American  products  and  manufac- 
tures would  be  likely  to  continue  after  the  completion  of  the  woric,  to  the 
benefit  of  our  manufacturing,  agricultural,  and  other  interests. 

"The  Nicaragua  route  lies  in  a  region  of  sparse  population  and  not  in 
a  pathway  of  much  trade  or  movement  of  people;  conditions  productive  of 
much  sickness  do  not  exist.  On  the  other  hand,  a  considerable  population 
has  long  existed  on  the  Panama  route,  and  it  lies  on  a  pathway  ot  compara- 
tively large  trade,  along  which  currents  of  moving  people  trom  infected 
places  sometimes  converge,  thus  creating  conditions  favorable  to  epidemics. 
Existing  conditions  indicate  hygienic  advantages  for  the  Nicaragua  route, 
although  it  is  probable  that  no  less  effective  sanitary  measures  must  be  taken 
durmg  construction  in  the  one  case  than  in  the  other" 

The  relative  estimated  cost  of  the  Nicaragua  and  Panama  canals  is  as 
follows:  Nicaragua  $189,864,962;  completing  the  Panama  canal  $144,233,r 
358+  $40,000,000  for  acquiring  the  rights  and  property  of  the  New  Panama 
Canal  Co..  making  a  total  of  $184,233,368.      [Actual  cost  will  be  double^ 

Estimates  of  annual  cost  of  maintenance  are:  Nicaragua  canal,  $8,800,- 
000:   Panama  canal  $2,000,000. 


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ISTHMIAN  CANAL  DISTANCES.    COST  DATA,  1S20 

The  Hariem  River  Ship  Ceiuil,  connecting  the  Hudson  River  and  long 
Island  Sound,  by  way  of  Spuyten  Duyvil  Creek  and  Harlem  River,  was 
opened  for  traffic  on  June  17. 1805,  and  coet  about  12,700.000. 

Coct  off  Maintenance  and  Opieration  of  Canab. — In  order  to  form  an 
estimate  of  the  cost  of  maintaining  and  operating  the  Ibthmian  Canal,  the 
Isthmian  Canal  Conmiission  obtained  data  bearing  on  this  point  from  the 
Sues,  Manchester.  Kiel,  and  St.  Marys  Palls  canals,  as  follows: 

There  are  no  locks  on  the  Suez  Canal,  but  the  channel  is  through  drifting 
sand  for  a  great  part  of  its  length.  The  entrance  to  the  harbor  of  Port  Said 
on  the  Mediterranean  intercepts  the  drift  of  sand  discharged  from  the  Nile 
and  carried  along  the  coast  by  the  easterly  current.  The  maintenance  of 
tbe  Sues  Canal  therefore  requires  a  large  amount  of  dredging  and  consists 
mainly  of  this  class  of  work.  The  operating  expenses  are  also  large,  the 
great  traffic  involving  heavy  costs  for  pilotage.  The  ffeneral  expenses  for 
administration  have  necessarily  been  greater  for  the  Suez  Canal  than  for 
the  Kiel  or  Manchester  Canals,  on  account  of  the  distance  of  the  wotk  from 
the  point  of  central  control,  a  disadvantage  which  would  also  attend  the 
operation  of  the  Isthmian  Canal.  The  annual  cost  of  maintenance  and 
operation  of  the  Suez  Canal  is  about  $1,300,000,  or  about  $13,000  per  mile. 

The  annual  cost  of  maintenance  and  operation  of  the  Kiel  Canal  is  $8, 600 
per  mile.  The  cost  of  maintenance  only  of  the  Manchester  Canal  is  $9,500 
per  mile.  These  canals  have  locks  and  other  mechanical  structures,  and 
therefore  might  be  expected  to  have  a  higher  cost  of  maintenance  than  the 
Suez  Canal,  which  has  none,  but  this  appears  to  be  more  than  offset  by 
reduccMl  cost  of  maintaining  the  prism  and  more  economical  central  control. 
The  traffic  being  light  on  these  canals,  the  cost  of  pilotage  and  port  service 
is  smidl.  The  mechanical  structures  are  now  nearly  new,  and  will  soon 
require  larger  annual  outlays  for  maintenance,  while,  with  the  increase  of 
traffic,  operating  expenses  will  become  larger. 

The  St.  Marys  Palls  Canal,  when  compared  with  those  just  mentioned. 
is  remarkable  by  reason  of  its  short  length,  large  proportion  of  mechuiicai 
structures,  and  immense  traffic.  Its  length  is  about  H  miles.  Its  annxml 
traffic,  limited  by  the  severity  of  the  winter  to  a  period  of  about  eight 
months,  is  nearly  three  times  that  of  the  Suez  Canal,  eight  times  that  of 
the  Kiel  Canal,  and  ten  times  that  of  the  Manchester  Canal.  Both  mainte- 
nance and  operating  expenses  are  therefore  very  large,  amounting  to  from 
$70,000  to  $90,000  per  year,  or  $46,000  to  $60,000  per  mile.  The  annual 
cost  per  mile  of  mamtenance  and  operation,  however,  for  comparison  with 
other  canals,  should  be  determined  by  considering  the  18i  miles  of  dredged 
channel  ways  in  St.  Marys  River  as  part  of  the  canal.  Then  for  the  20  miles 
of  canal  and  canalized  river  the  expenses  per  mile  would  be  from  $3,000  to 
$5,000  annually.  Tolls  were  collected  by  the  State  from  1855  to  1881. 
Since  its  ownership  by  the  jsovemment  no  tolls  have  been  charged. 

The  Principal  Commercial  Canals  of  the  U.  S.,  Showing  cost  of  construc- 
tion (which  includes  coet  of  improvements) ,  date  of  completion,  length, 
number  of  locks,  and  navigable  depth,  are  given  in  Table  3,  on  following 
page,  which  is  reproduced,  by  permission,  from  the  New  York  World 
Almanac 


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9n,'-WATERWAYS, 


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COMMERCIAL  CANALS  OF  THE  U.  S.  1831 


EXCERPTS  AND  REFERENCES. 

TIm  Relation  of  Depth  of  Water  to  Speed  and  Power  of  Ships  (Bng. 
I*7ew8,  Mar.  16,  1905). — Diagrams.    Contains  other  references. 

The  Relation  of  the  Depth  of  Harbor  Channels  to  Modem  Shipping 
CBng.  News,  Dec.  27,  1906).— Table. 

Construction  and  Unit  Costs  of  Concrete  Lock,  Rough  River,  Ky. 
(Bng.  News,  Jan.  9,  1908).— Illustrated,  with  tables  of  costs. 

The  Design  of  Emergency  Movable  Dams  for  Canal  Locks  (Bng. 
News.  June  24,  1909).— Illustrated. 

Water  Supply  for  the  Lock  Canal  at  Panama  (By  Julio  P.  Sorgano. 
Trans.  A.  S.  C.  E.,  Vol.  LXVIL.  June.  1910). 

The  Siphon  Lock  on  the  New  York  State  Barge  Canal  (By  D.  A.  Watt, 
Bng.  News,  Nov.  17,  1910).  Illustrated  description  of  the  general  design 
and  operation  of  the  siphon  lock  at  Oswego,  N.  Y. 

Cost  Data  on  the  Panama  Canal  ("Canal  Record,"  Nov.  9,  1910;  Bng. 
News,  Nov.  24,  1910). — General  statement  of  construction  expenditures,  to 
Sept.  30,  1910;  dam  construction;  lock  and  sp^lway  construction. 

mustratfons  of  Some  Important  Works: — 

Description.  Bng.  News. 

Plan  and  section  of  concrete  lock  for  small  craft,  Madison,  Wis.  Dec.  10.  1908. 

Suggested  new  type  of  lock,  Sault  Ste.  Marie  Canal  June  24,  '09. 

The  lock  gates  of  the  Panama  canal  Sept.  16,  '09. 

Typjical  sections  and  lock  on  N.  Y.  State  barge  canal  June    9,  '10. 

Design  and  cons,  of  movable  dam  and  lock.  Lockport  Oct.      6,  '10. 

Emergency  gates  on  the  Illinois  and  Mississippi  (Janal  Dec.  16,  '10. 

Eng.  Rec. 

Plan,  profile,  section,  C^pe  Cod  ship  canal,  also  breakwater  July  24,  '09. 

Siphon  lock  on  barge  canal  at  Oswego  July   30, '  10. 

Plans  of  new  canal  gates  at  Sault  Ste.  Marie  Dec.  10, '10. 


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t 


68.— WATER  POWER. 

IMIiiitioiis  and  PoraialM. — Power  is  the  raU  of  work  (see  page  Sll); 
and  Water  Power  is  the  rate  of  work  available  fttmi  stored  or  flowing  -water, 
through  the  agency  of  gravity.  The  unit  of  mechanical  power  is  the  Hone- 
Power  (if.  P.),  equivalent  to  the  enervy  expended  in  raising  S50  lbs.  one  ft. 
high. in  one  second,  or  to  the  energy  of  550  lbs.  falling  one  ft.  in  one  second. 
Hence,  the  theoretic  horse-power  of  a  stream  is —  i 

H.  P. -52i|^ -0.1184 (?A (1)   ' 

where  02. 37 -weight  of  a  cu.  ft.  of  water  at  M**P..  in  lbs.; 
7— discharge  of  stream,  in  cu.  ft.  per  sec.; 
»— fall  of  water,  or  available  head,  in  ft. 

Wh«.„  o.M?>^..* „, 

^  ,.8J2>^. ^^ 

"Horse-Power  Hours'*  is  a  term  tised  to  denote  a  certain  aiwowf  o£ 
work  or  energy,  and  not  the  rate  of  work.  It  is  the  maintenance  of  one  horse- 
power for  one  hour,  or  of  ten  horse-power  for  six  minutes,  etc.;  and  may 
De  applied  to  definite  quantities  or  volumes  of  stored  or  nmxiing  water. 
Thus, 

No.  of  H.-P.  hours-  ^^^^-0.0000316  V*. (4) 

where        V'  — volume  of  stored  water,  in  cu.  ft.; 
8600— No.  of  seconds  in  one  hour. 

Tiru  1/     31746XNO.  of  H.-P.  hours 

Whence  V— -r (f) 

.      31 746  X  No.  of  H.-P.  hours 
and  h" p (© 

At  the  Prime  Motor  the  available  horse-power  is  always  leas  than  the 
theoretic  horse-power,  the  decrease  being  due  to  loss  of  head,  leakage  or 
waste,  evaporation,  etc..  depending  upon  the  character  of  conduit  or  canaL 
Equation  (1)  will  give  the  available  horse-power  at  the  prime  motor  if— 

0— actual  discharge,  in  cu.  ft.  per  sec.,  at  prime  motor; 

li— effective  head,  in  ft.,  at  prime  motor. 

Economic  Design  of  Penstock. — For  a  high-pressure  water-power  pipe, 
the  volume  of  discharge  being  assumed  fixed  or  constant,  the  following  eco> 
nomic  relation  holds  true: 

"That  pipe  fulfills  the  requirements  of  greatest  economy  wherein  the 
value  of  the  energv  annuallv  lost  in  frictionai  resistance  equals  four-tenths 
(0.4)  of  the  annual  cost  of  the  pipe  line."'* 

Thus,  if  L— value  of  energy  annually  lost  in  frictionai  resistance, 
and  C— annual  cost  of  pipe  line; 
then  L— 0.4C,  for  economic  design  of  pipe. 


*  Mr.  A.  L.  Adams,  in  Trans.  Am.  Soc.  C.  E.,  Vol.  LIX,  page  177. 

Digitized  by 

1332  — 


HORSE'POWER  PER  CUBIC  FOOT  PER  SECOND.        1833 

1. — Number  of  Horsb-Powbr,  Equivalent  to  Flow  of  1  Cu.  Ft. 

PER  Sec.    Under  Various  Epfbctivb  Heads.    (Equa.  1.) 

(To  find  the  total  H.  P.,  mult,  valties  in  Table  by  No.  of  cu.  ft.  per  sec.) 

[Horsc-Power  per  Cu.  Ft.  per  Sec.  of  Flow.] 


♦Effective  head  and  actual  horse  power  are  proportional;  hence  the 
decimal  point  may  be  moved  in  each,  a  correspondmg  number  of  places  to 
right  or  left. 

Ex.—The  equivalent  to  a  flow  of  1  cu.  ft.  per  sec.  under  »  head  of  14  ft. 
is  1.6876  H.  P.;  under  a  140-ft.  head,  16.876  H.  P.;  under  a  140a-ft.  head, 
168.76  H.  P. 


1384  G&,— WATER  POWER, 

2. — ^NuiiBBR  OP  Horse-Power  Hours.  Equivalent  to  Storage  of 
1  000  000  Cu.  Ft.  Under  Various  Eppectivb  Heads.    (Equa.  4.) 
(To  find  total  H.-P.  H.,  mult,  values  in  Table  by  No.  of  millions  oC 
cu.  ft.  stored.) 
[Horse-Power  Hours  per  each  million  cu.  ft.] 


*  Effective  head  and  actual  horse-power  hours  are  proportional;  hence 
the  decimal  point  may  be  moved  in  each,  a  corresponding  number  of  places 
to  right  or  left. 

, .  ^5*- — ^The  equivalent  to  a  storage  of  1  000  000  cu.  ft.  with  a  head  of 
u  ^i-  *A*iJ[  ^■-^-  ^.*  with  a  140-ft.  head,  4410  H.-P.  H.\  with  a  1400-ft. 
head.  44100  H.-P.  H. 


CU,  FT.  AND  ACRE'FT.  TO  H.-P.  HOURS. 


1885 


8. — ^Nuif  BBR  OP  HORSB-POWBR  HoURS,  EqUIVALBNT  TO  StORAOB  OF 

1  AcRB-FooT.    Undbr  Various  Efpbctivb  Hbads.   (Equa.  4.) 
find  the  total  H.-P.  //.,  mult,  values  in  Table  by  No.  of  acre-feet  stored.) 
Note. — 1  acre-foot  — 43560  cubic  feet. 
[Horse-Power  Hours  per  each  acre-foot.] 


0.0000 

1.3721 

2.7443 

4.1164 

5.4886 

6.8607 

8.2328 

9.6050 

10.977 

13.721 

15.094 

16.466 

17.838 

19.210 

20.582 

21.954 

23.326 

24.699 

27.448 

28.815 

30.187 

81.559 

82.931 

34.804 

85.676 

37.048 

38.420 

41  164 

42.536 

43.908 

45.281 

46.653 

48.025 

49.397 

50.769 

62.141 

54.886 

66.258 

67.630 

69.002 

60.874 

61.746 

63.118 

64.491 

66.863 

68.607 

69.979 

71.351 

72.728 

74.096 

75.468 

76.840 

78.212 

79.584 

82.828 

g:^i 

85.073 

86.445 

87.817 

89.189 

90.561 

91.933 

93.306 

96.050 

98.794 

100.17 

101.64 

102.91 

104.28 

105.65 

07.03 

109.77 

111.14 

112.52 

113.89 

115.26 

116.63 

118.00 

119.38 

20.75 

123.49 

124.86 

126.24 

127.61 

128.98 

130.35 

131.73 

183.10 

134.47 

187.21 

138.69 

139.96 

141.33 

142.70 

144.07 

145.45 

146.82 

148.19 

150.94 

152.31 

153.68 

166.05 

156.42 

157.80 

159.17 

160.64 

161.91 

164.66 

166.03 

167.40 

168.77 

170.16 

172.89 

174.26 

175.63 

!S:?S 

179.75 

181.12 

182.49 

183.87 

185:24 

186.61 

187.98 

189.36 

193.47 

194.86 

196.22 

197.59 

198.96 

200.33 

201.70 

203.08 

205.82 

207.19 

208.57 

209.94 

211.81 

212.68 

214.05 

215.43 

816.80 

219.54 

222.29 

223.66 

225.03 

226.40 

227.78 

229.16 

230.62 

233.26 

234*64 

236.01 

237.38 

238.75 

240.12 

241.50 

242.87 

244.24 

246.99 

248.' 36 

249.73 

251.10 

262.47 

253.86 

256.22 

256.59 

257.96 

260.71 

262.08 

263.45 

264.82 

266.20 

267.57 

268.94 

270.31 

271.68 

275.80 

277.17 

278.64 

279.92 

281.29 

282.66 

284.03 

285.41 

288.15 

289.52 

290.89 

292.27 

293.64 

295  01 

296.38 

297.75 

299.13 

301.87 

303.24 

304.62 

305.99 

307.36 

308.73 

310.10 

311.48 

312.85 

315.59 

316.96 

318.84 

319.71 

321.08 

322.45 

323.83 

325.20 

326.57 

329.31 

830.69 

332.06 

333.43 

334.80 

336.17 

337.65 

338.92 

340.29 

343.04 

344.41 

345.78 

347.16 

348.52 

349.90 

351.27 

352.64 

354.01 

356.76 

358.13 

369.50 

360.87 

363.24 

863.62 

364.99 

366.36 

367.73 

270.48 

371.85 

373.22 

374.59 

375. 97 

377.34 

378.71 

380.08 

381.45 

884.20 

385.57 

386.94 

888.32 

339.69 

391.06 

392.43 

393.80 

395. 18 

397.92 

399.29 

400.66 

402.04 

403.41 

404.78 

406.15 

407.63 

408.90 

413.01 

414.39 

415.76 

417.13 

418.50 

419.87 

421.25 

422.62 

425  36 

426.74 

428.11 

429.48 

430.85 

432.22 

433.60 

434.97 

436.34 

439! 08 

440.46 

441.83 

443.20 

444.57 

445.95 

447.32 

448.69 

450.06 

46281 

454.18 

455.55 

456.92 

458.29 

459.67 

461.04 

462.41 

463.78 

467.90 

469.27 

470.64 

472.02 

473.39 

474.76 

476. 13 

477.50 

480! 25 

481.62 

482.99 

484.37 

485.74 

487.11 

488.48 

489.85 

491.23 

493.97 

495.34 

496.71 

498.09 

499.46 

500.83 

502.20 

603.58 

504.95 

607.69 

510.44 

611.81 

513.18 

514.55 

515.92 

617.80 

518.67 

621.41 

622:79 

524.16 

525.63 

526.90 

528.27 

529.65 

531.02 

532.39 

537.88 

539.25 

540.62 

542.00 

543.37 

544.74 

546.11 

548!  86 

650*23 

661.60 

552.97 

554.34 

555.72 

557.09 

558.46 

559.83 

563  58 

563.95 

665.32 

566.69 

568.07 

569.44 

570.81 

572. 18 

573.55 

576:30 

677.67 

579.04 

580.42 

581.79 

683.16 

584.53 

585.90 

587.28 

590.02 

691.89 

692.76 

694.14 

595.51 

696.88 

698.25 

599.63 

601.00 

603.74 

606.49 

607.86 

609.23 

610.60 

611.97 

613.35 

614.72 

617.46 

618:84 

620.21 

621.68 

622.95 

624.32 

625.70 

627.07 

628.44 

631  18 

632  66 

633.93 

635.30 

636.67 

638.05 

639.42 

640.79 

642.16 

644.91 

646:28 

647.65 

649.02 

650.39 

651.77 

653.14 

654.51 

655.88 

658.63 

660.00 

661.37 

662.74 

664. 12 

665.49 

666.86 

668.23 

669.60 

673.35 

673.72 

675.09 

676.47 

677.84 

679.21 

680.68 

681.95 

683.33 

686.07 

687.44 

688.81 

690.19 

691.56 

692.93 

694.30 

695.67 

697.05 

699.79 

701.16 

702.54 

703.91 

705.28 

706.65 

708.02 

709.40 

710.77 

JJIIJ 

714.88 

716.26 

717.63 

719.00 

720.37 

721.75 

723.12 

724.49 

728.61 

729.98 

731.35 

732.72 

734.09 

735.47 

736.84 

738.21 

740.96 

742.33 
756.05 

743.70 

745.07 

746.44 

747.82 

749.19 

750.56 

751.93 

754.68 

757.42 

758.79 

760.17 

761.54 

762.91 

764.28 

765.65 

768.40 

769.77 

771.14 

772.51 

773.89 

775.26 

776.63 

778.00 

779.38 

783.12 

783.49 

784.86 

786.24 

787.61 

788.98 

790.35 

791.72 

793.10 

796.84 

797.21 

798.59 

799.96 

801.83 

802.70 

804.07 

805.45 

806.82 

809.56 

810.93 

812.81 

813.68 

815.05 

816.42 

817.80 

819.17 

820.54 

823.28 

824.66 

826.03 

827.40 

828.77 

830.14 

831.52 

832.89 

834.26 

12.349 
26.071 
39.792 
63.513 
67.236 
80.956 
94.678 
108.40 
122.12 
135.84 
149.56 
163.28 
177.01 
190.73 
204.45 
218.17 
231.89 
246.61 
259.33 
273.00 
286.78 
300.60 
314.22 
327.94 
341.66 
355.38 
869.11 
382.83 
396.56 
410.27 
423.99 
437.71 
451.43 
465.16 
478.88 
492.60 
606.32 
520.04 
533.76 
547.48 
661.21 
574.93 
588.65 
602.37 
616.09 
629.81 
643.53 
657.26 
670.98 
684.70 
698.72 
712.14 
725.86 
739.58 
753.30 
767.03 
780.76 
794.47 
808.19 
821.91 
835.63 


•  Effective  head  and  actual  horse-power  hours  are  proportional;  hence 
B  decimal  point  may  be  moved  in  each,  a  corresponding  ntunber  of  places 
right  or  left. 

Ex. — ^The  equivalent  to  a  storage  of  1  acre-foot  with  a  head  of  14  ft.  it 
210  //..p.  H.;  with  a  140-ftJiead.  192.10  II.-P.  //.;  with  a  1400-ft.  head. 
n.OH.'P.H. 


1886  eB.'-WATER  POWER. 

Water  Motors^ — The  energy  of  flowing  water,  by  virtue  of  its  vekr^ 
weight  and  pressure,  all  acting  tc^ether  to  a  greater  or  less  extent,  ncay  ? 
transmitted  to  mechanical  motors  and  transformed  into  variotis  kinds  ' 
forms  of  energy.  The  principal  types  of  water  motors  comprise  many  i-'i 
various  forms  of  wheels,  among  which  are  the  following:* 

T)u  Current  Wheel  is  the  simplest  form.  It  consists  ^sentisLlly  al  i 
paddle  wheel  with  blades,  somewhat  similar  to  the  side  wheel  of  a  stesot:. 
and  is  motmted  on  a  horizontal  shaft,  supported  over  the  current  of  wazr 
at  the  bank  of  the  stream,  and  adjustable  to  height.  The  principal  use  of  tb 
current  wheel  in  the  West  is  for  raising  water  for  domestic  supply  and  irt 
gation  purposes.  Attached  to,  or  near,  the  periphery  of  the  wneel  are  ofxr 
metal  buclcets  which  scoop  up  the  water  from  the  stream. and  then  dehTV 
it  into  a  flume  whence  it  is  conveyed  into  reservoirs,  or  directly  on  the  laei 
A  small  wheel  will  irr^te  several  acres.  Prof  P.  H.  King,  in  descrilang  tia 
wheels  used  in  Bavaria  on  the  River  Regnitz,  a  branch  of  the  Main,  wte? 
he  counted  no  less  than  20  in  a  distance  of  li  to  li  miles,  says:t 

These  whe^  have  a  diameter  of  1 6  ft.  and  carry  upon  one  or  bo^  tfdea  a  rov  e£ 
24  chum-like  buckets  each  ItfUng  out  ot  the  stream,  and  to  a  bdRht  of  12  ft..  m« 
ten  than  3  galls,  ot  water,  from  which  it  Is  conveyed  to  the  bank  througb  a  oood^t 
hewn  from  a  log.  The  wheel  under  consideration  was  making  at  the  ttme  of  Use 
writer's  visit  four  revoluticms  each  minute,  so  that  the  water  lifted  was  not  to«  tfetf 
288  gallons  per  minute,  and  probably  exceeded  300  gallons:  Anotiier  wheel  witb  a 
row  of  buckets  on  each  side  was  making  three  revolutions  and  dischanrtng  not  les 
than  450  gallons  per  minute.  The  first  of  these  wheels  was  pumping  water  at  a  me 
sufficient  to  Irrigate,  to  a  depth  of  4  Inches  every  10  days.  38  acres,  and  the  seecoi 
60  acres. 

The  ordinary  current  wheel  Is  sometimes  cidled  an  "undershot  wheel."  alttaoogb 
this  Is  a  misnomer. 

The  Undershot  Wheel  of  approved  design  has  curved  blades  or  buckets^ 
The  current  is  accelerated  by  the  construction  of  a  flume  with  a  decide^i 
grade  and  perhaps  also  by  inserting  a  headgate  giving  increased  heac 
The  principle  is  somewhat  similar  to  that  of  the  current  wheel,  the  water 
flowing  beneath  it.    The  eflficiency  is  very  low,  rarely  exceeding  40  per  ceci^ 

The  Breast  Wheel  has  pronounced  buckets  and  acts  as  a  dam.  backit^ 
the  water  up  nearly  to  its  top  so  that  all  the  buckets  on  the  up-stream  side 
are  filled  with  water.  Being  thus  continually  tmbalanced  it  is  revolved. 
The  efficiency  ranges  at  about  60  to  66  per  cent. 

The  Overshot  Wheel  has  a  greater  efficiency  than  either  of  those  prexiomjj 
described,  reaching  in  some  cases  76  per  cent.  The  water  is  conveyed  by 
flume  over  the  top  of  the  wheel,  filling  the  buckets  on  the  down-stream  side, 
producing  an  unbalanced  force  on  the  horizontal  shaft,  which  is  connected 
up  with  the  working  machinery. 

Impulse  Wheels  and  Turbine  Wheels  are  the  most  common  forms  of  water 
motors,  and  are  discussed  below. 

Impulse  Water  Wheels. — ^This  type  is  the  most  efficient  and  econc»nica] 
of  any  of  the  pure  types  of  water  wheel  on  the  market.  It  also  compares 
favorably  with  turbines  for  moderate  heads  of  water,  and  sxxrpasses  theta 
for  high  heads.  In  principle,  the  impulse  water  wheel  consists  essentiaBr 
of  a  wheel  moimted  on  a  horizontal  shaft.  Attached  to  the  circumfenetsce 
of  the  wheel  are  numerous  double-cup-shaped  buckets  into  which  one  or 
more  tangential  jets  of  water  are  played  from  nozzles.  The  greatest  amount 
of  energy  of  the  let  has  been  imparted  to  the  wheel  when  the  velocity  of  tke 
jet  has  been  totally  destroyed,  and  this  is  accomplished  by  the  peculiar  shar* 
of  the  buckets  which  split  the  jet  in  the  middle  and  reverse  either  half  is. 
direction  by  180°.  When  the  water  simply  falls  from  the  buckets,  by  the 
action  of  gravity,  the  wheel  is  working  with  the  greatest  jet  efficiency. 

Fig.  1  illustrates  the  Pelton  water  wheel  with  needle  and  single  deflect- 
ing nozzle,  for  economic  regulation.  The  needle  nozzle  consists  of  a  tapered 
needle  which  may  be  operated  so  as  change  the  discharge  area  of  the  nozzle. 

*  The  hydraulic  ram  and  the  hydraulic  pressure  engine  are  not  included 
m  this  discussion. 

t  See  Farmer's  Bulletin  No.  46,  U.  S.  Dept.  of  Agricu|U|^. 


WATER  MOTORS,    IMPULSE  WATER  WHEELS,         1887 

deflecting  nozzle  is  simply  a  cast-iron  nozzle  provided  with  a  ball  and 
:et  joint.  It  can  be  arranged  automatically  to  raise  and  throw  the  jet 
.he  buckets  or  to  lower  and  throw  it  of!.  Intermediate  positions  are 
dated  by  change  of  "load." 


Fig.  1. 

The  number  of  nozzles  (one,  two.  or  more)  which  it  is  advisable  to  use 
wheel  depends  upon  the  head  ot  water  and  also  upon  the  amount  of 
rer  required.  As  a  general  rule  it  may  be  stated  that  the  power  devel- 
d  is  proportional  to  the  amotmt  of  water  or  number  of  nozzles  used, 
head  of  water  and  size  of  nozzles  remaining  constant.  Double  nozzles 
often  used  on  small  wheels  which  are  called  for  by  certain  speed  require- 
Its  and  where  the  single  nozzle  would  not  give  the  required  power. 
!  quintex  nozzle  wheel  is  specially  designed  for  very  low  head.  (See 
)le  6.  page  1342.) 


Digitized 


by  Google 


1888 


9&.--WATER  POWER. 


4. — SiNOLB  NozzLB  Pblton  Watbx  Whbbl  Data. 
(Suitable  for  high  heads.) 

Note. — Compare  with  Table  5  for  low  heads,  making  due  ailowaxsce  for 
5  nozzles  in  that  table. 

The  Calculations  for  Power  in  these  Tables  are  based  upon  the  appljcatiofl 
of  one  stream  to  the  wheel  and  on  effsctwe  heads.  In  using  these  taUes 
liberal  allowance  should  be  made  to  cover  the  friction  loss  in  pipe,  elbows, 
gates,  etc.  The  smaller  figures  under  those  denoting  the  vanotas  heads 
give  the  equivalent  pressure  in  pounds  per  square  inch,  and  spouting  velocit? 
of  water  in  feet  per  minute.  The  water  measurement  is  also  based  on  tb{ 
flow  per  minute. 


*Head 

in 
Feet. 

Slse  Of  Wheels. 

6 

Inch 

13 

Inch. 

15 

Inch. 

18 
Inch. 

24 

Inch. 

3 
Foot. 

4 
Foot. 

I 
Foot 

4 
Foot 

30 

8  Lbs. 
2161.97 

Horse  Power... 

Cubic  Feet 

Miner's  Inches. . 
Revolutioiis 

.05 
1.67 
1.04 

684 

.12 
3.91 
2.44 

342 

.20 
6.62 
4.00 

274 

.37 

11.72 

7.82 

228 

.66 
20.83 
18.88 

171 

1.50 

46.93 

31.28 

114 

2.64 

83.S 

55.53 

85 

4.18 

130.60 

86.90 

7^ 

ir  73 

125  « 

30 

13  Lbs. 

2635.62 

Horse  Power..., 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

.10 
2.05 
1.28 

837 

.23 

4.79 
2.91 
418 

.38 
8.11 
6.06 

335 

.69 

14.86 

9.57 

279 

1.22 

25.51 

17.00 

209 

2.76 

57.44 

38.28 

139 

4.88 

102.04 

68.00 

104 

7.«» 

15S.86 

108.44 

83 

11.94 

J2f.n 

153.  U 

• 

40 

17  Lbs. 
3043.39 

Horse  Power.... 

Cubic  Feet 

Miner's  Inchoi.. 
Revolutions 

,:J5 

1.48 
969 

.85 
6.53 
3.45 

484 

.59 
9.87 
6.85 

387 

1.0« 
16.69 
11.06 

323 

1.89 

29.46 

19.64 

242 

4.24 
66.36 
44.24 

161 

7.58 

107.84 

78.6« 

121 

11. SS 
184  81 

122  81 

91 

16.9< 
2S5.44 
176. « 

50 

21  Lba. 

8402.61 

Horse  Power.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

.21 
2.64 
1.65 
1083 

.49 
6.18 
3.86 

541 

.84 
10.47 
6.54 

433 

1.49 

18.64 

12.36 

361 

2.65 

32.93 

21.95 

270 

5.98 
74.17 
49.45 

180 

10.60 

131.72 

87.80 

135 

i6.ca 

206.13 

137.42 
108 

33.  $3 

ir  ^ 

60 

26  Lbs. 

3727.37 

Horsepower.... 
Cubic  Feet  .... 
Miner's  Inches.. 
Revolutions 

.28 
2.90 
1.81 
1186 

.66 
6.77 
4.23 

692 

1.10 

11.47 

7.16 

473 

1.96 

20.31 

13.54 

395 

3.48 

36.08 

24.05 

396 

7.84 

81.25 

54.16 

197 

13.  M 

144.32 

96.20 

148 

21.TT 
225.80 
150.53 

118 

31.S 
325.M 

216  44 

9t 

TO 

30  Lbs. 
4026.00 

Horse  Power.... 

Cubic  Feet 

Miner's  Inches.. 
Revolutions 

.35 
3.13 
1.95 
1281 

.82 
7.31 
4.56 

640 

1.39 

12.39 

7.74 

612 

2.47 

21.94 

14.63 

427 

4.39 

88.97 

25.98 

320 

9.88 

87.76 

58.52 

213 

17.58 

155.88 

103.92 

160 

27.61 
243.» 

162.80 
130 

39  U 

351M 

turn 

80 

34  Lbs. 
4303.99 

Horse  Power. . . . 

Cubic  Feet 

Miner's  Incties. . 
Revolutions 

.43 
3.35 
2.09 
1368 

1.00 
7.82 
4.88 
684 

1.70 

13.25 

8.28 

546 

3.01 

23.46 

15.64 

456 

5.36 

41.66 

27.77 

342 

12.04 

93.84 

62.56 

228 

21.44 

166.64 

Ul.OC 

171 

S3  54 

290  73 

173.82 

137 

48  l< 
375  34 
3SI.24 

114 

90 

39  Lbs. 
4565.04 

Horse  Power.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

.81 
8.55 
2.22 
1452 

1.20 
8.29 
5.18 
726 

2.03 

14.05 

8.78 

681 

3.60 

24.88 

16.58 

484 

6.39 

44.19 

29.46 

363 

14.40 

99.52 

66.32 

242 

25.59 

176.75 

117.83 

181 

40.04 

276.55 

184.3« 

14S 

57  68 

SM-ti 

361.9 

IS 

100 

43  Lbs. 
4812.00 

Horse  Power.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

.60 
3.74 
2.33 
1530 

1.40 
8.74 
5  46 
765 

2.32 

14.81 

9.25 

612 

4.21 

26.22 

17.48 

610 

7.49 

46.58 

31.05 

383 

16.84 

104.88 

69.93 

255 

29  93 

188.32 

124  21 

191 

44. 85 

291.51 
194.34 

tea 

8?  « 
419  S 

278:: 

110 

48  Lbs. 
6046.87 

Horse  Power.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

.69 
3.92 
2.45 
1605 

1.62 
9.16 
6.72 
802 

2.74 

16.53 

9.70 

642 

4.86 

27.50 

18.33 

535 

8.64 

48.85 

32.56 

401 

19.44 

110.00 

73.38 

Wl 

34.58 
195.41 
130  27 

200 

54.11 

305.73 

203.82 

1«8 

T7.?S 

440.W 

38133 

133 

*  Theoretic  head.  The  data  in  table,  except  in  first  odnmn.  axe  based 
on  effective  heads  at  86  per  cent  of  the  theoretic  heads;  or  in  other  wotrda* 
the  efficiency  of  wheel  is  assumed  at  86  per  cent. 


d  by  Google 


SINGLE  NOZZLE  PELTON  WHEELS. 


18S0 


4. — SiNGLB  Nozzle  Pblton  Water  Wheel  Data. — Continued. 


sue  of  Wheel!. 


6 
Inch 


12 

Inch. 


15 
Inch 


18 

Inch. 


24 
Inch. 


3 
Foot. 


4 
Foot. 


5 

Foot. 


6 

Foot. 


Hone  Power.. . 

Cable  Feet 

Miners  Inches. 
Revolutions. . . 


.79 
4.10 
2.56 
1677 


1.84 
9.57 
5.98 


3.12 

16.21 

10.13 

671 


5.54 

28.72 

19.15 

559 


9.85 

51.02 

34.01 

419 


22.18 

114.91 

76.60 

279 


39.41 

204.10 

136.06 

209 


61.66 

319.83 

212.89 

167 


88.75 

459.64 

806.43 

130 


Hone  Power... 

Cubic  Feet 

Miner's  Inches. 
Revtdutlons... 


.89 
4.27 
2.66 
1746 


2.08 
9.96 
6.22 
873 


3.53 
16.89 


6.25 
29.90 


10.55  19.93 
698 


11.11 

58.10 

35.40 

436 


25.02 

119.60 

79.73 

291 


44.46 

21^.43 

141.62 

218 


69.53 

332.37 

221.58 

174 


100.08 

478.41 

318.94 

145 


Horsepower... 

Cubic  Feet 

Miner's  Inches. 
Revc^utlons... 


.99 

4.43 
2.76 
1812 


2 

10.34 
6.46 
906 


3.94 

17.53 

10.95 

725 


6.99 

31.03 

20.68 

604 


12.41 

55.11 

36.74 

453 


27.96 

124.12 

82.72 

302 


•49.64 

220.44 

146.96 

226 


77.71 

344.92 

229.94 

181 


111.85 

496.48 

330.88 

151 


Horsepower... 

Cubic  Feet 

Miner's  Inches. 
Revolutions... 


1.10 
4.55 
2.84 
1875 


2.58 

10.70 

6.68 

937 


4.37 


18.14  32.11 
11.33  21.41 


7.75     18.77 


38.03 
468 


31.01 


85.64 
312 


55.08 

228.19 

152.12 

234 


86.22 

857.02 

238.05 

187 


124.04 

513.90 

342.59 

156 


Horsepower... 

Cubic  Feet 

Miner's  Inches. 
Rev(4utlons... 


1.22 
4.73 
2.96 
1 


2  84 

ll!05   18.741.33.17 
6.90 
969 


11.71 
775 


22.11 
646 


15.17 
58.92 
39.38 

484 


34.16 

132.68 

88.46 

323 


60.68 

235.68 

157.12 

242 


94.94 

868.73 

245.82 

193 


136.66 

530.76 

363.84 

161 


Hone  Power... 

Cubic  Feet 

Miner's  Inches. 
Revolutions... 


1.45 
5.02 
3.13 
2049 


8. 
11.72 
7.32 
1024 


5.75   10.19     18.10 


19.87 
12.41 


35.18 

23.45 

683 


40.77 
62.491  140.74 
41.66 
513        342 


72.41 

249.97 

166.64 

256 


113.30 

891.10 

260.73 

206 


163.08 

562.96 

875.29 

171 


Horsepower... 
Cubic  Feet.... 
Miner's  Inches. 
Revolutions. . . 


1.70 
5.29 
3.30 
2160 


3.97 
12.36 
7.72 
1080 


6.74 
20.94 


11.93 
37.08 


13.08  24.72 
864 


21.20 
65.87 
43.91 


47.75 
148.35 
98.90 


84.81 

263.49 

175.66 

270 


132.70 

412.25 

274.83 

216 


191.00 

593.40 

395.60 

180 


Horsepower... 

Cubic  Feet 

Miner's  Inches. 
Revolutions. . . 


1.96 
5.55 
8.46 
2268 


4.59 
12.96 
8.10 
1134 


7.77 

21.96 

13.72 

906 


25.93 
756 


24.46  55.09 

69.08  155.59 

46.05  103.73 

567  378 


97.85 

276.35 

184.23 

283 


153.10 

432.33 

288.25 

226 


220.36 

622.36 

414.91 

189 


Horse  Power. . . 

Cubic  Feet 

Miner's  Inches. 
Revolutions. . . 


2.24 
5  80 
3  62 
2370 


5.23 
13.54 
8.46 
1185 


8.86 

22.93 

14.33 

948 


15.69 

40.62 

27.08 

790 


27.87 
72.16 


62.77 
162.50 


48.10   108.34 
895 


111.50 

288.64 

192.43 

296 


174.45 

451.60 

301.07 

237 


251.10 
650.03 
433.36 

197 


Horsepower... 
Cubic  Feet. . . . 
Miner's  Inches. 
Revolutions. . . 


2.52 
6.04 
3.77 
2466 


6.89 
14.09 
8.80 


10.05 
23.88 
14.92 


17.69 
42.28 
28.1 


1233       986       822 


75.10 

50.07 

617 


169.14 

112.76 

411 


125.72 

300.43 

200.28 

308 


196.71 

470.04 

313.36 

247 


283.15 

676.59 

451.05 

206 


Horsepower... 

Cubic  Feet 

Miner's  Inches. 
Revc^utkms. . . 


2 

6.26 
3.91 
2562 


6.59 
14.62 
9.13 
1281 


11.16 
24.79 
15.49 
1025 


19.77 

43.88 

29.25 

854 


35.12 
77.94 


79.11 

175.53 

51.291  117.02 

427 


140.51 

311.77 

205. 18 

319 


219.84 

487.79 

325.19 

265 


316.44 

702.18 

468.06 

213 


Horse  Power. . . 
CuWc  Feet. . . . 
Miner's  Inches. 
Revolutions. . . 


3.13 
6.48 
4.05 
2652 


7.31 
15.13 
9.45 
1326 


12.38 

25.66 

16.03 

1060 


21.93 

45.42 

30.28 

884 


88.95 
80.67 


87.73 
181.69 


53.78   121.12 


156.83 

322.71 

215.14 

331 


243.82 

604.91 

336.60 

265 


350.94 

726.76 

484.51 

221 


Hone  Power. . . 

Cubic  Feet 

Miner^s  Inches. 
Revolutions... 


3  45 

6.70 
4.18 
2739 


8.05 
15.63 

9.76 


13.64 
26.50 
16.56 
1095 


24.16 

46.91 

31.27 

913 


42.91 
83.32 

55.5! 
685 


96.65 

187.65 

125.10 

456 


171.68 

333.29 

222.19 

342 


268.60 

621.46 

847.64 

274 


386.62 

750.60 

600.40 

228 


♦Sec  Note  and  Foot-note  on  preceding  page. 


Digitized 


byGoogk 


1840 


f/i.—WATER  POWER. 


4.— SiNOLB  NozzLB  Pblton  Watbr  Whbbl  Data.— Continaed. 

*Head 

la 
Feet. 

Slie  of  Wheels. 

6 

Inch 

13 

Inch. 

15 

Inch. 

18 

Inch. 

34 
Inch. 

3     |.      4             5 
Foot.l  Foot.   Foot 

f 

8 
.    Foot. 

340 

147 
Lbo. 

8872.89 

Horsepower.... 

Cubic  Feet 

Miner's  Inches. . 

3.78 
6.90 
4.31 
2823 

8.82 
16.12 
10.07 

1411 

14.94 
27.31 
17.06 
1130 

26.46 

48.35 

82.24 

941 

47.00   105.861  188.0£  2M.  18  423.44 
85.88   193. 42j'  343.55  537.51    771  7: 
57.26  128.98  239.04  S58.84   5I*-« 

706        470        353         28^       ZS 

3dO 

156 

Lbo. 

9130.14 

Horsepower.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

4.10 
7.10 
4  43 
2907 

9.61 
16.58 
10.36 

1453 

16.28 
28.10 
17.56 
1161 

28.83 

49.75 

33.17 

969 

51.21 

88.37 

58.91 

726 

115.34  204.86^  Sm,&  461.31 

499.03  353.51!  ftS3.  lOJ  T96.14 

132.68  2S5.64{  368.73   5S9.T5 

484        363        290        242 

380 

165 

Lbs. 
9380.32 

Horsepower.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

4.46 
7.30 
4.56 
2985 

10.42 
17.04 
10.65 
1492 

17.66 
28.88 
18.03 
1194 

31.27 

51.12 

34.08 

995 

55.54 

90.80 

60.53 

746 

125.08 

204.48 

136.32 

497 

232.16  347.(0(500.13 

363.20  568.2^  617.95 

242.13  878.  si  545.29 

373        3i^       248 

400 

173 

Lbo. 

9624.00 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

4.82 
7.49 
4.68 
3063 

11.25 
17.48 
10.92 
1531 

19.07 

29.63 

18.51 

1226 

33.77 
52.45 
84.96 
1021 

59.98 
93.16 
62.10 

766 

135.08 

109.80 

139.84 

SlO 

239  94  375.40  540.35 

372.641  583. Q2i  839.20 

248. 4A  »8.i8  S59.IS 

382        30f        255 

430 

183 

Lbs. 

9881.66 

Horsepower.... 

Cubic  Feet 

Miner's  InchM.. 
Revolutions 

5.19 
7.67 
4.79 
3141 

12.11 
17.91 
11.19 
1570 

20.52 

30.36 

18.93 

1255 

86  33 

53.74 

35.83 

1047 

64.54 

95.46 

63.64 

785 

145.34 

214.98 

143.32 

523 

358.16  403.91    581.38 

381.84  597.41   859.93 

254.56  398.28   573,28 

393        313        261 

440 

191 

Lbo. 

10093.74 

Horsepower.... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

5.56 
7.85 
4.90 
3213 

12.98 
18.33 
11.45 
1606 

22.01 
31.07 
19.41 
1285 

38.96 

55.01 

36.66 

1071 

69.20 

97  70 

65.13 

803 

155.85 

220.04 

146.64 

535 

276.82   433.11   623.49 

390.82  611.47  891.16 

260.53  407.65  586.56 

401        330'       2C; 

460 

200 
Lbs. 

10320.58 

Horse  Power. . . . 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

6.95 
8.03 
5.01 

13.88 
18.74 
11.71 
1642 

23.53 

31.77 

19.79 

1313 

41.65 

56.24 

37.60 

1095 

73.97 

99.90 

66.60 

821 

166.60 

224.98 

150.00 

547 

295.91 

399.61 

266.40 

410 

463.97 

625.22 

416.80 

32? 

666.40 

899.95 

ioo.oo 
2n 

480 

208  Lbs. 
10542.56 

Horse  Power... 

Cubic  Feet 

Miner's  Inches. . 
Revolutions 

6.34 
8.20 
5.12 
3357 

14.79 
19.15 
11.96 

1678 

25.07 
32.45 

44.39 
57.45 
38.30 
1119 

78.86 

102.05 

68.00 

839 

177.58 

229.82 

153.20 

559 

315.42 

408.20 

272.12 

419 

493.49 

638.61 

425.78 

333 

710.33 

919  39 

612.80 

279 

500 

217  Lbs. 
10759.96 

Horse  Power. . . . 

Cubic  Feet 

Miner's  InchM. . 
Revolutions 

6.74 
8.37 
6.23 
3426 

15.73 
19.54 
12.21 
1713 

26.66 

33.12 

20.72 

1370 

47.20 

58.64 

39.09 

1142 

83.83 

104.15 

69.41 

856 

188.80 

234.56 

156.36 

571 

835.84 

416.62 

277.64 

428 

524.66 

651.83 

434.56 

343 

753.29 

9^.25 

635.44 

285 

Horse  Power. . . . 

200.22 

239.21 

159.47 

582 

355.62 

424.87 

283.24 

436 

556.39 

664  74 

809  88 

530 

Cubic  Feet 

«S6  M 

226  Lbs. 

Miner's  Inches 

443  le  637  a 

10973.04 

Revolutions. . . , 

349 

291 

Horse  Power. . . . 

211.88 

243.76 

162.51 

593 

376.33 

433.96 

288.64 

445 

588.88 

677.41 

451.61 

356 

847.52 

540 

234  Lbs. 

Cubic  Feet  . . 

975  0? 

Miner's  Inches. . 

658  04 

11182.07 

Revolutions . 

296 

Horse  Power. . . 

221.76 

248.24 

165. 4f 

604 

397.43 

440.91 

298.94 

458 

621.82 

689.84 

459.81 

362 

MS  84 

560 

243  Lbs. 

11387.26 

Cubic  Feet 

992.91 

Miner's  Inches 

661  91 

Revolutions. . . . 

382 

1 

580 

252  Lbs. 

i 1588. 83 

Horse  Power.  . 

235.86 

252.63 

168.42 

615 

418.92 
448.TI 
299.14 

461 

655.43 
703  64 
488.03 

369 

943  44 

Cubic  Feet 

1016.54 

Miners  Inches.. 

673.69 

Revolutions. . . . 

39r 

*See  Note  and  Foot-note  on  second  page  precedi 

tized  by 


SINGLE  NOZZLE  PELTON  WHEELS, 


1841 


4. — SiNOLB  NozzLB  Pblton  Watbr  Whbbl  Data. — Concluded. 


•Head 

in 

Feet. 

Slse  of  Wheels. 

6 

Inch 

-|3 

Inch. 

15 

Inch. 

18 

Inch. 

24 

Inch. 

3 

Foot. 

4 
Foot. 

5 

Foot. 

6 

Foot. 

Hone  PowOT.  . . 



248. 16 

256.95 

171.30 

625 

440.77 

456.38 

304.24 

469 

689.83 

714.05 

476.03 

875 

992  65 

600 

Cubic  Feet 

1027.80 

260  Lbs. 

Miner's  Inches. . 

685  20 

11788.M 

312 

Horse  Power. . . . 

279.82 

267.44 

178.29 

651 

497.01 

475.02 

316.68 

488 

777.62 

743.21 

495.47 

390 

1119.29 

650 

Cubic  Feet 



1069  77 

282Lbfl. 

Miner's  Inches. . 

713  18 

12268  24 

Revolutions. . . . 

325 

Horse  Power. . . . 

313.73 

277.54 

185.02 

675 

555.46 

492.95 

328.63 

506 

869.06 

771.26 

514.18 

405 

1250  92 

700 

Cubic  Feet 

1110.16 

SCMLbs. 

Miner's  Inches 
Revolutions. . . . 

740.09 

12731.34 

337 



Horse  Power. . . . 

346.83 

287.28 

191. 5i 

699 

616.03 

510.25 

340.16 

524 

963.82 

798.33 

532.22 

419 

1387  34 

7M 

Cubic  Feet 

1149  13 

326  Lbs. 

Miner's  Inches. . 

766.09 

13178.19 

Rev(4utlons 

349 

Horse  Power. . . . 

382.09 

296.70 

197.80 

722 

678.66 
526.99 

1061.81 

824.51 

549.68 

433 

1528  36 

800 

Cubic  Feet 

1186.81 

348  Lbs. 

Miner's  Inches  . 
Revolutions 

791.21 

13610.40 

861 

Horse  Power. . . . 

455.94 

314.70 

209.80 

766 

809.82 

558.96 

372.64 

574 

1267.02 

874.63 

583.02 

459 

1823  76 

POO 

Cubic  Feet 

1258.81 

391  Lbs. 

Miner's  Inches.. 

839  20 

14436.00 

Revolutions 

383 

Horse  Power 

534.01 

331.72 

221.15 

807 

948.48 

589.19 

392.79 

606 

1483.97 

921. 8S 

614.56 

484 

2136.04 

lOOO 

Cubic  Feet 

1826  91 

434  Lb0. 

Miner's  Inches.. 

884.61 

15216.89 

Revolutions 

403 

""l 

*See  Note  and  foot-note  on  third  page  preceding. 


d  by  Google 


1843  ^.— WATER  POWER, 

5. — OUINTEX  NOZZLB  PELTOM  WaTER  WhREL  DaTA. 

(Five  nozzles,  suitable  for  low  heads.) 
Note. — Compare  with  Table  4,  preceding,  making  due  allowance  for  5 
nozzles  in  this  table. 

Revolutions  are  number  p^r  minute. 


Turbine  Water  Wheeb.— Turbines  differ  from  the  wheels,  described 
above,  in  this  respect:  That  in  the  case  of  the  wheels  the  water  acts  only 
upon  a  portion  of  their  circumference  at  an^  one  instant,  while  with  the 
turbines  the  water  acts  symmetrically  and  uniformly  upon  tne  moving  parts. 
Turbines  consist  essentially  of  two  main  parts,  namely,  (1)  the  wheel 
(runner)  with  vanes  arranged  around  the  circumference,  and  revolving  on 
a  vertical  or  horizontal  shaft;  and  (2)  the  casing,  provided  with  hxed 
guide  vanes  to  give  direction  to  the  now  of  water  before  it  reaches  thr 
vanes  of  the  wheel.  Turbines  are  sometimes  classified  as  "radial,"  "axial' 
and  "combined  or  mixed;"  and  again,  as  reaction-  and  impulse  turbines 
In  a  radial  turbine  the  water  may  flow  from  the  circumference  inward  to 
the  center,  or  the  reverse;  in  an  axial  turbine,  from  the  top  downwarl 
or  from  the  bottom  upward;  and  in  a  combined  turbine,  inwaid  and  down 
or  up,  or  outward  and  down  or  up.  Turbines  are  most  commonlv  mountevi 
on  vertical  shafts  with  water  flowing  simply  inward,  outward  or  downward 
The  difference  in  principle  between  a  reaction  turbine  and  an  impulse 
turbine  is  this:  A  reaction  turbine  is  driven  by  the  dynamic  force  oi  the 
flowing  water  augmented  by  static  pressure  to  a  greater  or  less  extent: 
when  there  is  no  static  pressure  it  becomes  an  impulse  turbine.  Standard 
makes  of  turbines  will  give  an  efficiency  of  from  65  to  85  per  cent.  An 
efficiency  of  80  per  cent  can  be  counted  upon  for  the  best  makes. 

Nomenclature  of  Terms. — Mr.  John  W.  Thurso  suggests  the  followxng, 
for  uniformity. 

For  "water  wheel"  say  "turbine"  whenever  a  turbine  is  meant. 

For  "Jonval"  turbine  say  "reaction"  turbine.  For  Girard,  Pelton. 
impulse  or  free  deviation  turbine  say  "action"  turbine.  For  Foomeytoa 
or  Boyden  turbine  say  "radial  outward  flow  reaction"  turbine,  or  ebc 
wniply  "outflow  reaction"  turbine. 


QUINTEX  NOZZLE  WHEELS,    TURBINES,  1843 

For  Piands  turbine  sa3r  "radial  inward  flow  reaction"  turbine,  or  sim- 
ply "inflow  reaction"  turbine,  as  this  type  is  usually  understood  by  the 
name  Francis  turbine.  WhUe  it  is  not  likelv  that  the  term  Francis  turbine 
-will  go  out  of  use,  the  term  "inflow  reaction  turbine  should  always  be  used 
"w^bere  an  exact  expression  is  of  importance,  as  in  contracts,  for  the  reason 
that  Mr.  Francis  also  designed  outflow  reaction  turbines. 

For  "parallel  flow"  tiu-bine  say  "axial"  flow  turbine,  or  axial  turbine. 
For  "segmental  feed"  turbine,  say  "partial  feed"  turbine,  or  "partial" 
turbine. 

For  one,  two.  three,  four  five  or  six  turbines  on  one  shaft  say  single, 
double,  triple,  quadruple,  quintuple  or  sextuple  turbine. 

For  "draft  chest'  or  "camelback"  say  "draft-tee."  For  "butterfly 
gate"  say  "wing-gate."  For  "feeder-pipe'  or  "water  feeder"  say  "pen- 
stock." 

For  open  flume  say  "turbine-chamber"  whenever  a  turbine  chamber  is 
meant,  leaving  the  term  "flume"  to  mean  a  water  conductor  only,  built  of 
-wood,  steel  or  masonry,  and  carrying  water  not  under  pressure. 

For  the  distance  to  which  a  vertical  draft  tube  reaches  below  the  surface 
of  the  tailwater,  say  dip  of  draft  tube. 

For  speed  ot  water  m  the  cylindrical  part  of  the  penstock  say  "penstock 
speed."  For  speed  of  water,  while  leaving  or  quitting  lower  end  of  draft 
tube,  say  "draft  tube  speed." 

For  the  part  of  the  head  that  is  above  the  turbine  say  "pressure  head." 
For  the  part  of  the  head  that  is  utilized  by  means  of  a  draft  tube,  say 
•'draft  head." 

The  water  available  tmder  the  head  utilized  should  be  called  "power 
vrater,"  corresponding  in  meaning  to  the  term  live  steam.  The  water 
having  descended  either  through  tne  turbines  or  over  the  falls,  should  be 
called  "tail-water,"  correspondmg  in  meaning  to  the  term  exhaust  steam. 
The  terms  horizontal  or  vertical  turbine  would  alwa^  mean  a  turbine 
on  a  horizontal  or  vertical  shaft,  and  never  one  revolving  in  a  horizontal  or 
vertical  plane,  as  it  is  now  sometimes  understood. 

The  area  left  open  or  clear  by  the  regulating  gate  or  gates  for  the  passage 
of  the  water  should  be  called  "gate  opening.  At  present  the  term  "gate 
opening"  or  "gate"  is  nearly  always  used  to  mean  the  amount  of  water 
flowing  through  the  gate  opening,  but  this  amount  should  be  designated  by 
discharge;  for  example,  instead  of  saying:  "This  turbine,  with  five-eighths 

gate  opening,  gave  an  efficiency,"  etc..  should  be  said:  "This  turbine,  with 
ve-eighths  discharge,  gave  an  efficiency,"  etc..  whenever  the  discharge  is 
meant. 

The  motor  furnishing  the  power  for  actuating  the  regulating  gates  of  a 
turbine,  and  usuallv  controlled  by  a  speed  governor,  should  be  called  a 
relay.     In  Europe  the  term  servomotor  is  used  for  such  auxiliary  machines. 

Losses  of  Enerty  in  Turbines, — ^These  losses  may  be  segregated  as 
follows: 

(1)  The  hydraulic  loss  in  the  casing,  from  the  penstock  flange  to  the 

entrance  to  the  guides  (guide  vanes) ;  this  is  dependent  to  a  large 
extent  on  the  velocity  of  flow  in  the  casing,  it  being  remembered 
that  for  a  "given  velocity"  the  percentage  of  loss  decreases  with 
the  increase  of  head. 

(2)  The  hydraulic  loss  in  the  guides  and  nmners;  this  is  affected  by  the 

type  of  rtmner  (wheel)  and  the  design  of  the  guides,  but  the 
percentage  of  hydraulic  loss  remains  practically_constant  for  any 
one  t^rpe  if  the  speed  is  allowed  to  vary  as  Vh,  in  which  A —the 
head,  in  feet. 

(3)  The  hydraulic  loss  due  to  the  leakage  around  the  runner;  this,  as 

weH  as  the  discharge,  varies  as  the  v^  hence  the  ratio  of  leakage 
to  discharge  remains  constant. 

(4)  The  hydraulic  loss  in  the  draft-tube. 

(6)  The  mechanical  loss  due  to  the  friction  of  the  revolving  parts*  this 
increases  with  the  head,  k,  but  the  percentage  of  mechanical  loss 
decreases  with  the  head. 

Efficiencies  of  Turbines.— The  term  "efficiency"  is  often  used  loo8el3^ 
and  it  is  very  important  that  in  turbine  tests,  and  in  specifications  and 


1S44  ^.-^WATER  POWER, 

oontnu^,  the  specific  kind  of  efiiciency  whSch  is  meant  should  be  stated 
There  are  four  kinds  of  efficiencies  which  may  be  empbyed,  namely:   - 

(a)  The  hydraulic  efficiency,  embracing  losses  (1),  (2)  and  (9).  aborc 

(b)  The  mechanical  efficiepcy,  embracing  less  (6),  above 

(c)  The  efficiency  of  the  turbine  as  a  whole,  behig  the  product  of  the 

hydraulic  and  mechanical  •ffidendes,  (a)  and  (b). 

(d)  The  efficiencv  of  the  plant  as  a  whole,  comprising  the  turbioc 

efficiency  (c)  and  embracing  the  draft-tube  loss  (4)  and  the  pes* 
stock  loss. 

Thtorftic  Horse-Power  of  Turbines. — The  theoretic  bonMower  o£  a 
turbine  varies  ask^K  in  which  A— the  head  of  water  in  feet.  This  is  tree 
since  the  horse-power  is  proportional  to  the  pressure  of  the  water  (which  in 
turn  varies  witn  k,  being  equal  to  about  02.37aA.  see  Table  1.  preceding), 
and  to  the  velocity  of  flow  per  second  (which  in  turn  varies  with  v^  being 
equal  to  v-8.02'v^.    Thus, 

The«eUcH.P.  _<«iZ2*^«i!2v^_  o.90»4««afc... C7) 

In  which  a— area  of  discharge  in  square  feet; 
/(—head  in  feet. 

Formula  (1),  preceding,  is  the  same  as  formula  (7),  but  expressed  in 
terms  of  discharge  0  instead  of  area  a. 

When  the  efficiency  of  the  turbine  (or  plant)  has  been  determined,  the 
acttial  H.  P.  is  obtained  by  multiplying  the  values  of  equations  (1)  or  (7) 
by  said  efficiency,  expressed  in  per  cent. 

The  Transmission  of  Power  from  water  motors  to  machinery  is  through 
the  main  shaft,  and  ma^  be  b]r  belt,  by  gearing  or  by  coupling.  If  the  power 
is  for  electric  transmission  it  is  customary  to  connect  the  main  shaft  of  the 
wheel  or  turbine  directly  with  the  electric  djrnamo  or  generator.  Hence  the 
term  "direct-connected  generator." 


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TURBINES.    MISCELLANEOUS  DATA.  1845 


EXCERPTS  AND  REFERENCES. 

Modem  Torbine  Practice  and  the  Devdopmeiit  of  Water  Powen  (By 

J.  W.  Thurso.    Eng.  News,  Dec.  4,  1902  and  Jan.  8,  1»08).— Illustrationi 
of  turbtnee,  hydraulic  governors,  and  power-house  installation. 

An  Analysto  of  the  *^Comiiiercial"  Vahie  off  Water  Power  per  Hone- 
Power  per  Annum  (By  A.  P.  Nagle.  Paper,  Am.  Soc.  Mech.  Bngrs.;  Bng. 
News,  Jan.  22.  ItMS). — Diacussioci  and  tables  of  cost. 

Water  Power  Devalopmeot  at  Chaodiece  Falls,  P.O.  (Bng.  News. 
May  7,  1M8). — Illustrations:  Sections  of  main  and  wing  dams,  bulkheaa 
-wall,  steel  framing  for  gates  and  screens,  operating  mechanism  for  gates 
and  screens,  supports  and  anchorages  for  penstocks  on  side  hill,  plan  and 
section  of  power  house,  traveling  platform  for  building  main  dam,  etc. 

The  Nianra  Power  Plant  of  the  Electrical  Devetopment  0>.,  of  Ont 
CEng.  NewsTNov.  0  and  30,  1006).— Fully  illustrated  with  details. 

Power  Plant  of  the  Chicago  Drainage  Canal  (Eng.  News.  Jan.  18, 
906).— Illustrated. 


Theory  off  DetermlnhiK  the  Prindpel  Dhneosloas  off   Water-TarUne 

tnners  (Bv  S.  J.  Zor-'"      "—   *^' —    '—    *    '"*""      '* '       '" 

trations  ana  diagrams. 


Runners  (By  S.  J.  Zowski.     Bng.  News,  Jan.  6.  1010) .^Formulas,  illus- 


Characteristics  of  the  Modem  Hydraulic  Turbines  (By  C.  W.  Lamer. 
Trans.  A.  S.  C.  E.,  Vol.  LXVI.,  Mar.,  1010).— Tables  of  tests,  of  28-in..  80-in., 
31-in.  and  32-in.  turbines.    Formulas  for  power,  speed,  etc. 

Some  Points  in  the  Design  of  Impulse-Wheel  Buckets  (By  Oeo.  M. 
Peck.     Eng.  News.  May  5,  1010). — Illustrated. 

Hydro-Electric  Development  of  the  Michoacan  Power  Co.,  Mexico  (By 
I.  C.  McBride.  Eng.  Rec.,  Aug.  27.  1010).— Illustrations:  Details  of  rating 
flume;  penstock  intake;  plan  and  details  of  sand  trap;  plan  and  details  ot 
beadgate  structure,  plan  and  section  of  power  house  substructure. 

Important  Designs  for  Reference  ^~ 

Description.  Eng.  News. 

8.000-H.  P.  turbine  for  a  Niagara  water-power  plant  Nov.  14.  1001. 

Concrete  dam  with  automatic  flashbocuds  June  12,  '02. 

Sec^on  through  power  house  and  wheel  pit,  Niagara  Plant  July     8,  '02. 

A  watcr-whuBcl  governor  of  novel  construction  Nov.  18,  '02. 

Designs  of  buckets  for  impulse  water  wheels  Oct.     8,  '08. 

Cross-section  of  power  house,  Puyallup  power  development  Sept.  20,  '04. 

Section  of  fltime  and  power  station,  De  Sabla,  Cal.  Aug.  10,  '05. 

Tuibines  at  Sewalls  Falls,  under  low  and  variable  heads  Jan.    18,  '06. 

10,000-H.  P.  single-wheel  turbine.  Snoqualmie  Palls  Mar.  20,  '06. 

Section  of  flume  and  power  house,  Ozadero,  Ore.  Time  27,  '07. 

Plan  and  section  of  power  house.  High  Falls.  Ont.  July  18,  '07. 

Sections  of  canal  and  flume,  Onterville,  CsA.  Mar.  10,  'OS. 

Hcischcl's  "Fall-increaser"  for  utilizing  waste  water  July  11, '08. 

Flumes,  gates,  power  station,  etc.,  Kem  River,  Cal.  Dec.  24,  '08. 

Comparison  ot  Am.  high-^>eed  runners  for  tiu-bines  Jan.   28,  '00. 

Designs  of  intakes  for  hyoxo-electric  plants  April   8,  '00. 

Eng.  Rec. 

Sections  of  dam,  sluice  gate,  power  house,  hydro-elec.  plant  Mar.  27,  '00. 
Expansion -joint  details  and  reinforcement  ot  concrete  conduit  May      1,  '00. 

A  low,  20-ft.  head  hydro-elec.  development  May   16,  '00. 

Plans  and  sections  of  Hennepin  power  plant  May  20,  '00. 
Details  turbine  flumes,  and  their  reinforcement,  Schnec.  Power 

Co.  July   24. '00. 

Sections  showing  turbine  settings.  Cent.  Ga.  Power  Co.  May  14,  '10. 
Details  header  pipe  and  upper  end  of  penstock,  Gt.  W.  Power 

Co.  June  18.  '10 

Plan  and  section  ix>wer  house.  Boulder  hydro-elec.  devel.  July  30. '10. 


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69.— STEAM  AND  GAS  POWER. 
A.— HEAT. 

Matter  and  Energy. — In  the  light  of  modern  science,  all  natural  pbt- 
nomena  are  due  to  matter  and  energy. 

MatUr  may  be  defined  as  anything  capable  of  entering  into  chemscal 
combination,  and  hence  is  made  ud  of  the  chemical  elements,  of  which  the 
total  known  number,  now  about  90.  may  vary  with  future  discoveries.  By 
the  Law  of  the  Conservation  of  Matter,  as  deduced  from  chemistry,  we  learn 
that  matter  is  indestructible:  it  may  appear  in  various  forms,  yet  the  cog- 
constituent  elements  are  never  actually  lost  or  destroyed.  Matter  nmy 
exist  in  a  solid,  liquid,  gaseous,  or  ethereal  state. 

Energy  is  matter  in  motion,  and  is  measured  by  the  formiila. 

Energy- i  mass X  (velocity)*;  or  £-i  Af  V« (1) 

in  which  mass  M— force  FX  acceleration  a, 

—weight  TV^ -I- gravity  acceleration  g. 

The  Law  of  the  Conservation  of  Energy,  proven  by  various  experiments . 
teaches  us  that  energy  is  indestructible:  it  can  appear  and  disappear  in 
various  forms,  yet  none  of  it  is  actiially  lost  or  destroyed. 

From  the  foregoing  laws  of  the  conservation  of  matter  and  enexKy.  and 
from  equation  (1),  we  deduce  the  following:  That  the  summation  of  each 
individual,  infinitesimal  sub-atom  of  matter  in  the  universe,  multiplied  by 
the  square  of  its  velocity,  at  any  single  instant,  is  equal  to  twice  tne  total 
energy  in  the  tmiverse  and  is  a  constant.  Or,  applied  to  any  independent 
system  protected  from  outside  influences,  the  same  statement  holda  true; 
hence  in  any  such  system,  we  have, 

IM  V»-a  constant CS) 

without  regard  to  any  change  in  form  of  the  matter  or  its  motion. 

Kinds  of  Eneriy. — ^There  are  two  kinds  of  energy  generally  referred  to. 

namely.  Kinetic  or  o^mu/  ("moving")  energy,  and  Potential  or  stortd  (static) 
energy.  Strictly  speaking,  potential  energy  is  simply  a  term  used  to  expieas 
the  amonut  of  kinetic  energy  which  would  be  expended  hy  a  mass  in  chang- 
ing itself  from  one  state,  condition  or  position  which  it  has  assumed,  to 
another  state,  condition  or  position  which  is  ^r§d€tirmm»d.  The  enexgy 
expended  may  be  in  one  or  more  forms. 

Forms  of  Energy. — ^There  are  four  principal  forms  or  outward  mani- 
festations of  energy: 

ExampUs. 
Mass  (?)  or        \ Potential:    A  raised  weight. 
Mechanical.       /Kinetic:       the  falling  ofa  raised  weight. 
Molecular  ( ?)     \  Potential:    the  latent  heat  of  liquefaction, 
or  Thermal.       f  Kinetic:       the  release  of  latent  neat. 
Atomic  (?)  or    I  Potential:    the  energy  stored  in  dynamite. 
(^emicaJ.  /Kinetic:       the  discharge  of  dynamite. 

Ethereal  (?)  or  \ Potential:    the  electric  charge  in  a  leyden  jar. 
Electrical.         /  Kinetic:       the  di8chsu:ge  of  a  leyden  jar. 
Other  manifestations  of  energy  are  light,  sound,  magnetism,  etc 

Transformation  of  Energy. — ^Energy  which  is  manifest  in  one  form  may 
appear  in  another  forms: 

Examples. 
Mechanical  to  Thermal:  (1)  Heat  resulting  from  impcurt  of  a  nroiectila 

]]  Chemical:         (2)  [No  direct  transformation  wholly  Kinetic?) 

Electrical:        (3)  Electric  current  generated  from  a  dynamo. 

1346 


THERMODYNAMICS, 


1347 


Thermal  to      Chemical:        (i)  Chemical  building  up  of  plant  life  bv  heat. 
Electrical:        (5)  Current  generate  by  heating  a  thermo- 
electric pile. 
"  Mechanical:     fg)  The  mechanical  work  of  a  steam  engine. 

Chemical  to     Electrical:        (7)  Current  generated  from  a  voltaic  battery. 
Mechanical:     (8)  Energy  of  all  animal  and  vegetable  life. 
Thermal:  (9)  Heat  from  oxidation,  as  combustion  of  fuel 

Electrical  to     Mechanical:   (10)  Energy  of  an  electric  motor  or  fan. 

Thermal:        (11)  Heat  evolved  by  current  through  non-con- 
ductor. 
**  Chemical:      (12)  Electrolytic  action,  as  electroplating,  etc. 

Therma]  Energy. — Heat  and  its  effects  may  be  considered  as  related  to 
molecular  action;  and  the  transference  of  heat,  simplv  as  the  transference 
of  molecular  action  from  oqe  body  to  another,  or  m>m  one  medium  to 
another. 

First  Law  of  Thennodyoainics:  Heat  and  mechanical  energy  are  mutu- 
ally convertible;  and  heat  rec^uires  for  its  production,  and  produces  by  its 
disappearance,  a  certain  definite  number  of  units  of  work  tor  tach  thermal 
unit. 

Thermal  Unlts.—There  are  three  units  as  follows: 

The  British  unit  of  heat  or  British  thermal  tmit  (B.  T.  U.)  is  equivalent 
to  778  foot-potmds  of  work,  and  may  be  defined  as  the  quantity  of  heat 
reqxiired  to  raise  the  temperature  of  one  pptmd  of  pure  water  1*  Fsuirenheit, 
at  or  near  its  maximum  density  at  39.1°  F.  (most  authors);  or  at  the  more 
prevailing  temperature  of  62**  F.  (Professor  Peabody). 

The  French  thermal  unit  or  calorie  (Cal.)  is  equivalent  to  426.84  meter- 
kilograms  of  work,  and  may  be  defined  as  tne  Quantity  of  heat  required  to 
raise  the  temperature  of  one  kilogram  of  water  1*  centigrade,  at  about  4°  C. 
(39.1*' P.). 

The  British-French  unit  of  heat  or  "pound-calorie"  (Lb.-Cal.)  is  equiva- 
lent to  1400.4  foot-poimds  of  work,  and  may  be  defined  as  the  quantity  of 
heat  reqtiired  to  raise  the  temperature  of  one  poimd  of  water  1**  C.,  at  about 
4**C. 

Mechanical  Equivalent  of  Heat,  J.— One  Joule*-/- 778  ft.-lbs.- 
1  British  thermal  unit  {B.  T.  U.),  is  generally  used  in  the  United  States  as 
the  mechanical  equivalent  of  heat  (see  above).  Hence,  7—  1  B.  T.  t/.— 
778     ft.-lbs.-1.41''45     horse-power     seconds -0.023^67      h.-p.  minute - 

0.00039^9  h.-p.  hour;  and  j-1  ft.-lb.- 0.001286  B.  T.  U.  One  horse- 
power hour— 1,980,000  ft. -lbs. «  2545  heat  uniu.  One  horse-power— 2545 
heat  units  per  hour  »■  25.450  heat  units  per  dav  of  ten  hours. 

Tables  1  and  2,  following,  will  be  fotma  useful  in  the  conversion  of 
mechanical  and  thermal  power  and  work. 

»  Joule's  original  experiments  gave  7  —  772  ft. -lbs. 


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1848 


«.— STSAikf  AND  GAS  POWER. 


1. — ^ThbrmaI/-Unit  Eouxvalbnts. 
(See  also  Table  2.  following.) 


Heat  Units. 

Brttlflli  Tbenn. 

Frencta  Therm. 

Br.-Fr.  Therm. 

Uniu. 
(1  Lb.  I*  F.) 

Units. 
(iKg.  l«a) 

Units. 
(1  Lb.  !«  C) 

Foot- 

Meter- 

B.  T.  U. 

CBl. 

Lb.-Cal. 

pounds. 

KUo«nuD& 

1. 

.252 

.5556 

778. 

107.57 

1.8 

.4536 

1. 

1400.4 

193  63 

2. 

.504 

l.llll 

1556. 

315.14 

3. 

.756 

1.6667 

2334. 

822.71 

3.« 

.9072 

2. 

2800.8 

387   26 

3.968 

2.3046 

3087. 

426.84 

4. 

r.008 

3.2222 

3112. 

430.28 

5. 

1.260 

2.7778 

3890. 

537.85 

.     5.4 

1.3608 

3. 

4201.2 

580.89 

6. 

1.512 

3.3383 

4668. 

645.42 

7. 

1.764 

3.8889 

6446. 

752.99 

7.2 

1.8144 

4. 

5601.6 

774.52 

7.936 

2. 

4.4092 

6174. 

853.68 

8. 

2.016 

4.4444 

6224. 

860.56 

9. 

2.268 

S. 

7002. 

968.13 

10. 

2.520 

5.5556 

7780. 

1075   70 

10.8 

2.7216 

«. 

8402.4 

1161.78 

11.904 

3. 

6.6188 

9261. 

1280.52 

12.6 

3.1752 

7. 

.     9802.8 

1355.41 

14.4 

3.6288 

8. 

11303.2 

1549.04 

15.872 

4. 

8.8184 

12348. 

1707.36 

16.2 

4.0824 

9. 

12603.6 

1742.67 

18.0 

4.5360 

10. 

14004. 

1936.38 

19.840 

8. 

11.0230 

15435. 

2134.28 

23.808 

€ 

13.2276 

18511. 

2561.04 

27.776 

7. 

15.4322 

11609. 

2987.88 

31.744 

8. 

17.6368 

24696. 

3414.73 

35.712 

9. 

19.8414 

27783. 

384l.it 

39.68 

10. 

22.046 

80870. 

4268. 40 

Ex.—^  B.  T.  U-2.268  Cal.-6  Lb.-Cal.-7002  ft.-lbs.-968.l3  meter- 
kilograms. 

Caution. — In  the  above  Table  it  is  to  be  noted  that  the  equivalents  are 
for  the  same  amount  of  work  in  each  case;  thus,  1  B.  T.  U.  and  0.252  Calorie 
and  0.5556  Lb.-Cal.  are  each  equal  to  778  ft.-lbs.  of  work.  But  using  com- 
pound units  we  have: 

1  B.  T.  U.  per  pound  — |  Cal.  per  kilogram  — |  Lb.-Cal.  per  pound. 
1 .8  B.  T.  U.  per  pound  - 1  Cal.  per  kilogram- 1  Lb.-Cal.  per  pound. 


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THERMAL  AND  MECHANICAL  EQUIVALENTS. 


1840 


2. — Mechanical  Equivalbnts  or  Hbat  (B.  T.  U.). 


Thermal. 

Mechanical. 

Heat  Unlta 

Rate  of  Work  In  Foot-Pounde. 

Amt.  of  Work  In  Hone-Power- 

(B.  T.  U.) 

Per  Hour 

for  1  Hour. 

PerMlD. 

Per  Hour. 

Per  Day. 
(24  Hours.) 

Mbiutea. 

Hours. 

(24£.) 

.0«53556 

.00069^4 

.041^6 

1 

.06^26 

.O721044 

.0087688 

.0810711 

.00138''8 

.083^3 

3 

.052^62 

.O742O88 

.0K17686 

.  .0816067 

.00808^3 

.125^0 

3 

.0>78 

.0763132 

.0826306 

-  .0s21422 

.00277^7 

.166^6 

4 

.0$6^05 

.0784176 

.0836078 

C  .0886778 
«  .0s38134 
**  ,0887489 

.00847^2 

.808^8 

3 

.016^81 

.0610522 

.0843841 

.00416''6 

.250^0 

6 

.057;;67 

.0012626 

.0852609 

.00486^1 

.291^6 

7 

.058^83 

.0814731 

.0861378 

.0848845 

.00655^6 

.333^3 

8 

.0*10^10 

.0el6836 

.0870146 

.0848200 

.00626^0 

.875^0 

9 

.0411^36 

Oe  18940 

.0878914 

.001285 

.016^6 

1 

24. 

. 00003^03 

.065^05 

.O72IO44 

.002571 

.083^3 

2. 

48 

00006^06 

.o»roi 

.0748088 

,    .008856 

.060^0 

3. 

72. 

00009^09 

.05^61 

.0r68138 

'^    .005141 

.066^6 

4. 

96. 

.00018^12 

.0»2>'08 

.Or84176 

^    .006427 
i    .007718 
^    .008997 

.083^3 

3. 

120. 

.00015''15 

.058^52 

.0810588 

.100^0 

6. 

144. 

00018^18 

.Oft3''08 

.0818636 

. 116^6 

7. 

168. 

.00081^21 

.053^58 

.0814731 

.010288 

.183^3 

8. 

192. 

.00024^24 

.0*4^04 

.0816886 

.011568 

.160^0 

9. 

216. 

.00027^27 

.054^54 

.0818940 

.07718 

1 

60. 

1440 

.001^81 

.00003^03 

.051^86 

.15424 

2. 

180. 

2880. 

.003''68 

. 00006^06 

.o!8''5a 

.      .23136 

3. 

180. 

4320. 

.006^45 

.  00009''09 

.058^78 

•^      . 30848 

4 

240. 

5760. 

.007^27 

00012^12 

.0;5^06 

C      . 88560 
£      . 46278 
'^      .53985 

3. 

800 

7200 

.009^09 

00016^15 

.0j6^81 

6. 

860. 

8640. 

.010^90 

.00018^18 

.0;7^57 

7. 

420. 

10080. 

.012^72 

.0002^21 

.068^83 

.61697 

8. 

480. 

11520. 

.014^54 

.00024^24 

.0410^10 

.69409 

9. 

540. 

12960. 

.016^36 

.00027^27 

.04ll''36 

1 

18.96^6 

778. 

18672. 

.023^57 

.00039^29 

.O4I687 

2. 

85.93^3 

1658. 

37344. 

.047^15 

.00078^58 

.048274 

3. 

88. 90^0 

2334. 

56016. 

.070^72 

.0011^78 

.044912 

^        4. 

61.86^6 

8112. 

74688. 

.094^30 

.0015^71 

.046549 

s  1; 

64.88^3 

8890. 

93360. 

.117^87 

.0019''64 

.048186 

77.80^0 

4668. 

112032. 

.14r45 

.0023^67 

.049828 

90.76^6 

5446. 

130704. 

. 166^03 

.0027^50 

.0S1146 

8. 

103.73^3 

6824. 

149376. 

.188^60 

.0031^43 

.081310 

9. 

116.70^0 

7002. 

168048. 

.212^18 

.0035^36 

.081478 

48.41^8 

650. 

83000. 

792000. 

1 

.016^6 

.00069^4 

84.88^8 

1100. 

66000. 

1584000. 

3*. 

.033^8 

.00188''8 

.187.86^0 

1650. 

99000. 

2376000. 

3. 

.050^0 

.00208^8 

"169.66^6 

8800. 

132000. 

8168000. 

4. 

.066^6 

.00277^7 

^312.08''8 
§254.50^0 
^206.  91^6 

2750. 

166000. 

8960000. 

3. 

.083^3 

.00347^8 

8800. 

198000. 

4752000. 

6. 

.100^0 

.00416''6 

8850. 

231000. 

5544000. 

7. 

.116^6 

.00486^1 

839.83^3 

4400. 

264000. 

6336000. 

8. 

.133^3 

.00566^6 

381.75^0 

4950. 

297000. 

7128000. 

9. 

.150^0 

.00625^0 

8645. 

83000. 

1980000. 

47520000. 

60. 

1. 

.041^6 

6090. 

66000. 

3960000. 

95040000. 

120. 

3. 

.088^8 

7635. 

99000. 

5940000. 

142560000. 

180. 

3. 

. 126^0 

»      10180. 

182000. 

7920000. 

190080000. 

240. 

4. 

.166^6 

5       18786. 
i      16870. 

^      17815. 

165000. 

9900000. 

287600000. 

300. 

3. 

.208^3 

198000. 

11880000. 

280120000. 

360. 

6. 

.860^0 

281000. 

13860000. 

332640000. 

420. 

7. 

.291^6 

80860. 

264000. 

15840000. 

880160000. 

480. 

8. 

.833^3 

88906. 

297000. 

J  7 820000. 

427680000. 

540. 

9. 

.876^0 

61080. 

792000. 

4752x10* 

114048x10* 

1440. 

24. 

1. 

122160. 

1584000. 

9504x104 

228096x10* 

2880. 

48. 

3. 

.    188240. 

2376000. 

14266x10* 

342144x10* 

4320. 

72. 

3. 

"    344820. 

3168000. 

19008X10* 

456192x10* 

5760. 

96. 

4. 

i    306400. 

3960000. 

23760x10* 

570240x10* 

7200. 

120. 

3. 

I    366480. 

4752000. 

28612x10* 

684288x10* 

8640. 

144. 

6. 

"    437660. 

6644000. 

33264x10* 

798386x10* 

10080. 

168. 

7. 

48M40. 

6386000. 

38016x10* 

912884x10* 

11520. 

192. 

8. 

043730. 

7188000. 

42768x10* 

1026432x10* 

12960. 

816 

9 

1860 


m.— STEAM  AND  GAS  POWER, 


ExampUs  in  th4  Usi  of  TabU  £,  prectding. 

Part  l.—l  000  000  f  t.-lbs.  per  day  is  at  the  rate  of  604  44  f  t.-lbs.  per  miiL. 
and  equivalent  to  63.556  heat  tinits  per  hour.  63.656  heat  units  represent 
an  amount  of  work  equal  to  1.2626  horse-power  min.,  or  .021  h.-p  hoar,  or 
.000877  h.-p.  day. 

Part «,— 5  000  000  tt.-lbs.  per  hour  -» 6427  heat  units  per  hotir.  5  000  OOi 
ft. -lbs.,  or  6427  heat  units,  are  equal  to  2.5262  horse-power  hours,  or  1  horse- 
power for  2.5252  hours,  or  2.5262  horse-power  for  1  nour. 

Part  5.-33  000  ft.-lbs.  per  min. «- 2313.6+ 231.36« 2545  heat  tmits  p& 
hour. 

Part  A. — One  heat  unit  for  any  time  T  is  equal  to  778  ft.-lb«.  in  time  T\ 
hence  Columns  1  and  3  may  be  used  independently  of  time,  throughout  the 
Table,  to  give  Equivalent  Work  in  Ft.-Lbs.  and  Heat  Units. 

Part  6. —  60  horse-power  min.  —  2545  heat  units. 

Part  e,—Zb7  horse-power  hours  -  763500+ 127260+ 17815->  008565  heat 
uniU,  and  equivalent  to  706  860  000  (-70686X10*)  ft.-lbs.  (per  hour  far 
1  hour.) 

Part  7. — Six  horse-power  days  -  366480  heat  uniU;  and  866480  heat 
units  per  hour  represent  work  at  the  rate  of  6  842  880  000  ft.-lbs.  per  day. 

B.— FUEL. 

Heatinx  Power  of  Pods. — ^The  amount  of  heat  energy,  in  B.  T,  C7.,  con- 
tained in  coal,  wood  and  other  fuels  may  be  determined  by  three  methods: 
(a)  by  chemical  analysis;  (d)  by  burning  the  fuel  in  a  calorimeter;  (c)  by 
practical  test  in  connection  with  d  steam  boiler. 

(a)  Chemical  Analysis. — ^There  are  two  kinds  of  analysis  of  coal  (or  ftiel). 
namely,  "proximate  analysis"  and  "ultimate  analysis. 

Proximate  Analysis  separates  the  coal  into  moisture,  volatile  noatter, 
fixed  carbon,  and  ash.  In  making  this  analysis  a  pulverised  sample  is 
weighed  carefully  and  then  heated  to  a  temperature  not  to  exceed  280^  P. 
When,  after  repeated  weighings,  it  ceases  to  lose  more  weight,  the  lo»  in 
weight  by  this  heating  is  recorded  as  "moisture."  The  heatmg  is  then  con- 
tinued in  a  crucible  with  a  lid  cover,  and  after  the  temperature  is  raised 
gradually  to  a  red  heat  and  continued  for  a  few  minutes  until  gas  ceases  to 
be  driven  off,  the  crucible  is  cooled  in  a  dessicator,  to  prevent  absorption  of 
moisture  from  the  air,  and  weighed,  the  loss  in  weight  by  this  heating  bexnc 
recorded  as  "volatile  matter."  The  heating  is  then  continued  and  the 
crucible  raised  to  a  white  heat,  the  lid  being  partly  OF>en  to  admit  air  to 
bum  the  coal,  and  when  the  carbon  is  burned  away,  leaving  nothing  but  the 
ash,  the  latter  is  weighed  when  cooled  and  the  loss  in  weight  by  this  heating 
is  recorded  as  "fixed  carbon."  The  weight  of  the  ash  is  of  course  recorded 
as  "ash".  If  the  weighings  are  recorded  in  percentages  the  sum  of  the  four 
constituent  parts  will  add  up  to  100  per  cent.  Sometimes  "sulphur"  is 
included  in  the  proximate  analysis,  either  as' part  of  the  100  per  cent  above 
mentioned  or  separately,  the  percentage  of  sulphur  being  determined  by 
separate  analirsis,  and  40  to  50%  assumed  to  have  escaped  with  the  volattk 
matter  and  60  to  60%  with  the  fixed  carbon. 

The  proximate  analysis,  above,  indicates  the  character  of  the  ooal. 
Omitting  the  moisture  and  the  ash.  and  letting  the  sum  of  the  "volatite 
matter"  and  "fixed  carbon"  equal  100  per  cent  of  the  "combustible."  we 
have  the  following  classification: 

3. — Coals  Classipibd  bt  Rblative  Pbrcbntagbs  or  Carbon  and 

VOLATILBS. 


Kind  of  Ooal. 

Percent 
Fixed 
Oarbon. 

Percent. 
Vdatne 
Blatter. 

Heating  Value. 

B.  T.  U. 
per  Lb.  Ooal. 

Relative 

Combostftito 

Value. 

Anthracite 

100  to  92 
92  to  87 
87  to  75 
75  to  60 
65  to  50 

under  50 

Oto    8 
8to  IS 
13  to  25 
25  to  40 
35  to  50 
over  50 

14600  to  14800 
14700  to  15000 
15600  to  16000 
14800  to  15300 
13500  to  14800 
11000  to  ISSOO 

93 

Seml-Anthrsclte 

Beml-Bltumlnous 

Bituminous.  Eastern .... 
Bituminous.  Western. . . . 
Lignite 

94 

100 
H 
M 

Tf 

COAL  AS  FUEL-CHEMICAL  ANALYSIS.  1361 


4. — Proximate  Analysis  and  Heating  Values  of  U.  S.  Coals. 
Note. — See  Table  5  for  Ultimate  Anaylses  of  Fuels. 


Note. — ^The  following  values  are  given  for  Anthracite  coal  from  one  mine: 
Bes  coal  (screen  2J'-lr)  88.49%  carbon,  6.66%  ash;  stove  coal  (screen 
Ir-li*)  83.67%  carbon,  10.17%  ash;  chestnut  coal  (screen  IK-i*)  80.72% 
carbon.  12.67%  ash;  pea  coal  (screen  T-D  79.05%  carbon,  14.66%  ash; 
buckwheat  coal  (screen  i'-i*)  76.92%  carbon,  16.62%  ash. 

Ultimate  Analysis  reduces  the  "combustible"  constitutents  of  the  fuel. 
4.  e.,  the  "volatile  matter"  and  "fixed  carbon"  (but  not  the  moisture  and 
aish)  to  the  ultimate  chemical  elements. 


Digitized 


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1352 


69.— STEAM  AND  GAS  POWER 


S.-— Chbiiical  Composition  op  Sbvbral  Kikds  of  Solid  Publs. 

(Ultimate  Analyses.) 
Note. — See  Table  4  for  Proximate  AnaXyaes  of  Coals. 


Kind  ot  Fuel. 

Moist- 
ure. 

Car- 
bon. 

Hydro- 
gen 

Oxy- 
gen. 

Nitro- 
gen. 

Sul- 
phur. 

Asll. 

B.r.r. 

Wood,  dry.  average 

10.0 

20.0 

40.0 

30.0 

12.0 

16  0 

10 

10 

1.4 

7.5 

11. 0 

17.4 

15  8 

49.5 

49.18 

49.06 

48.88 

48.99 

50.86 

50.16 

50.31 

44.5 

39.6 

29.7 

40.6 

84 

36. 

86. 

84. 

75 

67. 

56. 

50. 

66. 

6.1 

6.27 

6.11 

6.06 

6.20 

5.92 

6.02 

6.20 

6.5 

4.9 

3.7 

4.2 

1.0 

6.0 

1.0 

4.2 

5  0 

4.8 

5.0 

4.0 

4.5 

43.8 
48.91 
44.17 
44.67 
44  26 
43.  8» 
43.36 
43.08 
39.4 
35.0 
26.2 
21   7 
0. 

88.0 
l.O 
8.4 
8.0 
10.0 
11.0 
14.0 
16.9 

0.1 

0  07 

0.09 

0.10 

0.06 

0.05 

0.09 

0.04 

0.1 

0.1 

0.1 

0.5 

0.87 

0.67 

0  29 

0.50 

0  28 

0.37 

0.37 

0.5 

0.4 

0.8 

3  5 

3. 

5. 

10. 
6. 
8. 
8. 

13. 

13. C 
5.6 

8806 

••        *•     Adi 

8486 

"     Beech 

"     Birch 

8591 
8S8( 

"        "     Elm ,  X 

8510 

"     Fir 

9063 

••        ••     Oak 



9316 

"     Pine 

9113 

10%  moteture,av 
!!       20%      ;;       ;| 

Peat * 

CTharooal 

Straw 

Coal.  Anthracite 

'     Seml-BltumlDous. . . 

"    Bituminous  PItts'g.. 

"  Hocking  Val..  O 

••  Illinois 

Brown  Coal,  Pao.  Ooast . . . 

0.5 
0.8 
1.0 
1.2 
1.0 
1  0 
l.l 

0 
0 
1 

1 
3 

Lignite,  Pacific  Coast 

1.1 

Green  wood  contains  from  25  to  50  per  cent  moisture.  Air-dried  wood 
contains  from  10  to  20  per  cent  moisture — usually  12  to  15  per  cent. 

Calculations  of  the  Heat  of  Combustion  of  a  fuel,  based  on  the  tiltimate 
analysis,  are  usvially  performed  by  means  of  Dulong's  formula,  or  by  means 
of  other  formulas  which  resemble,  or  are  more  or  less  modificationa  of* 
Diilong's  formula.    Thtis. 

The  total  heat  unite  (B.  T.  U.)  per  lb.  of  coal — 

- 14660  C+ 62100  (H-iO) (Dulong) CD 

- 14660 C"+ 62100 H- 5400  (0-1- iV)  (Mahler) .(J) 

In  which  C,  H,  O  and  N  represent  the  relative  parts  of  carbon,  hydrogen. 
ox3rgen  and  nitrogen  in  the  coal. 

Example. — The  ultimate  analysis  of  a  certain  coed  gave,  in  parts  (per- 
centages expressed  in  parte  of  a  unit),  carbon  (C)  —  0.8666,  hydnwen  (W)  — 
0.0278,  nitrogen  (iV)«  0.0077,  oxygen  (O)- 0.0287,  ash -0.0738,  volatile 
sulphur  — 0.0059.  How  many  heat  unite  would  one  pound  of  this  coal  be 
expected  to  supply,  or  in  other  words,  what  is  the  total  heat  of  combustkm? 

Solution.— From  Dulong's  formula,  total  heat  -14650X. 8566-1- 62100 
(.0278-  iX  .0287) - 14052  B.  T.  U.;  and  from  Mahler's  formula,  total  beat 
-14079B.  r.  17. 

Mr.  Henry  J.  Williams*  gives  the  following  values  for  heat  of  combtis- 
tion,  as  calculated  by  Dulong  s  formula: — Anthracites:  Lehigh,  13963  B.  T. 
U.,  Lykens  Valley,  13964;  Drifton,  Pa^  14171.  Semi-bitvmMnous:  Poca- 
hontas, 14805:  Georges  Creek,  14484;  Clearfield.  Pa.,  14448;  New  River. 
W.  Va.,  14607.  Bituminous:  Connellsville  (coking).  14043;  Big  Muddy. 
Carterville,  Dl.,  12561;  Dominion,  Cape  Breton.  13755;  Pittsbmv  (steam- 
ing), 13719.  But  compare  these  heating  values  with  those  in  Table  4.  prfr- 
ceding. 

(6)  Calorimeter. — ^The  "bomb  calorimeter'*  is  an  instrument  used  to 
determine  the  actual  heating  value  of  coal.  Mahler's  instrument  consiste  of 
a  strong  steel  vessel  immersed  in  water.  One  gram  of  the  coal  is  placed  m 
a  platintmi  vessel  within  the  bomb,  oxygen  gas  is  introduced,  and  the  coal 

*  See  page  page  41,  Steam  Boilers,  by  Peabody  and  Miller;  John  Wikr 


FUELS.    TESTS— CALORIMETER;  BOILER. 


1353 


ignited  by  an  electric  sparic.  The  resultant  heat  of  combustion  is  radiated 
into  the  surrounding  water  and  is  measured  by  the  rise  in  temperature  of 
the  water,  making  the  necessary  corrections  for  absorption  of  heat  by  the 
instrument  itself. 

This  method  agrees  tisually  within  2  per  cent  of  the  calculations  from 
chemical  analysis,  when  the  tests  are  carefully  made. 

(c)  Practical  (Boiler)  Test. — ^The  following  Table  gives  the  summary  of 
nine  tests  made  on  one  250  H.  P.  Cahall  boiler  at  factory  of  the  Armstrong 
Cork  Co.,  Pittsburg.  Pa..  1896: 


6. — ^AVBRACB  OP   NiNB   BoiLBR  TbSTS — COAL   AS  FUBL. 


Duration  ot  test. hours. . 

No.  of  boilers 

Arerage  Fresswre  ot  Steam  in  Boiler  Ity  Oage 

Average  Temperatures. 

of  feed-water  entering  boiler deg.  F. . 

Of  steam  In  boUer deg.  F. . 

Fuel  (Nut,  Nut  and  Slack.  Run  ot  mine,  etc)  CotU. 

Cost  pet  Uui  ot  2,000  pounds,  delivered 

Calorific  power  by  Calorimeter B.  T.  U. . 

Total  quantity  consumed. lbs. . 

Total  ash,  dlnkers  and  unbomed  coal. lbs. . 

Proportion  ot  ash.  etc,  to  coal per  cent. . 

Total  combustible  burned. lbs. . 

Combustion  per  Hour. 

Coal  actually  consumed lbs. . 

Combustible  actually  consumed . .   lbs . . 

Per  sq.  ft.  grate  surface— coal lbs. . 

Per  sq.  ft.  grate  surtSoe — combustible lbs. . 

Per  sq  ft.  heating  surface— coal  lbs. . 

Per  sq.  ft.  heating  surface — combustible lbs. . 

Water. 

Amount  apparently  evaporated. lbs. 

Factor  ot  evaporation . .   

Equivalent  evaporation  Into  dry  steam  from  and  at  2 1 2<'F. . . lbs . . 
Economic  Bvaporationr—peT  pound  of  coal. 

Water  actually  evaporated bis. . 

Equivalent  from  and  at  212*  F lbs. . 

Per  pound  of  combustible — water  actually  evaporated lbs. . 

Equivalent  from  and  at  212^  F lbs. . 

jgvaporaHon  per  Hour. 

Water  actually  evaporated lbs. . 

Equivalent  from  and  at  2l2o  F lbs. . 

Per  sq.  ft.  heating  surface — water  actually  evaporated lbs  . 

Equivalent  from  and  at  212<*  F lbs. . 

Per  sq.  ft.  grate  surface — water  actually  evaporated lbs . . 

Equivalent  from  and  at  212*  F lbs.. 

gffieimcy. 

Percentage  of  total  calorific  power  utilised,  or  efficiency —  % . . 

Water  evaporated  per  $1.00  worth  of  fuel lbs. . 

Cost  of  evaporating  1,000  lbs.  or  water cents . . 

Coal  consumed  per  horse  power  per  hour lb<«. . 

Cost  of  same cents.. 

ffarse  Power. 

Actually  developed  on  basis  of  34}  IhB.  of  water  evaporated  per 
hour  from  and  at  212*  F 

Commercial  rating 

Proportion  capacity  devdoped  Is  ot  commercial  rating    ...  %   . 

Heating  surface  required  to  devdop  one  horse  power — 8q..ft 


08.8 


«2.6 
834.3 

11.01 

12,063.5 

10.132.8 

975.06 

9.69 

8.961.94 

1.190.29 

1,082.79 

31.03 

32.54 

.47 

.43 

86,199.08 

1.20 

103,007.73 

8.735 
10.43 

9.1106 
11.5869 

10,448.57 

12,582.82 

4  03 

4.9571 

298.53 

320.68 

77.867 

19,858.47 
4  98 
3.35 
0.1724 


364.708 

250.0 

145.889 

7.360t 


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ISM  W.— 5rEi4Af  AND  GAS  POWER. 

C— STEAM. 

Qratral  DifCiiitlofi.— If  one  pound  of  ice  at  abtolttte  zero  ^«  —  97S.r  C 
M  .  460.66''  P.)  is  gntdxially  heated,  its  temperature  will  rise  about  directk 
in  proportion  to  the  amount  of  heat  it  receives  (say  apptox.  r  C.  per  eacA 
Calorie,  or  l**  P.  for  each  B.  T.  U.)  until  it  reaches  the  melting  point  or 
fusion  point  ( —  0*  C.  —  +  32®  F.) ;  then  its  temperature  wiM  remam  constant 
during  melting  or  until  it  has  received  143  additional  B.  T.  U..  making  s 
total  of  about  460.66+  32+  143—  635.66  B.  T.  U.  to  change  one  pound  of  ice 
at  absolute  zero  into  one  pound  of  water  at  the  temperature  of  (reeziD^* 

The  143  B.  T.  U.  required  to  change  one  pound  of  ice  at  +  S2*»  P.  into 
one  potmd  of  water  at  32®  P.  is  called  the  latent  heat  of  fusion  of  ice,  and 
represents  the  work  required  to  change  the  molecular  condition  of  ice  to  the 
molecular  condition  of  water,  since  there  is  no  rise  in  temperature.  Con- 
versely, onepound  of  water  at  82®  P.  will  giw  out  148  B.  T.  U.  in  changing 
to  ice  at  32®  P. 

If  one  pound  of  water  is  gradually  heated  in  an  open  vessel,  under  an 
atmospheric  pressure  of  14.7  pounds  6eT  square  inch,  from  freesing  point  at 
32®  P.  u^  to  the  boiling  point  at  212®  P..  its  temperature  will  nse  almost 
directly  in  proportion  to  the  amount  of  heat  received,  i.  e..  1^  P.  for  each 
B.  T.  U.,  or  a  total  of  180  B.  T.  U.;  then  its  temperature  will  remain  con- 
stant during  the  process  of  boiling  away,  called  vaporization.  But  if  the  at- 
mospheric pressure  on  the  surface  of  the  water  had  been  increttsed.  its 
boiling  point  would  have  been  raised.  This  is  shown  clearlv  in  the  fifst  two 
columns  of  Tables  7  and  8.  following.  Thus,  from  Table  8,  an  nbs^vtt 
pressure  of  90  pounds  per  square  inch  would  raise  the  boiling  point  tempera- 
ture to  320®  P.  and  it  would  remain  at  that  temperature  until  completely 
vaporized.  In  this  case,  the  pound  of  water  would  become  the  receptacle  « 
about  320—212—108  B.  T  u.  more  than  it  could  receive  under  ordinanr 
atmospheric  pressure.  It  is  thus  seen  that  the  temperature  under  whkxi 
steam  is  generated,  depends  upon  the  pressure  of  the  liguid. 

Starting  with  one  pound  of  water  at  32®  P.,  and  heating  it,  we  find  from 
Column  3.  Tables  7  and  8.  the  number  of  heat  tmits  received  at  the  various 
boiling-point  temperatureSj  under  corresponding  pressures;  and  if  the  heot- 
in£[  is  continued  at  the  boiling  point.  Column  o  shows  the  number  of  beat 
umts  required  to  convert  the  water  into  steam  at  the  same  temperature, 
called  the  heat  of  vaporization;  and  Column  4  shows  the  total  heat  in  B.  T. 
U.,  of  the  steam  above  that  which  the  water  contained  at  32®  F.  Thus,  for 
a  temperature  of  320®  P..  the  toUl  heat-  1170.5-290.0+889.5-beat  of  the 
liquid  +  heat  of  vaporization. 

It  is  to  be  remembered  that  the  heat  of  vaporization,  or  latent  heat  d 
vaporization,  represents  the  number  of  heat  units  consumed  in  chaz«it« 
one  pound  of  water  into  steam  at  the  same  temperature.  Now  as  the 
temperature  is  not  raised,  it  is  evident  that  some  other  work  is  being  per- 
formed. In  fact,  the  latent  heat  is  converted  into  the  work  of  separattng 
the  molecules  of  the  water:  (1)  against  molecular  attraction,  and  (2)  against 
external  resistance  or  pressure.  The  1st  is  called  the  heat  equivalent  of 
internal  work  (Table  7,  Column  6).  and  the  2nd  is  called  the  heat  equivalent 
of  external  work  (Ck>lumn  7).  It  is  evident,  then,  that  the  value  in  Cohinm  5 
of  Table  7,  for  any  definite  temperature  or  pressure,  is  equal  to  the  sum  of 
the  corresponding  values  in  Columns  6  and  7. 

Steam  generated  in  a  closed  vessel  is  necessarily  in  contact  with  the 
water  and  must  have  the  same  temperature  and  pressure  as  the  water.  In 
this  condition  it  is  called  wet  saturated  steam  or  'wet  steam."  Its  specific 
volume,  or  volume  in  cubic  feet  of  one  pound,  and  its  density,  or  weie^t  in 
pounds  per  cubic  foot,  are  each  constant  for  any  definite  temperature  and 
pressure,  as  will  be  seen  from  the  last  two  columns  of  Table  7.  Just  at  the 
point  when  the  water  is  completely  evaporated  the  steam  is  known  as  dry 
saturated  steam  or  "saturateo  steam."  If  further  heated,  it  becomes  super- 
heated steam.  Summarizing,  we  have  wet  Meam  from  the  time  water 
begins  to  evaporate  up  to  the  time  of  complete  evaporation;  saturated  steam 
at  the  moment  of  complete  evaporation:  and  superheated  steam  when 
further  heated. 

Purthermore,  saturated  steam  is  dry  steam  of  a  temperature  due  to  its 
pressure-  that  is,  it  contains  no  moisture,  nor  is  it  superheated.  When  it 
18  heated  above  a  temperature  due  to  its  pressure  it  oecomes  superheased 

*  ?^^l^^^<^^>oi>  >s  given  simply  to  convey  graphically  to  the  mind  the 
general  effect  of  heat;   the  exact  values  are  not  important. 


STEAM— FORMULAS.  1366 

steam.  Dry  steam  may  be  either  saturated  or  superheated.  If  water  is 
injected  into  superheated  steam  it  will  immediately  vaporize,  reducing  the 
temperature  of  the  latter;  and  if  sufficient  water  is  injected  the  steam  will 
be  reduced  to  saturated  steam.  If  cold  water  is  injected  into  satiutited 
steam  some  of  the  steam  will  be  condensed,  and  the  temperature  and  pres 
sure  of  the  remainder  will  be  lowered.  Wet  steam  contains  mist  or  globules 
of  moisture,  but  its  temperature  and  pressure  bear  the  same  relation  as 
that  for  sattmited  steam.  Saturated  steam,  then,  can  have  but  one  tempera- 
ture for  any  given  pressure,  while  superheated  steam  can  have  any  higher 
temperature. 

Superheated  Steam  tends  to  follow  the  laws  of  perfect  gases,  the  more 
nearly  so  the  farther  it  is  removed  from  the  point  ot  saturation  Prom  the 
laws  of  gases,  we  have. 

pvRT (1) 

In  which  p— presstue  in  lbs.  per  sq.  in.; 
v— volume  in  cu.  ft.; 

T"»temp.  in  degrees  F.  above  absolute  rero; 
R^a.  constant,  depending  upon  the  gas; 
—foot-pounds  ot  external  work  done  in  altering  the  temp.  1" 

under  constant  pressure; 
"■63.2  for  air; 

—for  any  gas,  63.2-1- the  specific  gravity  of  the  gas,  referred  to 
air. 

Saturated  Steam. — ^The  laws  of  saturated  steam  do  not  follow  closely 
the  laws  of  perfect  gases,  yet  have  a  close  analogy  to  them.  The  following 
notation  and  formulas  are  mainly  those  used  m  Thermodynamics  of  the 
St4am  Engine,^  by  Prof  C.  H.  Peabody  (under  whom  the  writer  studied), 
and  are  used  here  with  his  permission.    See  also  Tables  7  to  10. 


Notation  and  Formulas. 
F-£ahrenheit  (absolute  zero-  -460.66  P.); 
C-centigrade  (absolute  zero-  -  273.7  C); 


f— temperature  in  degrees  P.  —  |<o4-82; 
to— temperature  in  degrees  C.  —  |  (/—  32) ; 
^-absolute  temperature  in  degrees  P. -460.66+/; 


Observe  the 

algebraic 

signs: 

+for  above  0*; 

-for  below  0^. 


To— absolute  temperature  in  decrees  C.  —  273.7  +  /o; 
p— pressure  (above  vacutun)  of  saturated  steam  in  lbs.  per  square  inch. 


Log 


n       n     (   In  which  i4- 6.1007; 
p-il-fr--^    \  log  5-3.43642;  loaD- 6.69873; 
^       ^    <  andusingr-<  +  461.2*»P. 


4— heat  of  the  liquid ;  that  is,  the  quantity  of  heat,  in  Prench  units  (num- 
ber of  heat  units  of  426.84  meter-kgs.),  required  to  raise  the  tem- 
perature of  one  kilogram  of  water  from  freezing  (0^  C.)  to  a  given 
temperature  to', 
-<o+  0.000002  ^+  0.0000003  tff. 

—  I  c  <f<,  in  English  tmits. 

;i— total  heat:   that  is,  the  quantity  of  heat  (number  of  heat  units  of 

778  ft.-lbs.)  required  to  raise  one  pound  of  water  from  freezing 

(32**  P.)  to  a  given  temperature  t,  and  to  entirely  vaporize  it  imder 

the  pressure  due  to  that  temperatxire; 

- 1001.7+  0.305  (f-  32).    But  see  Marks  and  Davis  formula,  page  1378. 

f — heat  of  vaporization,  which  may  be  defined  as  the  nxmiber  of  heat 

units,  of  778  ft.-lbs.,  required  to  vaporize  one  pound  of  water  at  a 

given  temperatxire  under  the  corresponding  pressure; 

—total  heat— heat  of  liquid—  X—q. 


p— heat  equivalent  of  internal  wortc;  that  is,  the  internal  latent  heat  or 
the  heat  units,  ot  778  ft.-lbs.,  required  to  do  the  disintegration 
work  during  the  vaporization  of  one  potmd  of  water; 
^r^A  pwr-A  p  (f—  9)-, 

where  A  —  reciprocal  of  mechanical  eqtiivalent  of  heat, 

-J- ^-0.00128636,  and 
•  Published  by  John  Wiley  &  Sons,  New  York.  Dignzed  by  GoOglc 


18M     *  G9.— STEAM  AND  GAS  POWER. 

's—cpedfic  volume  of  saturated  steam;  that  is,  the  vohxnc 
in  cubic  feet  of  one  pound  of  saturated  steftzn. 
d— specific  voltmie  of  the  water. 

pwp  (s—  a)— external  work. 
i4^— heat  equivalent  of  external  work;  that  is,  the  external  latent  heater 
the  heat  imits.  of  778  f  t.-lbs.,  required  to  overcome  the  external 
pressure,  and  do  the  woik  of  increasing  the  volume  from  ^  to  s. 

C"- specific  heat  of  the  liquid—  ■^. 

(ait 

I  -=r  => entropy  of  the  liquid;  the  term  entropy  is  used  to  denote  &  quaHty 
J  *  or  condition  of  the  liquid,  increasing  when  heat  is  added,  and  de- 

creasing when  heat  is  subtracted  j   the  entropy  remains  constant 
when  no  heat  is  added  or  subtracted;    it  is  a  very  useful  property  in  all 
thermodynamic  calculations  * 
5— specific  voliune,  or  volume  in  cubic  feet  of  one  pound  of  steam, 
ra  density,  or  weight  in  ix>unds  of  one  cubic  foot  of  steam; 

s 

Saturatbd-Stbam  Tables. — Tables  7  and  8,  following,  are  the  oW 
tables  which  have  been  used  by  en^eers  for  the  past  ten  years.  These 
are  followed  by  Tables  9  and  10,  which  are  calculated  from  more  recent  ex- 
perimental data.  The  older  tables  are  reproduced  here  simply  for  methods 
of  comparison,  and  Tables  9  and  10  should  be  used  because  the  values  are 
more  correct. 

The  formulas  given  above  are  the  old  formulas.  The  new  formula  for 
heat  of  vaporization,  in  English  units,  is 

r-  141.124  (689 --0^«*». 


*  Entropy  Diagrams  are  very  useful  for  this  purpose.  They  represent, 
graphically,  the  successive  thermal  changes  in  a  body  due  to  the  simidtazM- 
ous  variations  of  Temperatxu^  and  Entropy — two  of  the  coordinates 
characterizinfl  the  conditions  of  the  body.  In  this  connection  it  may  be 
stated  that  Total  Heat  represents  energy  or  Work.  Now,  Work  is  made  up 
of  two  factors,  force  and  aistance  (M^"=/o).  Similarly,  the  Total  Heat  may  be 
considered  as  made  up  of  two  factors,  temperature  axkd entropy  {H'^Te  or  i— 
T6);  or,  graphically,  the  total  heat  is  the  diagram  area  whose  ordinate  at 
the  extreme  right  of  the  area  considered  is  the  temperature  T,  laid  off  frmn 
the  abscissa  whose  value  is  the  entropy  0;  the  total  heat  being  the  sum- 
mation of  the  vertical  strips. 


d  by  Google 


SATURATED  STEAM—FORMULAS:  TABLES, 


1357 


7. — Saturatbd  Stbam — ^Enolisr  Units.* 
(Condensed  from  Prof.  Peabody's  Tables.) 
Note. — See  preceding  notation;  also  Table  8.  following. 


f 

d 

1 

1 

i 

1 

n 

1' 

11 

1^ 

1 

1 

Density. 

pli 

t 

P 

q 

X 

r 

P 

Apu 

Ccdt 

JT 

5 

r 

82 

0.0890 

0. 

1091.7 

1091.7 

1035.9 

56.8 

0.0000 

3387 

0.0002952 

34 

0.0963 

2.01 

1092.3 

1090.3 

1034.3 

56  0 

0.0041 

3138 

6.0003187 

86 

0.1043 

4.03 

1092.9 

1088.9 

1032.8 

66.1 

0.0081 

2910 

0.0003436 

88 

0.1126 

6.04 

1093.6 

1087.6 

1031.8 

66.2 

0.0122 

2700 

0.0003704 

40 

0.1216 

8.06 

1094.1 

1086.0 

1029.6 

66.4 

0.0162 

2506 

0.0003990 

46 

0.1471 

13.08 

1095.7 

1082.6 

1025.8 

66.8 

0.0262 

2087 

0.0004792 

50 

0.1773 

18.10 

1097.2 

1079. I 

1021.8 

57.3 

0.0361 

1745 

0.0005731 

56 

0.2128 

23.11 

1098  7 

1075.6 

1017.9 

57.7 

0.0459 

1466 

0.0006829 

60 

0.2546 

28.12 

1100  2 

1072.1 

1014.0 

68.1 

0.0566 

1234 

0.0008104 

70 

0.3602 

88.11 

1103.8 

1065.2 

1006.2 

69.0 

0.0746 

885.0 

0.001130 

80 

0.5027 

48.09 

1106.8 

1058.2 

998.3 

59.9 

0.0932 

643.8 

0.001553 

90 

0.6925 

58.04 

1109.4 

1051.4 

990.6 

60.8 

0  1114 

474.6 

0.002107 

100 

0.9421 

68.01 

1112  4 

1044.4 

982.7 

61.7 

0.1293 

354.0 

0.002824 

110 

1.2663 

78.0 

1115.5 

1037.6 

974.8 

62.7 

0.1470 

267.6 

0.003738 

120 

1.6828 

88.1 

1118.5 

1030.4 

966.7 

63.7 

0.1646 

2044 

0.004892 

130 

2.2119 

98.1 

1121.6 

1023.6 

958.9 

64.6 

0.1817 

157.8 

0.006336 

140 

2.8774 

108.2 

1124.6 

1016.4 

950.8 

65.6 

0.1986 

123.2 

0.008120 

ISO 

8.7063 

118.3 

1127.7 

1009  4 

942.8 

66.6 

0.2152 

97.03 

0  01031 

160 

4.7292 

128.4 

1130.7 

1002.3 

934.8 

67.5 

0.2316 

77.14 

0.01296 

170 

6.981 

138  5 

1133.8 

995.3 

926.8 

68.6 

0.2477 

61.86 

0.01617 

180 

7.600 

148.5 

1136.8 

988.3 

918.9 

69.4 

0.2636 

50  01 

0.02000 

190 

9.330 

158.6 

1139.9 

981.3 

911.0 

70.3 

0.2792 

40  73 

0  02455 

200 

11.520 

168.7 

1142.9 

974.2 

903.0 

71.2 

0.2946 

33.40 

0.02994 

210 

14.122 

178.8 

1146.0 

967.2 

895.2 

72.0 

0.3097 

27.67 

0.03628 

220 

17.186 

188.9 

1149.0 

960.1 

887.1 

78.0 

0.3246 

22.98 

0.04352 

230 

20.783 

198.9 

1152.1 

953.2 

879.4 

73.8 

0.3393 

19.20 

0.05208 

240 

24.982 

209.0 

1155.1 

946.1 

871.6 

74.5 

0.3538 

16.14 

0.06195 

290 

29.856 

219  1 

1158.2 

939.1 

863.8 

75.3 

0.3681 

13.65 

0.07327 

260 

35.483 

229.2 

1161.2 

932.0 

856.9 

76.1 

0.3822 

11.60 

0.08019 

270 

41.945 

289.3 

1164.8 

925.0 

848.1 

76.9 

0.3961 

9.918 

0.1008 

280 

49.828 

249.3 

1167.3 

918.0 

C40.4 

77.6 

0.4098 

8.521 

0.1173 

290 

57.72 

259.4 

1170.4 

911.0 

832.6 

78.4 

0.4233 

7.356 

0. 1359 

300 

67.22 

269.5 

1173.4 

903.9 

824.7 

79.2 

0.4366 

6.380 

0.1567 

310 

n.93 

279.6 

1176.6 

896.9 

817.0 

79.9 

0.4498 

5.568 

0.1799 

320 

89.96 

290.0 

1179.5 

889.6 

808.8 

80.7 

0.4633 

4.881 

0.2068 

330 

103.38 

300.5 

1182.6 

882.1 

800.8 

81.3 

0.4766 

4.267 

0.2343 

340 

118.34 

310.9 

1185.6 

874.7 

792.7 

82.0 

0.4897 

3.760 

0.2660 

350 

134.95 

321.4 

1188.7 

867.3 

784.7 

82.6 

0.6027 

3.324 

0.3008 

860 

153.33 

331.8 

1191.7 

859.9 

776.7 

83.2 

6.5156 

2.949 

0.3391 

370 

178.60 

842.3 

1194.8 

852.6 

788.7 

83.8 

0.5282 

2.623 

0.8812 

380 

195.91 

352.8 

1197.8 

845.0 

760.8 

84.2 

0.5407 

2.338 

0.4276 

390 

220.39 

363.2 

1200.9 

837.7 

753.0 

84.7 

0.5531 

2.092 

0.4780 

400 

247.21 

373.7 

1203.9 

830.2 

745.2 

85.0 

0.5653 

1.874 

0.5336 

410 

276.54 

384.1 

1207.0 

822.9 

737.6 

85.3 

0.5774 

1.682 

0.6945 

430 

308.57 

394  6 

1210.0 

815.4 

730.0 

85.4 

0.5893 

1.512 

0.661 

428 

836  26 

403.0 

1212.5 

809.5 

724.0 

85.5 

0.5988 

1.390 

0.710 

*See  Revised  Table,  second  page  following. 


d  by  Google 


1868 


eQ.— STEAM  AND  GAS  POWER. 


8. — Saturatbd  Stbau — ^English  Units.* 

(Prom  Peabody,  and  Babock  and  Wilcox.) 

Note. — See  Notation  and  Table  7,  preceding. 


III 

1^ 

ill 

Total  Heat  In 
Heat  Unlta 
From   Water 
at32«. 

•li 

llii 

Factor  of 
Equivalent 
Evaporation 
at2l2«». 

III 

1. 

p 

t 

4 

X 

f 

s 

r 

p 

101.99 

70.0 

1113.1 

1048.0 

.9661 

384.6 

0.00299 

126.27 

94.4 

1120.5 

1026.1 

.9738 

173.6 

0  00576 

141.62 

109.8 

1126.1 

1016.8 

.9786 

118.5 

0.00844 

153.09 

121.4 

1128.6 

1007.2 

.9622 

90.88 

0.01107 

162.34 

130.7 

1181.5 

1000.8 

.9652 

73.21 

0.01366 

170.14 

188.6 

1133.8 

996.2 

.9876 

61.65 

0.01682 

176.90 

146.4 

1135.9 

990.6 

.9897 

68.39 

0.01S74 

182.92 

151.5 

1137.7 

986.2 

.9916 

47.06 

0.02125 

188  33 

156.9 

1139.4 

982.5 

.9934 

42.12 

0.02874 

10 

193.25 

161.9 

1140.8 

979.0 

.9949 

88.15 

0.02621 

16 

213.08 

181.8 

1146.9 

965.1 

1.0008 

26.14 

0.08836 

20 

227.95 

196.9 

1151.6 

954.6 

1.0061 

19.91 

0.0SO23 

20 

25 

240.04 

209.1 

1155.1 

946.0 

1.0099 

16.13 

0  06199 

25 

30 

250.27 

219.4 

1158.8 

938.9 

1.0129 

13.59 

0.07360 

80 

35 

259.19 

228.4 

1161.0 

932.6 

1.0157 

11.75 

5.085M 

35 

40 

267.18 

236.4 

1163.4 

927.0 

1.0182 

10.37 

0.09644 

40 

45 

274.29 

243.6 

1165.6 

922.0 

1.0206 

9.285 

0.1677 

45 

50 

280.85 

250.2 

1167.6 

917.4 

1.0226 

8.418 

0.1188 

60 

56 

286.89 

266.3 

1169.4 

913.1 

1.0245 

7.698 

0.129* 

» 

00 

292.61 

261.9 

1171.2 

909.8 

1.0263 

7.09r 

0.1409 

•0 

06 

297.77 

267.2 

1172.7 

905.5 

1.0280 

6.588 

0.1519 

§B 

70 

302.71 

272.2 

1174.3 

902.1 

1.0295 

6.143 

0.1628 

79 

75 

307.38 

276.9 

1175  7 

898.8 

1.0309 

6.760 

0.1736 

75 

80 

311.80 

281.4 

1177.0 

895.6 

1.0323 

6.426 

0.1843 

85 

316.02 

285.8 

1178.3 

892.5 

1.0387 

5.186 

0.1951 

86 

M 

320.04 

290.0 

1179.6 

889.6 

1.0350 

4.859 

0.2058 

98 

95 

323.89 

294.0 

1180.7 

886.7 

1.0362 

4.619 

0.2165 

96 

100 

327.58 

297  9 

1181.9 

884.0 

1.0374 

4.403 

0.2271 

100 

105 

331.13 

301.6 

1182.9 

881.3 

1.0385 

4.206 

0.2378 

105 

110 

334.56 

305.2 

1184.0 

878.8 

1.0396 

4.086 

0.8484 

1»» 

115 

837.88 

308.7 

1185.0 

876.8 

1.0406 

8.882 

0.2589 

115 

120 

341.05 

312.0 

1186.0 

874.0 

1.0416 

3.711 

0.2695 

189 

126 

344.13 

315.2 

1186.9 

871.7 

1.0426 

8.571 

0.2800 

125 

130 

347.12 

318.4 

1187.8 

869.4 

1.0486 

3.444 

0.2904 

190 

140 

862.85 

824.4 

1189.5 

865.1 

1.0458 

3.212 

0.8118 

160 

150 

358.26 

830.0 

1191.8 

861.8 

1.0470 

3.011 

0.8821 

IM 

160 

363.40 

335.4 

1192  8 

857.4 

1.0486 

2.833 

0.8680 

166 

170 

368.29 

340.5 

1194.3 

853.8 

1.0602 

2.676 

0.3787 

171 

180 

372.97 

345.4 

1195.7 

850.3 

1.0517 

2.535 

0.3945 

189 

190 

377.44 

350.1 

1197.1 

847.0 

1.0531 

2.406 

0.41S8 

189 

200 

381.78 

854.6 

1198.4 

848.8 

1.0545 

8.294 

0.4859 

889 

225 

391.79 

365. 1 

1201.4 

836.3 

1.0576 

2.051 

0.4876 

835 

250 

400.99 

374.7 

1204.2 

829.5 

1.4)605 

1.854 

0.5393 

8se 

276 

409.50 

383.6 

1206.8 

828.2 

1.0682 

1.691 

0.5913 

275 

300 

417.42 

391.9 

1209.3 

817.4 

1.0667 

1.558 

0.644 

m 

325 

424.82 

399.6 

1211.5 

811.9 

1.0680 

1.487 

0.696 

885 

350 

431.90 

406.9 

1213.7 

806.8 

1.0703 

1.837 

0.748 

8B6 

875 

438.40 

414.2 

1215.7 

801.6 

1.0724 

1.250 

0.800 

875 

400 

445.15 
466.57 

421.4 

1217.7 

796.3 

1.0745 

1.172 

0.853 

466 

600 

444.3 

1224.2 

779.9 

1.0612 

.989 

1.065 

661 

*Sce  Revised  Table,  second  page  following 


d  by  Google 


SATURATED  STEAM— TABLES.  1369 

9. — ^Rbtxssd  SahiraUd  Sttam  Tablb — English  Units. 

(Condensed  from  Prof.  Peabody's  Tables.) 

Note. — See  also  Table  10.  following. 


d  by  Google 


1860 


l^STEAM  AND  GAS  POWER. 


10.->Rbvx8bd  Satufoud  Suctm  Tabl»— Bnoush  On  its. 

(Condensed  from  Prof.  Peabody's  Tables.) 

(Note. — See  also  Table  0,  preceding. 


if 

w 

3 

it 

Hi 

1 

Ik 

Bpeolfle  Vol- 
ume. Cublo 
Feet  per 
Pound. 

4 

V 

1 

ff 

r 

P 

Apu 

d 

T 
T 

• 

1 

101.84 

69.8 

1034.7 

978.1 

61.6 

0.1829 

1.8483 

333.1 

0.00306 

3 

126.15 

94.2 

1021.9 

967.8 

64.1 

0.1758 

1.7432 

173.1 

O.O0S78 

4 

158.00 

121.0 

1005.5 

938.6 

66.9 

0.2200 

1.6416 

90.4 

0.01106 

6 

170.07 

138.1 

995.6 

926.8 

68.7 

0.2476 

1.5812 

61.9 

0.01616 

8 

182.86 

150.9 

•87.8 

917.8 

70.0 

0.2678 

1.637fi 

47.36 

0.03116 

10 

193.21 

161.3 

981.4 

910.4 

71.0 

0.2838 

1.5036 

38.37 

0.936H 

12 

201.95 

170.1 

976.0 

904.1 

71.9 

0.2972 

1.4766 

32.40 

0.93068 

14 

209.55 

177.8 

971.2 

898.6 

72.6 

0.3088 

1.4516 

28.03 

0.03547 

14.7 

212.00 

180.3 

969.7 

896.9 

72.8 

0.8125 

1.4441 

26.78 

0.03714 

15 

213.03 

181.3 

969   I 

896.2 

72.9 

0.3140 

1 . 4409 

36.28 

o.osats 

20 

227.95 

196  4 

959.4 

885.1 

74.3 

0.3362 

1.8967 

20.09 

0  0497S 

25 

240.07 

208.7 

951.^ 

876.0 

76.4 

0.3593 

1.3600 

16.39 

0.0614 

30 

250.34 

219.1 

944.4 

868.2 

76.2 

0.3687 

1.3305 

13.74 

0  0738 

35 

259.29 

228.2 

938.2 

861.2 

77.0 

0.3815 

1.3064 

11.88 

0.0843 

40 

267.26 

236.4 

932.6 

855.0 

77.6 

0.8927 

1.2833 

10.49 

0.0953 

45 

274.46 

243.7 

927.5 

849.3 

78.2 

0.4027 

1.2638 

9.387 

0.1045 

50 

281.03 

250.4 

922.8 

844.1 

78.7 

0.4119 

1.2462 

8.507 

0.1174 

55 

287.09 

256.6 

918.4 

839.2 

79.2 

0.4202 

1.2302 

7.778 

0.13S6 

«0 

292.74 

262.4 

914.3 

834.7 

79.6 

0.4279 

1.2154 

7.16^  0.13« 

65 

298.00 

.267.8 

910.4 

830.4 

80.0 

0.4351 

1.2018 

6.647)  0.1504 

70 

302.96 

272.9 

906.6 

826.3 

80.3 

0.4418 

1.1892 

6.199   0.1613 

75 

307.64 

277.7 

903.1 

822.4 

80.7 

0.4480 

1.1772 

6.807.  0.1772 

80 

312.08 

283.2 

899.8 

818.9 

80.9 

0.4540 

1.1661 

6.466   0.1839 

85 

316.30 

286.5 

896.6 

815.4 

81.2 

0.4595 

1.1557 

6.161!   0.1938 

90 

320.32 

290.7 

898.5 

812.1 

81.4 

0.4649 

1.1457 

4.886 

0.3047 

95 

324.16 

294.6 

890.5 

808.8 

81.7 

0.4699 

1.1368 

4.644 

0.2153 

100 

327.86 

298.5 

887.6 

805.7 

81.9 

0.4748 

1.1273 

4.432 

0.3354 

105 

331.42 

302.1 

884.8 

802.7 

82.1 

0.4794 

1.1187 

4.233 

0.33a 

110 

334.83 

305.6 

882.1 

799.7 

82.4 

0.4838 

1.1105 

4.047 

0 . 3471 

115 

338.14 

309  0 

879.6 

797.0 

82.5 

0.4881 

1.1026 

3  876 

0.3580 

120 

341.31 

312.3 

876.9 

794.2 

82.7 

0.4922 

1.0951 

3.733 

0.3404 

125 

344.39 

315.5 

874.6 

791.6 

82.9 

0.4962 

1.0878 

3.581 

0.3?f3 

130 

347.38 

318.6 

872.1 

789.0 

83.1 

0.6000 

1.0808 

3.451 

0.3»i 

135 

350.27 

321.5 

869.8 

786.6 

83.3 

0.5087 

1.0741 

3.331 

0.3003 

140 

353.09 

324.4 

867.4 

784.0 

83.4 

0.5073 

1.0675 

8.220 

0.8104 

145 

855.83 

327.3 

865.2 

781.6 

83.6 

0.5108 

1.0612 

3.115 

0.3314 

150 

358.50 

330.0 

863.0 

779.3 

83.7 

0.5142 

1.0561 

8.014 

0.3318 

155 

361.09 

332.7 

860.9 

771.1 

83.8 

0.5175 

1.0491 

3.922 

0.3423 

160 

363.62 

335.3 

868.8 

774.9 

83.9 

0.5206 

1.0434 

2.834 

0.3138 

165 

366.09 

337.9 

856.8 

772.8 

84.0 

0.5237 

1.0378 

3.751 

4.3135 

170 

368.50 

340.4 

854.8 

770.6 

84.2 

0.5268 

1.0324 

2.673 

4.3741 

175 

370.86 

342.8 

852.fi 

768.5 

84.3 

0.5297 

1.0270 

2.600 

0.3844 

ISO 

373.16 

345.2 

860.9 

766.5 

84.4 

0.5326 

1.0219 

2.531 

0.3951 

185 

375.41 

347.5 

849.0 

764.5 

84.5 

0.5354 

1.0169 

2.467 

0.4454 

190 

377.61 

349.8 

847.1 

762.6 

84.6 

0.5381 

1.0121 

8.405 

4.41S8 

196 

379.78 

352.1 

845.3 

760.7 

84.6 

0.5408 

1.0071 

3.345 

0.4364 

200 

381.89 

354.3 

843.5 

758.8 

84.7 

0.5434 

1.0025 

3.388 

0.4371 

210 

386.02 

358.6 

840.0 

755.1 

84.9 

0.5485 

0.9939 

3.184 

0.4579 

220 

389.98 

362.7 

836.6 

761.6 

85.0 

0.5584 

0.9848 

3.08« 

0.4789 

230 

393.80 

366.6 

833.8 

748.1 

85.2 

0.5680 

0.9756 

3.001 

0.4997 

240 

397.60 

370.5 

830.1 

744.8 

85.3 

0.6625 

0.9686 

1.921 

0.521 

250 

401.10 

374.2 

826.9 

741.5 

85.4 

0.5669 

0.9609 

1.845 

0.542 

260 

404.56 

377.8 

823.9 

738.5 

85.4 

0.5711 

0.9SSV 

1.775 

0.543 

270 

407 . 90 

381.3 

820.9 

785.4 

85.6 

0.5761 

0.9464 

1.711 

0.584 

280 

411.19 

384.8 

818.0 

782.6 

85.5 

0.5791 

0.9898 

1.65^ 

0.045 

290 

414.35 

388.1 

815.2 

729.6 

85.6 

0.5829 

0.9831 

1.596 

0.437 

300 

417.45 

391.3 

812.4 

726.8 

85.6 

0.5866 

0.9864 

1.543 

0.449 

310 

420.45 

394.4 

809.7 

724.1 

85.6 

0.5902 

0.9201 

1.492 

0.474 

320 

423.40 

397.5 

807.1 

721.5 

85.6 

0.5937 

0.914! 

1.446 

0.493 

330 

426.26 

400.5 

804.5 

718.9 

86.6 

0.5970 

0.9083 

1.402 

O.TIB 

838 

427.94-   402.2 

803.0 

717.4 

85.6 

0.5990 

o.9«iii 

1.317 

o,ni 

STEAM—TABLE/  FLOWi  BOILERS,  1361 

Flow  of  StMm.— O.   H.   Babcock,   in  "Steam,"  gives  the  following 
fonxiula: 

Flow  through  pipes:  W~     |r(^|-^»)^* d) 


Where  H^  — weight  of  steam  which  will  flow  per  minute,  in  lbs.; 
d— diameter  of  pipe,  in  ins.; 
f— density  or  weight  per  cubic  foot  for  ^i,  in  lbs.; 
^1— initial  pressure,  at  entrance,  in  lbs.  per  sq.  in.: 
^—pressure  at  end  or  exit  of  pipe,  in  lbs.  per  sq.  m.; 
£— length  of  pipe,  in  feet. 

11.— Plow  op  Stbaii  trkougb  Pzpbs. 


Note. — "For  sizes  of  pipe  below  6-inch,  the  flow  is  calculated  from  the 
actual  areas  of  'standard'  pipe  of  such  nominal  diameters.  For  horse-power, 
multiply  the  figures  in  the  table  by  2.  For  any  other  loss  of  pressure, 
multiply  by  the  square  root  of  the  given  loss.  For  any  other  length  of  pipe, 
divide  240  oy  the  given  length  expressed  in  diameters,  and  muliiplv  the  figures 
in  the  table  by  the  square  root  of  this  quotient,  which  will  give  the  now  for  1  lb. 
loss  of  pressiu^.  Conversely,  dividmg  the  given  length  by  240  will  give  the 
loss  of  pressure  for  the  flow  given  in  the  table." 

Steam  Boilers. — The  Efficiency  of  a  steam  boiler  is  the  ratio  of  the  heat 
utilized  in  heating  the  water  and  raising  steam,  to  the  total  heat  generated 
by  the  combustion  of  the  fuel;  and  ranges  from  60  to  75  per  cent.,  the 
latter  being  rarely  exceeded.  Thus,  if  a  pound  of  coal  has  a  heating  value 
of  14.000  ff.  T.  If.  it  is  theoretically  capable  of  evaporating,  "from  and  at"* 
212**F(see  Table  7.  preceding).  14000-t-966  8- 14.6  lbs.  of  water;  while  if 
the  efficiency  of  the  cx>iler  is  76  per  cent.,  the  amount  actually  evaporated 
by  the  pound  of  coal  will  be  14.5  X  .76-  10.87  lbs.  of  water. 

One  commercial  horse  power  of  a  boiler  is  variously  defined  as  follows: 

(1)  The  evaporation  of  30  lbs.  of  water  per  hoiu"  from  a  feed-water  tempera- 

ture of  100  F  into  steam  at  70  lbs.  gage  pressiu-e    (above   atmos- 
phere): considered  eqxiivalent  to 

(2)  84.6  (34.488  exact)  units  of  vaporization  at  212**  F;   considered  equal 

to 

(3)  34.6  ppimds  of  water  evaporated  from  a  feed-water  temperature  of 

2l2^  F  into  steam  at  the  same  temperature. 

(5)  Prom  our  steam  Uble,  34.6  r-  34.6  X  066.8 »  33.320  B.  T.  U.  per  hour; 

but 

(6)  33.306  British  thermal  units  per  hour  is  sometimes  taken  as  a  standard 

( -  34.488  r,  using  r  at  966: 7) . 
Conclusion:   (1)  is  used  in  making  actual  tests  of  boilers;  the  others  for 
purposes  of  calculation. 

♦  "From  and  at"  212^  F,  means  that  the  vaporizatiQa>  takes j place  at 
212**  F  from  feed  water  at  the  same  temperature.       tizedby^^OOglC 


1362  W.—STEAM  AND  GAS  POWER. 

Consumption  of  Coal  per  boiler  horse-power  hour  may  be  detenntned  frees 
the  above  data.  Assuming  the  boiler  at  76  per  cent  eflRcicncy,  one  poo^ 
of  coal  will  generate  say  1 4000  X  .76  »  10600  British  heat  tmits  (if  feed  water 
is  at  217^  F).    Then  (1)  the  amount  of  coal  per  boiler  hoiae-ponFer  pe 

33  320 
hour-  73-755  «  3.17  lbs.    This  result  is  also  obtained  (2)  by  dividing  84.5 

by  10.87;  that  is,  the  number  of  pounds  of  water  evaporated  pn*  horse- 
power hour,  divided  by  the  nimiber  of  pounds  evaporated  per  pound  of 
coal,  as  calculated  above. 

In  practice,  we  generally  assume  that  one  pound  of  coal  will  generate 
about  lO  000  heat  units,  in  which  case  it  would  require  8.3S2  pounds  ci 
coal  to  develop  one  boiler  horse-power  per  hour,  which  is  very  clooe  to  die 
average  performance  of  the  Cahall  boiler.  Table  6.  preceding.  Now  a  boCer 
horse-power  per  hour  (-33  320  heat  units  or  33  320  X  778-  26.922.960  ft- 
Ibs.)  is  very  different  from  an  engine  horse-power  hour  (see  page  \9^ 
which  is  equal  to  1,980.000  ft. -lbs. 

Thiis,  1  boiler  H.-P.  hour—  13.0924  engine  H.-P.  hours, 
or  1  engine  H.-P.  hour- 0.07688  boiler  H.-P.  hours. 

Hence  the  number  of  poimds  of  coal  consumption  per  engine  borse> 
power,  is  approximately, 

3.332X007638-0.2646  ,^..    -               ...^ 
Efficiency  of  the  Engme  (See  also  page  1883) (1) 

provided  there  is  no  loss  between  the  boiler  and  the  engine. 

Kinds  of  Steam  Boilers. — In  the  discussion  of  impulse  water  wheeli, 
page  1363,  it  is  stated  that  the  greatest  amount  of  the  energy  of  the  jet  has 
been  imparted  to  the  wheel  when  the  water  loses  its  velocity  on  strikmg  the 
buckets.  The  same  principle  holds  good  in  the  construction  of  bodexs. 
They  should  be  so  designed  that  the  feed  water  shall  absorb  the  greatest 
amount  practicable  of  the  heat  of  combustion  of  the  fuel,  with  the  mini- 
mum waste  of  gases. 

Ordinary  steam  boilers  may  be  classified  as  water-tube  boilers,  fire-tube 
boilers  and  flue  boilers: 

(1)  Water-tube  boilers  have  a  large  number  of  tubes  of  moderate  sia 
connected  together  at  their  ends  and  also  with  a  rwervoir  of  water  above: 
and  are  placed  directly  over  the  grate  or  in  the  path  of  the  flames.  TTie 
tubes  may  be  horizontal,  vertical,  inclined,  straight,  curved,  etc.  There 
should  be  no  "dead"  ends.  They  are  especially  adapted  to  high  steam- 
pressure.    Notable  examples:    Babcock  and  Wilcox,  (Cahall.  Thomjrcroft, 

(2)  Fire-tube  boilers  consist  of  a  large  number  of  small  tubes  acting  as 
flues  and  surrounded  by  the  water  contained  in  an  outer  shell,  which  reqtnres 
special  design.  The  circular  tubular  boiler  is  of  this  type,  including  k>co- 
motive  boilers. 

(3)  Flue-boilers  differ  from  the  fire-tube  boilers  in  that  the  tubes  an 
reduced  to  one  or  more  in  number  and  greatly  increased  in  size.  If  the 
furnace  is  outside  the  flues  it  is  "extemaUy  fired;"  if  inside  the  flues  it  is 
"internally  fired."  Of  the  latter  class  the  (Romish  boiler  has  one  flue,  whik 
the  Lancaster  has  two.  The  Scotch  marine  boiler  is  a  flue-  and  fixe-tnbe 
boiler  combined. 

BoiUr  Settings. — The  following  is  from  the  notes  of  J.  B.  Staxxwood: 

The  brick-work  about  a  boiler  should  be  thick  to  prevent  loss  by  radia* 
tion — a  21'  wall  should  be  used  if  possible.  All  flues  and  surfaces  expooed 
to  action  of  heat  should  be  lined  with  best  fire-brick.  It  is  not  a  good  plan 
to  convey  gases  back  over  top  of  boiler,  unless  there  is  space  enough  tor  a 
man  to  enter  and  clean  off  soot.  The  distance  from  grate  bars  to  lower 
portion  of  boiler  shell  should  not  be  less  than  24";  26'  and  28*  are  not  too 
great,  and  in  large  shells  30*  can  be  employed. 

The  bridge-wall  should  curve  to  conform  to  shape  of  boUer  shell.  Tec 
inches  makes  a  good  space  between  wall  and  shell.  Back  of  bridge-wall  the 
surface  should  be  paved  with  nard  brick,  the  surface  dipping  down  to  a 
depth  at  rear  end  of  boiler  of  about  18*  to  24'  according  to  size  of  shcQ- 
The  distance  between  back  tube  sheet  and  back  wall  should  be  IS*  for  a  48* 
shell:    24' for  a  72*  shell. 

Boiler  walls  will  crack,  and  no  form  of  construction  seems  to  entirely 
prevent  this.  Walls  wiih  air  spaces  are  as  liable  as  those  without,  with  U« 
oanger  of  leaking  more  air  when  they  do  crack.    The  best  method   to  h<Ai 


STEAM  BOILERS,    STEAM  ENGINES.  1363 

boQer  walls  together  is  with  "buck-staves"  or  "buck-bars."  The  best  form 
is  railway  iron  with  ends  mashed  down  under  a  hammer,  to  allow  for  drilling 
loles  for  tie-rod.  Most  builders  do  not  supply  "buck-staves' '  unless  specially 
ordered.  The  cheapest  form  of  fire-front  is  the  so-called  "half -arch,  which 
ioes  not  cover  any  more  of  the  front  of  the  furnace  than  is  absolutely  decent. 
On  small  boilers  it  is  employed  as  a  support.  For  a  good  job  a  "null  flush 
[rent"  should  be  used  with  damper  plate  and  damper. 

Boilers,  npw-a-days,  are  not  set  in  batteries,  all  to  work  together  as  a  unit. 
rhey  are  and  should  be  set,  so  that  each  boiler  is  independent  of  the  other 
n  the  battery.  In  this  way  any  one  can  be  shut  down  for  cleaning  or  for 
repairs.  Tms  arrangement  does  away  with  the  old-fashioned  steam  and 
nud-drums,  which  connected  the  boilers  of  a  battery  together.  Do  not 
3uy  either  a  mud-drum  or  steam  drum;  they  are  a  sotuce  of  trouble,  danger 
uid  expense.  The  trade  usually  includes  with  the  boiler  front,  the  grate 
lars,  a  bearing-bar  to  support  same,  a  soot  or  ash-door  with  frame,  a 
>nck  arch  plate  or  supportmg  bars,  and  a  boiler  stand  for  small  boilers. 

Steam  Engines  are  steam  motors,  or  mechanisms  for  converting  the 
thermal  energy  of  steam  into  mechanical  work.  The  efficiency  of  an  engine 
s  the  ratio  M  the  mechanical  work  done,  to  the  energy  of  the  steam  con- 
(umed  in  doing  it;  or.  the  ratio  of  the  heat  changed  into  work,  to  the  heat 
ippUed.  A  perfect  heat  engine,*  working  to  absolute  zero  temperature, 
nrould  of  course  have  an  efficiency  of  100  per  cent;  that  is,  it  would  be  able 
JO  convert  all  the  applied  heat  into  work.  A  ** perfect"  steam  engine,  from  a 
nechanical  standpoint,  can  never  be  expected  to  exceed  an  efficiency  of 
ibout  26  per  cent.  The  best  types  of  steam  engines  have  an  efficiency  in 
ictual  practice  of  only  about  18  per  cent,  because  they  cannot  utilize  a 
greater  ratio  of  the  energy  of  the  steam  delivered  to  them.  Such  engines 
ire  of  the  condensing-  and  multiple-expansion  type.  Non-condensing 
•ngines  have  efficiencies  ranging  from  5  to  10  per  cent.  Recent  en^es  of 
noderate  power  and  high  superheat  have  attained  an  efficiency  of  22%. 

Engine  Horse-Power. — Steam  engines  are  rated  by  the  horse-power,  the 
mit  of  work  being  the  foot-pound.  1  H.-P.  second  — 550  ft.-lbs.;  1  H.-P. 
ninute-  33.000  ft.-lbs.;   1  H.-P.  hour»  1,980,000  ft.-lbs. 

Problem. — ^A  steam  engine  working  at  an  efficiency  of  8%  uses  40  lbs.  of 
roal  per  hour.    Assuming  that  each  pound  of  coal  generates  10  000  British 
Jiermal  units  in  the  steam,  what  horse-power  is  realized  P 
-  ,  ,.  40X10  000X778X.08     ,«  e^a  r/    d      a 

Solution. HsolOO ^^'^^^  ^"^'    ^'•*- 

In  the  above  problem  the  coal  consumed  per  horse-power  per  hour 

12  574 
m — jg— —  3.18  lbs.    This  result  can  also  be  obtained  from  equation  (1); 

Coal  Consumption  per  horse-power  per  hour  may  vary  from  2  lbs.,  for 
Bise  efficient  steam  plants,  to  4  lbs.  for  smaller  plimts,  lees  efficient.  It  is 
ireU  to  estimate  6  or  7  lbs.  for  hoisting  engines  ordinarily  used  by  contractors. 
>£  course  much  depends  upon  the  quahty  of  the  coal.  If  ox  poor  quality 
be  consumption  will  be  greater. 

Value  of  Wood  as  fuel. — Assuming  the  wood  to  be  thoroughly  air-dried, 
»ne  ton  of  coal  is  equivalent  to  1  cord  of  Douglas  (Oregon  or  Washington) 
'iT',  105  cords  of  hickory:  1.1  cord  of  maple;  1.2  cord  of  white  oak;  1.5 
ord  of  beechj  l.Ocordof  olackoak;  2.0  cords  of  elm;  2.1  cords  of  chestnut; 
1. 4  cords  of  pme.  These  values  are  necessarily  approximate  only.  (See  also 
tage  1352.) 

Principle  of  the  Steam  Enpne. — An  engine  has  one  or  more  "cylinders." 
I  cylinder  is  simply  a  cylindrical  barrel,  with  closed  ends,  in  which  is  fitted 
i  piston  P  (Fig.  1)  made  to  move  back  and  forth  by  the  pressure  of  steam 
idinitted  alternately  on  either  side  of  it.  The  piston  rod  is  connected, 
>erbaps  indirectly,  with  a  crank  or  wheel,  giving  the  latter  a  circular 
notion,  thus  producing  continuous  power  in  one  direction. 

*  This  is  used  in  a  distinct  sense  from  the  so-called  "heat  engines"  which 
oclude  gas-  and  oil  engines.  Such  engines  may  have  an  efficiency  of  20  per 
,ent  or  more. 


1864 


W,^STEAM  AND  GAS  POWER, 


1 


Pig.  1  shows  a  longitudinal  section  of  the  cylinder  of  a  Corliss  engiDe 
The  steam  enters  at  the  top  of  the  cylinder  through  a  steam  pipe  leading 
directly  from  the  boiler,  and  tmder  a  pressure  of  say  100  lbs.  (per  sq.  in.) 
more  or  less.  (The  exact  pressure  is  registered  by  a  pressuz^e  gake  or  wdi- 
cator.)   It  enters  the  cylinder  proper  through  one  of  the  steam  valves  5  or  s. 


Steam 


Fig.e, 


Zero  Line  of  Ptesswr^ 
A*  Admission 
A-  6  •  Admission  Line 
^•Compre$sioff 


and  after  it  has  performed  its  woric  of  pressure  and  expcmsion  it  escapes 
through  the  parts  E  and  e,  at  the  bottom  of  the  cvlinder.  into  the  exhaosC 
It  may  either  be  wasted,  or  condensed  into  hot  feed-water  for  the  boiler. 

Pig.  2  shows  a  typical  double  indicator  diagram  for  a  non-condensing 
engine,  and  illustrates  graphically  the  action  of  the  cylinder  sxkI  the  woddng 
pressure  on  the  piston  at  every  position.  The  full  diagram  is  for  the  pvet- 
sure  on  the  right  of  the  piston,  and  the  dotted  diagram  for  the  pressure  oo 
the  left;  the  two  togethier  illustrating  a  complete  cycle,  from  the  starting 
point  at  the  right  of  the  cylinder  to  its  rettim  to  that  position. 

Starting  with  the  piston  at  the  ri^t,  Pigs.  1  and  2.  and  oonsklertng  the 
steam  pressure  at  the  right  of  the  piston:  A  u  the  point  of  admission  gl 
steam;  A-B  the  admission  line;  B  tne  point  of  initial  pressure  (the  di'ttanrr 
between  B  and  the  boiler  pressure  line  shows  the  loss  in  pressure  frcun  the 
boiler  to  the  engine) ;  B-C  the  steam  line  (the  valve  5  being  open  froer. 
A  to  C)\C  the  cut-on,  at  which  point  the  valve 5  is  closed  and  bei^ond  winct 
the  steam  works  by  expansion;  C-R  the  expansion  line,  the  pressure  de- 
creasingas  the  volume  of  steam  increases  (this  curve  is  verv  noirtf  a  hyper- 
bola) :  R  the  point  of  release  produced  by  the  opening  of  the  exhaust  vslvc 
at  e\  R-X  the  exhaust  line;  X^K  the  back-pressure  line;  K  the  point  of 
compression;  K-A  the  compression  line.  The  area  of  this  curve,  A  BCR 
X  K  A,  divided  by  the  horizontal  length  of  figure,  practically  the  piston 
stroke,  gives  the  mean  effective  pressure  (M.  E.  P.)  per  sq.  in.  on  the  rigbt- 
h^d  side  of  the  piston  during  its  cycle.  Similarly,  the  M.  E.P.otkHut 
left-hand  side  of  piston  is  obtained  from  the  dotted  diagram.  Bofioe 
diagrams  should  be  started  at  admission  or  during  enkausit  atherwiss^MT 
niay  not  ck)se.  d g tized  byXjOOglc  j 


STEAM  ENGlNEr-MEAN  EFFECTIVE  PRESSURE.      IMfi 


Mean  Effective  Preasure  (Af .  E.  P.)— The  M.  E.  P.  for  any  particular 
ensine  should  be  obtained  by  indicator  diagrams  as  explained  above.  The 
following  table  gives  average  Af .  E.  P*s.  iot  non-condensing  engines: 

13. — ^Mban  Bppbctivb  Prbssurbs  for  Vartino  Cut-opfs  and 
Initial  Stbam  Prbssurbs:  Non-Condbnbino  Bnoinbs. 


^Initial 
PicMuie: 

QI&IL 

O^fl. 

Cot-ofl. 

Ca^fl. 

Ca^ 

OuSfl. 

Cu^tt. 

Cl^ 

40 

8.65 

9.05 

13.46 

17.34 

20.76 

23.70 

26.22 

80.50 

«5 

5.42 

11.32 

16.15 

20.39 

24.13 

27.32 

30.08 

84.75 

60 

7.19 

13.59 

18.85 

23.45 

27.60 

30.94 

33.95 

39.00 

55 

8.90 

15.86 

21.54 

26.50 

80.87 

34.56 

37.81 

43.25 

60 

10.73 

18.12 

24.24 

29.56 

34.24 

38.18 

41.68 

47.50 

65 

12.60 

20.39 

26.93 

82.61 

37.81 

41.80 

45.54 

51.75 

70 

14.27 

22.66 

29.68 

35.67 

40.98 

45.42 

49.41 

56.00 

75 

16.04 

24.92 

32.32 

38.72 

44.35 

49.05 

53.27 

60.25 

80 

17.81 

27.19 

35.02 

41.78 

47.72 

52.68 

57.14 

64.50 

85 

19.58 

29.46 

87.71 

44.83 

61.09 

56.81 

61.00 

68.75 

90 

21.36 

81.72 

40.41 

47.89 

54.46 

59.94 

64.87 

73.00 

95 

28.13 

88.93 

43.10 

50.94 

57.83 

68.57 

68.73 

77.85 

100 

24.90 

86.26 

45.80 

54.00 

61.20 

67.20 

72.60 

81.00 

With  throttUng  engines  results  are  obtained  dependent  upon  proportion 
of  steam-ports,  travel  of  valve,  piston  speed,  size  of  governor,  and  design  of 


The  theoretic  mean  effective  pressure  may  be  calculated  by  means  of  a 
formula  involving  the  use  of  a  table  of  hyperbolic  logarithms.  This  formula 
assumes  that  the  "expansion  line"  (see  Fig.  2)  is  a  hyperbola.  It  takes 
into  consideration  the  point  of  cut-off.  It  is  used  principally  in  the  design 
of  engines,  and  only  about  70  per  cent  of  the  theoretic  m.  E.  P.  it  attained 
in  practice. 

Hcnt-ponm  from  mtan  efficttM  pressure  (ilf .  E.  P.) — 
Notation. 
D-i diameter  of  cylinder: 
A -ana  of  cylinder- ^  -  0.7864  27*; 
d— diameter  of  piston  xtx!: 
a— area  of  piston  rod— ^  —  0.7864  d"; 

5— length  of  piston  stroke; 
M— number  of  revolutions  per  minute. 
All  dimensions  in  inches  and  square  inches. 
Then  the  horse-power  is — 

[(Af .  E.  P.  for  head  end)  XA  +  (M.  E.  P.  for  crank  end)  X  (A  -g)3CTt  ^ 

83  000X12  '^^^ 

Problem. — A  non-condensing  engine  is  working  at  3/10  cut-off  under  an 

mitial  pressure  (at  B — not  boiler  pressure)  of  90  lbs.,  and  at  a  speed  of  130 

revolutions  per  minute,  with  a  stroke  of  24  inches.    The  diameter  of  cylinder 

is  16  ins.,  and  of  piston  rod  2.6  ins.    What  horse-power  is  realised? 

SoliUum.'—FTom  Table  12.  preceding,  the  Af .  E.  P.  (for  both  head-  and 
crank  end)  is  64.46;  hence,  from  equation  (2),  the  horse  power— 
64.46X(2A-o)5n       ,^„  p        . 
33000x12 170  H.  P.     Ana. 

EcoHomk  Performance  of  S$eam  Engines, — The  foUowing  is  from  tlie 
notes  of  J.  B.  Stanwood: 

NON-CONDBNSINO  EnOINBS. 

SUdi'Vahe  Engine. — 76  to  80  lbs.  of  boiler  pressure;  stroke,  long;  mean 
effective  pressure,  88  to  88  lbs.  per  sq.  in;  26  to  100  H.  P.;  cut-off.  H  stroke; 
alxnit  40  lbs.  steam  per  indicated  H.  P.  per  hotir.  When  valves  and  piston 
are  tight  this  has  been  reduced  to  33  lbs.  of  dry  steam  per  indicated  horse- 
power (I.  H.  P.)  per  hour  by  careful  test. 


piston 
2%H 


1S66  eQ.—STEAAf  AND  GAS  POWER. 

AtUamaiic  Htgh-Speed  Engines  with  sin^fle  valves. — 75  to  80  lbs.  at 
boiler  pressure:  stroke,  about  equal  to  piston  dia.;  M.  B.  P..  40  lbs.  per  sq. 
in.;  50  to  150  H.  P.;  cut-off,  Mstroke;  about  40  lbs.  steam  per  I.  H.  P.  pef 
hour.  When  valves  and  pistons  are  tight  this  has  been  reduced  to  32  lbs.  oi 
dry  steam  per  I.  H.  P.  per  hour.    Valves  difficult  to  keep  tight. 

AuUmuaic  High  Speed  Engines  with  double  valves. — 75  to  80  lbs.  of 
boiler  pressure;  stroke  IHto  2  times  piston  dia.;  M.  B.  P.,  40  lbs.  persq.  in.; 
50 to  160  H.  P.;  cut-off,  H  stroke;  about  85  lbs.  steam  per  I.  H.  P.  per  hoar. 
When  valves  and  pistons  are  tight  this  has  been  raduoed  to  30  lbs.  of  dry 
steam  per  I.  H.  P.  per  hour  by  careful  test. 

AiUomaiic  Cut-off  Engines,  of  the  Corliss  type. — Stroke,  2  to  8  times  dk. 
of  piston;  75  to  90  lbs.  boilei  pressure;  M.  B.  P.,  40  lbs.  per  so.  in.;  onder 
200  H.  P.-  cut-off  Veto  Ji  stroke.  29-30  lbs.  steam  per  I.  H.  P.  per  hoar; 
over  200  H.  P.,  27  lbs.  steam  per  1.  H.  P  per  hour;  when  valves  and  mstcm 
are  tight,  this  has  been  reduced  to  23H  lbs.  of  dry  steam  per  L  H.  P.  per 
hour  by  careful. test. 

Compound  Engines. — High  speed,  automatic  cut-off.  short  stroke:  110  to 
120  lbs.  boiler _piessure;  M.  B.  P..  25  to  27  lbs.  per  sq.  in.;  6  expansiofis. 
100  to  250  H.  P.;  27  lbs.  steam  per  I.  H.  P.  per  hour. 

Condensing  Bnginbs. 
Automatic  Cut-Oif  Engines,  of  the  Corliss  type.— Stroke,  2  to  3  tunes 
Ml  dia.;  70  to  80  lbs.  boiler  pressure:  M.  E.  P.,  40  lbs.  per  sq.  in,;  over 
H.  P.;  cut-off,  Vfi  stroke,  about  19-20  lbs.  steam  per  I.  H.  P.  per  hoar. 
Compotmd  Engines',  high  speed,  automatic  cut-off;  short  stroke;  110 
to  120  lbs.  boiler  pressure:  M.  E.  P..  27  to  30  Ibe.  per  sq.  in.;  9  expansions: 
200  to  500  H.  P;    17  to  19  lbs.  steam  per  I.  H.  P.  per  hour. 

Compound  Automatic  Cut-off  Engines,  of  the  Corliss  type. — Stn^  on 
high  pressure  cylinder,  2  to  3  tmies  piston  dia.;  136  to  110  lbs.  boiler  pres- 
sure; M.  E.  P..  24  to  14  lbs.  persq.  in.;  over  400  H.  P.;  16to  20ezpan^as; 
14  to  17  lbs.  oi  steam  per  I.  H.  P.  per  hour.  One  or  two  special  cases,  13H 
lbs.  of  steam  per  I.  H.  P.  per  hour  has  been  obtained. 

Compound  Bnginbs. 

Compound  Engines  are  devices  by  which  high  grades  of  expansion,  and 
consequently  high  pressure  of  steam,  can  be  successfully  used;  and  the 
evils  of  leakage  also  can  be  reduced. 

By  expanding  steam  partially  in  one,  then  in  a  .aeoond.  and  perhaps  a 
third  cylinder,  the  internal  condensation  is  kept  small;  for  usually  late  cut- 
offs are  employed,  the  advantage  of  which  is  that  the  surfaces  of  the  cylin- 
ders presented  for  re-heating  to  the  fresh  charges  of  steam  are  smaU,  com- 
pared with  the  voltmie  of  steam  used;  and  the  difference  in  temperature 
between  fresh  and  exhausted  steam  is  sli^t. 

Leakage  of  steam  with  compound  en^mes  is  not  so  serious  a  matter;  the 
steam  that  leaks  through  one  cylinder  is  caught  bv  the  second  instead  of 
being  thrown  away.  As  the  cut-offs  are  frequently  late,  the  slide-valve  cao 
be  employed,  which  is  the  tightest  of  all  valves. 

The  Eppect  op  Load  Upon  Economy  of  Stbam  Enoinbs. 
A  large  engine  working  with  an  extremely  light  load  is  wasteful  of  fad 
and  steam;  it  is  worse  than  a  small  business  wi^  a  large  staff  of  expensive 
officers,  for  it  has  more  than  the  fixed  charges  always  with  it.  A  smaD 
engine  overloaded  ma^  be  an  annoyance  and  care,  but  if  in  good  cooditioo 
it  may  be  economical  in  fuel. 

Steam  Pumps. — Pig.  3  shows  a  longitudinal  section  of  a  Worth]ngt(» 
direct-acting  duplex  steam  pump.  It  is  'direct-acting"  because  theplunge- 
of  the  pump  (on  the  right)  is  directlv  connected  to  the  piston  rod  ofUie 
engine  (on  the  left).  It  is  "duplex"  because  two  of  the  pumps  are  placed 
side  by  side,  each  one  of  which  is  connected  by  links  and  a  rocker  to  the 
valve  of  the  other.  As  the  plunger  worics  back  and  forth  the  water  is 
sucked  through  the  valves  at  the  bottom,  at  either  e&d«  while  the  water 
previously  sucked  at  the  opposite  end  is  at  the  same  time  forced  through 
the  upper  valves  into  the  discharge  D. 

Duplex  Ptunps  are  durable  and  easy  acting,  and  are  used  for  all  classes 
of  pumping. 


STEAM  ENGINES.    STEAM  PUMPS. 


1367 


Centrifugal  Pumps  consist  essentially  of  a  pump  wheel  or  impeller  with 
curved  vanes  which  move  tightly  in  an  outer  casing.    The   wheel   is  fixed 


Fig.  3.— Worthington  Steam  Pump  (p.  1366). 

on  a  shaft  rotated  by  a  belt  running  over  a  pulley.  In  a  side-suction 
pump  the  water  enters  on  either  side  at  the  center  of  the  wheel  and 
IS  forced  out  at  the  periphery  through  a  tangential  outlet  from  the  casing. 
Centrifugal  pumps  are  economical  in   raising   water   against   low  heads. 


Fig.  4. — Centrifugal  Pump. 

say  up  to  30  ft.,  more  of  less;   reciprocating  pumps  are  more  efficient  for 
high  heads. 

Rotary  Pumps  arc  operated  by  two  rotating  valves  in  "gear,"  each 
moving  tightly  in  an  outer  casing. 

Duty  of  Pumps. — ^The  duty  of  a  pump  was  formerly  tested  and  measured 
by  the  number  of  foot-pounds  of  work  which  it  was  capable  of  performing 
from  the  combustion  of  100  pounds  of  coal  used.  As  the  quality  of  coal 
varies  a  new  standard  was  proposed,  in  1891,  by  a  Committee  of  the  A.  S. 
C.  E.:* 

_.       ^  No.  of  foot-pounds  of  work  done  X 1  OOP  OOP 
Number  of  heat  units  consumed 

This  would  be  equivalent  to  the  old  rule,  provided  100  lbs.  of  coal  will 

generate  1  000  000  (lOOX  10  000)  heat  units  (see  page  1362)  to  the  water 
1  the  boiler,  a  result  which  can  generally  be  obtained. 

*^  Transactions  A.  S.  C.  E.,  Vol.  XII..  page  58ftedbyGoOgle 


1808  09.— SrEAM  AND  GAS  POWER.  ^ 

D.— HEAT  (INTERNAL-COMBUSTION)  ENGINES. 

TESTS  OF  INTERNAL-COMBUSTION  ENOINES  ON  ALCOHOL  FUEL. 

(Digest  of  Bulletin  101.  U.  S.  Dept.  of  Agric.) 

Introduction. — Recently  in  this  country  great  interest  has  developed  ta 
the  P5>ssibilities  of  alcohol  as  fuel,  and  the  question  of  its  being  used  as  a 
substitute  for  the  pertoleum  fuels  will  become  of  increasing  importance  as 
time  goes  on.  The  supply  of  crude  oil  to  be  obtained  in  the  United  States 
must  ultimately  diminish,  and  the  history  of  the  past  indicates  that  a  con- 
stant increase  in  price  of  kerosene  and  gasoline  may  ultimately  be  expected. 
On  the  other  hand,  it  is  not  improbable  that  the  price  of  alcohol  may  fall, 
so  that  as  regards  cost  alcohol  may  be  used  advantageously  in  comparison 
with  the  petroleum  oils. 

Specific  objects  of  the  invettigatloa. — First,  to  determine  whether  the 
gasohne  and  kerosene  engines  at  present  on  the  American  market  can  run 
on  alcohol  as  fuel:  the  manipulation  to  be  followed  in  making  the  ensines 
run  on  alcohol;  tne  measurement  of  the  relative  maximum  powers  of  the 
engines  when  using  alcohol  and  the  fuels  for  which  they  were  originaUy 
made;  and  the  relative  consumptions  of  the  different  fuels.  Second,  to 
determine  as  far  as  possible  the  improvements  which  might  be  desirable  in 
the  design  of  engines  manufactured  especially  for  alcohol. 

Ontiine  of  the  ground  covered  by  the  tests. —  The  engines  used,  and 
range  of  tests,  were: 

No.  1.  Gasoline  engine,  16  h.  p.  at  280  rev.  per  min.;  2  cyl.,  stngle-acting, 
vertical,  4  cycle,  6i*  bore,  10"  stroke.  16  tests  reported,  giving 
consumption  of  alcohol  and  gasoline  tmder  different  brake  loads 
and  with  different  initial  compressions.  Lowest  consumptions  ob- 
tained were  0.71  lb.  (0.12  gal.)  ofgasoline  and  1.12  lb.  (O.iegal.) 
of  alcohol  per  brake  n.  p.  hour.  Tne  highest  working  m.  e.  p.  ob- 
tained was  about  00  lbs.  with  both  gasoline  and  alcohol,  but  at  best 
consumption  the  m.  e.  p.  were  considerably  lower 

No.  2.  Gasoline  engine,  6  h.  p.  at  800  rev.  per  min.;  1  cyl.,  water-cooled, 
horizontal,  4  cycle,  by  bore,  V  stroke.  24  tests  with  gasoline  and 
30  with  alcohol.  Highest  mechanical  efficiencies  were  86%  for 
gasoline  and  90%  for  alcohol. 

No.  3.  Gasoline  engine,  6  h.  p.  at  340  rev.  per  min.;  1  cyl.,  horizontal.  4  cycle. 
6i'  bore,  10*  stroke.  18  tests  with  gasoline  and  10  with  alcoboL 
Best  consumption  with  gaosline  was  0.86  lb.  (014  gal.)  per  brake 
h.  p.  hour;  and  with  alcohol,  at  320  r.  p.  m.,  1.26  lb.  (0.18  gal.). 

No.  4.  Gasoline  engine,  6  h.  p.  at  360  r.  p.  m..  1  cyl.,  vert.,  4  cycle,  6*  bore. 
8^^  stroke.  1 1  tests  on  gasoline  and  2e  on  alcohol ;  and  also  the  effect 
of  heating  the  air  in  advance  of  its  entrance  to  the  carburetter- 
Best  alcohol  consumption  was  1.13  lb.  (0.17  gal.)  per  brake  h.  p 
hour;  and  with  air  entering  the  carburetter  heated  to  126®  F..  the 
engine  would  self-ignite,  the  m.  e.  p.  at  best  consumption  being 
93  lbs. 

No.  6.  Kerosene  engine,  6  h.  p.  at  360  r.  p.  m.,  1  cyl^  horizontal,  3  circle  with 
crank  case  compression,  cyl.  dia.  V  with  8*  stroke.  The  engine  has 
no  carburetter,  but  is  fitted  with  a  separate  vaporizing  chamber. 
Oil  is  supplied  to  a  pump  on  top  of  the  engine,  which  deUvors  it 
directly  through  a  pipe  to  the  vaporizer  lip.  and  has  a  hand- 
operated  handle  to  deliver  oil  in  starting.  Four  tests  were  made 
with  kerosene  and  6  with  alcohol.  The  best  consumption  with  kero- 
sene was  0.98  lb.  (0.16  gal),  and  with  akohol  1.60  lb.  (0.38  ffal). 

No.  6.  Automobile  gasoline  engine,  40  h.  p.  at  900  r.  p.  m.,  4  cvcle.  4  cylin- 
der, single  acting,  vertical,  4|'  bore,  bl"  stroke.    All  valves  an 
cam  operated  and  the  carburetter  is  of  the  constant  level  type,  i 
Two  tests  each  were  made  with  gasoline  and  alcohol.  The  result  of  I 
these  tests  is  as  follows:  C^ r\r\ci\o 

Digitized  by  VjOOvIC  I 


TESTS  OF  HEAT  ENGINES— ALCOHOL  FUEL, 


1860 


Brake  Load. 

Revo- 

lUttOQS 

Fuel  oontumptlon 

No. 

Kind  Of 
Fad. 

Brake 
horse- 

Dura- 
tion of 

Vacuum 

of 

m  car- 

Test 

W 

to. 

ir-» 

per 
min- 
ute. 

power. 

Tew. 

Per 
Hour 

Per  Hone> 
Power  Hour 

buretter. 

Uu. 

Lte. 

Lte. 

MinSec 

Lb9. 

Lbi. 

Oalion, 

Inch,  of 

153 

QMoUne 

215 

25 

190 

660 

26.8 

2  19 

24.2 

0.93 

0.16 

154 

...do... 

200 

22 

178 

780 

29.2 

8    0 

29.9 

1.02 

.17 

toX 

155 

Alcohol 

218 

24 

194 

680 

27.7 

10     0 

37.9 

1.37 

.20 

toll 

15« 

...do... 

220 

26 

194 

670 

27.3 

19     0 

39.2 

1.44 

.21 

1 

in  which  TV— tv  is  the  force  used  in  computing  the  brake  hone- 
power. 

No.  7.  Automobile  gasoline  engine,  40  h.  p.  at  (MM)  r.  p.  m..  4  cycle,  4  cylin- 
der. 41'  bore,  6A'  stroke.  Twelve  tests  with  gasoline  and  7  with 
alcohol.  The  best  consumption  with  gasoline  was  0.69  lb.  (0. 13  gal.) 
per  brake  h.  p.  hour;  with  alcohol  1.80  lb.  (0.10  gal.). 

No.  8.  Boat  gasoline  engine,  2  h.  p.  at  700  r.  p.  m..  1  cyl..  vertical,  3  cycle, 
4' bore,  4'  stroke.  Ten  tests  with  gasoline  and  7  with  alcohol. 
Best  consumption  on  gasoline  was  1.86  lb.  (0.28  gal.)  per  brake  h.  p. 
hour;  and  with  alcohol  2.62  lb.  (0.37  gal.). 

Coaclosioos. — ^The  following  conclusions  are  drawn  as  a  result  of  the 
investigations: 

(1)  Any  gasoline  engine  of  the  ordinary  tyi)es  can  be  ran  on  alcohol  fuel 
without  any  material  change  in  the  construction  of  the  engine.  The  onhr 
difficulties  likely  to  be  encountered  are  in  starting  and  in  supplying  a  suffi- 
cient quantity  of  fuel,  a  quantity  which  must  be  considerably  greater  than 
the  quantity  of  gasoline  required. 

(2)  When  an  engine  is  run  on  alcohol  its  operation  is  more  noiseless  than 
when  run  on  gasoline,  its  maximum  power  is  usually  materially  higher  than 
it  is  on  gasolme  and  there  is  no  danger  of  any  injurious  hammering  with 
alcohol  such  as  may  occur  with  gasolme. 

(8)  For  automobile  air-cooled  engines  alcohol  seems  to  be  especially 
idapted  as  a  fuel,  since  the  temperature  of  the  engine  cvlinder  may  rise 
tniKm  higher  before  auto-ignition  takes  place  than  is  possible  with  gasoline 
fuel;  and  if  auto-ignition  of  the  alcohol  fuel  does  occur  no  injurious  hammer- 
ins  can  result. 

(4)  The  consumption  of  fuel  in  lbs.  per  brake  H.  P.,  whether  the  fuel  is 
j^asoline  or  alcohol,  depends  chiefly  upon  the  H.  P.  at  which  the  engine  is 
3eing  run  and  upon  the  settina  of  the  fuel  supply  valve.  It  is  easily  possible 
'or  the  fuel  consumption  per  H.  P.  hour  to  be  increased  to  double  the  best 
/alue,  either  by  running  the  engine  on  a  load  below  its  full  power  or  by  a 
ooor  setting  of  the  fuel  supply  valve. 

(6)  These  investigations  also  showed  that  the  fuel  consumption  was 
lifected  by  the  time  of  ignition,  by  the  speed,  and  by  the  initial  compres- 
sion of  the  fuel  charge.  No  tests  were  made  to  determine  the  maximum 
x^ssible  change  in  fuel  consumption  that  could  be  produced  by  rh^^pgrng 
he  time  of  ignition,  but  when  near  the  best  fuel  consumption  it  was  shown 
o  be  important  to  nave  an  early  ignition.  So  far  as  tested  the  alcohol  fuel 
xmsumption  was  better  at  low  than  at  high  speeds.  So  far  as  investigated, 
acreasing  the  initial  compression  from  70  to  125  lbs.  produced  only  a  very 
light  improvement  in  the  consumption  of  alcohol. 

(6)  It  is  probable  that  for  any  given  engine  the  fuel  consumption  is 
Iso  anected  by  the  quantity  and  temp,  of  cooling  water  used  and  the  nature 
i  the  cooling  syttem,  by  the  type  of  ignition  apparatus,  bv  the  quantity 
nd  quality  of  lubricating  oil.  by  the  temp,  and  humidity  of  the  atmosphere. 
nd  by  the  initial  temp,  of  the  fuel. 

(7)  It  seems  probable  that  all  well-constructed  engines  of  the  same  sixe 
rill  have  approximately  the  same  fuel  consumption  when  working  under 
he  most  advantageous  conditions. 


1370 


99.— STEAM  AND  GAS  POWER. 


(8)  With  any  good  small  stationary  engine  as  small  a  fuel  consamptkm 
as  0.70  lb.  of  gasoline,  or  1.16  lbs.  of  alcohol  per  brake  H.  P.  hour  majr 
reasonably  be  expected  under  favorable  conditions.  These  valxHss  corres- 
pond to  0.118  and  0.170  gallon  respectively,  or  0.05  pint  of  gasoline  and  1 JS 
pints  of  alcohol.  Based  on  the  high  calorinc  values  of  21.120  British  ther- 
mal units  per  pound  of  gasoline  and  ll.SSOper  pound  of  alcohol,  these  coo* 
sumptions  represent  thermal  efficiencies  of  17.2%  for  gasoline  and  18.5% 
for  alcohol. 

But  calculated  on  the  basis  of  the  low  calorific  values  of  10.660  B.  T.  U. 
per  pound  of  gasoline  and  10.620  for  alcohol,  the  thermal  efficiencies 
become  18.5  for  the  former  fuel  and  20.7  for  alcohol.  The  ratio  of  the  higfa 
calorific  values  used  above  is.  gasoline  to  alcohol.  1.78.  The  corre^xmdic^ 
ratio  of  the  low  calorific  values  is  1.85.  The  ratio  of  the  consamptioos 
mentioned  above  is.  alcohol  to  gasoline.  1.66  by  weight,  or  1.44  by  volume 

Properties  of  Uquid  Fuels. — All  liqxiid  fuels  available  for  c<»unercia] 
use  are  complicated  mixtures  of  many  different  chemical  substances,  and 
hence  are  always  liable  to  more  or  less  change  in  chemical  compositioci. 
Gasoline  and  kerosene  are  most  easily  examined  by  their  specific  gravities. 
but  since  each  is  a  mixture  of  numerous  lighter  and  heavier  oils,  a  definite 
constant  density  is  not  a  guarantee  that  the  composition  may  xK>t  change 
sufficiently  to  affect  the  action  of  the  fuel  in  an  engine. 

Commercially  pure  grain  or  ethyl  alcohol  is  sensibly  pure  except  for  the 
water  which  may  be  mixed  with  it.  In  this  country  alcohol  is  descnbed 
according  to  its  strength  by  stating  the  percentage  of  absolutely  pure  akoboU 
bv  volume,  which  exists  in  the  mixture  of  alcohol  and  water.  Thus.  9C% 
alcohol  contains  90%  alcohol  and  10%  water  by  separate  voltm^.  Since 
alcohol  is  lighter  than  water,  the  stronger  the  alcohol  the  lighter  the  specific 
gravity,  and  90%  alcohol  contains  less  than  90%  of  alcohol  by  weigfat. 
Moreover,  since  when  pure  alcohol  and  water  are  mLxed  the  volume  oi  the 
mixtiu^  is  less  than  the  SMm  of  the  volumes  of  the  water  and  alcohol  before 
mixing,  90%  alcohol  contains  more  than  10%  of  water  by  volume.  A 
U.  S.  "proof"  gallon  contains  60%  alcohol  by  volume,  the  remainder  oC  the 
mixture  being  water;  hence  a  quantity  oi  alcohol  when  stated  in  proof 
gallons  is  expressed  by  a  number  just  twice  as  large  as  it  would  be  if  stated 
in  gallons  of  100%  alcohol. 

The  denatured  alcohol  which  may  be  used  in  engines  in  the  U.  S.  mivt 
be  prepared  as  follows,  according  to  the  regulations  of  the  Commissioner  of 
Internal  Revenue:  To  100  volumes  of  ethyl  or  grain  akohol  of  a  strength 
not  less  than  90%  there  must  be  added  either  10  volumes  of  methyl  or  wood 
alcohol  and  i  o(  1  volume  ol  benzine  or  2  volumes  of  methyl  alcohol  and 
i  ot  1  volume  of  pyridin  bases.  The  substances  added  to  the  grain  alcohol 
will  probably  not  be  of  uniform  quality,  and  hence  there  will  be  some  van- 
ability  in  the  properties  of  the  denatured  alcohol  which  will  aScct  iis  use  as 
a  fuel.    The  following  figures  are  fair  average  values  of  the  different  fneb: 


Substance. 


Spec. 
Grav. 


Lbs.^ 

per 

Gallon 


Substance. 


Spec. 
Grav. 


Lbs. 
k^alkm 


Gasoline.. 
Kerosene . 


0.71 
0  80 


6.9  f  96%  ethyl  alcohol. 
6.7   I  90%  ethyl  alcohol. 


0  82 
0.83 


0  8 
6.9 


The  two  most  important  properties  of  a  liquid  fuel,  which  determine  its 
availability  or  adaptability  for  use  in  an  engine,  are  its  heat  of  combustioa 
and  its  volatility. 

Heat  of  Coinbustioii. — ^Por  the  various  petroleum  oils  the  heat  of  com- 
bustion varies  between  19  000  and  21  000  B.  T.  U.  per  lb.  of  ofl.  and  30  000 
is  an  average  value;   for  pure  alcohol,  about  12  700  B.  T.  U.  per  lb. 

All  liquid  fuels  contain  a  considerable  proportion  of  hydrogen,  which 
when  burned  forms  water  in  the  condition  of  steam.  When  the  fxael  is 
burned  in  a  calorimeter  this  steam  is  condensed  by  the  cold  water  sumnmd- 
ing  the  calorimeter  and  in  this  condensation  contributes  a  considamble  amotrot 
of  heat  to  the  total  amount  absorbed  by  the  cold  water.  When  a  fuel  is 
burned   in   an   internal-combustion   engme  the    products    of  combustioa 


PROPERTIES  OF  UQUID  FUELS,  1871 

tlways  leave  the  engine  cylinder  at  a  temperature  much  above  the  boiling 
>oint  of  water;  hence  the  engine  is  unable  to  make  use  of  the  latent  heat  of 
condensation  of  the  steam  formed  in  combustion,  although  this  latent  heat 
3  included  in  the  heat  measured  by  the  calorimeter.  On  this  account  it  is 
rxistomary,  in  comparing  fuels  used  in  explosion  engines,  to  calculate  the 
teat  of  condensation  of  the  steam  in  the  products  of  combustion  and  to 
leduct  this  amoimt  from  the  heat  of  combustion  as  meastired  in  the  calorim- 
:^er.  giving  what  is  called  the  low  value  of  the  heat  of  combustion.  Cor- 
■espondingly.  the  heat  as  measured  by  the  ciUorimeter  is  called  the  high 
ralue  of  the  heat  of  combustion. 

Air  Necessary  for  Combnstioii^— When  a  fuel  has  a  definite  chemical 
composition,  the  air  necessary  for  its  combustion  can  be  exactly  calculated. 
-ience,  this  calculation  can  be  made  for  pure  methyl  or  ethyl  alcohol,  but 
tan  be  made  only  approximately  for  a  fuel  like  Kasoiine,  which  is  a  mixture 
n  variable  proportions  of  a  laige  number  of  dinerent  chemical  substances. 
dy  the  formula  for  ethyl  alcohol.  C^HkOH,  its  molecular  weight  is  46; 
rarbon  24  (-12X2)+ hydrogen  6  (- 1  X6)+oxygen  16  (- 16X  l)-46.  For 
he  complete  combustion  of  1  molecule  of  alcohol  the  two  atoms  of  carbon 
equire  4  atoms  of  oxygen  to  form  carbon  dioxide,  and  the  6  atoms  of  hy- 
Lrogen  require  2  atoms  of  oxygen,  in  addition  to  the  1  atom  present,  to 
orm  steam,  thus  making  6  atoms  of  oxygen  in  all  to  be  supplied.  The 
veight  of  the  6  atoms  is  6  X  16—  96.  Hence  complete  combustion  of  1  lb.  of 
72  nt  OH  requires  96-1-46—  2.086  Ibe.  of  oxygen.  In  one  pound  of  pure  dry 
iir  there  is  0.230  lb.  of  oxygen,  so  that  the  combustion  of  1  lb.  of  Ct  Hn  OH 
equires  2.086-1-0.230-9.06  lbs.  of  air.  or  about  119  cu.  ft.  of  pure  air  at  a 
^mp.  of  60°  and  at  sea  level.  If  the  alcohol  contains  water,  1  lb.  of  the 
tlcotiol-water  mixture  requires  less  air  than  that  stated.  If  the  air  is  moist, 
L  lb.  of  it  contains  slightly  less  than  0.230  lb.  of  oxygen  and  hence  more  air 
vould  be  required.*  In  an  actual  engine  the  amount  of  air  is  proportioned  to 
he  amount  of  vapor,  not  by  any  exact  measurement  of  either,  but  by  trial 
;o  secure  either  the  best  results  in  maximum  power  or  in  minimum  fuel 
tonsumption. 

VaporizaHon  of  Fuel. — ^Before  any  liquid  fuel  can  be  used  in  the  usual 
bnn  of  explosion  engine,  it  must  be  vaporized,  and  this  vapor  must  be 
nixed  with  air  in  proper  proportions.  Thus  the  preparation  of  the  com- 
Mistible  mixttue  involves  three  steps;  First,  vaporization  of  the  fuel; 
econd.  mixttire  of  the  fuel  vapor  and  air;  and.  third,  the  proper  adjust- 
nent  of  the  proportions  of  fuel  and  air. 

The  differences  in  the  devices  used  in  engines  to  accomplish  these  objects 
tonstitute  the  widest  variations  in  the  detailed  design  of  existing  engines. 
j\  some  of  these  devices  the  fuel  is  boiled  in  a  separate  chamber,  called  a 
raporizer.  from  which  the  vapor  flows  into  a  stream  of  air  entering  the  en- 
:ine.  the  amount  of  vapor  being  regulated  by  a  valve  just  as  in  the  case  of 
in  engine  using  illuminating  or  producer  gas. 

In  another  type  of  vaporizer  the  fuel  is  dropped  on  a  hot  plate  over 
rhich  the  air  flows,  the  proportion  of  fuel  being  regulated  by  the  amount 
if  liquid  fuel  forced  agamst  the  plate.  Kerosene  requires  a  high  heat  to 
raporize  it  completely,  since  its  boiling  point  is  high,  and  hence  it  is  much 
laed  with  vaporizers  of  the  hot-plate  type.  Alcohol  will  work  satisfactorily 
pith  a  vaporizer  of  this  type  if  the  temperature  of  the  hot  plate  is  properly 
egulated. 

Gasoline  is  easily  vaporized  at  ordinary  atmospheric  temperatures  and 
lence  requires  no  hot  plate  or  heated  vaporizing  chamber.  Usually  the 
iquid  gasoline  is  admitted  directly  into  the  air  entering  the  engine  through 
i  device  known  as  the  carbureter,  which  is  intended  to  regulate  the  propor- 
ion  of  fuel  and  to  spray  it  uniformly  through  the  mass  ofair  so  that  as  the 
iquid  spray  turns  into  vapor  it  will  produce  a  homogeneous  mixture  of  air 
tnd  vapor.    Alcohol  can  also  be  used  in  a  gasoline  carbureter. 

As  with  all  substances  which  liquefy  at  ordinary  temperatures,  there  is 
I  definite  limit  to  the  amount  of  alcohol  vapor  which  can  exist  in  a  cubic 
bot  of  space  at  any  given  temperature.  Assuming  the  laws  for  perfect  gases 
x>  hold,  at  any  given  constant  temperature  the  weight  of  alcohol  vapor 
present  in  a  cubic  foot  of  space  is  proportional  to  its  vapor  pressure  and  is 
isually  measured  or  represented  by  this  vapor  pressure.     This  may  be 

*  Approx.  results  calculated  in  a  similar  manner  forti^^<^^troleum 
ucls  may  be  found  in  Sorel's  Alcohol  Engines. 


1872  m.—STEAM  AND  CAS  POWER. 

illustrated  by  ima^rining  a  cylinder  provided  with  a  tight  piston  and  conta:^ 
ing  alcohol  vapor  at  a  pressure  corresponding  to  10  millimeters  of  merctsr 
and  kept  constantly  throughout  the  experiment  at  a  temperature  of  70^  F 
If  now  the  vapor  is  compressed  by  the  piston  until  its  volume  is  reducec 
one-half,  the  vapor  pressure  will  rise  to  20,  there  being  of  course  twice  as 
much  vapor  per  cubic  foot  of  space  occupied  as  there  was  originally.  If  tk 
volume  is  again  halved  the  pressure  will  rise  to  40.  But  if  the  compresBce 
is  continued  until  the  vapor  pressure  rises  to  47  millimetersof  mercury  achuge 
takes  place  in  the  action.  The  pressure  will  not  rise  above  47  if  the  teffi^ 
is  kept  at  70^.  If  the  piston  is  moved  a  further  amount,  so  as  to  reduce  tk 
voliune  still  more,  part  of  the  alcohol  vapor  will  be  condensed  into  liquid, 
but  the  vapor  pressure  will  remain  the  same  and  the  amount  of  v^mt  per 
cu.  ft.  of  spcu^e  will  remain  constant.  Hence  there  is  a  definite  noaxxicna 
amount  of^  alcohol  vapor  which  can  exist  in  a  cu.  ft.  of  space  at  any  gives 
temp.  It  is  important  to  remember  that  the  space  may  contain  any  smalls 
amotmt  with  a  correspondingly  lower  vapor  pressure,  but  can  not  oontaia 
a  greater  amotmt  than  the  quantity  corresponding  to  the  saturate  sutc 

The  vapor  prcssiuie  of  saturation  increases  rapidly  with  the  temp.,  sod 
the  values  as  determined  by  experiment  for  alcohol  and  some  other  sab- 
stances  at  various  temperatures  are  given  in  Table  13.  next  page. 

When  different  gases  or  vapors  exist  simultaneously  in  the  same  mce 
if  they  have  no  chemical  action  on  each  other,  each  one  acts  by  itself  yjR 
as  though  no  other  gas  were  present.  Thus  if  air  were  also  present  in  th< 
cylinder  used  in  the  illustration  above,  the  oxygen  and  nitrogen  'wotild  est 
intcrefere  at  all  with  the  action  of  the  alcohol  vapor.  But  it  is  to  be  noten 
that  in  such  a  case  the  pressure  as  measured  by  the  barometer  column  o? 
pressure  gauge  would  be  the  sum  of  the  ser>arate  pressures  due  to  the  air 
and  due  to  the  alcohol  vapor.  If  moisture  were  presnet  it  would  profaaUy 
have  some  effect  on  the  alcohol- vapor  pressure,  because  water  and  alcohc- 
have  certain  affinity  for  each  other.  On  pa^e  1371  it  was  shown  that  in  a 
mixture  of  alcohol  vapor  and  air  the  proportion  for  complete  combustion  ct 
the  alcohol  should  be  9.06  lbs.  of  air  to  1  lb.  of  alcohol.  If  less  air  is  presect 
the  alcohol  cannot  be  completely  consumed  and  the  excess  passes  off  as 
alcohol  or  some  substance  formed  by  the  partial  decomposition  o£  tbe 
alcohol  molecule.  If  more  air  is  present  than  the  required  amount  no  harm 
is  done  provided  the  excess  is  not  too  great,  and  it  is  in  fact  better  so  far 
as  economical  consumption  of  fuel  is  concerned  to  have  some  excess  of  air 
present. 

The  vapor  pressure  of  alcohol  vapor  in  the  theoreticallv  best  mixture  o£ 
it  with  air  may  be  calculated  as  follows:  By  Avagadro's  law.  for  the  saase 
pressiu^  and  temp.,  the  densities  of  gases  are  proportional  to  their  nwlecokx 
weights.  Since  the  molecular  weight  of  hydrogen  is  2.  the  density  of  ethyl 
alcohol  vapor  is  46  +  2,  or  23,  compared  with  hydrogen.  Hence  1  lb-  of 
alcohol  vapor  occupying  any  stated  volume  has  a  vapor  pressure  equal  to 

rr  of  the  vapor  pressure  of  1  lb.  of  hydrogen  occupying  the  same  volume. 

Likewise,  since  the  density  of  air  is  14.44  compared  with  hydrogen.  906  Ibs^ 
of  air  occupying  the  same  stated  volume  has  a  vapor  pressure  equal  to 

0  06 

-  '    .  of  the  vapor  pressure  of  1  lb.  of  hydrogen  occupying  the  same  vohixne- 

Thcrefore  the  relative  vapor  pressures  of  the  alcohol  vapor  and  air  are  as 

1  Q  OR 

is  and  ^^.  oras  0.0435  and  0.627,  respectively.     But  0.0435-1-0.637- 

496 
0.670.    Hence,  of  the  total  vapor  pressure  produced  by  the  mixture,  -r^j^ 

627 
or  6.5%,  is  due  to  alcohol  vapor,  and  ;n;^,  or  93.5%,  is  due  to  the  air. 

070 

If  the  mixture  is  tmder  the  ordinary  atmospheric  pressure  of  14.7  ll» 
per  sq.  in.,  or  imder  760  mm.  of  mercupr,  the  vapor  pressure  of  the  akdbol 
m  the  combustible  mixture  is  0.065  times  14.7  or  0,956  lb.  per  sq.  in^  or 
0.065  times  760,  or  49.4  mm.  of  mercury.  Similarly,  the  pressure  of  the 
air  is  0.935  times  14.7,  or  13.74  lbs.  per  sq.  in.,  or  0.935  times  760,  or  711  mm 
of  mercury. 

Table  13,  following,  contains  the  vapor  pressure  of  saturation,  in  vase 
or  mercury,  for  pure  ethyl  or  grain  alcohol,  pure  methyl  or  wood  alcohol,  • 
sample  of  gasoline,  and  water,  at  various  tcmperattires: 


PROPERTIES  OF  UQUID  FUELS,  1878 

18. — ^Vapor  Prbssurb  of  Saturation  for  Various  Liquids.* 


Vapor  PretBure  of  Saturation  In  MUUmeters  of  Mercury 

Temperature. 

Pure  Ethyl 

Pure  Methyl 

Water. 

QasoUne. 

Alcohol. 

Alcohol. 

•C. 

«F. 

0 

32 

12 

30 

99 

5 

41 

17 

40 

115 

10 

50 

24 

54 

133 

15 

59 

82 

71 

154 

20 

68 

44 

94 

179 

25 

77 

59 

123 

210 

30 

86 

78 

159 

251 

85 

96 

103 

204 

301 

40 

104 

184 

259 

360 

45 

113 

172 

327 

422 

50 

122 

220 

409 

493 

55 

131 

279 

508 

117 

561 

50 

140 

350 

624 

149 

648 

55 

149 

437 

761 

187 

739 

*  The  values  for  ethyl  and  methyl  alcohol  are  taken  from  the  Smith- 
sonian physical  tables,  the  values  for  water  from  the  steam  tables  in  general 
use,  and  tne  values  for  gasoline,  which  were  based  upon  tests  of  a  sample  of 
French  commercial  gasoline,  are  taken  from  Sorel's  book  on  alcohol  engines. 
Since  gasoline  is  a  variable  substance,  the  values  given  for  it  are  to  be  con- 
sidered as  only  generally  representative. 

From  the  above  table  it  is  evident  that  ethyl  alcohol  can  have  a  vapor 
pressure  of  49  mm.  only  if  its  temp,  is  72**  F.  or  higher.  Hence,  a  mixture 
of  air  and  the  alcohol  vapor  in  the  theoretical  proportions  for  perfect  com- 
bustion can  not  exist  at  a  temp,  below  72^  P.  A  combustible  mixture  with 
some  excess  of  air  can  exist  at  lower  temperatures,  as  also  a  mixture  in  which 
a  part  of  the  alcohol  is  not  in  the  form  of  vapor,  but  is  carried  with  the  a^ 
mechanically  in  the  liquid  form  as  a  spray  or  fog. 

The  table  shows  that  methyl  alconOl  vaporizes  much  more  readily  than 
ethyl  alcohol,  and  gasoline  much  more  readily  than  either.  A  mixture  of 
different  fuels  will  usually  have  a  higher  vapor  pressure  than  either  of  the 
separate  ingredients  unless  one  is  present  in  too  small  a  quantity  to  produce 
saturation. 

Since  alcohol,  as  used  commercially,  is  always  mixed  with  some  propor- 
tion of  water,  a  combustible  mixttire  formed  by  the  vaporization  of  such 
alcohol  may  become  sattirated  with  the  water  vapor  before  it  is  saturated 
with  alcohol,  and  this  may  retard  the  complete  vaporization  of  the  alcohol. 
Such  a  state  is  more  likely  to  occur  if  the  air  originally  contains  a  consider- 
able amount  of  water  vapor — that  is,  if  the  relative  humidity  is  high.  La 
such  a  case  a  temp,  higher  than  72^  would  be  necessary  to  maintain  the 
required  amount  ot  alcohol  vapor  in  the  mixture. 

In  order  that  alcohol  may  change  from  a  liquid  to  a  vapor  it  must 
receive  a  large  amount  of  heat  either  from  the  air  with  which  it  mixes  or 
from  the  metal  parts  of  the  carbm^tter  with  which  it  comes  in  contact. 
The  hotter  these  parts  the  more  qxiickly  the  alcohol  can  absorb  the  re<^uisite 
airount  of  heat.  But  if  the  air  is  too  hot  there  is  danger  that  the  mixture 
of  air  and  alcohol  vapor  produced  may  be  too  rich  in  alcohol  and  some  of 
the  vapor  m\ist  remain  unbumed.  Still,  if  the  air  be  moist,  or  the  alcohol 
contain  water,  or  the  time  allowed  for  vaporization  be  too  short,  the  temp, 
of  the  air  must  be  higher  than  72°  to  form  a  proper  explosive  mixture. 

Air  at  any  temp,  will  take  up  some  alcohol  vapor,  and  the  higher  the 
temp,  the  quicker  it  will  take  up  the  amount  necessary  for  the  best  explo- 
sive mixture.  In  the  case  of  incomplete  vaporization,  some  of  the  fuel  may 
be  carried  along  as  spray,  which  may  or  may  not  be  vaporized  in  the  cylinder 
on  the  compression  stroke.  If  not,  it  certainly  will  be  vaporized  after  the 
explosion  of  the  rest.  It  would  seem  desirable,  therefore,  to  heat  consider- 
ably the  air  supplied  to  an  alcohol  carburetter.  But  too  much  heating  of 
the  air  will  bring  about  a  bad  effect  on  the  engine,  because  it  will  make  the 
charge  hotter  at  the  end  of  compression,  and  thxis  decrease  the  weight  <» 


1874  M.— SrEi4M  AND  GAS  POWER. 

the  charge  in  the  cylinder.  The  h.  p.  of  the  en^e,  other  thingi  beks 
equal,  w3l  be  decreased  in  direct  proportion  as  the  density  of  the  chains 
lowered  by  this  heating,  so  that  heating  of  the  air  before  carburettifig  t> 
good  for  complete  vaporisation,  but  bad  if  carried  too  far  in  its  e^cts  oc 
power  reduction. 

Methods  of  Testing. — Bach  engine  tested  was  fitted  wiUi  a  suitable 
brake  for  absorbing  the  power  developed.  No.  1  wasprovided  with  s 
special  water-cooled  pulley,  attached  to  the  fly  wheel.  The  pulley  had  sa 
internal  rim  for  retaining  the  cooling  water  and  an  external  rim  for  retains^ 
the  brake  in  place.  The  latter  was  formed  of  wooden  blocks,  attached  to  a 
belt  whose  length  could  be  adjusted  by  a  screw.  A  wooden  arm.  connected 
to  the  belt,  rested  upon  platform  scales.  On  all  the  slow-speed  engiees 
similar  wooden  block  oand  brakes,  bearing  upon  platform  scales,  were  used- 
Each  automobile  engine  was  ntted  with  a  special  water-cooled  pulkv. 
attached  to  its  fly-wheel.  The  pulley  was  made  by  cutting  out  a  diiuc  of  r 
boiler  plate,  which  was  bolted  to  the  fly  wheel.  The  outside  face  c^  the  d^ 
was  grooved  to  receive  the  rim  of  a  standard  cast-iron  belt  pulley  ^  wide. 
The  other  edge  of  the  pulley  rim  was  fitted  to  another  ring  of  boiler  plate 
in  a  similar  manner.  Bolts  passed  from  plate  to  plate.  A  rope  break  was 
used  on  this  pulley,  and  each  end  of  the  rope  was  fastened  to  a  sprinif  scak. 
which  in  turn  was  suspended  from  the  arm  of  a  beam  pivoted  to  a  standard. 
The  other  end  of  the  beam  was  held  by  a  chain  block.  A  movement  of  the 
chain  block  increased  or  decreased  the  tension  on  the  rope.  The  rotation  of 
the  engine  tended  to  pull  one  side  tighter  than  the  other,  just  as  in  the  case 
with  a  windlass.  A  heavy  scale,  capable  of  recording  400  lbs.,  was  attached 
to  the  beam  near  its  center  and  carried  the  tight  side  of  the  rope.  The  other 
end  of  the  rope  was  attached  to  a  lighter  scale,  capable  of  recording  a 
maximum  of  24  lbs.  With  this  brake  a  200-Ib.  pull  was  registered  onthe 
heavy  scale,  with  only  8  lbs.  on  the  smaller  scale,  and  the  tension  conld  be 
quicKly  and  rapidly  varied  by  the  chain  block. 

The  speed  of  the  en£[ines  was  obtained  by  actual  counting,  usin^^  a  stop 
watch,  by  a  hand  speed  counter  and  by  a  tachometer.  Usually  the  ^leed 
was  determined  by  more  than  one  observer,  so  as  to  reduce  the  chances  of 
error. 

The  ordinary  formula  was  used  for  computing  the  brake  horse-power. 

^"^"     33.000    • 
in  which  J?— the  brake  arm  in  feet,  fT— the  brake  load  in  pounds,  and 
N— the  number  of  revolutions  per  mmute. 

On  all  the  slow-speed  engines,  indicator  cards  were  taken  not  only  for 
the  purpose  of  determining  indicated  horse-power  but  also  for  studying  the 
characteristics  of  the  combustion,  compression,  and  other  conditions  in  the 
cylinder.  For  this  use  a  new  outside  spring  indicator  was  loaned  for  these 
tests  by  the  manufacturers  of  the  indicator. 

It  was  difficult  to  determine  the  proper  mean  effective  pressure  to  use 
in  computing  indicated  horse-power,  because  successive  strokes  often  gave 
indicator  diagrams  of  verjy  different  size  and  shape.  This  was  shown  on  some 
of  the  cards  reproduced  later.  Hence  it  was  impc^sible  to  detenmne 
exactlv  the  average  mean  effective  pressure  for  a  stated  period  of  time. 
This  difficulty  was  avoided  so  far  as  possible  by  taking  a  large  ntimber  of 
cards.  When  there  were  numerous  differing  cycles  drawn  on  one  sheet, 
usually  the  planimeter  point  was  moved  aroimd  on  a  line  as  near  the  average 
of  the  different  cycles  as  could  be  determined  by  eye.  This  gave  a  sort 
of  graphical  average  which  seemed  the  best  that  could  be  done  under  the 
circumstances.  In  certain  cases,  explained  in  detail  as  they  arise,  cycles  of 
different  size  were  separately  measured  and  the  different  areas  were  used  in 
computing  the  indicated  horse  power.  No  attempt  was  made  to  measure 
the  area  of  the  lower  or  suction  loop  on  the  indicator  cards  with  the  plani- 
meter; the  mean  effective  pressure  is  based  upon  the  measured  area  of  the 
upper  loop  only. 

The  number  of  explosions  per  minute  was  determined  in  hit-axui-oUss 

Sovemed  engines  both  by  counting  the  number  of  fuel  admissions  and  abo 
y  listening  to  the  exhausts.  This  dual  method  is  necessary  because,  under 
c^i^^n  circumstances,  a  charge  may  miss  fire  and  an  explosicm  may  be 
recorded  from  observations  of  fuel  admissions  where^one  did  not  reaUr 

occur-  tizedTyVLjOOgTe 


METHODS  OF  TESTING  HEAT  ENGINES.  1875 

The  indicated  hone-power  was  computed  by  the  usual  formula, 

^^^   'Wm- 

in  which  P^mean  effective  pressure  in  lbs.  per  sq.  in.,  L>- stroke  of  piston 
in  feet,  il— area  ot  piston  m  sq.  ins.  and  A^  — number  of  explosions  per 
minute. 

The  engines  were  in  all  cases  piped  for  alcohol  fuel  and  also  for  either 
gasoline  or  kerosene,  so  that  one  could  be  switched  on  and  the  other  off  at 
any  time.  In  addition  a  third  connection  was  provided  for  the  measuring 
tanks.  Any  variation  in  the  adjtistment  of  the  engine  was  sectu«d  when 
using  the  permanent  supply  tanks  before  switching  on  the  measuring  tanks, 
and  care  was  exercised  to  insiu«  that  there  was  no  residue  between  the  valve 
and  the  engine  itself  before  measurements  were  taken. 

Two  methods  of  measuring  fxiel  were  used:  (1)  bv  noting  the  drop  in 
level  in  a  glass  gage  attached  to  a  tank;  and  (2)  by  the  use  of  a  lame  glass 
beaker  on  a  small  spring  platform  scale,  which  could  be  read  to  tenths  of  an 


Poelt  tued. — ^The  alcohol  used  in  tests  was  bought  on  competitive  bids 
as  96%  commerical  alcohol  and  cost  in  barrels  38t  cents  per  wine  gallon 
without  the  tax. 

An  ultimate  analysis  of  the  alcohol  gives  the  following  composition: 

Per  cent. 

Carbon 47.6 

Hydrogen 13.7 

Oxygen  (by  differente) 39.7 

As  received  the  alcohol  had  a  spec.  grav.  of  0.82  at  60^  P.,  corresponding 
to  about  91.1%  by  weight  or  94%  oy  volume,  according  to  the  Smithsonian 
ph3^cal  tables.  It  was  tested  in  the  chemical  laboratory  in  the  usual  way 
to  determine  the  percentage  of  alcohol  present  after  treatment  to  eliminate 
impurities,  as  follows: 

Twenty-six  grams  were  diluted  with  water,  redistilled,  and  the  amount 
of  alcohol  in  the  distillate  determined.  From  this  the  percentage  by  weight 
in  the  original  sample  was  calculated.  Using  Richard's  tables  the  result  ob- 
tained was  93.1%.  Using  Morley's  table,  published  in  the  journal  of  the 
American  Chemical  Societ3r.  October,  1904.  the  residt  obtained  was  91.4%. 
The  ultimate  analysis  indicates  a  slightly  smaller  proportion  of  alcohol, 
since  a  strength  of  91.3%  would  have  the  following  composition: 

Percent. 

Carbon 47.6 

Hydrogen 12.9 

Oxygen 39 . 6 

These  discrepancies,  illustrating  the  difficulties  of  accurate  determina- 
tions, even  with  suitable  facilities  and  skillful  observers,  show  the  impossi- 
bility of  obtakung  more  than  approximate  results  except  under  exceptionally 
favorably  circumstances. 

The  percentage  of  alcohol  found  in  a  sample  is  always  likely  to  be 
greater  when  determined  chemically  than  when  aetermined  by  the  hydrom- 
eter, because  the  presence  of  impiurities  in  the  way  of  solids  dissolved  in 
the  alcohol  or  as  any  of  the  series  of  higher  alcohols  tends  to  make  the 
spec.  grav.  of  the  sample  greater  and  hence  indicate  too  low  a  percentage 
ol  akohol. 

The  calorific  power  or  heat  of  combustion  of  the  alcohol  used  in  these 
tests  was  found  by  calorimeter  determinations  to  be  11.880  British  thermal 
units  per  pound,  high  value.  The  corresponding  low  value  is  10,620. 
*  Using  the  customary  values  of  calorific  power  of  14.500  for  carbon  and  62,000 
for  hjrdrogen.  the  high  heat  value  of  combustion  for  pure  alcohol  would  be 
by  calculation  12,950.  The  Smithsonian  physical  tables  ^ve  12,930  as  the 
value  for  pure  alcohol  on  the  authority  of  Favre  and  Silbermann,  which 
would  correspond  to  11,800  for  91.3%  alcohol. 

The  gasoline  vised  in  the  experiments,  known  as  "motor  gasoline,"  was 
bought  in  New  York  City  at  15  cents  a  gallon  by  the  barrel  and  had  a  spec. 
gray,  of  about  0.71  at  6Cr  P.    Its  ultimate  composition  was  as  follows: 

Per  cent. 

Carbon 85.0 

Hydrogen ^^4.8 

Total D,g,tized^byC^^gIe 


1876 


m.—STEAM  AND  GAS  POWER, 


Its  heat  of  combustion,  high  value,  as  detennined  by  the  caknimdtiK, 
was  21,120  B.  T.  U.  per  pound.    The  corresponding  low  valtie  is  19,660. 

Using,  as  before,  14,500  for  carbon  and  62,000  for  hydrogen,  the  cake- 
lated  high  heat  value  would  be  21,500. 

To  show  the  nature  of  the  complex  mixture  forming  the  gasoline,  150 
cubic  centimeters  was  distilled  and  collected  in  fractions  of  10  cubic  centi- 
meters each.  The  temperatures  required  for  the  distillation  of  the  suc- 
cessive fractions  are  shown  in  the  fouowing  table: 

•   14. — Pbactional  Distillation  of  Gasolinb. 


Number 

of 
Fraction. 


Temperatures 


Temperatorea. 


46  to  60 
64  to  75 
75  to  80 
80  con- 
stant 
80  to  86 
86  to  92 
92  to  97 


OF. 

114. 8tO  140.0 
147. 2to  167.0 
167. Oto  176.0 
I76ooastant 

176. Oto  186.8 
186. 8tO  197.6 
197.6  to  206.6 


•C. 

97  to  100 
100  to  104 
104  to  108 
108  to  112 
112tO  120 
120  to  126 
126  to  140 
140  to  155 


206.6  to  212. i 
212.0  to  219.2 
219. 2  to  221.4 
226.4  to  2SS.C 
2S8.C  to  248.1 
248.0  to  258  8 
258.8  to  284.1 
284.0  to  211. • 


Prom  this  table  it  appears  that  when  distillation  began  the  vapor  showed 
a  temp,  of  46*' C.  or  114.8^  P.  and  that  the  distillation  was  stopped  at  a 
temp,  of  155^  C.  or  311°  P.,  and  that  at  this  temp,  there  was  left  5  cu.  cm. 
that  had  not  yet  been  vaporized. 

The  kerosene  used  for  testing  had  a  spec.  grav.  of  about  0.800  at  60*  P. 
It  was  assumed  to  have  the  same  heat  o£  combustion  as  the  gasoHne  oaed. 

In  making  computations  on  the  results  of  the  tests,  the  following 
weights  were  used. 


Substance. 

spec. 
Grav. 

Lbs. 

per 

Gallon 

Lbs. 
per 
Pint. 

Pints 
per 
Lb. 

Subetanoe. 

spec. 
Grav. 

Lbs. 

per 

GaUoo 

Lba. 

FiBtt 

Water 

Alcohol.... 

1.000 
0.820 

8.33 
6.83 

1.04 
0.85 

0.96 
1.17 

Gasoline.. 
Kerosene.. 

0.710 
0.800 

5.91 
6.66 

0.74 
0.83 

l.M 
1.26 

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HEAT-ENGINE  FUELS.    HEAT  RESISTANCE, 


1877 


EXCERPTS  AND  REFERENCES. 

The  Loomis  WateMlas  and  Prodocer-Qas  Process  (Eng.  News,  Sept. 
2.  1901). — ^Described  and  illustrated. 

Experlmeots  on  the  Escape  of  Steam  Through  Orifices  (Bv  M.  Rateau." 
aper.  Inter.  Eng.  Cong,  at  Glascow;  Eng.  News.  Sept.  19,  IQOI). — Sketch 
f  apparatus  used  in  the  experiments;  and  diagram  ulustrating  the  experi- 
ments. 

Heat  Resistance,  the  Reclorocal  of  Heat  Conductivity  (Eng.  News. 
)cc.  4.  1<M)2). — Includes  the  following  table: 

Hbat  Conducting  and  Rbsistino  Valubs  op  Difvbrbnt 
Insulating  Matbrials. 


NJO. 

Insulated  Biaterial. 

(Conductance 

B.T.U.  per 

sq.  ft.  per  day 

per  degree 

of  difference 

tem^ture. 

Coeffi- 
cient of 
heat, 
resist- 
ance. 

C* 

1 

l-in.  oak  board,  1-in.  lampblack.  J-in.  pine  b'd 
(ordinary  family  refrigerator) 

6.7 

4.89 

4.26 

4.6 

3.02 

3.38 
3.90 
2.10 

4.28 

8.71 

3.32 

\fo 

2.10 

1.20 
0.90 
1.70 
3.30 

2.70 

2.52 

2.48 

4.21 

2 

f -in.  board,  1-in.  pitch,  l-in.  board 

4.91 

8 

|-in.  board,  2-in.  pitch,  t-in.  board 

6.06 

4 

l-in.  board,  paper,  l-in.  mineral  wool,  paper, 
l-in.  board 

6.22 

6 

l-in.  board,  paper,  2i-in.  mineral  wool,  paper, 
|-in.  board 

0.08 

6 

l-in.  board,  paper,  2-in.  calcined  pumice.  |-in. 
board 

7.10 

7 

Same  as  above,  when  wet 

0.15 

8 
9 

l-in.  board,  paper,  3-in.  sheet  cork,  |-in.  board . 
Two  l-in.  boards,  paper,  solid,  no  air  space, 
paper,  two  |-in .  boards 

11.43 
6.01 

10 

Two  l-in.  boards,  paper,  l-in.  air  space,  paper, 
two  |-in.  boards 

0.47 

a 

Two  l-in.  boards,  paper,  l-in.  hair  felt,  paper, 
two  |-in.  boards 

7.28 

12 

Two  l-in.  boards,  paper,  8-in.  mill  shavings, 
paper,  two  |-in.  boards 

17.78 

13 

The  same  slishtlv  moist.. 

13  33 

14 

The  same,  damp 

11.48 

15 

Two  l-in.  boaros,  paper,  3-in.  air  space,  4-in. 
sheet  cork,  oaper.  t'wo  l-in  r  boards , . , 

20.00 

16 

Same,  with  6-in.  sheet  cork 

26.67 

17 

Same,  with  4-in.  granulated  cork 

14.12 

18 

Same,  with  l-in.  sheet  cork 

7.27 

19 

Four  deuble  |-in.  boMds  (8 boards),  with  paper 
bet.  three  8-in.  air  spaces 

8.89 

20 

Pour  l-in.  boards,  with  3  quilts  of  l-in.  hair 
bet.  papers  separating  boards 

9.52 

21 

l-in.  board.  6|in.  patented  silicated  strawboard 
fini^ed  inside  with  thin  cemftnt ,.,,,. 

9.68 

*K-conductance  per  hour;  C"— ^• 


Eng. 


Oas  Engine  Principles  and  Management   (By  E.  W.  Roberts. 
News,  Sept.  17,  1903).— Dlustrated. 

Notes  on  the  Arrangement  and  Construction  of  Steam  Pipes  and 
Their  Connections  (By  R.  C.  Monteagle.  Paper,  Soc.  of  Nav.  Arch,  and 
Ear.  Engr.;  Eng.  News,  Nov.  26.  1903).— Illustrated. 


d  by  Google 


1878  W.— STEAM  AND  GAS  POWER. 

SUybolts,  Braces  and  Flat  Surfacei  in  Boilers  (By  R.  S.  Hale.    Papc 

Am.  Soc.  M.  £..  Dec..  1904;  Bng.  News.  Dec.  16.  1904).— Diaciaaskn  wd 
Ubles. 

The    Use   of   Soperbeated   Steam    in   Locomotive  Boilers  (By  H.  H 

Vatighan.  Paper,  Am.  Ry.  M.  M.  Assn..  June,  1905;  Bng.  News,  June  S3. 
190^. 

Modem  Problems  in  Oas  Engineering  (By  Pred  B.Wheeler.  "Wis- 
consin  Engineer."  Dec..  1906;  Bng.  News,  Jan.  11.  1906). — l^doden  tabk 
of  standam  gases.  ^ 

The  Storage  of  Coal  by  Sobmergeoce  in  Salt  Water  (Bng.  News, 
Aug.  28,  1906). 

The  Use  of   OH   Fuels   for  Locomotives    (C>>m.  Rept.  TraT.    Bogrs. 

Assn.,  Aug..  1906;  Bng.  News.  Tan.  10.  1907). — Illustrations  of  the  Booth. 
Sheedy  and  Lassoe-Lovekin  oil  bumexs. 

Comparative  Cost  of  Gasoline,  Oas,  Steam  and  Electricity  for  SmaO 
Powers  (By  W.  O.  Webber.  Eng.  News.  Aug.  15,  1907).— Diagram.  Se<, 
also,  in  same  issue,  article  by  F.  W.  Ballard,  entitled  "Relative  EoonoinT 
of  Steam  and  Gsls  Power  Where  Exhaust  Steam  is  Used  for  Heatibag." 

The  Solution  of  Steam  Problems  by  the  Use  of  a  Diagram  (Bv  Laooel  & 

Marks,  "Steam  Tables  and  Diagrams."  Bng.  News.  Aug.  2o.  1909).— 
The  diagram  is  12  x  15  ins.  and  may  be  used  in  solving  steam  problems,  o( 
which  numerous  examples  are  given.  The  old  equation  (Regnault'a)  for 
the  total  heat  of  dry  and  satxirated  steam  is, 

H - 1091.7+0.806  (/- 32); 
The  Marks  and  Davis  equation  for  the  range  ol  temperature  from  212*  to 
400°  F.  is. 

H- 1160.3+0.8746  (/- 212) -0.000660  (/-212)«. 
Below  212**  the  new  values  are  well  fixed  by  a  number  of  individtial  deter- 
minations, but  have  not  been  represented  by  any  simple  equation. 

Unique  Direct-Actinc  Explosion  Pump  (Bng.  News.  Dec.  2,  1909).— 
Developed  by  H.  A.  Humpnrey.  an  English  engineer.  This  pomp  has 
neither  piston  nor  cylinder,  strictly  speaking:  as  the  water  serves  as  the  one 
and  the  waterway  the  other.  The  pumping  is  done  with  approx.  1  lb.  of 
coal  per  water  horse  power  in  comparison  with  2  lbs.  for  compound  higfe- 
duty  steam  engines.  1.7  lbs.  for  triple-expansion  engines,  and  1.5  Ibe.  for  a 
gas-engine  driving  a  centrifugal  pump.  Described  and  illustrated,  with 
tables  of  duty.  It  is  possible  that  this  tvpe  of  pump  might  prove  highly 
efficient  in  connection  with  hsrdraulic  dredjsmg. 

Illustrations  of  Various  Kinds:— 

Description.  Bog.  News. 
Front  and  side  views  of  Emerson  steam  vacuum  pump            Oct.  81.  190L 

Plans  of  the  Northern  Power  Sta.  of  St.  Louis  Transit  Co.  April  10.  'Ol 

Raw  Peat  briquetting  press,  and  coking  retort  1"***  ^^*  '•^ 

The  Francke  smgle-rotary -valve  engine  Feb.     6,  'OX 

An  adjustable  staybolt  for  locomotive  boilers  July  S3,  '01 

Malleable  packing  of  various  designs  Aug.    6,  '03. 

Steam  turbines  (4  articles),  well  iuustmted  June    0.  '04. 

Long.  vert,  section  of  Mietz  &  Weiss  oil  eng.  with  evap.  jacket  Sept.  15,  *9i. 
Section  through  lower  stories  of  Phipps  power  building.  PitU.  Sept.  15,  '04- 

300- H.  P.  2-stage  centrifugal  pump,  turbine  driven  Oct.     0.  'OL 

Street  railway  power  house  in  Kansas  (^ty  Oct.    19.  '05. 

Construction  details  of  a  modem  gas-holder                       •  Oct.  26.*05. 

Centrifugal  cinder  separator  for  power  plant  smoke  April  II.  '0«. 

Structural  details  of  Long  Island  Power  Station  May  31.  '(ML 

New  designs  in  flexible  stay-bolts  Jan.   21,  '09. 

General  arrangementof  suction  ash-conveying  plant  Aug.    8,  '09. 

Tarless  oil-^as  producers,  with  test  tables  Dec     9.  'Of. 

A  commercial  tuel-briquette  plant  Apr.  14.  '10. 

Smyth,  and  Humphrey,  direct-acting  explosion  pumps  May  19,  '10. 
Test  of  locomotive  using  superheated  steam,  A.  T.  St  S.  P.  Ry  June    2.  '10. 

The  physical  meaning  cS  Entropy;  illua.  Sept.    1.  '10. 


d  by  Google 


70.— ELECTRIC  POWER  AND  LIGHTING. 

Electricity  as  a  Form  of  Enei^Ky* — Under  Steam  and  Gas  Power  (page  1347) 
we  have  seen  that  heat  and  mechanical  work  are  mutually  contiovertible; 
that  is,  1  heat  unit  (B.  T.  U.)  is  equivalent  to  778  ft.-lbs.  of  work,  or  1  ft.-lb. 
of  work  —  0. 001 285  heat  unit.  We  will  now  show  that  mechanical-,  thermal-, 
and  electrical  work-  and  power  imits  are  mutually  convertible,  or  have 
definite  relations  to  each  other. 

Ths  Ehctric  Power  Unit  is  the  watt,  equivalent  to  a  flow  or  "current"  of 
1  ampere  under  a  "pressure"  of  1  w//.  Thus,  OOwattsmean^  60  volt-amperes, 
or  a  current  of  10  amperes  at  a  pressure  of  6  volts,  or  15  amperes  at  4  volts, 

etc.    Watts  (P) -volts  (£)X  amperes  (O.   Moreover.  1  watt-—    horse - 

74o 


po^ 
lbs 


jwer- 0.7373  ft.-  lb.  per  second -44.238  ft.-lbs.  per  minute -265.428  ft.- 
lbs.  per  hour.    Note  that  the  watt  does  not  represent  work  but  the  rate  of 

work,  or  power.    The  watt-  second,  minute,  or  hour  is  equal  to  =rs  horse- 

740 
power  second,  minute  or  hour,  when  applied  to  work.    The  watt  imit,  being 
small,  ia  generally  supplanted  by  the  kilowatt  in  the  design  and  rating  of 
electric  power  plants  and  machines.    (See  Tables  34  and  35.  Sec.  4,  page  88, 
etc.;  also  Tables  1  and  2,  Sec.  69,  page  1348,  etc.) 

The  KilowaU.  K.-W.  (-1000  watts)  =  1000X. 7373- 737.3  ft.-lbs.  per 
second- 44,238  ft.-lbs.  per  minute -266,428  ft.-lbs.  per  hour;  which  is 
equivalent  to  1.3405  horse  power.  (Conversely.  1  horse  power  — 0.746  kilo- 
watt. O^mparing  with  umts  of  mechanical  work,  it  is  evident  from  the 
above  that  1  kilowatt  hour- 1.3405  horse-power  hour;  and  that  1  horse- 
power hour— 0.746  kilowatt  hour.    Cx)mparing  with  vmits  of  thermal  work, 

265  428 
1  kilowatt  hour— —=Y^-  341.17  thermal  imits;  and  conversely,  1  thermal 

unit  (B.T.U.)- 0.002031  kilowatt  hour  (-2.031  watt  hours),  or  10,000 
B.  T.  U.  (—amount  of  heat  that  may  be  assimied  to  be  generated  in  a 
boiler  from  the  combustion  of  1  lb.  of  coal)  -  29.31  kilowatt  nouis. 

A  Kilowatt  is  an  "electric  horse-power." 

Problem  1  (Steam-Electric). — What  power  can  be  expected  from  a 
dvnamo  (generator)  operated  b^  a  steam  engine,  with  a  consumption  of 
500  lbs.  of  coal  per  hour  (asstuning  that  each  100  lbs.  generates  1,000,000 
B.  T.  U.  in  the  steam);  the  engine  having  an  efficiency  of  10  per  cent,  and 
the  dynamo  93_per  cent  ? 

Solutkm.— From  the  above  we  have  1,000.000>^  5X0.002  931  XO.IOX 
0.98- 1362.92  kibwatts  (or  1827  horse-power).    Ans, 

Problem  2  (Hydro-Electric). — A  direct-connected  dynamo  is  run  by  an 
impulse  water-wheel  under  astatic  head  of  200  feet,  and  using  water  at  the 
rate  of  48  cubic  feet  per  minute.  Assuming  the  loss  of  head  in  the  pipe 
line  (from  the  storage  to  the  wheel)  to  be  20  ft.,  the  efficiency  of  the  wheel 
8£  per  cent.,  and  the  generator  93  per  cent*;  what  power  will  be  furnished 
to  the  line? 

Solution.— -Theoretically,  the  water  power-  200 X  48 X  62.5-  600  000  ft.- 
lbs.  per  minute,  or  18.182  horse-power.  The  efficiency  of  the  pipe  line  is 
2O0--20  .r  f  f 

-200  ^'  ^  P*^  *^®"**  He^ce'  power  delivered  to  line  is  18.182X0.90X 
0.85X0.03X0.746-9.65  kilowatts  (or  18.182x0.90X0.85X0.98-12.94 
horse-power). 

What  are  Electrical  Machines? — Electrical  machines  are  machines  for 
generating,  controlling,  transforming  or  converting  electrical  energy. 

Dynamos  are  machines  for  converting  mechanical-  into  electrical  power, 
that  IS,  they  generate  electricity  and  hence  the  name  "generator. '    An 

high  as  96>per  cent. 

Digitized  by  VjOOQ  IC 


•  Generators  are  constructed  with  efficiencies  as  high  as  ^^r  cent. 


1379 


1380  Vi.— ELECTRIC  POWER  AND  UGHTING. 

electric  "motor"  differs  frqm  a  generator  in  that  it  converts  electrical*  into 
mechanical  power — a  reverse  operation.  The  essential  principles  dl  the 
motor  are  those  of  the  dynamo.  Dynamos  and  motors  may  be  dUier 
alternate-current  or  continuous-current  machines. 

Transformers  are  machines  placed  at  either  end  (or  at  any  point)  of  a 
transmission  line  to  change  the  potential  of  the  current.  For  insutnce,  if  it 
is  desired  to  carry  the  current  over  the  line  at  a  higher  potential  than  it  is 
practicable  for  the  dvnamos  to  generate,  the  step-up  transformer  is  used  at 
the  power-house  ena  of  the  line;  while  at  the  delivery  end  the  step^dcmm 
transformer  is  installed.  Transformers  are  either  air-cooled,  water-oookd 
or  oil-cooled.  In  the  latter  case  the  whole  transformer  is  placed  in  c^  whjdi 
penetrates  the  pores  and  insulates  the  wires. 

Cotwerters,  called  rotary  converters,  are  machines  for  converting  alter- 
nate currents  to  direct  currents,  or  vice  versa;  or  they  may  be  used  for 
changing  the  voltage  of  continuous  currents,  or  changing  the  voltage,  phase 
or  frequency  of  akemating  currents. 

Boosters  are  machines  inserted  at  distant  points  in  the  line,  as  at  the 
outer  ends  of  street-railway  circviits,  to  compensate  the  drop  in  voltage  io 
direct-current  mains.  A  booster  is  a  combination  motor-generator  cs 
motor-dynamo  or  series  motor  driving  an  armature  placed  as  a  shunt  across 
the  mains.  It  can  be  arranged  to  either  raise  or  lower  the  voltage,  bemg 
generally  used  for  the  former  purpose. 

Principles  of  Electricity  and  Magnetism. — Before  proceeding  imtnedi- 
ately  with  the  discussion  of  electrical  machines  let  us  first  consider  the 
question— 

What  is  Electricity? — Scientists  are  pretty  well  agreed  at  the  present 
day  that  electricity  and  magnetism,  closely  associated,  are  due  to  certain 
states  of  disturbance  in  the  universal  substance  ( ?)  called  ether,  which  per- 
vades all  space  and  gross  matter.  Other  states  of  disturbance  are  caJkd 
light  and  heat.  Ipdeed,  by  some  it  is  considered  not  improbable  that  gross 
matter  itself  is  ethereal  and  electrical  by  nature,  thus  accounting  for  the 
universal  law  of  gravitation.  It  is  not  unlikely  that  the  determination  of  the 
exact  nature  of  either  of  the  above  phenomena  will  reveal  the  nature  of  all 
the  others. 

Ether,  as  a  substance,  necessarily  has  mass,  and  it  has  been  estimated, 
from  experiments  made  on  the  energy  of  waves  of  light,  that  a  volume  oi 
ether  the  size  of  the  earth  will  weigh  as  much  as  4  cubic  feet  of  water.  Ii 
is  considered  to  be  perfectly  elastic  and  in  a  continual  state  of  unrest.  It 
is  not  difficult  to  imagine  that  it  may  be  a  fourth  state  of  "matter"  in  the 
rising  graduation  from  solid,  liquid  and  fi^aseous  to  the  ethereal;  the  first 
three  constituting  gross  matter,  with  definite  chemical  composition,  and  the 
last,  radiant  or  transcendental  matter,  whose  composition  is  as  yet  unknown. 

Ether  Waves  vary  greatly  in  lenj8:th  according  to  the  phenomena  pro- 
duced. The  shortest  wave  lengths  of  which  we  have  any  knowledge  (by  the 
action  of  the  photographic  plate)  number  about  300.000,000.000.000.000 
vibrations  per  second  (in  a  length  of  186,500  miles  or  ll,816,04CL0OO  inches) 
equivalent  to  less  than  one  25-millionth  of  an  inch  in  length.  These  waves 
are  able  to  penertate  paper,  wood  and  sheets  of  metal  as  ordinary  light 
waves  penetrate  glass.  They  are  far  beyond  the  range  of  the  eye  as  an 
also,  but  to  a  much  less  degree,  the  ultra-violet  rays,  estimated  to  be  about 
one  70- thousandth  of  an  inch  in  length.  As  the  waves  become  longer  they 
fall  within  the  visible  spectrum,  the  violet  rays  being  about  one  W-tbous- 
andth  of  an  inch,  and  the  red  rays  (the  long^t  rajrs  visible),  about  <m» 
37-thotisandth  of  an  inch  in  length.  Those  rays  from  the  violet  to  the  xed 
(including  all  the  known  colors)  have  the  peculiar  property,  by  virtue  of  the 
transverse  vibrations,  of  acting  on  the  retina  of  the  eye  (consisttng  of 
minute  protuberances  which  are  set  in  vibration)  and  producmg  the  sensa- 
tion of  light.  As  the  waves  increase  in  length  we  get  first  the  heat  wave 
and  finally  the  electric  wave,  the  latter  being  the  longest. 

Electricity  and  Magnetism  are  mutually  related,  and  it  is  owing  to  these 
peculiar  properties  or  phenomena  that  we  are  enabled  to  generate  eiectricit>' 
and  use  it,  commercially. 

Magnetic  Field. — ^When  a  current  of  electricity  flows  "through"  a  wire 
m  a  closed  circuit  it  induces  aroimd  the  wire  a  magnetic  "field."  Lei 
riS'  I  represent  a  section  of  such  a  circuit  with  the  copper  wire  piercing  a 


ELECTRICITY  AND  MAGNETISM, 


1381 


small  sheet  of  paper,  and  the  current  flowing  downward  as  shown  by  the 
vertical  arrows.  If,  now,  a  few  iron  filings  are  sprinkled  on  the  paper  and 
the  paper  tapped  gently,  it  wUl  be  found  that  the  filings 
will  arrange  themselves  in  concentric  rings  as  shown.  If. 
further,  a  compass  is  brought  close  to  the  wire,  the  needle 
will  be  foimd  to  swin^  in  a  position  tangent  to  the  filing 
rings,  with  the  N  pole  pointing  in  the  direction  of  the 
arrows  shown  on  the  paper.  Upon  reversal  of  the  current 
through  the  wire  the  magnetic  needle  will  also  reverse  in 
direction  by  180**.  We  may  say.  then,  that  the  "lines  of 
force**  in  the  induced  ma^etic  field  are  right-handed  or 
clockwise  when  looking  m  the  direction  of  the  circuit. 
The  rapid  reversal  of  the  electric  current  in  the  circuit, 
producing  what  is  called  the  alternating  current  (as  against 
the  continuous  or  direct  current)  induces,  therefore,  an  alternating  mag- 
netic field.  The  "strength'  of  the  field  is  directly  proportional  to  the  cur- 
rent strength,  and  decreases  with  the  distance  from  the  wire. 

The  Electro-Magnet. — ^The  principle  of  the  electro-magnet  is  based  on 
the  magnetic  field,  explained  above.  A  B,  ia  each  of  the  following  Figs.,  is 
the  primary  circuit  with  the  current  flowing  in  the  direction  A  8^03  ahown 


Pig.  6. 


by  the  arrows.  Now  we  have  seen,  Pi^.  1,  that  when  a  current  of  electricity 
flows  through  the  primary  circuit,  lines  of  force  are  set  up,  around  the 
conductor,  m  a  clock-wise  or  cock-screw  direction.  If  the  iron  filings  are 
replaced  by  a  circular  ring  of  metal,  as  in  Fig.  2,  lines  of  electro-magnetic 
force  will  be  induced  in  the  ring  in  the  direction  shown  by  the  arrows. 
Pig.  3  shows  the  same  phenomenon,  but  with  the  magnetic  circtut  forming 
merely  a  loop  around  the  primary.  Fig.  4  shows  the  circuit  of  the  loop 
"broken"  thus  forming  a  primitive  horse-shoe  magnet,  the  +  and  — ends  of 
which  attract  each  other,  tending  to  draw  together  and  "close"  the  circuit. 
Figs.  5  and  6  show  that  two  parallel  conductors  attract  each  other  when  the 
currents  flow  in  the  same  direction,  and  re^/ each  other  when  the  currents 
flow  in  opposite  directions.  By  reversing  the  direction  of  the  current  in 
A  B,  the  ciirection  of  the  magnetic  circuit  in  Figs.  2  and  3  will  also  be  re- 
versed, and  in  Fig.  4  the  ipoles  of  the  magnet  will  change  from  +  to  — , 
and  from  —  to  + .  Repulsion  will  now  take  place  between  the  parallel  con- 
ductors in  Fig.  5.  and  attraction  in  Fig.  6,  assuming  that  the  currents  a  b 
remain  unchanged.  Now  assume  a  b.  Pigs.  5  and  0,  to  be  uncharged  from 
any  secondary  batteries,  and  assume  the  current  in  the  primary  conductor 
to  flow  in  the  direction  A  B\  then,  if  the  current  is  continuous  there  will  be 
no  induced  current  in  a  b,  but  if  it  is  alternating  there  will  be.  durins  the 
time  the  current  is  increasing  in  strength  or  "setting  up  of  the  field,"  a 
tendency  toward  generating  currents  in  o6.  Such  currents  are  called  in- 
duced currents,  and  the  general  phenomenon  is  termed  Induction. 


Corr 


Pig.  7. 


Pig.  8. 


Inductkwi  can,  perhaps,  best  be  explained  by  the  theory  that  magnetism 
is  merely  electricity  in  a  whirl,  rotating  about  a  conductor  m  the  surrouna- 


1883  TO.—ELECTRIC  POWER  AND  UGHTING, 

ing  ether.  It  is  greatly  assisted  and  intensified  by  the  use  of  a  »oft-«of 
S?c  Mound  whiSl^  certain  number  of  turns  of  each  cipcmtfc  wound. 
PiT  rSSstraS^an  induction  coil  or  Transformer  consisting  esse- 
tiSy  of  a  coie  around  which  is  wound  x  turns  of  the  pnmary  wcuit, 
/S^P^aSd  then  y  turns  of  the  secondary  circuit.  S-S.  From  the  number  cc 
turns  of  wire,  we  have,  electro-motive  force  in  S-S^^-^K  (clcctio-motiw 
force  in  P-P).  therefore,  by  increasing  the  ratio  of  turns  in  secondary  coil  to 
those  in  primary  coU  the  E.  M.  F.*  is  increased.  . 

Faraday's  ring.  Fig.  8.  consisted  of  a  circular  core  with  the,  pnmary 
and  secondary  coi&  on  either  side.  The  arrows  on  the  rmg  indicate  ^ 
dS«:tion  of  the  electro-magnetic  stresses.  An  ^temating  current  m  ^ 
primwy  coil  P  (Figs.  7  and  8}  generates  an  alternating  current  m  the 
S^Siycoil  S\  imd  again,  5  may  be  used  as  the  pnmary  coil  and  Pas 

the  ^"jf^.*sh<;c  Magnet  is  commonly  made  by  bending  a  piece  of  si»€l 
in  the  form  of  a  horsc^oe  as  shown  in  Fig.  9.  winding  it  with  fine  copper 
^rire(either  partially  as  shown  by  the  double  hnes  — 

OT^mpletely^una  the  loop  as  shown  by  the  amgle 
SiS^d  posing  a  current  of  etectriaty  through  the 
^  M  shbwTby  the  arrows,  ^reakmg*  (shutting 
oS^the  current  occasionally.  Th^  "^TL^  a^v!^.  ST 
wound  and  it  is  found  that  the  b^  of  steel  has  bc- 
^me  a  permanefU  ma^et.  capable  of  attracting 
magnetic  substances  as  iron  or  steel.  If  so^ttronis 
Sedfor  the  "field  core"  instead  of  steel  it  will  retam 
thTproperties  of  a  magnet  only  when  the  current  ^ 
Sf  etoScitv  is  "exciting"  the  field  .Such  a  mag-  ^ 
net  iscaWedBnekctro^ma^t.  Note  that  the  arma- 
ture A  when  placed  withm  the.  "mfluence  '  of  Uie 
S^ctic  ^1<«  of  the  field  core  is  attracted  bv.  the 
StS    that  is,  the  armature  tends  to    close    the  -  -   "  .     .  , 

ma^nitic  circu  t.  The  telegraph  "sounder"  is  founded  on  this  prjnciole^ 
Efeitro-Sagnets  are  made  in  various  forms^  depending  on  the  kmd  of 
work  they  arelntended  to  do.  We  stated  m  the  &^  ,Para«raph^  ^t  the 
IJSature  A  (Fig^  9)  is  attracted  by  the  poles  of  the  field  core  and  tends  to 
"clSSe"  the  maSietic  circuit.  This  is  only  partly  true.  As  a  matter  ot  fact 
♦iJi^aanetic  ^uit  in  Fig.  9  is  already  complete  without  the  presence  oi 
thi  ^ture^^t  it  is  comparatively  feeble  and  grasps  the  armattrre  to 
S^^Tmore ''i^rmeable"  path  for  its  circuit  than  the  air  offers,  much  i^ 
s^e  tsTman^  a  plank  to  cross  a  small  stream  instead  of  wadmg.  The 
^lo^  of  lMtstw)rl?'  appUes  to  all  electric  and  magnetic  phenomraa  as 
it  d«^  to  mShaniS.  It  U  simply  another  name  for  the  '*ConservatK>n  of 
Energy." 

PrinclDle  of  the  AHemate-Curreiit  Oyoamo.— A  rimplc  form  of  genewtor 

is  illustrated  in  Fig.  10.    The  jnagjetic  _^ 

"field"  between  N  and  S  is  mduoed  by        y^  — ^..^^     | 

either  a  permanent  magnet  or  an  electro-       /  ^  -^5      1     |  < 

mcwnet  ^e  Fig.  9).    Between  the  poles      Iff  cTf^^/-'^ 

S^e  magnet  is  shown  a  loop  of  copper      U I  "J  ^     f^^ 

??u;  which  may  be  made  to  revolve  on  an      \^ ■--\JL-J     I 

axis  a  b;   we  have  also  to  ima^e  that        x ^ g 

there  are  Kn#s,  tubes,   or  cylinders,  of 

fore,  «V%^^,\^*^ow%hln^he  S>pper  loop  is  re.;olS^,  say  right- 

SSSruJ^eTt  de-Sd^o-t«^^^ 

V^^  ^n'^r  when'a- MO  tie  ^Kf^^^-P  ^ r7§?? 4^^ 

a  maximum  rate,  vmity;  when  a-  46*»  the  rate  is  0.7U7.  wnen  a- w-  no  una. 

*  Electro-motive  force  is  voltage  or  difference  of  potential.    E.  M.  F.  is 
increased  at  t^cxpense  of  current,  where  the  power  remains  the  same. 


ALTERNATE-CURRENT  DYNAMOS,  1883 

of  force  are  beins  cut  and  hence  no  current  is  flowing  in  the  circuit.  This 
last  position  is  also  the  point  of  alternation  of  the  current,  which  continues 
in  one  direction  for  every  ha^  revolution  of  the  coil  and  then  reverses. 

The  electricity  generated  in  the 
revolving  armature,  for  one-half 
turn,  is  conducted  to  the  revolving 
••collecting"*  ring,  R  (Pig.  II). 
thence  by  the  fixed  "brush^  B  to 
the  line  L,  where  it  is  made  to  per- 
form useful  woric  such  as  running 
amotor,  M.  Passing  through  M  it 
returns  to  the  armature  by  way  of 

L\  B*  and  /^,  thus  completing  the  _.     . . 

chpciait.     For  the  next  half  turn  it  '«•  **• 

reverses  in  direction,  thus  alternating.  If  the  circuit  is  disconnected  or 
broken  at  any  point  no  power  can  oe  furnished.  The  earth  is  some- 
times used  for  the  return  current  as  in  telegraph  circuits.  In  the  case 
of  electric  railways  the  rails  are  used.  If  they  are  bonded"  the  "resistance'* 
is  greatly  lessened. 

Now  instead  of  having  a  "revolving  armattue"  composed  of  only  ont 
copper  wire  loop  as  shown  in  Pig.  10,  we  may  increase  the  current  output 
of  uie  machine  by  using  a  cylindrical  armature  composed  of  a  largt  numbtr 
of  loops;  also,  the  field-magnet  with  only  two  poles  may  be  increased  so  as 
to  contain  a  lar^e  number  of  pairs  of  pofes. 

The  magnetic  field  of  laxge  commercial  alternate-current  dynamos  is 
generally  maintained  by  small  constant-current  generators  called  exciters." 
One  exciter  will  answer  for  one  or  more  of  the  uirge  alternators,  and  being 
continuous-current  machines  they  are  self -exciting  (see  page  1884). 

Classification  of  Altbrnatb-C^urrbnt  Dynamos. 
(See  also  page  1884.) 

A. — ^With  respect  to  stationary  and  moving  parts: 

(a)    Stationary  field  magnets  and  rotating  armatures; 
tb)    Stationary  armatures  and  rotating  field-magnets; 

(c)  Stationary  field-magnets  and  armatures,  and  revolving  induc- 

tors.   (Not  common.     Ex.:    Stanley-Kelly  inductor  alter- 
nator.) 
B. — ^With  respect  to  number  of  field-magnet  poles: 

(a)  8-pole  (bipolar),  4-pole.  6-pole,  8-pole  machines; 

(b)  Multipolar  machines  include  all  above  the  bipolar.  (Multipolar 

machines,  with  many  poles,  used  for  high  power.) 
C. — ^With  respect  to  form  of  armature: 
Ring  armature; 
Drum  armature; 
Disk  armature  (eore  disks,  sunk  wotmd,  are  preferred  to  thin 

disks  for  high  power  machines,  because  of  strength) ; 

(d)  Pole  armature. 

D. — -"With  respect  to  armature  coils: 


(a)    Open  coil;      )     ^y^\^^^    I^  paraUel  { ^^^S^^;^^  °^ 

:b)    Closed  coU;    )  <  (B)    In  series      | 

h  respect  to  armature  windings: 

[a)    Spiral  or  ring  winding  (ring  armatures); 


{<f)    Sunk  winding. 
P. — ^WxUi  respect  to  field-magnet  windings: 

(a)  Spiral  winding; 

(b)  Lap  winding;        ai^,  i  (A)    In  pcutiUel. 
?c)    Wavewfedmg;    '^^((B)    In  series, 
(d)    Sunk  winding. 

*0>llecting  rings  or  simply  collectors  are  used  on  alternate-current 
machines,  while  "commuUtors^*  (see  page  1884)  are  <»«J^?s??St^'*°"*' 
cunent  dynamos.  ^^^^  by  v^OOgie 


1384  T^.— ELECTRIC  POWER  AND  UGHTING, 


Si 


G. — With  respect  to  phase  of  machine: 

Single-phase,  2-phase,  3-phase  machines: 
Polvphase  machines  include  all  above  Z-phase. 

A  single-phase  alternator  is  one  in  which  the  currents  act  in 
unison,  rising  and  Calling  together;  while  in  a  polirphaae 
alternator  the  coils  are  arranged  so  that  the  impulses  are 
produced  closer  together,  thereby  maintaining  a  more  uni- 
form electro-motive  force.  2-pha8e  and  S-phase  alteraaton 
are  the  most  common. 

Principle  of  the  Continuous-Carrent  Dynamo. — Many  of  the  prifictpfes 
of  the  alternate-current  dynamos,  just  described,  apply  equally  as  weQ  lo 
the  continuous-current  machines.  We  have  the  field-magnet  and  also  the 
armature;  but  instead  of  using  collector  rings  or  collectors  as  for  the  alter- 
nators, we  use  commutators,  which  deliver  to  the  external  circuit  a  continMotu 
current,  that  is,  a  current  in  one  direction  through  the  external  circuit. 

Fig.  12  shows  a  simple,  two-part  com- 

mutator.  K  and  K\  joining  the  ends  of  a  1}  ~      § 1 

single-loop  armature    revolving  between  ^'— ^      ■  '       B<^=S 

the  poles  of  a  magnet  on  the  axis  a  6.  and  *"     l--y  ^^    | 

delivering  current  to  the  brush  B.    Note         b— "* ?j^^} -ai 

that  the  Drushes  B  and  B'  are  fixed,  and  ,        r\5^     t 

as  the  commutator  revolves   (with  the  ^^        — -|  ^''^l^-' 

armature)   the  /C-part  and  the  /C'-part  fj  '^    — ' 

alternate  in  delivering  current  to  B,  and  u— — — 

hence  it  always  flows  through  the  external  Pig.  12. 

circuit,  from  B  to  B\  in  one  direction. 

Continuous-current  dynamos  are  made  with  two,  four,  six  or  eight  poltt. 
the  two-pole  machines  being  the  most  common.  The  armature  winding, 
however,  is  very  complex.  Instead  of  one  loop,  as  in  Pig.,  12  thcl^  are 
many  loops;  and  the  commutator,  instead  of  bemg  composed  of  two  shells 
or  bars,  as  above,  may  be  composed  of  many  bars  (see  Fig.  13).  Haxd- 
drawn  copper  is  best  for  the  commutator  bars,  and  also  for  the  brashes.* 
All  field  and  armature  windings,  as  well  as  commutator  bars,  should  be  in- 
sulated.   The  latter  are  insulated  with  mica. 

Classification  op  Continuous-Currbnt  Dynamos. 
(See  also  page  1383.) 
I. — With  respect  to  excitation  of  field-magnets: 

(a)  Separately-excited  dynamo  (Pig.  13).  using  a  separate  (small) 

dynamo  as  an  exciter; 

(b)  Series  dynamo  (Fig.  14),  using  the  full  current  of  the  external 

circuit  as  an  exciter; 

(c)  Shunt  dynamo  (Fig.  15),  using  a  small  fraction  of  the  external 

circuit  (by  a  shxmt  circuit  of  thin  wire)  to  excite  the  fieki; 

(d)  Compound  dynamo  (  Pig.  16),  using  both  shunt  coils  and  i 

coils  to  excite  the  field. 


Pig.  13.  Pig.  14.  Pig.  16.  Fig.  16. 

Note. — In  addition  to  the  above  we  have  also  the  Magneto  dynamo . 
in  which  the  field-magnets  are  permanent  steefmagnets;  and 
the  Separate-coil  dynamo,  in  which  the  armature  is  wound 
with  a  separate  coil  to  act  as  an  exciter. 

^  Carbon  brushes  are  used  for  motors.         °  ^  '^^^  ""^  GoOglc 


CONTINUOUS-CURRENT   DYNAMOS.    TRANSMISSION.  1385 

II. — ^With  respect  to  other  characteristics  see  classification  o£  alternate- 
current  dynamos,  page  1383.  with  the  following  comments 
for  direct-current  machines: 

A. — (a)  Stationary  field^magnets  and  rotating  armatures,  is  the 
prevailing  type. 

B. — Bipolar  machines  are  generally  used;  although  4-,0-,  and  8-pol6 
machines  are  not  uncommon.  There  is  another  type,  namely, 
the  homopolar  (imipolar  or  1-pole)  machine  which  is  being 
developed  with  more  or  less  success. 

C— (b)  Drum  armatures  are  the  most  efficient  and  are  generally  used 
where  high  potential  is  required.  Ring  armatures  give 
•  lower  B.  M.  F.  and  less  current  for  the  same  ntunber  of  revo- 
lutions. 

D. — (b)  Closed-coil  armatures,  generally  speaking,  give  greater 
commercial  efficiency  than  open-coil  machines;  but  the  latter 
(whether  of  the  riM  or  dnmi  type)  are  better  adapted  to 
high  electro-motive  forces  because  of  the  methods  of  insulation 
of  commutator  bars.  The  Brush  and  the  Thomson-Houston 
open-coil  dynamos  are  especially  adapted  to  electric  lighting, 
and  it  may  be  said  that  they  practically  monopolize  the  field 
for  this  purpose. 

B.— (b)  Lap  winding  is  the  most  frequently  used. 

P. — ^Wave  winding  has  certain  disadvantages  and  has  not  come  into 
general  use. 

G. — Phase  applies  to  alternate-current  machines. 

Electric  Tnuumlssion  of  Power. — Important  considerations  come  up  in 
connection  with  the  projection  of  any  power  plant,  especially  for  long- 
distance transmission;  and  usually  the  combined  efforts  of  the  civil-,  elec- 
trical-, mechanical-  and  hydraulic  engineer  are  required  for  its  successftll 
installation.  « 

Uses  of  EUctric  Power. — Electric  power  can  be  used  for  every  purpoee 
for  which  power  is  required.  Its  practical  utility  as  compared  with  the 
direct  use  of  steam  and  water  power,  from  which  it  is  derived  mainly,  lies  in 
the  economic,  convenient  and  sanitary  distribution  from  a  central  station, 
where  it  can  be  generated  economically. 

Sources  of  EUctric  Power. — Entropy,  in  thermodynamics,  has  been 
defined  by  some  scientists  as  the  "available"  energy  in  any  system,  while 
others  denne  it  as  the  "non-available"  energy  in  any  system.  Electricity 
may  similarly  be  defined.  It  is  only  a  question  of  constructing  our  machines 
so  that  the  kind  of  energy  which  is  usually  lost  may  be  increased,  captured 
and  turned  into  useful  work  at  some  distant  point.  The  dynamo,  the  trans- 
mission line  and  the  motor  are  specially  designed  to  accomplish  this  result 
economically. 

The  primary  source  of  all  electric-  or  other  power  is  probably  electricity 
itself.  'The  immediate  source  appears  to  us  in  the  forms  of  chemical  and 
physical  actions,  the  latter  throti^h  the  agencies  of  heat  and  gravitation, 
acting  on  gross  matter,  either  solid,  liquid  or  gaseous.  Thus,  we  get  the 
battery,  thermopile,  steam-engine,  so-called  heat  engine  (including  the  gas 
engine),  and  the  water  wheel.  No  method  has  yet  been  discovered  oy 
which  electricity  can  be  generated  directly  from  heat  on  a  large  commercial 
scale.  The  present  indirect  use  of  heat  of  fuel  means  a  loss  of  90  per  cent  or 
ooore  of  heat  energy. 

For  large  electric  plants  the  steam  engine  and  the  water  wheel  only  can 
be  considered  as  prime  sources  of  power.  The  turbine  wheel  is  best  adapted 
to  low  heads,  and  the  impulse  (bucket)  wheel  for  high  heads.  The  exact 
dividing  line  between  "low"  and  "hi^h"  heads  is  not  well  marked.  They 
both  overlap  the  100-ft.  head,  sometimes  to  a  considerable  extent. 

Steam  and  Water-Power  Compared. — The  cost  of  fuel  on  the  one  hand, 
and  tjie  length  of  transmission,  on  the  other,  are  prime  factors  in  the  com- 
parison. For  example,  the  author  has  in  mind  a  proposed  change  from 
iteam-  to  water  power  in  the  generation  of  electric  power  for  a  street  rail- 
way, demanding  about  3000  horse-power.  The  fuel  for  the  steam  plant  was 
very  cheap,  consisting  of  sawdust  and  slabs  automatically  fed  from  a 
n^hboring  saw-mill.    This  could  have  been  supplanted  by  a  transmission 


1888  70.^ELECTRIC  POWER  AND  UGHTING. 

80  miles  long,  and  the  installation  of  a  power  house  with  impu^  wheab 
operating  under  a  flOO-ft.  head.  The  low  cost  of  fuel,  however,  favored  the 
steam  plant.  With  coal  as  a  fuel  the  water-power  proposition  would  have 
been  cheaper. 

AUemating'  vs»  Continuous  Currtnt. — ^Although  alternate-current  motois 
may  be  used  to  convert  altemate-cturent  directly  into  mechanical  wosk. 

E»t,  owin^  to  certain  disadvantages  they  have  not  come  into  general  tae. 
ven  in  lighting,  the  arc  lamp  on  a  contmuovis  current  circuit  gives  a  bei* 
ter  illumination,  and  it  is  also  free  from  the  humming  sound  produced 
when  the  lamps  are  on  altemate-ciurent  circuits.  With  the  incandescent 
lamp,  however,  there  is  less  contrast  in  candle  power.  But  there  are  other 
considerations  which  sometimes  outweigh  the  above,  and  we  find  both  the 
altematixig-  and  continxious  current  in  distributing  systems  for  motive  power 
and  lighting. 

The  electric  transmission  of  power  for  mocUrate  distances  is  almost  always 
by  direct  current.  This  system  mvolves  line  construction  of  the  moet  tmxpk 
character,  namely,  two  lines  of  wire.  The  current  is  generated  at  the  power 
station  by  contuiuous-current  dynamos.  Each  machine  may  be  designed 
to  yield  a  voltage  up  to  2500  or  even  4000  volts^  although  the  latter  is 
uncommon.  In  order  to  secure  a  high  voltage  m  transmission  (which 
means  a  saving  in  copper  or  aluminum  wire)  the  dynamos  are  placed  in 
"series."  Thus,  ten  dynamos  in  series,  each  generating  ciurent  at  say  2009 
volts,  will  deliver  about  10  X  2000-20,000  volts  to  the  line.  At  the  distri- 
buting end  of  the  line  the  total  voltage  of  the  motors  receiving  the  taaergw 
at  anyone  time  must  be  equal  to  that  of  the  generators,  minus  the  "drop 
in  volts  on  the  line.  Continuous-current  transmission  may  operate  in  three 
ways: 

"'  Constant  voltage  and  variable  current; 
Constant  current  and  variable  voltage; 
Variable  voltage  and  variable  current. 

Lonjg-Distance  Transmission  may  be  accomplished  by  either  aHematiaff 
or  continuous  current.  In  Europe  the  latter  has  many  adherents,  while  in 
America  "long-distance"  is  almost  synonjrmous  with  "altemate-cttrrent" 
transmission.  The  "first  cost"  of  installation,  however,  is  usually  greater 
for  alternate-current  transmission. 

Alternate-current  transmission  is  carried  out  with  three-phase  three- 
wire,  two-phase  four-wire  or  single-phase  two-wire  circuits,  the  first  named 
greatly  predominating,  and  the  last  being  seldom  used.  The  number  of 
wires  varies  from  three,  the  lowest,  to  say  six,  a  maximum  per  pole  in  good 
practice.  High  voltage  for  alternate-current  transmission  can  be  obtuncd 
only  by  step-up  transformers  installed  at  the  power  station  because  alter- 
nators cannot  be  connected  up  in  series  for  higher  voltage  as  can  continuous- 
ctirrent  dynamos.  They  may  be  designed,  however,  to  deliver,  individually, 
current  at  a  much  higher  voltage,  namely,  up  to  15,000  and  possibly  20,0M 
volts.  The  step-down  transformers  at  the  sub-stations  need  not  be  the  same 
in  nimiber  as  the  step-up  transformers  at  the  generating  stations.  Trans- 
formers can  be  wotmd  for  any  rating  of  voltage  of  primary  to  secondary 
coils,  but  there  are  certain  economic  ratios  related  more  or  leas  to  generator 
capacity.  Static  transformers  are  often  used  to  change  alternating  current 
from  3-phase  to  2-phase,  and  vice  versa. 

The  Transmission  Line. — ^The  material  for  line  conductors  has  settled 
down  to  a  choice  mainly  between  aluminum  and  copper.  In  fact,  the  former 
metal  has  recently  been  used  in  manv  of  the  largest  installations.*  Proan 
an  economic  stana point,  considering  the  electrical  and  mechanical  properties 
of  the  two  metals,  they  possess  equal  merit  when  the  price  of  aluminum 
wire,  per  pound ,  is  about  2  to  2. 1  times  the  price  of  copper;  or  when  the  price 
of  copper  wire  is  about  48  to  50  per  cent  of  the  price  of  aluminum.  Hence. 
with  copper  at  22  cents  per  poimd,  aluminum  would  be  selected  if  undo' 
45  cents  per  poundf.  Alimiintmi  cable  is  substituted  for  «Mfv  if  the  sixe  called 
for  is  lai^e,  say  larger  than  No.  1  B.  &  S.  gage,  and  sometimes  even  for 
smaller  sizes.  The  cables  sue  made  up  of  wires  ranging  in  size  usually  from 
0  to  9  B.  &  S.  gage,  sometimes  larger.  Seven  strands  per  cable  are  common, 
and  as  high  as  37  nave  been  used. 

.  .  *  J^c  ^^^M  of  aluminum  has  not  been  confined  to  main  transmissicm  lines. 
It  is  bcmg  tjaed  also  in  distributing  power  to  sub-stations  of  electric  rail- 
ways, and  for  city  distribution  of  both  light  and  power.    fSce  page  106. 


ELECTRIC  TRANSMISSION  OF  POWER.  1387 

The  Size  of  Conductors  which  it  is  advisable  to  use  in  a  transmission 
line  cannot  be  determined  by  any  simple  rule.  As  a  broad  proposition  it 
may  be  stated  that  the  whole  power  plant,  from  reservoir  (or  other  source 
of  power)  to  distribution,  should  be  so  designed  that,  when  furnishing  the 
teqmred  power,  it  is  found  that  no  slight  increase  or  decrease  of  powe¥  could 
have  been  effected  more  economically  at  one  part  of  the  plant  than  at  another. 
But  there  are  many  practical  considerations.  The  "required"  power  varies 
from  hour  to  hour  ot  the  day,  from  season  to  season  of  the  year,  and  also 
iroax  year  to  year.  We  may  perhaps  asstune  the  "required  power  to  be 
the  maximum  or  "peak"  load,  either  present  or  prospective;  or  we  may 
assume  it  to  range  somewhere  between  the  peak  load  and  the  average  load, 
generally  near  the  former  and  a  little  below  it.  If  storage  batteries  are 
installed  to  take  care  of  the  peak  load  the  "required"  p>ower  for  the  line 
may  be  lowered  accordingly,  but  if  this  is  not  done  the  peak  loads  must  of 
course  be  carried  by  bringing  into  action  additional  (reserved)  units  at  the 
power  house.  Such  units  consist  each  of  say  a  water  wheel  (or  an  engine) 
with  the  connected  generator  or  generators. 

Let  us  assume  that  the  "required"  power,  for  which  the  transmission 

line  is  to  be  designed,  has  been  determined  as  x  watts  (  "T^g  kilowatts  ) 

«-C  (amperes)  X£  (volts).  Now  we  have  as  limiting  pruides,  in  determining 
the  aze  of  the  wire,  the  following,  namely,  (1)  that  it  is  inadvisable  to  use  a 
single  copper  wire  of  a  size  less  than  No.  4  B.  &  S.  gage,  for  reasons  of 
strength  and  stiffness;  (2)  a  tentative  calculation  of  the  line  wire  should 
show  a  loss  of  say  from  5  to  10  per  cent  of  the  "required"  power  delivered 
to  the  Hne,  less  for  short-  and  perhaps  greater  for  long  transmission.  Then 
by  applying  the  above  rule  (in  italics)  see  whether  or  not  an  incremental 
increase  or  decrease  of  power  can  be  effected  in  the  line  (by  changing  the 
size  of  wire)  at  less  cost  than  could  be  effected  at  the  generator  station 
said  at  other  points. 

Transmission  Line  Problems. 

Problem  1. — ^What  size  of  copper  wire  is  required  in  a  2i^mile  oontinu- 
ou8-current  transmission  receiving  3.600  kilowatts  at  30,000  volts  pressure, 
allowing  a  "drop"  in  volts  of  10  per  cent  on  the  line? 

Solution. — 3. 600 kilowatts— 3,600,000  watts,  hence  the  current  in  am- 
peres—120  amperes.     With  a  10  per  cent  drop  in  voltage  the  line  loss  — 

30.000X0.10— 3,000  volts.     Now  applying  Ohm's  law  (  ^—;d  )  we  have. 

E     3000 
resistance  in  ohms— ?g-—  i2n'°^^  ohms.    As  this  resistance  is  distributed 

OR 

over  26X2  (2-wire  circuit)  — 60  miles,  the  resistance  per  mile— t^- 0.50 

ohm,  which,  from  table  1,  page  1380  corresponds  to  a  No.  0,  B.  &  S.  gage, 
copper  wire.  If  altuninum  is  used  it  would  require  a  No.  000.  In  general, 
there  is  a  difference  of  two  numbers  between  cqpper  and  aluminum  wire  for 
the  same  resistance.  Note  in  the  above  that  £— the  difference  of  potential 
between  the  two  ends  of  the  line.  Also  that  the  resistance  is  taken  at  1&*  P.. 
and  that  the  resistance  iricreases  with  increase  of  temperature  (see  Table  1, 
page  1389). 

The  above  method  of  solution  applies  to  all.continuous-current  two-wire 
circuits,  and  can  be  used  as  well  to  nnd  the  weight  of  wire  per  tmit  of  length, 
or  the  area  in  circular  mils.  It  is  a  question  simply  of  using  different 
tables  after  the  resistance  has  been  obtained.  Thus,  a  resistance  of  0.5  ohm 
per  mile  is  equal  to  0.0947  ohm  per  1,000  feet,  or  10.560  feet  per  ohm ;  equiva- 
umt  to  110,000  circular  mils,  or  3  feet  per  pound  of  wire,  at  75^  F. 

For  alternating-current  circuits  the  above  method  of  solution  may  be 
used  by  noting  the  following:  (1)  The  "virtual  volts"  and  "virtual  amperes" 
of  the  alternating  current*  (and  these  are  what  are  commonly  meant), 
such  as  are  recorcied  by  volt-  and  ampere  meters,  must  be  used  in  the  calcu- 
lations. (2)  There  are  two  additional  sources  of  loss  in  alternate-current 
lines  that  do  not  appear  with  the  continuous  cturent,  namely,  inductance 
((Continued  on  page  1392.) 


*  In  alternating  currents  the  maximum  volts  and  amperes  rise  to  about 
1.414  times  the  virtual,  alternating  between  that  and  zero,  the  virtual  bemg 
about  0.707  times  the  maximum. 


1888 


70.— ELECTRIC  POWER  AND  UGHTINC. 


1. — Copper  Wirb  Tablb  op  thb — 
(Supplement  to  Trans,  of  A.  I.  E.  B.,  Oct.,  1893.) 
Thp  data  from  which  this  table  has  been  computed  are  as  foUofWB:   Mat- 
thiessen's  standard  resistivity,  Matthiessen's  temperature  coefficient,  speci&c 
gravity  of  copper—  8.89.    Resistance  in  terms  of  the  international  oiun. 

Matthiessen's  standard   1  meter-gram  of  hard  drawn  copper— 0.14®! 
B.  A.  U.  at  0°  C.    Ratio  of  resistivity,  hard  or  soft  copper,  1.0226. 

Matthiessen's  standard  1  meter^ram  of  soft  drawn  copper  •■  0.14365 
B.  A.  U.  at  0**  C.    1  B.  A.  U.  -  0.9866  international  ohm. 

Matthiessen's  standard  1  meter-gram  of  soft  drawn  copper— 9. 141 729 
international  ohms  at  0**  C. 

Temperature  coefficients  of  resistance*  for  20°  C,  50**  C,  and  80^  C.  are 
(See  Opposite  Page  for  Areas  in  Square  Mils.) 


Oagee. 

Weight. 

Length. 

dec 

u 

Area 
Clrc. 
Mils. 

Lb.per 
Foot. 

Pounds  per  Ohm. 

Vt  nttr 

Feet  per  Otam. 

a 

@20°C. 
-68«F. 

@50«C. 
'-ia2®F. 

@80«C. 
-176«F. 

""iT 

®20«C. 

=  68^. 

-122T. 

-I76T. 

0000 

0000 
000 

.460 
.454 

.425 

211600 
206100 
180600 

.6405 
.6239 
.6468 

13090 
12420 
9538 

11720 
11120 
8687 

10570 
10030 
7704 

1.561 
1.603 
1.82« 

20440 
19910 
17460 

18200 
17830 
15620 

18616 

16880 
14690 

000 
00 

00 

.4096 
.380 
.3648 

167800 
144400 
133100 

.5080 
.4371 
.4028 

8232 
6096 
6177 

7369 
5456 
4684 

6647 
4924 
4182 

1.969 

2.2sa 

2.482 

16210 
13950 
12850 

14510 
12480 
11600 

13090 
11260 
10380 

0 

.340 
.8249 
.8000 

115600 
105500 
90000 

.8499 
.3195 
2724 

3907 
3256 
2868 

3497 
2914 
2120 

8156 
2630 
191S 

2.858 
3.130 
8.671 

11160 
10190 
8692 

9693 

0123 
7780 

6017 
8233 
7026 

1 

.2893 
.2840 
.2590 

83690 
80660 
67080 

.2533 
.2441 
.2031 

2048 
1902 
1316 

1833 
1702 
1178 

1664 
1536 
1068 

3.947 
4.096 
4.925 

8083 
7790 
6479 

7286 
6973 
6799 

66S6 

6398 
6233 

2 
8 

.2576 
.2380 
.2294 

66370 
56640 
52630 

.2009 
.1715 
.1593 

1288 
938.0 
810.0 

1153 
839.6 
725.0 

1040 
757.6 
654.2 

4.977 
5.832 
6.276 

6410 
5471 
5084 

5738 
4897 
4550 

5177 
4419 
4166 

4 

.2200 
.2043 
.2030 

48400 
41740 
41210 

.1466 
.1264 
.1247 

684.9 
509.4 
496.5 

613.0 
455.9 
444.4 

553.1 
411.4 
401.0 

6.826 
7.914 
8.017 

4675 
4031 
8980 

4184 
3608 
36(2 

3775 
3356 
3316 

5 

.1819 
.1800 
.1650 

33100 
32400 
27230 

.1002 

.09808 

.08241 

320.4 
306.9 
216.7 

286.7 
274.7 
IM.O 

258.7 
247.9 
175.0 

9.980 
10.20 
12.18 

8197 
3129 
3629 

28a 

2801 
2354 

3383 

2537 
3161 

6 
7 

.1620 
.1480 
.1443 

26250 
21900 
20820 

.07946 
.06630 
.06302 

201.6 
140.8 
126.7 

180.8 
125.8 
118.4 

162.7 
113.3 
102.3 

12.58 
15.08 
15.87 

2535 

2116 

aoii 

2869 
1894 
1800 

3648 

1706 
1C24 

8 

.1340 
.1285 
.1200 

17960 
16510 
14400 

.05435 

.04998 
.04359 

94.26 
79.69 
60.62 

84.37 
71.33 
54.26 

76.13 
64.36 
48.96 

18.40 
20.01 
23.94 

17S4 
1595 
1891 

1558 
1427 
1345 

1461 
1288 
1123 

9 
10 

.1144 
.1090 
.1019 

13090 
11880 
10380 

.03963 
.03596 
.03143 

60.12 
41.27 
31.52 

44.86 
36.94 
28.21 

40.48 
33.33 
25.46 

25.23 
27.81 
31.82 

1265 
1147 
1003 

1132 

1027 
887.6 

1621 

e$9 

886.9 

11 

.0950 
.09074 
.08300 

9025 
8234 
6889 

.02732 
.02493 
.02086 

23.81 
19.82 
13.87 

21.31 
17.74 
12.42 

19.23 
16.01 
11.21 

86.60 
40.12 
47.85 

871.7 
795.3 
666.4 

780.2 
711.8 
666.5 

764.9 

642.3 
537.4 

12 
13 

.08081 
.07200 
.07196 

6530 
5184 
6178 

.01977 
.01569 
.01568 

12.47 
7.857 
7.840 

11.16 
7.032 
7.017 

10.07 
6.846 
6.332 

60.59 
63.73 
63.79 

630.7 
500.7 
500.1 

564.5 

448.1 
447.7 

809.4 

4044 
4010 

14 

.06500 
.06408 
.0580 

4225 
4107 
3364 

.01279 
.01243 
.01018 

5.219 
4.931 
3.308 

4.671 
4.413 
2.961 

4.215 

3.962 
2.672 

78.19 
80.44 
98.23 

408.1 
896.6 
824.9 

365.2 
355.0 
290.8 

329.6 

2202 

*Based  on  a  resistance  of  unity  at  0**  C. 


byGoogk 


COPPER  WIRE  TABLE, 


1889 


— ^Am.  Inst,  of  Blbctrical  Enoinbbrs. 
1.07068.  1.20625.  and   1.33681,   raepectively.    1  foot -0.8048038  meter,  1 
potind  »  463.69256  grams. 

Although  the  entries  in  the  table  are  carried  to  the  fourth  significant 
digit,  the  computations  have  been  carried  to  at  least  five  figures.  The  last 
digit  is  therefore  correct  to  within  half  a  unit,  representtngan  arithmetical 
degree  of  accuracy  of  at  least  one  part  in  two  thousand.  The  diameters  of 
the  B.  &  S.  or  A.  W.  G.  wires  are  obtained  from  the  geometrical  aeries,  in 
which  No.  0000— 0.46  inch  and  No.  36— 0.006  inch,  the  nearest  fourth 
significant  digit  being  retained  in  the  areas  and  diameters  so  deduced. 

It  is  to  be  observed  that  while  Matthiessen's  standard  of  resistivity  mav 
be  permanently  recognized,  the  temperature  coefficient  of  its  variation  which 
be  mtroduced,  and  which  is  here  used,  may  in  future  undergo  slight  revision. 
(See  Opposite  Page  for  Areas  in  Circular  Mils.) 


0,gea. 

Reslstanoe. 

d,. 

6- 

Dlam. 

IQS. 

Area 

tin?; 

Ohms  per  Lb. 

Ohms  per  Foot. 

y 

d  200a 
-  68T. 

@  50OC. 
-122«»F. 

@  80«C. 
-176'F. 

@  20<»C. 
-  68-F. 

#  50-a 

-122«F. 

d  80«C. 

-176»F. 

oooJ 

0000 

000 

.460 
.454 
.425 

166190 
161883 
141863 

.00007639 
.00008051 
.0001048 

.00008535 
.00008996 
.0001171 

.00009459 
.00009969 
.0001298 

.00004893 
.00005023 
.00005732 

.00005467 
.00005612 
.00006404 

.00006058 
.00006220 
.00007097 

000 

00 

00 

.4096 
.380 
.8648 

131790 
113411 
104518 

.0001315 
.0001640 
.0001931 

.0001357 
.0001833 
.0002158 

.0001504 
.0002031 
.0002391 

.00006170 
.00007170 
.00007780 

.00006893 
.00008011 
.00008692 

.00007640 
.00008878 
.00009633 

.340 
.3240 
.3000 

90792 
82887 
70686 

.0002560 
.0003071 
.0004223 

.0002860 
.0003431 
.0004718 

.0003169 
.0003803 
.0005228 

.0000695^ 
.00009811 
.0001150 

.0001001 
.0001096 
.0001286 

.0001109 
.0001216 
.0001424 

.2893 
.2840 
.2590 

65782 
63347 
52685 

.0004883 
.0005268 
0007601 

.0006466 
.0005874 
.0008492 

.0006046 
.0006610 
.0009413 

.0001237 
.0001284 
.0001648 

.0M1382 
.0001434 
.0001724 

.0001532 
.0001589 
.0001911 

. 

.2576 
.2380 
.7294 

52128 
44488 
41339 

.0007765 
.001066 
.001335 

.0008675 

.001191 

.001379 

.0009614 

.001320 

.001629 

.0001660 
.0001828 
.0001967 

.0001743 
.0002042 
.0003196 

.0001932 
.0002263 
.0002435 

.2200 
.2043 
.2030 

38013 
32784 
32365 

.001460 
.001963 
.002014 

.001631 
.002193 
,002250 

.001808 
.002431 
.002494 

.0002139 
.0002480 
.0002613 

.0002890 
.0002771 
.0002807 

.0002649 
.0003071 
.0003111 

.1819 
.1800 
.1650 

25999 
25447 
21382 

.003122 
.003258 
.004615 

.003487 
.003640 
.005156 

.003865 
.004034 
.005714 

.0003128 
.0003196 
.0003803 

.0003496 
.0003570 
.0004249 

.0003873 
.0003957 
.0004709 

9 

.1630 
.1480 
.1448 

20618 
17203 
16351 

.004963 
.007129 
.007892 

.005545 
.007965 
.008817 

.006145 
.008827 
.009772 

.0003944 
.0004727 
.0004973 

.0004406 
.0005281 
.0005656 

.0004883 
.0005853 
.0006158 

10 
11 

.1340 
.1285 
.1200 

14103 
12967 
11310 

.01061 
.01255 
.01650 

.01185 
.01402 
.01843 

.01314 
.01554 
.02042 

.0006766 
.0006271 
.0007190 

.0006442 
.0007007 
.0008033 

.0007140 
.0007765 
.0008903 

12 

.1144 
.1090 
.1019 

10283 
9331 
8155 

.01996 
.02423 
.03173 

.02229 
.02707 
.03545 

.02471 
.03000 
.03928 

.0007908 
.0008715 
.0009972 

.0008835 
.0009736 
.001114 

.0009791 
.001079 
.001235 

13 
14 

.0950 
.09074 
.08300 

7088 
6467 
5411 

.04199 
.05045 
.07207 

.04692 
.05636 
.08052 

.05200 
.06246 
.08924 

.001147 
.001257 
.001603 

.001282 
.001405 
.001679 

.001420 
.001657 
.001861 

16 

.08081 
.07200 
.07196 

5129 
4072 
4067 

.08022 
.1273 
.1276 

.08962 
.1422 
.1425 

.09983 
1576 
.1679 

.001586 
.001997 
.001999 

.001771 
.002231 
.002234 

.001968 
.002473 
.002476 

14 

16 
17 

.06600 
.06408 
.0580 

3318 
3225 
2642 

.1916 
.2028 
.3028 

.2141 
.2266 
.8377 

.2878 
.2511 
.3742 

.002451 
.002531 
.003078 

.002738 
.002817 
.003439 

003084 
.003122 
.008811 

laoo 

70.- 

ELECTRIC  POWER  AND  UGHTING. 

] 

1. COPPBR  WiRB  TABLB  op  THB- 

_ 

(See  Opposite  Page  for  Areas  in  Squan  Bills.) 

Osges. 

Weight. 

Leocth. 

dasloi* 

U 

Ares 
Circ. 
MUs. 

Lb.  per 
Foot. 

Pounds  per  Obm. 

Pt. 

Feet  per  Ohm. 

^2^1 

@20»C. 
-68«F. 

d  80«C. 
-122T. 

%  80«»C. 

O20»C. 

-6«»F. 

-i22«Fl(-i:rr. 

15 
16 

18 

.06707 
.05082 
.049 

8257 
2583 
2401 

.009858 
.007818 
.007268 

3.101 
1.950 
1.685 

2.776 
1.746 
1.509 

2.504 
1.675 
1.361 

101.4 
127.1 
137.6 

314.5 
249.4 
231. S 

281. 5 
223.1 

207.6 

2S4( 

2ets 
iffi 

17 
18 

19 

.04626 

.042 

.0403 

2048 
1764 
1624 

.006200 
.005340 
.0049! 7 

1.226 

.9097 
.7713 

1.098 
.8143 
.6904 

.9906 

.7347 
.6230 

161.8 

187.8 
203.4 

rn.e 

170.4 

156.t 

m.i 

151.5 
140.4 

13;  fi 
iM.r 

19 

20 
21 

.03589 

.035 

.082 

1288 
1225 
1024 

.003899 
.003708 
.003100 

.4851 
.4387 
.8066 

.4348 

.3927 
.8744 

.8918 
.8543 

.2476 

256.5 

169.7 
822.6 

124.4 

118.J 
98-90 

111.4 
106.9 
88.52 

MS 

KM 

78.16 

10 

ai 

22 

.08196 
.02846 
.028 

1022 
810. 1 
784.0 

.003092 
.002452 
.002378 

.3051 
.1919 
.1797 

.2731 
.1717 
.1608 

.8464 

.1550 
.1451 

323.4 
407.8 
421.4 

9R.66 
78-24 
75.72 

88.21 
70.03 
67.78 

79-6 
$3.1! 

61.14 

2S 
2S 

23 

.02535 

.025 

.02257 

642.4 
625.0 
509.5 

.001946 
.001892 
.001542 

.1207 
.1142 
.07589 

.1080 
.1022 
.06793 

.09746 
.09224 
.06129 

514.2 
528.6 
648.4 

62.06 
00  36 
49.21 

59.54 
54-03 
44.04 

soil 
48:5 
29:4 

24 

24 

25 

.022 
.0201 
.020 

484.0 
404.0 
400.0 

.001465 
.001223 
.001211 

.06849 
.04771 
.04678 

.06130 
.04272 
.04187 

.05631 
.03855 
.03778 

681.6 
817.6 
825.9 

46.75 
89.02 
38.68 

41.8^ 
94. 83 

34.6^ 

37.75 
21.52 
21.21 

26 

26 
27 

.018 
.0179 
.016 

324.0 
82U  4 
266.0 

.0009808 
0009699 
.0007749 

.08069 
08002 
! 01916 

.02747 
.02687 
.01715 

.02479 
.02424 
.01548 

\m 

1081 
1290 

81  29 
30.95 
14.73 

28.81 
27.70 
22.13 

25.27 
24.  M 

19.  IT 

26 
27 

28 

.01594 
.0142 
.014 

254.1 
201.5 
196.0 

.0007692 
.0006100 
0005933 

.01888 
.01187 
.01123 

.01690 
.01063 
.01006 

01535 
.009588 
.009071 

1300 
1639 
1685 

24.54 

19.46 
18.91 

11.8? 
17.42 
16.  M 

18-83 
15.21 

28 

29 
30 

.013 

.01264 

.012 

169.0 
159.8 
144.0 

.0005116 
.0004837 
.0004359 

.008350 
.007466 
.006062 

.007474 
.006683 
.005426 

.006744 
.006030 
.004896 

1955 
2067 
2294 

1682 
16.43 
18.91 

14.61 
13.82 
12.49 

13  IS 
12  4- 
11  23 

29 
30 

31 

.01126 
.01003 
.010 

126.7 
100.5 
100.0 

.0003836 
.0003042 
.0003027 

.004696 
.002953 
.002924 

.004203 
.002643 
.002617 

.008792 
.002385 
.002361 

2607 
8287 
3304 

1124 

9.707 
9.658 

10. 9« 
8.68i 
8.845 

9  881 

7-S* 
7.8H 

31 

32 
33 

.009 

.008938 

.008 

81.00 
79.70 
64.00 

.0002452 
.0002413 
.0001937 

.001918 
.001857 
.001197 

.001717 
.001662 
.001072 

.001549 
.001500 
.0009672 

4078 
4145 
5162 

7.823 
7.698 
6.181 

7.082 
6.880 
6.533 

C.3I8 

6- 21: 
4.98Z 

32 
33 

34 

.00795 
.00708 
.007 

63.21 
50.13 
49.00 

.0001913 
.0001517 
.0001483 

.001168 
.0007346 
.0007019 

.001045 
.0006575 
.0006283 

.0009436 
.0005933 
.0009669 

5227 
6501 
6742 

6.105 
4.841 
4.733 

5.464 
4.331 
4.236 

4.836 
2.818 

2.822 

34 

35 
36 

85 

.006305 
005615 
.005 

39.75 
31.52 
25.00 

.0001203 
.00009543 
.00007668 

.0004620 
.0002905 
.0001827 

.0004135 
.0002601 
.0001636 

.0003731 
.0002347 
0001476 

8311 
10480 
13210 

ai.839 
3.045 
2.414 

8.436 
2.726 
2.161 

2.101 
2.459 

1.981 

37 

36 

.004453 

.004 

.003965 

19.83 
16.00 
15.72 

.00006001 
00004843 
.00004759 

.0001149 
.00007484 
.00007210 

.0001029 
.00006699 
.00006454 

.00009281 
.0000604& 
.00005824 

16660 
20650 

1.915 
1.54G 
1.519 

1. 714 
1.283 
1.2S9 

1.54J 
1  249 

38 

21010 

l!22l 

39 
40 

.003531 
.003145 

12.47 
9.888 

.00008774 
.00002993 

.00004545 
.00002858 

.00004068 
.00002559 

00003671 
.00002309 

33410 

1.101 

1.078 
.8648 

.8781 
.TTll 

Note.— Sq.  mils-circ.  mils X 0.785306;  circ.  mils-sq.  mUsXl.S7SI0. 

Digitized  by  VjOOQ  IC 


COPPER  WIRE  TABLE, 


1891 


,   — Am.  In8t. 

OF  Elbctrical  Enoinbbrs.— Concluded. 

■^h: 

(See  Opposite  Page  for  Areas  in  Circular  Mils.) 

-    Ini. 

Area 
iDSq. 
MU8.* 

Ohmi  per  Lb. 

Ohms  per  Ft. 

9  20^ 

^  60^. 

-i2rF. 

d  80-C. 

-176«F. 

d  20*^. 
-  68'F. 

^  6U«C. 
-122«F. 

^  80^ 
-176«F. 

'^^   .05707 
.05082 
.04900 

2558 
2029 
1886 

.3225 
.5128 
.5933 

.3603 
.5729 
.6629 

.3993 
.6349 
.7346 

.003179 
.004009 
.004312 

.003552 
.004479 
.004818 

.003936 
.004964 
.005339 

.045M 
.04200 
.04030 

1609 
1885 
1276 

.8158 
1.099 
1.296 

.9109 
1.228 
1.448 

1.010 
1.361 
1.605 

005065 
:006870 
.006374 

.005648 
.006658 
.007122 

.006269 
.007267 
.007891 

.03581 
1     .03600 
i     .08200 

1012 
962.0 
804  2 

2.061 
2.279 
8.262 

2.303 

2.547 
8.644 

2.652 
2.822 
4.039 

.008038 
.008453 
.01011 

.008980 
.009443 
.01130 

.009951 
.01047 
.01262 

.03198 

.02848 

2     .U2800 

802.0 
636.8 
615.8 

3.278 
6.212 
6.566 

8.662 
6.823 
6.217 

4.058 
6.453 
6.890 

.01014 
.01278 
.01321 

.01182 
.01428 
.01475 

.01255 
.01588 
.01635 

.02585 

:3     .0250 

.02257 

504.6 
490.9 
400.2 

8.287 
8.756 
13  18 

9.259 

9.783 
14.72 

10.26 
10.84 
16.32 

.01612 
.01657 
.02032 

.01801 
.01851 
.02271 

.01996 
.02051 
.02516 

24  .0220 
.02010 

25  .0200 

380  1 
317.3 
314.2 

14.60 
20  95 
21.38 

16.31 
23.41 
23.88 

18.08 
25.94 
26.47 

.02139 
.02.%63 
.02588 

.02390 
.02863 
.02892 

.02649 
.03173 
.03206 

26     .018 

.0171 

17      .016 

254.5 
251.7 
201  1 

82.68 
33.82 
62.19 

36.40 

37.22 
68.31 

40.34 
41.25 
64.62 

.03196 
.0.1231 
.04045 

.03570 
.03610 
.04519 

.03957 
.04001 
.05008 

.01504 
.0142 
9     .014 

199.6 
158.3 
158.9 

62.97 
84.28 
89.04 

59.18 
94.11 
99.48 

65.59 
104.3 
110.2 

.04075 
.05138 
.05283 

.04562 
.05740 
.05902 

.05045 
.06362 
.06541 

9     .013 

.01204 
0      .012 

132.7 
125.5 
118.1 

119.8 
133.9 
165.0 

133.8 
149.6 
184.3 

148.3 
16.5.8 
204.2 

.06127 
.06479 
.0719 

.06845 
.07239 
.08033 

.07586 
.08022 
.08903 

.01120 
.01003 
.010 

99.53 
78.94 
78.54 

2130 
338.6 
342.0 

237.9 
378.3 
382.1 

263.7 
419.3 
423.5 

.0817 
.1030 
.1035 

.09128 

.1151 

.1167 

.1018 
.1276 
.1282 

t      .000 
.008020 
.008 

63  62 
62.60 
50.27 

621.3 
638.4 
836.1 

582.5 
601  6 
933.0 

645.6 
666  7 
1034. 

.irs 

.1299 
.1618 

.1428 
.1451 
.1807 

.1583 
.1608 
.2003 

.00705 
.00708 
.007 

49.64 
89.37 
38.48 

856.2 
1361. 
1425. 

956.6 
1621. 
1592. 

1060 
1685. 
1764. 

.1638 
.3066 
.2113 

.1830 
.2308 
.2361 

.2028 
.2558 
.2616 

.006305 
.006019 
.005 

81.22 
24.76 
19.64 

2165. 
3441. 
5473. 

2418. 
3845. 
6114. 

2680. 
4262. 
6776. 

2605 
.3284 
.4142 

.2910 
.3G69 
.4627 

.3226 
.4067 
.5129 

.004458 

.004 

.008965 

15.57 
12.67 
12.36 

8702. 
13360. 
13870. 

9722. 
14930. 
15490. 

10770. 
16540. 
17170. 

.6222 

.6471 
.6686 

.5835 
.7230 
.7367 

.6466 
.8011 
.8164 

.003581 
.003145 

9.79 

7.77 

22000. 
34980. 

24580. 
39080. 

r2io. 

43320. 

.8304 
1.047 

.9277 
1.170 

1.028 
1.296 

find  area  in  square  inches,  divide  by  1.000,000. 


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ISdd  Td.— ELECTRIC  POWER  AND  UGHTING. 

and  impedana.  The  former  may  be  assumed  to  be  no  greater  thaa 
the  "drop"  in  volts  on  the  line  (and  from  that  down  to  about  one-thiid  of  the 
amount),  while  the  latter  is  usually  so  small  as  to  be  practically  negligible, 
say  5  per  cent  of  the  inductance.  Hence  from  5  to  10  per  cent  may  be 
added  for  losses  in  alternate-current  circuits  over  those  for  continuous; 
in  other  words  the  areas  of  the  wires  may  be  increased  by  this  amount. 
(3)  In  a  single-phase  two-wire  circuit  the  size  of  wires  is  the  same  as  for 
continuous  current  plus  5  to  10  per  cent  for  inductance.  (4)  In  a  two-phase 
four-wire  circuit  the  area  of  each  wire  is  one-half  that  for  the  continuous 
current  circuit  plus  6  to  10  per  cent  for  inductance;  that  is,  the  same  toritM 
of  wire  is  required  as  for  the  single-phase  two-wire  alternating  circuit.  (6)  ux 
the  three-phase  three-wire  circuit  the  area  of  each  wire  is  one-half  that 
for  the  continuous  ciurent  circuit  plus  5  to  10  per  cent  for  inductance;  that 
is,  only  three-fourths  the  weight  of  wire  is  required  as  for  the  l-phase  2-wire, 
and  2-phase  4-wire,  circuits. 

Problem  2. — In  solving  Problem  1  we  find  that  the  size  of  copper  wire 
required  is  about  110,000  circular  mills  in  area,  corresponding  to  about 
No.  0  B.  &  S.  gage.  Now,  from  the  foregoing  discussion,  what  sizes  of 
wire  would  probably  be  installed  for  the  three  types  of  alternating  circuits? 
And  what  would  be  the  theoretic  relative  weights  of  total  amount  of  copptr 
in  the  four  systems? 

Continuous  current       2-wire;  each  110,000  circ.  mills;  total  weight,  1.00 
AU*mo*,v,c  {  1-phase    2-wire;      "     120,000        "  "        ^^     IM 

ri^f^  ^  2-phase    4.wire:      "       60.000 1.09 

Current         /  s.phase    8-wire;      "       60,000        "  "  "       0.82 

The  3-pha8e  3-wire  system  is  the  most  commonly  used. 


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1308 


•NATIONAL  ELECTRIC  CODE." 


Rules  and  Requirements  of  the  National  Board  of  Fire  Underwriters 

for  the  Installation  of  Wiring  and  Apparatus  (for  Light,  Heat 

and  Power)  as  Recommended  oy  the  Underwriters' 

National  Electric  Association. 

Edition  of  1907. 

The  National  Electric  Code  (originally  drawn  in  1897)  is  the  result  of 
the  united  efforts  of  the  various  electrical,  architectural,  insurance  and 
other  allied  interests  which,  through  the  National  (inference  on  Standard 
Electrical  Rules,  composed  of  delegates  from  various  national  associations, 
unanimously  voted  to  recommend:  it  to  their  respective  associations  for 
approval  or  adoption. 

The  following  is  a  list  of  the  associations  composing  the  National  Con- 
ference on  Standard  Electrical  Rules: — American  Institute  of  Architects. 
American  Institute  of  Electrical  Engineers.  American  Society  of  Mechanical 
Engineers,  American  Institute  of  Mining  Engineers,  American  Street  and 
Interurban  Railway  Association,  Associated  Factory  Mutual  Fire  Ins.  Od's., 
Association  of  Edison  Illuminating  Companies,  International  Association  of 
Municipal  Electricians,  National  Board  of  Fire  Underwriters,  National 
Electric  Light  Association,  National  Electric  Contractors'  Association, 
National  Electric  Inspectors'  Association,  Underwriters'  National  Electric 
Association. 

GENERAL  PLAN  QOVERNINQ  THE  ARRANGEMENT  OP  RULES.* 

Class  A. — Stations  and  Dynamo  Rooms.     Includes  Ontral  Stations;    Dy- 
namo. Motor,  and  Storage-Battery  Rooms;    Transformer  Sub- 
stations, etc.    Rules  1  to  11. 
Class  B. — Outside  Work,  all  systems  and  voltages.    Rules  12  to  13A. 
Class  C. — Inside  Work.    Rules  14  to  39.    Subdivided  as  follows: 

General  Rules,  all  systems  and  voltages.    Rules  14  to  17. 
Constant-Current  Systems.    Rules  18  to  20. 
Constant-Potential  Systems: — 
General  Rules,  all  voltages.    Rules  21  to  23. 
Low-Potential  Systems,  550  volts  or  less.    Rules  24  to  34. 
High-Potential  Systems,  550  to  3500  volts.    Rules  35  to  87. 
Extra-High-Potential  Systems,  over  3500  volts.  Rules  38  to  89. 
Class  D. — Fittings,  Materials,  and  Details  of  Construction,  all  systems  and 

voltages.    Rules  40  to  63. 
Class  E. — Miscellaneous.    Rules  64  to  67. 
Class  F.— Marine  Work.    Rules  68  to  83. 


'  Central  Suggestions. — In  all  electric  work,  conductors,  however  well 
insulated,  should  always  be  treated  as  bare  to  the  end  that  under  no  condi- 
tions, existing  or  likely  to  exist,  can  a  ground  or  short  circuit  occur,  and  ao 
that  all  leakage  from  conductor  to  conductor,  or  between  conductor  and 
ground,  may  be  reduced  to  a  minimum.  ^ 

In  all  wiring,  special  attention  must  be  paid  to  the  mechanical  execution 
of  the  work.  Careful  and  neat  running,  connecting,  soldering,  taping  of 
conductors,  and  securing  and  attaching  of  fittings,  are  specially  conducive 
to  security  and  efficiency,  and  will  be  strongly  insisted  on. 

In  laying  out  an  installation,  except  for  constant  current  systems,  every 
reasonable  effort  should  be  made  to  secure  distribution  centers  located  in 
easily  accessible  places,  at  which  points  the  cut-outs  and  switches  controlling 
the  several  branch  circuits  can  be  grouped  for  convenience  and  safety  of 
operation.  The  load  should  be  divided  as  evenly  as  possible  among  the 
branches,  and  all  complicated  and  unnecessary  wiring  avoided. 

The  use  of  wire-ways  for  rendering  concealed  wiring  permanently  acces- 
sible is  most  heartily  endorsed  and  recommended;  and  this  method  of 
accessible  concealed  construction  is  advised  for  general  use. 

Architects  are  urged,  when  drawing  plans  and  specifications,  to  make 
provision  for  the  channeling  and  pocketing  of  buildings  for  electric  light  or 
power  wires,  and  also  for  telephone,  district  messenger  and  other  signaling 
system  wiring.  og^ed by GoOglc 


1804  70.— electric  power  and  ughting. 

cum  a.—stations  and  dynamo  rooms. 

Includes  Central  Stations,  Dynamo,  Motor  and  Storagb-Battbrt 
Rooms,  Transformer.  Sub-stations,  Etc. 

I.     Qeneratora. — a.   Mtist  be  located  in  a  dry  place. 
It  l8  recommended  that  water^proot  eovers  be  provided,  which  may  be  latd  ti 
oaae  of  emergency. 

b.  Must  never  be  placed  in  a  room  where  any  hazardous  process  is 
carried  on,  nor  in  places  where  they  woiild  be  exposed  to  inflammable  gases 
or  flyings  of  combustible  materials. 

c  Must,  when  operating  at  a  potential  in  excess  of  550  volts,  have  their 
base  frames  permanently  and  effectivelv  grounded. 

Must,  when  operating  at  a  potential  of  550  volts  or  less,  be  thorotichlT 
insulated  from  the  grotmd  wherever  feasible.  Wooden  base  frames  used  for 
this  purpose,  and  wooden  floors  which  are  depended  upon  for  insulation 
where,  for  any  reason,  it  is  necessary  to  omit  the  base  frames,  must  be  k^ 
filled  to  prevent  absorption  of  moisture,  and  must  be  kept  clean  and  dry. 

Where  frame  insulation  is  impracticable,  the  Inspection  Depcutment 
having  jurisdiction  may,  in  writing,  permit  its  omission,  in  which  case  the 
frame  must  be  permanently  and  effectively  grotmded. 

A  high  potential  machine  should  be  surrounded  by  an  Insulated  platfonn.  This 
may  be  made  of  wood,  mounted  on  Insulating  supports,  and  so  arran^d  ttttt  a  bbsq 
must  always  stand  upon  It  in  order  to  touch  any  part  of  the  machine. 


In  case  of  a  machine  having  an  insulated  frame,  it  there  is  trouble  trom  statte 
_..ptrlclty  due  to  bolt  friction.  It  should  be  overcome  by  placing  near  the  belt  a 
metnlllc  comb  connected  with  the  earth,  or  by  grounding  the  trame  thrmigh  a  re- 


eleotrlclty  due  to  bolt  friction,  Tt  should  be  overcome  by  placing  near  the  belt  a 
metnlllc  comb  connected  with  the         "    "~  """"      "*  '~' 

slstanoe  of  not  leas  than  300.000  c 

d.  Constant  potential  generators,  except  alternating  current  machines 
and  their  exciters,  must  be  protected  from  excessive  current  by  saie^  fuses 
or  equivalent  devices  of  approved  design. 

For  two-wire.  direct-curr«att  gmerDtors.  slnfde  pole  protection  will  be  eonaldera! 
as  satisfying  the  above  rule,  provided  the  safety  device  Is  located  In  ttie  toad  not 
connected  to  the  series  winding.  When  supplying  three-wire  systems,  the  gmen- 
tors  should  be  so  arranged  that  these  protective  devices  wni  come  in  the  outside 
l«*d8.  .       ^  _^ 

For  three-wire,  direct-current  generators,  a  safety  device  must  be  placed  in  each 


armature,  direct-current  lead,  or  a  double  pole,  double  trip  circuit  breaker  In  eacS 
outside  generator  lead  and  corresponding  equaliser  connection. 

In  general,  generators  should  preferably  have  no  exposed  live  parts  and  the 


leads  should  be  well  Insulated  and  thoroughly  protected  against  meehanlcal  bijiny. 
This  protection  of  the  bare  live  parts  against  accidental  ccmtaot  would  apply  also  to 
any  exposed,  uninsulated  conductors  outside  of  the  generator  and  not  on  Uke  switch- 
board unless  their  potential  is  practically  that  of  the  ground. 


Where  the  needs  of  the  service  make  the  above  requirements  Impraetlcabte.  the 
Inspectl(m  Department  having  Jurisdiction  may,  in  writing,  modify  them. 

e.  Must  each  be  provided  with  a  name-plate,  giving  the  maker's  name, 
the  capacity  in  volts  and  amperes,  and  the  normal  speed  in  revolutxcms  per 
minute. 

f .  Terminal  blocks  when  used  on  generators  must  1^  made  of  appro»d 
non-combustible,  non-absorptive,  instuating  material,  such  as  slate,  niaxi>]e 
or  porcelain. 

2.  Qondactors. — From  generators  to  switchboards,  rheostats  or  other 
instnmients.  and  thence  to  oustide  lines: — 

a.    Must  be  in  plain  sight  or  readily  accessible. 

Wires  from  generator  to  switchboard  may.  however,  be  placed  in  a  coodidt  Is 

I  brick  or  cement  pier  on  which  the  generator  stands,  provided  that  proper  — 

cautions  are  taken  to  protect  them  against  moisture  and  to  thoroughly  insulatie  t 


the  brick  or  cement  pier  on  which  the  generator  stands,  provided  that  proper  ]ve> 
cautions  are  taken  to  protect  them  against  moisture  and  to  thoroughly  insulatie  tnsa 
from  the  pier.  If  lead-covered  cable  Is  used,  no  further  proteetloo  will  be  reqidied. 
but  It  should  not  be  allowed  to  rest  upon  sharp  edges  which  in  tinoe  ml^t  cvt  tats 
the  lead  sheath,  especially  If  the  cables  were  liable  to  vibration.  A  smooth  nawt? 
Is  desired.  If  iron  conduit  Is  provided,  double  bialded  rubber-covered  wire  ttss 
No.  47)  wUl  be  satisfactory. 

b.  M\ist  have  an  approved  insulating  covering  hs  called  for  by  rules  ic 
Class  "C"  f or  similar  work,  except  that  in  central  stations,  on  exposed  circuits. 
the  wire  which  is  used  must  have  a  heavy  braided,  non-combustible  outer 
covering. 

Bus  bars  may  be  made  of  bare  metal. 

Rubber  insulaUons  Ignite  easily  and  bum  freely.  Where  a  number  of  vties  sic 
Drought  dose  together,  as  Is  generally  the  case  in  dynamo  rooms,  especially  about  Ike 


STATIONS  AND  DYNAMO  JUX>MS.  1806 

switchboard.  It  to  tberefore  neecBBair  to  surround  thto  InflamnmMe  material  with  a 
tight.  noQKombuBtible  outer  cover.  If  this  is  not  done,  a  fire  once  started  at  this 
point  would  spread  rapidly  a'ong  the  wires,  producing  Intense  heat  and  a  dense 
smoke  Where  the  wires  have  such  a  covering  and  are  well  Insulated  and  supported, 
using  only  nwi-eombustlble  materials.  It  Is  believed  that  no  appreciable  fire  nazard 
exists,  even  with  a  large  group  of  wires. 

Flame  proofing  should  be  stripped  back  on  all  eablesa  sufficient  amount  to  give 
the  necessary  insulation  distance  for  the  voltage  of  the  circuit  on  which  the  cable 
Is  used.  The  stripping  back  oi  the  flame  proofing  is  neoessary  on  account  o(  the  poor 
insulating  qualities  of  the  flame  proofing  material  now  available.  Flame  proofing 
may  be  omitted  where  satisfactory  fire-proofing  Is  accomplished  by  other  means, 
Mich  as  eompartments,  etc. 

c  Must  be  kept  so  rigidly  in  place  that  they  cannot  come  in  contact. 

d.  Must  in  all  other  respects  be  installed  with  the  same  precautions  as 
required  by  rules  in  Class  *C"  for  wires  carrying  a  current  of  the  same 
volume  and  potential. 

e.  In  wiring  switchboards,  the  gxotmd  detector,  voltmeter,  pilot  lights 
and  potential  transformers  must  be  connected  to  a  circuit  of  not  less  than 
No.  14  B.  &  S.  gage  wire  that  is  protected  by  an  approved  fuse,  this  circuit 
is  not  to  carry  over  660  watts. 

For  the  protectloo  of  Instruments  and  pilot  lights  on  switchboards,  approved 
ff.  E.  Code  Standard  f^doeed  Fuses  are  preferred,  but  approved  enclosed  nises  of 
other  designs  of  not  over  two  (.2)  amperes  eapacitv.  may  be  used. 

Voltmeter  switches  having  concealed  connections  must  be  idalnly  marked. 
Bbowlng  connections  made. 

3  Switchboards. — a.  Must  be  so  placed  as  to  reduce  to  a  minimum 
the  danger  of  communicating  fire  to  adjacent  combustible  material. 

Special  attention  is  called  to  the  fact  that  switchboards  should  not  be  built  down 
to  the  floor,  nor  up  to  the  celling.  A  space  of  at  least  ten  or  twelve  Inches  should  be 
left  between  the  floor  and  the  board,  except  when  the  floor  about  the  switchboard  Is 
of  concrete  or  other  fireproof  construction,  and  a  space  of  three  feet.  If  possible, 
betweoi  the  celling  and  the  board,  in  order  to  prevent  nre  from  communicating  from 
the  switchboard  to  the  floor  or  ceiling,  and  also  to  prevent  the  forming  of  a  partially 
concealed  space  very  liable  to  be  used  for  storage  of  rubbish  and  oily  waste. 

b.  Must  be  made  of  non-combustible  material  or  of  hardwood  in  skele- 
ton form,  filled  to  prevent  absorption  of  moisture. 

If  wood  is  used  all  wires  and  all  current  carrying  parts  of  the  apparatus  on  the 
switchboard  must  be  separated  therefrom  by  non-combustlUe.  non-absorptive  In- 
sulating material. 

c  Must  be  accessible  from  all  sides  when  the  connections  are  on  the  back, 
but  may  be  placed  against  a  brick  or  stone  wall  when  the  wiring  is  entirely 
on  the  face. 

If  the  wiring  Is  on  the  back,  there  should  be  a  dear  space  of  at  least  eighteen 
Inches  between  the  wall  and  the  apparatus  on  the  board,  and  even  if  the  wiring  Is 
entirely  on  the  face,  it  is  much  better  to  have  the  board  set  out  from  the  wall.  The 
space  back  of  the  board  should  not  be  dosed  In.  except  by  gratlne  or  netting  either 
at  the  sides,  top  or  bottom,  as  such  an  enclosure  Is  almost  sure  to  be  used  as  a  doset 
for  dothlng  or  for  the  storage  of  oil  cans,  rubbish,  etc.  An  open  space  Is  much  more 
likely  to  be  kept  dean,  and  Is  more  convenient  for  making  repali^  examinations,  etc 

d.  Must  be  kept  free  from  moisture. 

e.  On  switchboards  the  distances  between  bare  live  parts  of  opposite 
pobuitv  must  be  made  as  great  as  practicable,  and  must  not  be  less  than  those 
given  tor  tablet-boards  (see  No.  o3  A). 

4.  Resistance  Boxes  and  Eiyiializen. — (For  construction  rules,  see  No. 
60.)  a.  Must  be  placed  on  a  switchboard,  or  if  not  thereon,  at  a  distance  of 
at  least  one  foot  from  combustible  material,  or  separated  therefrom  by  a 
non-combustible,  non-absortive  insulating  material  such  as  slate  or  marble. 

This  will  require  the  use  of  a  dab  or  panel  of  non-combustlble,  non-abeorptlve 
insulating  material  such  as  slate  or  marble,  somewhat  larger  than  the  rheostat,  which 
shall  be  secured  In  position  Independently  of  the  rheostat  supports.    Bolts  for  sup- 

Krtlng  the  rheostat  shall  be  countersunk  at  least  i  Inch  below  the  surface  at  the 
ck  of  the  dab  and  filled.  For  proper  mechanical  strength,  dab  should  be  of  a 
thickness  consistent  with  the  size  and  weight  of  the  rheostat,  and  In  no  case  to  be 
leas  than  i  inch 

If  resbtance  devices  are  installed  In  rooms  where  dust  or  combustible  flyings 
would  be  liable  to  accumulate  on  them,  they  should  be  equipped  w  th  a  dust-proof 
face  plate. 

b.  Where  protective  resistances  are  necessary  in  connection  with  auto- 
matic rheostats  incandescent  lamps  may  be  used,  provided  that  they  do  not 


1396  70.—ELECTRIC  POWER  AND  LIGHTING. 

carry  or  control  the  main  current  nor  constitute  the  regulating  resistance  o^ 
the  device. 

When  so  used.  lamps  must  be  mounted  in  porcelain  receptables  upon  mm- 
combustible  supports,  and  mixst  be  so  arransed  that  they  cannot  have  its- 
pressed  upon  them  a  voltage  greater  than  that  for  which  they  are  rated. 
They  must  in  all  cases  be  provided  with  a  name-plate,  which  shaOl  be  peima- 
nently  attached  beside  the  porcelain  receptacle  or  receptacles  and  stamped 
with  the  candle-power  and  voltage  of  the  lamp  or  lamps  to  be  used  in  eadi 
receptacle. 

c.  Wherever  insulated  wire  is  used  for  connection  between  resistances 
and  the  contact  plate  of  a  rheostat,  the  insulation  must  be  slow  burning  (see 
No.  43).  For  large  field  rheostats  and  similar  resistances,  where  the  contact 
plates  are  not  mounted  upon  them,  the  connecting  wires  may  be  run  togethn* 
m  groups  so  arranged  that  the  maximum  difference  of  potential  between  any 
two  wires  in  a  group  shall  not  exceed  75  volts.  Each  ^^up  of  wires  must 
either  be  motmted  on  non -combustible,  non-absorptive  insulators  giving  at 
least  i  inch  separation  from  surface  wired  over,  or.  where  it  is  necessary  to 

Erotect  the  wires  from  mechanical  injury  or  moisture,  be  run  in  appromd 
aed  conduit  or  equivalent. 

5.  Lightning  Arresters. — (For  construction  rules,  see  No.  C8.) 

a.  Must  be  attached  to  each  wire  of  every  overhead  circuit  connected 
with  the  station. 

It  Is  rpcommendod  to  all  electric  lUcht  and  power  companies  that  arresters  be 
connected  at  Intervals  over  systems  In  such  numbers  and  so  located  as  to  prevtni 
ordinary  discharges  entering  (over  the  wires)  buUdlnga  connected  to  the  lines. 

b.  Must  be  located  in  readily  accessible  places  away  from  combustible 
materials,  and  as  near  as  practicable  to  the  point  where  the  wires  enter  the 
building. 

In  all  cases,  kinks,  coils  and  sharp  bends  in  the  wires  between  the  arresters 
and  the/ outdoor  lines  must  be  avoided  as  far  as  possible. 

The  switchboard  does  not  neces«arlly  afford  the  only  loeatioa  meettng  tiMse 
requirements.  In  fact,  ir  the  arresters  can  be  located  in  a  safe  and  accesafbte  plaee 
away  from  the  board,  this  should  be  done.  for.  In  case  the  arrester  should  taQ  or  be 
seriously  damaged  there  would  then  be  less  chance  of  starting  arcs  on  the  board. 

c.  Must  be  connected  with  a  thoroughly  good  and  permanent  ground 
connection  by  metallic  strips  or  wires  having  a  conductivity  not  less  than 
that  of  a  No.  6  B.  &  S.  gage  copper  wire,  which  must  be  run  as  nearly  in  a 
straight  line  as  possible  from  the  arresters  to  the  ground  connection. 

(around  wires  for  lightning  arresters  must  not  be  attached  to  gas  pipes 
within  the  bxiildings. 

It  Is  often  desirable  to  Introduce  a  choke  coll  In  efrcult  between  the  arrestees  and 
the  dynamo.  In  no  case  should  the  ground  wires  from  lightning  arresters  be  pm 
Into  Iron  pipes,  as  these  would  tend  to  impede  the  discharge. 

d.  All  choke  coils  or  other  attachments,  inherent  to  the  lightning  pro> 
tection  equipment,  shall  have*  an  insulation  from  the  ground  or  other  con* 
ductors  equal  at  least  to  the  insulation  demanded  at  other  points  of  the  cir> 
cuit  in  the  station. 

6.  Care  and  Attendance. — a.  A  competent  man  must  be  kept  on  doty 
where  generators  are  operating,  b.  Oily  waste  must  be  kept  in  approved 
metal  cans  and  removed  daily. 

Approved  waste  cans  shall  be  made  of  metaU  with  legs  raMng  can  three  laches 
from  the  floor,  and  with  self-closing  covers. 

7.  Testing  and  Insulation  Resistance. — a.  All  circuits  except  such  as 
are  permanently  grounded  in  accordance  with  No.  ISA  must  be  provided 
with  reliable  ground  detectors.  Detectors  which  indicate  contintKjusly  and 
give  an  instant  and  permanent  indication  of  a  ground  are  preferable.  Ground 
wires  from  detectors  must  not  be  attached  to  gas  pipes  within  the  building. 

b.  Where  continuously  indicating  detectors  are  not  feasible,  the  circuits 
should  be  tested  at  least  once  a  day,  smd  preferably  oftener. 

c.  Data  obtained  from  all  tests  must  be  preserved  for  examinatioii  by 
the  Inspection  Department  having  jurisdiction. 

These  rules  on  testing  to  bo  applied  at  such  places  as  may  be  dealgnated  by  the 
Inspection  Department  having  jurlBdlctloo.  tized  bJXjOOQTC 


STATIONS  AND  DYNAMO  ROOMS.  1397 

8  Motors. — Tbe  use  o(  motors  operating  at  a  potential  In  excess  of  560  rolts 
will  onljr  be  approved  when  every  practicable  safeguard  baa  been  provided.  Plans 
for  such  Instaiiattons  should  be  submitted  to  the  Inspection  Department  having 
jurisdiction  before  any  work  Is  begun 

a.  Must,  when  operating  at  a  potential  in  excess  of  660  volts,  have  no 
exposed  live  metal  parts,  and  have  their  base  frames  permanently  and  effect- 
ively grounded. 

Mctors  operating  at  a  potential  of  650  volts  or  less  must  be  thoroughly 
insulated  from  the  groimd  wherever  feasible  Wooden  base  frames  used  for 
this  purpose,  and  wooden  floors,  which  are  depended  upon  for  insulation 
where»  for  any  reason,  it  is  necessary  to  omit  the  base  frames,  must  be  kept 
filled  to  prevent  absorption  of  moisture,  and  must  be  kept  clean  and  dry. 
Where  frame  insulation  is  impracticable,  the  Inspection  Department  having 
jurisdiction  may,  in  writing,  permit  its  omission,  in  which  case  the  frame 
must  be  permanently  and  effectively  grounded. 

A  blgh-potential  machine  should  be  surrounded  with  an  Insulated  platform. 
This  may  be  made  of  wood,  mounted  on  Insulating  supports,  and  so  arranged  that  a 
man  must  stand  upon  It  In  order  to  touch  any  part  of  the  machine. 

In  case  of  a  machine  having  an  innulated  frame.  If  there  Is  trouble  from  static 
electricity  due  to  belt  friction.  It  should  be  overcome  by  placing  near  tbe  belt  a 
metallic  comb  connected  to  the  earth,  or  by  grounding  the  tnune  through  a  resistance 
of  not  lees  than  300.000  ohms. 

b.  Motors  operating  at  a  potential  of  650  volts  or  less  must  be  wired 
Bvith  the  same  precautions  as  required  by  rules  in  Class  "C"  for  wires  carry- 
ing a  current  of  the  same  volume. 

Motors  operating  at  a  potential  between  660  and  3,600  volts  must  be 
wired  with  approved  multiple  conductor,'  metal  sheathed  cable  in  approved 
unlined  metail  conduit  firmly  secured  in  place.  The  metal  sheath  must  be 
permanently  and  effectively  grounded,  and  the  construction  and  installation 
Df  the  conduit  must  conform  to  rules  for  interior  conduits  (see  No.  26 
ind  No.  49  a,  j.  and  k),  except  that  at  outlets  approved  outlet  bushings 
ihall  be  used. 

Tbe  motor  leads  or  branch  circuits  must  be  deslmed  to  carry  a  current  at  least 
25  per  cent  greater  than  that  for  which  the  motor  Is  rated.  In  order  to  provide  for 
;he  Inevitable  occasional  overloading  of  the  motor  and  the  Increased  current  required 
n  starting,  without  overfuslng  the  wires:  but  where  the  wires  under  this  rule  would 
)e  overfused.  In  order  to  provide  for  the  starting  current,  as  In  the  case  of  many  of  the 
iltemating  current  motors,  the  wires  must  be  of  such  size  as  to  be  properly  protected 
)y  these  larger  fuses. 

The  Insulation  of  the  several  conductors  for  high  potential  motors,  where  leaving 
lie  metal  sheath  at  outlets,  must  be  thoroughly  protected  from  moisture  and  me- 
;hanlcal  Injury.  This  may  be  accomplished  by  means  of  a  pot  head  or  some  equivalent 
nethod.  The  conduit  must  be  substantially  bonded  to  the  metal  casings  of  all 
Ittlngs  and  apparatus  connected  to  the  Inside  high  tension  circuit.  It  would  be 
aucb  preferable  to  make  the  conduit  system  continuous  throughout  by  connecting 
he  conduit  to  fittings  and  motors  by  means  of  screw  joints,  and  this  construction  Is 
trongly  recommended  wherever  practicable. 

High  potential  motors  should  preferably  be  so  located  that  the  amount  of  Inside 
rlrlng  wlU  be  reduced  to  a  minimum.  Inspection  Department  having  jurisdiction 
oay  permit  the  wire  for  high  potential  motors  to  be  Installed  according  to  the  general 
ules  for  high  potential  systems  when  the  outside  wires  directly  enter  a  motor  room 
see  Section  /).  Under  these  conditions  there  would  generally  be  but  a  few  feet  of 
rlre  inside  the  building  and  none  outside  the  motor  room. 

c  Each  motor  and  resistance  box  must  be  protected  by  a  cut-out  and 
onUroUed  by  a  switch  (see  No.  17a).  said  switch  plainly  indicating  whether 
cm  or  "off."  With  motors  of  one-fourth  horse  power  or  less,  on  circuits 
/here  the  voltage  does  not  exceed  300.  No.  21  d  must  be  complied  with,  and 
ingle  pole  switches  may  be  used  as  allowed  in  No.  22  c.  The  switch  and 
heostat  must  be  located  within  sight  of  the  motor,  except  in  cases  where 
pecial  permission  to  locate  them  elsewhere  is  given,  in  writing,  by  the  In- 
pection  Department  having  jurisdiction. 

The  use  of  circuit-breakers  with  motors  is  recommended,  and  may  be  required 
•y  the  Inspection  Department  having  Jurtsdiction. 

Where  the  circuit-breaking  device  on  the  motor-starting  rheostat  disconnects 
U  wires  of  the  circuit,  the  switch  called  for  in  this  section  may  be  omitted. 

Overload-release  devices  on  motor-starting  rheostats  Will  not  be  considered  to 
like  the  place  of  the  cut-out  required  by  this  section  if  they  are  Inoperative  during 
be  starting  of  the  motor 

The  switch  Is  necessary  for  entirely  dlsconnecttag  the  motor  when  not  In  use.  and 
be  cut-out  to  protect  the  motor  from  excessive  currents  due  to  accidents  or  careless 
andllng  when  starting.  An  automatic  circuit-breaker  disconnecting  all  wires  of 
be  cl rcult  may,  however,  serve  as  both  switch  and  cut-out.  ^  ^  ^  ^ I  ^ 

In  general,  motors  should  preferably  have  no  exposed  live  parts^  OOgLC 


1398  70.— ELECTRIC  POWER  AND  UGHTING, 

d.  Rheostats  mtist  be  so  installed  as  to  comply  with  aZ^the  reqinR- 
ments  of  No.  4.     Auto  starters  must  comply  with  requirements  of  No.  4  c 

Starting  rheostats  and  auto  starters,  unless  equipped  with  tl«ht  caatn^s  eadostet 
all  current-carrying  parts,  should  be  treated  about  the  same  as  knife  swltdtaB.  a:^ 
In  all  wet.  dusty  or  Ifnty  places,  should  be  enclosed  In  dust-tlsht.  fireproof  cab^fts. 
If  a  special  motor  room  Is  provided,  the  starting  apparatus  and  safety  derlcee  aiunU 
be  Included  within  It.  Where  there  Is  any  liability  of  short  circuits  acrasn  tbelr  ex- 
posed live  parts  being  caused  by  accidoital  contacts,  they  should  either  be  endoscd 
m  cabinets,  or  else  a  railing  should  be  erected  around  them  to  keep  inxamhorlKd 
persons  away  from  their  Immediate  vicinity. 

e.  Must  not  be  run  in  series-multiple  or  multiple-series,  except  on  oosi- 
stantjx>tential  systems,  and  then  only  by  special  permission  of  tne  Inspec- 
tion Department  having  jurisdiction. 

f.  Must  be  covered  with  a  waterproof  cover  when  not  in  use,  and,  i 
deemed  necessary  by  the  Inspection  Department  having  jurisdictton.  must 
be  enclosed  in  an  approved  case. 

When  it  is  necessary  to  locate  a  motor  In  the  vicinity  of  oombosUbles  or  in  wet 
or  very  dusty  or  dirty  places.  It  is  generally  advisable  to  endoae  It  as  above.  Sot* 
otclosures  should  be  readily  accessible,  dost  proof  and  sufficiently  ventilated  » 

Ere  vent  an  excessive  rise  of  temperature.    The  sides  should  prof«:ably  be  m^ 
irgely  of  glass,  so  that  the  motor  may  be  always  plainly  visible     This  leBsecs  the 
chance  of  Its  being  neglected,  and  allows  any  derangement  to  be  at  onoe  notlcod. 

The  use  of  enclosed  type  motor  Is  recommended  In  dusty  idaoes.  being  prefeiablf 
to  wooden  boxing.  From  the  nature  of  the  question  the  deelslan  as  to  details  of 
construction  must  be  left  to  the  Inspection  Department  havtng  Jurtsdlctton  to  deter* 
mine  In  each  Instance. 

ff.  Must,  when  combined  with  ceiling  fans,  be  hung  from  instilated  hookv 
or  else  there  must  be  an  insulator  interposed  between  the  nootor  and  is 
support. 

b.  Must  each  be  provided  with  a  name-plate,  giving  the  makers*  name, 
the  capacity  in  volts  and  amperes,  and  the  normal  speed  in  revolutiocis  per 
minute. 

i.  Terminal  blocks  when  used  on  motors  must  be  made  of  approved  non- 
combustible,  non-absorptive,  insulating  material  such  as  slate,  marfole  or 
porcelain. 

J.  Variable  speed  motors,  unless  of  special  and  appropriate  design,  if 
controlled  by  means  of  field  regulation,  must  be  so  arranged  and  conxiected 
that  they  cannot  be  started  imder  weakened  field. 

9.  Raflway  Power   Plants. — a.    Each  feed  wire  before  it  leaves  the 

station  must  be  equipped  with  an  approved  automatic  circuit-breaker  (see 
No.  62)  or  other  device,  which  will  immediately  cut  off  the  current  in  case 
of  an  accidental  ground.  This  device  must  be  mounted  on  a  fireproof 
base,  and  in  full  view  and  reach  of  the  attendant.' 

1 0.  Storage  or  Primary  Batteries. — a.  When  current  for  light  and  porvpcr 
is  taken  from  primary  or  secondary  batteries,  the  same  general  regulations 
must  be  observed  as  apply  to  similar  apparatus  fed  from  dynamo  generaton 
delevoping  the  same  dilierence  of  potential. 

b.  Storage  battery  rooms  must  be  thoroughly  ventilated. 

c.  Special  attention  is.  directed  to  the  rules  for  wiring  in  rooms  where 
acid  fumes  exist  (sec  No.  24,  i  and  j). 

d.  All  secondary  batteries  must  be  mounted  on  non-absorptive,  noo- 
combustible  insulators,  such  as  glass  or  thoroughly  vitrified  and  glazed  ixste- 
lain. 

e.  The  use  of  any  metal  liable  to  corrosion  must  be  avoided  in  cell  coa- 
nections  of  secondary  batteries. 

11.  Transformers. — (For  construction  rules,  see  No.  C2.)     (See  also 

Nos.  13,  13A.  36.)  a.  In  central  or  sub-stations  the  transformers  must  be 
so  placed  that  smoke  from  the  burning  out  of  the  coils  or  the  boiling  over 
of  the  oil  (where  oil  filled  cases  are  used)  cou^i  do  no  harm. 
■  It  the  Insulation  In  a  transformer  breaks  down,  ooosklerable  heat  Is  lOaeify  to  be 
developed.  This  would  cause  a  dense  smoke,  which  might  be  mistaken  Cor  a  are  ami 
reeuli  In  water  being  thrown  hi  to  the  building,  and  a  neavy  loss  thereby  eatafisl 
Moreover,  with  oil-cooled  transformers.  ecpedaUy  if  the  esses  are  filled  too  CaU.  thi 
ou  may  become  Ignited  and  boU  over,  producing  a  very  stubborn  lira. 


OUTSIDE  WORK— ALL  SYSTEMS  AND  VOLTAGES.     IMO 

b.  In  central  or  sub-stations,  casings  of  all  transformers  must  be  per^ 
znanently  and  eflfcctively  grounded. 

Transfonners  used  exduslvelT  to  supply  current  to  swltchboanl  Instrumenta 
need  not  be  grounded,  provided  tney  are  tnoroughly  Insulated. 

Class  B.— OUTSIDE  WORK. 

(LlOHT,  POWBR  AND  HbAT.      FoR  SIGNALING  StSTBMS,  SbB  CLABS  B.) 

ALL  SYSTEMS  AND  VOLTAGES. 

12.  Wires. — a.  Line  wires  must  have  an  approved  weatherproof  or 
rubber  insulating  covering  (see  No.  44  and  No.  41)-  That  portion  of  the 
service  wires  between  the  main  cut-out  and  switch  and  the  first  support  from 
the  cut-out  or  switch  on  outside  of  the  building  must  have  an  approved 
rubber  insulating  covering  (see  No.  41),  but  from  the  above-mentioned  sup- 
port to  the  line,  may  have  an  approved  weatherproof  insulating  covering 
(see  No.  44),  it  kept  free  from  awnings,  swinging  signs,  shutters,  etc. 

b.  Must  be  so  placed  that  moisture  cannot  form  a  cross  connection  be- 
tween them,  not  less  than  a  foot  apart,  and  not  in  contact  with  any  substance 
other  than  their  insulating  supports.  Wooden  blocks  to  which  insulators  are 
attached  must  be  covered  over  their  entire  surface  with  at  least  two  coats  of 
waterproof  paint. 

c.  Must  be  at  least  seven  feet  above  the  highest  point  of  fiat  roofs,  and 
at  least  one  foot  above  the  ridge  of  pitched  roofs,  over  which  they  pass  or  to 
which  they  are  attached. 

Roof  structures  are  freaumtly  found  which  are  too  low  or  much  too  Itffht  for  the 
work,  or  which  have  been  carelessly  put  up.  A  structure  which  Is  to  hold  the  wires 
a  proper  distance  above  the  roof  in  all  kinds  of  weather  must  not  only  be  of  sufficient 
height,  but  must  be  substantially  constructed  of  strong  material. 

d.  Must  be  protected  by  dead  insulated  guard  irons  or  wires  from  pos- 
sibility of  contact  with  other  conducting  wires  or  substances  to  which  cur- 
rent may  leak.  Special  precautions  of  this  kind  must  be  taken  where  sharp 
angles  occur,  or  where  any  wires  might  possibly  come  in  contact  with  electric 
light  or  power  wires. 

Ckmmb.  when  unavoidable,  should  be  made  as  nearly  at  right  angles  as  possible. 

€.  Must  be  provided  with  petticoat  insulators  of  glass  or  porcelain. 
Porcelain  knobs  or  cleats  and  rubber  hooks  will  not  be  approved. 

f .  Must  be  so  spliced  or  joined  as  to  be  both  mechanically  and  elec- 
trically secure  without  solder.  The  joints  must  then  be  soldered,  to  insure 
preservation,  and  covered  with  an  insulation  equal  to  that  on  the  conductors. 

All  Joints  must  be  soldered,  unless  made  with  some  form  of  approved  sidlebig 
device.  This  ruling  applies  to  Joints  and  siriioes  in  all  classes  of  wiring  covered  by 
these  rules. 

C.  Must,  where  they  enter  buildings,  have  drip  loops  outside,  and  the 
holes  through  which  the  conductors  pass  must  be  bushed  with  non-com- 
btistible,  non-absorptive,  insulating  tubes  slanting  upward  toward  the 
inside. 

For  low  potential  systems  the  service  wires  may  be  brought  Into  buildings 
through  a  single  Iron  conduit.  The  conduit  to  be  curved  downward  at  Its  outer  end 
and  carefully  sealed  or  equipped  with  an  approved  servloe-head  to  prevent  the 
entrance  of  moisture.  The  outer  end  must  bo  at  least  one  foot  from  any  wood-work 
and  the  inner  end  must  extend  to  tlie  service  cut-out.  and  If  a  cabinet  Is  required  by 
the  Code  must  rater  the  cabinet  hi  a  manner  similar  to  that  described  In  fine  print 
note  under  No.  256. 

h.  Electric  light  and  power  wires  must  not  be  placed  on  the  same  cross- 
arm  with  telegraph,  telephone  or  similar  wires,  and  when  placed  on  the 
same  pole  with  such  wires  the  distance  between  the  two  inside  pins  of  each 
cross-arm  must  not  be  less  than  twenty-six  inches. 

L  The  metallic  sheaths  to  bibles  must  be  permanently  and  efltectively 
connected  to  "earth." 

TrdUy  Wires. — ^J.  Must  not  be  smaller  than  No.O  B.  &  S.  gage  copper 
or  No. 4  B.  &  S.  gage  silicon  bronze,  and  must  readily  stand  the  strain  upon 
them  when  in  use. 

k.  Must  have  a  double  insulation  from  the  ground.  Iff^KP^A^^  Po^ 
construction  the  pole  will  be  considered  as  one  insulatidfi^d  by  VjUUy  H. 


1400  70.— ELECTRIC  POWER  AND  LIGHTING. 

I.  Must  be  capable  of  being  disconnected  at  the  power  plant,  or  of  beN 
divided  into  sections,  so  that,  in  case  of  fire  on  the  railway  route,  the  cnntst 
may  be  shut  off  from  that  particular  section  and  not  interf ete  with  tbe  wod 
of  the  firemen.    This  rule  also  applies  to  feeders. 

m.  Must  be  safely  protected  against  accidental  contact  where  crosei 
by  other  conductors. 

Guard  wires  should  be  Insulated  from  the  ground  and  should  be  deecrloilr 
dlsoonnected  In  sections  of  not  more  tiian  300  feet  in  length. 

Ground  Return  Wins. — n.  For  the  diminution  of  electrolytic  oorrosiaKi  of 
undei]Kroimd  metal  work,  groimd  return  wires  must  be  so  arranged  thai 
the  difference  of  potential  between  the  grounded  dynamo  terminal  and  any 
point  on  the  return  circuit  will  not  exceed  twenty-five  volts. 

It  Is  suggested  tbat  the  positive  wAe  of  the  dynamo  be  coonected  to  the  trolley 
line,  and  that  whenever  pipes  or  other  underground  metal  work  are  found  to  be 
electrically  positive  to  the  rails  or  surrounding  earth,  that  they  be  connected  br 
conductors  arranged  so  as  to  prevent  as  tar  as  possible  curroit  (low  from  the  pipei 
Into  the  ground. 

12  A.  Constant -Potential  Pole  Lines,  Over  5,000  Volts. —  (Over- 
head lines  of  this  class  unless  properly  arranged  may  increase  the  fire 
loss  from  the  following  cavises: — ^Accidental  crosses  between  such  lines  and 
low-potential  lines  may  allow  the  high-voltage  current  to  enter  build ingsovg 
a  large  section  of  adjoining  country.  Moreover,  such  high-voltage  hues,  if 
carried  close  to  buildings,  hamper  the  work  of  firemen  in  case  of  fire  in  the 
building.  The  object  of  these  rules  is  so  to  direct  this  class  of  oonstructioa 
that  no  increase  in  fire  hazard  will  result,  while  at  the  same  time  care  has  been 
taken  to  avoid  restrictions  which  would  luireasonably  impede  progress  in 
electrical  development. 

It  is  fully  understood  that  it  is  impossible  to  frame  rules  which  wiS 
cover  all  conceivable  cases  that  may  arise  in  construction  work  of  such  an 
extended  and  varied  nature,  and  it  is  advised  that  the  In^>ection  Department 
having  jurisdiction  be  freely  consulted  as  to  any  modification  of  the  rules  m 
particular  cases.) 

a.  Every  reasonable  precaution  must  be  taken  in  arranging  nnites  so  as 
to  avoid  expc)sure  to  contacts  with  other  electric  circuits.  On  existing  hces. 
where  there  is  a  liability  to  contact,  the  route  should  be  changed  by  mutual 
agreement  between  the  parties  in  interest  wherever  possible. 

b.  Such  lines  should  not  approach  other  pole  lines  nearer  than  a  distance 
equal  to  the  height  of  the  taller  pole  line,  and  such  lines  should  not  be  on  the 
same  poles  with  other  wires,  except  that  signaling  wires  used  by  the  Company 
operating  the  high-pressure  svstem.  and  which  do  not  enter  property  other 
than  that  owned  or  occupiea  by  such  Company,  may  be  carried  over  the 
same  poles. 

c.  Where  such  lines  must  necessarily  be  carried  nearer  to  other  pole  Kne$ 
than  is  specified  in  Section  b  above,  or  where  they  must  necessarily  be  carried 
on  the  same  poles  with  other  wires,  extra  precautions  to  reduce  the  liability 
of  a  breakdown  to  a  minimum  must  be  taken ,  such  as  the  use  of  wires  of  ampk 
mechanical  strength,  widely  spaced  cross-arms,  short  spans,  double  or  extn 
heavy  cross-arms,  extra  heavy  pins,  insulators,  and  poles  thoroughly  sup- 
ported. If  carried  on  the  same  poles  with  other  wires,  the  high-pressure 
wires  must  be  carried  at  least  three  feet  above  the  other  wires. 

d.  Where  such  lines  cross  other  lines,  the  poles  of  both  lines  must  be  of 
heavy  and  substantial  construction. 

Whenever  it  is  feasible.  end-insulat9r  guards  should  be  placed  on  the 
cross-arms  of  the  upper  line.  If  the  high-pressure  wires  crc^s  below  the  other 
lines,  the  wires  of  the  upper  line  should  be  dead-ended  at  each  end  of  the  spac 
to  double-grooved,  or  to  standard  transposition  insulators,  and  the  Ihae  com- 
pleted by  loops. 

One  of  the  following  forms  of  construction  must  then  be  adopted: — 
1.  The  height  and  length  of  the  cross-over  span  may  be  made  such  that 
the  shortest  distance  between  the  lower  cross-arms  of  the  upper  hne 
and  any  wire  of  the  lower  line  will  be  greater  than  the  length  of 
the  cross-over  span,  so  that  a  wire  breakmg  near  one  of  the  upper 
pins  would  not  be  long  enough  to  reach  any  wire  of  the  kiwer 
line.  The  high-pressure  wires  should  preferably  be  aboyrt  the 
other  wires. 


OUTSIDE  WORK— ALL  SYSTEMS  AND  VOLTAGES.      1401 

2.  A  joint  ^le  may  be  erected  at  the  crossing  point,  the  high-pressure 
wires  being  supported  on  this  pole  at  least  three  feet  above  tne  other 
wires.  Mechanical  gtiards  or  supports  must  then  be  jjrovided ,  so  that 
in  case  of  the  breaking  of  any  upper  wire,  it  will  be  impossible  for  it 
to  come  into  contact  with  any  ot  the  lower  wires. 

Such  llabnity  of  contact  may  be  prevented  by  the  use  of  suspension  wins, 
similar  to  those  employed  (or  suspendluR  aerial  telephone  cableB,  which  will 
prevent  the  hlffh-preasure  wires  from  (alUng,  in  case  they  break.  The  sus- 
pension wires  should  be  supported  on  high-potential  insulators,  should  have 
ample  mechanical  strength,  and  should  be  carried  over  the  high-pressure 
wires  for  one  span  on  each  side  of  the  Joint  pole,  or  where  suspension  wires 
are  not  desired  guard  wires  may  be  carried  above  and  below  tlie  lower  wires 
for  one  simn  on  each  side  of  the  Joint  pole,  and  so  spread  that  a  tailing  high- 
pressure  wire  would  be  held  out  of  contact  with  the  lower  wires. 


Such  guard  wires  should  be  supported  on  high-potential  insulators  or  should  be 

.   jan  sui    .   ^ ^ , 

be  delivered  by  any  of  the  high-pressure  wires.    Furtner,  the  construction 
must  be  such  that  the  guard  wires  will  not  be  destroyed  by  any  arcing  at  the 


grounded.    When  grounded,  they  must  be  of  such  size,  and  so  connected 
and  earthed,  that  they  can  surely  carry  to  groimd  any  current  which  may 


point  of  contact  lUcdy  to  occur  tmder  the  conditions  existing. 

3.    Whenever  neither  of  the  above  methods  is  feasible,  a  screen  of  wire 

should  be  interposed  between  the  lines  at  the  cross-over.     This 

screen  should  be  supported  on  high  tension  insulators  or  grounded, 

and  should  be  of  such  construction  and  strength  as  to  prevent  the 

upper  wires  from  coming  into  contact  with  the  lower  ones. 

If  the  screen  is  grounded,  each  wire  of  the  screen  must  be  of  such  size  and  so 

connected  and  earthed  that  It  can  surely  carry  to  ground  any  current  which 

may  be  delivered  bv  any  of  the  high-pressure  wires.     Further,  the  oraistruo- 

tlon  must  be  such  that  the  wires  oiscreen  will  not  be  destroyed  by  any  arcing 

at  the  point  of  contact  likely  to  occur  under  the  conditions  exlstbig. 

e.    When  it  is  necessary  to  carry  such  lines  near  buildings,  they  must  be 

at  such  height  and  distance  from  the  building  as  not  to  interfere  with  firemen 

in  event  of  nre;  therefore,  if  within  26  feet  of  a  building,  they  must  be  carried 

at  a  height  not  less  than  that  of  the  front  cornice,  and  the  height  must  be 

greater  than  that  of  the  cornice,  as  the  wires  come  nearer  to   the  building  in 

accordance  with  the  following  table: — 

Distance  of  wire  Elevation  of  wire 
fw>^i^,;i^;r«  above  cornice  of 
from  building.  building. 

Feet.  Feet. 

25  0 


Distance  of  wire  fJiTf,*!?"J?/.rl7 

from  building.  ^^^^^^d^^g^.^  °^ 
Feet.  Feet. 

10  6 


20  2  6  8 

16  4  2}  0 

It  Is  evident  that  where  the  roof  of  the  building  continues  nearly  In  line  with  the 
walls,  as  in  Mansard  roofs,  the  height  and  distance  of  the  line  must  be  reckoned  from 
some  part  ot  the  root  instead  of  from  the  cornice. 

13.  Transformers. — (For  construction  rules,  see  No.  62.)  (See  also 
Nos.  11.  13  A  and  36.)  [Where  transformers  are  to  be  connected  to  high- 
voltage  circuits,  it  is  necessary  in  many  cases,  for  best  protection  to  life  and 
property,  that  the  secondary  system  be  permanently  grounded,  and  pro- 
vision should  be  made  for  it  when  the  transformers  are  bviilt.] 

a.  Must  not  be  placed  inside  of  any  building,  excepting  central  stations 
and  sub-stations,  unless  by  special  permission  ofthe  Inspection  Department 
having  jurisdiction. 

An  outsldeloeatlOQ  Is  always  preferable;  6nt,  because  It  keeps  the  high-voltage 
primary  wires  entirely  out  of  the  building,  and  second,  for  the  reasons  given  in  the 
note  to  No.  lla. 

b.  Must  not  be  attached  to  the  outside  walls  of  buildings,  unless  separated 
therefrom  by  substantial  supports. 

It  Is  recommended  that  transformers  be  not  attached  to  frame  buildings  when 
any  other  locatl<»  is  practicable. 

I3A.  Qroundlns  Low-Potential  Circuits. —  Th^  grounding  of  low- 
pottnHal  circuits  under  the  following  regulations  is  only  allowed  when  such 
circuits  are  so  arranged  that  under  normal  conditions  of  service  there  will  be 
no  passage  of  current  over  the  ground  wire. 

Dtrect^urrent  d-Wire  Systems. — a.  Neutral  wire  may  be  grounded  and 
when  grounded  the  following  rules  must  be  complied  with: — 


1402  TO.-'ELECTRIC  POWER  AND  UGHTING. 

1.  Must  be  grounded  at  the  Central  Station  on  a  metal  plate  buried  in 
coke  beneath  permanent  moisture  level,  and  also  through  all  avafl- 
able  underground  water  and  gas  pipe  ssrstems. 

S.  In  undei^erroimd  sjrstems  the  neutral  wire  must  also  be  grounded  at 
each  distributing  box  through  the  box. 

8.  In  overhead  systems  the  neutral  wire  must  be  grounded  every  500 
feet,  as  provided  in  Sections  c  to  g. 

Inspeetloa  Departments  haying  Juilsdlctloa  may  raguirs  grounding  U  tbey  deem 
It  necessary. 

Two-wire  direct-current  systems  having  no  aooesslble  neotnl  point  are  not  to 
be  grounded. 

Attemating-Cufftnt  Secondary  SysUms. — b.  Transformer  secondaries  of 
distributing  systems  should  preferably  be  grotmded,  and  when  grounded, 
the  following  rules  must  be  complied  with:— 

1.  The  grotmding  must  be  made  at  the  neutral  point  or  wire,  whenever 
a  neutral  point  or  wire  is  accessible. 

8.  When  no  neutral  point  or  wire  is  acc^sibleonesideof  the  secondary 
circtiit  may  be  grounded,  provided  the  maximum  difference  of 
potential  between  the  grounded  point  and  any  other  point  in  the 
circuit  does  not  exceed  260  volts. 

8.  The  ground  connections  must  be  at  the  transformer  or  on  the  indi- 
vidual service  as  provided  in  sections  c  to  g,  and  when  transformexs 
feed  systems  with  a  neutral  wire,  the  neutral  wire  must  also  be 
grounded  at  least  every  250  feet  tor  overhead  systems,  and  every 
600  feet  for  underground  systems. 

Inspeetloa  Departments  having  jurlsdietloQ  may  raguirs  groondlng  if  tbey  deem 


Ground  Connections. — c.  When  the  ground  connection  is  inside  of  any 
building,  or  the  ground  wire  is  inside  of.  or  attached  to  any  building  (except 
Central  or  Sub-stations)  the  ground  wire  must  be  of  copper  and  have  an 
approved  rubber  insulating  covering  National  Electric  Code  Standard,  for 
from  0  to  600  volts.    (SeeNo.  41.) 

d.  The  ground  wire  in  direct-current  8-wire  systems  must  not  at  Central 
Stations  be  smaller  than  the  neutral  wire  and  not  smaller  than  No.  4  B.  &  S. 
gage  elsewhere.  The  ground  wire  in  alternating-current  systems  must  iiever 
be  less  than  No.  4  B.  &  S.  gage. 

On  three-ptasse  system,  the  ground  wire  must  have  a  carrying  capaelty  eqoal  to 
that  of  any  one  of  the  three  mains. 

e.  The  ground  wire  should,  except  for  Central  Stations  and  transfonne- 
sub-stations,  be  kept  outside  of  buildings  as  far  as  practicable,  but  may  be 
directly  attached  to  the  building  or  pole  by  cleats  or  straps  or  on  porcelaic 
knobs.  Staples  must  never  be  used.  The  wire  must  be  carried  in  as  nearly 
a  straight  Ime  as  practicable,  avoiding  kinks,  coils  and  sharp  bends,  and 
must  be  protected  when  exposed  to  mechanical  injury. 

This  protection  can  be  secured  by  use  or  an  approved  moulding,  and  aa  a  nde  tbe 
RTOund  wire  on  the  outside  of  a  building  should  be  In  moulding  at  ail  places  where  it 
is  in  within  seven  leet  trom  the  ground. 

f.  The  grotmd  connection  for  Central  Stations,  transformer  sub-stations, 
and  banks  of  transformers  must  be  made  through  metal  plates  btiried  in 
coke  below  permanent  moisture  level,  and  connection  shotud  also  be  made 
to  all  available  imderground  piping  sjratems  including  the  lead  sheath  of 
imderground  cables. 

g.  For  individual  transformers  and  building  services,  the  ground  con- 
nection may  be  made  as  in  Section  f,  or  may  be  made  to  water  piping 
svstems  running  into  buildings.  This  connection  may  be  made  by  carrying 
the  ground  wire  into  the  cellar  and  connecting  on  the  street  side  of  meters, 
main  cocks^  etc. 

Where  it  is  necessary  to  run  the  ground  wire  throu^  any  part  of  a  build- 
ing it  shall  be  protected  bjf  approved  porcelain  btishmgs  thirotigh  vnHs  or 
partitions  and  shall  be  run  in  approved  moulding,  except  that  in  basements 
It  may  be  supported  on  porcelain. 

In  connecting  a  ground  wire  to  a  plptng  system,  the  wire  should  be  sweat  Into  s 
lug  attached  to  an  approved  clamp,  and  the  damp  Ormty  bolted  to  the  wat«  pipe 
arter  all  rust  and  scale  have  been  removed;  or  be  soldered  Into  a  braas  plug  aad  tht 
l^^SJS^?^^^y  screwed  Into  a  pipe-flttlng.  or,  where  the  pipes  are  cast  Iron,  into  a  bole 
5^E£^'R5^w^^  P'P®  1^^'-  ^or  large  stations,  where  oonneeUng  to  undeneroond 
FiR^.^^^  ^"  and  spigot  joints,  it  is  weU  to  connect  to  several  lengths,  as  the  plpa 
Joints  may  be  of  rather  high  resistance.  «-•*-*  ••  we  j«t" 


mSIDB  WORK^ALL  SYSTEMS  AND  VOLTAGES,        1408 

Where  gitrand  platee  &re  itfed.  a  No.  18  Stubbs*  gage  copper  plate,  about  3x6 
feet  In  slxe.  with  about  2  feet  of  crushed  coke  or  charcoal,  about  pea  aUe.  both  under 
and  over  It.  would  make  a  ground  of  sufficient  capacity  for  a  moderate-sized  sta- 
tion, and  would  probably  answer  for  the  ordinary  sub-station  or  bank  of  transformers. 
For  a  large  central  station,  a  plate  with  considerable  more  area  might  be  necessary, 
depending  upon  the  other  underground  connections  available.  The  ground  wire 
should  be  riveted  to  the  plate  In  a  number  of  places,  and  soldered  for  Its  whole  loigth. 
Perhaps  even  better  than  a  copper  plate  Is  a  cast-Iron  plate  with  projecting  forks. 


the  Jdea  of  the  fork  being  to  distribute  the  connection  to  the  ground  over  a  fairly  broad 
area,  and  to  give  a  large  surface  contact.  The  ground  wire  can  probaMy  best  be 
connected  to  such  a  cast-Iron  plate  by  scAderlng  It  Into  brass  plugs  screwed  mto  holes 


area,  and  to  give  a  large  surface  contact.    The  ground  inre  can  probaMy  e 

connected  to  such  a  cast-iron  plate  by  scAderlng  It  Into  brass  plugs  screwed  mt 

tapped  m  the  plate.    In  all  cases,  the  Joint  between  the  plate  and  the  ground  wlro 

should  be  thorouf*-* ^^^^  — .-- * .—  w ttz. —  ..  _.w  _. 

paint  or  some  eau 


^i!f!^^]^.!^^*'<^  protected  against  oorroslon  by  palnttng  It  with  waterproof 


CLASS  C— INSIDE  WORK. 

(LlOBT    POWBR  AND  HbaT.     PoR  SIGNALING  StSTBMS.  8BB 

Class  B.) 
ALL  SYSTEMS  AND  VOLTAGES 

Gbnbral  Rulbs. 
14.   Wlnt^— (For   special  rules,   see  Nos.  16.  18.  34,  85,  88  and  89.) 

a.  Must  not  be  of  smaller  size  than  No.  14  B.  &  S.  gage,  except  as  al- 
lowed tinder  Noe.  24v  and  45b. 

b.  Tie  wires  must  have  an  insulation  equal  to  that  of  the  conductors 
they  confine. 

The  use  of  some  fonn  of  oonllnlng  knob  or  Insulator  which  will  dispense  with  tie 
wires  Is  recommended. 

c  Must  be  so  spliced  or  joined  as  to  be  both  mechanically  and  electrically 
secure  without  solder.  The  joints  must  then  be  soldered  to  insure  preserva- 
tion, and  covered  with  an  iniBulation  equal  to  that  on  the  conductors. 

Stranded  wires  must  be  soldered  before  being  fastened  under  clamps  or 
binding  screws,  and  ^lether  stranded  or  solid,  when  they  have  a  conduc- 
tivity greater  than  that  of  No.  8  B.  &  S.  gage  they  must  be  soldered  into 
lugs  for  all  terminal  connections. 

All  iotnts  must  be  soldered  unless  made  with  some  form  of  approved  splldng 
levlce.  This  ruling  applies  to  Joints  and  splices  In  all  dassee  of  wiring  covered  by 
these  rules. 

d.  Must  be  separated  from  contact  with  walls,  floora.  timbers  or  parti- 
tions through  which  they  may  pass  by  non-combustible,  non-absorptive 
insulating  tubes,  such  as  glass  or  porcelain,  except  as  provided  in  No.  24u. 

BusfalngB  must  be  long  enough  to  bush  the  entire  length  of  the  bole  In  one  oon- 
Jnuous  piece,  or  else  the  hole  must  first  be  bushed  by  a  continuous  waterproof  tube 
rhJs  tube  may  be  a  conductor,  such  as  Iron  pipe,  but  In  that  case  an  Insulating 
jusbing  must  oe  pushed  Into  each  end  of  It.  extending  far  enough  to  keep  the  wire  . 
kbaoltttely  out  of  contact  with  the  pipe. 

e.  Must  be  kept  free  from  contact  with  gas.  water  or  other  metallic 
wiping,  or  any  other  conductors  or  conducting  material  which  they  may 
zToaa,  by  some  continuotis  and  firmly  fixed  non-conductor,  creating  a  per- 
iianent  separation.  Deviations  from  this  rule  may  sometimes  be  allowed 
3y  special  permission. 

Where  one  wire  crosses  another  wire  the  best  and  usual  means  of  separating 
Jiem  Is  by  a  porodaln  tube  on  one  of  the  wires.  The  tubing  must  be  prevented  from 
novlng  out  of  place  either  by  a  deat  or  knob  on  each  end,  or  by  taping  It  securely  In 

'^The  same  method  may  be  adopted  where  wires  pass  dose  to  Iron  pipes,  beams. 
rtc..  or,  where  the  wires  are  above  the  pipes,  as  Is  generally  the  case,  aim)le  protection 


treiquently  be  secured  by  supporting  the  wires  with  a  porodam  cTeat  plaoed  as 

ty  above  the  pipe  as  pomlble. 

This  mU  mwil  tun  be  construed  as  in  any  way  modifying  No.  24.  Sections  h  and  ]. 


ff.  Must  be  so  placed  in  wet  places  that  an  air  space  will  be  left  between 
conductors  and  pipes  in  crossing,  and  the  former  must  be  nm  in  such  a  way 
hat  they  cannot  come  in  contact  with  the  pipe  accidentally.  Wires  should 
>e  run  over,  rather  than  tmder.  pipes  upon  which  moisture  is  likely  to 
^tlMT  or  which,  by  leaking,  might  cause  trouble  on  a  circuit. 

f  •  The  installation  of  electrical  conductors  in  wooden  moulding,  or  on 
nsulators,  in  elevator  shafts  will  not  be  approved,  but  conductors  may  bo 
nstalled  in  such  shafts  if  encased  in  approved  metal  conduitA^  t 

Digitized  by  VjOOQ  LC 


1404 


TO.—ELECTRIC  POWER  AND  LIGHTING. 


15.  Undersrotmd  Condnctors. — a.  Must  be  i>rotected  against 

and  mechanical  injury  where  brought  into  a  building,  and  all  oombostitit 
material  must  be  kept  from  the  immediate  vicinity. 

b.  Must  not  be  so  arranged  as  to  shunt  the  current  throxigh  a  btnldisf 
around  any  catch-box. 

c.  Where  underground  service  enters  building  through  tubes,  tbe  tabes 
shall  be  tightly  closed  at  outlets  with  asphaltum  or  other  non-cocidiictor. 
to  prevent  gases  from  entering  the  building  through  such  channels. 

d.  No  underground  service  from  a  subway  to  a  building  shall  supplT 
more  than  one  building  except  by  written  permission  from  uie  Inspectaoa 
Department  having  jurisdiction. 

16.  Table  of  Carrying  Capacity  of  Wlret.--a.  The  following  taUe. 
showing  the  allowable  carrying  capacity  ot  copper  wires  and  cables  ot 
ninety-eight  per  cent  conductivity,  according  to  the  standard  adopted  by 
the  American  Institute  of  Electric^  Engineers,  must  be  followed  in  pladi^ 
interior  conductors      (See  page  1388.) 

For  Insulated  aluminum  wire  tbe  safe  carrying  eapaclty  Is  elahty-four  per  eeot 
of  tbat  given  in  tbe  C<Hlowlng  tables  for  copper  wire  wlui  tbe  same  Und  of  ln«Mati«. 


Tablb  a. 

Tablb  B. 

Tablb  A. 

Tablb  B 

Rubber 

Other 

Conrl'd. 

Cond'd. 

Insula- 

Insula- 

Circular 

tion. 

tions. 

Mils. 

Amperes. 

Ampens. 

See 
NoTll. 

See  No.  42 
to  44. 

200.000 

200 

900 

B.&S. 

Circular 

800.000 

270 

400 

Gage. 

Amperes.Amperes. 

Mils. 

400.000 

830 

510 

18 

3 

5 

1.624 

500.000 

890 

590 

16 

6 

8 

2.588 

600.000 

450 

080 

14 

12 

10 

4.107 

700.000 

500 

700 

12 

17 

23 

6.530 

800.000 

550 

840 

10 

24 

32 

10.380 

900.000 

600 

9)0 

33 

46 

16.610 

1.000.000 

650 

1.000 

46 

66 

20.250 

1.100.000 

690 

l.OBO 

54 

77 

88.100 

1.200.000 

730 

1,140 

66 

02 

41.740 

1.300.000 

770 

1,230 

76 

110 

52.630 

1.400.000 

810 

tsoo 

90 

131 

66.370 

1.500.000 

850 

i.seo 

107 

156 

83.690 

1.600,000 

890 

1.4J0 

0 

127 

185 

105.500 

1.700.000 

930 

1.490 

00 

150 

220 

133.100 

1.800.000 

970 

1.550 

000 

177 

262 

167.800 

1.900.000 

1.010 

1010 

0000 

210 

312 

211.600 

2.000.000 

1.050 

1070 

The  lower  limit  Is  spedfled  for  rubber-covered  wires  to  prevent  gradual  detefto> 
ration  of  the  high  Insulations  by  tbe  beat  of  tbe  wires,  but  not  from  fear  of  tgnlltef 
the  Insulation.  The  question  of  drop  Is  not  taken  Into  consideration  in  tbe  above 
tables. 

Tbe  carrying  capacity  of  Kos.  1 6  and  18  B.  &  8.  joige  wire  Is  given.  Xnxt  no  sosiler 
tban  No.  1 4 18  to  be  used,  except  as  allowed  under  Nos.  24v  and  45b. 

17.     Switches,  Cut-Outs»    Circuit-Breakers,  Etc— (For     constnactioc 

rules,  see  Nos.  51.  62  and  53.)  a.  On  constant  potential  circuits,  all  service 
switches  and  all  switches  controlling  circuits  supplying  current  to  motors  or 
heating  devices,  and  all  cut-outs,  unless  otherwise  provided  (for  exceptkns 
as  to  switches  see  Nos.  8  c  and  21a;  for  exceptions  as  to  cut-outs  see  No.  21  a 
and  b)  must  be  so  arranged  that  the  cut-outs  will  protect  and  the  opening  of 
the  switch  or  circuit-breaker  will  disconnect  all  of  the  wires;  that  is,  in  t^ 
two-wire  system  the  two  wires,  and  the  three-wire  system  the  three  wijt*. 
miist  be  protected  by  the  cut-out  and  disconnected  by  the  operation  of  Ae 
switch  or  circuit-breaker. 

This,  of  course,  does  not  apply  to  the  grounded  droult  of  street  railway  systtoa 
b.  Must  not  be  placed  in  the  immediate  vicinity  of  easily  ignitabte  sto^ 
or  where  exposed  to  inflammable  gases  or  dust  or  to  flyings  oTcombustibk 
material.  ^  t 

Digitized  by  VjOOQ  IC 


INSIDE  WORK'-CONSTANT'CURRENT  SYSTEMS.       1405 

When  the  oeeuptney  of  a  building  Is  such  that  switches,  cut-oats,  etc.  eannot  be 
located  so  as  not  to  be  exposed  to  dust  or  flyings  of  combustible  material  tber  must  be 
oi dosed  in  ai»proved  dust-proof  cabinets  with  self-closing  doors,  except  oil  switches 
and  circuit-breakers  whldi  tiaye  dust-tight  casings. 

c.  Must,  when  exposed  to  dampness,  either  be  enclosed  In  a  moisture- 
proof  box  or  mounted  on  porceUin  knobs. 

The  cover  of  the  box  should  be  so  made  that  no  moisture  which  may 
collect  on  the  top  or  sides  of  the  box  can  enter  it. 

d.  Time  switches,  sign  flashera  and  similar  appliances  must  be  of  ap- 
proved design  and  enclosed  in  a  steel  box  or  cabinet  lined  with  fiire-resisting 
material. 

The  oover  of  the  box  should  be  so  made  that  no  moisture  which  may  collect  on 
tbe  top  or  sides  of  the  box  can  enter  It. 

If  a  steel  box  is  used,  the  minimum  thickness  of  the  steel  must  be  0.1 28  oC  an  Inch 
(No.  8  B.  A  8.  gage). 

If  a  cabinet  Is  used.  It  must  be  imed  with  marble  or  slate  at  least  three-eighths 
of  an  inch  thick,  or  with  steel  not  lees  than  0. 1 28  of  an  inch  thick.  Box  or  cabinet 
must  be  so  oonstrueted  that  when  switch  operates  blade  shall  dear  the  door  by  at 
least  one  Inch. 

C0NSTANT4:URRENT  SYSTEMS. 

Principally  Sbribs  Arc   Liohtino. 

18.  WirM.~(8ee  also  Nos.  14.  15  and  15.)  a.  Must  hat  an  a^ 
protmd  rubber  insulating  covering  (see  No.  41). 

b.  Must  be  arranged  to  enter  and  leave  the  building  through  an  approvd 
double-contact  service  switch  (see  No.  51b).  mounted  in  a  non-combustible 
case,  kept  free  from  moisture,  and  easy  of  access  to  police  or  firemen. 

c  Must  alwairs  be  in  plain  sight,  and  never  encased,  except  when  fv- 
qmred  by  the  Inspection  Department  having  jurisdiction. 

d.  Must  be  supported  on  glass  or  porcelain  insulators,  which  separate 
the  wire  at  least  one  inch  from  the  surface  wired  over  and  must  be  kept 
rigidly  at  least  8  inches  from  each  other,  except  within  the  structure  of  lamps, 
on  hanger-boards  or  in  cut-out  boxes,  or  luce  places,  where  a  leu  distance 
is  necessary. 

e.  Must,  on  side  walls  be  protected  from  mechanical  injury  by  a  sub- 
stantial boxing,  retaining  an  air  space  of  one  inch  around  the  conductors, 
closed  at  the  top  (the  wires  passing  through  bushed  holes),  and  extending 
not  less  than  7  feet  from  the  floor.  When  crossing  floor  timbers  in  cellars, 
or  in  rooms  where  they  might  be  exposed  to  injury,  wires  must  be  attached 
by  their  insulatinf;  supports  to  the  imder  side  of  a  wooden  strip  not  leas  than 
one-half  an  inch  m  thickness.  Instead  of  the  running-boards,  guard  strips- 
on  each  side  of  and  close  to  the  wires  will  be  accepted.  These  strips  to  oe 
not  less  than  seven-eighths  of  an  inch  in  thickness  and  at  least  as  high  as  the 
insulators. 


^Excegpt  OD^Jotated  oefllngB.  a  strip  one-half  of  an  taoh  thick  Is  not  considered 

.  tock  Is  generally  sufficiently  sUL. , 

longer  than  this  or  there  Is  coosldeiable  Ylbratlon.  stUl  oeavler  stock  should  be  used. 


sufficiently  stiff  and  strong,  ^or  spans  of  say  eight  or  ten  feet,  where  there  Is  but 
little  Tlbntlon.  ooe-lnoh  stock  Is  generally  sufficiently  sUtt;  but  where  the  span  Is 


19.    SeriM  Arc  Lamps. — (For  construction  rules,  see  No.  57.) 

a.  Must  be  carefully  isolated  from  inflammable  material. 

b.  Must  be  provided  at  all  times  with  a  glass  globe  surrounding  the  arc. 
and  securely  fastened  upon  a  closed  base.  Broken  or  cracked  globes  must 
not  be  used. 

c.  Must  be  provided  with  a  wire  netting  (having  a  mesh  not  exceeding 
one  and  one-fourth  inches)  around  the  globe,  and  an  approved  spark  arrester 
(see  No.  68),  when  readily  inflammable  material  is  m  the  vicinity  of  the 
lamps,  to  prevent  escape  of  sparics  of  carbon  or  melted  copper.  It  is  recom- 
mended that  plain  carbons,  not  copper-plated,  be  used  for  lamps  in  such 
places. 

Outside  are  lamps  must  be  suspended  at  least  eight  ftet  above  ridewalks.  Inside 
arc  lamps  must  be  placed  out  of  reach  or  suitably  protected. 

Arc  lamps,  when  used  in  places  where  they  are  exposed  to  flyings  of  easily 
mflammable  material,  should  have  tbe  carbons  enclosed  completely  m  a  tight  globe 
In  such  manner  as  to  avoid  the  necessity  for  spark  arresters. 

"Enclosed  arc"  lamps,  haying  tight  inner  globes,  may  be  used,  and  the  reoulre- 
mtfits  of  Sections  b  and  c  above  would,  of  course,  not  apply  to  them,  except  that  a 


1400  TO.—BLECTRIC  POWER  AND  LIGHTING. 

wire  netting  around  tbe  Inner  globe  may  In  some  caiee  be  required  It  the  outer  gtote 
li  omitted. 

d.  Where  hanger-boards  (see  No.  56)  are  not  used,  lamps  xntist  be  hia% 
from  insulating  supports  other  than  their  conductors. 

e.  Lamps  when  arranged  to  be  raised  and  lowered,  either  for  carbooiag 
or  other  purposes,  shall  be  connected  up  with  strandea  conductors  from  tbe 
last  point  of  support  to  the  lamp,  when  such  conductor  is  laxner  ttma 
No.  HB.&S.gage. 

30.    Incandescent  Lamns  in  Series  Circuits. — a.   Must  have  the  coc- 

ductors  installed  as  required  in  No.  18.  and  each  lamp  must  be  prorided  witk 
an  automatic  cut-out. 

b.  Must  have  each  lamp  suspended  from  a  hanger-board  by  meanss  as 
rigid  tube. 

c  No  electro-magnetic  device  for  switches  and  no  multiple-aeries  or 
series-multiple  system  of  lighting  will  be  approved. 

d.  Must  not  under  any  circumstances  be  attached  to  gas  fizturca. 

CONSTANT-POTENTIAL  SYSTEMS. 

General  Rules — All  Voltaobs. 
3L    Automatic  Cut-OuU  (Fuses  and  Cifcnit-Breaicen).~(See    No.  17. 

and  for  construction,  Noa.  52  and  58.)  [Excepting  on  main  swit^boaids. 
or  where  otherwise  subject  to  expert  supervision,  circuit-breakers  will  not 
be  accepted  tmless  fuses  are  also  provided.] 

a.  Must  be  placed  on  all  service  wires,  either  overhead  or  ondeisnnmd, 
as  near  as  possible  to  the  point  where  they  enter  the  building  and  inside  the 
walls,  and  arranged  to  cut  oflE  the  entire  current  of  the  btiilding. 

Where  tbe  switch  required  by  No.  22a  Is  Inside  tbe  building,  tbe  cahoot  iwjttfnd 
by  this  section  must  be  placed  so  as  to  protect  It. 

For  three-wire  (not  three-phase)  systems  the  fuse  In  tbe  neuttal  wire  may  br 
oml tted.  providtd  the  neutnU  wire  it  of  equal  carrying  copacUy  U>  the  larger  of  the  omttfr 
wiree,  and  itorounded  as  provided  for  in  No,  IZA, 

In  risks  havlnK  private  plants,  tbe  yard  wires  running  from  bundtng  to  traOdlBf 
are  not  generally  considered  as  service  wires,  so  that  cut-outs  would  not  be  i^utiwl   | 
where  tbe  wires  enter  buildings,  provided  that  tbe  next  fuse  back  Is  amaU  enougb  to 
properly  protect  tbe  wires  Inside  tbe  building  in  question. 

b.  Must  be  placed  at  every  point  where  a  change  is  made  in  the  aiae  d 
wire  [unless  the  cut-out  in  the  larger  wire  will  protect  the  smaller  (see  No.  16)1 

For  three-wire  (not  three-phase)  systems  tbe  fuse  In  tbe  neutral  wire,  exeepi  tbst 

called  for  under  No.  2  id.  may  he  omitted,  provided  the  neutral  wire  iM  o(  eovtal  curry  tie 

^capacity  to  the  Uxrgtr  of  the  outtrtde  wtret,  and  it  grounded  as  provided  for  la  So,  fU. 

c  Must  be  in  plain  sight,  or  enclosed  tn  an  approved  cabinet  (see  No.  54). 
and  readily  accessible.  They  must  not  be  placed  in  the  canopies  or  sbeDi 
of  fixtures. 

The  ordinary  porcelain  link  fuse  cut-out  wOl  not  be  approved.  Link  foses  maj 
be  used  only  when  mounted  on  slate  of  marble  bases  oonformlng  to  Na  51  and  asA 
bo  endoerd  In  dust-tight,  flreproofed  cabinets,  except  on  switchboards  located  wd 
away  from  any  combustible  material,  as  In  tbe  ordinary  engtne  and  dynamo  nam 
and  where  these  conditions  will  be  maintained. 

d.  Must  be  so  placed  that  no  set  of  incandescent  lamps  reoairing  more 
than  660  watts,  whether  grouped  on  one  fixture  or  on  several  fixtures  or 
pendants,  will  be  dependent  upon  one  cut-out. 

Special  permission  may  be  given  in  writing  by  the  Inspection  Depart- 
ment having  jurisdiction,  for  departure  from  this  rule,  in  the  case  of  laisc 
chandeliers.  (For  exceptions,  see  No.  81  A.  b,  W>]  and  4  [6]  for  border  Ugbts. 
see  List  of  Fittings  for  rules  for  electric  signs  )  All  branches  or  taps  from  asr 
three-wire  system  which  are  directly  connected  to  lamp  sockets  or  other 
translating  devices,  must  be  run  as  two-wire  circmta  if  the  fuses  are  omitted 
in  the  neutral,  or  if  the  difference  of  potential  between  the  two  outside 
wires  is  over  250  volts,  and  both  wires  pf  such  branch  or  tap  circuits  most 
be  protected  by  proper  fuses. 

Tbe  above  rule  shall  alsc  apply  to  motors  when  more  than  one  is  dependent  flo  a 
single  cut-out. 

.  The  fusee  In  the  branch  out-outs  should  not  have  a  rated  oapaolty  greater  tfeaa 
6  amperes  on  1 10  volt  systems,  and  3  amperes  on  220  volt  systems. 

^The  idea  Is  to  have  a  small  fuse  to  protect  tbe  lamp  socket  and  the  snaB  ve^ 
used  for  fixtures,  pendants,  etc  It  also  lessens  the  euAoes  of  extinguishing  a  Isir 
number  oTlights  ft  a  short  circuit  occurs.  r^ r^i^n]c> 

Digitized  by  V^OOQLC 


INSIDE  WORK— CONSTANT  POTENTIAL  SYSTEMS,     1407 

On  open  work  m  lai^  mUfl  ap]m>fMd  Unk  fOBOd  rowttM  may  be  used  ftt  ft  voltage 
of  not  over  125  and  approved  enoloeed  fused  rosettes  ftt  ft  voltage  of  not  over  250.  tne 
fuse  tn  tbe  rosettes  not  to  exceed  3  amperes,  and  a  fuse  of  over  25  amperes  must  not 
be  used  In  tbe  brancb  circuit. 

e.  The  rated  capacity  of  fuses  must  not  exceed  the  aUowable  carrjring 
capacity  of  the  wire  as  given  in  No.  16.  Circuit-breakers  must  not  be  set 
more  than  30  per  cent  above  the  allowable  carrying  capacity  of  the  wire, 
unless  a  fusible  cut-out  is  also  installed  in  the  circuit. 

In  the  arms  of  fixtures  carrying  a  single  socket  a  No.  18  B.  A  8.  gage  wtre  sap- 
plytng  only  one  socket  wlU  be  considered  as  properly  protected  by  a  o  ampeie  fuss. 

33.   SwHclie8.~(See  No.  17,  and  for  construction.  No.  51.) 

a.  Must  be  placed  on  all  service  wires,  either  overhead  or  underground, 
in  a  readily  accessible  place,  as  near  as  possible  to  the  point  where  the  wires 
enter  the  building,  and  arranged  to  cut  off  the  entire  current. 

Service  cut-out  and  switch  must  be  arranged  to  cut  oft  ourrent  from  all  devices 
including  meters. 

In  risks  having  private  plants  the  yard  wires  running  from  building  to  building 
are  not  generally  considered  as  service  wires,  so  that  switches  would  not  be  required 
m  each  DuUdlng  If  there  are  other  switches  conveniently  located  oa  the  mains  or  If 
the  generators  are  near  at  hand. 

b.  Must  always  be  placed  in  dry,  accessible  places,  and  be  grouped  as 
far  as  possible.  (See  No.  17  c.)  Smgle-throw  knife  switches  must  be  so 
placed  that  gravity  will  tend  to  open  rather  than  close  them.  Double-throw 
knife  switches  may  be  mounted  so  that  the  throw  will  be  either  vertical  or 
horizontal  as  preferred. 

When  possible,  switches  Should  be  so  wired  that  blades  will  be  "dead"  when 
switch  is  open. 

If  switches  are  used  In  rooms  where  combustible  flyings  would  be  llkdy  to  accu- 
mulate around  them,  they  should  be  radosed  In  dust-tight  cabmets.  (See  note 
under  No.  17  b.)  Ev&x  in  rooms  where  there  are  no  combustible  materials  it  Is 
better  to  put  all  knife  switches  in  cabinets,  m  order  to  lessen  the  danger  of  accidental 
ahOrt  circuits  being  made  across  their  exposed  metal  parts  by  cardeai  workmen. 

Up  to  250  volts  and  30  amperes,  approved  indicaUng  snap  switches  are  advised 
In  preference  to  knite  8?ntches  on  lighting  circuits  about  the  workrooms. 

c.  Single  pole  switches  must  never  be  used  as  service  switches  nor  placed 
in  the  neutral  wire  of  a  three-wire  system,  except  in  the  two-wire  branch  or 
tap  circuit  described  in  21  d. 

This,  of  course,  does  not  apply  to  the  grounded  circuits  of  street  railway  systems. 
Tliree-way  switches  are  considered  as  single-pole  switches  and  must  be  wired  so 
tiux  only  one  pole  of  tbe  circuit  Is  carried  to  either  switch. 

d.  Where  flush  switches  or  receptacles  are  used,  whether  with  conduit 
systems  or  not,  they  must  be  enclosed  in  boxes  constructed  of  iron  or  steel. 
No  push  button  for  bells,  gas-lighting  circuits,  or  the  like  shall  be  placed  in 
the  same  wall  plate  with  switches  controlling  electric  light  or  power  wiring. 

This  requires  an  approved  box  In  addition  to  tha  porcelain  enclosure  of  the 
switch  or  reoeptade. 

e.  Where  possible,  at  all  switch  or  fixture  outlets,  a  I-inch  block  must 
3c  fastened  between  studs  or  floor  timbers  flush  with  the  back  of  lathmg  to 
lold  tubes,  and  to  support  switches  or  fixtures.  When  this  cannot  be  done, 
nrooden  base  blocks  not  less  than  i-inch  in  thickness,  securely  screwed  to 
athing,  must  be  provided  for  switches,  and  also  for  fixtures  which  are  not 
attached  to  gas  pipes  or  conduit. 

The  above  wiU  not  be  necessary  where  outlet  boxes  are  used  which  will  give 
>roper  support  for  fixtures,  etc. 

f*  Sub-bases  of  non-combustible,  non-absorptive  insulating  material, 
vhich  will  separate  the  wires  at  least  i-inch  from  the  surface  wired  over, 
nust  be  installed  under  all  snap  switches  used  in  exposed  knob  and  cleat 
(Tork.  Sub-bases  must  also  be  used  in  moulding  work,  but  they  may  be 
oade  of  hardwood. 

23.  Electric  Heaters. — It  Is  often  desirable  to  connect  In  multiple  with  the 
testers  and  between  the  heater  and  the  switch  controlling  same,  an  incandescent 
i.nip  of  low  candle  power,  as  it  shows  at  a  glance  whether  or  not  the  switch  is  open, 
Jia  tends  to  prevent  its  being  left  dosed  through  oversight.  Inspection  Depart- 
xoits  havmg  jurisdiction  may  require  this  provision  to  be  carried  out  If  they  deem 
^  neoeasary. 

a.  Mtist  be  protected  by  a  cut-out  and  controlled  by  indicating  switches. 
;witches  must  be  double  pole  except  when  the  device  controlled  docs  not 
equire  more  than  660  watts  of  energy.  izedbyLjOOQlC 


1408  70.— ELECTRIC  POWER  AND  LIGHTING, 

b.  Must  never  be  oonoealed,  but  must  at  all  times  be  in  plain  sight. 
,.^^f9f^  9^™^^  ^'^IL^  ^^^i'l^^'^  ^  ^^  InspoctioQ  Department  bar^ 


jurlnuetloQ  n>r  departure  trom  this  rule  In  < 

c.  Flexible  conductors  for  smoothing  irons  and  sad  iitms.  and  for  al 
devices  requiring  over  250  watts  must  comply  with  No.  45  g. 

d.  For  portable  heating  devices  the  flexible  conductors  must  be  ooc' 
nected  to  an  approved  plug  device,  so  arranged  that  the  plug  will  pull  oo: 
and  open  the  circuit  in  case  any  abnormal  strain  is  put  on  the  flexibte  ooc* 
ductor.  This  device  may  be  stationary,  or  it  may  be  placed  in  the  cord  itaelf . 
The  cable  or  cord  must  be  attached  to  the  heating  apparatus  in  such  manner 
that  it  will  be  protected  from  kinking,  chafing  or  luce  injtiry  at  or  near  the 
point  of  connection. 

e.  Smoothing  irons,  sad  irons,  and  other  heating  appliances  that  are 
intended  to  be  applied  to  inflammable  articles,  such  as  clothing,  must  ctm- 
form  to  the  above  rules  so  far  as  they  apply.  They  must  also  be  provided 
with  an  approved  stand,  on  which  they  should  be  placed  when  not  in  tise< 

An  approved  automatic  attachment  which  will  cut  off  the  cmreot  when  tte  Iron 
Is  not  on  the  stand  or  In  actual  use  Is  desirable.  Inspection  Depanments  liavtB« 
JurlsdlcUon  may  require  this  provision  to  be  carried  out  It  they  deem  it  advlaaUa 

f.  Stationary  electric  heating  apparatus,  such  as  radiatora.  ranges,  plate 
warmers,  etc..  must  be  placed  in  a  safe  location,  isolated  from  inflammahk 
materials,  and  be  treated  as  sources  of  heat. 

Devices  or  this  description  win  often  require  a  suitable  beat-reslsttDg  matcfU 
placed  between  the  device  and  Its  surroundings.  Such  protection  mav  ben  be 
secured  by  Installins  two  or  more  plates  of  tin  or  sheet  steel  with  a  one-Inch  air  mpmee 
betwe^,  or  by  alternate  layers  of  sheet  steel  and  asbestos  with  a  sUnllar  air  ^taoe. 

f.  Must  each  be  provided  with  name-plate,  giving  the  maker's  name 
and  the  normal  capacity  in  volts  and  amperes. 

CONSTANT-LOW-POTENTIAL  SYSTEMS. 

550  Volts  or  Lbss. 

Any  circuit  attached  to  any  machine,  or  combination  of  machines,  wh^ 
develops  a  difference  of  potential  between  any  two  wires,  of  ova- 
ten  volts  and  less  than  650  volts,  shall  be  considered  as  a  low- 
potential  circuit,  and  as  coming  under  this  class,  unless  an  approved 
transforming  device  is  used,  which  cuts  the  difference  of  potential 
down  to  ten  volts  or  less.  The  primary  circuit  not  to  exceed  a 
potential  of  3.500  volts  unless  the  primary  wires  are  installed  in 
accordance  with  the  requirements  as  given  in  No.  12  A,  or  are  under 
ground. 

For  550  volt  motor  equipments  a  margin  of  ten  per  cent  above  the  550  vdt  Itanli  wfU 
be  allowed  at  the  generator  or  transformer. 
Before  ^essure  is  raised  above  300  volts  on  any  previously  extsting  system 

of  wirtng.  the  whole  must  be  strictly  brought  up  to  all  of  the  requireimenis  of  tJm 

rules  qf  date, 

34.    Wires.— General  Rules.      (See  also   Nos.  14,    15  and   16.) 

a.  Musi  be  so  arranged  that  under  no  circumstances  will  there  be  a  differ- 
ence of  potential  of  over  300  volts  between  any  bare  metal  ^arts  in  any  distnbm- 
ing  switch  or  cut-out  cabinet,  or  equivalent  center  of  distribution. 

This  rule  Is  not  Intended  to  prohibit  the  tracing  of  switches  or  single  pole  est* 
outs  for  motor  systems  of  voltages  above  300  In  cabinets,  but  would  require  thst  tte 
cabinets  be  divided  by  approved  barriers  so  arranged  that  no  one  sectfon  shall  cos- 
tain  more  than  one  switch  nor  more  than  one  single  pole  out-out. 

b.  Must  not  be  laid  in  plaster,  cement  or  similar  finish,  and  must  nevtr 
be  fastened  with  staples. 

c.  Must  not  be  fished  for  any  great  distance,  and  only  in  places  where 
the  inspector  can  satisfy  himself  that  the  rules  have  been  complied  with. 

d.  Twin  wires  must  never  be  used,  except  in  conduits,  or  where  fieziUe 
conductors  are  necessary. 

e.  Must  be  protected  on  side  walls  from  mechanical  injury.  Whea 
crossing  floor  timbers  in  cellars,  or  in  rooms  where  they  might  be  exposed  to 
nvjury,  wires  must  be  attached  by  their  insulating  supports  to  the  under  sid« 
of  a  wooden  strip,  not  less  than  one-half  inch  in  thickness  and  not  less  thr" 
three  mches  in  width.    Instead  of  the  running-boards,  guard  strips  on  eact 


INSIDE  WORK^-CONSTANT-LOW'POTENTIAL,         1400 

side  of  and  close  to  the  wires  will  be  accepted.    These  strips  to  be  not  less 
than  seven-eighths  of  an  inch  in  thickness,  and  at  least  as  high  as  the  instila- 

tOXB. 

Suitable  protection  on  side  walls  should  extend  not  leas  than  five  feet  from  the 
floor.  This  may  be  secured  by  subetantial  boxing,  retaining  an  air  space  of  one  Inch 
around  the  conductors,  dosed  at  the  top  (the  wires  passing  through  bushed  holes)  or 
by  approved  metal  conduit,  or  pipe  of  equivalent  strength. 

When  metal  conduit  or  pipe  Is  used,  the  Insulation  of  each  wire  must  be  rein- 
forced by  approved  flexible  tubing  extending  from  the  insulator  next  below  the  pipe 
to  the  one  next  above  It,  unleas  the  conduit  is  installed  according  to  No.  25  (sections 
c  and  f  excepted),  and  the  wire  used  complies  with  No.  47.  The  two  or  more  wires 
of  a  circuit  eacJi  with  its  flexible  tubing  (when  required).  If  canylng  alternating  curroit 
must,  or  If  direct  ciurent.  may  be  placed  within  the  same  pipe. 

In  damp  places  the  wood^i  boxing  may  be  preferable  because  of  the  precautions 
which  would  be  necessary  to  secure  proper  insulation  if  the  pipe  were  used.  With 
this  exception,  however.  Iron  piping  is  considered  preferable  to  the  wooden  boxing. 
and  Its  use  is  strongly  urged.  It  is  especially  suitable  for  the  protection  of  wires 
near  belts,  pulleys,  etc. 

f.  When  run  in  unfinished  attics,  will  be  considered  as  concealed,  and 
when  run  in  close  proximity  to  water  tanks  or  pipes,  will  be  considered  as 
exposed  to  moisture. 

In  unfinished  attics  wires  are  considered  as  exposed  to  mechanical  injury,  and 
must  not  be  run  on  knobs  on  upper  edge  of  joists. 

Spbcial  Rulbs. 

For  Op€n  Work — In  dry  places. 

f .  Must  have  an  approved  rubber,  8low>buming  weatherproof,  or  slow- 
burning  insulation   (see  Nos.   41.   42  and   43). 

A  slow-bumlng  covering,  that  is,  one  that  will  not  carry  fire,  is  considered  good 
enough  where  the  wires  are  entirely  on  Insulating  supports.  Its  main  object  is-  to 
prevent  the  copper  ccmduotors  from  coming  aoddentaUy  Into  contact  with  each 
other  or  anything  else 

h.  Must  be  rigidly  supported  on  non-oombustible,  non-absorptive  in- 
sulators, which  will  separate  the  wires  from  each  other  and  from  the  sur- 
face wired  over  in  accordance  with  tho  following  table: — 

Distance  from  Distance  between 

Voltage.  Surface.  Wires. 

0  to  300  i  inch  2i   inch 

301  to  560  1     ••  4      " 

Rigid  supporting  requires  under  ordinary  coodlttons,  where  wiring  along  flat 
surfaces,  supports  at  least  every  four  and  one-half  feet.  If  the  wires  are  liable  to  be 
disturbed,  the  distance  between  supports  should  be  shortened.  In  buildings  of  mill 
construction,  mains  of  not  less  than  No.  8  B.  ft  8.  gage,  where  not  liable  to  be  dis- 
turbed, may  be  separated  about  six  Inches,  and  run  from  timber  to  timber,  not  break- 
ing around,  and  may  be  supported  at  each  timber  only. 

This  rule  not  to  be  Interpreted  to  forbid  the  placing  of  the  neutral  of  an  Edison 
three-wire  system  In  the  center  of  a  three-wire  cleat  where  the  difference  of  potential 
between  the  outside  wires  Is  not  over  300  volts,  provided  the  outside  wires  are 
separated  two  and  one-half  inches. 

For  Open  Work — In  damp  places ^  or  buildings  specially  subject  to  moisture 
or  to  cuid  or  other  fumes  liable  to  injure  the  wtres  or  their  insulation. 

i.    Must  have  an  approved  insulating  covering. 

For  protection  against  water,  rubber  insulation  must  be  used.  For  protection 
against  corrosive  vapors,  either  weatherproof  or  rubber  insulation  must  be  used. 
(SmNos.  41  and  44.) 

J.  Must  be  rigidly  supported  on  non-combustible,  non-absorptive  in- 
sulators, which  separate  the  wire  at  least  one  inch  from  the  surface  wired 
over,  and  must  be  kept  apart  at  least  two  and  one-half  inches  for  voltages 
up  to  300.  and  four  inches  for  higher  voltages. 


Rigid  supporting  requires  under  ordinary  conditions,  where  wiring  over  flat 
surfaces,  supports  at  least  every  four  and  one-half  feet.  If  the  wires  are  liable  to  be 
disturbed,  ttw  distance  between  supports  should  be  shortened.    In  buildings  of  mill 


construction,  mains  of  not  less  than  No.  8  B.  ft  S.  gage,  where  not  liable  to  be  dis- 
turbed, may  be  separated  about  six  Inches,  and  run  from  timber  to  timber,  not  break- 
ing around,  and  may  be  supported  at  each  timber  only. 

For  Moulding  Work  (Wooden  and  Metal).  (For  construction  rules  see 
No.  50.     See  also  No.  25  A.) 

k.  Must  have  an  approved  rubber  insulating  covering.  (For  wooden 
moulding  see  No.  41,  for  metal  moulding  see  No.  47.)        C^r^r^n\t> 

Digitized  by  VjOOvLC 


1410  TO.^ELECTRIC  POWER  AND  UGHTING. 

L  Must  never  be  placed  in  either  metal  or  wooden  moulding  in  ooooealed 
or  damp  places,  or  where  the  difference  of  potential  between  any  two  wires 
in  the  same  moulding  is  over  300  volts.  Metal  mouldings  mtist  not  be  used 
for  circuits  requiring  more  than  660  watts  of  energy' 

As  a  rule,  wooden  moulding  should  not  be  plaeed  dtreotiv  anlnst  a  brtck  wal, 
as  the  wall  Is  likely  to  "sweat"  and  thus  Introduce  moisture  Daok  of  the  nioiMlDf. 

m.  Must,  for  alternating  current  systems  if  in  metal  moulding,  have  the 
two  or  more  wires  of  a  circuit  installed  in  the  same  moulding. 


It  Is  advised  that  this  be  done  for  direct  currrat  svstems  also,  so  that  they  ias7 
DO  ohaniKid  to  alternating  systems  at  any  time.  Induction  troubles  preventing  soeh  a 
dumge  II  the  wires  are  In  separate  mouldings. 


For  Conduit  Work. 

n.    Must  have  an  approved  rubber  insulating  covering  (see  No.  47). 

0.  Must  not  be  drawn  in  tintil  all  mechanical  work  on  the  building  has 
been,  as  far  as  possible,  completed. 

Conductors  in  vertical  conduit  risers  must  be  supported  within  the  con- 
duit system  in  accordance  with  the  following  table: — 

No.  14  to  0  every  100  feet. 

No.  00  to  0000  every  80  feet. 

0000  to  350.000  C.  M.  every  60  feet. 

360.000  C.  M.  to  600.000  C.  M.  every  60  feet. 

600.000  C.  M.  to  760.000  C.  M.  every  40  feet. 

760.000  C.  M.  every  36  feet. 

A  turn  of  90  degrees  in  the  conduit  system  will  constitute  a  satisfactory 
support,  as  per  above  table. 

The  following  methods  of  supporting  cables  are  recommended: — 

1.  Jtmction  boxes  mayr  be  inserted  in  the  conduit  system  at  the  re- 

quired intervals,  in  which  insulating  supports  of  approved  type 
must  be  installed  and  secured  in  a  satisfactory  manner  so  as  to 
withstand  the  weight  of  the  conductors  attached  thereto,  the  boxes 
to  be  provided  with  proper  covers. 

2.  Cables  may  be  supported  in  Sipproved  junction  boxes  on  two  or  more 

insulating  supports  so  placea  that  the  conductors  will  be  deflected 
at  an  angle  of  not  less  than  90  degrees,  and  carried  a  distance  of 
not  less  than  twice  the  diameter  of  the  cable  from  its  vertical 
position.     Cables  so  suspended  may  be  additionally  secured  to 
these  insulators  by  tie  wires. 
Other  methods,  if  used,  must  be  approved  by  the  Inspection  Depart- 
ments  having    jurisdiction. 
p.    Must,  for  alternating  systems,  have  the  two  or  more  wires  of  a  cir- 
cuit drawn  in  the  same  conduit. 

It  Is  advised  that  this  be  done  for  direct  current  systems  also,  so  that  they  mar 
be  changed  to  alternating  systems  at  any  time,  induction  troubles  preventing  suco 
a  change  if  the  wires  are  In  separate  conduits. 

The  same  conduit  must  never  contain  circuits  of  different  STStems,  but  may  oon- 
taln  two  or  more*  circuits  of  the  same  system. 

For  Concealed  "Knob  and  Tube"  Work. 

q.    Must  have  an  approved  rubber  insulating  covering  (see  No.  41). 

r.  Must  be  rigidly  supported  on  non-combustible,  non-absorptive  in- 
sulators which  separate  the  wire  at  least  one  inch  from  the  sujrface  wired 
over.  Should  preferably  be  run  singly  on  separate  timbers,  or  studdings. 
and  must  be  kept  at  least  five  inches  apart. 

Must  be  separated  from  contact  with  the  walls,  floor  timbers  and  parti- 
tions through  which  they  may  pass  by  non-combustible,  non-«ibaorptive 
insulating  tubes,  such  as  glass  or  porcelain. 

Rigid  supporting  requires  under  ordinary  conditions,  where  wiring  atoog  tkt 
surface,  supports  at  least  every  four  and  one-naif  feet.  If  the  wires  arellableto  bs 
dlBturl)ed  the  distance  )»etween  supports  should  be  shortened. 

At  distributing  centers,  outlets  or  switches  urtiere  space  Is  limited  and  the  tve- 
tnch  separation  cannot  be  maintained,  each  wire  must  be  separately  encased  la  a 
continuous  length  of  approved  flexible  tubing. 

Wirce  pasnlng  through  timbers  at  the  bottom  of  plastered  partitkms  rauat  be 
protected  by  an  additional  tube  extending  at  least  tour  Inches  above  the  timber. 

1  *"  When  in  a  concealed  knob  and  tube  system,  it  is  impracticable  to 
Pvf  ♦^  whole  of  a  circuit  on  non-combustible  supports  of  gla^  or  poro^aio, 
wi*J  portion  of  the  circuit  which  cannot  be  so  supported  must  be  installed 
witn  approved  metal  conduit,  or  approved  armored  cable  (see  No.  24  t),  ex- 


INSIDE  WORK—CONSTANT'LOW'POTENTIAL.         1411 

cept  that  if  the  difference  of  potential  between  the  wires  is  not  over  300  volts, 
and  if  the  wires  are  not  exposed  to  moisture,  they  may  be  fished  if  separately 
encased  in  approved  flexible  tubing,  extending  in  continuous  lengths  from 
porcelain  support  to  porcelain  support,  from  porcelain  support  to  outlet, 
or  from  outlet  to  outlet. 

t.  Mixed  concealed  knob  and  tube  woric  as  provided  for  in  No.  24  s, 
must  comply  with  requirements  of  No.  24  n  to  p,  and  No.  25.  when  conduit 
is  used,  and  with  requirements  of  No.  24  A,  when  armored  cable  is  used. 

tt.  Must  at  all  outlets,  except  where  conduit  is  used,  be  protected  by 
approved  flexible  insulating  tubing,  extending  in  continuous  lengths  from  the 
last  porcelain  support  to  at  least  one  inch  bevond  the  outlet.  In  the  case 
of  combination  fixtures  the  tubes  must  extend  at  least  flush  with  outer  end 
of  gas  cap. 

It  18  recommended  but  not  required  that  approved  outlet  boxes  or  plates  be 
InstBlled  at  all  outlets  In  coooealed  "knob  and  tube"  work,  tbe  wires  to  be  protected 
by  approved  flexible  Insulating  tubing,  extending  In  continuous  lengths  from  the 
last  porcelain  support  Into  tbe  box. 

For  Fixture  Work.  v.  Must  have  an  approved  rubber  insulating  cover- 
ing (see  No.  46).  and  be  not  less  in  size  than  No.  18  B.  &.  S.  gage. 

See  Na  46  €1  fine  print  note,  for  exeepUons  to  tbe  use  of  nibbeiHX)vered  wire. 

w.  Supply  conductors,  and  especially  the  splices  to  fixture  wires,  must 
be  kept  clear  of  the  gzotmded  part  of  ras  pipes,  and,  where  shells  or  outlets 
boxes  are  used,  they  must  be  made  sufficiently  large  to  allow  the  fulfillment 
of  this  requirement. 

X.  Must,  when  fixtures  are  wired  outside,  be  so  secured  as  not  to  be  cut 
or  abraded  by  the  pressure  of  the  fastenings  or  motion  of  the  fixture. 

y.  Under  no  circumstances  must  there  be  a  difference  of  potential  of  more 
than  300  volts  between  wires  contained  in  or  attached  to  the  same  fixture. 

24  A.   Armored  Cables. — (For  construction  rules,  see  No.   48.) 

a  Must  be  continuous  from  outlet  to  outlet  or  to  junction  boxes,  and 
the  armor  of  the  cable  must  property  enter  and  be  secured  to  all  fittings,  and 
the  entire  system  must  be  mechanically  secured  in  position. 

In  case  of  underground  service  connections  and  main  runs,  this  involves  running 
auch  armored  cable  oontlnuoudy  Into  a  main  out-out  cabinet  or  gutter  surrounding 
the  panel  board,  as  the  case  may  be.    (See  No.  54.) 

b.  Must  be  equipped  at  every  outlet  with  an  approved  outlet  box  or 
plate,  as  required  in  conduit  work.     (See  No.  40  A.) 

Outlet  plates  must  not  be  used  where  it  Is  practicable  to  Install  outlet  boxes. 

Tbe  ouuet  box  or  plate  shall  be  so  installed  that  It  wUl  be  flush  with  the  finished 
aurfaee.  and  If  this  suriaee  is  broken  it  shall  be  repaired  so  that  it  will  not  show  any 
gapa  or  opoi  spaces  around  the  edge  of  the  outlet  box  or  plate. 

In  buildings  already  ooustructed  where  the  conditions  are  such  that  neltlm 
outlet  box  nor  plate  ran  be  installed,  these  appliance  may  be  omitted  by  special 
permlsston  of  the  Inspection  Department  having  Jurisdiction,  provided  the  armored 
cable  Is  firmly  and  rigidly  secured  in  place. 

c  Must  have  the  metal  armor  of  the  cable  permanently  and  effectively 
grounded. 

It  Is  essential  that  tbe  metal  armor  of  such  systems  be  Joined  so  as  to  afford 
electrical  oonduotlvity  sufllelent  to  allow  tbe  largest  fuse  of  circuit-breaker  In  the 
circuit  to  operate  before  a  dangerous  rise  in  temperature  in  the  system  can  occur. 
Armor  of  caoles  and  gas  pipes  must  be  securely  fastened  In  metal  outlet  boxes  so  as 
to  secure  good  electrical  connections.  Where  boxes  used  for  centers  of  distribution 
do  not  afford  good  eleetrlcal  connection  the  armor  of  the  cables  must  be  Joined 
around  them  by  suitaMe  bond  wires.  Where  sections  of  armored  cable  are  installed 
without  being  otstened  to  the  metal  structure  of  buildings  or  grounded  metal  piping. 
tbey  must  be  bonded  together  and  Joined  to  a  permanent  and  efficient  ground  con- 
oectloo. 

d.  When  installed  in  so-called  fireproof  buildings  in  course  of  construc- 
tion or  afterwards  if  concealed,  or  where  it  is  exposed  to  the  weather,  or  in 
damp  places  such  as  breweries,  stables,  etc.,  the  cable  must  have  a  lead  cover- 
ixig  at  least  one  thirty-second  inch  in  thickness  placed  between  the  outer 
tsraid  of  the  condtictors  and  the  steel  armor. 

e.  Where  entering  junction  boxes,  and  at  all  other  outlets,  etc.,  must  be 
provided  with  approved  terminal  fittings  which  will  protect  the  insulation 
of  the  conductors  from  abrasion,  xmless  such  junction  or  outlet  boxes  are 
specially  designed  and  approved  for  use  with  the  cab%.g^  by  CjOOqIc 


1412  TO.--ELECTRIC  POWER  AND  LIGHTING. 

f.  Junction  boxes  must  alwmys  be  installed  in  such  manner  as  to  be 
accessible. 

g.  For  alternating  current  systems  must  have  the  two  or  more  conductors 
of  the  cable  enclosed  in  one  metal  armor. 

35.    Interior  Condiiite.— (See  also  Nos.  24  n  to  p.  and  49.) 
Tlio  object  of  a  tube  or  conduit  Is  to  Csellltate  the  Insertion  or  eztraetioa  of  tite 
conductors  and  to  protect  them  from  mechanical  Injury.    Tubes  or  conduits  axo  to 
be  considered  merely  as  raceways,  and  are  not  to  be  relied  upon  tor  InsulatKm  betveea 
wire  and  wire,  or  between  the  wire  and  the  ground. 

a.  No  conduit  tube  having  an  internal  diameter  of  less  than  five-Hghths 
of  an  inch  shall  be  used.  Measurements  to  be  taken  inside  of  metal  ooc' 
duits. 

b.  Must  be  continuous  from  outlet  to  outlet  or  to  jimction  boxes,  and  the 
conduit  must  properly  enter,  and  be  secured  to  all  fittings  and  the  entire 
system  must  be  mechanically  secured  in  position. 

In  case  of  service  connections  and  main  runs,  this  involves  running  each  eoodvit 
continuously  Into  a  main  cut-out  cabinet  or  gutter  suxroundlng  the  panel  board,  as 
the  case  may  be  (see  No.  64). 

c.  Must  be  first  installed  as  a  complete  conduit  system,  without  the 
conductors. 

d.  Must  be  equipped  at  every  outlet  with  an  approoed  outlet  box  or 
plate  (see  No.  49  A). 

Outlet  plates  must  not  be  used  where  It  Is  practicable  to  Install  outlet  twzea. 

The  outlet  box  or  plate  shall  be  so  installed  that  It  will  be  flush  with  the  fInlBiied 
surface,  and  If  this  surface  is  broken  it  shall  be  repaired  so  that  It  wlU  not  show  any 
gaps  or  open  spaces  around  the  edge  of  the  outlet  box  or  plate. 

In  buildings  already  constructed  where  the  conditions  are  such  that  neither 
outlet  box  nor  plate  can  be  Installed,  these  appliances  may  be  omitted  by  speolsl 
permission  of  the  Inspection  Department  having  jurisdiction,  providing  the  coodKt 
ends  are  bushed  and  secured. 

e.  Metal  conduits  where  they  enter  junction  boxes,  and  at  all  other  cmt- 
lets.  etc..  must  be  provided  with  apprcmed  bushing  fitted  so  as  to  protect 
wire  from  abrasion,  except  when  such  protection  is  obtained  by  the  use  of 
approved  nipples,  properly  fitt^  in  bosAs  or  devices. 

f.  Must  have  the  metal  of  the  conduits  permanently  and  effectually 
grounded. 

It  Is  essential  that  the  metal  of  conduit  systems  be  lotaied  so  as  to  aflocd  ele^ 
trical  conductivity  sufllci^t  to  allow  the  largest  (use  or  circuit  breaker  In  the  axcm 
to  operate  before  a  dangerous  rise  In  temperature  In  the  conduit  system  can  oocsr. 
Ckindults  and  gas  pipes  must  be  securely  fastened  In  metal  outlet  boxes  so  as  to  secare 
good  electrical  connection.  Where  boxes  used  for  centers  of  distribution  do  not 
afford  good  electrical  connection,  the  conduits  must  be  joined  around  them  by  call- 
able bond  wires.  Where  sections  of  metal  conduit  are  Installed  without  being  Cm* 
teiied  to  the  metal  structure  of  buildings  or  grounded  metal  piping,  they  must  be 
bonded  together  and  joined  to  a  permanent  and  efficient  ground  ooonectloa. 

g.  Junction  boxes  must  always  be  installed  in  such  manner  as  to  be  ac- 
cessible. 

h.  All  elbows  or  bends  must  be  so  made  that  the  conduit  or  Imtng  of 
same  will  not  be  injured.  The  raditas  of  the  curve  of  the  inner  edge  of  any 
elbow  not  to  be  less  than  three  and  one-half  inches.  Must  have  not  more 
than  the  equivalent  of  four  qtiarter  bends  from  outlet  to  outlet,  the  bends  at 
the  outlets  not  being  counted. 

25  A.   Metal  Mouldings.    (See  also  Nos.  24  k  to  m.  and  60.) 

a.  Must  be  continuous  from  outlet  to  outlet,  to  junction  boxes,  or  ap- 
proved fittings  designed  esi>ecially  for  use  with  metaJ  motildings.  and  must 
at  all  outlets  be  provided  with  approved  terminal  fittings  which  will  protect 
the  insulation  of  conductors  from  abrasion,  unless  such  protection  is  anorded 
by  the  construction  of  the  boxes  or  fittings. 

b.  Such  moulding  where  passing  through  a  floor  must  be  carried  throti|h 
an  iron  pipe  extending  from  trie  ceiling  below  to  a  point  five  feet  above  the 
floor,  which  will  serve  as  an  additional  mechanical  protection  and  exclude  the 
presence  of  moisture  often  prevalent  in  such  locations. 

,.^_lp,  fesldences.  office  buildings  and  similar  locations  where  appeanmee  is  sa 
5|isentlal  feature,  and  where  the  mechanical  strength  of  the  moulding  itself  is  i ' 
9^\^<  this  ruling  may  be  modified  to  require  the  protecting  piping  from  the  i  ' 
below  to  a  point  at  least  three  Inches  above  the  flooring.         oOqIc 


INSIDE  WORK-^ONSTANT-LOW'POTENTIAL,         141t 

.   Backing  mxist  be  sectired  in  position  by  screws  or  bolts,  the  heads  of 

1  must  be  flush  with  the  metal. 

.   The  metal  of  the  moulding  must  be  permanently  and  effectively 

ided,  and  must  be  so  installed  that  adjacent  lengths  of  moulding  wiU 

ecbanically  and  electrically  secured  at  all  poinu. 

i  Is  eiBontla!  (hat  the  metal  of  each  systems  be  Jotned  so  as  to  aflMd  eleotrlo 

ctlvlty  suflteleol  to  allow  the  largest  (use  In  the  circuit  to  opentte  before  a 


roQS  rtoe  or  temperature  In  tbe  system  can  occur.    Mouldings  and  ns  iMpet 
"^  leourely  fastened  In  metal  outlet  boxes,  so  as  to  secure  good  eleotneal  oon- 
Wbere  boxes  used  (or  center  of  distribution  do  not  afford  good  electrical 


ctlon  the  metal  moulding  must  be  Joined  around  tbem  by  suitable  bond  wires. 
)  sections  are  Installed  without  being  tastmed  to  tbe  metal  structure  of  tbe 
ng  or  grounded  metal  piping,  they  must  be  bonded  togetber  or  Joined  to  a 
kuent  and  effective  ground  connemon. 

Must  be  installed  so  that  for  alternating  sjrstems  the  two  or  more 
of  a  circuit  will  be  in  the  same  metal  moulding. 

Is  ad  vised  that  this  be  done  (or  dlreot  systems  also,  so  that  they  may  be  changed 
alternating  system  at  any  time,  Induction  troubles  preventing  such  change 
wires  must  DC  In  separate  mouldings. 


L   Phrturet.— (See  also  Nos.  22  e,  24  v  to  y.) 

Must  when  supported  from  the  gas  piping  or  any  grounded  metal 
of  a  building  be  wsulated  from  such  piping  or  metal  woric  by  means  of 
U0d  insulating  joints  (see  No.  69)  placed  as  close  as  possible  to  the  ceil- 
r  walls. 

\a  outlet  pipes  must  be  protected  above  the  Insulating  Joint  by  approvtd  In- 
ig  tubing,  and  where  ouUet  tubes  are  used  they  must  be  of  sufficient  length  to 
i  below  the  Insulating  Jomt.  and  must  be  so  secured  that  they  will  not  be  pushed 
rben  the  canopy  Is  put  In  place. 


»r  ceilings. 

Must  have  all  burs  or  fins  removed  before  the  conductors  are  drawn 
he  fixture. 

Must  be  tested  for  "contacts"  between  conductors  and  fixture,  for 
;  circuits"  and  for  ground  connections  before  it  is  connected  to  its 
r  conductors. 

AH  fixture  arms  made  of  tubing  smaller  than  i-inch  outside  diameter, 
le  arms  of  all  one-light  brackets,  must  be  secured  after  they  are  screwed 
osition  by  the  tise  of  a  set-screw  properly  placed,  or  by  soldering  or 
ting  or  some  eqtially  good  method  to  prevent  the  arms  from  becoming 
iwed.  Arms  must  not  be  made  of  tubing  lighter  than  No.  18  B.  ft 
t,  and  must  have  at  screw  joints  not  less  than  nve  threads  all  engaging. 
uJe  does  not  apply  to  fixtures  or  brackets  with  cast  or  heavy  arms. 

.    Sockets. — (For  construction  rules,  see  No.  55.) 

In  rooms  where  inflammable  gases  may  exist  the  incandescent  lamp 
•cket  must  be  enclosed  in  a  vapor-tight  globe,  and  supported  on  a 
anger,  wired  with  approved  rubber-covered  wire  (see  No.  41)  soldered 
y  to  the  circuit, 
y  soefeelt  eonloiii  a  svttcA  (see  No.  17  b). 

In  damp  or  wet  places  "waterproof*  sockets  must  be  used.  Unless 
Lip  on  fixtures  they  must  be  hung  by  separate  strandsd  rubber-covered 
lot  smaller  than  No.  14  B.  &  S.  gage,which  shotild  preferably  be  twisted 
er  when  the  pendant  is  over  three  feet  long. 

ese  wires  must  be  soldered  direct  to  the  circuit  wires  but  supported  tn« 
lently  of  them. 

Key  sockets  will  not  be  approved  if  Installed  over  specially  inflam* 

stuff,  or  where  exposed  to  flyings  of  combustible  material. 

Flexible  Cord.— 

Must  have  an  approvtd  insulation  and  covering  (see  No.  45). 

Must  not  be  used  where  the  difference  of  potential  between  the  two 
iS  over  300  volts. 

>  above  rule  does  not  apply  to  the  grounded  circuits  In  street  rsllway 
Must  not  be  used  as  a  support  for  clusters.     Digitized  by  CiOOglc 


1414  If^,— ELECTRIC  POWER  AND  UGHTING. 

d.  Must  not  be  used  except  for  pendants,  wiring  of  fixtures,  portable 
lamps  or  motors,  and  portable  heating  apparatus. 

ten  loopios  tbam 
aptaUon  to  <mny 
le  cord  adjusien 

tble  to  be  mored 
lexlble  vires  and 
tlie  marlEet.  aad 

1  It  it  Is  propoly 
le  o(  cord  may  be 
1  with  substantial 
o(  the  ovcriiead 
td  soldered  to  the 

(h  to  Ignite  paper. 
Dt  It  from  coming 
Ce.  every  portable 

e.  Must  not  be  used  in  show  windows  except  ^^len  provided  with  an 
approved  metal  armor. 

f.  Must  be  protected  by  insulating  bushings  where  the  oord  entexm  the 
socket. 

g.  Must  be  so  suspended  that  the  entire  weight  of  the  socket  and  bunp 
will  be  borne  by  some  approved  device  under  the  bushing  in  the  socket,  and 
above  the  point  where  the  cord  comes  through  the  ceiling  block  or  rosette. 
in  order  that  the  strain  may  be  taken  from  the  joints  and  binding  screws. 

This  Is  usuaUy  acoompllshed  by  knots  in  the  cord  InsMe  the  socket  and  rosette 

29.  Arc  Lamps  on  Coostant-Poteatial  Circuits. — a.  Must  have  a 
cut-out  (see  No.  17  a)  for  each  lamp  or  each  series  of  lamps. 

The  branch  conductors  should  have  a  carrying  capadlj  about  fifty  per  cent  In 
excess  of  tbe  normal  current  required  by  the  lamp,  to  provMe  tar  heavy  correot  re- 
quired when  lamp  Is  started,  or  when  carbons  become  stuek  without  overfustng  the 
wires. 

b.  Must  only  be  furnished  with  such  resistances  or  regulators  as  are 
enclosed  in  non-combustible  material,  such  resistances  being  treated  as 
soiutres  of  heat.     Incandescent  lamps   must  not  be  used  for  this  purpose. 

c.  Must  be  supplied  with  globes  and  protected  by  spark  arresters  and 
wire  netting  around  the  globe,  as  in  case  of  series  arc  lamps  (see  Noa.  II 
and    58) . 

Outside  arc  lamps  must  be  suspended  at  least  eight  feet  above  sldewalkSL  Inslds 
arc  lamps  must  be  ^aced  out  of  reach  or  suitably  protected. 

d.  Lamps  when  arranged  to  be  raised  and  lowered,  either  for  carboo- 
ing  or  other  purposes,  shall  be  connected  up  with  stranded  conductors  from 
the  last  point  of  support  to  the  lamp,  when  such  conductor  is  larger  than 
No.  14  B.  &  S.  gage. 

30.  Economy    Coils. — a.    Economy    and    compensator   coils   for  arc 

lamps  must  be  moimted  on  non-combustible,  non-absorptive,  insulating 
supports,  such  as  glass  or  porcelain,  allowijig  an  air  space  of  at  least  one  inch 
between  frame  and  support,  and  must  in  general  be  treated  as  sources 
of  heat. 

31.  Decorative  Lighting  Systems. — a.  Special  permission  may  be 
given  in  writing  by  the  Inspection  Department  having  jurisdiction  for  the 
temporary  installation  of  approved  Systems  of  Decorative  Lighting,  pro- 
vided the  difference  of  potential  between  the  wires  of  any  circuit  riuil  not 
be  over  150  volts  and  also  provided  that  no  group  of  lamps  reqtiiring  morB 
than  1.320  watts  shall  be  dependent  on  one  cut-out. 

No  "Ssrstem  of  Decorative  Lighting"  to  be  allowed  under  this  mle  which  is  not 
listed  in  tbe  Supplement  to  the  National  Electrical  Oode  oootalning  list  of  approved 
fittings. 

31  A.  Theater  Wiring. — (For  rules  governing  Moving  IMctxire  Machine, 
see  No.  65  A.) 

All  wiring,  apparatus,  etc.,  not  specifically  mm^M^fmit^'^s  **«■ 


INSIDE  WORK—CONSTANT'LOW'POTENTIAU  1415 

given  must  conform  to  tht  Standard  RuUs  and  Rg<tHiremenis  of  th$  National 

In  so  far  as  these  Rules  and  Requirements  are  concerned,  the  term 
''theater"  shall  mean  a  building  or  part  of  a  building  in  which  it  is 
designed  to  make  a  presentation  of  dramatic,  operatic  or  other  per- 
formances or  shows  for  the  entertainment  of  spectators  whicn  is 
capable  of  seating  at  least  four  hundred  persons,  and  which  has  a 
stage  for  suck  performances  that  can  be  used  for  scenery  and  other 
stage  appliances. 

a.  Sbryicbs. — ^1 .  Where  source  of  supply  is  outside  of  building,  there 
must  be  at  least  two  separate  and  distinct  services  where  practic^le,  fed 
from  separate  street  mams,  one  service  to  be  of  sufficient  capacity  to  supply 
current  for  the  entire  equipment  of  theater,  while  the  other  service  must  be 
at  least  of  sufficient  capacity  to  supply  current  for  all  emergency  lights. 

By  "emergency  lights"  are  meant  exit  lights  and  all  lights  In  lobbies,  stairways, 
oorridors  and  other  portions  of  theater  to  which  the  pubTlc  have  exoess  which  are 
normally  kept  lighted  during  the  performance. 

2.  Where  source  of  supply  is  an  isolated  plant  within  same  building,  an 
auxiliary  service  of  at  least  sufficient  capacity  to  supply  all  emergency  lights 
mtist  be  installed  from  some  outside  source,  or  a  suitable  storage  battery 
within  the  premises  may  be  considered  the  equivalent  of  such  service. 

b.  Stage. — ^1.  All  permanent  construction  on  stage  side  of  proscenium 
wall  must  be  approved  conduit,  with  the  exception  of  border  and  switchboard 
wiring. 

2.   Switchboards. — ^Must   be   made  of  non-combustible,  non-absorptive  ' 
material,  and  where  accessible  from  stage  level  must  be  protected  by  an 
approved  guard  rail  to  prevent  accidental  contact  with  live  parts  on  the  board. 

8.  Footlights. — a.  Must  be  wired  in  approved  conduit,  each  lamp  re- 
ceptacle being  enclosed  within  an  approved  outlet  box,  the  whole  to  be 
enclosed  in  a  steel  trough,  metal  to  be  of  a  thickness  not  less  than  No.  20 
gage,  or  each  lamp  receptacle  may  be  mounted  on  or  in  an  iron  or  steel  box 
so  constructed  as  to  enclose  all  the  wires  and  live  parts  of  receptacles. 

b.  Must  be  so  wired  that  no  set  of  lamps  requiring  more  than  1,320  watts 

will  be  dependent  on  one  cut-out. 
4.    Borders. — a.    Must  be  constructed  of  steel  of  a  thickness  not  less 
than  No.  20  gage,  treated  to  prevent  oxidization,  be  suitably  stayed  and  sup- 
ported by  a  metal  framework,  and  so  designed  that  flanges  of  reflectors  will 
protect  lamps. 

h.    Must  be  so  wired  that  no  set  of  lamps  requiring  more  than  1 ,  320  watts 
will  be  dependent  upon  one  cut-out. 

c.  Must  be  wired  in  approved  conduit,  each  lamp  receptable  to  be  en- 

closed within  an  approved  outlet  box,  the  whole  to  be  enclosed  in 
a  steel  trough,  or  each  lamp  receptacle  may  be  mounted  on  or  in 
the  cover  of  a  steel  box  so  constructed  as  to  enclose  all  the  wires  and 
the  live  parts  of  receptacles,  metal  to  be  of  a  thickness  not  less 
than  No.  20  gage. 

d.  Must  be  provided  with  suitable  ^niards  to  prevent  scenery  or  other 

combustible  material  coming  in  contact  with  lamps. 
#.  Cables  must  be  continuous  from  stage  switchboard  to  border;  conduit 
construction  must  be  used  from  switchboard  to  point  where  cables 
must  be  flexible  to  permit  of  the  raising  and  lowering  of  border, 
and  flexible  portion  must  be  enclosed  in  an  approved  fixeproof  hose 
or  braid  and  be  suitably  supported. 

Junction  boxes  win  be  allowed  on  fly  floor  and  rigging  loft  In   existing 
theaters  where  the  wiring  has  been  completed  and  approved  by  Inspeo- 
Uon  Department  having  JunsdlctKm. 
/.    For  the  wiring  of  the  border  proper,  wire  with  slow  burning  insulation 

should  be  used. 
g.    Must  be  suspended  with  wire  rope,  same  to  be  insulated  from  border 

by  at  least  two  approved  stram  insulators  properly  inserted. 
6.    Stage  Pockets. — Must  be  of  approved  type  controlled  from  switch- 
t>oard.  each  receptacle  to  be  of  not  less  than  fifty  amperes  rating,  and  each 
r^Mreptacle  to  be  wired  with  a  separate  circuit  to  its  full  capacity. 

6.     Proscenium  Side  Lights .—Uu&t  be  so  installed  that  they  cannot  in 
t^rfere  with  the  operation  of  or  come  in  contact  with  curtam. 


1416  70,— ELECTRIC  POWER  AND  UGHTING. 

7.  Sc0m  Docks.-^When  Uunps  are  installed  in  Scene  Docks,  they  must 
be  so  located  and  installed  that  they  will  not  be  liable  to  mechanical  mjuiy. 

8.  Curtain  Motors, — Must  be  of  ironclad  type  and  installed  ao  as  to 
conform  to  the  requirements  of  the  National  Blectncal  Code.     (See  No.  8.) 

0.  Control  for  Stagt  Fluts:^ 

a.  In  cases  where  dampers  are  released  by  an  electric  device*  the  electric 
circuit  operating  same  must  be  normally  closed. 

6.  Ma^et  operating  damper  must  be  wotmd  to  take  full  voltage  of 
circuit  by  which  it  is  supplied,  using  no  resistance  device,  and 
must  not  heat  more  than  normal  for  apparatus  of  similar  construc- 
tion. It  must  be  located  in  loft  above  scenery,  and  be  installed  is 
a  suitable  iron  box  with  a  tight  self-closing  door. 

C,  Such  dampers  must  be  controlled  by  at  least  two  standard  singk^  pok 
switches  moimted  within  approved  iron  boxes  provided  with  seK- 
dodng  doors  without  lock  or  latch,  and  located,  one  at  the  Blec* 
trician's  station,  and  others  as  designated  by  the  Inspection  De- 
partment having  jurisdiction. 

c   Drbssino  Rooms. 

1.  Must  be  wired  in  approved  conduit,  except  that  in  existing  brnkiings 
where  it  is  impracticable  to  install  approved  conduit,  a^^owd  armored  cable 
may  be  used,  provided  it  is  installed  in  accordance  with  No.  24  A. 

8.  All  pendant  lights  must  be  equipped  with  approved  reinforced  cord 
or  cable. 

3.    All  lamps  must  be  provided  with  approved  guards. 

d.     PORTABLB  EqUIPMBNTS. 

1.  Arc  lamps  used  for  stage  effects  must  conform  to  the  following 
requirements: — 

a.  Must  be  constructed  entirely  of  metal  except  where  the  use  of  approved 

insulating  material  is  necessary. 

b.  Must  be  substantially  constructed,  and  so  designed  as  to  provide  for 

proper  ventilation,  and  to  prevent  sparks  being  emitted  trom  lamps 
when  same  is  in  operation,  and  mica  must  be  used  for  frame  in- 
sulation. 

c.  Front  opening  must  be  provided  with  a  self-closing  hinged  door  foame 

in  which  wire  gauze  or  glass  must  be  inserted,  excepting  lens 
lamps,  where  the  front  may  be  stationary,  and  solid  dotv  be  pn>> 
video  on  back  or  side. 

d.  Must  be  provided  with  a  one-aixteenth-inch  iron  or  steel  guard  having 

a  mesh  not  larger  than  one  inch,  and  be  substantially  placed  over 
top  and  upper  half  of  sides  and  back  of  lamp  frame;  this  guard  to  be 
suDstantially  riveted  to  frame  of  lamp,  and  to  be  placed  at  a  dis- 
tance of  at  least  two  inches  from  the  lamp  frame. 

#.  Switch  on  standard  must  be  so  constructed  that  accidental  contact 
with  any  live  portion  of  same  will  be  impossible. 

/.  All  stranded  connections  in  lamp  and  at  switch  and  rheostat  must  be 
provided  with  approved  lugs. 

g.  Rheostat,  if  mounted  on  standard,  must  be  raised  to  a  height  of  at 
least  three  inches  above  floor  line,  and  in  addition  to  being  properly 
enclosed  must  be  surrotmded  with  a  substantially  attached  met^ 
f^uard  having  a  mesh  not  larger  than  one  square  inch,  which  guard 
IS  to  be  kept  at  least  one  inch  from  outside  frame  of  rheostat. 

k,  A  competent  operator  must  be  in  charge  of  each  arc  lamp,  except 
that  one  operator  may  have  charge  of  two  lamps  when  they  are 
not  more  than  ten  feet  apart,  and  areso  located  that  he  can  prop- 
erly watch  and  care  for  both  lamps. 

2.  Bunches: — a.  Must  be  substantially  constructed  of  metal,  and  must 
not  contain  anv  exposed  wiring. 

b.  The  cable  feeding  same  must  be  bushed  in  an  approved  manner 
where  passing  through  the  metal,  and  must  be  properly  secured  to 
prevent  any  mechanical  strain  from  coming  on  the  connection. 

3.  Strips. — a.  Must  be  constructed  of  steel  of  a  thickness  not  less  ibsn 
No.  20  gage,  treated  to  prevent  oxidization,  and  suitably  stayed  and  sup- 
ported by  metal  framework. 

b.  Cable  feeding  must  be  bushed  in  an  approved  manner  where  passing 
through  the  metal,  and  must  be  properly  secured  to  prevent  any 
mechanical  strain  from  coming  on  the  connections. 


INSIDE  WORK—CONSTANT-LOW'POTENTIAL.  1417 

4.  PortabU  Plugging  Box€S. — Mtist  be  constructed  so  that  no  current 
carrying  part  will  be  exposed,  and  each  receptacle  must  be  protected  by 
approved  fuses  mounted  on  slate  or  marble  bases  and  enclosed  m  a  fireproof 
cabinet  equipped  with  self-closing  doore.  Bach  receptacle  must  be  con- 
structed to  carry  thirty  amperes  without  undue  heating,  and  the  bus-bars 
must  have  a  carrying  capacity  equivalent  to  the  ciurent  required  for  the 
total  number  of  receptacles,  allowing  thirty  amperes  to  each  receptacle. 
and  approved  lugs  must  be  provided  for  the  connection  of  the  master  cable. 

6.  Pin  Plug  Conductors — a.  When  of  approved  tyge  may  be  used  to 
connect  approved  portable  lights  and  appliances. 

h.  Must  be  so  mstalled  that  the  "female"  part  of  plug  will  be  on  the  live 
end  of  cable,  and  must  be  so  constructed  that  tension  on  the  cable 
will  not  cause  any  serious  mechanical  strain  on  the  connections. 

6.  Lights  on  Scenery. — ^Where  brackets  are  used  they  must  be  wired 
entirely  on  the  inside,  fixture  stem  must  come  through  to  the  back  of  the 
scenery  and  end  of  stem  be  properly  biished. 

7.  String  or  Festoon  Lights. — Wiring  for  same  should  be  approved 
cable,  joints  where  taps  are  taken  from  same  for  lights  to  be  properly  ouide, 
soldered  and  taped,  and  where  lamps  are  used  in  lanterns  or  similar  devices 
lamps  must  be  provided  with  approved  guards.  Where  taps  are  taken  from 
cable,  they  should  be  so  staggered  that  joints  of  different  polarity  will  not 
come  immediately  opposite  each  other  and  must  be  properly  protected 
from  strain. 

8.  Special  Electrical  Effects. — Where  devices  are  used  for  producing 
special  effects  such  as  lightning.waterfalls.  etc..  the  apparatus  must  be  so  con- 
structed and  located  that  flames,  sparks,  etc..  resultmg  from  the  operation 
cannot  come  in  contact  with  comoustible  material. 

e.  Auditorium. — 1.  All  wiring  must  be  installed  in  approved  conduit, 
except  that  in  existing  buildings  where  it  is  impracticable  to  mstall  approved 
conduit,  approved  armored  cable  may  be  used,  provided  it  is  installed  in 
accordance  with  No.  24  A. 

2.  All  fuses  used  in  connection  with  lights  illuminating  all  parts  of  the 
house  used  by  the  audience  must  be  installed  in  fireproof  enclosures  so  con- 
structed that  there  will  be  a  space  of  at  least  six  inches  between  the  fuses 
and  the  sides  and  face  of  enclosure. 

3.  Exit  lights  must  not  have  more  than  one  set  of  fuses  between  same 
and  service  fuses. 

4.  Exit  lights  and  all  lights  in  halls,  corridors  or  any  other  part  of  the 
building  xised  by  the  audience,  except  the  general  auditorium  lighting, 
must  be  fed  independently  of  the  stage  lighting,  and  must  be  controlled 
only  from  the  lobby  or  other  convenient  place  in  front  of  the  house. 

5.  Every  portion  of  the  theater  devoted  to  the  use  or  accommodation 
of  the  public,  also  all  outlets  leading  to  the  streets  and  including  all  open 
courts,  corridors,  stairwavs.  exits  and  emergency  exit  stairways,  should  be 
well  and  properly  lighted  during  every  performance,  and  the  same  should 
remain  lighted  until  the  entire  audience  has  left  the  premises. 

32.  Car  Wiring  and  Equipment  off  Cars. —  a.  Protection  of  Car 
Body,  etc. — 1.  Under  side  of  car  bodies  to  be  protected  by  approved  fire- 
resisting,  insulating  material,  not  less  than  i-inch  in  thickness,  or  by  sheet 
iron  or  steel,  not  less  than  .04-inch  in  thickness,  as  specified  in  Section  a,  2, 
3  and  4.  This  protection  to  be  provided  over  all  electrical  apparatus,  such 
as  motors  with  a  capacity  of  over  76  H.  P.  each,  resistances,  contactors, 
lightning  arresters,  air-brake  motors,  etc.,  and  also  where  wires  are  run, 
except  that  protection  may  be  omitted  over  wires  designed  to  carry  25 
amperes  or  less  if  they  are  encased  in  metal  conduit. 

2.  At  motors  of  over  75  H.  P.  each,  fire-resisting  material  or  sheet  iron  or 
steel  to  extend  not  less  than  8  inches  beyond  all  edges  of  openings  in  motors. 
and  not  less  than  6  inches  beyond  motor  leads  on  all  sides. 

3.  Over  resistances,  contactors,  and  lightning  arresters,  and  other 
electrical  apparatus,  excepting  when  amply  protected  by  their  casing,  fire- 
resisting  material  or  sheet  iron  or  steel  to  extend  not  less  than  8  mches 
beyond  all  edges  of  the  devices. 

4.  Over  conductors,  not  encased  in  conduit,  a^i^ti^^y^^^^Wt^***^^* 


1418  TO.^ELECTRIC  POWER  AND  LIGHTING. 

when  designed  to  carry  over  25  amperes,  unless  the  conduit  is  so  supported 
as  to  give  not  less  than  i-inch  clear  air  space  betw^n  the  conduit  and  t^ 
car,  fire-resisting  material  or  sheet  iron  or  steel  to  extend  at  least  6  indss 
beyond  conductors  on  either  side. 

Hie  flre-reslstlno;  fnsulattng  material  or  sheet  fron  or  steel  may  be  omitted  cmt 
cables  made  up  of  flameproof  Dmided  outer  oovertng  when  sunroonded  by  ^-tuk 
flameproof  ooTerlng.  as  called  for  by  SecUoo  U  4. 

6.  In  all  cases  fireproof  material  or  sheet  iron  or  steel  to  have  ioiats 
well  fitted,  to  be  securely  fastened  to  the  sills,  fioor  timbers  and  croos  braces. 
and  to  have  the  whole  surface  treated  with  a  waterproof  paint. 

0.  Cut-out  and  switch  cabinets  to  be  substantially  made  of  hard  wood. 
The  entire  inside  of  cabinet  to  be  lined  with  not  less  than  |-inch  fiie-resistsK 
insulating  material  which  shall  be  securely  fastened  to  uie  woodwoirk.  acd 
after  the  fire-resisting  material  is  in  place  the  inside  of  the  cabinet  shall  be 
treated  with  a  waterproof  paint. 

b.  Wirts,  CabUs,  0tc. — 1.  All  conductors  to  be  stranded,  the  allowable 
carrying  capacity  being  determined  by  Table  "A"  of  No.  16,  except  that 
motor,  trolley  and  resistance  leads  shall  not  be  less  than  No.  7  B.  &  S.  gage, 
heater  circtuts  not  less  than  No.  12  B.  &  S.  gage,  and  lighting  and  other 
auxiliary  circuits  not  less  than  No.  14  B  &  S.  gage. 

The  current  used  in  determining  the  size  of  motor,  trolley  and  resist^ 
ance  leads  shall  be  the  per  cent  of  the  full  load  current,  based  on  one  hoar's 
nm  of  motor,  as  given  by  the  following  table: — 

Size  of  each  Motor  Trolley  Resistanoe 

Motor.  Leads.  Leads.  Leads. 

76H.P.orless 60%  40%  15% 

Over76H.P 46%  36%  16% 

Fixture  wire  complying  with  ffo.  46  will  be  permitted  for  wlrmgc^jrrocwd  elosttr. 

2.  To  have  an  insulation  and  braid  as  called  for  by  No.  41  for  wires 
carrying  ctirrents  of  the  same  potential. 

3.  When  nm  in  metal  conduit,  to  be  protected  by  an  additional  braid 
as  called  for  by  No.  47. 

Where  c(»ductOTS  are  laid  In  conduit,  not  being  drawn  through,  the  addltknal 
braid  will  not  be  required 

4.  When  not  in  conduit,  in  approved  moulding,  or  in  cables  sixrronnded 
|-inch  flameproof  covering,  must  comply  with  the  requirements  of 

_.,.  41  (except  that  tape  may  be  substituted  for  braid)  and  be  protected 
by  an  additional  flameproof  braid,  at  least  1-32  of  an  inch  in  tnicknesi, 
the  outside  being  saturated  with  a  preservative  flameproof  compound. 

This  rule  wUi  be  Interpreted  to  include  the  leads  from  the  motors. 

6.  Mtist  be  so  spliced  or  joined  as  to  be  both  mechanically  and  electric- 
ally secure  without  solder.  The  joints  must  then  be  soldered  and  covered 
with  an  insulation  equal  to  that  on  the  conductors. 

Joints  made  with  approved  splicing  devices  and  those  connecting  the  leads  st 
moton,  idowB  or  third-rail  shoes  need  not  be  soldered. 

6.  All  connections  of  cables  to  cut-outs,  switches  and  fittings,  except 
those  to  controller  connection  boards,  when  designed  to  carry  over  56 
amperes,  must  be  provided  with  lugs  or  terminals  soldered  to  the  cable,  and 
securely  fastened  to  the  device,  by  bolts,  screws  or  by  clamping;  or,  the 
end  of  the  cable,  after  the  insulation  is  removed,  shall  be  dipped  in  solder 
and  be  fastened  into  the  device  by  at  least  two  set  screws  having  check  nuts. 

All  connections  for  conductors  to  fittings,  etc.,  designed  to  cany  less 
than  26  amperes,  must  be  provided  with  up-tiuned  lugs  that  will  gnp  the 
conductor  between  the  screw  and  the  lug,  the  screws  being  provided  with 
fiat  washers;  or  by  block  terminals  having  two  set  screws,  and  the  end  of 
the  conductors  must  be  dipped  in  solder.  Soldering,  in  addition  to  the 
connection  of  the  binding  screws,  is  strongly  recommended,  and  will  be 
insisted  on  when  above  requirements  are  not  complied  with. 

This  rule  will  not  be  construed  to  apply  to  droults  where  the  maTimHm  potftttlil 
Is  not  over  25  volts,  and  current  does  not  exceed  5  amperes. 

c.  Cut-outs,  Circuit-Breakers  and  Switches. — 1.  All  cut-outs  and  switdies 
haying  exposed  live  metal  parts  to  be  located  in  cabinets.  Cut-outs  and 
switches,  not  in  iron  boxes  or  in  cabinets,  shall  be  mounted  on  not  leas  thsn 
i-inch  fire-resistins  insulating  material,  which  shall  Dzpject  at  least  f>tncfa 
beyond  all  sides  of  the  cut-out  or  switch.        Digitized  by LjOOglC 


^o 


INSIDE  WORK—CONSTANT'LOW'POTENTIAL.    '     1410 

2.  Cut-outs  to  be  of  the  approved  cartridge  or  approved  bbw-out  t3rpe. 

8.  All  switches  controlling  circuits  of  over  5  ampere  capacity  shall  be 
of  approved  single-pole,  quick-break  or  approved  magnetic  blow-out  type. 

Switches  controlling  circuits  of  6  ampere  or  less  capacity  may  be  of  the 
approved  single-pole,  double-break,  map  type. 

i.  Circuit  breakers  to  be  of  approved  type. 

6.  Circuits  must  not  be  fused  above  their  safe  carrying  capacity. 

8.  A  cut-out  must  be  placed  as  near  as  possible  to  the  current  collector, 
so  that  the  opening  of  the  fuse  in  this  cut-out  will  cut  off  all  current  from 
the  car. 

When  cars  are  opemted  by  metaUic  return  circuits,  the  circuit  breakers  ooanected 
to  both  sides  of  the  clroult.  no  fuses  In  addition  to  the  ciroult  breakers  wUl  be  reaulied. 

d.  Conduit. — [When  from  the  nature  of  the  case,  or  on  account  of  the 
size  of  the  conductors,  the  ordinary  pipe  and  junction  box  construction  is 
not  permissible,  a  special  form  of  conduit  system  majr  be  used,  provided 
the  general  requirements  as  given  below  are  complied  with.] 

1.  Metal  conduits,  outlet  and  junction  boxes  to  be  constructed  in  accord- 
ance with  Nos.  49  and  49  A,  except  that  conduit  for  lighting  circuits 
need  not  be  over  fi/10  inch  internal  diameter  and  i-inch  external  diameter, 
and  for  heating  and  air  motor  circ\iits  need  not  be  over  |-inch  internal 
diameter  and  9/ld-inch  external  diameter,  and  all  conduits  where  exposed 
to  dampness  must  be  water  tight. 

2.  Must  be  continuous  between  and  be  firmly  secured  into  all  outlet  or 
junction  boxes  and  fittings,  making  a  thorough  mechanical  and  electrical 
connection  between  same.  ^ 

3.  Metal  conduits,  where  they  enter  all  outlet  or  junction  boxes  and 
fittings,  must  be  provided  with  approved  bushings  fitted  so  as  to  protect 
cables  from  abrasion. 

4.  Except  as  noted  in  Section  i,  2,  must  have  the  metal  of  the  conduit 
permanently  and  effectively  grounded. 

5.  Junction  and  outlet  boxes  must  be  installed  in  such  a  manner  as  to 
be  accessible. 

6.  All  conduits,  outlets  or  junction  boxes  and  fittings  to  be  firmly  and 
substantially  fastened  to  the  fxumework  of  the  car. 

e.  Motdding. — 1.  To  consist  of  a  backing  and  a  capping  and  to  be 
constructed  of  nre-resistinff  insulatmg  material,  except  that  it  may  be  made 
of  hard  wood  where  the  circuits  which  it  is  designed  to  sup()ort  are  normally 
not  exposed  to  moisture. 

2.  When  constructed  of  fire-reaisting  insulating  material,  the  backing 
shall  not  be  less  than  i-inch  in  thickness  and  be  of  a  width  sufficient  to 
extend  not  less  than  1  inch  beyond  conductors  at  sides. 

The  capping,  to  be  not  le^  than  i-inch  in  thickness  shall  cover  and 
extend  at  least  f-inch  beyond  conductors  on  either  side. 

The  joints  in  the  moulding  shall  be  mitered  to  fit  close,  the  whole 
material  being  firmlv  secured  in  place  by  screws  or  nails,  and  treated  on 
the  inside  and  outside  with  a  waterproof  paint. 

When  flre-reslstlng  moulding  Is  used  over  surfaces  already  protected  by  i-Inch 
flre-resistlng  insulating  material  no  backing  wlU  be  required. 

8.  Wooden  mouldings  must  be  so  constructed  as  to  thoroughly  encase 
the  wire  and  provide  a  thickness  of  not  less  than  l-tnch  at  the  sides  and 
back  of  the  conductors,  the  capping  being  not  less  than  3/16-inch  in  thick- 
ness.   Must  have  both  outside  and  inside  two  coats  of  waterproof  paint. 

The  backing  and  the  capping  shall  be  secured  in  place  by  screws. 

f«  Lighting  and  Lighting  Circuits. — 1.  Each  outlet  to  be  provided  with 
an  approved  porcelain  receptacle,  or  an  approved  cluster.  No  lamp  of  over 
82  candle  power  to  be  used. 

2.  Circuits  to  be  nm  in  approved  metal  conduit,  or  approved  moulding. 

3.  When  metal  conduit  is  used,  except  for  sign  lights,  all  outlets  to  be 
provided  with  approved  outlet  boxes. 

4.  At  outlet  boxes,  except  where  approved  clusters  are  used,  porcelain 
receptacles  to  be  fastened  to  the  inside  of  the  box,  and  tlje  metal  cover  to 
have  an  insulating  bushing  around  opening  for  the  lamp.   ^OOQ  Ic 


1420     ^  T^.— ELECTRIC  POWER  AND  LIGHTING. 

When  approved  clusters  are  used,  the  cluster  shall  be  thoroughly  inse- 
lated  from  the  metal  conduit,  being  mounted  on  a  block  of  hara  "wood  or 
fire-resisting  insulating  material. 

6.  Where  conductors  are  run  in  moulding  the  porcelain  raceptades  or 
cluster  to  be  mounted  on  blocks  of  hard  wood  or  of  fireproof  msulati&g 
material.  • 

g.  Hfoters  and  Heating  Circuits. — 1.  Heaters  to  be  of  approved  type. 

2.  Panel  heaters  to  be  so  constructed  and  located  that  when  beaters 
are  in  place  all  current-carrying  parts  will  be  at  least  4  inches  Lxom  afl 
woodwork. 

HeateiB  for  cross  seats  to  be  so  located  that  current-carrying  parts  wiH 
be  at  least  6  inches  below  xmder  side  of  seat,  imless  under  side  of  aeai  is 
protected  by  not  less  than  i-inch  fire-resisting  insulating  material,  of  .04 
mch  sheet  metal  with  1  inch  air  space  over  same,  when  the  distance  may  be 
reduced  to  3  inches. 

2.  Circuits  to  be  nm  in  approved  metal  conduit,  or  in  approved  motxldin^. 
or  if  the  location  of  conductors  is  such  as  wiU  permit  an  air  space  of  not 
less  than  2  inches  on  all  sides  except  from  the  stirface  wired  over,  they  may 
be  supported  on  porcelain  knobs  or  cleats,  provided  the  knobs  or  cleats 
are  movmted  on  not  less  than  i-inch  fire-rwisting  insulating  material  exteiui- 
ing  at  least  3  inches  bejrond  conductors  at  either  side,  the  supports  raising 
the  conductors  not  less  than  i-inch  from  the  surface  wired  over,  and  being 
not  over  12  inches  apart. 

h.  Air  Pump  Motor  and  Circuits. — 1.  Circuits  to  be  run  in  afprcu^ 
metal  conduit  or  in  approved  moulding,  except  that  when  run  below  the 
floor  of  the  car  they  may  be  supported  on  porcelain  knobs  or  cleats,  pro- 
vided the  supports  raise  the  conductor  at  least  f-inch  from  the  suruce 
wired  over  and  are  not  over  12  inches  apart. 

2.  Automatic  control  to  be  enclosed  in  approved  metal  box.  Air  pomp 
and  motor,  when  enclosed,  to  be  in  approved  metal  box  or  a  wooden  box 
lined  with  metal  of  not  less  than  1/32  inch  in  thickness. 

When  conductors  are  nm  in  metal  conduit  the  boxes  surroimding  auto- 
matic control  and  air  pump  and  motor  may  serve  as  outlet  boxes. 

1.  Main  Motor  Circuits  and  Devices. — 1.  Conductors  connecting  between 
trolley  stand  and  main  cut-out  or  circuit  breakers  in  hood  to  be  protected 
where  wires  enter  car  to  prevent  ingress  of  moistuie. 

2.  Conductors  connecting  between  third  rail  shoes  on  same  truck,  to 
be  supported  in  an  approved  fire-resisting  insulating  moulding,  or  in  apprised 
iron  conduit  supported  by  soft  rubber  or  other  approved  insulating  cleats. 

3.  Conductors  on  the  under  side  of  the  car,  except  as  noted  in  Section  i.  4, 
to  be  supported  in  accordance  with  one  of  the  foUbwing  methods:— 

a.  To  be  run  in  approved  metal  conduit,  junction  boxes  being  provided 
where  branches  in  conduit  are  made,  and  outlet  boxes  when 
conductors  leave  conduit. 

h.  To  be  run  in  approved  fire-resisting  insulating  moulding. 

c.  To  be  supported  by  insulating  cleats,  the  supports  bemg  not  over 
12  inches  apart. 

4.  Conductors  with  flameproof  braided  outer  covering,  connecting 
between  controllers  at  either  end  of  car,  or  controllers  and  contactors,  may 
be  nm  as  a  cable,  provided  the  cable  where  exposed  to  the  weather  is  en- 
cased in  a  canvas  nose  or  canvas  tape,  thoroughly  taped  or  sewed  at  ends 
and  where  taps  from  the  cable  are  made,  and  the  hose  or  tape  enters  the 
controllers. 

Conductors  with  or  without  flameproof  braided  outer  covering  connect- 
ing between  controllers  at  either  end  of  the  car.  or  controllers  and  contactors, 
may  be  run  as  a  cable,  provided  the  cable  throughout  its  entire  length  is 
surrounded  by  i-inch  flameproof  covering,  thoroughly  taped  or  sew«l  at 
ends,  or  where  taps  from  cable  are  made,  and  the  flameproof  covering 
enters  the  controllers. 

Cables,  where  run  below  floor  of  car.  may  be  supported  by  approved 
insulating  straps  or  cleats.  Where  run  above  floor  of  car.  to  be  in  a  metal 
conduit  or  wooden  box  painted  on  the  inside  with  not  less  than  two  coats 
of  flameproof  paint,  and  where  this  box  is  so  placed  that  it  is  exposed  to 
water,  as  by  washing  of  the  car  floor,  attention  should^be  given  to  making 
tae  box  reasonably  waterproof.  izedbyVjODgEC 


INSIDE  WORK^CONSTANT-LOW-POTENTIAL.  1421 

Canvas  hose  or  tape,  or  flameproof  material  surrounding  cables  after 
conductors  are  in  same,  to  have  not  less  than  two  coats  of  waterproof 
insulating  material. 

S.  Motors  to  be  so  drilled  that,  on  double  truck  cars,  connecting 
cables  can  leave  motor  on  side  nearest  to  kingbolt. 

0.  Resistances  to  be  so  located  that  there  will  be  at  least  6-inch  air 
space  between  resistances  proper  and  fire-resisting  material  of  the  car. 
To  be  mounted  on  iron  supports,  being  insulated  by  non-combustible 
bushing  or  washers,  or  the  iron  supports  shall  have  at  least  2  inches  of 
insulatmg  surface  between  them  and  metal  work  of  car,  or  the  resistances 
mav  be  moimted  on  hard  wood  bars,  supported  by  iron  stirrups,  which 
shall  have  not  less  than  2  inches  of  insulating  surface  between  foot  of 
resistance  and  metal  stirrup,  the  entire  surface  of  the  bar  being  covered 
with  at  least  i-inch  fire-resisting  insulating  material. 

The  insulation  of  the  conductor,  for  about  6  inches  from  terminal  of 
the  resistance,  should  be  replaced,  if  any  insulation  is  necessary,  by  a 
porcelain  bushing  or  asbsetos  sleeve. 

7.  Controllers  to  be  raised  above  platform  of  car  by  not  less  than 
1-inch  hard  wood  block,  the  block  being  fitted  and  painted  to  prevent 
moisture  working  in  between  it  and  the  platform. 

J.  Lightning  Arrtsters. — 1.  To  be  preferably  located  to  protect  all 
auxiliary  circuits  in  addition  to  main  motor  circuits. 

2.  The  ground  conductor  shall  be  not  less  than  No.  6  B.  &  S.  gage, 
run  with  as  few  kinks  and  bends  as  possible,  and  be  securely  grounded. 

k.  General  RuUs. — 1.  When  passing  through  floors,  conductors  or 
cables  must  be  protected  by  approved  insulating  bushings,  which  shall  fit 
the  conductor  or  cable  as  closely  as  possible. 

3.  Moulding  should  never  be  concealed  except  where  readily  acces- 
sible.   Conductors  should  never  be  tacked  into  moulding. 

8.  Short  bends  in  conductors  should  be  avoided  where  possible. 

4.  Sharp  edges  in  conduit  or  in  motddi&g  must  be  smoothed  to  pre- 
vent injury  to  conductors. 

33.  Car  Houses.— a.  The  trolley  wires  must  be  securely  supported  on 
Insulating  hangers. 

b.  The  trolley  hangers  must  be  placed  at  such  a  distance  apart  that, 
in  case  of  a  break  in  the  trolley  wire,  contact  with  the  floor  cannot  be 
oiade. 

c.  Must  have  an  emergency  cut-out  switch  located  at  a  proper  place 
outside  of  the  building,  so  that  all  the  trolley  wires  in  the  building  may  be 
cut  out  at  one  point,  and  line  insulators  must  be  installed,  so  that  when 
this  emergency  switch  is  open,  the  trolley  wire  will  be  dead  at  all  points 
within  100  feet  of  the  buildmg.  The  cturent  must  be  cut  out  of  the  build- 
ing when  not  needed  for  use  in  the  bxiilding. 

This  may  be  done  by  the  emergency  switch,  or  If  preferred,  a  second  switch  may 
be  used  that  will  cut  out  all  current  from  the  building,  but  which  need  not  cut  out 
tbe  troUey  wire  outside  as  would  be  the  case  with  the  emergency  switch. 

d.  All  lamps  and  stationary  motors  must  be  installed  in  such  a  way 
that  one  main  switch  mav  control  the  whole  of  each  installation,  lij^hting 
and  power,  independently  of  the  main  cut-out  switch  called  for  in 
Section  c. 

e.  Where  current  for  lighting  and  stationary  motors  i»  from  a  groimded 
trolley  circuit,  the  following  special  rules  to  apply:— 

1.  Cut-outs  must  be  placed  between  the  non-grounded  side   and 

lights  or  motors  the^r  are  to  protect.  No  set  or  group  of  incan- 
descent lamps  requiring  over  2,000  watts  must  be  dependent 
upon  one  cut-out. 

2.  Switches  must  be  placed  between  non-grounded  side  and  lights 

and  motors  they  are  to  protect. 
8.  Must  have  all  rails  bonded  at  each  joint  with  a  conductor  having 
a  carrving  capacity  at  least  equivalent  to  No.  00  B.  &  S.  gage 
annealed  copper  wire,  and  all  rails  must  be  connected  to  the  out- 
side ground  return  circuit  by  not  less  than  No.  00  B.  &  S.  gage 
copper  wire  or  by  equivalent  bonding  through  the  track.    AU 


1423  TO.^ELECTRIC  POWER  AND  LIGHTING. 

lighting  and  stationary  motor  drcuita  must  be  thoroti«hly  mmi 
permanently  connected  to  the  rails  or  to  the  wire  leading  to 
the  outside  ground  return  circuit. 
ff.   All  pendant  cords  and  portable  conductors  will  be  consideied  as 
subject  to  hard  usage  (see  46,  t). 

ff.  Must,  except  as  provided  in  Section  e,  have  all  wiring  and  apparatus 
installed  in  accordance  with  the  rules  for  constant  potential  ssratems. 

h.  Must  not  have  any  system  of  feeder  distribution  centering  in  the 
building. 

I.  Cars  must  not  be  left  with  the  trolley  in  electrical  connection  with 
the  trolley  wire. 

34.  Lighting  and  Power  from  Railway  Wires. — a.  Must  not  6*  pfr- 
mitUd.  under  any  pretense,  in  the  same  circuit  mith  trolley  wires  with  a 
ground  return,  except  in  electric  railway  cars,  electric  car  houses  and  their 
power  stations;   nor  shall  the  same  dynamo  be  used  for  both  purpos€s. 

C0NSTANT.HIQH4H>TENnAL  SYSTEMS. 

560  TO  3,600  Volts. 

Any  circuit  attached  to  any  machine  or  combination  of  machines  which 
develops  a  difference  of  potential  between  any  two  wires,  of 
over  650  volts  and  less  than  3.600  volts,  shall  be  considered  as  a 
high-potential  circuit,  and  as  coming  under  that  class,  unles  an 
approved  transformins  device  is  used,  which  cuts  the  difference 
ot  potential  down  to  550  volts  or  less. 
<See  note  following  first  paragraph  under  Low-Potential  tyscems.  page  1406.) 

35.  Wires.— (See  also  Nos.  14.  15  and  16.)  a.  Must  have  an  approswi 
rubber-insulating  covering  (see  No.  41). 

b.  Must  be  always  in  plain  sight  and  never  encased,  except  as  provided 
for  in  No.  8  b,  or  where  required  by  the  Inspection  Department  having 
jurisdiction. 

c  Must  (except  as  provided  for  in  No.  8  b),  be  rigidly  supported  on 
glass  or  porcelain  msulators,  which  raise  the  wire  at  least  1  inch  from  the 
surface  wired  over,  and  must  be  kept  about  8  inches  apart. 

RlKld  supporting  requires  under  ordinary  oondltlons.  where  wlrlnf  aloog  flst 
surfaces,  supports  at  least  about  every  4i  feet.  If  the  wires  are  unusoally  liable  to 
be  disturbed,  the  distance  between  suppons  should  be  shortened. 

In  bulldtngs  of  mill  construction,  mains  of  not  less  than  No.  8  B.  A  S.  fsgi. 
where  not  liable  to  be  disturbed,  may  be  separated  about  toi  Inches  and  run  nrom 
timber  to  timber,  not  brealUng  around,  and  may  be  supported  at  each  timber  oolr. 

d.  Must  be  protected  on  side  walls  from  mechanical  iniury  by  a  sub- 
stantial boxing,  retaining  an  air  space  of  1  inch  around  the  conductors, 
closed  at  the  top  (the  wires  passing  through  bushed  holes)  and  extending 
not  less  than  7  feet  from  the  floor.  When  crossing  floor  timbers,  in  cellars, 
or  in  rooms  where  thcjr  might  be  exposed  to  injury,  wires  must  be  at- 
tached by  their  insulatin|[  supports  to  the  under  side  of  a  wooden  strip 
not  less  than  i-inch  in  thickness. 

For  general  suggestions  on  protection,  see  note  under  No.  24  e.  See  also  note 
under  No.  18  e. 

36.  Transformers. — (When  permitted  inside  buildings  under  No.  11) 
(For  construction  rules  see  No.  62.)     (See  also  Nos.  13  and  ISA.) 

Transformers  must  not  be  plaoed  Inside  of  buildings  without  speelal  permlaslaB 
from  the  Inspection  Department  having  Jurlsdletton. 

a.  Must  be  located  as  near  as  possible  to  the  point  at  which  the 
primary  wires  enter  the  building. 

b.  Must  be  placed  in  an  enclosure  constructed  of  fire-resisting  material; 
the  enclosure  to  be  used  only  for  this  purpose,  and  to  be  kept  securely 
locked,  and  access  to  the  same  allowed  only  to  responsible  parties. 

c  Must  be  thoroughly  insulated  from  the  ground,  or  permanratly 
and  effectually  grounded,  and  the  enclosure  in  which  they  are  placed 
must  be  practically  air-tight,  except  that  it  must  be  thoroughly  ventilated 
to  the  outdoor  air,  if  possible  through  a  chimney  or  flue.  There  should 
oe  at  least  6  inches  air  space  on  all  sides  of  the  transformer. 


INSIDE  WORK'-CONST.'POTEN,    FITTINGS,  1428 

37  Seiiet  Lamps. — a.  No  multiple-series  or  series-multiple  system 
of  lighting  will  be  approved. 

b.   Must  not,  tmder  any  circumstances,  be  attached  to  gas  fixtures. 

CONSTANT  EXTRA-HIQH4>0TENTIAL  SYSTEMS. 

OvBR  3.500  Volts. 

Any  circuit  attached  to  any  machine  or  combination  of  machines  which 
develops  a  difference  of  potential,  between  any  two  wires,  of  over 
3,600  volts,  shall  be  considered  as  an  extra-high-potential  circuit, 
and  as  coming  under  that  class,  unless  an  approved  transforming 
device  is  used,  which  cuts  the  difference  ot  potential  down  to 
3,500  volts  or  less. 

38.  Primary  Wires, — a.  Must  not  be  brought  into  or  over  buildings,  ex- 
cept power  stations  and  sub-stations. 

39.  Secondary  Wires. — a.  Must  be  installed  under  rules  for  high- 
potential  systems  when  their  immediate  primary  wires  carry  a  current  at  a 
potential  of  over  3.500  volts,  tmless  the  primary  wires  are  installed  in 
accordance  with  the  requirements  as  given  in  No.  12  A  or  are  entirely  under- 
ground, within  city,  town  and  village  limits. 

Oast  D.— FITTINGS,  MATERIALS  AND  DETAILS  OF 
CONSTRUCriON. 

(Light,  Power  and  Hbat.    For  Signalino  Systbics,  sbb  Class  E.) 

ALL  SYSTEMS  AND  VOLTAGES. 

The  followtaig  rules  are  but  a  partial  outline  of  requirements.  Devices 
or  materials  which  fulfill  the  conditions  of  these  requirements 
and  no  more,  will  not  necessarily  be  acceptable.  All  fittings  and 
materials  should  be  submitted  for  examination  and  test  oefore 
being  introduced  for  use. 

Insulated  Wires — Rules  40  to  43. 

40.  General  Rules. — a.  Copper  for  insulated  solid  conductors  of  No.  4 
B.  &  S.  gage  and  smaller  must  not  vary  in  diameter  more  than  .002  of  an 
inch  from  the  standard.  On  solid  sizes  larger  than  No.  4  B.  &  S.  gage 
the  diameter  shall  not  vary  more  than  one  per  cent  from  the  specified 
standard.  The  conductivity  of  solid  conductors  shall  not  be  less  than  97% 
of  that  of  pure  copper  of  the  specified  size. 

In  all  stranded  conductors  the  s\im  of  the  circular  mils  of  the  individual 
wires,  shall  not  be  less  than  the  normal  circular  mils  of  the  strand  by  more 
than  one  and  one-haif  per  cent  The  conductivitv  of  the  individual  wires 
in  a  strand  shall  not  be  less  than  is  given  in  the  following  table: — 


Number.             Per  cent. 

Number. 

Percent 

14  and  larger.     «7.0 

23 

95.2 

16                       00.8 

24 

96.0 

16                       96.0 

25 

94.8 

17                       96.4 

26 

94.6 

18                        06.2 

27 

94.4 

10                        96.0 

28 

94.2 

20                        95.8 

29 

94.0 

21                        95.0 

30 

93.8 

22                        95.4 

The  Standard  for  diameters  and  mileages  shall  be  that  adopted  by  the  American 
Institute  of  Electrical  Engineers. 

b.  Wires  and  cables  of  all  kinds  designed  to  meet  the  following:  specifi- 
cations must  have  a  distinctive  marking  the  entire  length  of  the  coil  so  that 
they  may  be  readily  identified  in  the  field.  They  must  also  be  plainly 
tagged  or  marked  as  follows: — 

1.  The  maximum  voltage  at  which  the  wire  is  designed  to  be  used. 

2.  The  words  "National  Electrical  Code  Standard."     GoOqIc 


14S4  n.^ELECTRIC  POWER  AND  UGHTINC. 

9.  Name  of  the  manufacturing  company  and,  if  desired,  trade  name  of 

the  wire. 
4.  Month  and  year  when  manufactured. 

Wires  described  under  Nos.  42.  43  and  44  need  not  have  the  dlsUnctlve  msrfctnc 
but  are  to  be  tagged. 

41.  Rubber-Covered  Wire.— «.  Copper  for  conductors  must  be  tlusr- 
oughly  tinned. 

Insukaion  for  VoUag0s,  0  to  600  inclusioe. — b.    Must  be  of  rubber  or 
other  approvea  substances,  homogeneous  in  character,  adhering  to  the  cod- 
ductor  and  of  a  thickness  not  less  than  that  given  in  the  following  tabk: — 
B.  &  S.  Gage.  Thickness. 

18  to      16 1-32  inch. 

16  to        8 3-64     '• 

7to        2 1-16     •• 

1  to  0000 6-64     " 

Circular  Mils. 

260.000  to     600,000 3-32     " 

600.000  to  1.000.000 7-64     " 

Over  1.000,000 1-8       " 

Measurements  of  Insulating  wall  are  to  be  made  at  the  thinnest  portion  of  the 
dielectric. 

c.  The  completed  coverings  must  show  an  instilation  resistance  of  at 
least  100  megonms  per  mile  during  thirty  days'  immersion  in  water  at 
70*  Fahrenheit  (21*  Centigrade). 

d.  Each  foot  of  the  completed  covering  must  show  a  dielectric  strength 
sufficient  to  resist  throughout  five  minutes  the  application  of  an  electro- 
motive force  proportionate  to  the  thickness  of  insulation  in  accordance 
with  the  following  table: — 


Thickness      Breakdown  Test 
in  64th8  inches.      on  1  foot.             in 

Thickness 
64ths  inches. 

Breakdown  Test 
on  1  foot. 

1 
2 
3 
4 
6 
6 

3.000  Volts  A.  C. 
6.000     " 

0,000    •• 

11,000     " 
13.000     •• 
15.000     " 

7 
8 

10 
12 
14 
16 

16.600  Volts  AC 
18.000     • 
21.000     " 
23.500      • 
26.000     " 
28,000     •• 

The  source  of  alternating  electro-motive  force  shall  be  a  transfonner  of 
at  least  one  kilowatt  capacity.  The  application  of  the  electro-motive  iotot 
shall  first  be  made  at  4,000  volts  for  nve  minutes,  and  then  the  voltage 
increased  by  steps  of  not  over  3,000  volts,  each  held  for  five  minutes,  until 
the  rupture  of  the  insulation  occurs.  The  tests  for  dielectric  strength  sbeU 
be  made  on  a  sample  of  wire  which  has  been  immersed  in  water  for  wtveaty- 
two  hours.  One  foot  of  the  wire  under  test  is  tQ  be  submerged  in  a  conduct- 
ing liquid  held  in  a  metal  trough,  one  of  the  transformer  terminals  being 
connected  to  the  copper  of  the  wire  and  the  other  to  the  metal  of  the  txou^ 

Insulations  for  Voltages,  601  to  8,500  inclusiu*.—^  The  thickness  of  the 
insulating  wall  must  not  be  less  than  that  given  in  the  following  table: — 
B.  &  S.  Gage.  Thickness. 

14  to        1 3-32  inch. 

0  to  0000 3-32   "     covered  by  tape  or  braid. 

Circular  Mils. 

260,000  to  600,000 8-32   " 

Over  500,000 1-8     " 

f.  The  requirements  as  to  insulation  and  breakdown  resistance  for  wires 
for  low-potential  systems  shall  apply,  with  the  exception  that  an  insulatioa 
resistance  of  not  less  than  300  megohms  per  mile  shall  be  required. 

Insulations  for  Voliaggs  Over  9,500. — g.  Wire  for  arc  light  circuits  exceed- 
ing 3,600  volts  potential  must  have  an  insulating  wall  not  less  than  A  of 
an  inch  in  thickness,  and  shall  withstand  a  breakdown  test  of  at  MSt 
23.600  volts,  and  have  an  insulation  of  at  least  600  megohms  per  nrile. 

The  tests  on  this  wire  to  be  made  imder  the  same^eonditiqns  as  for  low- 
potential  wires.  Digitized  by  CjOOgle 


CONSTRUCTION—FITTINGS,  MATERIALS.  ETC,         14 W 

SpedflcatfoDi  for  lnnilfttl<mfl  for  altenatlng  cumntfl  ezceedlnff  3,500  Tolta  bave 
been  coosldered.  but  on  account  of  tbe  somew£nt  complez  conditions  of  such  work. 
It  has  80  Car  been  deemed  Inexpedient  to  specify  general  Insulations  for  this  use. 

General. — h.  The  rubber  compound  or  other  approved  substance  used 
as  insulation  must  be  sufficiently  elastic  to  permit  all  wires  smaller  than  No.  7 
B.  &  S.  gage  and  larger  than  No.  11  B.  &  S  gage  to  be  bent  without  injury 
to  the  insulation  around  a  cylinder  twice  the  diameter  of  the  insulated 
wire  measured  over  the  outer  covering.  All  wires  No.  11  B.  &  S.  gage  and 
smaller  to  be  bent  without  injury  to  the  insulation  around  a  cylinder  equal 
to  the  diameter  of  the  insulated  wire  measured  over  the  outer  covering. 

i.  All  the  above  insulations  must  be  protected  by  a  substantial  braided 
covering  propnerly  saturated  with  a  preservative  compound.  This  covering 
must  be  sufficiently  strong  to  withstand  all  the  abrasions  likely  to  be  met 
with  in  practice,  and  must  substantially  conform  to  approved  samples 
submitted  by  the  manufacturer. 

43.  Slow-biimiiis  Weatheniroof  Wire. — [This  wire  is  not  as  burnable 
as  "weatherproof"  nor  as  subject  to  softening  tmder  heat.  It  is  not  suitable 
for  outside  work.] 

a.  The  insulation  must  consist  of  two  coatings,  one  to  be  fireproof  in 
character  and  the  other  to  be  weatherproof.  The  fireproof  coating  must  be 
on  the  outside  and  must  comprise  about  0/10  of  the  total  thickness  of  the 
wall.  The  completed  covering  must  be  of  a  thickness  not  less  than  that 
given  in  the  following  table: — 

B.  &  S.  Gage.  Thickness. 

14  to        8 3-64  inch. 

7to        2 1-16     " 

1  to  0000 6-64     *• 

Circular  Mils. 

250.000  to     600.000 3-32    " 

500,000  to  1.000.000 7-64     " 

Over  1,000.000 1-8      " 

Ifeasareinents  of  Insulating  wall  are  to  be  made  at  the  thinnest  portion. 

b.  The  fireproof  coating  shall  be  of  the  same  kind  as  that  required  for 
**tlcw-buming  wire."  and  must  be  finished  with  a  hard,  smooth  surface. 

c  The  weatherproof  coating  shall  consist  of  a  stout  braid,  applied  and 
treated  as  required  for  "weatherproof  wire." 

43.  Slow-biimiiig  Wire. — a.  The  insulation  must  consist  of  three 
braids  of  cotton  or  other  thread,  all  the  interstices  of  which  must  be  filled 
with  the  fireproofing  compound  or  with  material  having  equivalent  resisting 
and  insulating  properties.  The  outer  braid  must  be  specially  designed  to 
withstand  abrasion,  and  its  siuiace  must  be  finished  smooth  and  hard. 
The  completed  covering  must  be  of  a  thickness  not  less  than  that  given  in 
the  table  under  No.  42  a. 

The  solid  constituent  of  the  fkreprooflng  compound  must  not  be  susceptible  to 
moisture,  and  must  not  bum  even  when  ground  in  an  oxidlzable  oil.  making  a  com- 
pound, which,  while  proof  against  Are  and  moisture,  at  the  same  time  has  connderable 
elastloity.  and  which  when  dry  will  suffer  no  change  at  a  temperature  of  2b(y  Fahren- 
beit  il2l<'  Centigrade) .  and  which  will  not  bum  at  even  a  higher  temperature. 

This  is  practically  the  old  so-called  "underwriter!"  insulation.  It  is  especially 
useful  in  hot,  dry  places  where  ordinary  msulatkms  would  perish,  and  where  wires 
are  bunched,  as  on  the  back  of  a  large  switchboard  or  in  a  wire  tower,  so  that  the 
accumulation  of  robber  Insulation  would  result  in  an  obJeetionaMy  large  mass  of 
highly  inflammable  material. 

44  Weatherproof  Wire. — a.  The  insulating  covering  shall  consist  of 
at  least  three  braids,  all  of  which  must  be  thoroughly  saturated  with  a 
dense  moisture-proof  compound,  applied  in  such  a  manner  as  to  drive  any 
atmospheric  moisture  from  the  cotton  braiding,  thereby  securing  a  covering 
to  a  great  degree  waterproof  and  of  high  insulating  power.  This  compound 
must  retain  its  elasticity  at  0^  Fahrenheit  (minus  18**  Centigrade),  and 
must  not  drip  at  160°  Fahrenheit  (7P  Centigrade).  The  thickness  of  insu- 
lation must  not  be  less  than  that  given  in  the  table  under  No.  42  a,  and  the 
outer  surface  must  be  thoroxighly  slicked  down. 

This  wire  is  for  use  outdoors,  where  moistxire  is  certain^-and  where  fire- 
proof qualities  are  not  necessary.  Digitized  by  V^OOglC 


142«  n.^ELECTRlC  POWER  AND  UGHTING. 

45.    FtoxiMe  Cord. — (For  installation  rules,   see  No.  28).     a.     Must 

except  as  required  for  portable  heating  apparatus  (see  Section  g).  be  made 
of  stranded  copper  conductors,  each  strand  to  be  not  larger  than  No.  2$ 
or  smaller  than  No.  30  B.  &  S.  gage,  and  each  stranded  conductor  most  be 
covered  by  an  approved  insulation  and  protected  from  mechanical  utpuf 
by  a  tough,  braided  outer  covering. 

For  Pendant  Lamps. — [In  this  class  is  to  be  included  all  flexible  coxd 
which,  under  usual  conditions,  hangs  freely  in  air,  and  which  is  not  likelT 
to  be  moved  sufficiently  to  come  in  contract  with  surrounding  objects. 

It  should  be  noted  that  pendant  lamps  provided  with  lon^  cords,  so 
that  they  can  be  carried  about  or  hung  over  nails,  or  on  machinery,  etc^ 
are  not  included  in  this  class,  even  though  they  are  usually  allowed  to  hang 
freely  in  air  .J 

b.  Each  stranded  conductor  must  have  a  carrying  capacity  equivaleat 
to  not  less  than  a  No.  18  B.  &  S.  gage  wire. 

c.  The  covering  of  each  stranded  conductor  must  be  made  up  as  fol- 
lows:— 

1.  A  tight,  close  wind  of  fine  cotton. 

2.  The  insulation  proper,  which  shall  be  waterproof. 

3.  An  outer  cover  of  silk  or  cotton. 

The  wind  of  cotton  tends  to  prevmt  a  broken  strsnd  puncturing  the  tnsplatipii 
and  causing  a  short  circuit.    It  slso  keeps  the  rubber  from  oorrodlag  the  eoppor. 

d.  The  insulation  must  be  solid,  at  least  1/32  of  an  inch  thick,  and  most 
show  an  insulation  resistance  of  60  megohms  per  mUe  thxotishout  two 
weeks  immersion  in  water  at  70^  Fahrenheit  (21**  Centigrade),  and  stand  the 
tests  prescribed  for  low-tension  wires  as  far  as  they  apply. 

ۥ  The  outer  protecting  braiding  should  be  so  put  on  and  sealed  in  place 
that  when  cut  it  will  not  tray  out,  and  where  cotton  is  used  it  should  be 
impregnated  with  a  flameproof  paint  which  will  not  have  an  injurioua  e&ct 
on  the  insulation. 

For  PoriabUs. — [In  this  class  is  included  all  cord  used  on  portable  lamp*, 
■mall  ()ortable  motors,  or  any  device  which  is  liable  to  be  carried  about  J 

ff.  Flexible  cord  for  portable  use,  except  in  offices,  dwellings  or  aimdar 
places,  where  cord  is  not  liable  to  rough  usage  and  where  appearance  is  an 
essential  feature,  must  meet  aU  the  requirements  for  flexible  <x>rd  for  "pend- 
ant lamps,"  both  as  to  construction  and  thidcness  of  insulation,  and  in 
addition  must  have  a  tough,  braided  cover  over  the  whole.  There  mmt 
also  be  an  extra  layer  of  rubber  between  the  outer  cover  and  flexible  «mL 
and  in  moist  places  the  outer  cover  must  be  sattirated  with  a  moistu2«<prD0( 
compound,  thoroughly  slicked  down,  as  required  for  "weatherproof  wire." 
(See  No  44.)  In  offices,  dwellings,  or  in  similar  places  where  cord  is  sot 
liable  to  rough  usage  and  where  appearance  is  an  essential  feature,  &xxble 
cord  for  portable  xise  must  meet  all  of  the  requirennents  for  flexible  coxd  for 
"pendant  lamps."  both  as  to  construction  and  thickness  of  insulation,  and 
in  addition  must  have  a  tough,  braided  cover  over  the  whole,  or,  proVidifif 
there  is  an  extra  layer  of  rubber  between  the  flexible  cord  and  the  outer 
cover,  the  insulation  proper  on  each  stranded  conductor  of  cord  may  be 
1/64  of  an  inch  in  thickness  instead  of  1/32  of  an  inch  as  required  for 
pendant  cords 

Flexible  cord  for  portable  use  may,  histead  of  the  oaler  covertngs  desulbwl 
above,  have  an  approved  metal  flexible  armor. 

For  Portable  Heating  Apparatus. — [Applies  to  all  smoothing  and  sad 
irons,  and  to  any  other  device  requiring  over  250  watta.] 
g.  Must  be  made  up  as  follows:-^ 

1.  O>nductors  must  be  of  braided  copper,  each  strand  not  to  be  laffcr 

than  No.  30  or  smaller  than  No.  36  B.  &  S.  gage. 
When  conductors  have  a  greater  carrying  capacity  than  no.  1 2  B.  ft  S.  gaae  tfeef 
may  be  braided  or  stranded  with  eadi  strand  as  large  as  No.  2 IB.  *  5. 
gage.    If  stranded,  there  must  be  a  tight,  dose  wind  of  ootton  bervtea 
the  conductor  and  the  insulation. 

2.  An  insulating  covering  of  rubber  or  other  approved  material  not  kis 

than  1/64  inch  in  tbickness. 
8.  A  braided  covering  of  not  less  than  1/32  inch  thick,  composed  of  best 
quality  long  fiber  asbestos,  containing  not  over  five  per  ca  ' 
vegetable  fiber.  P r^oalf> 

Digitized  by  VjOOv  LC 


CONSTRUCTION— FITTINGS,  MATERIALS,  ETC,         1427 

4.  The  several  conductors  comprising  the  cord  to  be  enclosed  by  an  outer 
reinforcing  covering  not  less  than  1/64  inch  thick,  especially 
designed  to  resist  abrasion,  and  so  treated  as  to  prevent  tne 
cover  from  fraying. 

46.  Fixture  Wire.— (For  installation  rules,  see  No.  24,  v  to  y.)   a.  May 

be  made  of  solid  or  stranded  conductors,  with  no  strands  smaller  than 
No^  30  B.  &  S.  gage,  and  must  have  a  carrying  capacity  not  less  than  that 
of  a  No  18  B.  &  S.  gage  wire. 

!>.  Solid  conductors  must  be  thoroughly  tinned.  If  a  stranded  con- 
ductor is  used^  it  must  be  covered  by  a  tight,  close  wind  of  fine  cotton. 

c  Must  have  a  solid  rubber  insulation  of  a  thickness  not  less  than 
1/32  of  an  inch  for  Nos.  18  to  16  B.  &  S.  gage,  and  3/64  of  an  inch  for  Nos.  14 
to  8  B.  &  S.  gage,  except  that  in  arms  of  fixtures  not  exceeding  24  inches 
in  length  and  used  to  supply  not  more  than  one  16-candle-ppwer  lamp  or 
its  equivalent,  which  are  so  constructed  as  to  render  impracticable  the  use 
of  a  wire  with  1/32  of  an  inch  in  thickness  of  rubber  insulation,  a  thicknewt 
of  1/64  of  an  inch  will  be  permitted. 

d.  Must  be  protected  with  a  covering  at  least  1/64  of  an  inch  in  thick- 
ness, suffidentlv  tenacious  to  withstand  the  abrasion  of  being  pulled  into 
the  fixture,  and  sufficiently  elastic  to  permit  the  wire  to  be  bent  around  a 
cylinder  with  twice  the  diameter  of  the  wire  without  injury  to  the  braid. 

e.  Must  successfully  withstand  the  tests  specified  in  Nos.  41  c  and  41  d. 
In  wiring  certain  deslms  of  show-ease  fixtures,  oelllog  bulls-eves  and  similar 

appllanoee  in  which  the  wiring  is  exposed  to  temperatures  In  excess  of  1 20^  Fahrenheit 
(49*  OeDtlffrade).  from  the  heat  of  lamps,  sloyr-bumlng  wire  may  be  used  (see  No  43). 
All  such  forms  of  fixtures  must  be  submitted  for  examination,  test  and  approval 
before  beUig  introduced  lOr  use. 

47.  Conduit  Wire.— (For  installation  rules,  see  No.  24  n  to  p.) 

a.  Single  wire  for  lined  conduits  must  comply  with  the  requirements 
of  No.  41.  For  unlined  conduits  it  must  comply  with  the  same  require- 
ments (except  that  tape  may  be  substituted  for  braid)  and  in  addition  there 
must  be  a  second  outer  fibrous  covering,  at  least  1/32  of  an  inch  in  thick- 
ness and  sufficiently  tenacious  to  withstand  the  abrasion  of  being  hauled 
through  the  metal  conduit. 

b.  For  twin  or  duplex  wires  in  lined  conduit,  each  conductor  must  com- 
ply with  the  requirements  of  No.  41  (except  that  tape  may  be  substituted 
for  braid  on  the  separate  conductors),  and  must  have  a  substantial  braid 
covering  the  whole.  For  tmlined  conduit  each  conductor  must  comply 
with  requirements  of  No.  41  (except  that  tape  may  be  substituted  for  braid), 
and  in  addition  must  have  a  braid  covering  the  whole,  at  least  1/32  of  an 
inch  in  thickness  and  stUficiently  tenacious  to  withstand  the  abrasion  of 
being  hauled  through  the  metal  conduit. 

c.  For  concentric  wire,  the  inner  conductor  must  comply  with  the 
requirements  of  No.  41  (except  that  tape  may  be  substituted  for  braid), 
and  there  must  be  outside  of  the  outer  conductor  the  same  insulation  as 
on  the  inner,  the  whole  to  be  covered  with  a  substantial  braid,  which,  for 
unlined  conduits,  must  be  at  least  1/32  of  an  inch  in  thickness,  and  suffi- 
ciently tenacious  to  withstand  the  abrasion  of  being  hauled  through  the 
metal  conduit. 

The  braid  or  tape  required  around  each  conductor  In  duplex,  twin  and  oonoentrte 
cables  Is  to  bold  the  rubber  Insulation  In  place  and  prevent  Jamming  and  flattening. 
All  the  braids  specified  In  this  rule  must  oe  properly  saturated  with  a  preservative 
compound. 

48.  Armored  Cable. — TFor  installation  rules,  see  No.  24  A),  a.  The 
airmor  of  such  cables  must  nave  at  least  as  great  strength  to  resist  penetra- 
tion of  nails,  etc..  as  is  required  for  metal  conduits  (see  No.  49  b),  and  its 
thickness  must  not  be  less  than  that  specified  in  the  following  table: — 

Actual  Actual 

Internal  External  Thickness 

Diameter.  Diameter.  of  Wall. 

Inches.  Inches.  Inches. 

.27  .40  .06 

.36  .64  ^.08 


49  .67         Digitized  by  LjXDOQle 

62  .84  .10  0 


.62 


1438 


lO.—ELECTRIC  POWER  AND  LIGHTING. 


Nominal 

Actual 

Actual 

Internal 

Internal 

External 

ThickneaB 

Diameter. 

Diameter. 

Diameter. 

ofWaU. 

Inches 

Inches. 

Inches. 

Inches. 

H 

.82 

1.05 

.11 

1 

1.04 

1.31 

.13 

IM 

1.38 

1.66 

.14 

IH 

1.61 

l.M 

.14 

2 

2.06 

2.37 

.15 

3H 

2.46 

2.87 

.20 

3 

3.00 

3.60  . 

.21 

3H 

3.54 

4.00 

.22 

4r 

4.02 

4.50 

.23 

4H 

4.60 

5.00 

.24 

5 

5.04 

6.56 

.25 

6 

6.00 

6.62 

.28 

An  allowance  of  .02  of  an  Inch  for  variation  In  manufacturing  and  loss  of  thick- 
nesB  by  cleaning  will  l>e  permitted. 

b.  The  conductors  in  same,  single  wire  or  twin  conductors,  mvist  have 
an  insulating  covering  as  required  by  No.  41*  if  anjr  filler  is  used  to  seccre 
a  round  exterior,  it  must  be  impregnated  with  a  moisture  repellent,  and  the 
whole  bunch  of  conductors  and  fillers  must  have  a  separate  exterior  covezins- 

49.  Interior  Conduits. — (Pot  installation  rules,  see  Nos.  24  n  to  p  axMl 
25.)  a.  Each  length  of  conduit,  whether  lined  or  unlined,  must  tuLW  the 
maker's  name  or  initials  stamped  in  the  metal  or  attached  thereto  in  a 
satisfactory  manner,  so  that  inspectors  can  readily  see  the  same. 

The  use  of  paper  stickers  or  tags  cannot  be  considered  satlslb^tory  meUiods  of 
marking,  as  they  are  readily  loosened  and  lost  Off  In  too  ordinary  handltoK  oC  tiie 
conduit. 

Metal  Conduits  with  Lining  of  Insuiating  Material. — b.  The  metal  corer* 
ing  or  pipe  must  be  at  least  as  strong  as  the  ordinary  commercial  forms  of 
gas  pipe  of  the  same  size,  and  its  thickness  must  be  not  lesss  than  that  ni 
standard  gas  pipe  as  specified  in  the  table  given  in  No.  48. 

c.  Must  not  be  seriously  affected  externally  by  burning  out  a  wipe 
inside  the  tube  when  the  iron  pipe  is  connected  to  one  side  of  the  circmt. 

d.  Must  have  the  insulating  lining  firmly  secured  to  the  pipe. 

e.  The  insulating  lining  must  not  crack  or  break  when  a  length  of  the 
conduit  is  uniformly  bent  at  temperature  of  212**  Fahrenheit  (lOO^Coiti- 
ffrade),  to  an  angle  of  ninety  degrees,  with  a  curve  having  a  radius  of  IS  Ins.. 
for  pipes  of  one  inch  and  less,  and  fifteen  times  the  diameter  of  pipe  for 
larger  sizes. 

f.  The  insulating  lining  must  not  soften  injuriously  at  any  temperatore 
below  212^  Fahrenhiet  (100^  Centigrade),  and  must  leave  water  in  which  it 
is  boiled  practically  neutral. 

ff.  The  insulating  lining  must  be  at  least  1/32  of  an  inch  in  thirkneas. 
The  materials  of  which  it  is  composed  must  be  of  such  a  nature  as  will  not 
have  a  deteriorating  effect  on  the  insulation  of  the  conductor,  and  be 
sufficiently  tough  and  tenacious  to  withstand  the  abrasion  test  ot  draws^ 
long  lengths  of  conductors  in  and  out  of  same. 

h.  The  insulating  lining  must  not  be  mechanically  weak  after  three 
days'  immersion  in  water,  and  when  removed  from  the  pipe  entire.  mtiK 
not  absorb  more  than  ten  per  cent  of  its  weight  of  water  during  100  boors 
of  submersion. 

i.  All  elbows  or  bends  must  be  so  made  that  the  conduit  or  Hnhis  of 
same  will  not  be  injured.  The  radius  of  the  curve  of  the  inner  edge  of  any 
elbow  must  not  be  less  than  8H  inches. 


Unlined  Metal  Conduits. — J.  Pipe  sizes  to  run  as  follows:— 

Trade  Size.            Approximate  Internal  Minimum  Thickness 

Inches.                           Diameter.  of  Wall. 

Inches.  Inches. 

.62  .100 

.82  .106 

1.04  r^r      " 

J    ag  Digitized  by  VjOL 


.» 

IH 


ximate  Internal 
Diameter. 
Inches. 

Minimum  Thickness 
of  Wall. 
Inches. 

1.61 
2.06 
2.46 
3.06 
3.54 

.140 
.160 
.200 
.210 
.220 

CONSTRUCTION— FITTINGS,  MATERIALS,  ETC,         1429 

Trade  Size. 
Inches. 

3H 

At  no  point  (except  at  screw  thread)  shall  the  thickness  of  wall  of  finished 
midalt  be  less  than  the  minimum  specified  In  last  c<4umn  of  above  table. 

k.  Pipe  to  be  thorovighly  cleaned  to  remove  all  scale.  Pipe  should  be 
:>{  stifficientlv  true  circular  section  to  admit  of  cutting  true,  clean  threads, 
ind  should  be  very  closely  the  same  in  wall  thickness  at  all  ()oints  with 
:lean  square  weld. 

I.  Cleaned  pipe  to  be  protected  against  effects  of  oxidation,  by  baked 
mamel.  zinc  or  other  approved  coating  which  will  not  soften  at  ordinary 
:emperature8,  and  of  sufficient  weight  and  toughness  to  successfully  with- 
stand rough  usuage  likely  to  be  received  during  shipment  and  installation; 
ind  of  sufficient  elasticity  to  prevent  flaking  when  ^-inch  conduit  is  bent  in 
k  curve  the  inner  edge  of  which  has  a  radius  of  3}  mches. 

m.  All  elbows  or  bends  must  be  so  made  that  the  conduit  will  not  be 
njured.  The  radius  of  the  curve  of  the  inner  edge  of  any  elbow  not  to  be 
ess  than  8}  inches. 

49  A.  Switch  and  Outlet  Boxes. —  a.  Must  be  of  pressed  steel  having  a 
vail  thickness  not  less  than  .081  inch  (No.  12  B.  &  S.  gage),  or  of  cast  metal 
laving  a  wall  thickness  not  less  than  .128  inch  (No.  8  B.  &  S.  gage.) 

b.  Must  be  well  galvanized,  enameled  or  otherwise  properly  coated, 
nside  and  out,  to  prevent  oxidation. 

C*  Must  be  so  made  that  all  openings  not  in  use  will  be  effectively  closed 
>y  metal  which  will  afford  protection  substantially  equivalent  to  the  walls 
>t  the  box. 

d.  Must  be  plainly  marked,  where  it  may  readily  be  seen  when  installed, 
rith  the  name  or  trade-mark  of  the  manufacturer. 

e.  Must  be  arranged  to  secure  in  position  the  conduit  or  flexible  tubing 
protecting  the  wire. 

This  mle  wUI  be  compiled  with  If  the  ooodult  or  tablng  Is  firmly  secured  In 
oaltlofi  by  means  of  some  approved  device  which  may  or  may  not  be  a  part  of  the 
ox. 

ff.  Boxes  used  with  lined  conduit  must  comply  with  the  foregoing 
equirements.  and  in  addition  must  have  a  tough  and  tenacious  insulating 
mng  at  least  1/32  inch  thick,  firmly  seciwed  in  position. 

g.  Switch  and  outlet  boxes  must  be  so  arranged  that  they  can  be  securely 
utened  in  place  independently  of  the  support  afforded  by  the  conduit 
ipinff.  except  that  when  entirely  exposed,  approved  boxes,  which  are 
Kreaned  so  as  to  be  firmly  supported  by  screwing  on  to  the  conduit  pipe, 
lay  be  used. 

h.  Switch  boxes  must  completely  enclose  the  switch  on  sides  and 
ack,  and  must  provide  a  thoroughly  substantial  support  for  it.  The  re- 
fining screws  for  the  box  must  not  be  used  to  secure  the  switch  in  position. 

I.  Covers  for  outlet  boxes  must  be  of  metal  equal  in  thickness  to  that 
pecified  for  the  walls  of  the  box,  or  must  be  of  metal  lined  with  an  insu- 
lting noaterial  not  less  than  1/32  inch  in  thickness,  firmly  and  permanently 
-cured  to  the  metal. 

50.    MouldiDgt. — (For  wiring  roles,  see  No.  24  k  to  m.) 

Woo(Un  Mouldings. — a.  Must  have,  both  outside  and  inside^  at  least 
iro  coats  of  waterproof  material,  or  be  impregnated  with  a  moisture  re- 
ellent. 

b.  Must  be  made  in  two  pieces,  a  backing  and  a  capping,  and  must  afford 
titable  protection  from  abrasion.  Must  be  so  constructed  as  to  thoroughly 
-ica^ae  the  wire,  be  provided  with  a  tongue  not  less  than  J  inch  in  thickness 
Btweesk  the  conductors,  and  have  exterior  walls  which,  under  grooves. 


1430 


TO.^ELECTRIC  POWER  AND  UGHTING. 


shall  not  be  less  than  H  inch  in  thickness,  and  on  the  sides  not  less  than 
H  inch  in  thickness. 

It  Is  reoommended  that  only  hard-wood  inoaldln«r  be  used. 

Metal  Mouldings. — (For  wiring  rules,  see  Nos.  24.  k  to  m,  and  25  A^ 

c  Each  length  of  such  moulding  must  have  maker's  najne  or  txade- 
mark  stamped  in  the  metal,  or  in  some  manner  permanently  attacbed 
thereto,  in  order  that  it  may  be  readily  identified  in  the  field. 

The  use  of  paper  stickers  or  tags  cannot  be  considered  satlsfaetory  methods  ol 
marking,  as  they  are  readUy  loosened  snd  lost  off  In  ordinary  handling  of  tiie  raoidd- 
Ing. 

d.  Must  be  constructed  of  iron  or  steel  with  backing  at  least  .050  inch 
in  thickness,  and  with  capping  not  less  than  .040  inch  in  thickness,  aod 
so  constructed  that  when  in  place  the  raceway  wDl  be  entirely  closed ;  most 
be  thoroughly  galvanized  or  coated  with  an  approved  rust  preventative 
both  inside  and  out  to  prevent  oxidation. 

e.  Elbows,  coupling  and  all  other  similar  fittings  must  be  constmcted 
of  at  least  the  same  thickness  and  Quality  of  metal  as  the  moulding  xts^ 
and  so  designed  that  they  will  both  electrically  and  meduuiicaUy  secure 
the  different  sections  together  and  maintain  the  continuity  of  the  raceway. 
The  interior  surfaces  must  be  free  from  burrs  or  sharp  comers  which  sc^^ 
cause  abrasion  of  the  wire  coverings. 

f.  Miost  at  all  outlets  be  so  arranged  that  the  conductors  cannot  come 
in  contact  with  the  edges  of  the  metal,  either  of  capping  or  backing.  Specially 
designed  fittings  which  will  interpose  substantial  beirriers  between  condocton 
and  the  edges  of  metal  are  recommended. 

f.  When  backing  is  secured  in  position  bv  screws  or  bolts  £rom  the  inacfe 
of  the  racewav,  depressions  must  be  provided  to  render  the  beads  of  the 
fastenings  flush  with  the  moulding. 

h.  Metal  mouldings  must  be  used  for  exposed  work  only  and  most  be 
so  constructed  as  to  form  an  open  raceway  to  be  closed  by  the  capping  or 
cover  after  the  wires  are  laid  in. 

50  A.  Tubes  and  Bushinn. — a.  Construction. — ^Must  be  made  straight 
and  free  from  checks  or  rough  projections,  with  ends  smooth  and  nnznded 
to  facilitate  the  drawing  in  of  the  wire  and  prevent  abrasion  of  its  covering. 

b.  Material  and  Test. — Must  be  made  of  non-combustible  insulating 
material,  which,  when  broken  and  submerged  for  100  hours  in  pure  water 
at  70**  Fahrenheit  (21^  Centigrade),  will  not  absorb  over  one-half  of  one  per 
cent  of  its  weight. 

c.  Marking. — ^Must  have  the  name,  initials  or  trade-mark  of  the  manu- 
facturer stamped  in  the  ware. 

d.  Sims. — Dimensions  of  walls  and  heads  must  be  at  least  as  great  as 
those  given  in  the  following  table: — 

Diameter  External  Thickness  External  Length 

of  Diameter.  of  Diameter           of 

Hole.  Wall.  of  Head.  Head. 

Inches.  Inches.  Inches.  Inches.  Inches. 


a 

h 

1 

h 

iy£ 

I 

1^ 

2^ 

\\£ 

h 

2 

2 

2K 

h 

2K 

3 

An  allowance  of  1-64  of  an  Inch  tor  variation  In  manuCsetore  will  be  permttted. 
except  m  the  thickness  of  the  wsU. 

.   50  B.    Cleats. — a.    Construction. — Must  hold  the  wire  firmly  in  place 
without  injury  to  its  covering.  Pooalf> 

Sharp  edges  which  may  cut  the  wire  should  be  avoi^^^  ^-^uuy  n. 


CONSTRUCTION—FITTINGS,  MATERIALS,  ETC,         1481 

b.  Supports. — Bearing  points  on  the  sufface  must  be  made  by  ridges 
or  rings  about  the  holes  for  supporting  screws,  in  order  to  avoid  crackmg 
and  breaking  when  screwed  tight. 

c  Material  and  Ttst. — ^Must  be  made  o£  non-combustible  insulating 
material,  which,  when  broken  and  submerged  for  100  hours  in  pure  water 
at  70^  Fahrenheit  (2V*  Centigrade),  will  not  absorb  over  one-half  of  one 
per  cent  of  its  weight. 

d.  Marking. — ^Mtist  have  the  name,  initials  or  trade-maric  of  the  manu- 
facturer stamped  in  the  ware. 

e.  Si»s. — Must  conform  to  the  spacings  given  in  the  following  table: — 

Distance  from  Wire        Distance  Between 
Voltage.  to  Surface.  Wires. 

0-300  k  inch.  2}  inches. 

This  rule  wUl  not  he  Interpreted  to  forbid  the  pladns  of  the  neutral  of  an  Edlsoo 
three-wire  syRtem  In  the  center  of  a  tbree-wire  deat  where  tbe  dUferenoe  of  potential 
between  tbe  outside  wires  Is  not  over  300  volts,  inovlded  the  outside  wires  are  sepa- 
rated 2i  Incbee. 

50  C.  Flexible  Tabtag. — a.  Must  have  a  sufficiently  smooth  interior 
surface  to  &llow  the  ready  introduction  of  the  wire. 

b.  Must  be  constructed  of  or  treated  with  materials  which  will  serve  as 
moisture  repellents. 

c.  The  tube  mtist  be  so  designed  that  it  will  withstand  all  the  abrasion 
likely  to  be  met  with  in  practice. 

d.  The  linings,  if  any,  must  not  be  removable  in  lengths  of  over  3  feet. 

e.  The  i-inch  tube  must  be  so  flexible  that  it  will  not  crack  or  break 
when  bent  in  a  circle  with  0-inch  radius  at  60**  Fahrenheit  (10*  Centigrade), 
and  the  covering  must  be  thoroughly  saturated  with  a  dense  moisture- 

8 roof  compound  which  will  not  slide  at  160*  Fahrenheit  (66*  Centigrade), 
^her  sizes  must  be  as  well  made. 

f.  Must  not  convey  fire  on  the  application  of  a  flame  from  Bunsen  burner 
to  the  exterior  of  the  tube  when  held  in  a  vertical  position. 

g.  Must  be  sufficiently^  toti^h  and  tenacious  to  withstand  severe  tension 
without  injury;  the  interior  diameter  must  not  be  diminished  or  the  tube 
opened  up  at  any  point  by  the  appliottion  of  a  reasonable  stretching  force. 

h.  Must  not  close  to  prevent  the  insertion  of  the  wire  after  the  tube  has 
been  kinked  or  flattened  and  straightened  out. 

51.    Switches.— (For  installation  rules,  see  Noe.  17  and  22.) 
General  Rules. 

a.  Must,  when  used  for  service  switches,  indicate,  on  inspection,  whether 
the  current  be  "on"  or  "off." 

b.  Must,  for  constant-current  systems,  close  the  main  circuit  and  dis- 
connect the  branch  wires  when  turned  "oft;"  must  be  so  constructed  that 
they  "^hall  be  automatic  in  action,  not  stopping  between  points  when  started, 
ana  must  prevent  an  arc  between  the  pomts  under  all  circtmistances.  They 
xnttst  indicate  whether  the  current  be  "on"  or  "off." 

Knife  Switches. 
Knife  switches  must  be  made  to  comply  with  tbe  following  speolfloatlOQS.  except 
la  those  few  cases  where  peculiar  design  allows  tbe  switch  to  fulfil  tbe  general  re- 
gulrements  In  some  otber  way.  and  wbere  tt  can  BuccesBfullv  withstand  tbe  test  of 
Section  i.  In  such  cases  tbe  switch  should  be  submitted  for  special  examination 
before  being  used. 

c.  Base. — Must  be  mounted  on  non-combustible,  non-absorptive  insulat- 
ing bases,  such  as  slate  or  porcelain.  Bases  with  an  area  of  over  26  square 
inches  must  have  at  least  lour  supporting  screws.  Holes  for  the  supporting 
screws  must  be  so  located  or  coimtersimk  that  there  will  be  at  least  i  an 
inch  space,  measured  over  the  surface,  between  the  head  of  the  screw  or 
washer  and  the  nearest  live  metal  part,  and  in  all  cases  when  between 
parts  of  opposite  polarity  must  be  coimtersunk. 

d.  Mounting. — Pieces  carrying  the  contact  jaws  and  hinge  clips  must 
be  secured  to  the  base  by  at  least  two  screws,  or  else  made  with  a  square 
shoulder,  or  provided  with  dowel  pins,  to  prevent  possible  ttimings,  and 


1432  TO.—ELECTRIC  POWER  AND  UGHTING. 

the  nuts  or  screw-heads  on  the  under  side  of  the  base  must  be  ootmtefsaak 
not  less  than  i  inch  and  covered  with  a  waterprcwf  compound  which  will 
not  melt  betow  IW*  Fahrenheit  (66**  Centigxade). 

e.  Hing/is. — Hinges  o£  knife  switches  mtist  not  be  used  to  carry  correot 
unless  they  are  equipped  with  spring  washers,  held  by  lock-nuts  or  pins,  or 
their  equivalent,  so  arranged  uiat  a  firm  and  secure  connection  win  be 
maintained  at  all  positions  of  the  switch  blades. 

Spring  washers  must  be  of  sufficient  strength  to  take  up  say  wear  In  tlM  kiB0i 
and  niftintiiln  a  good  oootact  at  all  times. 

f .  Metal. — All  switches  must  have  ample  metal  for  stiffness  and  to  pre- 
vent rise  in  temperature  of  any  part  of  over  50^  Fahrenheit  (28°  Centigxade). 
at  full  load,  the  contacts  bein^  arranged  so  that  a  thoroughly  good  bearing 
at  every  point  is  obtained  with  contact  surfaces  advisea  for  pure  oopper 
blades  of  about  one  square  inch  for  each  75  amperes;  the  whole  device 
must  be  mechanically  well  made  thiotighout. 

g.  Cross-Bars. — All  cross-bars  less  than  3  inches  in  length  must  be 
made  of  insulating  material.  Bars  of  3  inches  or  over,  which  are  made  of 
metal  to  insure  greater  mechanical  strength,  miist  be  sufficiently  separated 
from  the  jaws  of  the  switch  to  prevent  arcs  following  from  the  contacts  to 
the  bar  on  the  opening  of  the  switch  under  any  circumstances.  Metal  baxs 
should  preferably  be  covered  with  insulating  material. 

To  prevent  possible  turning  or  twisting  the  cross-bar  must  be  secured 
to  each  blade  by  two  screws,  or  the  joints  made  with  square  shoulders  or 
provided  with  dowel-pins. 

h.  Connections. — Switches  for  currents  of  over  30  amperes  must  be 
equipped  with  lugs,  firmly  screwed  or  bolted  to  the  switch,  and  into  which 
the  conducting  wires  shall  be  soldered.  For  the  smaller  sized  switches 
simple  clamps  can  be  employed,  provided  they  are  heavy  enough  to  staid 
considerable  hard  usage. 

Wbeie  lugs  are  not  provided,  a  ragged  double-V  groove  damp  Is  advised.  A 
set-screw  gives  a  contact  at  only  oQejpoInt.  Is  more  likely  to  become  looeened.  snd 
Is  almost  sure  to  eut  Into  the  wire.  For  the  smaller  sises,  a  screw  aod  wartier  cod- 
nectloa  with  up-tumed  lugs  on  the  switch  terminal  gives  a  satls&tctory  eontact. 

i.  Test. — Must  operate  successfully  at  60  per  cent  overioad  in  axnperei 
and  26  per  cent  excess  voltage,  under  the  most  severe  conditions  with  whid 
they  are  liable  to  meet  in  practice. 

This  test  Is  designed  to  give  a  reasonable  margin  between  the  ordmary  rating  of 
the  switch  and  the  breaking-down  point,  thus  securing  a  switch  which  can  aluayt 
safely  handle  Its  normal  load.  Moreover,  there  Is  enough  leeway  so  that  a  modenttc 
amount  ot  overloading  would  not  Injure  the  switch. 

J.  Marking. — Must  be  plainly  marked  w^here  it  win  be  visible,  when  the 
switch  is  installed,  with  the  name  of  the  maker  and  the  current  and  the 
voltage  for  which  the  switch  is  designed. 

^  Switches  designed  for  use  on  Edison  three-wire  systems  must  be  marked  wttk 
both  Vintages,  that  Is,  the  voltage  between  the  outside  wires  and  the  neutxaL  aad 
also  that  betwe^i  the  outside  wires,  followed  by  the  ampere  ratmg  and  the  wMito 
"three-wire."    (For  example,  " l26-i50  v.  SO  a.,  three-wire.") 

k.  Spacings. — Spacings  must  be  at  least  as  great  as  those  given  in  the 
following  table.  The  spacings  specified  are  correct  for  switches  to  be'  used 
on  direct-current  systems,  and  can  therefore  be  safely  followed  in  devices 
designed  for  alternating  currents. 

Minimum  Separation  of  Minimum 

Nearest  Metal  ParU  of  Break- 

126  Volts  or  Less:  Opposite  Polarity.  Distance. 

For  Switchboards  and  Panel  Boards'. 

10  amperes  or  less H  inch  -  -  -     Hinch. 

11-30  amperes 1      "  -  -  -     H'  " 

31-60        ••         IM  ••  -  -  -  1      " 

For  Individual  Switches'. 
10  amperes  or  less 1      inch  -       -       -     >^xndi. 


11-30  amperes \M 

31-100      ••  IH 

101-800      '•         2H 

301-600      "         2?2 

601-1000    ••         3 


Hby  VflOC- 


1 

2M 


CONSTRUCTION— FITTINGS,  MATERIALS,  ETC.        1488 

126  TO  260  Volts:  Min. 

For  all  Switches:  Sep. 

10  amperes  or  less IH  inch - 

11-30  amperes 1%    "     - 

81-100     ^'         2>2    "     -       - 

101-300     "         2H    ••     -       - 

801-600      •*         2H    "     -       - 

601-1000    '•         8       ••     -       - 

For  100  ampere  swltehes  and  larger,  the  above  epactngs  for  250  volU  dlreet 
current  are  also  aporoved  for  SOO  voiXM  alternating  current.  Swltebes  with  tlieae 
spadngs  int^ded  for  use  on  alternating-current  systems  with  voltage  above  250 
volts  must  be  stamped  "250-volt  D.  C."  followed  by  the  alternating-current  voltage 
Cor  wbleh  they  are  designed,  and  the  letters  "A.  C. 

251  TO  600  Volts: 

For  all  Switches: 

10  amperes  or  less 8H  inch  -       -       -   8     inch. 

11-85  amperes 4       "      -       -       -    8H    " 

86-100     ^'         4H    "      -       -       -   4       •* 

Auxlllanr  breaks  or  the  equivalent  are  recommended  for  switches  designed  for 
over  300  volts  and  lesi  than  100  amperes,  and  will  be  required  on  switches  designed 
ten"  ute  In  brtaking  curretua  greater  than  100  amperes  at  a  pressure  of  more  than  800 
volts. 

For  three-wire  Edison  systems  the  separations  and  break  distances  for  plain 
three-pole  knlfte  switches  must  not  be  lees  than  those  required  in  the  above  table  tor 
swltebes  designed  for  the  voltage  between  the  neutral  and  outside  wires. 

Snap  Switches. 
Flush,  push-button,  door.  Oxture  and  other  snap  switches  used  on   constant- 
itootlal  systems,  roust  be  constructed  in  accordance  with  the  following  specifics- 


potoo 

UODB. 


L  Bas$. — Current-carrying  parts  must  be  mounted  on  non-combustible, 
non-absorptive,  insulating  bases,  such  as  slate  or  porcelain,  and  the  holes 
for  supporting  screws  should  be  countersunk  not  less  than  i  of  an  inch. 
There  must  in  no  case  be  less  than  3/64  of  an  inch  space  between  supporting 
screws  and  current-carrying  parts. 

Sub-bases  of  non-combustible,  non-absorptive  insulatmg  material,  which 
will  separate  the  wires  at  least  i  inch  from  the  surface  wired  over,  must  be 
ftirnifi^ied  with  all  snap  switches  used  in  exposed  or  moulding  work. 

m.  Mounting. — Pieces  carrying  contact  jaws  must  be  secured  to  the 
base  bv  at  least  two  screws,  or  else  made  with  a  square  shoulder,  or  provided 
with  dowel-pins  or  otherwise  arranged  to  prevent  possible  turnings;  and 
the  nuts  or  screw-heads  on  the  under  side  of  the  base  must  be  countersunk 
not  less  than  i  inch,  and  covered  with  a  waterproof  compound  which  will 
not  melt  below  150*  Fahrenheit  (65**  Centigrade). 

n.  Metal. — ^All  switches  must  have  ample  metal  for  stiffness  and  to 
prevent  rise  in  temperature  of  any  part  of  over  50**  Fahrenheit  (28**  Centi- 
grade) at  full  load,  the  contacts  being  arranged  so  that  a  thoroughly  good 
bearing  at  every  point  is  obtained.  Tne  whole  device  must  be  mechanically 
well  made  throughout. 

In  order  to  meet  the  above  requirements  on  temperature  rise  without  causlnf 
exoeflslve  friction  and  wear  on  current-carrying  parts,  contact  surfaces  of  from  0.1 
to  0. 1 S  square  inch  for  each  1 0  amperes  will  be  required,  depending  upon  the  metal 

"I  and  the  form  of  construction  adopted. 


o.  Insulating  Material. — Any  material  used  for  insulating  current- 
carrying  parts  must  retain  its  insulating  and  mechanical  strength  when 
subject  to  continued  use,  and  must  not  soften  at  a  temperature  of  212* 
Fahrenheit  (100*  Centigrade).    It  must  also  be  non-absorptive. 

p.  Binding  Posts. — Binding  posts  must  be  substantially  made,  and  the 
screws  must  be  of  such  size  that  the  threads  will  not  strip  when  set  up  tight. 

A  set-screw  Is  likely  to  become  loosened  and  is  almost  sure  to  cut  Into  the  wire. 
A  binding  screw  under  the  head  of  which  the  wire  may  be  clamped  and  a  terminal 
plate  provided  with  upturned  lufn  or  some  other  equivalent  arrangemrat.  afford 
rdfiaMe  contact.  After  July  1,  1908.  switches  with  the  set-screw  form  of  contact 
wtU  not  be  approved. 

q.  Covers: — Covers  made  of  conducting  material,  except  face  plates  fo* 
fltish  switches,  must  be  lined  on  sides  and  top  with  insulating,  tough  and 
tenacious  material  at  least  1/32  inch  in  thickness,  firmly  seciu^  so  that  it 


1484  70.— ELECTRIC  POWER  AND  UGHTING. 

will  not  fall  out  with  ordinary  handling.  The  side  lining  mtiat  extend 
slightly  beyond  the  lower  edge  of  the  cover. 

r.  Handle  or  Button. — ^The  handle  or  button  or  any  exposed  parts  most 
not  be  in  electrical  connection  with  the  circuit. 

s.  Test. — ^Must  "make"  and  "break"  with  a  quick  snap,  and  must  not 
stop  when  motion  has  once  been  imparted  by  the  button  or  handle. 

Must  operate  successfully  at  60  per  cent  overload  in  amperes  and  at 
125  volt  duect  current,  for  all  125  volt  or  less  switches,  and  at  250  volt 
direct  current,  for  all  126  to  250  volt  switches  imder  the  most  severe  coodi* 
tions  which  they  are  liable  to  meet  in  practice. 

When  slowly  turned  "on"  and  "off  at  the  rate  of  about  two  or  three 
times  per  minute,  while  carrying  the  rated  current  at  rated  voltage,  misst 
"make  '  and  "break"  the  circuit  6.000  times  before  failing. 

t.  Marking. — Must  be  plainlv  marked,  where  it  may  be  readily  seen 
after  the  device  is  installed,  with  the  name  or  trade-mark  of  the  maker 
and  the  current  and  voltage  for  which  the  switch  is  designed. 

On  flush  switches  these  markings  may  be  placed  on  the  back  of  the 
face  plate  or  on  the  sub-plate.  On  other  types  they  mtiat  be  placed  on  the 
front  of  the  cap,  cover  or  plate. 

Switches  which  indicate  whether  the  current  is  "on"  or  "off"  are  recom- 
mended. 

52.  Cut^>iits  and  arcuit  Breakers. — (For  installation  rules,  see  Noa.  17 
and  21.)  These  requirements  do  not  apply  to  rosettes,  attachment  fihtgs,  car 
lighting  cut-outs  and  protective  devices  for  signaling  systems. 

General  Rules. 

a.  Must  be  supported  on  bases  of  non-combustible,  non-«b0orptive 
insulating  material. 

b.  Cut-outs  must  be  of  plug  or  cartridge  t3rpe,  when  not  arranged  id 
approved  cabinets,  so  as  to  obviate  any  danger  of  the  melted  fuse  xnetal 
coming  in  contact  with  any  substance  which  might  be  ignited  thereby. 

c  Cut-outs  must  operate  successfully  on  short-circtiits.  under  the  most 
severe  conditions  with  which  they  arc  liable  to  meet  in  practice,  at  26  per 
cent  above  their  rated  voltage,  and  for  link  fuse  cut-outs  with  fuaes  rated 
at  50  per  cent  above  the  current  for  which  the  cut-out  is  designed,  and  fcr 
enclosed  fuse  cut-outs  with  the  largest  fuses  for  which  the  cut-ont  is  de- 
signed. 

With  link  fose  oat-oitts  there  Is  always  the  ponlbnity  of  a  larger  fuse  betn^  iiut 
Into  the  cut-out  than  It  was  dedgned  for.  which  Is  not  true  of  oaelosed  (use  cut-oim 
doaslfled  as  required  under  No.  52  q.  Again,  tbe  voltage  In  most  plants  can.  oiHbf 
some  coDdltlons.  rise  considerably  above  the  normal.    The  need  of  some  mandn  as  a 


factor  of  safety  to  prevrat  the  out-onts  from  being  ruined  m  ordinary 
therefore  evident. 

The  most  severe  service  which  can  be  required  of  a  cut-out  In  praotloe  la  to  opca 
a  "dead  short-circuit"  with  only  one  fuse  Mowing,  and  It  Is  with  these  eoodltlona  l^ 
all  tests  should  be  made.    (See  Section  J.) 

d.  Circuit-breakers  must  operate  successfully  on  short-circuits  tmder 
the  most  severe  conditions  with  which  they  are  Uable  to  meet  in  practicr. 
at  25  per  cent  above  their  rated  voltage  and  with  the  circuit-breaker  aet  at 
the  highest  possible  opening  point. 

For  the  same  reason  as  In  Section  c. 

e.  Must  be  plainly  marked  where  it  will  always  be  visible,  with  the  name 
of  the  maker,  and  current  and  voltage  for  which  the  device  is  dea^ned. 

LiNK-PusB  Cut-Outs. 
{Cut-ouis  of  porcelain  are  not  approved  for  link  fuses.) 
The  followlnff  rules  are  Intended  to  cover  open  link  fuses  mounted  on  Hate  or 
marble  bases.  Including  switchboards.  UMct-boards  and  single  fuse-blocks.  Tk^ 
do  not  apply  to  fuses  moimted  (m  porcelain  bases,  to  the  ordlnaryporeelain  eot-ooK 
bloeks.  endoaed  fuses,  or  any  spedal  or  covered  type  of  fuse.  When  taUet-boardi 
or  BinRic  fuse-blocks  with  such  open  link  fuses  on  them  are  used  In  general  wirtac< 
they  must  be  enclosed  In  cabinet  boxes  made  to  meet  the  requirements  of  No.  Si 
Thfs  is  necessary,  because  a  severe  flash  may  occur  when  such  fuses  melt,  so  tHat  the} 
would  be  dangerous  If  exposed  In  the  neighborhood  of  any  oombasUbie  materlaL 

f.  Base.  Must  be  mounted  on  slate  or  marble  bases.  Bases  with  an 
«jea  of  over  25  sgtiare  inches  must  have  at  least  four  supporting  screws 
noles  for  supporting  screws  must  be  kept  outside  of  the  area  incIiKled  bj 


CONSTRUCTION^FITTINGS,  MATERIALS,  ETC.        I486 

tlie  outside  edges  of  the  fuse-block  terminals,  and  must  be  so  located  or 
countersunk  that  there  will  be  at  least  H  inch  space,  measured  over  the 
surface*  between  the  head  of  the  screw  or  washer  and  the  nearest  live  part. 

S.  Afoim<«nf .— Nuts  or  screw  heads  on  the  under  side  of  the  base  must 
be  cotmtersunk  not  less  than  H  inch,  and  covered  with  a  waterproof  com- 
pound which  will  not  melt  bebw  160^  Fahrenheit  (66^  Centigrade). 

h*  M9tal. — ^AIl  fuse-block  terminals  must  have  ample  metal  for  stiffness 
and  to  prevent  rise  in  temperature  of  any  part  over  50^  Fahrenheit  (28^ 
Centigrade)  at  full  load.  Terminals,  as  far  as  practicable,  should  be  miade 
of  compact  form  instead  of  being  rolled  out  in  thin  strips;  and  sharp  edges 


or  thin  projecting  pieces,  as  on  wing  thumb  nuts  and  the  like,  should  be 
avoided.  Thin  metal,  sharp  edges  and  projecting  pieces  are  much  more 
likely  to  cause  an  arc  to  start  than  a  more  soud  mass  of  metal.    It  is  a  good 


plan  to  round  aU  comers  of  the  terminals  and  to  chamfer  the  edges. 

i.  Connections. — Clamps  for  connecting  the  wires  to  the  fuse-block  ter- 
minals must  be  of  solid,  rugged  construction,  so  as  to  insure  a  thorotu;hly 
good  connection  and  to  withstand  considerable  hard  usage.  For  fuses 
rated  at  over  30  amperes,  lugs  firmly  screwed  or  bolted  to  the  terminals 
and  into  which  the  conducting  wires  are  soldered  must  be  used. 

See  note  under  No.  51  h. 

J.  Test. — Must  operate  successfully  when  blowing  only  one  fuse  at  a 
time  on  short  circuits  with  fuses  rated  at  60  per  cent  above  and  with  a 
voltage  26  per  cent  above  the  current  and  voltage  for  which  the  cut-out  is 
designed. 

k.  Marking. — Must  be  plainly  marked,  where  it  will  be  visible  when  the 
cut-out  block  is  installed,  with  the  name  of  the  maker  and  the  current 
and  the  voltage  for  which  the  block  is  designed. 

I.  Spacings. — Spacings  must  be  at  least  as  great  as  those  given  in  the 
following  table,  which  smplies  only  to  plain,  open  link-fuses  movmted  on 
slate  or  marble  bases.  The  spaces  given  are  correct  for  fuse-blocks  to  be 
used  on  direct-current  systems,  and  can  therefore  be  safely  followed  in 
devices  designed  for  alternating  currents.  If  the  copper  fuse-tips  overhang 
the  edges  of  the  fuse-block  terminals,  the  spacings  should  be  measured 
between  the  nearest  edges  of  the  tips. 

Minimum  Separation  of  Minimum 
Nearest  Metal  Parts  of  Break 

136  Volts  OR  Lbss:  Opposite  Polarity.  Distance. 

10  amperes  or  less. ^  inch-       -  -    fi  inch. 

11-lOOamperes 1        "  -       -  -   H    " 

101-300       ^      1        "  -       -  -  1       " 

301-1000     ••       IH    "  '       -  'IH    " 

136  TO  360  Volts: 

10  amperes  or  less IH  inch        -       -  l}i  inch. 

11-100  amperes 1^    "-       -       -  IH    " 

101-300       ^-       2        "  -       -       'IH    " 

301-1000     "       2H     •  -       -       -2       *• 

A  space  must  be  maintained  between  fuse  terminals  of  the  same  polarUv  of  at 
least  k  Inch  tor  voltages  up  to  125.  and  of  at  least  }  Inch  for  voltages  from  126  to  250. 
This  IS  the  minimum  dlstuice  allowable,  and  greater  separation  should  be  provided 
when  practlealHe 

For  250  volt  boards  or  Uoeks  with  the  ordinary  tront-oonnected  terminals, 
except  where  these  have  a  mast  of  compact  form,  equivalent  to  the  back-connected 
temunals  usually  found  In  switchboard  work,  a  substantial  barrier  of  Insulating 
material,  not  less  than  i  of  an  Inch  In  thickness,  must  be  placed  In  the  "break"  gap-^ 
tun  barrier  to  extend  out  from  the  base  at  least  i  of  an  Inch  farther  than  any  bare 
live  part  of  the  fuse-block  terminal.  Including  binding  screws.  nuU  and  the  like. 

For  three-wire  systems  cut-outs  must  have  the  break-dlstanoe  required  tor 
circuits  of  the  potwtial  of  the  outside  wires. 

Emclosbd-Fusb  Cut-Outs — Pluo  and  Cartridok  Type, 
m.  Base. — Must  be  made  of  non-combustible,  non-absorptive,  insulating 
material.  Blocks  with  an  area  of  over  26  square  inches  must  have  at  least 
four  supporting  screws.  Holes  for  supporting  screws  must  be  so  located  or 
countersvmk  that  there  will  be  at  least  i  inch  space,  measured  over  the 
surface,  between  the  screw-head  or  washer  and  the  nearest  live  metal  part, 
and  in  all  cases  when  between  parts  of  opposite  polarity  must  be  counter- 
sunk 


I486  TO.'-ELECTRIC  POWER  AND  UGHTING. 

n.  Mounting. — Nuts  or  screw-heads  on  the  under  side  of  the  base  must 
be  countersunk  at  least  i  of  an  inch  and  covered  with  a  waterpioof  ocunpoaad 
which  will  not  melt  below  150^  Fahrenheit  (65^  Centigxade). 

o.  Terminals. — ^Terminals  must  be  of  either  the  Ediaon  phis,  spriag 
clip  or  knife-blade  type,  of  approved  design,  to  take  the  oorrespondix^ 
standard  enclosed  fuses.  They  must  be  secured  to  the  base  by  two  screws  or 
the  equivalent,  so  as  to  prevent  them  from  turning,  and  must  be  so  made 
as  to  secure  a  thoroughly  good  contact  with  the  fuse.  End  stops  must  be 
provided  to  insure  the  proper  location  of  the  cartridge  fuse  in  tne  cut-out. 

p.  Connections. — Clamps  for  connecting  wires  to  the  terminals  must 
be  of  a  design  which  will  msure  a  thoroughly  good  connecticm,  and  mtst 
be  sufficiently  strong  and  heavy  to  withstand  considerable  hard  usage. 
For  fuses  rated  to  carry  over  thirty  amperes,  lugs  firmly  screwed  or  boltd 
to  the  terminals  and  into  which  the  connecting  wires  shall  be  severed  most 
be  used. 

9.  Classification. — Must  be  classified  as  r^^ards  both  current  and  voltage 
as  given  in  the  following  table,  and  must  be  so  designed  that  the  bases  of 
one  class  cannot  be  used  with  fuses  of  another  cla»  rated  for  a  higher 
current  or  voltage. 

0-260  Volts:  251-600  Volts: 

0-  30  amperes.  0-  80  amperes. 

31-  60       ^'  31-  60       ^' 

61-100        ••  61-100       •• 

101-200        ••  101-200       " 

201-400        "  201-400       " 

401-600 
r.   Design. — Must  be  of  such  a  design  that  it  will  not  be  easy  to  farm 
accidental  short  circuit  across  live  metal  parts  of  opposite  polarity  cm  the 
block  or  on  the  fuses  in  the  block. 

8.  l&arking. — Must  be  marked,  where  it  will  be  plainly  visible  when  the 
block  is  installed,  with  the  name  of  the  maker  and  the  voltage  and  xanfle 
of  current  for  which  it  is  designed. 

53.    Fuses. — (For  installation  rules,  see  Nos.  17  and  21.) 
Link  Fuses. 

a.  Terminals. — Must  have  contact  surfaces  or  tips  of  harder  nuetal. 
having  perfect  electrical  connections  with  the  fusible  part  of  the  strip. 

The  use  of  the  bard  metal  tip  Is  to  afford  a  strong  mechsnleal  bearfng  tor  the 
screws,  damps  or  other  devices  provided  for  holding  the  fuse. 

b.  Rating. — Must  be  stamped  with  about  80  per  cent  of  the  maximam 
current  which  they  can  carry  indefinitely,  thus  aUowing  about  26  per  cent 
overload  before  the  fuse  melts. 

With  naked  open  fuses,  or  ordinary  shapes  and  with  not  over  500  amperat 
oapaclty,  the  minimum  current  which  will  melt  them  in  about  five  minutes  may  be 
safely  taken  as  the  melting  point,  as  the  fuse  practically  reaches  Its  maximum  tem- 
perature In  this  time.  With  larger  fuses  a  longer  time  Is  neoessary.  Tbla  data  is 
glv^  to  facilitate  testing. 

c  Marking. — Fuse  terminals  must  be  stamped  with  the  maker's  name 
or  initials,  or  with  some  known  trade-mark. 

Enclosed  Fuses — Plug  and  Cartridge  Type. 

These  requirements  do  not  apply  to  fuses  for  rosettes,  attachment  phtgs,  av 
lighting  cut-outs  and  protective  devices  for  signaling  systems. 

d.  Construction. — ^The  fuse  plug  or  cartridge  must  be  sufficiently  dust- 
tight  so  that  lint  and  dust  cannot  collect  around  the  fusible  wire  and  be- 
come ignited  when  the  fuse  is  blown. 

The  fuEible  wire  must  be  attached  to  the  plug  or  cartridge  terminals 
in  such  a  way  as  to  secure  a  thoroughly  good  connection  anoT  to  make  H 
difficult  for  it  to  be  replaced  when  melted. 

e.  Classification. — Must  be  classified  to  correspond  with  the  different 
Classes  of  cut-out  blocks,  and  must  be  so  designed  that  it  will  be  impossibJe 
to  put  any  fuse  of  a  given  class  into  a  cut-out  block  which  is  designed  for  a 
current  or  voltage  lower  than  that  of  the  class  to  which  the  fuse  bekyogs. 


CONSTRUCTION—FITTINGS,  MATERIALS,  ETC.        1487 

f.    Terminal:. — The  fuse  terminals  must  be  sufficiently  heavy  to  insure 
mechanical  strength  and  rigidity.   The  styles  of  terminals  must  be  as  follows: 

0-260  Volts: 


_  .    .   . .  terminals. 

0-80  Amps,     "i       I  (femile  contact) )  fit  \b,  Edison  plug  casings. 


{  A  i  Cartridge  fuse  )  to  ( a,  spring  clip  t 
"J  '^  I  (ferrule  contact)  J  fit  \b,  Edison  plug 
(  B  Approved  plugs  for  Edison  cut-outs. 

ai-AO      "         i   Cartridge  fuse    )  to  ( a.  spring  clip  terminals. 

*  I  (ferrule  contact)  /fit  \b.  ^ison  plug  casings. 

61-100  ;;       I 

201-400^    '*  [cartridge  fuse  (knife-blade  contact). 

401-000    ••  J 

261-600  Volts: 

81^60  ^*^'     \  Cartridge  fuse  (ferrule  contact). 

61-100    ••         ) 
101-200    *'         >- Cartridge  fuse  (knife-blade  contact). 
201-400    *•         ) 

g.  Dimensions. — Cartridge  enclosed  fuses  and  corresponding  cut-out 
blocks  must  conform  to  the  dimensions  given  in  the  Table,  on  next  page. 

h.  Rating. — Puses  must  be  so  constructed  that  with  the  surrounding 
atmosphere  at  a  temperature  of  76^  Fahrenheit  (24^  Centigrade)  they  will 
carry  mdefinitely  a  current  10  per  cent  greater  than  that  at  which  they  are 
rated,  and  at  a  current  26  per  cent  greater  than  the  rating,  they  will  open 
the  circuit  without  reaching  a  temperattire  which  will  injure  the  fuse  tube 
or  terminals  of  the  fuse  block.  With  a  current  60  per  cent  greater  than 
the  rating  and  at  room  temperature  of  76®  Fahrenheit  (24®  Centigrade),  the 
fuses  starting  cold,  must  blow  within  the  time  specified  below:— 
0-  80  amperes,  80  seconds. 

81-  60        "  1  minute. 

01-100        "  2  minutes. 

101-200        "  4 

201-400        "  8 

401-600        ••  10      ." 

i.  Marking. — Must  be  marked,  where  it  will  be  plainly  visible,  with 
the  name  or  trade-mark  of  the  maker,  the  voltage  and  current  for  which 
the  fuse  irf  designed,  and  the  words  "National  Electrical  Code  Standard." 
Each  fuse  must  have  a  label,  the  color  of  which  must  be  green  for  260- 
volt  fuses  and  red  for  600-volt  fuses. 

It  will  be  satisfactory  to  abbreviate  the  above  destgnaUoa  to  "N.  E.  Oode  St'd** 
where  space  Is  necessarily  limited. 

J.  Temperature  Rise. — ^The  temperature  of  the  exterior  of  the  fuse  en- 
closure must  not  rise  more  than  125*  Fahrenheit  (70®  Centigrade)  above  that 
of  the  surrounding  air  when  the  fuse  is  carrying  the  current  for  which  it  is  rated. 

k.  Test. — Must  not  hold  an  arc  or  throw  out  melted  metal  or  sufficient 
flame  to  ignite  easily  inflammable  material  on  or  near  the  cut-out  when 
only  one  fuse  is  blown  at  a  time  on  a  short  circuit  on  a  system  of  the  voltage 
for  which  the  fuse  is  rated. 

The  normal  capacity  of  the  system  must  be  in  excess  of  the  load  on  it 
just  previous  to  tne  test  by  at  least  five  times  the  rated  capacity  ot  the 
fuse  under  test. 

The  resistance  of  the  circuit  up  to  the  cut-out  terminals  must  be  such 
that  the  impressed  voltage  at  the  terminals  will  be  decreased  not  more 
than  one  per  cent,  when  a  current  of  100  amperes  is  passed  between  them. 

For  oonvenlenoe  a  current  of  different  value  may  be  used.  In  which  case  the  per 
oent  drop  In  voltage  allowable  would  vary  in  direct  proportion  to  the  difference  in 
current  used: 

The  above  requirement  regarding  the  capacity  of  the  testing  circuit  Is  to  guard 
against  making  the  test  on  a  system  of  so  small  a  capacity  that  the  conditions  would 
|>e  sufficiently  favorable  to  allow  really  poor  fuses  to  stand  the  test  acceptably.  On 
the  other  hfljid,  it  must  be  remembered  that  If  the  test  Is  made  on  a  system  of  very 
lance  capacity;  and  especially  if  there  Is  but  little  resistance  between  toe  generators 
and  fuse,  the  conditions  may  be  more  severe  than  are  liable  to  be  met  with  in  praetMo 
ootside  of  the  large  power  stations,  the  result  being  that  fuses  entirely  safe  for  general 
iHe  may  be  re]e<»ea  If  such  test  is  insisted  upon. 


1438 


TO.—ELECTRIC  POWER  AND  UGHTING, 


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CONSTRUCTION— FITTINGS,  MATERIALS,  ETC,        1430 

53  A.  Tablet  and  Panel  Boards. — ^The  following  nUnimum  distance 
between  bare  live  metal  parts  (bus-bars,  etc.)  must  be  maintained: — 

Between  parts  of  opposite  polarity,  except  at  Between  parts  of  same 

switches  and  link  fuses,  polarity. 

When  mounted  on  the            When  held  free  in  At  link 

same  surface.                            the  air.  ftises. 

0-126  volts    Hinch          H  inch  14  inch. 

126-250  volts  IH  "              Ji    '  H  •* 

lay  be  placed  as  dose 

m  allowable,  and  It  is 
as  will  permit, 
eh  coaauctora  where 
re  used,  the  spaclngs 

llstanoe  between  the 
>yer  which  they  pass, 
revent  the  melting  of 
&rity. 

S4.  Cut-Oot  Cabinets. — a.  Af o/ma/.— Cabinets  must  be  substantiallv 
constructed  of  non-combustible,  non-absorptive  material,  or  of  wood. 
When  wood  is  used  the  inside  of  the  cabinet  must  be  completely  lined  with 
a  non-combustible  insulating  material.  Slate  or  marble  at  least  \  inch  in 
thickness  is  strongly  recommended  for  such  lining,  but,  except  with  metal 
conduit  systems,  asbestos  board  at  least  i  inch  m  thickness  may  be  used 
in  drv  places  if  firmly  secured  by  shellac  and  tacks. 

With  metal  conduit  systems  the  lining  of  either  the  box  or  the  gutter 
must  be  of  1/16  inch  galvanized,  painted  or  enameled  steel,  or  prefer- 
ably H  inch  slate  or  marble. 

The  object  of  the  lining  of  such  outpout  cabinets  or  gutters  Is  to  render  the  same 
approxlmateiy  fireproof  la  case  of  short  circuit  after  the  wires  leave  the  protecting 
metal  conduits. 

Two  thicknesses  of  1-^3  Inch  steel  may  be  used  Instead  of  one  1-16  inch. 

With  wood  cabinets  the  wood  should  be  thoroughly  flUed  and  painted  before  the 
lining  is  put  Into  plaoe. 

b.  Door. — ^The  door  must  close  against  a  rabbet,  so  as  to  be  perfectly 
dust-tight.  Strong  hinges  and  a  strong  hook  or  catch  are  required.  Glass 
doors  must  be  glazed  with  heavv  glass,  not  less  than  i  inch  in  thickness, 
and  panes  shotud  not  exceed  300  square  inches  in  area.  A  space  of  at  least 
two  inches  must  be  allowed  between  the  fuses  and  the  door.  This  is  necessarv 
to  prevent  cracking  or  breaking  by  the  severe  blow  and  intense  heat  which 
may  be  produced  under  some  conditions. 

A  cabinet  is  of  little  use  unless  the  door  is  kept  tightly  closed,  and  especial  at- 
tention is  therefore  called  to  the  importance  of  having  a  strong  and  reliable  catch  or 
other  fastening.  A  spring  catch  Is  advised  If  a  good  one  can  be  obtained,  but  most 
of  those  sold  for  use  on  cupboards,  etc.,  are  so  small  that  they  fall  to  catch  when  the 
door  shrinks  a  little,  or  are  so  weak  that  they  soon  give  out. 

It  Is  advised  that  the  bottoms  of  cabinets  be  given  a  decided  slant  to  prevent 
tbelr  use  as  a  shelf,  as  well  as  the  accumulation  of  dust.  etc. 

c.  Bushings. — Bushings  through  which  wires  enter  must  fit  tightly 
the  holes  in  the  box,  and  must  be  of  approved  construction.  The  wires 
should  completely  fill  the  holes  in  the  busnmgs,  using  tape  to  build  up  the 
wire,  if  necessary,  so  as  to  keep  out  the  dust. 

54  A.  Rosettes. — Ceiling  rosettes,  both  fused  and  fuseless,  must  be 
constructed  in  accordance  with  the  following  specifications: — 

A.  Base. — Current-carrying  parts  must  be  mounted  on  non-combustible, 
non-absorptive,  instdating  bases.  There  shotild  be  no  openings  through 
the  rosette  base  except  those  for  the  supporting  screws  and  in  the  concealed 
type  for  the  conductors  also,  and  these  openmgs  should  not  be  made  any 
laxiger  than  necessary. 

There  must  be  at  least  i  inch  space,  measured  over  the  surface,  between 
supporting  screws  and  current-carrying  parts.  The  supporting  screws 
must  be  so  located  or  cotmtersunk  that  the  flexible  cord  cannot  come  in 
contact   with   them. 

Bases  for  the  knob  and  cleat  type  must  have  at  least  two  holes  for 
supporting  screws;  must  be  high  enough  to  keep  the  wires  and  terminals  at 
least  i  inch  from  the  surface  to  which  the  rosette  is  attached,  and  must 
have  a  porcelain  lug  \mder  each  terminal  to  prevent  the  rasette  from  being 

tizedbyUOOgle 


1440  70.— ELECTRIC  POWER  AND  LIGHTING. 

flaoed  over  projections  which  would  reduce  the  separation  to  less  tiias 
inch. 
Bases  for  the  moulding  and  conduit  box  types  must  be  hijBh  enough  to 
keep  tbe  wires  and  terminals  at  least  |  inch  £iom  the  surface  wired  over. 

b.  MoHHting. — Contact  pieces  and  terminals  must  be  secured  in  position 
by  at  least  two  screws,  or  made  with  a  square  shoulder,  or  otherwise  arranged 
to   prevent   turning. 

The  nuts  or  screw  head  on  the  tmder  side  of  the  base  must  be  counter- 
sunk not  less  than  i  inch  and  covered  with  a  waterproof  compound  which 
will  not  melt  below  IbV*  Fahrenheit  (GS*"  Centigrade). 

c.  Terminals. — ^Line  terminal  plates  must  be  at  least  .07  inch  in  ttuckness, 
and  terminal  screws  must  not  be  smaller  than  No..  6  standard  screw  with 
about  32  threads  per  inch. 

Terminal  plates  for  the  flexible  cord  and  for  fuses  must  be  at  least 
.06  inch  in  thickness.  The  connection  to  these  plates  shall  be  by  binding 
screws  not  smaller  than  No.  h  standard  screw  with  about  40  threads  per 
inch.  At  all  binding  screws  for  line  wires  and  for  flexible  cord,  up-turned 
higs.  or  some  equivalent  arrangement,  must  be  provided  which  wm  secure 
the  wires  being  held  imder  the  screw  heads. 

d.  Cord  InUt. — ^The  diameter  of  the  cord  inlet  hole  shoukl  measure 
13/32  inch  in  order  that  standard  portable  cord  may  be  used. 

e.  Knot  Space. — Ample  space  must  be  provided  for  a  substantial  knot 
tied  in  the  cord  as  a  whole. 

All  parts  of  the  rosette  upon  which  the  knot  is  likely  to  bear  most  be 
smooth  and  well  rounded. 

f.  Cover. — ^When  the  rosette  is  made  in  two  parts,  the  cover  must  be 
secured  to  the  base  so  that  it  will  not  work  loose. 

In  fused  rosettes,  the  cover  must  fit  closely  over  the  base  so  as  to  prevent 
the  accumtilation  of  dtist  or  dirt  on  the  inside,  and  also  to  prevent  any  flash 
or  melted  metal  from  being  thrown  out  when  the  fuses  melt. 

g.  Markings. — Must  be  plainly  marked  where  it  may  readily  be  seen 
after  the  rosette  has  been  installed,  with  the  name  or  trade-mark  of  the 
manufacturer,  and  the  rating  in  amperes  and  volts.  Fuseless  rosettes  may 
be  rated  3  amperes,  250  volts;  fused  rosettes,  with  link  fuses,  not  over 
2  amperes,  125  volts. 

h.  r«s<.— rPused  rosettes  must  have  a  fuse  in  each  pole  and  must  operate 
successfully  when  short-circuited  on  the  voltzige  for  which  they  are  designed, 
the  test  being  made  with  the  two  fuses  in  circuit. 

When  link  fuses  are  used  the  test  shall  be  made  with  fuse  wire  which  melts  at 
aboat  7  amperes  In  ooe-lnch  l^igths  The  larger  fuse  Is  spedfled  for  the  test  In  order 
to  more  nearly  approximate  tl^  severe  conditions  obtained  when  only  one  2-«mpere 
fuse  (the  rating  of  the  rosette)  Is  blown  at  a  time. 

Fused  rosettes  equipped  with  enclosed  (uses  are  much  prefSrable  to  the  link  fuse 
rosettes. 

55.  Sockets.-— (For  installation  rules,  see  No.  27.)  Sockets  of  all  kinds. 
including  wall  receptacles,  must  be  constructed  in  accordance  with  the  follow- 
ing specifications: — 

a.  Standard  Sises. — ^The  standard  lamp  socket  must  be  suitable  fc»r  use 
on  any  voltage  not  exceeding  250  and  with  any  size  lamp  up  to  fifty  candle- 
power.  For  lamps  larger  than  fifty  candle-power  a  standard  keyless  socket 
may  be  used,  or  if  a  key  is  required,  a  special  socket  designed  for  the  current 
to  be  used  must  be  made.  Any  special  sockets  must  foltow  the  general 
spirit  of  these  specifications. 

b.  Marking. — All  sockets  must  be  marked  with  the  manufacturer's 
name  or  trade-mark.  The  standard  key  socket  must  also  be  plainly  mariced 
250  V.  50  c.  p.  Receptacles,  keyless  sockets  and  special  sockets  must  be 
marked  with  the  current  and  voltage  for  which  they  are  designed. 

c.  Sfull. — Metal  used  for  shells  must  be  moderately  hard,  but  not  hard 
enough  to  be  brittle  or  so  soft  as  to  be  easily  dented  or  knocked  out  of  shape. 
Brass  shells  must  be  at  least  thirteen  one-thousandths  of  an  inch  in  thidcncsa. 
and  shells  of  any  other  material  must  be  thick  enough  to  give  the  same 
stiffness  and  strength  as  the  required  thickness  of  brass. 

d.  L«ntn^.— The  inside  of  the  shells  must  be  lined  with  insolatiBi 
material,  which  must  absolutely  prevent  the  shell  from  becoming  a  part « 


CONSTRUCTION— FITTINGS.  MATERIALS,  ETC.         1441 

the  circuit,  even  though  the  wires  inside  the  sockets  should  become  loosened 
or  detached  £rom  their  position  under  the  binding  screws. 

The  material  used  tor  lining  must  be  at  least  1/32  of  an  inch  in  thick- 
ness, and  must  be  tough  and  tenacious.  It  must  not  be  injxiriously  affected 
by  the  heat  from  the  largest  lamp  permitted  in  the  socket,  and  must  leave 
water  in  which  it  is  boiled  practically  neutral.  Is  must  be  so  firmly  se- 
cured to  the  shell  that  it  will  not  fall  out  with  ordinary  handling  of  the 
socket.   It  is  preferable  to  have  the  lining  in  one  piece. 

The  eap  must  also  be  lined,  and  this  lining  must  comply  with  the  requirements 
tor  shell  llnlnKS. 

The  shell  Ilomg  should  extend  beyond  the  shell  far  enough  so  that  no  part  of  the 
lamp  base  is  exposed  when  a  lamp  Is  in  the  socket.  The  standard  Edison  lamp  base 
measures  15-16  InctMS  In  a  vertical  i^ane  from  the  bottom  of  the  center  contact  to 
the  upper  edge  of  the  screw-shell. 

In  sockets  and  receptacles  of  standard  forms  a  ring  of  any  material  Inserted 
between  an  outer  metal  shell  of  the  device  and  the  Inner  screw  shell  for  Insulating 
purposes  and  separable  from  the  device  as  a  whole.  Is  considered  an  undesirable 
form  of  construction.  This  does  not  apply  to  the  use  of  rings  In  lamp  clusters  or  In 
devices  where  the  outer  shell  Is  of  porce£ain,  where  such  rings  serve  to  hold  the  several 
porcelain  parts  together,  and  are  thus  a  necessary  part  of  the  whole  structure  of  the 
device. 

e.  Cap. — Caps,  when  of  sheet  brass,  must  be  at  least  thirteen  one- 
thousandths  of  an  inch  in  thickness,  and  when  cast  or  made  of  other  metals 
must  be  of  equivalent  strength.  The  inlet  piece,  except  for  special  sockets, 
must  be  tapped  with  a  standard  i  inch  pipe  thread.  It  must  contain  suffi- 
cient metal  for  a  full,  strong  thread,  and  when  not  in  one  piece  with  the  cap, 
must  be  joined  to  it  in  such  a  way  as  to  give  the  strength  of  a  single  piece. 

There  must  be  sufficient  room  in  the  cap  to  enable  the  ordinary  wire- 
man  to  easily  and  quickly  make  a  knot  in  the  cord  and  to  push  it  into  place 
in  the  cap  without  crowding.  All  parts  of  the  cap  upon  which  the  .knot  is 
likely  t^  bear  must  be  smooth  and  well  insulated. 

The  cap  lining  called  for  In  the  note  to  Section  d  will  i»ovlde  a  sufficiently 
smooth  and  well  Insulated  surface  for  the  knot  to  bear  upon. 

Sockets  with  an  outlet  threaded  for  l-lnch  pipe  wUl.  of  course,  be  approved 
where  circumstances  demand  their  use.  The  slse  outlet  Is  necessary  with  most  stiff 
pendants  and  for  the  proper  use  of  reinforced  flexible  cord,  as  explained  in  the  note 
ioNo.  28  d. 

f.  Frarns  and  Screws. — ^The  frame  which  holds  the  moving  parts  must 
be  sufficiently  heavy  to  give  ample  strength  and  stiffness. 

Brass  pieces  containing  screw  threads  must  be  at  least  six  one-hundredths 
of  an  inch  in  thickness. 

Binding  post  screws  must  not  be  smaller  than  No.  5  standard  screw 
with  about  40  threads  per  inch. 

g.  Spacing. — Points  of  opposite  polarity  must  everywhere  be  kept  not 
less  than  3/64  of  an  inch  apart,  unless  separated  by  a  reliable  insulation. 

h.  Connections. — ^The  connecting  points  for  the  flexible  cord  must  be 
made  to  very  securely  grip  a  No.  16  or  18  B.  &  S.  gage  conductor.  An  up- 
turned lug,  arranged  so  that  the  cord  may  be  gripped  between  the  screw 
and  the  lug  in  such  a  way  that  it  cannot  possibly  come  out,  is  strongly 
advised. 

i.  Lamp  Holder. — ^The  socket  mtist  firmly  hold  the  lamp  in  place  so 
that  it  cannot  be  easily  jarred  out,  and  must  provide  a  contact  good  enough 
to  prevent  undue  heating  with  the  maximum  current  allowed.  The  holding 
pieces,  springs  and  the  Iflce,  if  a  part  of  the  circuit,  mtist  not  be  sufficiently 
exposed  to  allow  them  to  be  brought  in  contact  with  anything  outside  of 
the  lamp  and  socket. 

J.  Base. — ^With  the  exception  of  the  lining,  all  parts  of  insulating 
material  inside  the  shell  must  be  made  of  porcelain. 

k.  Key. — ^The  socket  key-handle  must  be  of  such  a  material  that  it 
will  not  soften  from  the  heat  of  a  fifty  candle-power  lamp  hanging  down- 
wards from  the  socket  in  the  air  at  70°  Fahrenheit  (2 1*>  Centigrade),  and 
must  be  securely,  but  not  necessarily  rigidly,  attached  to  the  metal  spin- 
dle which  it  is  designed  to  turn. 

I.  Sealing. — All  screws  in  porcelain  pieces,  which  can  be  firmly  sealed 
in  place,  must  be  so  sealed  by  a  waterproof  compoimd  which  will  not  melt 
betow  200*  Fahrenheit  (93<»  Centigrade.) 

m.  PiUiing  Together. — ^The  socket  as  a  whole  must  be  so  put  together 
that  it  will  not  rattle  to  pieces.  Bayonet  joints  or  an  equivalent  m  recom- 
mended. Digitized  by  VjOOQ  IC 


1443  70.— ELECTRIC  POWER  AND  UGHTING. 

n.  Test. — ^The  socket,  wh«n  slowly  turned  "on  and  off*  at  the  zmte  od 
about  two  or  three  times  per  minute,  while  carrying  a  load  of  one  ampere  at 
260  volts,  must  "make"  and  "l»ieak"  the  circuit  6,000  times  befo««  Ruling. 

o.  Keyless  Sockets. — Keyless  sockets  of  all  kinds  must  comply  with  the 
requirements  for  key  sockets  as  far  as  they  apply. 

p.  Sockets  of  Insulating  Material. — Sockets  made  of  porcelain  or  other 
insulating  material  must  conform  to  the  above  requirements  as  far  as  they 
apply,  and  all  parts  must  be  strong  enough  to  withstand  a  moderate  amoant 
ot  hard  usage  without  breaking. 

Porcelain  shell  sookets  being  sabject  to  breakage,  and  oonstltming  a  taasard  wlia 
broken.  wlU  not  be  aooepted  tor  use  In  plaees  wbere  they  would  be  exposed  to  hard 


q.  Inlet  Bushing. — When  the  socket  is  not  attached  to  a  fixture,  the 
threaded  inlet  must  be  provided  with  a  strong  insulating  bushing  having 
a  smooth  hole  at  least  9/32  of  an  inch  in  diameter.  The  edges  of  the  bushxng 
must  be  rounded  and  all  inside  fins  removed,  so  that  in  no  place  will  the 
cord  be  subjected  to  the  cutting  or  wearing  action  of  a  sharp  edge. 

Bustainss  for  sockets  having  an  outlet  threaded  for  |-tnch  pipe  should  have  a 
hole  1 3-32  ot  an  inch  in  diameter,  so  that  they  will  aooommodate  approoed  reinfiorted 
flexible  cord. 

S6,  Hang er-boards  for  Series  Arc  Lamps. — a.  Han^r-boards  must  be 
so  constructed  that  all  wires  and  current-carrying  devices  thereon  wHl  be 
exposed  to  view  and  thorotighly  insulated  by  being  mounted  on  a  oon- 
combustible,  non-absorptive,  insulating  substance.  All  switches  attached 
to  the  same  must  be  so  constructed  that  they  shall  be  automatic  in  their 
action,  cutting  ofE  both  poles  to  the  lamp,  not  stopping  between  points 
when  started  and  preventmg  an  arc  between  points  imderall  circumstances. 

$7.    Arc  Lamps. — (For  installation  rules,  see  Nos.  10  and  30.)     a.  Must 

be  provided  with  reliable  stops  to  prevent  carbons  from  falling  out  in  case 
the  clamps  become  loose. 

b.  All  exposed  parts  must  be  carefully  insulated  from  the  circtdt. 

c.  Must,  for  constant-current  systems,  be  provided  with  an  approved 
hand  switch,  and  an  automatic  switch  that  will  shunt  the  current  around 
the  carbons,  should  they  fail  to  feed  properly. 

The  hand  switch  to  be  approved,  if  placed  anywhere  except  on  the 
lamp  itself,  must  comply  with  requirements  for  switches  on  hanger-boaidf 
as  laid  down  in  No.  66. 

$8.    Spark  Arresters. — (For  installation  rules,  see  Nos.  19  c  and  29  c.) 

a.  Spark  arresters  must  so  close  the  upper  orifice  of  the  globe  that  it 
will  be  impossible  for  any  sparks,  thrown  on  by  the  carbons,  to  escape. 


$9.  Insulating  Joints. — (See  No.  26  a.) — a.  Must  be  entirely  made  of 
material  that  will  resist  the  action  of  illuminating  gases,  and  will  not  give 
way  or  soften  imder  the  heat  of  an  ordinary  gas  flame  or  leak  under  a  modeiate 
pressure.  Must  be  so  arranged  that  a  deposit  of  moisture  will  not  destroy 
the  insulating  effect;  must  show  a  dielectric  strength  between  gas-pipe 
attachments  sufficient  to  resist  throughout  five  minutes  the  application  of 
an  electro-motive  force  of  4,000  volts;  and  must  be  sufficiently  stxxnif^  to 
resist  the  strain  to  which  they  are  liable  to  be  subjected  during  instaUatxm. 

Insulating  Joints  having  soft  rubber  In  their  construction  wlU  not  be  aroroved. 

60.  Rheostats. — (For  installation  rules,  see  Nos.  4  a  and  8  cO 

a.  Materials. — Must  be  made  entirely  of  non'Combustible  materiftk, 
except  such  minor  parts  as  handles,  magnet  insulation,  etc.  All  segments, 
lever  arms,  etc.,  must  be  mounted  on  non-combustible,  non'Obaorptive, 
insulating    material. 

Rheostats  used  In  dusty  or  llnty  places  or  where  exposed  to  flyings  of  eoobw* 
tlble  material,  must  be  so  oonstructea  that  even  It  the  restsUve  conductor  be  tuRd 
by  excessive  current,  the  arc  or  any  attendant  flame  wfll  bo  quickly  and  safely 
extinguished.  Rheostats  used  In  places  where  the  above  conditions  do  not  exlsi  nsy 
be  ot  any  approved  type. 

b.  Construction. — Must  be  so  constructed  that  when  motmted  on  s 
plane  surface  the  casing  will  make  contact  with  such  surface  only  at  the 


CONSTRUCTION^FITTINGS,  MATERIALS,  ETC.        1448 

points  of  support.  An  air  space  of  at  least  H  inch  between  the  rheostat 
casing  and  the  sui>porting  surface  will  be  reauired. 

The  construction  throughout  must  be  heavy,  nigged  and  thoroughly 
workmanlike. 

c.  Connections. — Clamps  for  connecting  wires  to  the  terminals  must 
be  of  a  design  that  will  insure  a  thoroughly  good  connection,  and  must  be 
sufficiently  strong  and  heavy  to  withstand  considerable  hard  usage.  For 
currents  above  fifty  amperes,  lugs  firmly  screwed  or  bolted  to  the  terminals, 
and  into  which  the  connecting  wires  shall  be  soldered,  must  be  used. 

aampe  or  lugs  will  not  be  required  when  leads  designed  (or  soldeied  connectloot 
are  provided. 

d.  Marking. — Must  be  plainly  marked,  where  it  may  be  readily  seen 
after  the  device  is  installed,  with  the  rating  and  the  name  of  the  maker; 
and  the  terminals  of  motor-starting  rheostats  must  be  marked  to  indicate 
to  what  part  of  the  circuit  each  is  to  be  connected,  as  "line."  "armature" 
and  "field." 

a.  Contacts. — ^The  design  of  the  fixed  and  movable  contacts  and  the 
resistance  in  each  section  must  be  such  as  to  secure  the  least  tendency  toward 
arcing  and  roughening  of  the  contacts,  even  with  careless  handling  or  the 
presence  of  dirt. 

In  motor-startinjg  rheostats,  the  contact  at  which  the  circuit  is  broken 
by  the  lever  arm  when  moving  from  the  running  to  the  starting jposition. 
must  be  so  designed  that  there  will  be  no  detnmental  arcing.  The  final 
contact,  if  any,  on  which  the  arm  is  brought  to  rest  in  the  starting  position 
must  have  no  electrical  connection. 

Ezpertrace  bas  shown  tbat  sharp  edges  and  seffmaits  of  thin  material  help  to 
malntafn  an  arc.  and  It  Is  reoonuneoded  that  these  be  avoided.  Segments  of  heavy 
eoDStnictloo  have  a  considerable  ooollDg  effect  on  tbe  air,  and  rounded  corners  tend 
to  SOTead  It  out  and  thus  dissipate  It.  ^ 

It  Is  recommended  tliat  the  circuit-breaking  contacts  be  so  constructed  as  to 
"bieak"  with  a  quick  snap.  Independently  of  the  slowness  ot  movement  of  the  oper^ 
ator's  hand,  or  that  a  magnetic  blowout  or  equivalent  device  be  used.  For  dial  tjrpe 
rheostats  the  movable  contact  should  be  flexible  In  a  plane  at  right  angle  to  toe 
plane  o(  Its  movement,  and  for  medium  and  larger  sizes  the  stationary  contacts  should 
be  readUy  renewable. 

f.  No-Voltag9  Rtkast. — Motor-starting  rheostats  must  be  so  designed 
that  the  contact  arm  cannot  be  left  on  intermediate  segments,  and  must  be 
provided  with  an  automatic  device  which  will  interrupt  the  supply  circuit 
oefore  the  speed  of  the  motor  falls  to  less  than  one  third  of  its  normal  value. 

j|,  Ovtrload-Release. — Overload-release  devices  which  are  inoperative 
diirmg  the  process  of  starting  a  motor  will  not  be  approved  unless  other 
circuit-breakers  or  fuses  are  installed  in  connection  with  them. 

If,  (or  Instance,  the  over-release  device  simply  releases  the  starting  arm  and  allows 
It  to  fly  back  and  break  the  circuit.  It  is  inoperative  while  the  arm  Is  being  moved 
trom  the  starting  to  the  nmnlng  pceltlon. 

h.  Test. — Must,  after  100  operations  under  the  most  severe  normal 
conditions  for  which  the  device  is  designed,  show  no  serious  burning  of  the 
contacts  or  other  faults,  and  the  release  mechanism  of  motor-starting 
rheostats  must  not  be  impaired  by  such  a  test. 

Field  rheostats,  or  main-line  regulators  intended  for  continuous  use. 
xnturt  not  be  biutied  out  or  depreciated  by  carrying  the  full  normal  current  on 
any  step  for  an  indefinite  period.  Regulators  intended  for  intermittent  use 
(such  as  on  electric  cranes,  elevators,  etc.)  mtist  be  able  to  carry  their 
rated  current  on  any  step  for  as  long  a  time  as  the  character  of  the  apparatus 
which  they  control  will  permit  them  to  be  used  continuously. 

61.  Reactive  Coib  and  Condensers. — a.  Reactive  coils  must  be  made  of 
non-combustible  material,  mounted  on  non-combustible  bases  and  treated. 
In  general,  as  sources  of  heat. 

b.  Condensers  must  be  treated  like  other  apparatus  operating  with 
equivalent  voltage  and  currents.  They  must  have  non-combustible  cases 
and  aupports,  and  must  be  isolated  trom  all  combustible  material  and, 
in  general,  treated  as  sources  of  heat. 

62.  Transformers. — (For  installation  rules,  see  Nos.  11, 13. 18  A  and  86.) 
a.   Must  not  be  placed  in  any  but  metallic  or  other  non-combustible 

Digitized  by  VjOOQ  LC 


1444  lO.-^ELECTRIC  POWER  AND  UGHTING, 

On  account  of  the  poaiible  dangers  £fom  bum-outs  in  the  ooOs.  (S* 
note  under  No.  11  a.) 

It  is  advised  that  every  transformer  be  so  designed  and  connected  that 
the  middle  point  of  the  secondary  ooil  can  be  reached  if.  at  any  fature  trmf, 
it  should  be  desired  to  ground  it. 

b.  Must  be  constructed  to  comply  with  the  following  tests: —    * 

1.  Shall  be  run  for  eight  consecutive  hours  at  full  load  in  watts  under 
conditions  of  service,  and  at  the  end  of  that  time  the  rise  in  tem- 
perature, as  measured  by  the  increase  of  resistance  of  the 
primary  and  secondary  coils,  shall  not  exceed  176°  Pahneaheit 
(97°  Centigrade). 

3.  The  insulation  of  transformers  when  heated  shall  withstand  oon- 
tinuousljr  for  five  minutes  a  difference  of  potential  of  10,000  yohs 
(alternating)  between  primary  and  secondary  coils  and  between 
the  primary  coils  and  core,  and  a  no-load  "run"  at  double  vintage 
for  thirty  minutes. 

63.  Lif  htnlng  Arrssters. — (For  installation  rules,  see  No.  6.)  a.  Li^bXr 
ning  arresters  must  be  of  approved  construction.  (See  list  of  Blectrkal 
Fittings.) 

Clast  E.— MISCELLANEOUS. 

64.  SlgnaUng  Systems. — Govtming  wiring  for  tekphon*,  Ukgrafh^  dis- 
trict m$ssen^9r  and  call-bell  circuits,  fire  and  Burglar  alarms,  and  all  simiiar 
systems  whtch  are  hasardcus  only  because  of  their  liability  to  beconm  crossed 
with  electric  light,  heat  or  power  circuits, 

a.  Outside  wires  should  be  nm  in  underground  ducts  or  strung  on  poles, 
and.  kept  ofT  the  roofs  of  buildings,  except  bv  special  permission  c»  the 
Inspection  Department  having  iurisdiction,  ana  must  not  be  placed  on  the 
same  cross-arm  with  electric  Ijgnt  or  power  wires.  They  should  not  occupy 
the  same  duct,  manhole  or  handhole  of  condmt  systems  with  electric  light  or 
power  wires. 

Single  manholes,  or  handhdes.  may  be  separated  Into  secttoos  by  means  of  par- 
titions of  bnck  or  tile  so  as  to  be  oonsloered  as  confonnlog  with  the  above  rule. 

The  liability  of  accidental  crossing  of  overhead  slpisllnK  elreolts  with  i  ~ 
light  and  power  circuits  may  be  guarded  against  to  a  ooosldersble  extent  by  e_ 
orlng  to  keep  the  two  classes  of  circuits  on  different  sides  of  the  same  street. 

Whbn  thb  Entire  Circuit  from  Cbntral  Station  to  Buildino  is 

Run  in  Underground  Conduits.  Sbctions  b  to  m 

Inclusive  do  Not  Apply. 

b.  When  outside  wires  are  run  on  same  pole  with  electric  light  or  powcr 
wires,  the  distance  between  the  two  inside  pins  of  each  cross-ann  most 
not  be  less  than  twenty-six  inches. 

Signaling  wires  being  smaller  and  more  liable  to  break  and  tan.  should  gaosnOy 
be  plaoed  on  the  lower  oross-arms. 

c.  Where  wires  are  attached  to  the  outside  walls  of  buildings  they  mtot 
have  an  approved  rubber  insulating  covering  (see  No.  41),  and  on  frame 
buildings  or  frame  portions  of  other  buildings  shall  be  supported  on  glass 
or  porcelain  insulators,  or  knobs. 

d.  The  wires  from  last  outside  support  to  the  cut-outs  or  protectofs 
must  be  of  copper,  and  must  have  an  approved  rubber  insulation  (see  No.  41); 
must  be  provided  with  drip  loops  immediately  outside  the  building  and  at 
entrance;  must  be  kept  not  less  than  2i  inches  apart,  except  whcmbrought 
in  through  approved  metal  cables. 

e.  Wires  must  enter  building  through  approved  non-oombustible.  noo- 
absorptive,  insulating  bushings  sloping  upward  from  the  outside. 

Installations  where  the  Currbnt-Carrtino  Parts  of  the  AppARATtrs 

Installed  are  Capable  of  Carrtino  Indbfinitblt 

A  Current  of  Ten  Amperes. 

L  An  all-metallic  circuit  shall  be  provided,  except  in  telegraph  systems. 

.*•   At  the  entrance  of  wires  to  buildings,  approved  single-pole  cut-outs. 

aligned  for  251-600  volts  potential  and  containing  fuses  rated  at  not  over 

iHf^uL^^  capacity,  shall  be  provided  for  each  wire.    These  cut-outs  must 

noi  De  placed  m  the  immediate  vicinity  of  easily  ignitible  stuff,  or  what 


MISCELLANEOUS^SIGNAUNG  SYSTEMS.  1445 

exposed  to  inflammable  gases  or  dust  or  to  flyings  of  combustible  material. 

h.  The  wires  inside  buildings  shall  be  of  copper  not  less  than  No.  16 
B.  &  S.  gage,  and  must  have  insulation  and  be  supported,  the  same  as  would 
be  required  for  an  installation  of  electric  light  or  power  wiring,  0-600  volts 
potential. 

i.  The  instruments  shall  be  motmted  on  bases  constructed,  of  non- 
combustible,  non-absorptive  insulating  material.  Holes  for  the  supporting 
screws  must  be  so  located,  or  countcrsuijlc,  that  there  will  be  at  least  i  inch 
space,  measiued  over  the  surface,  between  the  head  of  the  screw  and  the 
nearest  live  metal  part. 

Installations  wrbrb  thb  Currbnt-Carrtino  Parts  of  the  Apparatus 
Installed  are  Not  Capable  op  Carrtino  Indbfinitblt 
A  Current  of  Tbn  Amperes. 

J.  Must  be  provided  with  an  a^provfd  protective  device  located  as 
near  as  possible  to  the  entrance  of  wires  to  building.  The  protector  must 
not  be  placed  in  the  immediate  vicinity  of  easily  ignitible  stuff,  or  where 
exposed  to  inflammable  gases  or  dust  or  flyings  of  combustible  materials. 

k.  Wires  from  entrance  to  building  to  p>rotector  must  be  supported  on 
porcelain  insulators,  so  that  they  will  come  in  contact  with  nothing  except 
their  designed  supports. 

I.  The  ground  wire  of  the  protective  device  shall  be  run  in  accordance 
with  the  following  requirements: — 

1.  Shall  be  of  copper  and  not  smaller  than  No.  18  B.  &  S.  gage. 

2.  Must  have  an  approvtd  insulating  covering  as  described  in  No.  41, 

for  voltages  from  0  to  600.  except  that  the  preservative  compoimd 
specified  in  No.  41,  Section  h  may  be  omitted. 

8.  Must  nm  in  as  straight  a  line  as  possible  to  a  good  permanent  ground. 
This  may  be  obtained  by  connecting  to  a  water  or  gas  pipe 
connected  to  the  street  mains  or  to  a  ground  rod  or  pipe  driven  in 
•  permanently  damp  earth.  When  connections  are  made  to  pipes, 
preference  shall  be  given  to  water  pipes.  If  attachment  is  made 
to  gas  pipe,  the  connection  in  all  cases  must  be  made  between  the 
meter  and  the  street  mains.  In  every  case  the  connection  shall 
be  made  as  near  as  possible  to  the  earth. 

When  the  grotmd  wire  is  attached  to  water  or  gas  pipes,  these 
pipes  shall  be  thoroughly  cleaned  and  tinned  with  rosin  flux 
solder,  if  such  a  method  is  practicable:  the  ground  wire  shall  then 
be  wrapped  tightly  arotmd  the  pipe  and  thoroughly  soldered  to  it. 
When  the  above  method  is  impracticable,  then,  if  there  are 
fittings  where  a  brass  plu^  can  be  inserted,  the  ground  wire  shall 
be  thoroughly  soldered  to  it;  if  there  are  no  such  fittings,  then  the 
pipe  shall  be  thoroughly  cleaned  and  an  approved  ground  clamp 
fastened  to  an  exposed  portion  of  the  pipe  and  the  ground  wire 
well  soldered  to  the  grotmd  clamp. 

When  the  grotmd  wire  is  attached  to  a  grotmd  rod  driven  into 
the  earth,  the  grotmd  wire  shall  be  soldered  to  the  rod  in  a  similar 
nwnner. 

Steam  or  hot  water  pipes  must  not  be  used  for  a  protector 
ground. 

m.  The  protector  to  be  approved  must  comply  with  the  following 
requirements: — 

For  Instrument  Circuits  of  Telegraph  Systems. — 1.  An  approved  single- 
pole  cut-out.  in  each  wire,  designed  for  2,000  volt  potential,  and 
containing  fuses  rated  at  not  over  one  ampere  capacity.  When 
main  line  cut-outs  are  installed  as  called  for  in  Section  g.  the  instru- 
ment cut-outs  may  be  placed  between  the  switchboard  and  the 
instrument  as  near  the  switchboard  as  possible. 

For  All  Other  Systems. — 1.  Must  be  mounted  on  non-combustible,  non- 
absorptive,  insulating  bases,  so  designed  that  when  the  protector 
is  in  place,  all  parts  which  may  be  alive  will  be  thoroughly  insu- 
lated from  the  wall  to  which  the  protector  is  attached. 

2.  Must  have  the  following  parts: — 

A  lightning  arrester  which  will  operate  with  a  difference  of 
potential  between  wires  of  not  over  500  volts,  and  so  arranged  that 
the  chance  of  accidental  grounding  is  redttced  to  a  minimum. 


144fl  n.^ELECTRIC  POWER  AND  UGHTING, 

A  fuie  designed  to  open  the  circuit  in  case  the  wires  becooM 
crossed  with  li^t  or  power  circtiits.  The  fuse  most  be  aUe  to 
oi>en  the  circuit  without  arcing  or  serious  flashing  when  croMcd 
with  any  ordinary  commercial  light  or  power  circuit. 

A  heat  coil,  it  the  sensitiveness  of  the  instrument  demands  it, 
which  will  operate  before  a  sneak  current  can  damage  the  insuii> 
ment  the  protector  is  giiarding. 


Heat  ooUs  are  neoesBarr  In  aU  etrcults  DormaUy  oloaed  thztmsh  mafnel 
olnga  which  cannot  Indefinitely  carry  a  current  ot  at  lease  Sampeies. 
The  heat  coll  Is  designed  to  warm  up  and  melt  out  with  a  curreot  laite 


enough  to  endanger  the  Instrummts  If  continued  for  a  long  time,  hut  ss 
smallthat  it  would  not  blow  the  fuses  ordinarily  found  neoessary  ror  sodi 
instruments.    The  smaUtf  currents  are  often  called  "sneak"  eufrents. 

8.  The  fuses  must  be  so  placed  as  to  protect  the  arrester  and  heat  coils, 
and  the   protector  terminals  must  be  plainly   marked    "Hoe, 
"instrument/'  "ground.*' 

An  easay  read  abbrerlattOQ  of  the  abore  words  wlli  be  snowed. 

Thb  Pollowino  Rulbs  Apply  to  All  Sybtbms  whbthbr  thb  Wntss 
PROM  TUB  Central  Oppicb  to  thb  Buildiko  arb 

OVBRBBAO  OR  UnDBRGROUNO. 

n.  Wires  beyond  the  protector,  or  wires  inside  buildings  where  no  pro- 
tector is  used,  must  be  neatly  arranged  and  secxirely  fastened  in  place  in  some 
convenient,  workmanlike  manner.  They  must  not  come  nearer  than 
0  inches  to  anv  electric  light  or  power  wire  in  the  building  unless  et 
in  approved  tubing  so  secured  as  to  prevent  its  slipping  out  of  place. 

The  wires  would  ordinarily  be  insulated,  but  the  kind  of  InsulaUcn  is  not  SDcd- 
fled,  as  tbe  protector  is  relied  upon  to  stop  all  dangerous  currents.  Poroelain  tnblBc 
or  ai^proraif  flexible  tubing  may  be  used  for  enoasmg  wires  where  required  as  above. 

o.  Wires  where  bunched  together  in  a  vertical  nm  within  any  building 
must  have  a  fire-resisting  covering  sufficient  to  prevent  the  wires  from 
carrying  fire  from  floor  to  noor  unless  they  are  nm  either  in  non-combustible 
tubing  or  in  a  fireproof  shaft,  which  shaft  shall  be  provided  with  fire  stops 
at  each  floor. 

Signaling  wires  and  electric  light  or  power  wires  may  be  run  in  ttke  same 
shaft,  provided  that  one  of  these  classes  of  wires  is  run  in  non-combustibk 
tubing,  or  provided  that  when  nm  otherwise  these  two  classes  of  wires 
shall  be  separated  from  each  other  bv  at  least  2  inches. 

In  no  case  shall  signaling  wires  Se  run  in  the  same  tube  with  electric 
light  or  power  wires. 

Ordinary  rubber  insulation  Is  toflammable,  and  when  a  number  of  wires  are 
contained  in  a  shaft  extending  through  a  building  they  afford  a  ready  means  o( 
carrying  Are  from  floor  to  floor,  unleas  they  are  covered  with  a  flre-reslsting  matettsi, 
or  unless  the  shaft  is  provided  with  flre  stops  at  each  floor. 

65.  Electric  Qas  Lightiog . — a.  Electric  gas  lighting  must  not  be  used 
on  the  same  fixture  with  the  electric  light. 

The  above  rule  does  not  apply  to  frictlonal  systems  of  gas  lighting. 

68  A.  Moviof  Picture  Machines. — a.  Arc  lamp  used  as  a  part  of  moving 
picture  machines  must  be  constructed  similar  to  arc  lamps  ol  theatexa.  and 
wiring  of  same  must  not  be  of  less  capacity  than  No.  0  fi.  &  S.  gage.  (See 
No.aiAd.  [1].) 

b.  Rheostats  must  conform  to  rehostat  requirements  for  theater  arcs. 
(See  No.  81 A  d.  [1].) 

c.  Top  reel  must  be  encased  in  a  steel  box  with  hole  at  the  bottom  onhr 
large  enough  for  film  to  pass  through,  and  cover  so  arranged  that  this  bole 
can  be  instantly  closed.  No  solder  to  be  used  in  the  construction  of  this 
box. 

d.  A  steel  box  must  be  used,  for  receiving  the  film  after  being  shown, 
with  a  hole  in  the  top  only  large  enough  for  the  film  to  pass  through  freely* 
with  a  cover  so  arranged  that  this  hole  can  be  instantly  dosed.  An  opening 
naay  be  placed  at  the  side  of  the  box  to  take  the  film  out.  with  a  door  hung 
at  the  top.  so  arranged  that  it  cannot  be  entirely  opened,  and  provided 
with  a  spnngHcatch  to  k>ck  it  closed.    No  soWer  to  be  used  m  the  < 

*•  Digitized  by  CjOOQIC 


MISCELLANEOUS,    MARINE  WORK.  1447 

••  The  handle  or  crank  used  in  operating  the  machine  must  be  secured 
to  the  spindle  or  shaft,  so  that  there  will  be  no  liability  of  its  coming  off 
and  allowing  the  film  to  stop  in  front  of  lamp. 

f.  A  shutter  must  be  placed  in  front  of  the  condenser,  arranged  so  as 
to  be  readily  closed. 

g.  Extra  films  must  be  kept  in  metal  box  with  ti^t-fitting  cover. 

h.  Blachines  must  be  operated  by  hand  (motor-driyen  will  not  be  per- 
mitted.) 

i.  Picture  machine  must  be  placed  in  an  enclosure  or  house  made  of 
suitable  fireproof  material,  be  thoroughly  ventilated  and  large  enough  for 
operator  to  walk  freely  on  either  side  of  or  back  of  machine.  All  openings 
into  this  booth  must  be  arranged  so  as  to  be  entirely  closed  by  doors  or 
shutters  constructed  of  the  same  or  equally  good  nre-resisting  material 
as  the  booth  itself.  Doors  or  covers  must  be  arranged  so  as  to  be  held 
normally  closed  by  spring  hinges  or  equivalent  devices. 

66.  Insalatioii  Resistance.— The  wiring  in  any  building  must  test  free 
from  grounds:  «'.#..  the  complete  installation  must  have  an  insulation 
between  conductors  and  between  all  conductors  and  the  ground  (not  incltiding 
attachments,  sockets,  receptacles,  etc.)  not  less  than  that  given  in  the  fol- 
lowing table: — 

Up  to         5  amperes 4.000.000  ohms. 

10        *•       2,000.000 

26        ••       800.000 

60        •*       400,000 

100        ••       200.000 

200        ••       100.000 

400        ••       60.000 

800        ••       26.000 

"      1.600        ••       12.600 

The  test  must  be  made  with  all  cut-outs  and  safety  devices  in  place.  If 
the  lamp  sockets,  receptacles,  electroliers,  etc..  are  also  connects,  only  one- 
half  of  the  resistances  specified  in  the  table  will  be  required. 

67.  Solderiiig  Fluid. — a.  The  following  formula  for  soldering  fluid  is 
suggested: — 

Saturated  solution  of  zinc  chloride 6  parts. 

Alcohol 4  parts. 

Glycerine 1  part. 

Class  F.— MARINE  WORK. 

68.  Qencrators. — a.    Must  be  located  in  a  dry  place. 

b.  Must  have  their  frames  insulated  from  their  bed -plates. 

c  Must  each  be  proivded  with  a  waterproof  cover. 

d.  Must  each  be  provided  with  a  name-plate,  giving  the  maker's  name, 
the  capacity  in  volts  and  amperes,  and  the  normal  speed  in  revolutions  per 
minute. 

69.  Wires. — a.  Must  be  supported  in  approv0d  moulding  or  conduit, 
except  at  switchboards  and  for  portables. 

Special  pennlsston  may  be  given  for  deviation  from  this  rule  m  dynamo  rooms. 

b.  Must  have  no  single  wire  larger  than  No.  12  B.  &  S.  ffage.  Wires  to 
be  stranded  when  greater  carrying  capacity  is  required.  No  single  solid 
wire  smaller  than  No.  14  B.  &  S.  gage,  except  in  fixture  wiring,  to  be  used. 

Stnnded  wires  must  be  soldered  before  being  testened  under  damps  or  binding 
screws,  and  when  tbey  have  a  oonduetlvlty  greater  than  that  of  No.  8  b.  ^k  8.  gage 
eopper  wire  they  must  be  soldered  Into  lugs. 

c  Splices  or  taps  in  conductors  must  be  avoided  as  far  as  possible. 
Where  it  is  necessary  to  make  them  they  must  be  so  spliced  or  joined  as  to 
be  both  mechanically  and  electrically  secure  without  solder.  They  must  then 
be  soldered,  to  insure  preservation,  covered  with  an  insxilating  compound 
equal  to  the  insulation  of  the  wire,  and  further  protected  by  a  waterproof 
tape.  The  joint  must  then  be  coated  or  painted  with  a  waterproof  com- 
pound. 


1448 


70.— ELECTRIC  POWER  AND  LIGHTING. 


All  Joints  must  be  soldered  imless  made  with  some  toem  of  oppuwetf  spUdBf 
deyloe. 

For  Moulding  Work. — d.  Must  have  an  approv9d  insulating  co'vcnng. 

The  Insulatkm  for  ooodiiotors.  to  be  approred.  most  be  at  least  S-32  of  an  lock  m 
thloknesB  and  be  covered  with  a  substantial  waterproof  braid. 


The  physical  obaraoteristlos  shall  not  be  affected  by  any  change  tn  temperatsR 
up  to  200<*  Fahrenheit  (93°  Oentlnade).  After  two  weeks'  submeralon  In  salt  wat^ 
at  70»  Fahrenheit  (21*"  Oentlgrade).  It  must  show  an  Insulation  reslstanoe  of  IM 
mesohms  per  mile  after  three  minutes'  electrlfloatlon  with  550  volts. 

e.  Must  have,  when  cussing  through  water-tight  bulkheads  and  thxough 
all  decks,  a  metallic  sttimng  tube  lined  with  hard  rubber.  In  case  of  deck 
tubes,  they  must  be  boxed  near  deck  to  prevent  mechanical  injury. 

f.  Must  be  bushed  with  hard  rubber  tubing.  H  of  an  inch  in  thickness, 
when  passing  through  beams  and  non-water-tight  bulkheads. 

For  Conduit  Work. — g.   Must  have  an  approved  insulating  covering. 

The  Insulation  ^  conductors,  for  use  In  Ihied  eoodults.  to  be  approved.  m«t  te 
at  least  3-32  of  an  Inch  In  thickness  and  be  covered  with  a  substantial  watierprool 
braid.  The  physical  characteristics  shall  not  be  affected  by  any  change  In  toa- 
perature  up  to  200*  Fahrenheit  (93*>  Oentlgrade). 

After  two  weeks'  submersion  In  salt  water  at  7(r>  Fahrenheit  (21®  Oentlgrade). 
It  must  show  an  insulation  reslstanoe  of  100  megohms  per  mile  after  three  lunates* 
eleotrifloatlon  with  550  volts. 

For  unlined  metal  conduits,  conductors  must  conform  to  the  specifica- 
tions given  for  lined  conduits,  and  in  addition  have  a  second  outer  fibrous 
covering  at  least  1/33  of  an  inch  in  thickness  and  sufficiently  tenacions  to 
withstand  the  abrasion  of  being  hauled  through  the  metal  condiut. 

h.  Must  not  be  drawn  in  until  the  mechanical  work  on  the  Conduit  is 
completed  and  same  is  in  place. 

i.  Where  nm  through  coal  bunkers,  boiler  rooms,  and  where  they  are 
exposed  to  severe  mechanical  injtuy.  miast  be  encased  in  approv0d  coxiduit. 

70.  Portable  Conductors. — a.  Must  be  made  of  two  stranded  conductors 
each  having  a  carrying  capacity  equivalent  to  not  less  than  No.  14  B.  &  S. 
gage,  and  each  covered  with  an  approved  insulation  and  covering. 

Where  not  exposed  to  moisture  or  severe  mechanical  Injurv.  each  stranded 
conductor  must  have  a  solid  Insulation  at  least  1-33  of  an  Inch  m  thickness,  and 
must  show  an  Insulation  r^stance  between  conductors,  and  between  either  eoa- 
ductor  and  the  ground,  of  at  least  50  megohms  per  mile  after  two  weeks'  subnaexslan 
In  water  at  70^  Fahrenheit  (21*'  Oenttgnde).  and  be  protected  by  a  slow-bummg. 
tough-braided  outer  covering. 

Where  exposed  to  moisture  and  mechanical  Injury  (as  for  use  on  decks,  holds 
and  fire-rooms),  each  stranded  conductor  shall  have  a  solid  Insulation,  to  be  aprooved. 
of  at  leasT  1-32  of  an  Inch  In  thickness  and  protected  by  a  tough  bmld.  The  two 
conductors  shall  then  be  stranded  together,  using  a  Jute  filling.  The  whole  shall  tbea 
be  covered  with  a  layer  of  flax,  either  woven  or  braided,  at  lekst  1-32  of  an  tn^  m 
thickness  and  treated  with  a  non-lnflanunable.  waterpix>of  compound.  After  one 
week's  submersion  In  water  at  70^  Fahrenheit  (21°  Cfentlgrade).  It  must  show  an 
Insulation  between  the  two  oonduotofs.  or  between  either  conductor  and  the  gzomd. 
of  50  megohms  per  mile. 


71.    Bell  or  Other  Wires - 

lighting  or  power  wires. 


Must  never  be  nm  in  same  duct  with 


72.    Table  of  Capacity  of  Wires.— 


Area 

Actual 

B.&S.G. 

CM. 

19 

1,288 

18 

1.624 

2.048 

2.583 

8,257 

4.107 

6.630 

0.016 

11.368 

14.336 

18.081 

22.  TOO 

30,856 

Size  of 
No.  of  Strands. 
Strands.    B.  &  S.  G.  Amperes. 


'i 

•  • 

6 

ii 

17 

7 

10 

31 

7 

18 

35 

7 

17 

10 

7 

M 

3ft 

T  r.       .^^tjpOOgl^ 


I A        Digitized  Id 


MARINE  WORK,  1449 


Area 

Size  of 

Actual 

No.  of 

Strands 

B.&S.G. 

CM. 

Strands 

B.  &  S.  G. 

Amperes. 

88.912 

19 

17 

60 

49.077 

19 

16 

70 

60.088 

87 

18 

85 

76.776 

87 

17 

100 

09.064 

61 

18 

120 

124.928 

61 

17 

145 

157.563 

61 

16 

170 

198.677 

61 

15 

200 

250.527 

61 

14 

235 

296.387 

91 

15 

270 

873.737 

01 

14 

820 

413.639 

127 

15 

340 

When  greater  conduotlnR  area  than  that  or  No.  12  B.  A  S.  mige  Is  required,  the 
ocmductor  shall  be  stranded  m  a  series  of  7.  I9.  37.  61.  91.  or  127  wires,  as  may  be 
required:  the  strand  consisting  of  one  central  wire,  the  remainder  laid  around  it 
ooncentrlcaUy.  each  layer  to  be  twisted  In  the  opposite  direction  from  the  preceding. 

73.  Switchboards. — a.  Must  be  made  of  non-combustible,  non-absorp- 
tive insulating  material,  such  as  marble  or  slate. 

b.  Must  be  kept  free  from  moisture,  and  must  be  located  so  as  to  be 
accessible  from  all  sides. 

c.  Must  have  a  main  switch,  main  cut-out  and  ammeter  for  each  gene- 
rator. 

Must  also  have  a  voltmeter  and  groimd  detector. 

d.  Must  have  a  cut-out  and  switch  for  each  side  of  each  current  leading 
from  board. 

e.  Must  be  wired  with  conductors  having  an  insulation  as  required  for 
moulding  or  conduit  work  and  covered  with  a  substantial  flame-proof 
braid. 

74.  Resistance  Boxes. — (For  construction  rules,  see  No.  60.)  a.  Must 
be  located  on  switchboard  or  away  from  combustible  material.  When  not 
placed  on  switchboard  they  must  be  moimted  on  non-inflammable,  non- 
absorptive  insulating  material. 

75.  Switches. — (For  construction  rules,  see  No.  51 )  a.  When  exposed 
to  dampness,  they  must  be  enclosed  in  a  water-tight  case. 

b.  Must  be  of  the  knife  pattern  when  located  on  switchboard. 

c.  Must  be  provided  so  that  each  freight  compartment  may  be  separately 
controlled. 

76.  Cut-Oifts. — (For  construction  rules,  sec  No.  52.)  a.  Must  be 
placed  at  every  point  where  a  change  is  made  in  the  size  of  the  wire  (unless 
the  cut-out  in  the  larger  wire  will  protect  the  smaller). 

b.  In  such  places  as  upper  decks,  holds,  cargo  spaces  and  fire-rooms,  a 
water-tight  and  fire-proof  cut-out  may  be  used,  connecting  directly  to  mains 
when  such  cut-out  supplies  circuits  requiring  not  more  than  660  watts 
energy. 

c.  When  placed  anjrwhere  except  on  switchboards  and  certain  places, 
as  cargo  spaces,  holds,  fire-rooms,  etc.,  where  it  is  impossible  to  run  from 
center  of  distribution,  they  must  be  in  a  cabinet  lined  with  fire-resisting 
material. 

d.  Except  for  motors,  searchlights  and  diving  lamps  must  be  so  placed 
that  no  group  of  lamps,  requiring  a  current  of  more  than  660  watts,  shall 
ultimately  be  dependent  upon  one  cut-out. 

77.  Fixtures. — a.  Must  be  mounted  on  blocks  made  from  well-seasoned 
timber  treated  with  two  coats  of  white  lead  or  shellac. 

b.  Where  exposed  to  dampness,  the  lamp  must  be  surrounded  by  a 
vapor-proof  globe. 

c.  Where  exposed  to  mechanical  injurv.  the  lamp  must^se  surpimded 
by  a  globe  protected  by  a  stout  wire  gxiard.  Digitized  by  LjOOglC 


1460  TO.— ELECTRIC  POWER  AND  LIGHTING, 

d.  Must  be  wired  with  same  grade  of  insulation  as  portable  conductors 
which  are  not  exposed  to  moisture  or  mechanical  injury. 

e.  Ceiling  fixtures  over  two  feet  in  length  must  be  provided  with  stay 
chains. 

78.  Sockets. — (For  construction  rules,  see  No.  55.) 

79.  Wooden  Mouldings. — (For  construction  rules,  see  No.  50.) 

a.  Where  moulding  is  run  over  rivets,  beams,  etc.,  a  baddng  strip 
must  first  be  put  up  and  the  moulding  secured  to  this. 

b.  Capping  must  be  secured  by  brass  screws. 

80.  Interior  Conduits. — (For  installation  rules,  see  No.  25.)  (For  con- 
struction rules,  see  No.  49.) 

81.  Signal  L4ghts. — a.  Must  be  provided  with  approvid  telltale  boarl 
located  preferably  in  pilot  house,  which  will  immediately  indicate  a  burned- 
out  lamp. 

83.  Motors. — a.  Must  be  wired  under  the  same  precautions  as  with  a 
current  of  same  volume  and  potential  for  lighting.  The  motor  and  resist- 
ance box  must  be  protected  oy  a  double-pole  cut-out  and  controlled  by  a 
double-pole  switch,  except  in  cases  where  one-q\iarter  horse  power  or  Urn 
is  used. 

The  motor  leads  or  branch  circuits  most  be  designed  to  cany  a  ourrent  at  leasl 
2 R  per  cent  greater  than  that  for  which  the  motor  Is  rated.  In  order  to  proTlde  for 
the  inevitable  oooaslon&l  overioadlng  of  the  motor,  and  the  Ineresaed  eorrent  rt- 
quired  In  starting,  without  overfusins  the  wires,  but  where  the  wires  under  this  nde 
would  be  overfused.  In  order  to  provide  for  the  starting  current,  as  In  the  case  ot  maay 
of  the  alternating  current  motors,  the  wires  must  be  of  such  else  as  to  be  ptopertf 
protected  by  these  larger  (uses. 

In  general,  motors  should  preferably  have  no  exposed  live  parts. 

b.  Must  be  thoroughly  insulated.  Where  possible,  should  be  set  on  base 
frames  made  from  filled,  hard,  dry  wood  and  raised  above  surroundiag 
deck.  On  hoists  and  winches  they  must  be  insulated  from  bed-plates  by 
hard  rubber,  fiber  or  similar  insulating  material. 

c  Must  be  covered  with  a  waterproof  cover  when  not  in  use. 

d.  Must  each  be  provided  with  a  name-plate,  giving  maker's  name,  the 
capacity  in  volts  and  amperes,  and  the  normal  speed  in  revolutkus  per 
mmute. 

83.  Insulation  Resistance. — ^The  wiring  in  any  vessel  must  test  free 
from  grounds;  i.  e.,  the  complete  installation  must  have  an  tnsulatioci 
between  conductors  and  between  all  conductors  and  the  ground  (not  indod- 
ing  attachments,  sockets,  receptacles,  etc.).  of  not  less  than  the  following: — 

Up  to     25  amperes 800,000  ohms. 

••       60        "       400.000     •• 

'•     100        "       200,000     " 

"     200        ••       100,000     " 

••     400        *•       60,000     - 

"     800        "       26,000     •' 

••  1.600        "       12.600     •' 

All  cut-outs  and  safety  devices  in  place  in  the  above*. 
Where  lamp  sockets,  receptacles  and  electtoUers,  etc.,  are  connected, 
one-half  of  the  above  will  be  required. 


d  by  Google 


DEFINITIONS.  1451 

ELECTRICAL  STANDARDIZATION. 

Stakdardization  Rulbs  of  thb  Au.  Inst,  or  Elbc.  Bnors. 

Approved  bv  the  Board  of  Directors,  June  21,  1907. 

Accepted  by  the  24th  Annual  Convention.  June  27,  1007. 

I.— DEFINITIONS  AND  TECHNICAL  DATA. 

1  NoU. — ^The  following  definitions  and  classifications  are  intended  to  be 

.    practicaUy  descriptive  and  ziot  scientifically  rigid. 

A.— DEFINITIONS.    CURRENTS. 

2  A  Dirtct  Current  is  a  unidirectional  current.  ^  • 

3  A  CofUinuoHs  Current  is  a  steady,  or  non-pulsating,  direct  current. 

4  A  Pulsating  Current  is  a  current  equivalent  to  the  superposition  of 
an  alternating  current  upon  a  continuous  current. 

5  An  Alternating  Current  is  a  current  which,  when  plotted,  consists  of 
half-waves  of  equal  area  in  successively  opposite  directions  from  the 
zero  line. 

6  An  Oscillating  Current  is  a  current  alternating  in  direction,  and  of 
decreasing  amplitude. 

B.— DEFINITIONS.    ROTATING  MACHINES. 

7  A  Generator  transforms  mechanical  power  into  electrical  power. 

8  A  Direct-Current  Generator  produces  a  direct  current  that  may  or 
may  not  be  continuous. 

9  An  Alternator  or  Alternating-Current  Generator  produces  alternating 
current,  either  single-phase  or  polyphase. 

10  A  .Polyphase  Generator  pioduces  currents  differing  symmetrically  in 
phase;  sucn  as  two-phase  currents,  in  which  the  terminal  voltages  on 
the  two  circuits  differ  in  phase  by  00°;  or  three-phase  currents,  in  which 
the  terminal  voltages  on  the  three  circuits  differ  in  phase  by  120°. 

11  A  Double-Current  Generator  produces  both  direct  ancf  alternating 
currents. 

13         A  Motor  transforms  electrical  into  mechanical  power. 

13  A  Booster  is  a  machine  inserted  in  series  in  a  circuit  to  change  its 
voltage.  It  may  be  driven  by  an  electric  motor  (in  which  case  it  is  termed 
a  motor-booster)  or  otherwise. 

14  A  Motor-Generator  is  a  transforming  device  consisting  of  a  motor 
mechanically  connected  to  one  or  more  generators. 

15  A  Dynamotor  is  a  transforming  device  combining  both  motor  and 
generator  action  in  one  magnetic  field,  with  two  armatures;  or  with  an 
armature  having  two  separate  windings  and  independent  commutators. 

16  A  Converter  is  a  machine  employing  mechanical  rotation  in  changing 
electrical  energy  from  one  form  to  another.  A  converter  may  belong  to 
either  of  several  types,  as  follows: 

17  a.  A  Direct-Current  Converter  converts  from  a  direct  current  to  a 
direct  current. 

IS  6.  A  Synchronous  Converter  (commonly  called  a  rotary  converter) 
converts  from  an  alternating  to  a  direct  current,  or  vice  versa. 

19  c.  A  Motor-Converter  is  a  combination  of  an  induction  motor  with 
a  synchronous  converter,  the  secondary  of  the  former  feeding  the  arma- 
ture of  the  latter  with  current  at  some  frequency  other  than  the  impressed 
frequency;  i.e.,  it  is  a  sjmchronous  converter  concatenated  with  an 
induction  motor. 

30  d.  A  Frequency-Converter  converts  from  an  alternating-current  sys- 
tem of  one  frequency  to  an  alternating-current  system  of  another 
frequency,  with  or  without  a  change  in  the  number  of  phases  or  in 
voltages. 

21  e.  A  Rotary  Phase  Converter  converts  from  an  alternating-current 
system  of  one  or  more  phases  to  an  alternating-current  system  of  a  dif- 
ferent number  of  phases,  but  of  the  same  frequency. 

a— DEFINITIONS.    STATIONARY  INDUCTTION  APPARATUS. 

J3  Stationary  Induction  Apparatus  change  electric  energy  to  electric 
energy  through  the  medium  of  magnetic  energy. /^Thevia>m prise 
several  forms,  distinguished  as  follows:  tized  by  ^^OOgLL 


Itf  2  70.— ELECTRIC  POWER  AND  UGUTING. 

39         a.  In  Transfonmrs  the  primary  and  secondary  windings  aie  I&- 

snlated  from  one  another. 
34         6.   In  Auto-Transformtrs,  also  called  oompeniatort,  a  part  of  ti» 

primarv  winding  is  used  as  a  secondary  winding,  or  conversely. 
39         c.   In  Potential  Regulators  a  coil  is  in  shunt  and  a  coil  is  in  aeries 

with  the  circuit,  so  arranged  that  the  ratio  of  transformation  between 

them  is  variable  at  will.  They  are  of  the  following  three  classes: 
3#         (a)  Compensator  Potential  Reguiators  in  which  a  number  of  turns 

of  one  of  the  coils  are  adjustable. 

37  (6)  Induction  Potential  Regulators  in  which  the  re]atrv«  positions 
of  the  primary  and  secondary  coils  are  adiustable. 

38  (c)  Magneto  Potential  Reptlators  m  whidi  the  direction  of  the 
magnetic  flux  with  respect  to  the  coils  is  adjustable. 

3f  d.  Reactors,  or  Reactance  Coils,  formerly  called  choking  ooils.  are 
a  form  of  stationary  induction  apparatus  uaed  to  produce  reactance  or 
phase  displacement. 

D.-OENERAL  CLASSIFICATION  OP  APPARATUS. 

30  Commutating  Machines.  Under  this  head  may  be  classed  the  follow- 
ing: Direct  ciuient  generators:  direct-current  motois;  direct-current 
boosters;  motor-generators;  dynamotors;  converters,  compensators  or 
balancers;  closed-coil  arc  machines,  and  alternating-current  commu- 
tating motors. 

31  Commutating  machines  may  be  further  classified  as  follows: 

33  a.  Direct-Current  Commutattng  Machines,  which  comprise  a  magnetic 
field  of  constant  polarity,  a  closed-coil  armature,  and  a  multisegmental 
commutator  connected  therewith. 

33  b.  AUemaiing-Current  Commutating  Machines,  which  comprise  a 
magnetic  field  of  alternating  polarity,  a  closed-coil  armature,  and  a 
multisegmental  commutator  connected  therewith. 

34  c.  Synchronous  Commutating  Machines,  which  comprise  syncfaionota 
converters,  motor  converters  and  double-current  generators. 

39  Synchronous  Machines,  which  comprise  a  constant  magnetic  field. 
and  an  armature  receiving  or  delivering  altemating-ctirrents  in  ssmchron- 
ism  with  the  motion  of  the  machine;  i^.,  having  a  freouency  equal  to  the 
product  of  the  number  of  pairs  of  poles  and  the  speed  of  the  machine  in 
revolutions  per  second. 

3#.  Stationary  Induction  Apparatus,  which  includes  transfomwrs.  auto- 
transformers,  potential  regulators,  and  reactors  or  reactance  coils. 

37  Rotary  Induction  Apparatus,  or  Induction  Machines,  which  include 
apparatus  wherein  the  primary  and  secondary  windings  rptate  with  re- 
spect to  each  other;  i^.,  induction  moton,  induction  generators,  fre- 
quency converters,  and  rotary  phase  converters. 

38  Unipolar  or  Acyclic  Machines,  in  which  the  voltage  generated  in  the 
active  conductors  maintains  the  same  direction  with  respect  to  those 
conductors. 

39  Rectifying  Apparatus,  Pulsating-Current  Generators, 

40  Electrostatic  Apparatus,  such  as  condensers,  etc. 

41  Electrochemical  Apparatus,  such  as  batteries,  etc. 

43         Electrothermal  Apparatus,  such  as  rheostats,  heaters,  etc 

43  Protective  Apparatus,  such  as  fuses,  lightning  arresters,  etc 

44  Luminous  Sources. 

E.— MOTORS.    SPEED  CLASSIFICATION. 

45  Motors  may,  for  convenience,  be  classified  with  reference  to  their 
speed  characteristics  as  follows: 

46  a.  Constant-Speed  Motors,  in  which  the  speed  is  either  constant  or 
does  not  materially  vary;  such  as  synchronous  motors,  induction 
motors  with  small  slip,  and  ordinary  direct-current  shunt  motors. 

47  b.  Multispeed  Motors  (two-speed,  three-speed,  etc.),  which  can  be 
operated  at  any  one  of  several  distinct  speeds,  these  speeds  being  prae* 
tically  independent  of  the  load,  such  as  motors  with  two  armature  wind- 
ings. 

48  c.  Adjustable-Speed  Motors,  in  which  the  speed  can  be  varied  grad- 
ually over  a  considerable  range;  but  when  once  adjusted  remains  prac- 
tically unaffected  by  the  load,  such  as  shimt  motors  designed  for  a  coo- 
sidcrable  range  of  field  variation. 

^^  .  »•  Varying-Speed  Motors,  or  motors  in  which  the  speed  varies  with 
tne  load,  decreasing  when  the  load  increases;  such  as  series  motors. 


DEFINITIONS  AND  TECHNICAL  DATA.  1458 

F.— DEFINITION  AND  EXPLANATION  OF  TERMS. 

(I)  Load  Factor. 

50  The  Load  Factor  of  a  machine,  plant  or  system  is  the  ratio  of  the 
average  power  to  the  maximum  power  during  a  certain  period  of  time. 
The  average  power  is  taken  over  a  certain  interval  of  time,  such  as  a  da^ 
or  a  yea^.  and  the  maximum  is  taken  over  a  short  interval  of  the  maxi- 
mum load  within  that  interval. 

51  In  each  case  the  interval  of  maximum  load  should  be  definitely  speci- 
fied. The  proper  interval  is  usually  dependent  upon  local  conditions  and 
upon  the  purpose  for  which  load  factor  is  to  be  determined. 

(II)  Non-Inductive  Load  and  Inductivx  load. 

S3  A  non-inductive  load  is  a  load  in  which  the  current  is  in  phase  with 
the  voltage  across  the  load. 

B3  An  inductive  load  is  a  load  in  which  the  current  lags  behind  the 
voltage  across  the  load.  A  load  in  which  the  current  leads  the  voltage 
across  the  load  is  sometimes  called  in  anti-inductive  load. 

(III)  Power-Factor  and  Reactivb-Factor. 

84  The  Power-Factor  in  alternating-current  circuits  or  apparatus  is  the 
ratio  of  the  electric  power  in  watts  to  the  apparent  power  in  volt-amperes. 
It  may  be  expressed  as  follows: 

true   power     ^        watts       ^  energy  current     energy  voltage 
apparent  power     volt-amperes       total  ciurent        total  voltage 
89         The  Rtactive-Factor  is  the  ratio  of  the  wattless  volt-amperes  («.#.. 
the  product  of  the  wattless  component  of  current  by  voltage,  or  wattless 
component  of  voltage  by  current)  to  the  total  amperes.  It  may  be  ex- 
pressed as  follows: 

wattless  volt-amperes     wattless  current     wattless  voltage 
total  volt-amperes  total  current  total  voltage 

M         Power-Factor  and  Reacttve-Factor  are  related  as  follows: 

Up  ^  power-factor,  9  »  reactive-factor,  then  with  sine  waves  of  voltage 
and  cturent, 

p«+fl«-  1. 
With  distorted  waves  of  voltage  and  current, 
i>*+(f  -  or  <  L 

(IV)  Saturation-Factor. 

57  The  Saturation-Factor  of  a  machine  is  the  ratio  of  a  small  percentage 
increase  in  field  excitation  to  the  corresponding  percentage  mcrease  m 
voltage  thereby  produced.  The  saturation-factor  is,  therefore,  a  criterion 
of  the  degree  of  saturation  attained  in  the  magnetic  circuits  at  any  ex- 
citation selected.  Unless  otherwise  specified,  however,  the  saturation- 
factor  of  a  machine  refers  to  the  excitation  existing  at  normal  rated 
speed  and  voltage.  It  is  determined  from  measurements  of  saturation 
znade  on  open  circuit  at  rated  speed. 

SS  The  Percentage  of  Saturation  of  a  machine  at  any  excitation  may 
be  found  from  its  saturation  curve  of  generated  voltage  as  ordinates. 
against  excitation  as  abscissas,  by  drawing  a  tangent  to  the  curve  at  the 
ordinate  corresponding  to  the  assigned  excitation,  and  extending  the 
tangent  to  intercept  the  axis  of  ordinates  drawn  through  the  origin.  The 
ratio  of  the  intercept  on  this  axis  to  the  ordinate  at  the  assigned  excita- 
tion, when  expressed  in  percentage,  is  the  percentage  of  saturation  and  is 
independent  of  the  scale  selected  for  excitation  and  voltage.  This  ratio 
is  equal  to  the  reciprocal  of  the  saturation-factor  at  the  same  excitation, 
deducted  from  unity.  Thus,  if /be  the  saturation-factor  and  p  the  per- 
centage of  saturation  ratio, 

,..-f 

(V)  Variation    and    Pulsation. 

W  The  Variation  in  Prime  Movers  which  do  not  give  an  absolutely 
uniform  rate  of  rotation  or  speed,  as  in  reciprocating  steam  engines^fc 
the  «^airi*^v*^  angular  displacement  in  position  of  the  revolving  member 


1454  TO.—ELECTRIC  POWER  AND  UGHTINC, 

ezpRSMed  in  degreec.  £rom  the  position  it  wouM  occupy  with  tmifbfia 

iDtation,  and  with  one  revolution  taken  as  860°. 
<(0        The  Pulsation  in  Prime  Movers  is  the  ratio  of  the  diflference  between 

the  maximum  and  minimum  velocities  in  an  engine-c3rcle  to  the  avcrasc 

velocity. 
41         The  VariaUan  in  Alternators  or  alternating-current  ciictiits  in  general 

is  the  maximum  difference  in  phase  of  the  generated  voltage  wave  from  a 

wave  of  absolutely  constant  frequencv,  expressed  in  electrical  degrees 

(one  cycle  equals  860^)  and  may  be  due  to  the  variation  of  the  prime 

mover. 

62  The  Pultation  in  Ahemators  or  alternating-current  circuits,  in  gen- 
eral, is  the  ratio  of  the  difference  between  maximum  and  minimum  fre- 
qtaency  during  an  en^e  cycle  to  the  average  frequency. 

63  Relation  of  Variation  in  jmme  mover  and  alternator: 

64  If  M  <-  number  of  pairs  of  poles,  the  variation  of  an  alternator  is  m 
times  the  variation  of  its  prime  mover,  if  direct-connected,  and  u/p  time* 
the  variation  of  the  prime  mover  if  rigidly  connected  thereto  in  the  ve- 
locity ratio  p, 

II.— PERFORMANCE  SPECIFICATIONS  AND  TESTS. 

A.— RATING. 

65  Rating  bjf  Output.  All  electrical  apparatus  should  be  rated  by  oatp>iii 
and  not  by  input.  Generators,  transformers,  etc..  should  be  rated  by 
electrical  output:  motors  bv  mechanical  output. 

66  Rating  in  Kilowatts.  Electrical  power  should  be  expressed  in  kilo- 
watts, except  when  otherwise  specified. 

67  Apparent  Power,  Kilovoit- Amperes.  Apparent  power  in  alternating^ 
current  circuits  shoxild  be  expressed  in  kilovolt-amperes  as  distinguished 
from  real  power  in  kilowatu.  When  the  power  factor  is  100  per  cent^ 
the  apparent  power  in  kilovolt-amperes  is  equal  to  the  kilowatts. 

68  The  Rated  (Full  Load)  Current  is  that  current  which,  with  the  rated 
terminal  voltage,  gives  the  rated  kilowatts,  or  the  rated  kik>volt-ampeiee. 
In  machines  in  which  the  rated  voltage  differs  from  the  no-load  voltage, 
the  rated  current  should  refer  to  the  former. 

69  Determination  of  Rated  Current.  The  rated  current  xxMy  be  de> 
termined  as  follows:  If  P  «  rating  in  watts,  or  apparent  watts  if  the 
power  factor  be  other  than  100  per  cent.,  and  E  <-  full -load  terminal 
voltage,  the  rated  current  per  terminal  is: 

p 

70  /  —  -^  in  a  direct-current  machine  or  single-phase  alternator. 

1      P 

71  /— — =: -r:  in  a  three-phase  alternator. 

V3    ^ 

1    P 
73         /  — =•  "^  in  a  two-phase  alternator. 

73  Normal  Conditions.  The  rating  of  machines  or  apparatus  diould  be 
based  upon  certain  normal  conditions  to  be  assumed  as  standard,  or  to  be 
specified.  These  conditions  include  voltage,  current,  power-factor,  frt- 
quency ,  wave  shape  and  speed ;  or  such  of  them  as  may  apply  in  each  par- 
ticular case.  Performance  tests  should  be  made  under  these  standard 
conditions  unless  otherwise  specified. 

74  a.  Power  Factor.  Alternating-current  apparatus  should  be  rated  in 
kilowatts,  at  100  per  cent  power  factor;  i.e.,  with  current  in  phase  with 
terminal  voltage,  unless  a  phase  displacement  is  inherent  in  the  apparatus 
or  is  specified.  If  a  power  factor  other  than  100  per  cent  is  specified, 
the  rating  should  be  expressed  in  kilovolt-amperes  and  ppwer  factor,  at 
rated  load. 

75  b.  Wave  Shape.  In  determining  the  rating  of  alternating-current  ma- 
chines or  apparatus,  a  sine  wave  shape  of  alternating  current  and 
voltage  is  assumed,  except  where  a  distorted  wave  shape  is  inherent  to 
the  apparatus.    See  Sees.  70-83. 

...  Ptoses.  The  rating  of  a  fuse  should  be  tne  maximum  current  which  it 
Will  continuously  carry. 
77         Circuit-Breakers.  The  rati^  of  a  circuit-breaker  should  be  the  i 
imum  current  which  it  is  designed  to  carry  continuously.. 


PERFORMANCE  SPECIFICATIONS  AND  TESTS,        14M 

78  a.  Note.  In  addition  theretOi  the  maximum  current  and  voltage  at 
which  a  fuse  or  a  circuit^breaker  will  open  the  circuit  should  be  specified. 
It  is  to  be  noted  that  the  behavior  ot  fuses  and  of  circuit-brc»akers  is 
much  influenced  by  the  amount  of  electric  power  available  on  the  circuit. 

B.— WAVE  SHAPE. 

79  The  Sin*  Wave  should  be  considered  as  standard,  except  where  a  dif- 
ference in  the  wave  form  from  the  sinusoidal  is  inherent  in  the  operation 
of  the  apparatus. 

80  A  Maximum  Dtviation  of  the  wave  from  sinusoidal  shape  not  exceed- 
ing 10  per  cent  is  permissible,  except  when  otherwise  specified. 

81  The  Deviation  of  wave  form  from  the  sinusoidal  is  measured  by  de- 
termining the  form  by  oscill^raph  or  wave  meter,  computing  therefrom 
the  equivalent  sine  wave  of  equal  length,  superposing  the  latter  upon  the 
observed  wave  in  such  a  manner  as  to  give  least  difference,  and  then 
dividing  the  maximum  difference  at  any  ordinate  by  the  maximum  value 
of  the  eouivalent  sine  wave. 

83  The  Equivalent  Sine  Wave  is  a  sine  wave  having  the  same  frequency 
and  the  same  effective  or  r.m.s.  (root  of  mean  square)  value  as  the  actual 
wave. 

83  Non-Sine  Waves.  The  phase  displacement  between  two  waves  which 
are  not  sine  waves,  is  that  phase  displacement  between  their  equivalent 
sine  waves  which  woxild  give  the  same  average  product  of  instantaneous 
values  as  the  actual  waves;  «'.#..  the  same  electro-dynamometer  reading. 

C— EFFICIENCY. 
(I) — Dbfinitions. 

84  The  Efficiency  of  an  apparatus  is  the  ratio  of  its  net  power  output 
to  its  gross  power  input. 

88  a.  Note.  An  exception  should  be  noted  in  the  case  of  storage  batteries 
or  apparatus  for  storing  energy  in  which  the  efficiency,  unless  otherwise 
qualined.  shotild  be  understood  as  the  ratio  of  the  energy  output  to  the 
energy  intake  in  a  normal  cycle.  An  exception  should  also  be  noted  in 
the  case  of  luminotis  sources. 

86  Apparent  Efficiency.  In  apparatus  in  which  a  phase  displacement  is 
inherent  to  their  operation,  apparant  efficiency  should  be  understood  as 
the  ratio  of  the  net  power  output  to  volt-ampere  input. 

87  a.  Note,  Such  apparatus  comprise  induction  motors,  reactive  syn- 
chronous converters,  synchronous  converters  controlling  the  voltage  of 
an  alternating-current  system,  self-exciting  synchronous  motors,  poten- 
tial regulators  and  open  magnetic  circuit  transformers,  etc. 

88  b.  Note.  Since  the  apparent  efficiency  of  apparatus  delivering  electric 
power  depends  upon  the  power-factor  of  the  load,  the  apparent  efficiency, 
unless  otherwise  specified,  should  be  referred  to  a  load  power-factor  of 
unity. 

(II) — ^Dbtbrmination   o»  Efpicibnct. 

89  Methods.  Efficiency  may  be  determined  bv  either  of  two  methods. 
viz.:  by  measurement  of  input  and  output;  or,  by  measurement  of  losses, 

90  a.  Method  of  Input  and  Output.  The  input  and  output  may  both 
be  measured  directly.  The  ratio  of  the  latter  to  the  former  is  the 
efficiency. 

91  h.  Method  by  Losses.  The  losses  may  be  measured  either  collectively 
or  individually.  The  total  losses  may  be  added  to  the  output  to  derive 
the  input,  or  subtracted  from  the  input  to  derive  the  output* 

92  Comparison  of  Methods.  The  output  and  input  method  is  preferable 
with  small  machines.  When,  however,  as  in  the  case  of  large  machines, 
it  is  impracticable  to  measure  the  output  and  input;  or  wien  the  per- 
centage of  power  loss  is  small  and  the  efficiency  is  nearly  unity,  the 
method  of  determining  efficiency  by  measuring  the  loMes  should  be 
followed. 

93  Electric  Power  should  be  measured  at  the  terminals  of  the  appa- 
ratus. In  tests  of  polyphase  machines,  the  measurement  of  power  should 
not  be  confined  to  a  single  circuit  but  should  be  extended  to  all  the  cir- 
cuits in  order  to  avoid  errore  of  unbalanced  loading. 

94  Mechanical  Power  in  machines  should  be  measured  at  the  pulley, 
gearing,  coupling,  etc.,  thus  excluding  the  loss  of  power  in, said  pulley 
gearing  or  coupling,  but  including  the  oearing  friction  and  windage.  Tue 


14M  T^.'-ELBCTRIC  POWER  AND  UGHTING. 

magnittide  of  bearing  frictkm  and  w^pdage  may  be  considered,  with  ooa* 
Btant  speed,  as  independent  of  the  load.  The  loss  of  power  in  the  belt  and 
the  increase  of  bearing  friction  due  to  belt  tension  shouM  be  exchidgri. 
Where,  however,  a  machme  is  mounted  upon  the  shaft  of  a  prime  mover, 
in  such  a  manner  that  it  cannot  be  separated  therefrom,  the  frktknal 
losses  in  bearings  and  in  windage,  which  ought,  by  definition,  to  be  included 
in  determining  the  efficiency,  should  be  excluded,  owing  to  the  practkal 
impossibility  of  determining  them  satisfactorily. 

95  In  Auxtliary  Apparatus,  such  as  an  exciter,  the  ix>wer  kwt  in  the 
auxiliary  apparatus  should  not  be  charged  to  the  principal  machine,  bet 
to  the  plant  consisting  of  principal  machine  and  auxiliary  apparatia 
taken  together.  The  plant  efficiency  in  such  cases  should  be  distinguished 
from   the   machine   efficiency. 

96  Normal  Conditums.  Efficiency  tests  should  be  made  tmder  nonoal 
conditions  herein  set  forth  and  which  are  to  be  assumed  as  standard. 
These  conditions  include  voltage,  current,  power-factor,  freauency.  ware 
shape,  speed  and  barometric  pressure,  temperature,  or  such  of  them  as 
may  apply  in  each  particular  case.  Performance  tests  should  be  made 
under  these  standard  conditions  unless  otherwire  specified.  See  Sees. 
73-76. 

97  a.  Temp9raturt.  The  efficiency  of  all  appcuatus.  except  such  as  may 
be  intended  for  intermittent  service,  should  be  either  measured  at,  or  re- 
duced to,  the  temperatiire  which  the  apparatus  assumes  under  continaous 
operation  at  rated  load,  referred  to  a  room  temperature  of  25^  C.  See 
Sees.  267-292. 

98  With  apparatus  intended  for  intermittent  service,  the  efficiency 
should  be  determined  at  the  temperature  assumed  under  specified  con- 
ditions. 

99  b.  Pawfr  Factor.  In  determining  the  efficiency  of  altematins-ctment 
apparatus,  the  electric  power  shotdd  be  measured  when  the  current  is  in 
phase  with  the  voltage,  unless  otherwise  specified,  except  when  a 
definite  phase  difference  is  inherent  in  the  apparatus,  as  in  induction 
motors,  mduction  generators,  freqtiency  converters,  etc^ 

100  c.  Wao9  Shap9.  In  electrical  apparatus,  the  sine  wave  should  be 
considered  as  standard,  except  where  a  difference  in  the  wave  form  Crofxc 
the  sinusoidal  is  inherent  in  the  operation  of  the  apparatus.  See  Sees. 
79-88. 

(Ill) — Mbasurbmbnt  or  Lossbs. 

101  Losses.  The  usual  sources  of  losses  in  electrical  apparatus  and  the 
methods  of  determining  these  losses  are  as  follows: 

(A) — Bbarino  Friction  and  Winoaob. 
103         The  magnitude  of  bearing  friction  and  windage  (which  nmy  be  con- 
sidered as  independent  of  the  load)  is  conveniently  measured  by  driving 
the  machine  from  an  independent  motor,  the  output  of  which  may  be 
suitably  determined.  See  Sec.  04. 

(B) — Commutator  Brush  Friction. 

103  The  magnitude  of  the  commutator  brush  friction  (whidi  may  be 
considered  as  indepednent  of  the  load)  is  determined  by  measuring  the 
difference  in  power  required  for  driving  the  machine  with  bruahes  on 
and  with  brxishes  off  (the  field  being  unexdted). 

(O — COLLECTOR-RINO   BrUSH    FrICTION. 

104  Collector-ring  brush  friction  may  be  determined  in  the  same  mannrf 
as  commutator  brush  friction.   It  is  ustially  negligible. 

(D) — ^Molecular  Magnbtic  Friction  and  Eddy  Currents. 

105  These  losses  include  those  due  to  molecular  masnetic  friction  and 
eddy  currents  in  iron  and  copper  and  other  metallic  parts,  also  the 
losses  due  to  currents  in  the  cross-connections  of  cross-connected 
armatures. 

106  In  Macfmus  these  losses  should  be  determined  on  open  circuit  sad 
at  a  voltage  equal  to  the  rated  voltage  -♦-  /  r  in  a  generator,  and  — 
/  r  in  a  motor,  where  I  denotes  the  current  strength  and  r  denotes  the 
mtemal  resistance  of  the  machine.  They  should  be  measured  at  the 
correct  speed  and  voltage,  since  they  do  not  usually  vary  in  any  deftute 
proportion  to  the  speed  or  to  the  voltage,     ized  by  V^jOOQUC 


PERFORMANCE  SPECIFICATIONS  AND  TESTS,        1467 

107  NoU.  The  Total  Losses  in  bearing  friction  and  windage,  bniih  fric- 
tion, magnetic  friction  and  eddv  currents  can,  in  general,  be  deter- 
mined by  a  single  measurement  by  driving  the  machine  with  the  field 
excited,  either  as  a  motor,  of  by  means  of  an  independent  motor. 

108  Rrtardation  Method.  The  no-lcMid  iron,  friction*  and  windage  losses 
may  be  segregated  by  the  Retardation  Method,  in  which  the  generator 
should  be  brought  up  to  full  speed  (or,  if  possible,  to  about  10  per 
cent,  above  full  speed)  as  a  motor,  and,  after  cutting  off  the  driving 
fK)wer  and  excitation,  frequent  readings  should  be  taken  of  speed  and 
time,  as  the  machine  slows  down,  from  which  a  speed-time  curve  can 
be  plotted.  A  second  curve  should  be  taken  in  the  same  manner,  but 
with  full  field  excitation;  from  the  second  curve  the  iron  lose^  may  be 
found  by  subtracting  the  losses  found  in  the  first  curve. 

109  The  speed -time  curves  can  be  plotted  automatically  by  belting  a 
small  separately  excited  generator  (say  1/10  kwO  to  the  generator 
shaft  and  connecting  it  to  a  recording  voltmeter.  When  the  retardation 
method  is  not  feasible,  the  frictional  losses  in  bearings  and  in  windage, 
which  ought,  bv  definition,  to  be  included  in  determining  the  efficiency, 
may  be  excluaed:  but  this  should  be  expressly  statea. 

(£) — Armaturb-Rbsistancb   Loss. 

1 10  This  loss  may  be  expressed  hy  p  Pr;  where  r  «  resistance  of  one 
armature  circuit  or  branch.  /  ">  the  current  in  such  armature  circuit  or 
branch,  and  p  »  the  number  of  armature  circuits  or  branches. 

(F) — Commutator  Brush  and  Brush-Contact  Rbsistancb  Loss. 

111  It  is  desirable  to  point  out  that  with  carbon  brushes  these  losses  may 
be  considerable  in  low-voltage  machines. 

(G) — Collector-Rino  and  Brush-Contact  Rbsistancb  Loss. 
113         This  loss  is  usually  negligible,  except  in  machines  of  extremely  low 
voltage  or  in  tmipolar  machines. 

(H) — Field  Excitation  Loss. 

113  With  separately  excited  fields,  the  loss  of  power  in  the  resistance  of 
the  field  coils  alone  should  be  considered.  With  either  shunt-  or  series- 
field  windings,  however,  the  loss  of  power  in  the  accompanying  rheostat 
should  also  be  included,  the  said  rheostat  being  considered  as  an 
essential  part  of  the  machine,  and  not  as  separate  auxiliary  apparatus. 

(/) — Load  Losses. 

114  The  load  losses  may  be  considered  as  the  difference  between  the 
total  losses  under  load  and  the  sum  of  the  losses  above  specified. 

115  a.  In  Commutating  Machines  of  small  field  distortion,  the  load 
losses  are  usually  trivial  and  may,  therefore,  be  neglected.  When, 
however,  the  field  distortion  is  large,  as  is  shown,  for  instance,  by  the 
necessity  for  shifting  the  brushes  between  no  load  and  full  load,  or  with 
variations  of  load,  these  load  losses  may  be  considerable,  and  should  be 
taken  into  account.  In  this  case  the  efficiency  may  be  determined 
either  by  input  and  output  measurements,  or  the  load  losses  may  be 
estimated  by  the  method  of  Sec.  116. 

116  6.  Estimation  of  Load  Losses.  While  the  load  losses  cannot  well 
be  determined  individually,  they  may  be  considerable  and.  therefore, 
their  joint  influence  should  be  determmed  by  observation.  This  can  be 
done  oy  operating  the  machine  on  short-circuit  and  at  full-load  current, 
that  is.  by  determining  what  may  be  called  the  "short-circuit  core  loss. 
With  the  low  field  intensity  and  great  lag  of  current  existing  in  this  case, 
the  load  losses  are  usually  greatly  exaggerated. 

117  One-third  of  the  short-circuit  core  loss  may,  as  an  approximation, 
and  in  the  absence  of  more  accurate  information,  be  assumed  as  the 
load  loss. 

(IV) — ^Efficiency  of  Different  Types  of  Apparatus. 

(A) — Direct-Current  Commutatino  Machines. 

118  In  Direct'Current  Commutating  Machines  the  losses  are: 

1 19  a.  Bearing  Friction  and  Windage.  See  measurement  of  Losses  (A), 
Sec.  102. 


1468  70,^ELECTRIC  POWER  AND  LIGHTING. 

120  fr.  MoUcuIar  MagnHic  Friction  and  Eddy  Cnmnts.  See  meftsaie- 
ment  of  Losses  (D)  Sec.  106. 

121  c.  Amuunr§  Rtsistanct  Losses.  See  Measuremeat  of  Losses   {£), 

Sec.  no. 

122  d.  Commutator  Brush  Friction.  See  Measurement  of  Losses  (&). 
Sec.   103. 

123  #.  Commutator  Brush  and  Brush  Contact  Rtsistanc0.  See  Mea»> 
tuement  of  Losses  (F)i  Sec.  111. 

124  /.  Fitid  Excitation  Loss.  See  Meastiretnent  of  Losses  (H),  S#c  US. 

125  c.  Load  Losses.  See  Measurement  of  Losses  (/),  Sec,  114. 

126  Note,  b  and  c  are  losses  in  the  armature  or  "armature  losses"; 
d  and  e  "commutator  losses";  /  "field  losses." 

(B) — ^Altbrnatino-Currbnt  Commutatzno  Macrikbs. 

127  In  Altematine-Currtnt  Commutatittg  Machines,  the  losses  are; 

128  a.  Bearing  Friction  and  Windagf.  See  Measurement  of  Losses  (A). 
Sec.  102. 

129  6.  Rotation  Loss,  measured  with  the  machine  at  open  circoit,  the 
brushes  on  the  commutator;  and  the  field  excited  by  alternating  cur- 
rent when  driving  the  machme  by  a  motor. 

130  This  loss  includes  molecxilar  msgnetic  friction,  and  eddy  currents, 
caused  by  rotation  through  the  magnetic  field,  /V  losses  in  cross-con- 
nections of  cross-connected  armatures,  Pr  and  other  losses  in  amoature- 
coils  and  armature-leads  which  are  short-circuited  by  the  brushes  as  far 
as  these  losses  are  due  to  rotation. 

131  c.  Alternating  or  Transformer  Loss.  These  losses  are  measured  by 
wattmeter  in  the  field  circuit,  under  the  conditions  of  test  b.  They 
include  molecular  magnetic  friction  and  eddy-currents  due  to  the  alter- 
nation of  the  magnetic  field,  TV  losses  in  cross-connections  of  cross-con* 
nected  armatures,  TV  and  other  losses  in  armature  coil  and  commutator 
l«uls  which  are  short-circuited  by  the  brushes,  as  far  as  these  losses  ars 
due  to  the  alteration  of  the  magnetic  flux. 

132  The  losses  in  armature  coils  and  commutator  leads  short-ctrcoited 
by  the  brushes,  can  be  separated  in  6,  and  c,  from  the  other  lotscs.  by 
nmning  the  machine  with  and  without  bruwes  on  the  commutator. 

133  d.  Pr  Loss,  Other  Load  Losses  in  armature  and  compensating  wind- 
ing and  Pr  loss  of  brushes,  measured  by  wattmeter  connected  across  the 
armature  and  compensating  winding. 

1 34  #.  Fieid  Excitation  Loss.    See  Measurement  of  Losses  (H) .  Sec.  118. 

135  /.  Commutator  Brush-Friction.  See  measurement  of  Looses  IB), 
Sec.  108. 

(O — StNCHRONOUS  CoifMUTAT!NO  MaCHXNBS. 

136  I.  In  Double-Current  Generators,  the  efficiency  (^  the  fw***.** 
should  be  determined  as  a  direct-current  generator,  and  also  as  an  alter* 
nating-ciurent  generator.  The  two  values  of  efficiency  may  be  different, 
and  fluould  be  clearly  distinguished. 

137  2.  In  Converters  the  losses  should  be  determined  when  driving  the 
machine  by  a  motor.    These  losses  are: 

138  a.  Bearing  Friction  and  Windage.  See  Measurement  of  Losses  (A), 
Sec.  102. 

139  b.  Molecular  Magnetic  Friction  and  Eddy  Currents.  See  Measure- 
ment of  Losses  {D),  Sec.  106. 

140  c.  Armature  Resistance  Loss.  This  loss  in  the  armature  is  qPr, 
where  /"direct  current  in  armature,  r* armature  resistance  snd  0,  a 
factor  which  is  equal  to  1.47  in  single-circuit  single-phase.  1.16  in  doui^ 
circuit  single-phase,  0.69  in  three-phase.  0.89  in  two-phase,  and  0.27  ts 
six-phase  converters. 

141  d.  Commutator-Brush  Friction.  See  Measurement  of  Losses  (£). 
Sec.  103. 

142  e.  Collector-Ring  Brush  Friction.  See  Measurement  of  Losses  (O 
Sec.  104. 

143  /.  Commutator-Brush  and  Brush-Contact  Resistance  Loss.  See 
Measurement  of  Losses  (F),  Sec.  111. 

144  g.  Collector-Ring  Brush-Contact  Resistance  Loss.  See  Measurement 
of  Losses  (G),  Sec.  112. 

145  h.  Field  Excitation  Loss.    See  Measurement  of  Losses  (H).  Sec.  IM 
■40         i.  Load  Losses.    These  can  generally  be  neglected,  owing  to  ibe 

absence  of  field  distortion.  r^r^^rrl/^ 

Digitized  by  VjOOv  IC 


PERFORMANCE  SPECIFICATIONS  AND  TESTS.         1450 

147  3.  The  Efficiency  of  Two  Similar  Cofwerters  may  be  determined  by 
operating  one  machine  as  a  converter  from  direct  to  alternating,  and 
the  other  as  a  converter  from  alternating  to  direct,  connecting  the  alter- 
nating sides  together,  and  measviring  the  difference  between  the  direct- 
ctarrent  input,  and  the  direct-current  output.  This  process  may  be 
modified  by  returning  the  output  of  the  second  machine  through  two 
boosters  into  the  first  machine  and  measuring  the  losses.  Another  modi- 
fication is  to  supply  the  losses  by  an  alternator  between  the  two  ma- 
chines, using  potential  regulators. 

(D) — Synchronous  Machinbs. 

148  In  Synchronous  Machines  the  losses  are: 

149  a.  Bearing  Friction  and  Windage.  See  Measurement  of  Losses  (A), 
Sec.  102. 

150  b.  Molecular  Maptetic  Friction  and  Eddy  Currents.  See  Measure- 
ment of  Losses  (D),  Sec.  105. 

IS!  c.    Armature  Resistance  Loss.     See  Measurement  of  Losses  (E). 

Sec.  110. 
152         d.  Collector-Ring  Brush  Friction.    See  Measiirement  of  Losses  (C), 

Sec.  104. 


1 53  e.  Collector-Ring  Brush  Contact  Resistance  Loss.    See  Measurement 
of  Losses  (G),  Sec.  112. 

154  /.  Field  Excitation  Loss.    See  Measurement  of  Losses  (H),  Sec.  113. 


of  Losses  (C;),  Sec. 

/.  Field  Excitai  

155  g.  Load  Losses.    See  Measurement  of  Losses  (/).  Sec.  114. 

(E) — Stationary  Induction  Apparatus. 

156  In  Stationary  Induction  Api^ratus,  the  losses  are: 

157  a.  Molecttlar  Magnetic  Frtction  and  Eddy  Currents  measured  at 
open  secondary  circuit,  rated  frequency,  and  at  rated  voltage  ~/r. 
where  /  —  rated  current,  r^- resistance  of  primary  circuit. 

155  b.  Resistance  Losses,  the  sum  of  the  /V  losses  in  the  primary  and 
in  the  secondary  windings  of  a  transformer,  or  in  the  two  sections  of  the 
coil  in  a  compensator  or  auto-transformer,  where  /  —  rated  current  in 
the  coil  or  section  of  coil,  and  r— resistance. 

159  c.  Load  Losses,  i.  e  ,  eddy  currents  in  the  iron  and  especially  in  the 
copper  conductors,  caused  by  the  current  at  rated  load.  For  practical 
purposes  they  may  be  determined  by  short-circuiting  the  secondary  of 
the  transformer  and  impressing  upon  the  primary  a  voltage  sufficient 
to  send  rated  load  current  through  the  transformer.  The  loss  in  the 
transformer  tmder  these  conditions  measured  by  wattmeter  gives  the 
load  losses +/V  losses  in  both  primary  and  secondary  coils. 

160  In  Closed  Magnetic  Circuit  Transformers,  either  of  the  two  circuits 
may  be  used  as  primary  when  determining  the  efficiency. 

161  In  Potential  Regulator s^  the  efficiency  should  be  taken  at  the  maxi- 
mtun  voltage  for  which  the  api^aratus  is  designed,  and  with  non-induct- 
ive load,  tmless  otherwise  specified. 

CF) — ^Rotary  Induction  Apparatus,  or  Induction  Machines. 
163         In  Rotary  Induction  Apparatus,  the  losses  are: 

163  a.  Bearing  Friction  and  Windage.  See  Measurement  of  Losses  {A), 
Sec.  102. 

164  b.  Molecular  Magnetic  Friction  and  Eddy  Currents  in  iron,  copper 
and  other  metallic  parts:  also  Pr  losses  which  may  exist  in  multiple- 
circxiit  windings,  a  and  b  together  are  determined  by  runnixig  the 
motor  without  load  at  rated  voltage,  and  measuring  the  power  input. 

165  c.  Primary  PR  Loss,  which  may  be  determined  by  measurement  of 
the  current  and  the  resistance. 

166  d.  Secondary  PR  Loss,  which  ma^  be  determined  as  in  the  primary, 
when  feasible:  otherwise,  as  in  squirrel-cage  secondaries,  this  loss  is 
measured  as  part  of  e. 

167  e.  Load  Losses;  i.  e.,  molecular  magnetic  friction,  and  eddy  currents 
in  iron,  copper,  etc.,  caused  by  the  stray  field  of  primary  and  secondary 
currents,  and  secondary  PR  loss  when  undeterminable  imder  id).  These 
losses  may  for  practical  purposes  be  determined  by  measuring  the  total 
power,  with  the  rotor  short-circuited  at  standstill  and  a  current  in  the 
primary  circuit  equal  to  the  primary  energy  current  at  full  load.  The 
loss  in  the  motor  under  these  conditions  may  be  assumed  to  be  equal  to 
the  load  losses +/V  losses  in  both  primary  and  secondary  coxls. 


IMO  TO.^ELECTRIC  POWER  AND  UGHTING. 

(Cr) — ^Umipolar  or  Acyclic  Machines. 

168  In  Uni^Iar  Machines,  the  losses  are: 

169  (a)  Bearing  Friction  and  Windage.  See  Measurement  of  Locses  (A), 
Sec.  102. 

170  (6)  Molecular  Magnetic  Friction  and  Eddy  Currents.  Sec  Mcasaxe* 
ment  of  Losses  (E).  Sec.  106. 

171  (c)  Armature  Resistance  Losses.  See  Measurement  of  Losses  (£). 
Sec.  110. 

173  (d)  Collector  Brush  Friction.  See  Measurement  of  Losses  (C). 
Sec.  104. 

173  (e)  Collector  Brush  Contact  Resistance.  See  Measurement  of  Losses 
(G).Sec.  112. 

174  (/)  Field-Excitation  as  in  Sec.  113.  See  Measurement  of  Losses  {H), 
Sec.  113. 

175  (g)  Load  Losses.    See  Measurement  of  Losses  (/).  Sec.  114. 

(H) — Rectifying  Apparatus,  Pulsating-Currbnt  Gbkbrators. 

176  This  Division  Inclttdes:  open-coil  arc  machines  and  mechanical  and 
other  rectifiers. 

177  In  Rectifiers  the  most  satisfactory  method  of  determining  the  effi- 
ciency is  to  measure  both  electric  input  and  electric  output  by  vatt- 
meter.  The  input  is  usually  inductive,  owing  to  phase  displacement 
and  to  wave  oistortion.  For  this  reason  the  power  factor  and  the 
apparent  efficiency  should  also  be  considered,  since  the  latter  may  be 
much  lower  than  the  true  efficiency.  The  power  consumed  by  auxiliary 
devices,  such  as  the  83rnchronous  motor  or  cooling  devices,  should  be 
included  in  the  electric  input. 

178  In  Constant-Current  Rectifiers,  transforming  from  constant  potential 
alternating  to  constant  direct  current,  by  means  of  constant-current 
transformmg  devices  and  rectifying  devices,  the  losses  in  the  transfonc- 
ing  devices  are  to  be  included  in  determining  the  efficiency  and  have  to 
be  measiu^d  when  operating  the  rectifier,  smce  in  this  case  the  losses 
may  be  greater  than  when  feeding  an  aJtematiiu;  secondary  circuit. 
In  constant-current  transforming  devices,  the  load  losses  may  be  con- 
siderable, and,  therefore,  should  not  be  neglected. 

179  In  Open  Coil  Arc  Machines,  the  losses  are  essentially  the  same  as  in 
direct-current  (closed  coil)  commutating  machines.  In  this  case,  how- 
ever, the  load  losses  are  usually  greater,  and  the  efficiency  should  prefer- 
ably be  measured  by  input-  and  output-test,  usin^  wattn^eteis  fn^ 
measuring  the  output.  In  alternating-current  rectifiers,  the  output 
should,  in  general,  be  measured  by  wattmeter  and  not  by  x-olt meter  and 
ammeter,  smce  owing  to  pulsation  of  current  and  voltage,  a  considerable 
discrepancy  may  exist  between  the  watts  and  volt-amperes.  U.  Iww- 
ever,  a  direct-current  and  an  alternating-current  meter  in  the  rectified 
circuit  (either  a  voltmeter  or  an  ammeter)  give  the  same  reading,  the 
output  may  be  measured  by  direct-current  voltmeter  and  ammeter. 
The  type  of  alternating-current  instrument  here  referred  to  should 
indicate  the  effective  or  root-of-mean-square  value  and  the  t3rpe  oi 
direct -current  instrument  the  arithmetical  mean  value,  which  would 
be  zero  on  an  altemating-cturent  circuit. 

(/) — ^Transmission  Lines. 

180  The  Efficiency  of  transmission  lines  should  be  measured  with  noa- 
inductive  load  at  the  receiving  end,  with  the  rated  receiving  volta^  and 
frequency,  also  with  sinusoidal  impressed  wave  form,  except  where 
expressly  specified  otherwise,  and  with  the  exclusion  of  transformers  or 
other  apparatus  at  the  ends  of  the  line. 

(J) — Phase-Displacing  Apparatus. 

181  In  Apparatus  Producing  Phase  Displacement  as,  for  example, 
synchronous  compensators,  exciters  of  induction  generators,  reactors, 
condensers,  polanzation  cells,  etc.,  the  efficiency  should  be  understood 
to  be  the  ratio  of  the  volt-amperes  minus  power  loss  to  the  volt-amperes. 

182  The  Efficiency  may  be  calculated  by  determining  Uie  losses,  sob* 
tracting  them  from  the  volt-amperes,  and  then  dividing  the  difference 
by  the  volt-amperes. 

183  In  Syndtronous  CompenscUors  and  exciters  of  induction  gennatofs. 
the  determination  of  losses  is  the  same  as  in  other  syBchronous  n^- 
chines.  Digitized  by  V^OOg le 


PERFORMANCE  SPECIFICATIONS  AND  TESTS.         1461 

184  In  Rtactors  the  lossea  are  molecular  magnetic  friction,  eddy  losses 
and  Pr  loss.  They  should  be  meastired  hy  wattmeter.  The  efiKciency  of 
reactors  should  be  determined  with  a  sme  wave  of  impressed  voltage 
except  where  expressly  specified  otherwise. 

185  In  C<m<Uns9rs,  the  losses  are  due  lo  dielectic  hysteresis  and  leakage, 
and  should  be  determined  by  wattmeter  with  a  sine  wave  of  voltage. 

186  In  Polaritation  Cells,  the  losses  are  those  due  to  electric  resistivity 
and  a  loss  in  the  electrolyte  of  the  nattve  of  chemical  hysteresis.  These 
losses  may  l?e  considerable.  They  depend  upon  the  frequency,  voltage 
and  temperature,  and  should  be  determined  with  a  sine  wave  of  im- 
pressed voltage,  except  where  expressly  specified  otherwise. 

D.— REGULATION. 
(I) — Dbpinitions. 

187  DefiniiioH.  The  regulation  of  a  machine  or  apparatus  in  regard  to 
some  characteristic  quantity  (such  as  terminal  voltage,  current  or 
speed)  is  the  ratio  of  the  deviation  of  that  quantity  from  its  normal 
value  at  rated  load  to  the  normal  rated  load  value.  The  term  "regula- 
tion," therefore,  has  the  same  meaning  as  the  term  "inherent  regula- 
tion." occasionally  used. 

188  Constant  Standard.  If  the  characteristic  quantity  is  intended  to  re- 
main constant  (*.£.,  constant  voltage,  constant  sp«ed.  etc.)  between 
rated  load  and  no  bad.  the  regulation  is  the  ratio  of  the  maximiun  varia- 
tion from  the  rated-Ioad  value  to  the  no-load  value. 

189  Varying  Standard.  If  the  characteristic  quantity  is  intended  to 
vary  in  a  definite  manner  between  rated  load  and  no  load,  the 
regulation  is  the  ratio  of  the  maximum  variation  from  the  specified 
condition  to  the  normal  rated-load  value. 

190  (a)  Note. — If  the  law  of  the  variation  (in  voltage,  ciurent,  speed, 
etc.)  Detween  rated-load  and  no-load  is  not  specified ,  it  should  be 
assumed  to  be  a  simple  linear  relation;  i.  #..  one  tmdergoing  imiform 
variation  between  rated-load  and  no-load. 

191  (6)  Note. — ^The  regulation  of  an  apparatus  may.  therefore,  differ 
according  to  its  qualification  for  use.  Thus,  the  regulation  of  a  com- 
pound-wotmd  generator  specified  as  a  constant-potential  generator, 
will  be  different  from  that  which  it  possesses  when  specified  as  an  over- 
compounded  generator. 

192  In  Constant-Potential  Machines,  the  regiilation  is  the  ratio  of  the 
maximum  difference  of  terminal  voltage  from  the  rated-load  value 
(occurring  within  the  range  of  rated  load  to  open  circuit)  to  the  rated- 
load  terminal  voltage. 

193  In  Constant-Current  Machines,  the  regulation  is  the  ratio  of  the 
maximum  difference  of  current  from  the  rated-load  value  (occurring 
within  the  range  from  rated-load  to  short-circuit,  or  minimum  limit  of 
operation),  to  the  rated-load  current. 

194  In  Constant-Power  Apparatus,  the  regtilation  is  the  ratio  of  maxi- 
mum difference  of  power  from  the  rated-load  value  (occurring  within 
the  range  of  operation  specified)  to  the  rated  power. 

195  In  Constant-Speed  Direct-Current  Motors  and  Induction  Motors  the 
regulation  is  the  ratio  of  the  maximum  variation  of  speed  from  its 
rated-load  value  (occurring  within  the  range  from  rated-load  to  no-load) 
to  the  rated-load  speed. 

196  The  regulation  of  an  induction  motor  is,  therefore,  not  identical  with 
the  slip  of  the  motor,  which  is  the  ratio  of  the  drop  in  speed  from 
synchronism,  to  the  synchronous  speed. 

197  In  Constant- Potential  Transformers,  the  regulation  is  the  ratio  of 
the  rise  of  secondary  terminal  voltage  from  rated  non-inductive  load  to 
no-load  (at  constant  primary  impressed  terminal  voltage)  to  the 
secondary  terminal  voltage  at  rated  load. 

198  In  Over-Compounded  Machines,  the  reflation  is  the  ratio  of  the 
maximum  difference  in  voltage  from  a  straight  line  connecting  the  no- 
load  and  rated-load  values  of  terminal  voltage  as  function  of  the  load 
current,  to  the  rated-load  terminal  voltage. 

199  In  Converters,  Dynamotors,  Motor-Generators  and  Frequency  Con- 
verters, the  regulation  is  the  ratio  of  the  maximum  difference  of  terminal 
voltage  at  the  output  side  from  the  rated-load  voltage,  to  the  rated- 
load  voltage  on  the  output  side.  .      ,         *,      # 

200  In  Transmission  Lines,  Feeders,  etc.,  the  regulation  is  the  ratio  o« 


1402  70.^ELECTRIC  POWER  AND  LIGHTING, 

the  maximum  voltage  difference  at  the  receiving  end.  between  rated 
non-inductive  load  and  no-load  to  the  rated-load  voltage  at  the  re- 
ceiving end  (with  constant  voltage  impressed  upon  the  ■^**«^^g  end). 

201  In  St€am  Enginss,  the  regulation  is  the  ratio  of  the  mazinnsn 

variation  of  speed  in  passing  slowly  from  rated-load  to  no-load  (with 
constant  steam  presstue  at  the  throttle)  to  the  rated-load  speed.  For 
variation  and  pulsation,  see  Sees.  69-64. 

303  In  a  Hydraulic  Turbint  or  Othtr  Wattr-Motoft  the  regulation  is  tl» 
ratio  of  the  maximum  variation  of  speed  in  passing  slowly  fct>m  rated- 
load  to  no-load  (at  constant  head  of  water;  t.  #.,  at  constant  diflerence 
of  level  between  tail  race  and  head  race),  to  the  rated-load  speed.  For 
variation  and  pulsation,  see  Sees.  69-64. 

303  In  a  GentraiGr-UnU,  consisting  of  a  generator  united  with  a  prime- 
mover,  the  regulation  should  be  determmed  at  constant  oonditxns  of 
the  prime-mover;  i.  #..  constant  steam  pressure,  head,  etc.  It  includes 
the  mherent  speed  variations  of  the  prime-mover.  For  this  reason  ibe 
regulation  of  a  genera tor-tmit  is  to  be  distinguished  from  the  reffulatka 
of  either  the  prime-mover,  or  of  the  generator  contained  in  it«  when 
taken  separately. 

(II) — Conditions  for  and  Tests  of  Rboulation. 

304  Spetd.  The  Regulation  of  Generators  is  to  be  detennined  at  ocn- 
stant  speed,  and  of  alternating  apparattis  at  constant  impressed  fre- 
quency. 

305  Non-Inductive  Load.  In  apparattis  generating,  transforming  or 
transmitting  alternating  currents,  regulation  tdiould  be  tmderstood  to 
refer  to  non-inductive  load,  that  is,  to  a  load  in  which  the  current  is  in 
phase  with  the  e.m.f.  at  the  output  side  of  the  appcuatus,  except  where 
expressly  specified  otherwise. 

306  Wave  Form.  In  alternating  apparatus  receiving  electric  power. 
regulation  should  refer  to  a  sine  wave  of  e.m.f.,  except  where  expressly 
specified  otherwise. 

307  Excitation.  In  commutating  machines,  rectifjring  machines,  and 
synchronous  machines,  such  as  direct-current  generators  and  rootors, 
alternating-current  and  polyphase  generators,  the  regulation  is  to  be 
determined  under  the  followins^  conditions: 

(I)  At  constant  excitation  m  separately  excited  fields. 
i2)  With  constant  resistance  in  shunt-neld  circuits^  and 
(3)  With  constant  resistance  shunting  series-field  circuits;  i,  «.,  the 
field  adjustment  should  remain  constant,  and  should  be  so  chosen  as  to 
give  the  required  full-load  voltage  at  full-load  current. 
3(M         Impedance  Ratio.    In  alternating-current  apparatus,  in  addition  to 
the  non-inductive  regulation  .the  impedance  ratio  of  the  apparatus  shoold 
be  specified;    i.  e.,  the  ratio  of  the  voltage  consumed  by  the  total 
internal  impedance  of  the  apparatus  at  fun-load  current,  to  its  rated 
full-load  voltage.     As  far  as  possible,  a  sinusoidal  current  should  be 
used. 

309  Compntation  of  Regulation.  When  in  synchronous  machines  the 
regulation  is  computed  from  the  terminal  voltage  and  impedance 
voltage,  the  exciting  ampere-turns  corresponding  to  terminal  voltage 
plus  armature-resistance-drop,  and  the  ampere-turns  at  short-circtzit 
corresponding  to  the  armature-impedance-orop.  should  be  combined 
vectorially  to  obtain  the  resultant  ampere-turns,  and  the  correspoDdxog 
internal  e.  m.  f.  should  be  taken  from  the  saturation  curve. 

E.— INSULATION. 
(I) — Insulation  Rbsistancb. 

3 1 0  Insulation  Resistance  is  the  ohmic  resistance  o£Fered  by  an  insniatint 
coating,  cover,  material  or  support  to  an  impressed  voltage,  tending  to 
produce  a  leakage  of  current  through  the  same. 

311  Ohmic  Resistance  and  Dielectric  Strength.  The  ohmic  resistance  ot 
the  insulation  is  of  secondary  importance  only,  as  compared  with  tbe 
dielectric  strength,  or  resistance  to  rupture  by  high  voltage.  Since  thf 
ohmic  resistance  of  the  insulation  can  be  very  greatly  increased  by 
baking,  but  the  dielectric  strength  is  liable  to  be  weakened  thereby,  it 
18  preferable  to  specify  a  high  dielectric  strength  rather  than  a  hiffc 
»"»«lation  resistance.  The  high-voltage  test  for  dielectric  ctxvogtb 
should  always  be  applied.  ^  i 

Digitized  by  VjOOQ  IC 


PERFORMANCE  SPECIFICATIONS  AND  TESTS.         1463 

212  Recommended  Value  of  Resistance.  The  insulation  resistance  of 
complete  apparattts  should  be  such  that*the  rated  voltage  of  the 

apparatus  which  will  not  send  more  than  <  aaq  qqq  oi  the  rated-load 

current,  at  the  rated  terminal  voltage,  through  the  insulation.    Where 
the  value  found  in  this  way  exceeds  1  megohm,  it  is  usually  sufficient. 

213  Insulation  Resistance  Tests  should,  if  possible,  be  made  at  the  pres- 
sure for  which  the  apparatus  is  designed. 

(II) — ^DlBLBCTRIC  StRBNGTH. 

(A) — ^Test  Voltaobs. 

214  Definition.  The  dielectric  strength  of  an  insulating  wall,  coating 
cover  or  path  is  measured  by  the  voltage  which  must  be  applied  to  it 
in  order  to  effect  a  disruptive  discharge  through  the  same. 

215  Basis  for  Determining  Test  Voltages.  The  test  voltage  which  should 
be  applied  to  determine  the  suitability  of  insulation  for  commercial 
operation  is  depesident  upon  the  kind  and  size  of  the  apparatus  and 
its  normal  operating  voltage,  upon  the  nature  of  the  service  in  which  it 
is  to  be  used,  and  the  severity  of  the  mechanical  and  electrical  stresses 
to  which  it  may  be  subjected.  The  voltages  and  other  conditions  of  test 
which  are  recommended  have  been  determined  as  reasonable  and 
proper  for  the  great  majority  of  cases  and  are  proposed  for  general 
adoption,  except  when  specific  reasons  make  a  modification  desirable. 

216  Condition  of  Apparatus  to  be  Tested.  Commercial  tests  should,  in 
general,  be  made  with  the  completely  assembled  apparatus  and  not 
with  individual  parts.  The  apparatus  should  be  in  sood  condition  and 
high- voltage  tests,  tmless  otherwise  specified,  should  be  applied  before 
the  machine  is  put  into  commercial  service,  and  should  not  be  applied 
when  the  insulation  resistance  is  low  owing  to  dirt  or  moisture.  High- 
voltage  tests  should,  in  general,  be  made  at  the  temperature  assumed 
under  normal  operation.  High-voltage  tests  considerably  in  excess  of 
the  normal  voltages  to  determine  whether  specifications  are  fulfilled 
are  admissible  on  new  machines  only. 

217  Points  of  Application  of  Voltage.  The  test  voltage  should  be  suc- 
cessivelyr  applied  between  each  electric  circuit  and  all  other  electric 
circuits  including  conducting  material  in  the  apparatus. 

218  The  Frequency  of  the  alternating-current  test  voltage  is,  in  general, 
immaterial  within  commercial  ranges.  When,  however,  the  frequency 
has  an  appreciable  effect,  as  in  alternating-current  apparatus  of  high 
voltage  and  considerable  capacity,  the  rated  frequency  of  the  apparatus 
should  be  used. 

219  Table  of  Testing  Voltages.  The  following  voltages  are  recommended 
for  testing  all  apparatus,  lines  and  cables,  by  a  continued  application 
for  one  mmute.  The  test  should  be  with  alternating  voltage  having  an 
cfTective  value  (or  root  mean  square  referred  to  a  sine  wave  of  voltage) 
given  in  the  table  and  preferably  for  tests  of  alternating  apparatus  at 
the  normal  frequency  of  the  apparatus. 

Rated  Terminal  Voltage  of  Rated  Testing 

Circuit.  Output.  Voltage. 

220  Not  exceeding  400  volts Under  10  kw 1.000  volts, 

400     *'     10  kw.  and  over 1.600     ** 

400  and  over,  but  less  than  800  volts.  Under  10  kw 1,600     ** 

400        "  *'         800    "       10  kw.  and  over 2.000     " 

800        *'  **      1,200    *•      Any 3.600     " 

1.200        "  "      2.600    "      Any 5,000     " 

2,500        "  Any  . .  Double  the  normal  rated 

Voltages. 

221  Exception. — Transformers.  Transforme«  having  primary  pressures 
of  from  650  to  6,000  volts,  the  secondaries  of  which  are  directly  con- 
nected to  consumption  circuits,  should  have  a  testing  voltage  of  10,000 
volts,  to  be  applied  between  the  primary  and  secondary  windings,  and 
also  between  the  primary  winding  and  the  core. 

222  Exception. — Field  Windings.  The  tests  for  field  windings  should  be 
based  on  the  rated  voltage  of  the  exciter  and  the  rated  output  of  the 
machine  of  which  the  coifs  are  a  part.  Field  windings  of  synchronous 
motors  and  converters,  which  are  to  be  started  by  applying  alternating 


1404  70.— ELECTRIC  POWER  AND  UGHTING. 

cttrrent  to  the  armature  when  the  field  is  not  excited  and  a  high  voltaic 
is  induced  in  the  field  windings,  should  be  tested  at  6.000  volts. 

333  Rattd  Terminal  Voltage. — Definition.  The  rated  tenninal  voltsf: 
of  circuit  in  the  above  table,  means  the  voltage  between  the  conducted 
of  the  circuit  to  which  the  apparatus  to  be  tested  is  to  be  connected.— 
tor  instance,  in  three-phase  circuits  the  delta  voltage  should  be  takes 
In  the  following  specinc  cases,  the  rated  terminal  voltage  of  the  circclt 
is  to  be  determined  as  specified  in  ascertaining  the  testing  voltage: 

334  (a)  Transformers.  The  test  of  the  insulation  between  the  ptiscMrj 
and  secondary  windings  ot  transformers,  is  to  be  the  same  as  that 
between  the  high-voltage  winding  and  core,  and  both  tests  ^kouid  be 
made  simultaneously  by  connecting  the  low-tension  winding  and  cose 
together  during  the  test.  If  a  voltage  equal  to  the  specined  testis^ 
voltage  be  induced  in  the  high-tension  winding  of  a  transformer  it  taaj 
be  used  for  insulation  tests  instead  of  an  independently  induced  voltage. 
These  tests  should  be  made  first  with  one  end  and  then  with  the  other 
end  of  the  high-tension  winding  connected  to  the  low-tension  winding 
and  to  the  core. 

335  (b)  Constant-Current  Apparatus.  The  testing  voltage  is  to  be  based 
upon  a  rated  terminal  voltage  equal  to  the  maximum  voltage  which 
may  exist  at  open  or  closed  circuit. 

336  (c)  Apparatus  in  Series.  For  tests  of  machines  or  apparatus  to  be 
operated  in  series,  so  as  to  employ  the  sum  of  their  separate  voltages 
the  testing  voltage  is  to  be  based  upon  a  rated  terminaJ  voltage  equal 
to  the  sum  of  the  separate  voltages  except  where  the  frames  of  the 
machines  are  separately  insulated,  both  from  the  ground  and  froc: 
each  other,  in  which  case  the  test  for  insulation  between  machinrs 
should  be  based  upon  the  voltage  of  one  machine,  and  the  test  between 
each  machine  and  ground  to  be  based  upon  the  total  voltage  of  the  series 

(B) — Mbthods  op  Testing. 

337  Classes  of  Tests.  Tests  for  dielectric  strength  cover  such  a  wide 
range  in  voltage  that  the  apparatus,  methods  and  precautions  whick 
are  essential  in  certain  cases  do  not  apply  to  others.  For  conveniesce, 
the  tests  will  be  separated  into  two  classes: 

33S  Class  1.  This  class  includes  all  apparatus  for  which  the  test  voltage 
does  not  exceed  10  kilovolts.  tmless  th?  apparatus  is  of  very  large  static 
capacity,  e.  g.,  a  large  cable  system.  This  '^lass  also  includes  all  appazstv 
of  small  static  capacity,  such  as  line  insuictors,  switches  and  tne  ^ke, 
for  all  test  voltages. 

339  Method  of  Test  for  Class  1.  The  test  volta^  is  to  be  continisooslr 
applied  for  the  prescribed  interval. — (one  mmute.  tmless  otherwise 
specified).  The  test  voltage  may  be  taken  from  a  constant-potentisl 
source  and  applied  directly  to  the  apparatus  to  be  tested,  or  it  may  be 
raised  gradually  as  specified  for  tests  under  Class  2. 

330  Class  2.    This  class  includes  all  apparatus  not  included  in  Qass  1. 

331  Method  of  Test  for  Class  2.  The  test  voltage  is  to  be  raraed  to  the 
required  value  smoothly  and  without  sudden  large  increments  and  is 
then  to  be  continuously  applied  for  the  prescribed  interval. — (one 
minute,  unless  otherwise  specified),  and  then  gradually  decreased. 

333  Conditions  and  Precautions  for  Class  1  aind  Class  2.  The  foUowisff 
apply  to  all  tests: 

333  The  Wave  Shape  should  be  approximatel3r  sinusoidal  arMi  the 
apparatus  in  the  testing  circuits  should  not  materially  distort  this  wave. 

334  The  Supply  Circuit  should  have  ample  current-supply  capacity  so 
that  the  charging  current  which  may  be  taken  by  the  apparatus  under 
test  will  not  materially  alter  the  wave  form  nor  materially  affect  tl» 
test  voltage.    The  circuit  should  be  free  from  accidental  interruptsoos^ 

335  Resistance  or  Inductance  in  series  with  the  primary  of  a  ratfii^ 
transformer  for  the  purpose  of  controlling  its  voltage  is  liable  aericwsiT 
to  affect  the  wave  form,  thereby  causing  the  maximum  value  of  the 
voltage  to  bear  a  different  and  unknown  ratio  to  the  root  mean  square 
value.  This  method  of  voltage  adjustment  is.  therefore,  in  general. 
undesirable.  It  may  be  noted  that  if  a  resistance  or  inductance  ^ 
employed  to  limit  the  current  when  burning  out  a  fault,  such  re«$tance 
or  inductance  should  be  short-circuited  during  the  regular  voltage  tesi 

*30  The  Insulation  under  test  should  be  in  normal  condition  as  to  drr* 
ness  and  the  temperature  should,  when  possible,  be  that  readted  ic 
normal  service. 


PERFORMANCE  SPECIFICATIONS  AND  TESTS.        1465 

2J7  Additional  Conditions  and  Precautions  for  Class  2.  The  following 
conditions  and  precautions,  in  addition  to  the  foregoing,  apply  to  tests 
of  apparatus  included  in  Class  2. 

238  Sudden  Increment  of  Testing  Voltage  on  the  apparatus  under  test 
shotild  be  avoided,  particularly  at  high  voltages  and  with  apparatus 
having  considerable  capacity,  as  a  momentarily  excessive  rise  in  testing 
voltage  will  result. 

239  Sudden  Variations  in  Testing  Voltage  of  the  circuit  supplying  the 
voltage  during  the  test  should  be  avoided  as  they  are  likely  to  set  up 
injurious  oscillation. 

240  Good  Connections  in  the  circuits  supplying  the  test  voltage  are 
essential  in  order  to  prevent  injurious  high  frequency  disturbances  from 
being  set  up.  When  a  heavy  current  is  carriea  by  a  small  water  rheo- 
stat, arcing  may  occur,  causing  high-frequency  disturbances  which 
should  be  carefull/  avoided. 

241  Transformer  Coils.  In  high-tension  transformers,  the  low-tension 
coil  should  preferably  be  connected  to  the  core  and  the  groimd  when 
the  high-tension  test  is  being  made,  in  order  to  avoid  the  stress  from 
low-tension  to  core,  which  would  otherwise  result  through  condenser 
action.  The  various  terminals  of  each  winding  of  the  high-tension 
transformer  tmder  test  should  be  connected  together  during  the  test  in 
order  to  prevent  undue  stress  on  the  insulation  between  turns  or 
sections  of  the  winding  in  case  the  high-voltage  test  caxisea  a  break- 
down. 

(O — Methods  for  Measuring  the  Test  Voltage. 
142        For  Measuring  the  Test  Voltage,  two  instruments  are  in  common 
use,  (1)  the  spark  gap,  and  (2)  the  voltmeter. 

243  1.  The  Spark  Gap  is  ordinarily  adjusted  so  that  it  will  break  down 
with  a  certain  predetermined  voltage,  and  is  connected  in  parallel  with 
the  insulation  under  test.  It  ensures  that  the  voltage  applied  to  the 
insulation  is  not  greater  than  the  break-down  voltage  of  tne  spark  gap. 
A  given  setting  of  the  spark  gap  is  a  measure  of  one  definite  voltage, 
and,  as  its  operation  depends  upon  the  maximum  value  of  the  voltage 
wave,  it  is  independent  of  wave  form  and  is  a  limit  on  the  maximum 
stress  to  which  the  insulation  is  subjected.  The  spark  gap  is  not  con- 
veniently adapted  for  comparatively  low  voltages. 

244  In  Spark-Gap  Measurements,  the  spark  gap  may  be  set  for  the 
required  voltage  and  the  auxiliary  apparatus  adjusted  to  give  a  voltage 
at  which  this  spark  gap  just  breaks  down.  This  spark  gap  should  then 
be  adjusted  for,  say,  10  per  cent  higher  voltage,  and  the  auxiliary 
apparatus  aeain  adjusted  to  give  the  voltage  of  the  former  breakdown, 
wluch  is  to  be  the  assumed  voltage  for  the  test.  This  voltage  is  to  be 
maintained  for  the  required  interval. 

245  The  Spark  Points  should  consist  of  new  sewing  needles,  supported 
axially  at  the  ends  of  linear  conductors  which  are  each  at  least  twice  the 
l^gth  of  the  gap.  There  should  be  no  extraneous  body  near  the  G[ap 
within  a  radius  of  twice  its  length.  A  table  of  approximate  strikmg 
distances  is  given  in  Appendix  D.  This  table  should  be  used  in  con- 
nection with  tests  made  by  the  spark-gap  methods. 

246  A  Non-inductive  Resistance  of  about  one-half  ohm  per  volt  should  be 
inserted  in  series  with  each  terminal  of  the  gap  so  as  to  keep  the  discharge 
current  between  the  limits  of  one-quarter  ampere  and  2  amperes.  The 
purpose  of  the  resistance  is  to  limit  the  current  in  order  to  prevent  the 
surges  which  might  otherwise  occur  at  the  time  of  break-down. 

247  2.  The  Voltmeter  gives  a  direct  reading,  and  the  different  values  of 
the  voltage  can  be  read  during  the  application  and  duration  of  the  test. 
It  is  suitable  for  all  voltages,  and  does  not  introduce  disturbances  into 
the  test  circuit. 

24S  In  VoUmeter  Measurements,  the  voltmeter  should,  in  general,  derive 

its  voltage  from  the  high-tension  testing  circuit  either  directly  or  through 
an  auxiliary  ratio  transformer.  It  is  permissible,  however,  to  measure 
the  voltage  at  other  places, — ^for  example,  on  the  primary  of  the  trans- 
former, provided  the  ratio  of  transformation  does  not  materially  vary 
during  tne  test;  or  that  proper  accotmt  is  taken  thereof. 

149  Spark  Gap  and  Voltmeter.    The  spark  gap  may  be  employed  as  a 

check  upon  the  voltmeter  used  in  high-tension  tests  in  order  to  de- 
termine the  transformation  ratio  of  the  transformer,  the  variation  from 
the  sine  wave  form  and  the  like.    It  is  also  useful  in  conjunctKm  witii 


1460  -m.—ELECTRIC  POWER  AND  UGHTING. 

voltmeter  measurements  to  limit  the  stress  applied  to  the  insulating 
material. 

(D) — Apparatus  for  Supplying  Test  Voltage. 

250  The  Gtntrator  or  Circuit  supplying  voltage  for  the  test  should  have 
ample  current-carrying  capacity,  so  that  the  current  whi^  may  be 
taken  for  charging  the  apparatus  to  be  tested  will  not  materially  aher 
the  wave  form  nor  othe^Hse  materially  change  the  voltage. 

The  Testing  Transformtr  should  be  such  that  its  ratio  of  trans- 
formation does  not  vary  more  than  10  per  cent  when  delivering  the 
charging  current  required  by  the  apparatus  under  test.  (This  may  be 
determined  by  short-circuiting  the  secondaxv  or  high  voltage  windicg 
testing  transformer  and  supplying  1/10  of  the  primary  voltage  to  thr 
primary  under  this  condition.  The  primarv  current  that  flows  under 
this  condition  is  the  maximum  which  should  be  permitted  in  xegula? 
dielectric  tests.) 

251  The  Voltage  Control  may  be  secured  in  either  of  several  irays, 
which,  in  order  of  preference,  are  as  follows: 

252  1.  By  generator  field  circuit. 

253  2.  By  magnetic  commutation. 

254  8.  By  change  in  transformer  ratio. 

255  4.  B^  resistance  or  choke  coils. 

256  In  Generator  Voltage  Control,  the  voltage  of  the  genetatbr  8hou3d 
preferably  be  about  its  approximate  normal  rated-load  value  when  tlv 
full  testing  voltage  is  attained,  which  reqtiires  that  the  ratio  €d  the 
raising  transformer  be  such  that  the  full  testing  voltage  is  reached  whes 
the  generator  voltage  is  normal.  This  avoids  the  instability  in  the  en- 
erator  which  may  occur  if  a  considerable  leading  current  is  tun 
from  it  when  it  has  low  voltage  and  low  field  current. 

257  In  Magnetic  Commutation,  the  control  is  effected  by  shunting  the 
magnetic  nux  through  a  secondary  coil  so  as  to  vary  the  inductic« 
through  the  coil  and  the  voltage  induced  in  it.  The  shunting  should  be 
effected  smoothly,  thus  avoiding  sudden  changes  in  the  induced  voltage. 

258  In  Transformer  Voltage  Control,  by  change  of  ratio,  it  is  neces- 
sary that  the  transition  from  one  step  to  another  be  made  without  inter- 
ruption of  the  test  voltas^.  and  by  steps  sufficiently  small  to  prevent 
stirges  in  the  testing  circuit.  The  necessity  of  this  precaution  is  greater 
as  the  inductance  or  the  static  capacity  of  the  apparatus  in  the  testing 
cinniit  under  test  is  greater. 

259  When  Resistance  Coils  or  Reactors  are  used  for  voltage  control,  i: 
is  desirable  that  the  testing  voltage  should  be  secured  when  the  coc- 
trolling  resistance  or  reactance  is  very  nearly  or  entirely  out  of  circuit  ir 
order  that  the  disturbing  effect  upon  the  wave  form  which  results  mav 
be  negligible  at  the  highest  volatge. 

F.— CONDUCTIVITY. 

260  Copper.  The  conductivity  of  copper  in  electric  wires  and  cabki 
should  not  be  less  than  98^  of  Matthiessen's  standard  of  conductivity, 
as  defined  in  the  Copper  W  ire  Table  of  the  American  Institute  of  Electn- 
cal  Engineers.     [See  Table  1.  page  1388.] 

G.— RISE  OP  TEMPERATURE. 
(I) — Measurbuent  of  Tbiipbraturb. 
(A) — Methods. 

261  There  are  two  methods  in  common  use  for  determining  the  rise  ic 
temperature,  viz. :  (1)  by  thermometer,  and  (2)  by  increase  m  resisiaace 
of  an  electric  circuit. 

262  1.  By  Thermomet^.  The  following  precautknis  diould  be  observed 
in  the  use  of  thermometers: 

263  a.  Protection.  The  thermometers  indicating  the  room  tempecatare 
should  be  protected  from  thermal  radiation  emitted  by  heatea  bodks. 
or  from  draughts  of  air  or  from  temporary  fluctuations  <A  tempera- 
ture. Several  room  thermometers  diould  be  used.  In  using  the  thermo- 
meter by  applying  it  to  a  heated  part,  care  should  be  taken  so  to  pfo- 
tect  its  bulb  as  to  prevent  radiation  from  it.  and.  at  the  same  time,  not 
to  mterfere  seriously  with  the  normal  radiation  from  the  part  to  iitikh 
It  IS  applied. 


PERFORMANCE  SPECIFICATIONS  AND  TESTS.        1M7 

364  6.  BuJb.  When  a  thermometer  is  applied  to  the  free  surface  of  a 
machine,  it  is  desirable  that  the  bulb  of  the  thermometer  should  be 
covered  by  a  pad  of  definite  area.  A  convenient  pad  may  be  formed  of 
cotton  waste  m  a  shallow  circular  box  about  one  and  a  half  inches  in 
diameter,  through  a  slot  in  the  side  in  which  the  thermometer  bulb  is 
inserted.  An  tmduly  lai^e  pad  over  the  thermometer  tends  to  interfere 
with  the  nattiral  liberation  of  heat  from  the  siuface  to  which  the  ther- 
mometer is  applied. 

365  2.  By  Increase  in  Rtsistance.  The  resistance  may  be  measiured 
either  by  Wheatstone  bridge,  or  by  drop-of  potential  method.  A  tem* 
perature  coefi&cient  of  0.42  per  cent  per  degree  C,  from  and  at  0°C., 
may  be  assumed  for  copper. 

The  temperature-coemcients  from  and  at  each  degree  cent,  between 
0^.  and  6(rC.  are  given  in  Appendix  E.  The  temperature  rise  may  bo 
determined  either  (1)  by  dividmg  the  percentage  mcrease  of  initial  re- 
sistance by  the  temperature-coemcient  for  the  initial  temperature  ex- 
pressed in  per  cent;  or  (2)  by  multiplying  the  increase  in  per  cent  of  the 
mitial  resistance  by  238.1  plus  the  initial  temperature  in  degrees  C,  and 
then  dividing  the  product  by  100. 

366  8.  Comparison  of  Methods.  In  electrical  conductors,  the  rise  of  tem- 
perature shoidd  be  determined  by  their  increase  of  resistance  where  prac- 
ticable. Temperature  elevations  measured  in  this  way  are  usually  in 
excess  of  temperature  elevations  measured  by  thermometers.  In  very 
low  resistance  circuits,  thermometer  measurements  are  frequently  more 
reliable  than  measurements  by  the  resistance  method.  Where  a  ther- 
mometer applied  to  a  coil  or  winding,  indicates  a  higher  temperature  ele- 
vation than  that  shown  by  resistance  measurement,  the  uiermometer 
indication  should  be  accepted. 

(B) — Normal  Conditions  for  Tests. 

367  1.  Duration  of  Tests.  The  temperature  should  be  measured  after  a 
run  of  sufficient  duration  for  the  apparatus  to  reach  a  practically  con- 
stant temperature.  This  is  usually  from  6  to  18  hours,  according  to  the 
size  and  construction  of  the  apparatus.  It  is  permissible,  however,  to 
shorten  the  time  of  the  test  bv  nmning  a  lesser  time  on  an  overload  in 
current  and  voltage,  then  reducing  the  load  to  normal,  and  maintaining 
it  thus  until  the  temperature  has  become  constant. 

368  2.  Room  Temperature.  The  rise  of  temperatiue  thould  be  referred 
to  the  standard  condition  of  a  room  temperature  of  25°C. 

369  Temperature  Correction.  If  the  room  temperature  during  the  test 
differs  from  26^.,  correction  on  accoimt  of  difference  in  resistance 
should  be  made  by  changing  the  observed  rise  of  temperature  by  one- 
half  per  cent  for  each  degree  C.  Thus  with  a  room  temperature  of  35^.. 
the  observed  rise  of  temperature  has  to  be  decreased  by  6  per  cent,  and 
with  a  room  temperature  of  16**C.,  the  observed  rise  of  temperature  has 
to  be  increased  by  6  per  cent.  In  certain  cases,  such  as  shunt-field 
circuit  without  rheostat,  the  current  strength  will  be  changed  by  a 
change  of  room  temperature.  The  heat-production  and  dissipation  may 
be  thereby  affected.  Correction  for  this  should  be  made  by  changing  the 
observed  rise  in  temperature  in  proportion  as  the  l^R  loss  in  the  re- 
sistance of  the  apparatus  is  altered  owing  to  the  difference  in  room 
temperature. 

370  3.  Barometric  Pressure.  Ventilation.  A  barometric  pressure  of  760 
mm.  and  normal  conditions  of*  ventilation  should  be  considered  as 
standard,  and  the  apparatus  under  test  should  neither  be  exposed  to 
draught  nor  enclosed,  except  where  expressly  specified.  The  baro- 
metric pressure  needs  to  be  considered  only  when  differing  greatly  from 
760  mm. 

371  Barometric  Pressure  Correction.  When  the  barometric  pressure 
differs  greatly  from  the  standard  pressure  of  760  mm.  of  mercury,  as  at 
high  altitudes,  a  correction  should  be  applied.  In  the  absence  of  more 
accurate  data,  a  correction  of  1%  of  the  observed  rise  in  temperature  for 
each  10  mm.  deviation  from  the  760  mm.  standard  is  recommended. 
For  example,  at  a  barometric  pressure  of  680  nam.  the  observed  rise  of 

7fl0—  Aftn 

temperature  is  to  be  reduced  by ^n —  "*  ^%' 

Digitized  by  VjOOQIC 


1468  TO.—ELECTRIC  POWER  AND  UGHTING. 

(II) — Limiting  Tbupbraturb  Rise. 
373         General.  The  temperature  of  electrical  machinery  under  reguki 
service  conditions,  should  never  be  allowed  to  remain  at  a  point  c4 
which  permanent  deterioration  of  its  insulatiim  material  takes  place 

373  Limits  Recommended.  It  is  recommended  that  the  foUowing  max- 
imum values  of  temperature  elevation,  referred  to  a  standard  room  tem- 
perature of  26^  centigrade,  at  rated  load  under  normal  conditiotts  ci 
ventilation  or  cooling,  should  not  be  exceeded. 

(A) — Machines  in  Gbnbral. 

374  In  commutating  machines,  rectifying  machines,  piiTsatrng-ctgrent 
generators,  synchronous  machines,  synchronous  commutating  machinfs 
and  unipolar  machines,  the  temperatxire  rise  in  the  parts  specified 
should  not  exceed  the  following: 

375  Field  and  armature,  50°C. 

376  Commutator  and  brushes,  by  thermometer,  5SK. 

377  Collector  rings,   65**C. 

378  Bearings  and  other  parts  of  machine,  by  thermometer,  40^. 

(B) — Rotary  Induction  Apparatus. 

379  The  temperature  rise  should  not  exceed  the  following: 

380  Electric  circuit,   50**C..  by  resistance. 

381  Bearings  and  other  parts  of  the  machine  40*C.,  by  thermocDeter. 
383         In  squirrel-cage  or  short-circuited  armatures,  65^.,  by  tbenao- 

meter,  may  be  allowed. 

(O — Stationary  Induction  Apparatits. 

383  a.  Transformers  for  Continuous  Service.  The  temperatxue  rise 
shotUd  not  exceed  60°   centigrade   in  electric  circuits,  by  resistaxMx; 

and  in  other  parts,  by  thermometer. 

384  b.  Transformers  for  Intermittent  Service.  In  the  case  of  trans- 
formers intended  for  intermittent  service,  or  not  operationg  continu- 
ously at  rated  load,  but  continuously  in  circuit,  as  in  the  ordinary  case  of 
lighting  transformers,  the  tcmperatiuie  elevation  above  the  sorroundii^ 
air-temperature  should  not  exceed  60**C.,  by  resistance  in  electric  cir- 
cuits and  by  thermometer  in  other  parts,  after  the  period  correspandii^ 
to  the  term  of  rated  load.  In  this  instance,  the  test  load  should  not  be 
applied  until  the  transformer  has  been  in  circuit  for  a  sufficient  time  to 
attain  the  temperatxire  elevation  due  to  core  loss.  With  transformers 
for  commercial  lighting,  the  duration  of  the  rated-load  test  may  be 
taken  as  three  hours,  unless  otherwise  specified. 

385  c.  Reactors,  induction-  and  magneto-regulators — electric  circuts  by 
resistance  and  other  parts  by  thermometer,  50*C. 

386  a.  Large  Ap^ratus.  Large  generators,  motors,  transformers,  or 
other  apparatus  m  which  reliabihty  and  reserve  overload  capacity  are 
important,  are  frequently  specified  not  to  rise  in  temperature  more  than 
40^  centigrade  imder  rated  load  and  56°  centigrade  at  rated  overload. 
It  is,  however,  ordinarily  xmdersirable  to  specify  lower  temperatmre 
elevations  than  40°  centigrade  at  rated  load,  measured  as  above. 

iD) — ^Rheostats. 

387  In  Rheostats,  Heaters  and  other  electrothermal  apparatus,  no  com- 
bustible or  inflammable  part  or  material,  or  portion  liable  to  come  in 
contact  with  such  material,  should  rise  more  than  60°C.  above  the  snr- 
rounding  air  tmder  the  service  conditions  for  which  it  is  designed. 

388  a.  Parts  of  Rheostats.  Parts  of  rheostats  and  similar  apparatus  rising 
in  temperature,  under  the  specified  service  conditions,  more  than  60^-, 
should  not  contain  any  combustible  material,  and  should  be  arranged  or 
installed  in  such  a  manner  that  neither  they,  nor  the  hot  air  issuing  from 
them,  can  come  in  contact  with  combustible  material. 

(E) — Limits  Rbcommbndbd  in  spbcial  Casbs. 

389  a.  Heat  Resisting  Insulation.  With  apparatus  in  which  the  insu- 
lating materials  have  special  heat-resisting  qualities,  a  higher  tempefa- 

^^  ture  elevation  is  permissible. 

^''O  bi  High  Air  Temperature.  In  apparatus  intended  for  service  in 
places  ot  abnormally  high  temperature,  a  lower  temperatare  ele^vatioc 
should   be   specified.  Digitized  by  CjUOglC^ 


PERFORMANCE  SPECIFICATIONS  AND  TESTS,        1400 

291  e.  Apparatus  Subj4ct  to  Ovtrload.  In  apparatus  which  by  the  nature 

of  •its  service  may  be  exposed  to  overload,  or  is  to  be  used  in  very 
.  high  voltage  circuits,  a  smaller  rise  of  temperature  is  desirable  than 
in  apparatus  not  liable  to  overloads  or  in  low-voltage  apparatus.  In 
apparatus  built  for  conditions  of  limited  space,  as  railway  motors,  a 
higher  rise  of  temperattu^  must  be  allowed. 

192  d.  Apparatus  for  Intermittent  Service.  In  the  case  of  apparatus 
intended  for  intermittent  service,  except  railway  motors,  the  tempera- 
ture elevation  which  is  attained  at  the  end  of  the  period  corresponding 
to  the  term  of  rated  load,  should  not  exceed  the  values  specified  for 
machines  in  general.  In  such  apparatus  the  temperature  elevation,  in- 
cluding railway  motors,  should  be  measured  after  operation,  under  as 
nearly  as  possible  the  conditions  of  service  for  whicn  the  apparatus  is 
intended,  and  the  conditions  of  the  test  should  be  specified. 

H.— OVERLOAD  CAPACITIES. 

393  Performance  with  Overload.  All  apparatus  should  be  able  to  carry 
the  overload  hereinafter  specified  without  serious  injury  by  heating, 
sparking,  mechanical  weakness,  etc.,  and  with  an  additional  tempera- 
ture rise  not  exceeding  16°C.,  above  those  specified  for  rated  loads,  the 
overload  being  applied  after  the  apparatus  has  acquired  the  tempera- 
ture corresponding  to  rated  load  continuotis  operation.  Rheostats  to 
which  no  temperature  rise  limits  are  attached  are  naturally  exempt  from 
this  additional  temperature  rise  of  16°C.  under  overload  specified  in 
these  rules. 

394  Normal  Conditions.  Overload  guarantees  should  refer  to  normal  con- 
ditions of  operation  reguarding  speed,  frequency,  voltage,  etc.,  and  to 
non-inductive  conditions  in  alternating  apparatus,  except  where  a  phase 
displacement  is  inherent  in  the  apparatus. 

395  Overload  Capacities  Recommended,  The  following  overload  capaci- 
ties are  recommended: 

396  a.  Generators.  Direct-current  generators  and  alternating-current 
generators,  25  per  cent  for  two  hours. 

397  b.  Motors.  Direct-current  motors,  induction  motors  and  synchronous 
motors,  not  including  railway  and  other  motors  intended  for  intermittent 
service,  26  per  cent  for  two  hours,  and  50  per  cent  for  one  minute. 

398  c.  Converters.  Synchronous  converters,  25  per  cent  for  two  hours, 
50  per  cent  for  one-half  hour. 

399  d.  Transformers  and  Rectifiers.  Constant-potential  transformers  and 
rectifiers,  25  per  cent  for  two  hours;  except  m  transformers  connected 
to  apparatus  lor  which  a  different  overload  in  guaranteed,  in  which  case 
the  same  guarantees  shall  apply  for  the  transformers  as  for  the  apparatus 
connected  thereto. 

300  e.  Exciters.  Exciters  of  alternators  and  other  synchronous  machines, 
10  per  cent  more  overload  than  is  required  for  the  excitation  of  the  syn- 
chronous machine  at  its  guaranteed  overload,  and  for  the  same  period 
of  time.  All  exciters  of  alternating-current,  single-phase  or  polyphase 
generators  should  be  able  to  give  at  its  rated  speed,  sufficient  voltage 
and  current  to  excite  the  alternator,  at  the  ratea  speed,  to  the  full-load 
terminal  voltage,  at  the  rated  output  in  kilovolt-amperes  and  with 
50  per  cent  power  factor. 

301  /.  A  Continuous-Service  Rheostat,  such  as  an  armature-  or  field- 
regulating  rheostat,  should  be  capable  of  carrying  without  injury  for 
two  hours,  a  current  25  per  cent  greater  than  that  at  which  it  is  rated. 
It  should  also  be  capable  of  carrying  for  one  minute  a  current  50  per 
cent  greater  than  its  rated  load  current,  without  injury.  This  excess  of 
capacity  is  intended  for  testing  purposes  only,  and  this  margin  of  capa- 
city should  not  be  relied  upon  in  the  selection  of  the  rheostat. 

303  g-  An  Intermittent  Service  or  Motor -Starting  Rheostat  is  used  for 
starting  a  motor  from  rest  and  accelerating  it  to  rated  speed.  Under 
ordinaiy  conditions  of  service,  and  unless  expressly  stated  otherwise,  a 
motor  is  assumed  to  start  in  fifteen  seconds  and  with  150%  of  rated 
current  strength.  A  motor-starter  should  be  capable  of  starting  the 
motor  imder  these  conditions  once  every  four  minutes  for  one  hour. 

303  (a)  This  Test  may  be  carried  out  either  by  starting  the  motor  at 
four-minute  intervals,  or  by  placing  the  starter  at  normal  temperatiue 
across  the  maximum  voltage  for  which  it  is  marked,  and  movmg  the 
lever  uniformly  and  gradually  from  the  first  to  the  last  poaitiaa  aMpȤ^ 


1470  70.— ELECTRIC  POWER  AND  UGHTING. 

I>eriod  of  fifteen  seconds,  the  cutrent  being  maintained  substantiilj 
constant  at  said  50%  excess  by  introducing  resistance  in  series  (»  br 
other  suitable  means. 

304  (&)  Othif  Rhsostats  for  lnUnmit0tU-S€rvu»  are  employed  under 
such  special  and  varied  conditions,  that  no  general  rules  are  applicsbk 
to   them. 

111.— VOLTAQES  AND  FREQUENCIES. 

A.— VOLTAGES. 

305  Direct'Current  Generators,  In  direct-cturent,  low-voltage  gBier> 
ators.  the  following  average  terminal  voltages  are  in  general  use  ssd 
are  recommended: 

126  volts.  250  volte.  550  to    000  volte. 

306  LoW'Voltage  Circttits.  In  direct-curreiit  and  ahemating-current  kyv- 
voltage  circuite,  the  following  average  terminal  voltages  are  in  geoei^ 
use  and  are  recommended: 

110  volte.  220   volte. 

307  Primary  Distributum  Circuits.  In  alternating-current,  oonstent- 
potential,  primary -distribution  circuite,  an  average  voltage  of  2.260 
volte,  with  step-down  transformer  ratkM  1/10  and  1/20,  is  in  genial  use. 
and  is  recommended. 

308  Transmission  Circuits.  In  alternating-current  constant-potential 
transmission  circuits,  the  following  average  voltages  are  reconuxiended. 

0.600     11.000    22.000     33.000    44.000    00,000    88.000 

309  Transformer  Ratio.  It  is  recommended  that  the  standard  tran^or- 
mer  ratios  should  be  such  as  to  transform  between  the  standard  voltages 
above  named.  The  ratio  will,  therefore,  usually  be  an  exact  multipk 
of  5  or  10.  e.  g..  2.200  to  11.000;  2.200  to  44.000. 

310  Range  in  Voltage.  In  altemating-ciurent  generators,  or  seneratinfi 
systems,  a  range  of  terminal  voltage  shoiild  be  provided  £nom  rated 
voltage  at  no  load  to  10  per  cent  in  excess  thereof,  to  cover  drop  in  trans- 
mission. If  a  greater  range  than  ten  per  cent  is  specified,  the  generator 
should  be  considered  as  special. 

B.— FREQUENCIES. 

311  In  Alternating-Current  Circuits,  the  following  frequencies  are 
standard: 

25^  00^ 

312  These  frequencies  are  already  in  extensive  use  and  it  is  deemed  ad- 
visable to  adhere  to  them  as.  closely  as  possible. 

IV.— GENERAL  RECOMMENDATIONS. 

313  Name  Plates.  All  electrical  apparatus  should  be  provided  with  a 
name  plate  giving  the  manufacturer  s  name,  the  voltage  and  the  currect 
in  amperes  for  which  it  is  designed.  Where  practicable,  the  kilowatt 
capacity,  character  of  curreilt,  speed,  irequency.  type,  designatioa  and 
serial  number  should  be  added. 

314  Diagrams  of  Connections.  All  electrical  apparatus  when  leaving  the 
factory  should  be  accompanied  by  a  diagram  showing  the  electrical 
connections  and  the  relation  of  the  different  parte  in  sufiBcient  detail 
to  give  the  necessary  information  for  proper  installation. 

315  Rheostat  Data.  Every  rheostet  should  be  clearly  and  pemmneatlv 
marked  with  the  voltage  and  amperes,  or  range  of  amperes,  for  whi» 
it  is  designed. 

316  Colored  Indicating  L^hts.  When  using  colored  indicating  us^txts 
on  switch-boards,  red  should  denote  danger  stich  aa  "switch  ^osed.  * 
or  "circuit  alive;"  green  should  denote  safety,  such  as  "switch  open,** 
or  "circuit  dead." 

317  When  white  lights  are  used  a  light  turned  on  should  dezx>te  danger. 
such  as  "switch  closed"  or  "circuit  alive;"  while  the  light  out  show 
denote  safety,  such  as  "switch  open,"  or  "circuit  dead.*'  Low-«CS- 
ciency  lamps  should  be  used. 

31o        The  use  of  colored  lighte  is  recommended,  as  safer  than  white  lights- 


VOLTAGE,  FREQUENCY.    GENERAL.    APPENDIX,       1471 

319         Grounding  Metal  Work.  It  is  desizmble  that  All  metal  work  xiear 

high  potential  circuits  be  grounded. 
330      <uircuit  Opening  Devices.  The  following  definitions  are  recommended. 

321  a.  A  Circuit-Breaker  is  an  apparatus  for  breaking  a  circuit  at  the 
highest  current  which  it  may  be  called  upon  to  carry. 

322  b.  A  Z>»5c<mn«c/i'n£  5tt;i^  is  an  apparatus  designed  to  open  a  circuit 
onl^  when  carrying  little  or  no  current. 

32 J  c.  An  Automatic  Circuit-Breaker  is  an  apparatus  for  breaking  a 
circuit  automaticall]^  imder  an  excessive  strength  of  current.  It  should 
be  capable  of  breaking  the  circuit  repeatedily  at  rated  voltage  and  at 
the  maximum  current  which  it  may  be  called  upon  to  carry. 


v.— APPENDICES  AND  TABULAR  DATA. 

APPENDIX  A.— NOTATION. 

The  following  notation  is  recommended: 

324  E,   e,   voltage,   e.m.f..   potential   difference 
/.   f,   cturent 

P,   power 

#,    magnetic  flux 

B,  B,  magnetic  density 
R,    r,    resistance 

X,  reactance 

£,  M,  impedance 

L,  I,  inductance 

C,  c,  capacity 

y,  y,  admittance 

b^  susceptance 

G^  g,  conductance 

Vector  qtiantities  when  used  should  be  denoted  by  capital  italics. 

APPENDIX  B.— RAILWAY  MOTORS. 
(I)— Rating. 

325  Introductory  Note  on  Rating.  Railway  motors  usually  operate  in 
a  service  in  which  both  the  speed  and  the  torque  developed  by  ttie  motor 
are  varying  almost  continually.  The  average  requirements,  however, 
during  successive  hours  in  a  given  class  of  service  are  fairly  uniform. 
On  accotmt  of  the  wide  variation  of  the  instantaneous  loads,  it  is  im- 
practicable to  assign  any  simple  and  definite  rating  to  a  motor  which  will 
mdicate  accurately  the  absolute  capacity  of  a  given  motor  or  the  rela- 
tive caF>acity  of  different  motors  imder  service  conditions.  It  is  also 
impracticable  to  select  a  motor  for  a  particular  service  without  much 
fuller  data  with  regard  both  to  the  motor  and  to  the  service  than  is 
required,  for  example,  in  the  case  of  stationary  motors  which  nm  at 
constant  speeds. 

326  Scope  of  Nominal  Rating.  It  is  common  usage  to  give  railway 
motors  a  nominal  rating  in  horse  power  on  the  basis  of  a  one-hour  test. 
As  above  explained,  a  simple  rating  of  this  kind  is  not  a  proper  measure 
of  service  capacity.  The  nominal  rating,  however,  indicates  approxi- 
mately the  maximum  output  which  the  motor  should  ordinarily  be 
called  upon  to  develop  dunng  acceleration.  Methods  of  determining 
the  continuous  capacity  of  a  railway  motor  for  service  requirements 

are  given  under  a  subsequent  heading. 

327  The  Nominal  Rating  of  a  railway  motor  is  the  horse-power  output 
at  the  car-axle,  that  is,  including  gear  and  other  transmission  losses, 
which  gives  a  rise  of  temperature  above  the  surroimding  air  (referred 
to  a  room  temperature  ot  25*  Cent.)  not  exceeding  9(rCent.  at  the 
commutator  and  76**  Cent,  at  any  other  part  after  one  hour's  con- 
tinuous run  at  its  rated  voltage  (and  frequency,  in  the  case  of  an  alter- 
nating-ctirrent  motor)  on  a  stand,  with  the  motor-covers  removed,  and 
with  natural  ventilation.  The  rise  in  temperature  is  to  be  determined 
by  thermometer,  but  the  resistance  of  no  electrical  ciici^t  in  the  nM>tor 
shall  increase  more  than  40%  during  the  test,      tized  by  CjOOQIc 


1472  TO.-'ELECTRIC  POWER  AND  UGHTING. 

(II>— Selbction  Op  Motor  for  Spbcifibd  Sbrvicb. 
S2S         General  Requirements.  The  stiitability  of  a  railway  motor  for  t 
specified  service  depends  upon  the  following  considerations: 

329  a.  Mechanical  ability  to  develop  the  requisite  torqtie  and  q>eeds  ts 
given  by  its  speed -torque  curve. 

330  b.  Ability  to  commutate  successfully  the  current  demanded. 

331  c.  Ability  to  operate  in  service  without  occasioning  a  temperature 
rise  in  any  part  which  will  endanger  the  life  of  the  insulation. 

332  Operating  Conditions,  Typical  Run.  The  operating  conditions  which 
are  important  in  the  selection  of  a  motor  include  the  weight  of  load,  the 
schedule  speed,  the  distance  between  stops,  the  duration  of  stops,  the 
rate  of  acceleration  and  of  breaking  retardation,  the  grades  and  the 
curves.  With  these  data  at  hand,  the  outputs  which  are  required  of  the 
motor  may  be  determined,  provided  the  service  requirements  are  with- 
in the  limits  of  the  speed-torque  curve  of  the  motor.  These  outputs  may 
be  expressed  in  the  form  of  curves  giving  the  instantaneous  values  of 
current  and  of  voltage  which  must  be  applied  to  the  motor.  Such  curves 
may  be  laid  out  for  the  entire  line,  but  they  are  usually  construct^ 
only  for  a  certain  average  or  typical  run,  which  is  fairly  representative 
of  the  conditions  of  service.  To  determine  whether  the  motor  has 
sufficient  capacity  to  perform  the  service  safely,  further  tests  or  in- 
vestigations must  be  made. 

333  Capacity  Test  of  Railway  Motor  in  Service.  The  capacity  of  a 
railway  motor  to  deliver  the  necessary  output  may  be  determined  by 
measurement  of  its  temperature  after  it  has  readied  a  mayimnm  in 
service.  If  a  running  test  cannot  be  made  tmder  the  actual  conditions 
of  service,  an  equivalent  test  may  be  made  in  a  typical  run  back  and 
forth,  xmder  such  conditions  of  schedule  speed,  length  of  run,  rate  oi 
acceleration,  etc.,  that  the  test  cycle  of  motor  losses  and  conditions  of 
ventilation  are  essentially  the  same  as  would  be  obtained  in  the  speci- 
fied service. 

334  Methods  of  Comparing  Motor  Capacity  with  Service  Rstjuirwmenis 
Where  it  is  not  convenient  to  test  motors  under  actual  service  condi- 
tions or  in  an  equivalent  typical  nm,  recourse  may  be  had  to  one  of  the 
two  following  methods  of  determining  temperature  rise  now  in  genera! 
use: 

335  1.  Method  bv  Losses  and  Thermal  Capacity  Curves.  The  beat  de- 
veloped in  a  railway  motor  is  carried  partly  by  conduction  through  the 
several  parts  and  partly  by  convection  tmotigh  the  air  to  the  motor- 
frame  whence  it  is  distributed  to  the  outside  air.  As  the  temperature  of 
the  several  parts  is  thus  dependent  not  only  upon  their  own  internal 
losses  but  also  upon  the  temperature  of  neighboring  parts,  it  becomes 
necessary  to  determine  accurately  the  actual  value  and  distribution  <& 
losses  in  a  railway  motor  for  a  given  service  and  reproduce  them  in  an 
equivalent  test-nm.  The  results  of  a  series  of  typical  runs  expressed  is 
the  form  of  thermal  capacity  curves  will  give  the  relation  between  degrees 
rise  per  watt  loss  in  the  armature  and  in  the  field  for  all  ratios  of  losses 
between  them  met  with  in  the  commercial  application  of  a  given  znoior. 

336  This  method  consists,  therefore,  in  calculating  the  several  intenul 
motor  losses  in  a  specified  service  and  determining  the  temperature  rise 
with  these  losses  from  thermal  capacity  curves  giving  the  degrees  rise 
per  watt  loss  as  obtained  in  experimental  track  tests  made  under  the 
same  conditions  of  ventilation. 

337  The  following  motor  losses  cause  its  heating  and  should  be  carefully 
determined  for  a  given  service:  PR  in  the  field;  PR  in  the  armature: 
PR  in  the  brush  contacts,  core  loss  and  brush  friction. 

338  The  loss  in  the  bearings  (in  the  case  of  geared  motors)  also  adds 
somewhat  to  the  motor-heating,  but  owing  to  the  variable  nature  of 
such  losses  they  are  generally  neglected  in  making  calculations. 

339  2.  Method  by  Continuous  Capacity  of  Motor.  The  essential  k>sses 
in  the  motor,  as  fotmd  in  the  typical  run,  are  in  most  cases  those  in  the 
motor  windings  and  in  the  core.  The  mean  service  conditions  nay  bs 
expressed  in  terms  of  the  current  which  would  produce  the  same  losses 
in  the  motor  windings  and  in  the  voltage  which,  with  the  curmit. 
would  produce  the  same  core  losses  as  the  average  in  service.  The 
continuous  capacity  of  the  motor  is  ^ven  in  terms  of  the  amperw 
which  it  will  carry  when  nm  on  the  testing  stand — ^with  covers  on  or  o5 
as  specified— at  different  voltages,  say,  40,  60.  80  and  100  per  cent  a 


RAILWAY  MOTORS.    PHOTOMETRY  AND  LAMPS,      1473 

the  rated  voltage — ^with  a  tempcratore  rise  not  exceeding  90**  at  thb 
commutator  and  76®  at  any  otner  part,  provided  the  resistance  of  no 
electric  circuit  in  the  motor  increase  more  than  40  per  cent.  A  com- 
parison of  the  equivalent  service  conditions  with  the  continuous  capacity 
of  the  motor  will  determine  whether  the  service  requirements  are  within 
the  safe  capacity  of  the  motor. 

340  This  method  affords  a  ready  means  of  determining  whether  a  speci- 
fied service  is  within  the  capacity  of  a  given  motor  and  it  is  also  a  con- 
venient approximate  method  for  comparing  the  service  capacities  of 
different    motors. 

APPENDIX  C— PHOTOMETRY  AND  LAMPS. 

341  Candh'Power.  The  luminous  intensity  o^  sotirces  of  light  is  ex- 
pressed in  candle-power.  The  imit  of  candle-power  should  be  derived 
from  the  standards  maintained  by  the  National  Bureau  of  Standards  at  - 
Washington,  D.  C,  which  standard  unit  of  candle-power  equals  100/88 
of  the  Hefner  unit  imder  Reichsanstalt  standard  conditions  for  the 
Hefner.  In  practical  measurements  seasoned  and  carefully  standard- 
ized incandescent  lamps  are  more  reliable  and  accurate  than  the  primary 
standard. 

342  Candle-Lumen.  The  total  flux  of  light  from  a  source  is  equal  to  its 
mean  spherical  intensity  multiplied  by  4;r.  The  tmit  of  flux  is  called 

the  candle-lumen.    A  candle-lumen  is  the  -p  th  part  of  the  total  flux 

of  light  emitted  by  a  source  having  a  mean  spherical  intensity  of  one ' 
candle-power. 

343  Candle-Meter.  The  unit  of  illumination  is  the  candle-meter.  This  is 
the  normal  illumination  produced  by  one  unit  of  candle-power  at  a  dis- 
tance of  one  metre. 

344  a.  Candle-Foot.  Illumination  is  occasionally  expressed  in  candle-feet. 
A  candle-foot  is  the  normal  illumination  produced  by  one  unit  of  candle- 
power  at  a  distance  of  one  foot. 

345  1  candle-foot»  10.764  candle-metres. 

The  use  of  the  candle-metre  unit  is  preferable  and  is  recommended. 

344S         The  Efficiency  of  Electric  Lamps  is  properly  stated  in  terms  of  mean 

spherical  candle-power  per  watt  at  lamp  terminals.  This  use  of  the 

term  efficiency  is  to  be  considered  as  special,  and  not  to  be  confused 

with  the  generally  accepted  definition  of  efficiency  in  Sec.  86. 

347  a.  Efficiency,  Auxiliary  Devices.  In  illuminants  requiring  atixiliary 
power-consuming  devices  outside  of  the  luminous  body,  s\ich  as  stead y- 
mg  resistances  in  constant  potential  arc  lamps,  a  distinction  should  be 
made  between  the  net  efficiency  of  the  luminous  source  and  the  gross 
efficiency  of  the  lamp.  This  distinction  shot^d  always  be  stated.  The 
gross  efficiency  should  include  the  power  consumed  in  the  auxiliary 
resistance,  etc..  The  net  efficiency  should,  however,  include  the  power 
consumed  in  the  controlling  mecminism  of  the  lamp  itself.  Comparison 
between  such  sources  of  light  should  be  made  on  the  basis  of  gross 
efficiency,  since  the  power  consumed  in  the  auxiliary  device  is  essential 
to  the  operation. 

348  b.  A  Standard  Circuit  Voltage  of  1 10  volts,  or  a  multiple  thereof  may 
be  assumed,  except  where  expressly  stated  otherwise. 

349  Watts  per  Candle.  The  specific  consumption  of  an  electric  lamp  is 
its  watt  consumption  per  mean  spherical  candle-power.  "Watt  per 
candle"  is  the  term  used  commercially  in  connection  with  incandescent 
lamps,  and  denotes,  watts  per  mean  horizontal  candle-power. 

350  Photometric  Tests  in  which  the  results  are  stated  in  candle-power 
should  always  be  made  at  such  a  distance  from  the  source  of  li^t  that 
the  latter  may  be  regarded  as  practically  a  point.  Where  tests  are  made 
at  shorter  distances,  as  for  example  in  the  measurement  of  lamps  ^ith 
reflectors,  the  result  thould  always  be  given  as  "apparent  candle-power" 
at  the  distance  employed,  which  distance  should  always  be  specifically 
stated. 

351  Basismfor  Comparison.  Either  the  total  flux  of  light  in  candle- 
lumens,  or  the  mean  spherical  candle-power,  should  always  be  used  as 
the  basis  for  companng  various  luminous  sources  with  each  other, 
tmless  there  is  a  clear  understanding  or  statement  to  the  contrary. 

352  Incandescent  Lamps,  Rating.  It  is  customary  to  rate  incandescent 
lamps  on  the  basis  of  their  mean  horizontal  candle-power;  but  in  com- 


1474 


TO.^ELECTRIC  POWER  AND  UGHTING, 


353 


354 
355 


'356 


357 


35« 


359 


paring  incandeacent  lamps  in  which  the  relative  distribtttion  of  lanrainoat 
intensity  differs,  the  comparison  should  be  based  on  their  total  flux  ol 
lii^t  measured  in  lumens,  or  on  their  mean  spherical  candle-power. 

The  Spherical  Bsductton-Factor  of  a  lamp 

mean  spherical  candle-power  ^ 
mean  horizontal  candle-power 

The  Total  Flux  of  light  in  candle-lumens  emitted  by  a  lamp*  4c X 
mean  horisontal  candle-power  X  spherical  reduction-factor. 

The  Spherical  Reduction-Factor  should  only  be  tised  when  properly 
determined  for  the  i>articular  type  and  characteristics  of  ea^  lamp. 
The  spherical  reduction-factor  permits  of  substantially  accurate  ocec- 
parisons  being  made  between  the  mean  spherical  candle-powers  of 
different  tvpes  of  incandescent  lamps,  and  may  be  used  in  the  absence 
of  proper  lacilities  for  direct  measurement  of  mean  spherical  intensity. 

Reading  Distance."  Where  standard  photometric  measorexnents 
are  impracticable,  approximate  measurements  of  illuminants  each  ss 
street  lamps  may  be  made  by  comparing  their  "reading  distances;" 
i.e.,  bv  determining  alternately  the  distances  at  which  an  ordinary 
sire  of  reading  print  can  jtist  be  read,  by  the  same  person  or  persons, 
when  all  other  light  is  screened.  The  angle  below  the  honsontal  at 
which  the  measurement  is  made  shotild  be  specified  when  it  exceeds  1^. 

In  Comparing  Different  Luminous  Sources  not  only  should  their 
candle-power  be  compared,  but  also  their  relative  form,  intxicsic 
brilliancy,  distribution  of  illumination  and  character  of  light. 

APPENDIX  D.— SPARKING  DISTANCES. 

Table  of  Sparking  Distances  in  Air  between  Opposed  Sharp  Needle- 
points, for  Various  Effective  Sinusoidal  Voltages,  in  inches  and  in 
centimeters.  The  table  applies  to  the  conditions  specified  in  Sees. 
240-246. 


Kilovolts 

Kilovolts 

Sq.  Root  of 

Distance. 

Sq.  Root  of 

Distance. 

Mean  Square. 

Inches. 

Cms. 

Mean  Sqtiare. 

Inches. 

Cms. 

6... 

.   0.226 

0.67 

140 

.18.95 

86.4 

10 

.   0.47 

1.19 

160 

.16.0 

88.1 

16 

.   0.726 

1.84 

160 

.16.05 

40.7 

20 

.    1.0 

2.64 

170 

.17.10 

43.4 

26 

.    1.8 

3.3 

180 

.18.16 

46.1 

30 

.   1.626 

4.1 

190 

.19.20 

48.8 

36 

.   2.0 

5.1 

200 

.20.26 

51.4 

40 

.   2.46 

6.2 

210 

.21.80 

54.1 

45 

.   2.96 

7.6 

220 

.22.85 

56.8 

60 

.    3.66 

9.0 

230 

.28.40 

50.4 

60 

.   4.66 

11.8 

240 

.24.45 

62.1 

70 

.   6.86 

.  14.9 

260 

.26.50 

04.7 

80 

.    7.1 

18.0 

260 

.26.50 

07.8 

90 

.   8.36 

21.2 

270 

.27.50 

09.8 

100 

.   9.6 

24.4 

280 

.28.50 

72.4 

110... 

.10.75 

27.8 

290 

.20.50 

74.9 

120 

.11.86 
.12.90 

30.1 
82.8 

800 

.80.50 

77  4 

130 

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SPARKING  DISTANCES.    TEMP,  COEFFICIENTS.       1476 


APPENDIX  E.— TEMPERATURE  COEFFICIENTS. 

360         Table  of  Temperature  Coefficients  of  Resistivity  in  Copper  at 
Different  Initial  Temperatures  Centigrade. 


Initial 

Temp.  Coefficient 

Initial 

Temp.  Coefficient 

temperature 

in  per  cent  per 

temperature 
Cent. 

t 

in  per  cent  per 

Cent. 

f 

Degree  Cent. 

Degree  Cent. 

0 

0.4200 

26 

27 

28 

0.3786 

1 

0.4182 

0.3772 

2 

0.4166 

0.3768 

3 

0.4148 

29 

0.3744 

4 

0.4131 

80 

0.3730 

6 

0.4114 

31 

0.3716 

6 

0.4097 

32 

0.3702 

7 

0.4080 

33 

0.3689 

8 

0.4063 

34 

0.3676 

9 

0.4047 

86 

0.8662 

10 

0.4031 

86 

0.3648 

11 

0.4016 

37 

0.3635 

12 

0.3999 

88 

0.8622 

13 

0.3983 

89 

0.3609 

14 

0.3967 

40 

0.3696 

16 

0.3961 

41 

0.3688 

16 

0.3936 

42 

0.3670 

17 

0.3920 

43 

0.3667 

18 

0.3906 

44 

0.3646 

19 

0.3890 

46 

0.3532 

20 

0.3876 

46 

0.3620 

21 

0.3860 

47 

0.8508 

22 

0.3845 

48...... 

0.3496 

23 

0.3830 

49 

0.3483 

24 

0.3816 

60 

0.8471 

25 

0.3801 

The  fundamental  relation  between  the  increase  of  resistance  in 
copper  and  the  rise  of  temperature  may  be  taken  as 

/?,-i?o  (1  +  0.0042  0 
where  Ro  is  the  resistance  of  the  copper  conductor  at  0°  C.  and  Ri  is  the 
corresponding  resistajice  at  t^  C.  Tnis  is  equivalent  to  taking  a  tempera- 
ture coefficient  of  0.42%  per  deg.  C.  temperature  rise  above  0®C.  For 
initial  temperatures  other  than  0°C.,  a  similar  formula  may  be  used 
substitutifig  the  coefBcients  in  the  above  table  corresponding  to  the 
actual  initial  temperature.    The  formula  thus  becomes  at  25°  C. 


-■^'-M-'^»-) 


where  Ri  is  the  initial  resistance  at   26*^  C.    R,+r  the  final  resistance 
and  r  the  temperature  rise  above  26**  C. 

In  order  to  find  the  temperature  rise  in  degrees  Centigrade  from  the 
initial  Resistance  Ri  at  the  initial  temperattire  «^  C.  and  the  final  resist- 
ance Ri+t  we  may  use  the  formula 


See  Sec.  266. 


-(238.1  +  0   (~  -  l)  degrees  C. 


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1470  TO.^ELECTRIC  POWER  AND  UGHTING, 

EXCERPTS  AND  REFERENCES. 

Qeaeratora  and  Transformers  for  the  Bay  Counties  Power  Co.,  CaL 

(By  E.  Heltmann  and  W.  Currie.    Eng.  News,  Nov.  21,  1001). — Illustrated. 

Electric  Switches  and  Fuses  for  Currents  of  Very  High  Voltase  CTbe 

Jl.  of  Elec.,  Power  and  Gas,"  Jtme,  1001;   Eng.  News.  Oct.  3.  1001). 

The  50,000-Volt  Transmission  Plant  of  the  Missouri  River  Power  Co. 
in  Mont.  (By  W.  G.  McConnon.  Eng.  News,  June  6,  1002). — Details  of 
insulators  and  spacing  of  poles. 

Success  in  Long  Distance  Electric  Power  Transmission  (By  P.  A.  C. 

Perrine.  "Technology  Quarterly;'*  Eng.  News,  Aug.  21,  1002). — See,  abo. 
Eng.  News.  Sept.  20,  1004. 

An    Analytical    Method    of    Determining    Illumination    (By  Van    R. 

Lansin^h.  Eng.  News,  Feb.  10,  1003). — Illustrated  diagram  for  determin- 
ing horizontal  distribution  of  light  from  a  given  surface. 

Long  Spans  for  Electric  Transmission  Lines  (By  P.  O.  Blackwell. 
Paper.  Am.  Inst.  E.  E.,  June,  1004;  Eng.  News.  July  7,  1004). — Mcdnlus 
of  elasticity:  Copper  hard -drawn  wire,  10.000.000;  aluminum  hard-drawn 
wire,  10.200,000;  iron  telegraph  wire.  24,000.000;  copper  hard-drawn  wire 
cable.  16,300,000.  Coefncient  of  expansion  (F.):  Copper.  0.000000<; 
alumintun,  0.000013:  steel,  0.0000064. 

The    Kern    River   ComtMiny's    Hydro-Electric    Power   Enterprise  (By 

Burr  Bassell.    Eng.  News,  July  21,  1004). — Sixteen  illustrations. 

Medium-Span    Electric    Transmission    Line    Construction     (By    C.  A. 

Copeland.  Pac.  Coast  Elec.  Transmission  As»i.,  June.  1004;  Eng.  News, 
Aug.  18,  1004). — Illustration  of  steel  pole  construction  for  SOO-ft.  span; 
also  an  experimental  medium-span  construction. 

The  Design  of  Generators  for  Electric  Power  Transmission  (By  D.  B. 

Rushmore.    Eng.  News,  Oct   27.  1004).— Illustrated. 

Storage  Batteries  for  Block  Signal  Work  (By  E.  L.  Reynolds.  Paper. 
Ry.  Signal  Assn.,  Jan.,  1006;  Eng.  News,  Jan.  10.  1005).— Tables:  CD 
First  cost;    (2)  Maintenance  cost. 

Long   Distance   Electric    Power   Transmission    Line   in   Nevada    (By 

E.  Prince.    Eng.  News,  July  6,  1005). 

Electric  Ught  and  Power  Plant   of   Brigham   City,  UUh  (By  W.  P. 

Hardesty.  Eng.  News,  Sept.  7,  1006). — Illustrations:  Power  house;  iron- 
work for  gates  for  diverting  dam;  concrete  anchorage  for  steel  pressure 
supply  pipe  on  slope;  diverting  dam  and  intake;  details  wood-stave  pipe; 
cast-iron  hub  for  connecting  steel  pipe  with  wood  stave  pipe. 

Qas  Engine  Electric  Plant  as  Auxiliary  and  Reserve  for  a  Long- 
Distance  Transmission  System  (Eng.  News,  Sept.  14.  1005). 

A  High  Head  Water  Power  Electric  Plant  on  the  Animas  Riv«r. 
Colo.  (By  G.  M.  Peek.  Eng.  News,  Jan.  4.  1006).— Illustrations:  Crcss- 
section  of  power  house;  reinforced-concrete  pole  with  spread  base,  for 
single  3-phase  power  transmission  line;  four-post  reinforcea -concrete  tower 
with  prismatic  base,  for  single  3-pha8e  power  transmission  line. 

Transmission  and  Distributing  System,  Long  Island  R.  R  (Eng. 
News,  June  14.  1006). — Illustrations:  Top  of  steel  transmission  line  pole; 
strain  insulators  for  transmission  line  cables;  details  of  third -rail  giiarcf  and 
supports;  standard  wooden  side  approach  block  construction;  standard 
arrangement  of  third-rail  connecting  cables  at  public  crossings. 

Cost  of  Construction  and  Operating  Expenses  of  the  Municipal  Elec- 
tric Lighting  Plant  at  Buriington,  Vt.  (Eng.  News,  May  80.   10()7).— Six 

tables  of  costs. 

Some  New   Methods  in   High  Tension  Line  Construction    (By  H.  W. 

Buck     Eng.  News.  Aug.  8,  1007).— Illustrated.    See,  also.  Paper  by  E.  \L 

rlewlett,  in  same  issue.  ^-^  i 

The  McCaii  Ferry  Hydro-Electric  Power  ^PiiftitbA^fig'^i 


MISCELLANEOUS  DATA.    COSTS.  1477 

River  (Eng.  News,  Sept.  12,  1907). — Illustrations:  Alternate  dam  sections, 
showing  expansion  joints  and  butt  blocks  for  steel  forms;  details  of  steel 
forms;  details  of  steel  traveler;  concrete  mixer  plant;  section  through 
power  house. 

Concrete  Tdegraph  Poles  (Eng.  Rec.,  Dec.  17,  1910).  17}  ft.  high  above 
the  roof  have  been  erected  on  one  of  the  buildings  of  the  U.  S.  Aluminum 
Co..  at  Niagara  Falls.  They  are  10*  sq.  at  base.  IC  sq.  at  top  and  rein- 
forced with  eight  \'  bars  bound  with  J'  hoops  18*  c.-c. 

Cost   of   Cofutmctiiic   Steam-Driven   Electric   Power   Plants  (By   P. 

Koester.  Eng.  News,  Dec.  19.  IW^Ti.—SuptTStfuciuft. — $15  to  $26  for 
plants  up  to  6000  K  W.;  116  where  there  is  a  compact  arrangement  with 
walls  of  common  brick,  wooden  doors  and  window  frames,  steefroof  trusses 
supported  by  the  walls  and  a  roof  of  the  cheapest  construction,  such  as 
corrugated  iron,  tin,  etc.;  about  120  to  126  per  K  W.  for  construction  of 
higher  grade  masonry  with  fireproof  windows  and  doors,  roof  trusses  carried 
by  steel  columns  which  at  the  same  time  carry  the  crane  runway,  and  the 
roof  itself  consisting  of  reinforced -concrete  covered  by  tar  and  gravel.  The 
cost  of  superstructure  for  large  size  plants  t^ually  runs  from  $10  to  $20  per 
KW.;  these  are  constructed  of  self-supporting  steel  skeleton  and  self- 
8up|porting  walls.  The  superstructure  at  $20per  K  W.  may  embrace 
multiple  boiler  floors,  while  those  at  $10  per  K  W.  cover  single  boiler  floor 
plapts  only.  Chimney. — A  radial  bnck  chimney  for  large  size  power 
plants  may  be  built  for  from  $1.76  to  $2.26  per  K  W.  Reinforced -concrete 
chimneys  and  plate  steel  chimneys  may  cost  from  $1.60  to  $2  per  K  W. 
Coal  and  Ash  Handling  Systems. — Experience  shows  that  the  ^ures  for 
equipment  for  handling  coal  and  ashes  range  from  $1.60  to  $3  per  K  W. 
Boilers. — ^The  cost  of  water  tube  boilers  ranges  from  $8  to  $10  per  K  W., 
depending  upon  the  sqtiare  feet  of  heatixig  surface  in  the  boiler.  These 
figures  do  not  include  mechanical  stokers,  for  which  from  $2  to  $3  may  be 
assumed.  Breeching,  of  course,  is  also  a  separate  item  and  varies  con- 
siderably as  to  cost  per  K  W.  The  boiler  setting  is  included  in  the  above 
cost.  Blowers. — In  many  of  the  modem  power  plants,  especially  plants  for 
railway  purposes,  forced  or  induced  draft  is  adopted.  The  blowers  are 
usually  steam-driven.  The  cost  of  such  equipment  is  about  $1  per  K  W. 
Economizers. — Where  economizers  are  installed  of  sufficient  capacity  to 
heat  the  water  to  200*  or  220°  F.  such  apparatus  costs  about  $2  per  K  W., 
provided  that  there  are  not  too  many  additional  smoke  flues  necessary  for 
by-passing,  etc.  Boiler  Feed  Pumps. — ^The  cost  of  such  pumps  alone  is 
some  60  cents  per  K  W.  When  storage  tanks  are  necessary  the  cost  of  the 
combined  outfit  amounts  to  76  cents  or  $1,  depending  on  the  number  and 
size  of  the  tanks.  Piping. — From  $2  to  $6  per  K  W.  For  plants  of  10.000 
to  20,000-K  W.  capacity,  the  piping  system  not  being  elaborate  but  suffi- 
cient for  continuous  operation,  $2.60  to  $2.76  has  covered  the  cost.  This 
includes  a  high  grade  of  covering  for  steam  piping  valued  at  about  20  cts. 
per  K  W.  Prime  Movers. — A  6000-K  W.  turbo-generator  should  cost  from 
920  to  $22  per  K  W.  Reciprocating  engines  of  this  capacity  are  sold  roughly 
at  the  same  price,  and  about  $10  per  K  W.  needs  to  be  added  for  the  gener- 
ator. The  total  cost  for  smaller  units,  600  to  3000  K  W.  capacity,  is  from 
$20  to  $26  per  K  W.,  whether  they  consist  of  turbine  or  reciprocating- 
engine  apparatus.  Condensers. — ^The  cost  of  jet  condenser  equipment  runs 
from  $3  to  $6  per  K  W.,  depending  upon  the  type  of  pump  used.  The  cost 
of  surface  condenser  apparatus  will  vary  from  $6  to  $8,  depending  partly 
upon  the  vacuum  to  Be  carried  and  whether  the  casing  necessary  forms 
part  of  the  condenser  equipment.  Exciters. — A  steam-driven  exciter  unit 
costs  from  36  cts.  to  40  cts.  per  K  W.  If  a  condenser  should  be  installed 
in  connection  with  it  the  cost  may  run  as  high  at  70  cts.  per  K  W.,  assum- 
ing that  the  exciter  capacity  is,  approximately,  1%  the  total  capacity  of 
the  plant.  Switchboards. — For  a  high  tension  voltage  the  cost  will  run  from 
$2  to  $3.60.  which  for  a  low  tension  voltage  (2,300  volts  or  lower)  the 
switchboard  equipment  may  be  obtained  for  $1  to  $2  per  K  W.,  depending 
largely  upon  the  system  of  wiring  adopted.  Miscellaneous. — ^Traveling 
cranes,  26  or  60  cts.  per  KW.;  smaller  items,  like  house  pumps,  water 
meters,  blow-off  tanks,  painting,  supervision,  etc,  from  $1  to  $2  per  K  W. 
Tabulations. — A  summary  of  the  preceding  figures  is  shown  in  the  table 
below,  to  which  should  be  added  the  engineering  fee.  All  these  figures 
represent  costs  (per  K  W.)  of  plants  of  large  capacity,  but  some  have  cost 
as  high  as  $125  or  even,  in  an  exceptional  case,  $160  per  K  W. 


1478 


n,^ELECTRlC  POWER  AND  UGHTING. 


Corr  ov  Stbam  Plamts  or  Lakgb  CArAcmr. 


Itotna. 


Bzcavmtions  and  fomuUtioni. . 
Boiidinc. 


Ttmseli  (coodcnMr  water  cooduit). 
Ploea  and  stacks . 


BoUenand  stokers 

8aperheatcf« 

Ecooomtsen 

Coal  and  ash  handling  systems. . 

Bk»wers  and  ducta , 

Pumps  and  tanks 

Piping  systems 

Turbo-generators 

Engines 

Condensers  (surface) 

Condensers  (jet) 

EzciterB 

Gcnefmtofs 

Crane 

Switchboards 

Phambing.  painting,  labor,  etc . . 


Coat  of 

Ste*m  Turbaxw 

Placta. 

per  K  W. 


10 

1 
s 

8 
2 
2 
1 
1 
1 
I 
S3 


00  to  $2 
00        IS 


Costal 
Rectprocsts* 
Engine  Pica 


76 
50 
60 
00 
00 
60 
00 
00 
26 
00 

.00 

.76 


4 

3 

12 

2 
2 
3 
1 
1 
4 
25 

8 

1 


50  $  3 
00  10 
00  I 
50 
00  ' 
50  I 
25 


.26 

00  3 

00  2. 


00 
50 
25 
50 
00 

00 

00 

50 
50 


00toU» 
00      2*)* 


60 
56 
60 

75 
00 
.60 
00 
00 
.60 


]5i 

12  « 

3« 
1» 
1  a 


18  00    nm 


10 


5K 

1« 

MM 
3  J» 


Totals $66.60     $92.00    $70.25  1104  51 

I 

Smaller  planU  of  about  SOOO  K  W.  capacity  ha've  been  erected  in  the 
West  at  from  1120  to  $110  per  K  W..  which  cost  may  be  reduced  if  a  siiE?^ 
oombinatkjo  of  machiw«  is  provided. 


Ratas  for  Etoctric  CorrwC  Panlshad  ky  tke  Mmlciptf  Plant  of  I 

Cat  (Eng.  News,  Peb.  10  and  Apr.  7.  1010). — Rates  are  shown  in  ioUovicS 
table: 


Incan- 
descent 
LighUng. 

Lighting.        Power. 

Uo  to  100  KW.-hrs.  oer  mo 

7  cts. 
0     '• 
6     *• 

6  75  cts.      4      ctL 

100  to  600                    "       

5  75     ••       9  1- 

600  to  1000     "            "       

4.75     •• 

■ 

1000  to  1600     *'            *•       

2 

1000  to  2000     "            •'       

4     •• 
$    " 

Over  SOOO         "             "       

1600  to  6000     ••            "       

If* 

Over    6000*      "             "       

1.75  " 

Over    6000t      "            **       

1-5   - 

1.5   - 

Over  10000       "            **       

1 

*  If  used  between  6  p.  m.  and  10  p.  m. 
t  If  not  used  from  6  p.  m.  to  10  p.  m. 


d  by  Google 


MISCELLANEOUS  DATA,    COSTS. 


1479 


Cost  of  Overhead  Trolley  Systenu  (By  A.  D.  T^lliams,  Jr.  Ens.  News. 
Dec.  23. 1909).— Tables:  (1)  Cost  per  nule  of  overtiead  materials:  (2)  Bracket- 
arm  construction  (a — ^with  37-ft.  poles  placed  in  center;  b— ^th  30-ft.  poles 
placed  in  center);  (3)  Cross-span  construction,  with  37  and  30-ft.  poles; 
(4)  Transmission  une.  and  feeoer  line;  (6)  Comparison  of  costs,  per  nule: — 


Bracket 

arm. 

Cross  span 
30  and  37-ft.  poles. 

Cross  span 
30  and  30-ft.  poles. 

Trolley  wire  and  poles 

Transmission  line 

Feeder  line 

12.136.06 
732.67 
682.69 

$2,420.99 
732.57 
682.69 

$2,264.99 
732.67 
682.69 

Total 

13.561.31 

$3,836.25 

$3,680.26 

inostrations  of  Electrical  Works:— 

Description.  Bng.  News. 

Transmission  line  for  Bay  Counties  Power  Co.  Oct.  3.  1901. 

Electric  conduit  construction  at  Cincinnati,  O.  Aug.  20,  '03. 

Section  of  subway  for  i>ipes  and  wires  Feb.  16.  '06. 

Line  construction  for  high-pressure  electric  railroads  April    6,  '05. 
High-pressxire  line  construction  for  alternating-current  rail'ys   April    6.  '05. 

New  high-duty  electric  storage  battery  plate  May     4,  '05. 

High  voltage  electrostatic  voltmeter  operating  in  oil  Jan.   11, '06. 

Details  of  transmission  line  poles.  N.  Y.  C.  &  H.  R.  R.  R.  June  14.  '06. 

Carbon  regulator  for  storage  battery  Sept.  27.  '06. 

♦Details  of  steel  towers  for  hip:h  tension  transmission  Mar.  12,  '08. 

Rein.-conc.  conduit  for  electric  cables,  L.  I.  R.  R.  July  23.  '08. 

New  type  of  switchboard.  Salt  River  Project  Aug.  27.  '08. 

Divided  manhole  for  high  and  low-tension  conduit  lines  Sept.  24,  '08. 

Insulator  for  16,000  volt  trolley  line.  Switzerland  Nov.  11,  '09. 

Circuit  breaker  for  110,000-volt  lines  Dec.  23,  '09. 

Underground  conduit  construction  for  large  transmissions  Sept.  29. '  10. 

Bng.  Rec. 

Hydro-elec.  power  development;  powerhouse,  dam,  etc.  Apr.     8, '09. 
Power  house,  penstocks,  dam,  etc..  Wis.  Hydro-Elec.  Power  Co.Sept.    4,  '09. 


*  Failed.    See  Eng.  News.  May  13.  1908. 


d  by  Google 


71.— MISCELLANEOUS  DATA  AND 
ILLUSTRATIONS. 

DERRICKS  AND  CRANES. 

Description.  BoS.  Ncfws. 
A  30-ton  gantry  crane  for  C.  &  O.  Ry.  wharves                        Sept.  19,  IMI. 

Modem  types  of  cranes  for  shipyard  service  Hmy  2S,  '01. 

A  30-ton -locomotive  crane;  a  2^ton  derrick  crane  Nov.  20.  '02. 

An  electric  traveling  crane  with  transfer  carriage  May     7.  '03. 

The  120-ton  floating  derrick  for  the  Noriolk  Navy  Yard  Tunc  25,  '03. 

Portable  pneumatic  revolving  cranes  July  23,  '03. 

Electric  pillar  cranes  for  handling  cupola  charges  Ttily   30.  '03. 

A  gantry  crane  with  double  cantilever  bridge  Nov.  26,  '03. 

A  10-ton  stiff-leg  der.  with  ball  and  socket  toot-block  bearing  Sept.  22,  '04. 

Ore-unlocking  machines  for  use  at  receiving  docks  Aug.     3.  '05. 

Recent  heavy  cranes  in  English  shops  Aug.  29,  '07. 

A  reversible  hoist  for  elevators  and  derricks  on  construction  Jnly     2,  '08. 

A  combined  gantry  crane  and  coal  elevator  Sept.  1 7,  'OS. 

Traveling  cranes  equipped  with  scales  June  17,  '09. 

Eng.  Rec 

Steel  guyed  derrick  (mast  70  ft.)  for  building  erection  Mar.  27,  '09. 

Details  of  steel  stiff-leg  derrick  April  23,  '10. 

A  detachable  seat  for  a  boom  derrick  June  18,  '10. 

Derrick  tower  for  erecting  the  Montana  capitol  Aug.  18,  '10. 


CHIMNEYS. 


Eng.  News. 


Section  and  plan  of  concrete  chimney  in  Switzerland  Sept.  19.  '01. 

Steel  chimneys  for  power  station  of  St.  Louis  Transit  Co.  Dec.   19,  '01. 

The  design  of  self-supporting  steel  chimneys  July  20.  '05. 

Details  of  300-ft.  chimney  of  reinforced-concrete  Aug.     3, '05. 

A  350-ft.  brick  chimney  for  acid  chemical  gases  Feb.   15.  '06. 

The  design  of  reinforced-concrete  chimneys  Tan.      3,  '07. 

Method  of  building  a  steel  chimney  Mar.  14.  '07. 
Lightning  protection  for  power  plant  chimneys.  U.S.  Navy  .Yds.  Aug.  22,  '07. 

Heat  expansion  stresses  in  chimneys.    Not  illustrated  Mar.     5.  '08. 

Wind  stresses  in  reinforced-concrete  chimneys.    Diagram  Sept.  10.  *08. 

Largest  Chimney  in  the  world:    50^  x  500^  Nov.  20,  '08. 

Tapering  concrete  chimney,  258  ft.  high  Jan.    13.  'II. 

Eng.  Rec 

Underpinning  a  leaning  chimney,  illustrated  July     3.  '09. 

MECHANISM  AND  QEARINQ. 

Eng.  News. 

High-speed  toothed  gearing  Feb.  28,  'OL 

Chains  and  chain  gearinjs  Sept.  6i.  '01. 

Two  new  power  transmission  devices  Tune     8,  '#5. 

A  mammoth  sheave  wood  block:   ht..  53* ;  wt..  640  lbs.  Mar.  21,  '07. 

Friction  coefficient  of  wire  rope  drives  Tone  27,  '07. 

The  Schmidt  silent  drive  chain  Kov.  28.  '07. 

The  design  of  friction  clutches  (mainly  for  automobiles)  Oct.     1,  *08L 

MARINE  ENQINEERINO. 

Eng.  Newt. 

r . ,, , Aug.  29.  '01. 

Cunningham-Seaton  system  of  coalmg  war  vessels  at  sea  Tan.   21.  '04. 

Notes  on  design  of  steamships  Minnesota  and  Dakota  Sept.    1,  '04. 

Half  cross-section  of  car-ferry  steamer  "Detroit;"  M.  C.  R.  R-   May     4,  '05i, 


A  comparison  of  typical  marine  engines  Aug.  29.  '01. 

o : — 1 o__. . '--Img  war  vessels  at  sea  Tar     *'  **' 

inesota  and  Dakota  Sej 

mcr  "Detroit;"  M.C.R.R.  Ma 

1480  Digitized  by  VjOOQ  IC 


DERRICKS,  CRANES,  CHIMNEYS,  ETC, 


1481 


Description. 
Bxperience  in  the  design  of  marine  screw  propellers 
A  pneumatic  submarine  signalling  bell 
Ocean  steamers  with  steam  turbines 
The  Ctmard  steamship  "Mauretania" 

Steel  barges  for  transporting  steel  products,  O.  and  Miss.  R. 
Rein  forced-concrete  barges  on  the  Panama  Canal 

CABLEWAYS  AND  CONVEYORS. 

A  cheap  cableway:   for  building  concrete  piers 
Lubricating  the  wheels  of  chain  conveyors 
Method  of  nandling  ore  at  Bingham  Canon,  Utah 
Conveyor  for  loading  iron  ore  in  ships  off  rocky  coast 
Cable  haulage  for  transporting  marl  to  cement  mill 
Aerial  tramways  of  the  U.  S.  Mining  Co.,  Bingham.  Utah 
The  Ridgeway  **two-bclt"  conveyor 
Side  and  end  elevations  of  extensible  16*  belt  conveyor 
Cableway  for  cars  in  filling;  cost  compared  with  trestle 
Formulas  for  the  design  of  cableways 
Traveling  bridge  suspended  from  cableway  for  making  fills 
A  uniaue  belt  conveyor  2000-ft.  long,  with  equaliser 
The  Wetterhom  cableway  incline,  illustrated  details 

REVETMENTS. 

Bank  Revetment  on  the  Lower  Mississippi  River 
Recent  experiments  with  bank  protection  works,  Ark. 
The  Davia  Neale  System  of  bank  protection 
Du  Muralt  system  of  reinforced-concrete  shore  protection 
A  wave-break  added  to  a  concrete  sea  wall 
Separately-molded  sections  for  a  concrete  sea-wall 

WELL  BORING. 

An  oil-well  i>ump  rod  joint  protector 
Diamond  drill  woric  on  the  deep  waterways  survey;  cost 
Electric  rock  drills;  by  E.  J.  Munby.    Not  illustrated 
Competitive  tests  of  rock  drills  for  air  consumption 
The  manufactxu^  and  use  of  diamond  tools 
Recovery  of  a  diamond-crown  from  a  deep  bore-hole 
A  rotary  drill  core  from  a  steel  I-beam  * 

The  work  of  well-drilling  machines  on  the  P.  R.  R. 
A  direct-acting  gasoline  rock  drill 

Double  wells,  and  casings,  for  pumping  diff.  waters 
MACHINES. 

Evolution  of  drop  hammer  for  die  forging 

Centrifugal  machines  and  their  uses 

Requirements  of  machine  tool  operation — motor  drive 

Concrete  mixing^  and  handling  machine — sea  wall 

Machines  for  bnquetting  Hue  dust,  fine  ore  and  fuel 

A  new  pneumatic  hammer 

Diagrams  for  estimating  hydraulic  machinery 

A  trussed  wagon  for  hauling  heavy  machinery 

A  rock  crusher  of  800  tons  per  hour  capacity 

A  molding  machine  for  building  cement  sidewalks 

A  machine  for  handling  coke  in  storage 

BUNKERS  AND  BINS. 


Bng.  News. 
Nov.  2. '06. 
July  12. 'OC. 
Aug.  23. '06. 
Sept.  27.  '00. 
Tune  9,  '10. 
July  28. '10. 


Eng.  News. 
June  26,  '02. 
July  10. '02. 
July  24, '02. 
Sept.  4. '02. 
Jan.  21. '04. 
Feb.  11, '04. 
June  16.  04. 
June  21, '06. 
Oct.  10, '07. 
April  16.  '08. 
April  22.  '09. 
May  13, '09. 
July   22. '09. 


Eng.  News. 
Oct.  31,  01. 
Jan.  28, '08. 
Oct.  22. '08. 
Dec.  17, '08. 
Aug.  18,  '10. 
Sept.  29,  '10. 


Eng.  News. 

uly  31, '02. 

uly  23, '03. 
Jept.  3. '03. 
July  16.  04. 
Jan.  19, '06. 
June  29,  '05. 
Nov.  30,  '06. 
April  12,  '06. 
Nov.  26.  '08. 
Eng.  Rec. 
Feb.  20.  '09. 


Eng.  News. 
Jan.  1.  '02. 
Dec.  11, '02. 
Jan.  8,  '03. 
Jan.  16, '03. 
Feb.  12, '03. 
Mar.  14. '03. 
Oct.  22, '03. 
Tan.  21,  04. 
June  4,  '08. 
June  18, '08. 
July  16. '08. 


Safe  and  proper  design  of  grain  storage  elevators 
Grain  pressures  in  deep  bins.    Tables  and  illustr 


illustrations 


byGoOg 


Eng.  News 
.Mar.  10. '04. 
Mar-  10. '04. 

39[e 


1482    71,— MISCELLANEOUS  DATA  AND  ILLUSTRATIONS. 

Description. 
Hydraulic  diaphragms  and  grain  pressure  tests 
Design  of  reintorced-concrete  grain  elevator  bins 
Grain  pressures  in  deep  bins;  strength  of  wooden  bins 
Tests  of  grain  pressxires  in  deep  bins.  Argentina 
A  problem  in  detailing  hopper  work 

lATge  reinforced-concrete  coal  pocket  at  Charlestown,  Btaas. 
Disastrotis  grain  elevator  explosion 
Reinforced-concrete  bins  for  storage  of  crushed  stone 
Reinforced-concrete  storage  bins  for  crushed  stone 
Reinforced-concrete  cylindrical  storage  bins 
Rein. -cone,  locomotive  coaling  station,  2,000  tons  capacity 
Rein.-conc.  grain  bins,  Gt.  Nor.  Ry.,  Superior,  Wis. 

Sections,  coal  and  ash  handling  plant  and  coal  bunker 
Large,  10,000  ton,  concrete  and  timber  coal  pocket 
Plans  of  rein.-conc.  coal  btmkers.  Annapolis,  Md. 

COMPRESSED  AIR. 

Use  of  comp.  air  for  contractor's  plant.   4-stage  air  comp'r 

Apparatus  and  methods  for  testing  air  motors  and  hammers 

Caisson  illness  and  diver's  palsv*  experimental  study 

An  ingenious  and  effective  air-lift  pump 

Ignitions  and  explosions  in  discharge  pipes  and  receivers 

Specifications  for  an  air  compressor 

New  method  of  pumping  sand  by  means  of  compressed  air 

A  new  positive-pressure  blower;  high  pressure 

Compressed  air  plant  used  in  boring  the  E.  River  tunnels 

Emergency  air-hft  equipment  for  deep  wells 

Hydraulic  compressed  air  plant,  Victoria  mines,  Mich. 

A  high-speed  oil  engine  air  compressor 

Effect  of  moistiu*  in  air  on  compressed  air  machinery 

Experimental  studies  of  air-lift  pumps;  tests 

Controlling  the  output  of  the  air  compressor 

The  Rateau  centrifugal  air  compressors  and  blowers 

HEATING  AND  VENTILATION. 

Some  experiments  with  ventilating  fans 

Recent  tests  of  centrifugal  mine-ventilating  fans 

Problem  of  ventilating  N.  Y.  subwavs  and  similar  tunnels 

A  fan  blower  driven  by  a  steam  turbine 

A  rapid  current  hot  water  heating  system 

Data  for  the  design  of  hot  water  heating  systems 

Air  washing  and  humidifying 


TELEPHONES. 


Long  spans  in  telephone  work 
The  development  of  telephony 


MININa 


Methods  of  mining,  hauling  and  screening,  in  Alabama 
New  type  of  iig  for  separation  of  metallic  ores 
Hammer  drills  for  overhand  stoping  in  gold  mines 

METAL  SPRINGS. 

New  Helical  Spring  Formulas  (following  is  excerpt) 

.     N«w  Helical  Sprint  Fonnnlas  have  been  arranged  bv  Mr.  CheMer  B. 

Albree  and  are  explained  in  his  paper  "Spring  Formulas  Amplified,"  viocli 


Bng.News. 

Apnl28.*0i. 

.  une 

23. '04. 

My 

14.  01 

16. '04- 

Aug. 

24. 'OS. 

Au8. 

27. '08. 

Oct. 

22.  -08. 

Nov. 

26, '08. 

Nov. 

21.  '09. 

Dec. 

2. 'Of. 

June 

22.  '10. 

Aug. 

4, -10. 

Eng.  Rec. 

Hay 

l.'OO. 

May 

8. 'Of. 

May 

15. '00. 

Rng 

.  News. 

Nov. 

26. 'OJ. 

Dec 

10.  03^ 

May 

5.  04. 

NoV. 

24,  04. 

Mar. 

2.  05. 

Mar. 

2.  05. 

Dec. 

7.  05. 

Feb. 

l.'O*. 

Aug. 

2, '08. 

Dec. 

13.  08. 

May 

2.  07. 

May 

7.'08w 

June 
Jtme 
Nov. 

18. '08. 

1S.'08- 

6.  08. 

Jan. 

20.  'la 

Ens.  Newt. 

Nov. 

3.  04. 

Nov. 

10. '04. 

Tune 
Nov. 

22.  "05. 

O.'OJL 

"Nov. 

22.'0flL 

Jan. 
Aug. 

80.  08. 

131  08. 

^18.  News. 

Mar. 

2.'fi 

April 

8.00. 

Bng.  News. 

Aug. 

80.08. 

Dec. 

7. '08. 

July  28.  11. 

Bng.  News. 

Jan. 

7, '09, 

COMPPRESSED  AIR,  ETC.    METAL  SPRINGS.  1483 

is  published  in  the  November  issue  of  the  "Proceedinss"  of  the  Engineers' 
Society  of  Western  Pennsylvania.  These  are  not  strictly  new,  being  derived 
from  the  well-known  Reideaux'  formulas: 

P-mS  — 

'*"«    Gd* 
in  which  /{"iradius  of  coil  to  center  of  wire. 

L«  uncoiled  length  of  wire, 
and  the  other  symbols  correspond  to  those  used  below.    The  process  of 
simplification  is  explained  by  Mr.  Albree,  in  pcut,  as  follows: 

In  comparing  tne  various  formulas,  it  was  found  that  certain  quantities 
could  be  combined  giving  formulas  of  much  simpler  character  and  yet 
equally  exact.  This  was  accomplished  by  cancellations  and  reductions, 
eluninating  the  third  and  fourth  powers  and  replacing  them  with  areas, 
diameters  and  constants.  This  is  done  with  the  intention  of  rendering  the 
solution  of  helical  spring  problems  easy  for  anyone  having  at  hand  standard 
tables  of  areas  and  decimal  equivalents.  The  writer  is  not  in  the  spring 
manufacturing  business  and  is  not  an  authority  on  the  subject.  The  formu* 
las  derived  with  the  terms  used  are  given  below: 

^      2D 
P       f_      L. 

/-^lorS- 100,000  lbs 

-  ^  for  S  -  80,000  lbs. 

-  ^  for  S- 60.000  lbs. 

P  fW        D^W 

^•"'•T*"''4o7? 

in  which  P"^  closing,  or  maximum  permissible,  load  of  spring. 

5  » torsional  strain,  outer  fiber. 
W-=anv  load  on  spring. 

f  "defection  of  one  coil  under  closing  load. 

]— deflection  tmder  any  load. 

_'  *  total  deflection  under  closing  load. 
Ff* total  deflection  under  any  load. 

J— diam.  of  bar  of  wire. 

a«area  of  bar  or  wire. 

Z>"idiam.  of  coil,  center  to  center  of  bar  or  wire. 

/f  >"free  height  of  coiled  spring. 

n<"  number  of  free  coils. 

(?"■  modulus  of  torsion. 
-12.600.000  lbs. 
The  formulas  are  bcwed  on  a  spring  designed  so  that  when  it  is  closed 
under  a  certain  load,  the  strain  5.  selected,  will  be  reached.  The  deflection 
formulas  give  the  pitch  of  coils  to  produce  strain  5,  when  closed.  With 
what  is  known  ordinarily  as  "spring  steel,"  it  is  safe  to  use  5-"  100,000  lbs., 
which  is  the  practice  of  the  spring  manuiacturers  of  Pittsburg. 

The  value  to  be  used  for  5^  should  depend,  of  course,  upon  the  nature  of 
the  work  for  which  the  spring  is  designed  and  the  conditions  tmder  which 
it  must  operate.  The  value  given  above  (S—  100,000  lbs.  per  sq.  in.)  is 
rather  high  for  general  conditions.  The  German  engineer's  pocketbook, 
"Hutte,"  gives  5—4,600  kg.  i>er  sq.  cm.  (which  is  closely  equivalent  to 
04,000  lbs.  per  sq.  in.)  for  spring  steel  with  fairly  constant  loading.  In 
springs  designed  for  continual  removal  and  application  of  load,  such  as 
inlet  or  exhaust-valve  springs  of  gas  engines,  5  should  not  exceed  46,000 
lbs.  per  sq.  in.  DgtizedbyGoOglc 


1484    n.— MISCELLANEOUS  DATA  AND  ILLUSTRATIONS. 

Tests  of  seed  Sprioffs  (Proc.  A.  S.  T.  M.,  Vol.  VIII..  1008).— The  foBow- 
ing  table  shows  the  effects  of  different  methods  of  tempering  on  the  eksac 
limit  and  modulus  of  elasticity  of  steel. 


Annealed 
in  lead 
at 

Hardened 

in  oil 

at 

Hardened 

in  water 

at 

Drawn 
to 

Ela8.Limit. 

Lbs.  per 

sq.  m. 

Mod.  of  Elas. 
Lbs.  per 

sq.  in. 

1400*  P. 

78  500 
187  500 
160  400 
177  600 
187  400 
180  700 
288  900 
240  800 
219  800 
212  000 

27  550  000 

1450*  P. 
1450*  P. 
1450*  P. 
1450*  P. 

560*  P. 
560*  P. 
400*  P. 

28  700  000 

27  150  000 

29  000  000 

28  610  000 

1426*  F. 
1425*  P. 
1425*  P. 
1425*  P. 
1425*  P. 

1060*  P. 
900*  P. 
750*  P. 
600*  P. 

28  070  000 

28  860  000 

29  220  000  broke 



30  430  000  broke 

39  960  000  broke 

METAL  HOISTING  CHAINS. 

Iron,  Oval,  Open-Link  Chains. — ^The  following  formulas  ^ve  the  dimen- 
sions, weights  and  strengths  of  iron  chains  with  open,  oval  hnks: — 

Let  d  -i  diam.,  in  ins.,  of  round  iron  used;  then — 

1.5  d  »  transverse  inside  diam.  of  oval  link,  in  ins., 

2.6  d  —  longitudinal  inside  diam.  of  oval  link,  in  ins., 

"»  effective  length  of  each  link  of  chain,  in  ins. 
/  =a  length  of  round  iron  in  each  link,  in  ins.. 

"9.475  df 
fc^»  weight  of  each  link,  in  lbs.. 

-0.m6/<i", 

-  2.108  iP; 
W  »  weight  per  Un.  ft.  of  chain,  in  lbs., 

-9.73(i»; 
5  «  ultimate  strength  of  chain,  in  lbs.. 

»  1.625  X  strength  of  single  rod  of  diam.  d. 


SOLAR  POWER. 


Power  from  the  sun's  heat 


EXPERT  VALUATIONS  AND  REPORTS. 

Mine  valuation  by  mining  experts 
Report  on  Chicago  street  railways  and  subways 
Depreciation  allowances  for  varioiispublic  service  industries 
Valuation  and  inspection  woric  of  Wis.  Tax  &  R.  R.  Com. 
Provision  for  depreciation  by  public  utility  corporations 
Table  of  freight  rates  on  coal,  iron  and  cement 
Necessary  elements  for  water  works  valuation. — Alvord 
Valuation  of  track  of  Detroit  St.  Ry.  System 

Diagram  illustrating  method  of  estimating  "Going  Value" 

CONTRACTS  AND  SPECIFICATIONS. 

Schedule  of  120  clauses  as  guide  in  drawing  specifications 


Eng.  News. 
Bfay  13. '01 


Bng.  News. 
Oct,  30,  03. 
July  19. 'Ol 
Jan.  33. '08^ 
Mar.  4.  '•9. 
Mar.  4.  '99. 
Mar.  11. '09. 
Mar.  10, '10. 
Sept.  8,  "10. 
Eng.  Rec 
June  19. '991 


Eng.  News. 
April  31,  'Oi 


d  by  Google 


GLOSSARY. 

(See,  also»  Index,  page  169B,  etc.) 


Abaciscus. — A  diminutive  of  abacus. 

Abacus. — ^The  flat  slab  (plinth)  forming  the  upper  member  of  the  capital  of 

a  column  to  support  the  architrave. 
Abscissa. — ^The  horizontal  or  %  distance,  measured  parallel  with  the  horizontal 

axis  X,  from  the  vertical  or  inclined  co-ordinate  axis  Y  to  any  jxtint  on 

a  curve  whose  ordinate  is  y;  x  and  y  are  co-ordinates  to  any  point  on  a 

curve,  measured  from  the  origin  or  from  the  axes  Y  and  X.    See  Analytic 

Geometrv,  page  266. 
AccllvitY. — An   upward  slope  or  inclination  of  the  grotmd;    opposed  to 

declivitv,  or  a  slope  considered  as  descending. 
Adit. — A  * 'horizontal'  excavation  or  drift,  specially  used  to  drain  or  operate 

a  mine;   it  is  not  continuous  as  a  tunnel  proper,  which  strictly  has  two 

openings.    Word  tunnel  often  wrongly  used  for  adit. 
Adiee. — A  tool  with  a  curved  blade  placed  at  right  angle  to  the  position  of 

an  axe  blade,  and  used  by  ship-  and  bridge  carpenters  in  dressing  the 

top  surfaces  of  timber,  ties,  etc. 
Alternate. — ^To  pass  from  one  state,  as  motion  or  position,  to  a  second,  then 

back  to  the  first,  and  so  on  in  rotation. 
Aftemations. — A  complete  alternation  is  a  change  in  the  direction  of  a  current 

in  a  circuit  from  its  former  direction  back  again  to  that  dirrction; 

symbol  '^. 
Aftemator. — A  common  term  for  an  alternate  current  d3mamo. 
Ammeter. — An  instrument  for  measuring  the  amperes  of  a  ciurent. 

Ampere. — ^The  unit  of  electric  current;    symbol,  C.     C  =  -^  in  which  £  — 

electromotive  force  in  volts,  and  R  =  resistance  in  ohms.  Current  flowing 
at  the  rate  of  one  ampere  transmits  a  quantity  equal  to  one  coulomb 
per  second.    One  volt-ampere —one  watt=»T}B  horse-power. 

Angl^bar. — A  bar  of  angle-iron. 

Angle^bead. — A  plaster-bead  or  staff-bead  used  to  protect  plaster  from 
injury. 

Ancle-beam. — A  beam  with  flange  set  at  an  angle  with  the  main  portion. 

Angle-bevel. — Bevel-sqiiare. 

Angle-Uock. — In  Howe  trusses,  a  "triangtxlar"  block  of  cast-iron  or  wood 
set  at  the  junction  of  the  wooden  chords  and  braces,  and  through  which 
pass  the  vertical  iron  or  steel  rods  called  ties. 

Ani^rafter. — A  rafter  joining  the  inclined  planes  of  a  hipped  roof. 

Angle-splice. — A  splice  tor  rails. 

Anneal. — ^To  remove  the  brittleness  of  metals,  earthenware,  glass,  etc.,  by 
heating  them  and  then  allowing  them  to  cool  gradually.  This  toughens, 
but  lowers  the  tensile  strength. 

Anticlinal. — ^The  incline  or  dip  of  stratified  rocks  in  an  upward  fold;  opposed 
to  synclinal. 

Anticlinal  Axis. — ^The  ridge  of  an  anticlinal. 

Apex. — ^The.top  jtmction  of  two  or  more  lines  or  members;  as  the  apex  of  a 
roof. 

A  priori. — From  that  which  precedes;  from  the  former. 

Apron. — ^Anjrthing'resembling  a  common  apron  in  form  or  use.  The  bridge 
of  a  ferry  dock.  A  platform  or  flooring  at  a  dock  entrance.  A  covering 
to  protect  anything,  as  a  dam,  from  water  flowing  over  it. 

Arbor. — An  axle  or  spindle  of  a  pinion  or  wheel.  A  mandrel,  in  lathe  turn- 
ing. 

Architrave. — ^The  lower  part  of  an  entablature,  which  rests  directly  on  the 
columns  and  supports  those  parts  of  the  building  above.  The  molding 
around  the  extrados  of  an  arch.  Sometimes  applied  to  ornamental 
moldings  on  faces  of  jambs  and  lintels  of  doors,  wmdows,  etc. 


1486 


Digitized 


by  Google 


1486  GLOSSARY, 

Archlvolt. — Ornamental  molding  on  extrados  of  arch. 

Armature. — ^That  part  of  a  magnet,  dynamo,  or  motor  designed  to  act  opoo* 

or  to  be  acted  upon  by,  the  lints  of  fores  set  up  by  the  poles  of  the  odd- 

magnet,  in  order  to  produce  motion  and  power  (when  placed  directly 

at  the  pole  of  a  permanent  magnet  it  is  called  a  keeper). 
Clxissification  (1): 

Polariud  a. — One  made  of  steel  or  of  another  electro  magnet  and  hay- 
ing poles  which  act  upon  and  are  acted  upon  by  the  field  magnet  poles. 
Non-polarised  a. — One  made  of  soft  iron  with  coils  of  wire  arranged 

in  any  form. 

Classification  (2): 

Ring  a. — Round  and  usually  of  circular  cross-section. 

Drum  a. — An  armature  of  cylindrical  form. 

Disc  a. — 

Pole  i-or-radial)  a. — 

Spherical  a. — Thomson-Houston  type. 
Classification  (3): 

Unipolar  a. — One  whose  polarity  is  never  reversed. 

Bipolar  a. — One  whose  polarity  is  reversed  twice  in  every  revolutk»i 
through  the  field  of  the  machine. 

Multipolar  a. — One  whose  polarity  is  reversed  "multi"  times  (more  than 
twice)  in  every  revolution. 
Armature.  Flat-Ring. — A  ring  armature  with  a  core  shaped  like  a  diort 

cylinaer. 
Armature,  Girder. — H-shaped  core. 
Armature,  Toothed-Ring. — A  ring  armature  with  core   provided   with  a 

number  of  teeth  forming  spaces  between  which  the  armature  coils  axe 

placed. 
Arrester,  Lightning. — An  apparatus  for  protecting  an  electric  circuit  from 

lightning. 
Arrester,  Lightning,  Transformer. — A  lightning  arrester  for  protecting  ttai^ 

formers. 
Arris. — The  edge-line  of  an  exterior  angle  formed  at  the  junction  of  two 

surfaces  meeting. 
Arris-gutter. — A  V-gutter  fisCed  to  the  eaves. 
Aslilar. — Cut-stone  masonry.    See  Masonry,  page  432. 
Astragal. — A  small  convex  molding  in  the  torm  of  a  string  of  beads. 
Axis. — ^The  imaginary  line,  relatively  motionless,  about  which  a  rotating 

body  turns. 
Axle. — A  shaft  in  the  position  of  the  axis  of  a  rotating  body. 
Axle-box. — ^The  box  containing  the  bearings  for  the  spindle  of  the  axle. 
Axle-guard. — ^The  parts  of  a  car  in  which  the  axle-box  moves  vertically 

when  the  springs  yield. 
Axle-seat. — ^The  hole  m  the  car  wheel  to  receive  the  axle. 
Axle-tree. — A  fixed  axle  as  for  a  carriage,  the  wheels  revolving. 
Azimuth. — An  arc  of  the  horizon  intercepted  between  the  meridian  of  a 

place  and  the  vertical  circle  passing  through  the  center  of  a  celestiaJ 

object.    A  star's  asimuth  and  altitude  determine  its  exact  positioa. 


Backing. — The  rough  masonry  of  an  arch,  abutment  or  wall,  faced  with  a 
better  class  of  masonry.  Of  an  arch,  it  is  the  course  of  masonry  resting 
upon  the  extrados. 

Balance-bar  =»  balance-beam. — A  long  bar  or  beam  attached  to  canaMock 
gates  and  drawbridges,  and  used  in  opening  and  closing  them  (usuallT 
serving  partly  as  counterbalances). 

Balk. — A  beam  or  timber  of  considerable  size.  In  coal  mining:  the  saddn 
contraction  of  a  bed  of  coal,  for  a  certain  distance. 

Ballast. — Broken  stone,  gravel,  slag,  sand,  or  other  suitable  material  placed 
on  the  su1>grade  of  a  roadbed  to  support  the  railroad  ties,  give  them 
lateral  stability,  and  decrease  the  dust  due  to  passing  trains. 

Ball-cock. — A  lever  with  a  hollow  metal  ball  attached  to  one  end  and  float- 
ing in  a  tank,  and  operating  (as  the  ball  rises  and  falls  with  tl^  water) 
a  valve  of  the  cistern  at  the  other  end. 

Ball-valve. — A  valve  formed  by  a  ball  resting  on  a  circular  seat  when  valve 
IS  closed;   but  which  is  free  to   rise  with  the  uMrard  nressuxe  o£  tie 

^^^'-  Digitized  by  GOOgFe 


ARCHIVOLT.  BOASTER.  1487 

Barco-board. — Gable-board  of  a  house. 
Ban,  Bus. — Omnibus  bars.    (See  Bars,  Omnibus.) 

Bars^  NegativM)moibas. — The  bus-bars  that  are  connected  with  the  nega- 
tive terminal  of  the  dynamos. 
Bars,  Neutral-Omnibus.— The  bus-bars  that  are  connected  with  the  neutral 

dynamo  terminal  in  a  three-wire  system  of  distribution. 
Bars»  Omnibus. — Heavy  bars  of  conducting  material  connected  directly  to 
the  poles  of  dynamo-electric  machines,  in  electric  incandescent  light  or 
electric  railway  installation,  and  therefore  receiving  the  entire  current 

produced  by  the  machine Main  conductors  common  to  two  or 

more  dynamos  in  an  electrical  generating  plant.  (The  terms  "bus"  and 
"omnibus"  bars  refer  to  the  tact  that  the  entire  or  whole  ciurent  is 
carried  by  them.) 

Bars,  Positive-Omnibus. — ^The  bus-bars  that  are  coxmected  with  the  posi- 
tive terminal  of  the  dynamos. 

Bascul»4>ridge. — A  counterpoised  drawbridge,  dating  back  to  medieval 
times;  as  the  leaf  of  the  span  rises,  the  counterpoise  weights  descend. 

Batter  (not  batir). — ^The  incline  (as  ot  a  masonry  wall)  from  the  perpendicu- 
lar; the  ratio  of  horizontal  to  vertical  distance,  as  1  in  12— 1  in.  hor. 
to  12  ins.  vert. 

Bay. — A  panel  of  one  span;  sometimes,  one  span  of  several  in  a  bridge. 
The  plain  part  of  anything  enclosed  or  bordered  by  featiires  in  relief. 

Bead. — Any  small  projecting  cylindrical,  globular  or  annular  body. 

Bearing. — The  direction  of  an  object  by  the  compass.  In  mining:  the  nm, 
course  or  strike.  In  architecture:  the  clear,  unsupported  span  of  a 
beam  or  timber.  In  engineering:  the  actual  surface  of  contact  of  and 
with  something  supported,  as  of  a  beam,  girder,  pivot,  axle,  etc.  In  ship- 
building: the  widest  part  of  a  vessel  below  the  plank -sheer:  also,  the 
line  of  notation  of  a  vessel  when  ready  for  sea;  using  in  each  case  the 
plural,  bearings. 

Bed-molding » bedding-molding. — A  molding  of  the  cornice  of  an  entabla- 
ture, above  the  frieoe  and  beneath  the  corona. 

Bed-plate. — A  plate  (usualljr  of  iron  or  steel)  laid  on  a  foundation  (say  of 
masonry)  and  used  to  give  direct  support  to  something  (as  a  machine 
or  bridge)  and  distribute  the  stresses  quite  tmiformly  (above  or  below 
or  both). 

Beetle. — A  heavy  wooden  mallet  (maul)  to  drive  wedges,  with  handle  for 
swinging;  a  rammer,  with  handle  set  in  middle  of  one  head,  used  by 
pavers. 

BeU-crank. — A  right-angle  lever  pivoted  at  angle,  for  changing  direction 
of  motion,  force,  etc. 

Bench-mark. — A  permanent  bench  of  known  or  determined  elevation  with 
reference  to  a  datum  plane,  in  a  line  of  levels. 

Berm  (old  form,  berme) «- i>erm-bank. — A  terrace;  a  strip  reserved  between 
top  of  cut  and  the  waste  bank  in  excavation,  or  between  the  bottom  of 
fill  and  the  borrow-pit  in  embankment;  the  bank  of  a  canal  opposite 
the  tow-path. 

Bessemer  steel. — Steel  made  bjr  the  pneumatic  process,  consisting  in  blow- 
ing air  through  molten  pig-iron  in  a  "converter"  lined  with  a  refractory 
material,  decarbonizing  the  iron;  later  a  certain  amotmt  of  carbon  is 
restored  by  introducing  spiegeleisen  or  ferromanganese. 

Beton. — Hydraulic-cement  concrete. 

Bevel. — An  instrument  with  a  blade  and  a  handle  or  stock,  movable  on  an 
adjustable  pivot  or  joint,  for  including  any  angle. 

Bevel-angle. — Any  angle  except  a  right  angle. 

Bevd-gear. — ^Toothed  wheels  which  gear  at  an  angle,  most  often  at  right 
angle. 

Bilge. — ^The  belly  or  widest  part  of  a  cask;  the  nearly  horizontal  part  of  a 
ship's  bottom,  adjacent  to  the  keel. 

Bilge-keelson. — A  fore-and-aft  timber  placed  inside  the  bilge  to  strengthen  it. 

Bit. — ^The  biting  or  boring  part  of  a  tool.  The  boring-bit  is  held  or  turned 
by  the  brace  of  bit-stock.    Old  form,  "bitt." 

Blast-pipe. — The  exhaust-pipe  of  a  steam  engine ;  in  locomotives,  it  leads 
into  the  smoke  stack  to  create  a  strong  draft. 

Board,  Switch. — A  board  provided  with  a  switch  or  switches,  by  means  of 
which  electric  circuits  connected  therewith  may  be  opened,  closed,  or 
interchanged.  ,  ...  ,    „       i  ^ 

Boaster -boasting-chisel.— A  broad  chisel  for  rough-hewmg  and  dre«ing 
stone.    The  use  of  such  a  chisel  is  called  "boasting.      ^OOglC 


1488  GLOSSARY, 

Body. — Consistency  or  density,  as  in  paints,  oils,  etc. 
Bolster. — A  "pillow"  of  timber  for  various  purposes;  a  short  timber  or  cap- 
piece  resting  on  a  post  or  column  to  give  more  extended  bearing  to  ibe 

string-piece  or  beam. 
Bond. — ^The  particular  arrangement  of  brick,  stone,  or  timber  to  give  certain 

specified  joints  and  courses.     Friction-resistance  of  steel  in  coiKrete. 
BofUMt. — A  cast-iron  plate  for  covering  the  opening  in  a  pipe  or  the  opening 

in    the    valve-chamber  of    a    pump;   the  cap  or  lid  of  an  iron  pipe;  a 

wire  netting  for  the  smoke  stack  of  a  locomotive,  to  serve  as  a  spark 

arrester. 
Bore. — ^The  internal  diameter  or  caliber  of  a  hole,  as  ih  a  pipe  or  hollow 

cylinder;  need  not  have  been  "bored." 
Borrow-pit. — ^The  site  where  excavated  material,  as  earth,  is  obtained  for 

filling  elsewhere. 
Boss. — A  projecting  mass,  as  of  stone,  to  be  cut  or  carved  later.    The  en- 
larged part  in  diam.  of  a  shaft  for  keying  a  wheel  or  (if  at  end)  making  a 

coupling. 
Box-drain. — A  rectangular  (or  square)  drain  of  masonry,  or  timber,  etc., 

under  an  embankment  (or  under  ground). 
Brace. — A  strut,  or  auxiliary  compression  member  in  a  frame:   a  bit-stodc, 

or  curved  handle  for  holding  and  turning  boring-tools  or  bits. 
Bracket. — A  projecting  piece  of  wood  or  metal,  fastened  to  a  wall,  or  ceiling. 

etc.,  and  used  as  a  support  for  some  object;  hence,  wall-brackets,  hang- 
ing-brackets, etc. 
Bracket,  Telegraphic — A  support  or  cross-piece  placed  on  a  telegraph  pole 

for  the  support  of  the  insulators,  which  are  supported  on  either  arms 

or  brackets. 
Brake. — Any  mechanical  device  for  retarding  motion  (as  of  a  vehicle)  by 

means  of  friction. 
Brake-hanger. — A  bar  or  link  suspending  brake-beams  and  accessories  from 

the  truck-frame  or  from  the  oody  of  car. 
Brake-head. — ^The  brake-block  (usually  cast-iron)  fastened  to  the  brake- 
beam  and  bearing  on  the  circumference  of  the  car  wheel,  forming  at  the 

same  time  the  brake-shoe. 
Brake-shaft. — ^The  shaft  on  which  the  chain  operating  a  car-brake  (by  hand) 

is  wound. 
Brass. — A  useful  alloy  of  copper  and  zinc;   harder  than  copper;   malleable 

and  ductile. 
Braze. — ^To  solder  with  "hard"  solder,  as  an  alloy  of  "brass  and  zinc" 

(» copper  and  zinc  in  different  proportions  than  that  composing  bruss). 
Break. — A  want  of  continuity  in  a  circuit. 
Breaker,  Circuit. — A  device  for  breaking  a  circuit. 
Break  joint. — To  arrange  parallel  members  so  the  ^ints  will  not  be  opposite; 

thus,  with  the  splicing  of  the  leaves  composing  the  chord  of  a  Howe 

truss,  or  the  two  rails  comp>osing  a  track,  etc. 
Breast-beam. — ^The  transverse  forward  beam  of  a  locomotive. 
Breast-board. — The  weighted  board  or  sled  used  in  rope  walks  to  keep  the 

yams  taut  while  bemg  twisted  into  a  strand. 
Breast-drill. — A  drill-stock  having  a  breast  piece  against  which  the  workman 

bears  while  operating  the  drill. 
Breasting. — The  (curved)  channel  in  which  a  breast-wheel  turns. 
Breast-line. — ^The  roi>c  used  to  connect  the  pontoons  of  a  floating  bridge. 
Breast-wall. — A  (low)  retaining  wall  at  the  bottom  of  a  slope. 
Breast-wheel. — A  water-wheel  with  radial  floats  or  buckets  on  its  periphery. 

the  water  being  confined  to  the  floats  by  the  "breasting"  of  timber  or 

masonry,  nearly  touching  the  wheel. 
Breech. — ^The  hind  part  of  anything;  the  angle  of  a  knee-timber,  opposite 

the    "throat." 
Brest-summer. — A  lintel;  a  beam  or  summer  placed  to  support  an  upper 

wall,  as  over  a  shop  window  or  door. 
Bricknog. — A  timber  framing,  as  a  partition,  filled  with  brickwork. 
Brick-trimmer. — A  brick  arch  to  protect  a  wooden  trimmer  in  front  of  « 

fireplace. 
Bridge-bar. — ^Thc  tension  bar  of  a  car-coupling. 

Bridge-boards  notch-board. — A  notched  board  of  a  stair  to  receive   the 
P   ^nds  of  the  wooden  steps  (treads)  and  risers. 
g]1y®"P'^«~-The  pit  for  the  counterpoise  of  a  bascule-bridge. 
Driages.--Heavy  coppwjr  wires  suitably  shaped  for  connecting  the  dvnamo- 

eiectnc  machmes  in  an  incandescent  light  station  to  the  bus-rods  or  wires 


^     BODY,  BY-WASH.  1480 

Bronze. — An  alloy  of  85%  ±  of  copper  and  usually  15%  T  of  tin;  variable; 
sometimes  no  tin;  sometimes  contains  zinc. 

Bnuh-HoMers  for  Dynamo-Electric  Machines. — Devices  for  supporting  the 
collecting  brushes  of  dynamo-electric  machines.  Brushes  ^ould  be 
adjusted  carefully  to  speed  of  machine  and  resistance  of  external  circuit. 
Carbon  brushes  are  plates  of  carbon  for  leading  current  to  electric 
motors.  Collecting  brushes  are  conducting  brushes  which  bear  on  the 
commutator  cylinder,  and  takes  off  the  current  generated  by  the 
difference  of  potential  in  the  armature  coils.  Copper  is  almost  univer- 
sally  employed. 

Bocicet^ngine. — An  inprovised  water-wheel  for  a  high  fall  with  scarcity  of 
water,  consisting  of  a  series  of  buckets  on  an  endless  chain  nmning  over 
a  pair  of  sprocket-wheels. 

Bucket-lift. — In  mining,  a  set  of  iron  pipes  attached  to  a  lifting-pump. 

Bucket-pftch. — ^The  circular  line  intersecting  the  elbows  of  the  buckets 
of  an  overshot  water-wheel. 

Bucket-valve. — The  valve  at  top  of  the  air-pump  bucket  in  a  steam'  engine. 

Bucket-wheel. — A  series  of  buckets  arranged  on  an  endless  chain  passing 
over  a  wheel,  for  raising  water;  or,  the  buckets  may  be  attached  to 
the  rim  of  the  wheel. 

Bnckinf  iron. — A  tool  for  pulverizing  ore  on  a  plate  called  a  "bucking- 
plate." 

Buckram. — Coarse  linen  cloth  stiffened  with  glue  and  used  for  binding 
books. 

Buffer. — An  apparatus  for  deadening  the  concussion  of  railway  cars. 

Bulkhead. — A  partition;  in  a  ship,  to  form  separate  apartments;  in  a  tunnel, 
conduit  or  mine,  to  prevent  the  passage  of  water,  mud  and  air.  An 
improvised  wharf,  sometimes  constructed  of  sunken  cribs,  to  form  a 
basin,  or  to  run  parallel  with  the  shore. 

Bull-pump. — A  pum ping-engine  with  piston-rod  attached  directly  to  the 
pumpmg-rod,  the  weight  of  the  rods  producing  the  down  stroke. 

Bumper-timber. — A  timber  to  which  the  cow-catcher  of  a  locomotive  is 
fastened. 

Bumpinc-post. — A  fender  or  buffer  at  the  end  of  a  raijroad  track  to  stop 
the   cars. 

Bunker. — See  "coal-bunker." 

Bnnker-friate. — An  iron  plate  covering  the  hole  in  a  ship's  deck  leading  to 
the  coal-bunker. 

Buoy. — A  fk>ating  body  anchored  in  a  harbor  or  stream  to  indicate  the  posi- 
tions of  objects  beneath  the  surface,  as  rocks,  shoals,  etc.,  or  to  locate 
channels.  Among  the  various  kinds  are  spar-buoys,  can-buoys,  bell- 
buoys,  whistHng-Duo3rs,  etc.  In  the  U.  S.,  red  buoys  mark  the  right- 
hand,  and  black  buoys  the  left-hand,  side  of  channels  coming  into 
port.  Buoys  with  black  and  red  transverse  stripes  mark  dangers  in 
mid-channel;  while  buoys  with  black  and  white  longitudinal  stripes 
indicate  fairway.    Green  buoys  indicate  sunken  wrecks. 

Burnish. — ^To  polisn  by  friction,  as  metals. 

Bur-pump  — burr-pump  =  bilge-pump. — Has  a  cup^shaped  cone  of  leather 
fastened  to  end  of  pump-rod,  the  sides  collapsing  as  the  rod  descends. 

Bush ->  bushing. — A  lining  of  harder  material  fitted  into  an  orifice  to  reduce 
wear  by  friction;  used  in  machinery  of  all  kinds. 

Bushel. — U.  S.  standard » 2150.42  cu.  ins.  British  imperial  bushel » 
2218.192  cu.  ins. 

Butt. — A  door-hinge.   A  large  cask,  containing  110  imperial  gallons. 

Butte. — A  rising  ground  or  mound. 

Butterfly-valve  =>  butterfly-cock. — Employed  in  lift-buckets  of  large  water- 
pumps  and  for  air-pump  buckets  of  condensing  steam-engines.  It  is 
a  double  clack-valve  or  wing-valve,  the  two  wings  being  hinged  to  a 
cross-rib  cast  in  the  pump  bucket. 

Butt-joint  — bntting-ioint. — Opposed  to  lap-joint.  A  joint  formed  by  the 
two  pieces  of  metal  or  timber  abutting  endwise,  and  usually  8plice<i 
togetner  with  other  pieces. 

Buttress. — A  prop  or  support  of  masonry.  A  bearing  or  thrusting  structure 
built  against  a  wall  to  give  it  stability. 

Buzz-saw. — A  circular  saw;  it  creates  a  *  buzzing"  noise. 

By-pus. — An  extra  gas-  or  water-pipe  passing  around  a  valve  or  chamber  so 
as  to  give  some  now  when  valve  or  chamber  is  closed. 

By-wash  -  by-lead. — A  channel   for  surplus  water  from  a^reservjoir  or 
aqueduct,   to   prevent  overflow.  Digitized  by  vjOOQIC 


14M  GLOSSARY, 


CaUeway. — A  taut  suspended  cable  for  conve3riiig  loads  suspended  in  t 
car  and  moved  by  a  hauling-rope  or  other  device. 

Caisson. — A  water-tight  casing  used  in  building  the  foundation  of  structtoes 
in  water  too  deep  for  the  coffer-dam.  It  is  sunk  by  under-mining  and 
the  masonry  is  laid  on  top  as  it  descends  into  the  mud. 

Calcination. — The  process  ot  expelling  volatile  matter  from  a  substance 
by  heat,  and  reducing  it  to  a  triable  state:  as  carbonate  of  lime,  to  hn». 

Caliber™ calibre. — ^The  diameter,  especially  the  inner  diameter  or  bore. 
In  firearms,  a  44  caliber  rifie  is  one  whose  bore  is  0.44  in.  dia. 

Caliper  "Calipers. — ^An  instrument  like  a  pair  of  dividers,  but  with  curved 
legs,  for  measureng  inside  and  outside  diameters. 

Calking —caiilking. — ^The  operation  of  filling  seams  of  vessels  with  oakum 
to  prevent  lecucs;  or.  the  joints  of  cast  iron  pipes  with  oakum  and  lead, 
the  oakum  and  lead  being  calked  with  a  calkmg-iron  or  chisel,  hammered 
with   a   calking-mallet. 

Calorimeter. — An  apparatus  for  measiuing  the  quantity  of  heat  givea  off 
by  a  body,  etc. 

Cam. — ^A  device,  usually  upon  a  shaft,  for  converting  a  regular  nx>tion  into 
an  irregular,  an  alternating,  or  a  reciprocal  one.  An  eccentric.  An 
elliptical  lever  for  raising  the  ends  of  drawbridges,  when  closed,  to  a 
firm    bearing. 

Canii>er. — In  a  bridge,  a  slight  upward  curve  in  the  span,  to  allow  for  settHng 
when  loaded,  or  for  appearance.  In  laying  cast-iron-pipe  culverts 
tmder  a  railroad  embankment,  they  should  be  jointed  or  laid  tn  a  vertkal 
curve,  convex  upward,  to  allow  for  settlement  in  the  middle. 

Camel. — A  water-tight  apparatus  which  is  filled  with  water,  sunic,  attadied 
to  vessel's  bottom,  water  pumped  out.  and  which  then  assists  in  floating 
the  vessel  over  a  shoal,  or  raising  her  from  wreckage. 

Candle-foot. — A  unit  of  illumination  equal  to  that  produced  by  a  standard 
candle  at  a  distance  of  I  foot.  The  ix>wer  is  inversely  proportional  to 
the  square  of  the  distance;  thus,  the  illtunination  at  S  feet  is  one-nintii 
that  at  1  foot. 

CandleH>ower. — The*  standard  is  a  spermaceti  burning  at  the  rate  of  III 
grains  of  sperm  i>er  hour. 

Cantilever. — A  clock  or  bracket  framed  into  the  wall  of  the  building,  pro- 
iectingfrom  it,  and  used  for  supr>ortin^  a  molding,  balcony,  eavea,  etc 

Capital.— -The  top  of  a  column,  pillair  or  pilaster. 

Cap^an. — An  apparatus  something  on  the  principle  of  a  windlass,  but  with 
a  vertical  axis.  The  man-power  is  applied  to  capstan-bars  inserted 
horizontally  in  holes  near  top  of  windlass,  a  few  turns  of  the  rc^, 
cable  or  chain  being  wound  around  the  barrel  of  the  latter.  At  the  bottom 
of  the  barrel  is  a  pawl-head  with  pawls  to  engage  a  ratchet-rins  secured 
to  the  platform. 

Carbonize. — ^To  combine  with  carbon,  as  in  the  manufacture  of  steel  by  the 
cementation  process.     Hence  the  term  carbomsation. 

Carburize. — ^To  combine  with  carbon  or  a  carbon  compound.  (The  vapors 
of  volatile  hvdrocarbons  are  often  mingled  with  combustible  gases  in 
order  to  produce  higher  illuminating  power  in  the  latter).  The  process 
is  called  carburisaticn. 

Case-liardeninf . — A  quick  process  of  cementation  or  converting  the  outer 
surface  of  iron  into  steel  by  heating  it  in  contact  with  charcoal  or  uxoe 
animal  matter  as  bone,  hoof  parings,  or  leather. 

Casemate. — ^The  masonry  vault  in  the  rampart  of  a  fortress,  or  the  armcMcd 
bulkhead  in  warships,  pierced  in  front  with  embrasures  or  port-he^ 
through  which  guns  are  fired. 

Casting-pit. — ^The  part  of  a  foundry  where  molds  are  placed  and  ^^Tti^y 
made. 

Causeway. — A  raised  path  or  road  over  bad  ^roimd.  A  raised  sidewalk. 

Cavetto. — A  concave  molding  of  at  least  }i  circle  used  in  cornices,  etc  A 
recessed  pattern;  opposed  to  relief. 

Cementation. — In  metallurgy,  a  process  of  effecting  a  desired  important  ^letn- 
ical  change  in  a  substance  when  heated  in  contact  with  another 
substance.  Bar-iron  may  be  made  into  steel  by  heating  it  above  zednMt 
while  embedded  in  charcoal-powder.  Such  a  process  is  termed  carbon- 
sation  by  cementation.  Decarburization.  or  the  converting  of  cast- 
iron  into  malleable-iron,  is  effected  by  embedding  the  «*y«^nc  in  red- 
hematite  powder  and  keeping  it  some  time  at  a  red  heat. 


CABLEWAY,  CLAW-WRENCH,        1491 

Cemcat-copper. — Copper  precipitated  by  the  process  of  cementation. 
Center i-cemerinc — ^Tne  uame  supporting  an  arch  during  construction. 
Center  of  oscQIaaon. — Coincides  with  the  center  of  percussion. 
Center  of  percussion. — ^That  point  in  a  revolving  or  swinging  body,  or 

pendtdum,  at  which  if  all  the  mass  were  concentrated  the  ettect  would 

remain  unchanged;  the  point  of  greatest  impact  with  another  body, 

remaining  immovable  without  rotation  at  time  of  contact  if  the  opposing 

body  is  fixed. 
Center-plate. — ^A  plate  which  supports  a  car-body  on  the  center  of  a  truck. 
Centei^valve. — A  four-way  gasncock. 
CentrifuRaL — Radiating  or  outward  (force)  from  the  center.  Opposed  to 

centripetal. 
CeaspooL — ^A  shallow  welt  of  large  diameter  for  receiving  sewerage  from 

isolated  buildings.   Brat  constructed  in  sand  or  gravel,  with  linings, 

say  of  brick,  for  the  side  walls  only.  Covered  top. 
Chamfer. — ^To  cut  away  the  edge  of  a  square  comer  so  as  to  form  a  bevel 

edfle,   generally   projecting. 
ChamfeTMl. — ^Anything  in  which  the  surface  is  beveled.     See  Side-hatchet. 
Chase. — ^To  decorate  metal-wotk  by  tooling. 
Cbeck-nut — A  nut  placed  on  a  screw  or  bolt  to  prevent  the  main  nut  from 

turning  when  in  place. 
Check^op. — In  deep  dredging,  a  device  to  prevent  the  dredge-line  from 

breaking  when  the  dredge  louls. 
Check-valve. — A  valve  placed  in  a  pipe  to  prevent  the  backward  fiow  of 

the  water,  steam,  or  other  fluid. 
Cheek. — One  of  two  symmetrical  pieces  enclosing  something  between  them: 

one  of  the  jaws  ot  a  vice,  one  of  the  walls  of  a  vein  of  ore,  one  r-t  the 

sides  of  a  pillow-block,  etc. 
QdlL — ^A  metal  mold  for  making  certain  kinds  or  parts  of  iron  castings; 

the  surface  in  contact  with  the  mold  cools  rapidly  and  hardens. 
CUmney-cap. — ^A  device  on  top  of  a  chimney  which  is  turned  by  the  wind 

so   the   exit-aperture   is   always    to  leeward,  thus  helping  the  smoke 

to  escape.  A  chimney  jack. 
Chimnnr-stack. — Several  chimneys  carried  up  together. 
Chisel-draft. — ^The  dressed  edge  of  a  stone,  either  complete  or  as  a  guide  in 

dressing  the  stone. 
Qiock. — ^A  piece  of  wood  inserted  to  prevent  movement,  as  the  chock  nailed 

on  the  cap  of  a  trestle  between  the  two  lines  of  stringers. 
Chuck. — A  block  or  device  in  a  lathe  for  holding  anything  to  be  turned. 
Chttm-drifl. — A  \oas  stone-drill  operated  by  hand:  raised  and  let  fall. 
Cinder. — A  mass  ot  ashes,  containing  more  or  less  unconsumed  coal.  Pig- 
iron  slag  from  a  blast-furnace. 
Clfcnit,  CwMd-Magnctic — A  magnetic  circuit  which  lies  wholly  in  iron 

or  other  substance  of  high  magnetic  permeability.  All  lines  of  magnetic 

force  form  cloeed  circuits.  An  iron  nng  forms  a  closed-magnetic  circuit. 

Where  an  air  gap  is  formed,  as  in  the  case  of  a  horse-shoe  magnet  with  its 

keeper,  it  is  called  an  open-magnetic  circuit.   In  other  words  a  closed 

circuit  is  formed  by  a  rizi^  of  high  magnetic  permeability. 
Circuit,  Electric. — ^The  path  m  which  electricity  circulates  or  passes  from 

a  ^ven  point,  around  or  through  a  conducting  path,  to  its  starting 

pomt. 
Circuit,  ExternaL — ^That  part  of  a  circuit  which  is  external  to,  or  outside 

the  electric  source. 
Circuit,  Magnetic. — ^The  path  through  which  the  lines  of  magnetic  force 

pass.   (They  always  form  closed  circuits.) 
Circuit,    Short. — Shunt    circuit. 
Clack-valve. — A  hinged  valve  placed  in  a  clack-box.  and  consisting  of  a  plate 

of  leather  strengthened  above  by  a  plate  of  iron  larger  in  dia.  than  the 

main  pipe,  and  below  by  a  plate  of  iron  smaller  in  dia.  than  the  main 

pipe.  The  dia.  of  box  is  about  IJ  times  dia.  of  pipe.   Used  in  pumping. 

A   flap-valve  or  clapper. 
damp. — Any  instrument  used  to  hold  anything  or  to  hold  two  or  more 

pieces  together,  bv  pressure.  Various  forms  for  different  trades  and  uses. 
Clapboards. — Long  thin  boards,  thicker  on  one  edge  than  on  the  other, 

and  nailed  horizontally  on  the  sides  of  a  house,  lapping  shingle-fashion. 
Claw. — A  part  of  a  tool  resembling  a  claw  (hand). 
Cfaw-hammer. — A  hammer  cleft  for  drawing  nails. 
Claw-wrench. — A  common  wrench  with  one  jaw  fixed  an^  t@(5(Wfe™°^^' 


1492  GLOSSARY. 

Clayiilf«bar. — In  blasting,  a  rod  for  driving  clay  into  crevices,  to  protect 
the  charge. 

Cleat — Any  piece,  as  wood  or  iron,  for  fastening  a  rope;  or  by  nailing  to 
other  pieces  to  fasten  them  together. 

Clevis. — ^An  iron  shaped  like  a  horseshoe,  or  stirrup,  or  U,  with  provision  for 
tnserting  a  bolt  acroes  or  between  the  ends  in  order  to  form  a  link. 

CUck— clicker. — A  kind  of  rachet.  A  small  bar  pivoted  at  one  end.  free  to 
move  backward  on  a  toothed  rack,  but  in  moving  forward  it  engages 
one  of  the  teeth  and-raoves  the  object  forward,  leaving  it  at  rest  durxsg 
the    backward    stroke. 

CUmbiag-lrons — cllwbers  — cjsciwf >. — Iron  frames  with  spikes,  for  climbing 
telegraph  poles,  trees,  etc. 

Clliiclier4mUt«cUnker-birilt. — Composed  of  pieces  overlapping  one  another, 
as  in  clincher-built  boats  where  the  boards  overlap  Uke  clapboards. 

Clinker. — ^The  fused  or  melted  ash  formed  by  the  combustion  of  coal;  par* 
tiall3r-vitrified  bricks. 

Clip. — A  metal  clasp,  as  for  holding  a  bunch  of  paper,  or  a  Y-level  telescope, 
etc. 

Clip-yoke. — ^The  small  plate  through  which  the  ends  of  a  U-shaped  clip  pass, 
and  serving  as  washer-plate  for  the  nuts  of  the  clip. 

Cloister. — A  covered  walk  or  arched  way  aroimd  the  walls  of  a  building, 
the  outer  edge  being  supported  on  a  series  of  arcades  or  arches  resting 
on  columns. 

Close-hauled. — Sailing  as  close  to  the  wind  as  possible. 

Qtatch. — A  movable  coupling,  as  for  connecting  or  disconnecting  the  ends 
of  two  adjacent  shafts  to  make  them  revolve  together  or  to  aik>w  them 
to  revolve  separately.  If  operating  by  friction  it  is  called  a  friction- 
clutch;  bv  engaging  prongs,  a  bayonet-clutch.  The  cross-head  of  a 
piston  rod  is  a  form  of  clutch. 

Coal-bresker. — A  person  occupied  in  breaking  the  lan[e  masses  of  coal  as 
they  come  from  the  mine;  or  who  operates  a  machme  for  this  purpose : 
or  the  machine  itself;  or  the  building  or  structure  in  which  the  oreakicg 
is  done. 

Coal-bunker. — A  place  for  storing  coal. 

Coal-gas. — An  illuminating-gas  obtained  by  heating  coal  in  ck>acd  iroc 
vrssels  free  from  air;  contains  about  46%  hjrdrogen,  35%  mar^  gas, 
7%  carbonic  oxid.  4%  olefiant  gas,  tetrylene,  sulphureted  hydrogen, 
nitrogen  and  carbonic  add  and  traces  of  other  gases. 

Coal-oU-petroleuin  — rock-oil. — By  refining,  we  get  kerosene,  naphtha,  etc 

Coaming— combing. — ^The  raised  borders  or  edges  of  the  hatches,  to  prevent 
water  on  the  deck  of  a  vessel  from  rtmning  into  the  hold. 

CoaMar. — ^The  thick,  black  liquid  which  condenses  in  pipes  when  gas  is 
distilled  from  coal.  Contains  anthracene,  benzol,  carbohc  acid,  creosote. 
naphtha,  naphthalin, paraffin,  pitch. etc.  Used  for  metal coatiags,  as  far 
cast-iron  pipe;  in  making  asphalt  tor  pavements,  etc. 

Cock. — A  faucet,  turn-valve,  or  valve,  for  regulating  the  flow  of  fltxids; 
as  air-cock,  gage-cock,  feed-cock.  etc. 

Cock-brass  => cock-metal. — An  alloy  of  two  parts  copper  and  one  of  lead: 
used  for  large  vessels,  cocks  or  taps. 

Cock-water. — Water  used  to  wash  away  sand  from  ores. 

Coefficient. — ^A  quantity,  number  or  constant  (as  1/10,  4.  b.  etc.)  tased  as  a 
multiplier  into  some  algebraic  expression  or  physical  property  of  a  scb- 
stance  or  condition :  The  coefficient  ot  friction  is  the  tangent  of  the  ai^-* 
of  repose  of  a  body;  the  differential  coefficient  (in  the  (Calculus)  is  itf  ' 
rate  of  change  of  a  fimction;  the  coefficient  c  in  Kutter's  formidfc.  | 
c = vVrl^  is  the  coefficient  of  velocity  of  flow  for  the  particular  condition 
imposed,  as  roughness  ot  surface  n,  hydraulic  radius  r .  and  hydraula: 
slope  s;  the  coefficient  of  safety,  as  6,  means  that  the  conditions  aDo-rrd 
are  1/5  the  ultimate.  "(Efficient"  is  synonymous  with  *"aaodulus"  a 
many  cases,  as  "Cxxjf.  of  Elasticity"  —  '  mod.  of  elas." 

Coffer^lara. — A  water-tight  enclosure  built  in  a  body  of  water  in  order  to 
exclude  the  water  and  maintain  a  dry  space  for  the  constructioa  ci 
foundations,  bridge  piers,  etc.   Sheet  piling  is  useful  for  this  purpose.. 

Cog. — ^The  tooth,  catch  or  projection,  as  of  a  cog-wheel.  I 

Cog-rail. — A  rack  or  rail  with  cogs,  placed  between  the  rails  of  a  track  t.  I 
engage  the  cogged  driving-gear  of  the  locomotive  in  drawing  trains  t;  I 
inclined  railways,  too  steep  for  ordinary  traction.  The  rack  is  oompoeec  I 
of  cogs  fastened  between  two  angle-irons.  GoOqIc  I 


CLAYING'BAR.  COMBUSTION.  1493 

Coil,  Cliokiiig. — A  coil  of  wire  so  wound  on  a  core  of  iron  as  to  possess  high 

self-induction.  Such  coils  are  used  to  obstruct  or  cut  off  an  alternating 

current  with  a  loss  of  power  less  than   with   the  use  of  mere  ohmic 

resistance. 

Coil,  Electric. — A  convolution  of  insulated  wire  through  which  an  electric 

current  may  be  passed. 
Coilf   Impedance. — A  term   sometimes  applied   to   a  choking-coil.   (Self- 

mduction  produces  impedance.) 
Coil,  Induction. — An  apparatus  consisting  of  two  parallel  coils  of  insulated 
wire  employed  for  the  production  of  currents  by  mutual  induction. 
It  consists  essentially  of  a  ffrimary  coil,  a  stcondary  coil,  and  an  iron 
core,  usually  laminated.  The  primary  coil  is  woimd  around  the  core, 
and  over  that  the  secondary  coil.  The  former  is  composed  of  thick  wire, 
and  the  latter  of  thin  wire.   If  a  current  is  passed  through  the  primary  coil 
its  voltage  is  raised  in  the  secondary  coil. 
Cofl,  Induction.  Inverted. — ^An  induction  coil  in  which  the  primary  coil  is 
made  of  a  long,  thin  wire,  and  the  secondary  coil  of  a  short  thick  wire. 
Hence,  a  current  passing  through  the  primary  coil  induces  a  current  of 
hwer  potential  in  the  secondary  coil. 
CoH,  Magnet. — A  coil  ot  insulated  wire  surrounding  the  core  of  an  electro- 
magnet, and  through  which  the  magnetising  current  is  passed. 
Coil,  Pnmaiy. — ^That  coil  or  conductor  of  an  induction  coil  or  transformer, 
through  which  the  rapidly  interrupted  or  alternate  inducing  currents 
are  sent. 
Coil;  Secondary. — ^That  coil  or  conductor  of  an  induction  coil  or  transformer, 
m  which  alternating  currents  are  induced  by  the  rapidly  interrupted 
or  alternating  currents  in  the  primary  coil. 
Coil,  Shunt. — A  coil  placed  in  a  derived  or  shtmt  circuit. 
CoHs,  Armature,  or  Dynamo-Electric  Machine. — The  coils,  strips  or  bars 
that  are  wotmd  or  placed  on  the  armature  core.  The  wire  is  as  thick  as 
possible  consistent  with  the  desired  electromotive  force  without  requiring 
excessive  speed  of  rotation.  The  armature  coils  should  enclose  as  many 
lines  of  force  as  possible.     If  rods  or  bars  are  used  they  should  be  lami- 
nated in  planes  parallel  to  the  lines  of  force  so  as  to  avoid  eddy  currents. 
The  coUs  of  pole  armatures  should  be  wound  near  the  poles  rather  than 
on  the  middle  of  the  cores.  Open-circuit  coils  or  simply  open  coils  are 
those  which  are  independent  of  one  another,  either  for  a  part  or  the 
whole  revolution.  Closed-circuit  coils  or  simply  closed  coils  are  con- 
nected coils.   In  alternate  current  dynamos  the  separate  coils  that  are 
used  on  the  armature  may  be  coupled  either  in  serus  or  in  muUij^-Qrc 
(multiple-arc  or  multiple  circuit  means  a  compotmd  circuit  in  which  all 
positive  poles  are  joined  to  one  end  of  a  conductor,  and  all  negative 
poles  to  the  other  end.)   They  are  connected  in  series  usually  in  altera 
nate  current  machines  of  high  electromotive  force  where  the  converter  is 
at  a  considerable  distance;  and  in  parallel  where  low  electromotive  force 
is  sufficient,  as  for  incandescent  lamps  in  multiple  arc. 
Coke. — A  useful  product  of  coal,  for  the  manufacture  of  iron.  Coke  is  the 

"charcoal"   of  coal. 
CoUtltude. — W*  minus  the  Latitude  of  the  place. 

Cold-chisel. — ^A  tempered  steel  chisel  with  a  cutting  edge  for  cutting  metal. 
Coid-ehot*- cold-shut. — In  fotmdry  work,  small  particles  of   iron  totmd  in 

chilled  parts  of  a  casting. 
Collar. — A  ring,  or  anything  resembling  a  common  collar:  an  enlarged  part  of 

a  shaft,  or  the  enlarged  portion  of  a  car-axle,  etc. 
CoUar-beam  — wind-beam. — A  timber  beam  stretching  horizontally  between 

two  rafters  (forming  a  letter  A)  in  order  to  prevent  sagging,  etc. 
Collectors  of  Dynamo-Electric  Machines. — In  a  restricted  sense  collectors 
are  brushes  or  points  used  to  carry  off  the  current  generated  in  alter- 
nate-current machines,  being  distinguished  from  comtnutatots  which 
carry  off  the  current  generated  in  continuous-current  machines.  In 
other  words,  commutators  change  alternate  currents,  generated  on  ro- 
tation of  the  armature,  to  continuous  currents,  while  collectors 'do  not. 
Nevertheless,  the  name  "collectors"  is  sometimes  used  to  embrace 
"commutators". 
Column  "pillar. — A  vertical  "shaft"  set  on  a  "base"  and  surmounted  by 
a  "capital."  In  classic  architecture  we  have  the  Doric,  Ionic  and 
Corintnian.  -  ,.    ^i. 

Combustion.— A  rapid  oxidation  of  a  combustible  subetan<wj  OMwefi  by  tne 
chemioal  union  with  the  oxygen  of  the  air.  i^^d  by  ^^uuy  le 


1404  GLOSSARY. 

Commutator. — A  device  for  changing  the  direction  of  an  electric  cttncnt 

Commutator,  Dynamo-Electric  Macmncs. — ^That  part  of  a  dynamo-electric 
machine  which  is  designed  to  cause  altematmg  cturents,  produced  m 
the  armature,  to  flow  in  one  and  the  same  direction  in  the  eztenal 
circuit;  that  is,  to  change  alternate  to  continuous  currents. 

Concrete. — ^The  compact  mass  formed  by  an  agitregate  of  broken  stone  or 
.other  coarse   material   mixed   with  a   matrix  of   (hydraulic-cement) 
mortar.  There  are  other  kinds,  as  asphalt-conciete,  etc. 

Concrete  rubUe-maaonry. — Rubble  masonry  in  which  concrete  is  taed 
instead  of  the  usual  cement  mortar:  for  economy  of  cement. 

Condenser. — A  device  for  accumulating  or  condensing,  as  electricity,  water 
etc.  The  stuiace  condenser  in  a  steam-engine  is  one  in  which  the  ex- 
haust-steam passes  through  a  large  number  of  pipes  immersed  in  cold 
water,  constantly  renewed. 

Conductivity. — ^The  property  which  a  body  or  substance  has  of  condoctixig 
electricity,  heat  or  soimd.  It  vares  with  the  temperature  and  the  physi- 
cal stress  (as  tension)  of  the  substance.  In  electricity,  it  varies  inversely 
with  the  resistance,  as  Co£-4-R;  and  is  defined  as  the  reciprocal  (U 
electric  resistance,  R. 

Conductor. — ^A  sdbstance  which  will  permit  the  passage  of  an  electric 
current.  The  term  "conductor"  is  used  in  a  relative  sense,  as  we  have  no 
knowledge  of  any  material  that  is  absolutely  a  non-conductor. 

Conductor,  Anti-Induction. — A  conductor  so  constructed  as  to  avoid  'exoe»> 
sive  inductive  effects  from  neighboring  circuits. 

Conductor,  Armored. — One  provided  with  a  covering  of  metal  over  the 
insulating  covering  for  protection  from  abrasion. 

Conductor,  Potential  of. — The  relation  existing  between  the  quantity  of 
electricity  in  a  conductor  and  its  capacitjr.  For  a  given  quantity:  the 
smaller  the  wire,  the  higher  the  potential.  For  a  given  conductor: 
the  greater  the  quantity  the  higher  the  potential. 

Cone-gear. — ^Two  cones  transmitting  motion  by  rolling  friction. 

Connecting-rod. — ^The  "rod"  which  connects  the  (^rank  of  a  body  having 
a  circular  motion,  in  order  to  transmit  motion  or  force  to  or  from 
some  other  body,  as  the  connecting-rod  of  a  locomotive  or  of  a  beazo- 
engine. 

Console. — A  bracket  or  corbel  with  ornamental  carvings  or  shape  like  an  S: 
used  for  support  of  cornice,  etc.  A  wall-bracket  forsupporting  machinery. 

Contacts,  Lamp. — Metallic  plates  or  rings  connected  with  the  terminate  of 
an  incandescent  lamp  for  ready  connection  with  the  line. 

ContouMine. — A  line  on  a  topographical  map  joining  points  of  equal  eleva- 
tion. A  10-ft. -contour  map  shows  contour-lines  marking  surface  eleva- 
tions 10  ft.  apart,  vertically. 

Controller. — Any  device  used  to  regulate  the  flow  of  air,  water,  electricity,  etc 

Controlling-nozzle. — A  device  for  regulating  the  sise  of  stream  issoing 
from  a  nozzle. 

Convective,  Electric. — ^The  air  particles,  or  air  streams,  which  are  thrown 
off  from  the  pointed  ends  of  a  charged,  insulated  conductor.  These 
streams  act  magnetically,  and  are  themselves  acted  on  by  magnets. 

Converter. — A  vessel  swung  on  an  axis,  lined  with  some  refractory  material, 
in  which  molten  pig-iron  is  converted  into  Bessemer  steel. 

Coping. — The  top  or  finishing  course  of  a  masoniy  wall,  usually  projectiag 
a  few  inches  beyond  the  line  of  neat-work  of  the  facing,  and  beveled 
for  appearance  and  to  shed  water. 

Corbel. — A  horizontal  projecting  piece,  acting  as  a  cantilever  in  assisting  to 
support  a  beam  or  piece  resting  or  partly  restii«  upon  it.  In  nii3- 
building  construction,  the  columns  are  often  capped  with  corbels  whkk 
project  a  short  dist€mce  tmder  the  superimposed  beams.  Their  tztihty 
IS  questioned  by  many  engineers. 

Corduroy-road. — A  road  constructed  of  logs  laid  transversely  axKi  doae 
together,  usually  across  muddy  or  mar^y  ground. 

Core. — ^The  inner  portion  or  filling  of  a  wall.  The  izmer  mold  of  a  ^^«»*«g  to 
make  the  hollow  space,  as  of  a  pipe.  The  iron  body  of  an  electronagnet. 
The  comparatively  thm  wall  of  masonry  constructed  in  the  heart  ol  aa 
earth  dam  to  prevent  leakage. 

Core,  Armature,  Filamentous. — Aa  armature  core,  the  iron  of  which  ooo- 
sists  of  wire. 

Core,  Armature,  H. — An  armature  core  in  the  shape  of  the  letter  H,  generally 
Known  as  the  shuttle-  or  the  girder  armature.    We  j^so  ha\|o  the  I  r  — ^ 

^^^'  tized  by  Google 


COMMUTATOR.  CRANK.  1496 

Coce,  Armature,  LaminatJoii  of. — ^The  subdivision  of  the  core  of  the  arma- 
ture of  a  ajmamo-electric  machine  into  separate  insulated  plates  or 
strips  to  prevent  eddy  currents. 

Core,  Armature,  of  Dynamo-Electric  Machine. — ^The  iron  core,  on,  or  around 
which,  the  armature  coils  ot  a  d3mamo-electric  machine  are  wound  or 
placed.  It  is  laminated  to  prevent  eddy  currents.  In  drum,  and  in 
ring  armatures  the  lamin«e  are  in  the  form  of  thin  insulated  discs  or 
soft-iron  plates;  in  polt  armatures,  in  bundles  of  insulated  wires. 

Core,  Armature,  Radlally-Ljuninated. — ^An  armattire  core,  the  iron  of  which 
consists  of  thin  iron  washers. 

Core,  Armature,  Ribbed. — A  cylindrical  armature  core  provided  with  longi- 
tudinal projections  or  ribs  that  serve  as  spaced  channels  or  grooves  for 
the  reception  of  the  armatiuv  coils. 

Cornice. — ^An  ornamental  or  molded  projection  at  the  top  of  a  building- 
wall,  masonry  wall.  etc. 

Corrugated. — Wrinkled  in  regular  furrows,  as  corrugated  iron. 

Cotter  oCotter4N>lt«cotter4cey. — A  wedge  inserted  to  fasten  or  tighten.  A 
split  bolt  whose  ends  are  spaced  apart  when  inserted  as  a  key. 

Cooloaib. — ^The  unit  of  electrical  quantity.  That  quantity  of  electricity 
that  will  pass  in  one  second  in  a  circuit  whose  resistance  is  one  ohm, 
and  electnc-motive  force  one  volt. 

Coulomb- Volt. — Volt-coulomb  or  Joule  — 0.7373  foot-pound. 

Counterbrace. — In  a  frame,  the  brace  which  crosses  the  main  brace  and  is 
designed  to  transmit  the  compressive  stress  in  a  panel  due  to  negative 
shear,  i.  e.,  when  the  stress  in  the  main  brace  would  change  from  com- 
pression to  tension. 

Counterfort. — A  buttress,  or  portion  projecting  from  the  face  of  a  wall  to 
stiffen  it. 

Counter-rod— counter. — In  a  frame,  a  rod  which  crosses  the  main  diagonals 
and  is  designed  to  transmit  the  tensile  stress  in  a  panel  due  to  negative 
shear,  i.  e.,  when  the  stress  in  the  main  diagonals  would  change  from 
tension  to  compression. 

Counter-Abaft. — A  secondary  shaft  running  parallel  with  and  driven  by  a 
main  shaft. 

Countersink. — A  drill  or  bit  for  reaming  or  making  a  countersink  ( —counter- 
sunk hole).  A  hole  enlarged  at  the  top  to  receive  the  counterstmk  head 
of  a  bolt  or  rivet,  so  as  to  be  flush  with  face  of  plate. 

Counterweight. — A  weight  used  to  balance  another;  a  counter-poise. 

Coupling. — A  device  for  connecting  two  shafts  so  they  will  act  as  one  in 
running.    Generally,  anything  that  connects,  as  couplings  for  cars. 

Courslng-ioint. — A  joint  between  two  courses  of  masonry. 

Cover. — ^The  cap-head  of  an  upright  steam  cylinder. 

Crab. — A  portable  windlass  for  hoisting;  used  in  building  operation  for 
hoisting  bricks  and  mortar.  A  horizontal  shaft  with  one  or  two  cranks 
for  turning  by  hand,  and  geared  to  a  drum  on  which  the  hoisting  rope 
winds.    The  whole  thing  set  in  a  wooden  or  iron  frame. 

Cradle. — A  frame  placed  under  the  bottom  of  a  ship,  on  the  "ways,"  to  give 
support  in  launching  or  on  marine  railways.  Any  contrivance  having 
a    cradle"  form  for  enclosing  or  supporting. 

Cramp— cramp-iron. — A  piece  of  iron  bent  at  the  ends  for  holding  together 
pieces  of  stone,  timber,  etc.,  in  structtires. 

Crane. — A  machine  for  moving  heavy  weights  and  placing  them  in  any 
desirable  position;  hence  there  must  be  provision  for  motion  in  three 
directions,  as  vertical,  longitudinal  and  lateral.  The  two  latter  may  be 
combined  in  a  circular  motion  by  a  rotary  crane,  consisting  of  a  jib 
or  swinging  arm  rigidly  attached  to  a  vertical  post  and  rotating  together 
about  the  axis  of  the  post.  In  a  derrick-crane  the  top  of  the  post  is 
held  in  position  by  guys  or  guy-ropes.  A  traveling  crane  is  one  in  which 
the  longitudinal  motion  is  provided  for  by  the  whole  crane  traveling 
longitudinally  on  a  track,  as  with  the /ocomof«vecran«  and  various  forms 
in  heavy  machine  shops;  the  lateral  motion  being  obtained  by  the  mova- 
ble hoisting  carriage  operating  on  the  main  transverse  girder  of  the  crane. 

Crank. — A  bent  arm  attached  to  a  shaft  or  axle  and  forming  a  radial  leverage 
for  turning.  A  single  crank  is  used  only  at  the  end  of  an  axis,  as  m 
the  common  grindstone.  A  double  crank  is  used  in  the  middle  of  a 
shaft  and  has  foiu*  bends,  thus  _l'~l__;   or,  sometimes  used  to  denote 

two  double  cranks  for  reciprocating  motion,  thus  — '    L|""*     ^®*  ^'•^ 

Bell-crank.  D,g,,ized  by  GoOglc 


1496  GLOSSARY. 

Crematory  f ymace.— A  furnace  for  burning  garbage. 

Crest. — ^Tne  top,  as  of  a  dam. 

Croee-cut. — In  mining,  a  level  driven  across  so  as  to  connect  two  otber 
levels. 

Croes-hair— croea-wire. — A  very  fine  strand  of  spider's  web  or  metal  win 
stretched  across  the  diameter  of  a  telescope  to  mark  the  directscm  ci 
sight  on  a  distant  object.  Used  in  transits  and  levels.  Two  together, 
crossing  each  other  at  an  angle  of  90°,  form  cross-hairs.  Two  ot  three 
arranged  horizontally  and  parallel  in  a  transit  are  used  as  stadia  wires 
for  measuring  distances  instead  of  by  chaining. 

Croes-bead. — ^The  sliding  bar  at  the  end  of  the  piston-rod  of  a  steam  engine. 

Cross-cut  saw. — A  large  saw  operated  by  a  man  at  each  end,  and  used  for 
sawing  logs  or  large  timbers  across  the  grain.  Opposed  to  whip-saw 
which  is  used  to  saw  (also  by  handj  with  the  gram,  as  planking  from 

CrosMectioii. — ^A  section  at  right  an^le  to  the  (longest)  axis. 
CroM-valve. — A  valve  placed  at  the  junction  of  two  or  more  pipes. 
Crow— crowbar. — An  iron  bar  with  end  pointed  or  sligthly  bent,  and  used 

for  prying,  as  a  lever,  etc. 
Crowfoot. — ^A  mark  used  by  surveyors  when  chaining,  consisting  of  a 

central  line,  marking  the  exact  distance,  and  two  flajing  lines,  forming 

a  sort  of  arrow-head. 
Crowii««fch. — ^The  arched   plate  which  supports  the  crown-sheet  <^  ibe 

fire-box  of  a  boiler. 
Crown-bar. — One  of  the  bars  on  which  the  crown-sheet  rests. 
Crown-gate. — ^The  head  gate  of  a  canal  lock. 
Crown-fllass. — A  good  quality  of  common  window-glass. 
Crown-saw. — ^A  cylindrical  saw  with  teeth  on  edge  of  cylinder. 
Crowtti^heet. — ^The  sheet  forming  the  upper  part  of  the  fire-box  of  the 

furnace  of  a  steam-boiler. 
Crown-tile = hip-tile » ridge-tile. — A  bent  or  curved  tile  used  at  the  crown 

as  a  finish  for  pan-tile  or  flat-tile  roofs. 
Crown-wheel —contrat^wtaeel—face-wbeel. — A  wheel  with  teeth  or  cogs 

at  right  angles  with  its  plane. 
Crucible. — A  pot  for  melting  metals,  ores,  etc.    The  hollow  at  the  bottom 

of  a  chemical  furnace  for  collecting  the  molten  metaL 
Crucible  steel.— Cast-steel. 

Crypt. — ^The  part  of  a  church  or  cathedral  below  the  main  floor. 
Cupola^umace. — A  furnace  for  remelting  cast-iron. 
Cup-valve. — A  sort  of  semi-spherical   valve,   or  balance-valve,   over  an 

opening  to  which  it  fits  when  valve  is  closed. 
Curb. — Anything  used  to  curb  or  check.    The  outer  casing  of  a  turbine- 
wheel.    The  wall-plate  at  the  bottom  of  a  dome.  The  casmg  of  masonry, 

wood  or  iron  built  inside  a  well  that  is  being  sunk.    Stones  or  limber 

at  edge  of  a  well  or  of  a  street,  etc. 
Current,  Alternating. — A  current  which  flows  alternately  in  opposite  direc- 
tions;  that  is.  Its  direction  is  rapidly  reversed. 
Current,  Assumed  Direction  of  Flow. — ^T^e  direction  the  current  is  assumed 

to  take,  i.  c.,  from  the  positive  pole  of  the  source  through  the  circuit 

to  the  negative  pole  of  the  source. 
Current-breaker. — Any  device   for  breaking  the  circuit  of  an   electrical 

current. 
Current,  Constant. — A  current  that  continues  to  flow  in  the  same  directioB 

for  some  time  without  varying  in  strength. 
Current,  Continuous. — A  current  which  flows  in  one  and  the  same  directioo. 
Current,  Direct. — ^A  continuous  current. 
Current,  Electric. — ^The  quantity  of  electricitv  which  passes  per  second 

through  any  conductor  or  circuit;  that  is,  the  ral0  of  flow.  (Sec  Amftrr. 

Coulomb.) 
Current,  Induced. — ^The  current  produced  in  a  conductor  by  cutting  lines 

of  force.     It  results  from  differences  of  potential  produced  by  electro- 

dynamic  induction. 
Current-meter. — ^Any  device  for  measuring  the  flow  of  water  in  streams. 
Current-meter. — A  form  of  galvanometer. 
Current,  Multi-phase. — A  rotating  current. 
Current,  Periodic. — A  simple  periodic  current. 
i'Urrent,  Rotating. — A  term  applied  to  a  current  which  results  by  combinxi^ 

a  number  of  alternating  currents,  whose  phases   are    displaced    witS 

respect  to  one  another.     A  rotating  current  is  sometimes  called  a  pcif 


CREMATORY  FURNACE.  DIE.  1407 

phase  or  mulUf>U-phas9  current,  particularly  if  there  are  more  currents 
combined.  When  three  currents  are  combined  the  displacement  between 
each  set  of  phases  is  120  degrees.  A  rotary  current,  unlike  an  alternating 
current,  possesses,  in  a  certain  sense,  a  definite  direction  of  flow.  Its 
effect  on  a  magnetic  needle  is  to  cause  rotation. 
Current  strragth. — ^The  product  obtained    by  dividing  the  electromotive 

force  by  the  resistance.    ^"'"^-    (See  Ampere.) 

Cnrrents,  Eddy. — Useless  currents  produced  in  the  pole-pieces,  armatures, 
field  magnet  cores  of  dynamo-electric  machines  or  motors,  or  other 
metallic  masses,  either  by  their  motion  through  magnetic  fields,  or  by 
variation  in  the  strength  of  electric  currents  fiowing  near  them. 

Current-wheel. — A  wheel  driven  by  the  current  of  a  stream. 

CutK»ff. — A  device  for  automatically  cutting  off  the  steam  from  the  steam* 
chest  to  the  cylinder  before  the  piston  has  made  its  full  stroke,  the  bal- 
ance of  the  stroke  being  made  by  thecx(>ansive  force  of  the  steam  in  the 
cylinder.  A  channel  cut  across  a  bend  thereby  shortening  the  main 
coxirse  of  the  river. 

Cutwater. — The  up-stream  angle-edge  of  a  bridge  pier,  designed  to  more 
effectived  lessen  the  impact  of  moving  water,  ice,  logs,  etc. 

Cyclopean  Masonry. — Rubble  concrete  masonry.  Massive  concrete  in 
which  large  rubble  stone  is  added  or  filled  in  as  the  mass  is  built  up; 
each  piece  of  rubble  stone  must  be  thoroughly  embedded  in,  and  sur- 
rounded by,  the  concrete. 

Cyma— cyme  — cima. — A  cornice  molding  having  the  profile  of  an  ogee, 
letter  S,  or  curve  of  oontra-flexure. 


Dado. — ^The  shaft  of  a  pedestal,  between  cornice  and  base. 

Damp— fir»idamp. — ^A  gas  in  coal-mines  which  explodes  when  mixed  with 
air  and  ignited;  very  dangerous.  Black-damp  or  choke-damp  is  a  carbon- 
dioxide  gas  in  coUieriee  and  differs  from  fire-damp  but  often  found  mixed 
with  it.    See  Davy. 

Damper. — A  metal  plate,  slide  or  door,  used  to  regulate  the  draft  of  or  to  a 
stove  or  furnace,  in  order  to  control  the  rate  of  combustion.  Many  are 
regulated  automatically,  as  by  heat  or  by  steam. 

Davy. — A  safety-lamp  for  use  in  mines. 

Dead-bead -siiikhiK4iead— sprue. — The  extra  length  of  metal  in  a  gun- 
casting,  not  used  because  of  its  inferior  quality. 

Dead  load. — ^The  "dead  weight"  or  non-moving  weight  of  a  structure.  Op- 
posed to  live  load  and  wind  load,  but  may  include  snow  load.  The  dead 
load  should  always  be  specified  in  detail.  The  empty  or  non-paying 
rolling-stock  of  a  train. 

Dead-oil— heavy  oil. — ^The  oils  obtained  in  the  distillation  of  coal-tar 
above  340^  P.,  and  which  are  heavier  than  water. 

Deat^pobit. — ^That  position  of  the  crank  of  an  engine  when  the  engine  is  on 
its  dead<9nter,  i.  e.,  when  the  crank  and  connecting-rod  are  in  a  straight 
line. 

Declinatioa  of  a  heavenly  body  is  its  angle  north  or  south  of  the  equator; 
i.  e..  it  is  its  distance  from  the  celestial  eauator  measured  on  a  great 
circle  passing  through  the  body  and  the  pole. 

Declivity. — ^A  downward  slope  of  groimd. 

Densimeter. — An  apparatus  for  finding  the  specific  gravity  of  a  substance. 

Dentil— denteL — One  of  a  series  of  small  blocks,  uniformly  spaced,  in  a 
cornice. 

Derrick. — A  machine  for  lifting  heavy  weights,  something  similar  to  a 
crane  but  having  the  boom  (corresponding  to  the  jib  of  the  crane) 
pivoted  or  hinged  at  its  lower  end  (to  the  post).  It  is  therefore  more 
convenient  than  a  crane,  for  use  in  general  building  operations. 
Floating  derricks  are  large  derricks  erected  on  barges  or  vessels  specially 
constructed. 

Diaphragm. — ^A  thin  plate,  serving  as  a  partition,  placed  across  a  small 
opening  or  hollow  tube,  as  the  diaphragm  of  a  telephone. 

Die. — The  cubical  part  of  a  pedestal  between  its  cornice  and  base.  An 
enffraved  steel  for  stamping  a  design.  Pieces  of  hardened  steel  fomntig 
a  female  screw  for  cutting  screw  threads;   they  are  fitted  into  a  ate- 


1408  GLOSSARY. 

stock  and  mn  adjtutable  for  use  in  cutting  threads  o£  difiiex«nt  dia- 
meters. 

Dike  (formerly  JyJfe#).— See  Dykt. 

Dip. — In  geology,  tne  aiigle  which  a  stratum  of  rock  makes  with  the  hori- 
zontal The  point  of  (Uf  is  the  directkm  of  the  compass  to  which  the 
stratum  inclines.    Tne  dip  of  a  compass  needle  from  a  horiaontal  phuie. 

Disk  -  disc  ->  discus. — ^A  flat  circular  plate. 

Disk-dutch. — A  form  of  friction-clutch. 

Dock. — An  inclosed  water-space  for  vessels  while  handling  cargo;  a  space 
or  structure  for  loading  or  unloading  cargo,  for  repairs,  etc.  See 
"Wharves,  'Piers  and  Docks,"  page  882. 

Dog— dof-iroa. — An  iron  hook  with  one  or  more  points  at  one  end.  to 
drive  into  timber  for  the  purpose  of  moving  it.  Used  largely-  in  saw- 
mills.   Has  many  forms  and  uses.    A  cramp  (which  see). 

Doiikey-«ii^ae. — A  small  engine  used  for  performing  light  work,  as  pumping 
water  into  boilers,  hoisting  anchors,  handling  building  material,  etc. 

Donkey-pump. — A  feed-pump  for  boilers.  An  extra  pump  for  special 
purposes. 

Dormer-window. — A  vertical  window  in  the  face  of  a  projection  built  out 
from  a  sloping  roof. 

DouUing-frame. — A  machine  for  winding  double  silk  threads. 

DovetaiT — One  of  a  series  of  wedge-like  projections  or  tenons  and  of  corres- 
ponding mortises  in  boards  or  timbers  for  fastening  them  together. 

Dowel. — A  wooden  or  metallic  pin  inserted  part  way  into  two  pieces  of 
wood  or  stone  to  unite  them. 

Down-draft. — A  downward  draft  of  air  in  a  mine,  chimney,  etc. 

Draft. — ^The  vertical  depth  of  water  which  a  vessel  requires  or  "draws.*' 
The  dressed  edge  of  a  stone.    See  Chis^Udrajt. 

Draw-plate. — A  drilled  plate  of  hard  steel,  or  a  drilled  ruby  or  diamond. 
for  drawing  wire  to  reduce  its  diameter,  make  it  uniform,  or  shape  it. 
The  holes  are  somewhat  conical.  The  wire  may  be  drawn  successively 
through  holes  of  decreasing  diameter. 

Drift. — A  nearly^  horizontal  ttmnel  in  a  mine.  Loose  material,  as  timber, 
trees,  etc.,  m  a  current.  In  geology,  loose  rocks,  boulders,  gravel,  sand, 
etc..  which  have  been  deposited  on  bed  rock;  glacial  drift  if  deposited  hy 
glacier. 

Drift— drift>i>in. — A  long,  round,  tapering  pin  of  steel,  used  in  enlarging 
the  punched  holes  in  metal  plates,  or  smoothing  the  inner  edges. 

Drift-bolt. — ^A  steel  bolt  used  in  driving  out  other  bolts.  A  rotmd.  steel  pin 
for  driving  into  auger-holes  in  timbers  to  fasten  them  t<«ether;  brxkpe* 
stringers  are  thus  drift-bolted  to  caps.  When  pointed;  it  is  called^  a 
pointed  drift-bolt. 

Dri|». — Any  small  tube  or  channel  to  lead  water  from  a  structure  and  kt 
it  fall  to  the  ground;  as  a  projecting  member  of  a  cornice,  or  a  smaD 
channel  cut  under  the  edge  of  a  coping. 

Drop. — One  of  a  series  of  short  cylinders  or  trtmcated  cones  placed  in  a  row 
m  cornices,  as  ornamental. 

Drum. — A  revolving  cylinder  around  which  ropes  are  wound  in  hoistmg. 

Dry-rot. — A  rot  in  timber  which  has  not  been  seasoned  sufficiently.  Thor^ 
oughly  seasoned  timber  will  not  rot  if  protected  &om  dampness;  or  if 
treated  with  a  preservative  the  decay  will  be  slow,  even  in  oiamp  places. 

Ductility  of  a  metal  is  that  property  which  renders  it  capable  of  being  ex* 
tended  by  drawing,  as  through  a  draw-plate,  with  lessening  diameter, 
and  without  fracture.  Gold  is  the  most  ductile;  then  silver,  platinuxr., 
iron,  copper,  palladium,  aluminum,  zinc,  tin,  l«ad. 

Dyke  (more  modem  spelling  is  dike). — A  long  bank  of  earth  thrown  up  to 
prevent  low  lands  from  being  overflowed.  A  levee.  In  geology,  a 
fissure  in  rocks,  filled  with  lava  or  other  material  while  in  a  molten  slat*. 

Dynamics,  Electro. — ^That  branch  of  electric  science  which  treats  of  the 
action  of  electric  currents  on  one  another  and  on  themselves  or  oc 
magnets. 

Dynamo. — Dynamo-electric  machine  or  generator. 

Dyne. — ^The  unit  of  force  in  the  centimeter-gram-aeoond  system.  It  s 
about  1.02  times  the  weight  of  a  milligram. 

E. 

Eccentric. — A  sort  of  crank  device  for  converting  a  regular  circle  motioc 
into  an  irregular  reciprocating  straight-line   motion.     Thus,  in  the 


DIKE,  FELLOE.  1409 

.gteam  engine,  it  consists  of  a  circular  disk  rigidiv  attached  to  a  shaft, 

but  not  at  center  of  disk,  and  revolving  around  with  it ;  the  circular  di^ 

being  surrounded  by  a  loose  ring  attached  to  the  eccentric  rod  leading 

to  the  valve-gear  of  the  cylinder,  thereby  r^ulating  the  cut-off  and 

making  the  engine  self-acting. 
Electrolysis. — Chemical  decomposition  effected   by  means  of  an  electric 

current.    Water-  and  gas-pipes  are  affected  by  electrolysis  when  forming 

the  return  circuit  of  electric  distribution  as  in  street  railways.     The 

electrolytic  action  occurs  when  the  current  jumps  from  the  pipe,  carrying 

atoms  of  metal  along  with  it. 
Electrometer. — An  apparatus  for  measuring  differences  of  potential. 
Entablature. — In  architecture,  a  sort  of  lintel  construction  supported  on 

columns  and  extending  toward  the  roof,  and  comprises  the  architrave, 

frieze,  and  cornice. 
Eff . — ^The  unit  of  work  or  the  work  done  when  unit  force  is  overcome 

through  imit  distance.    A  djme-centimeter. 
Escarpment. — ^The  abrupt  face  of  natural  rock  or  soil  in  a  cliff  or  high  ridge. 

In  fortifications,  ground  cut  away  forming  a  nearly  vertical  slope  about 

a  position  to  render  it  inaccessible. 
Escutcheon. — ^The  little  plate  for  protecting  the  keyhole  of  a  door;  or  the 

plate  to  which  the  handle  is  attached. 
Expansion-drum. — A  drum  with  adjustable  diameter,  used  in  connection 

with  driving  an  endless  cable. 
Eye. — ^A  circular  hole  in  a  plate,  or  formed  by  a  loop  of  iron.    The  center 

hole  of  a  wheel  on  a  shsift. 
Eye*bolt. — A  bolt  with  an  eye  or  ring  at  one  end. 
Eyepiece. — ^The  lense  or  combination  of  lenses  in  an  optical  instrument  to 

which  the  eye  is  applied. 


Face. — ^The  front  of  anirthing.  The  face  of  a  valve  is  the  part  of  the  sur- 
face which  comes  in  contact  with  the  seat. 

Face-hammer. — One  with  a  flat  face.  A  hammer  with  a  cutting  and  blunt 
end,  used  in  preparing  stone  for  finer  tool-work. 

Face-lathe. — A  lathe  for  turning  face-work. 

Fac^wheel. — See  Crown-wheel. 

Fall —fall-rope. — ^The  fall  of  a  tackle,  or  the  rope  tised  with  pulleys  in 
hoisting.    "Fall  and  tackle"  means  "block  and  tackle." 

Ffdse-work. — A  temporary  structure  to  aid  in  the  erection  of  the  permanent 
one. 

Farad. — ^The  practical  tmit  of  electric  capacity. 

Farad,  Micro. — ^The  millionth  part  of  a  farad. 

Fascines. — Sticks  or  brush  tied  in  bundles  and  used  as  a  protection  for 
river-banks;  also  used  in  the  construction  of  sea-walls  in  connection 
with  piling.     Fascines  are  weighted  with  stone. 

Fatif  lie. — ^The  weakness  of  metal,  as  a  bar.  produced  by  repeated  applica- 
tion of  stress  well  within  the  breaking  load. 

Fauc^. — A  device  in  a  pipe  for  regulating  the  flow  of  a  liquid.  The  primi- 
tive form  is  a  hollow  plug  in  a  cask,  with  a  transverse  hole  near  the 
outer  end  to  be  filled  with  a  hollow  plug  when  not  in  use. 

Feather. — A  thin  rib  cast  on  iron-framing  to  give  it  strength.  A  rib  cast  on 
a  shaft  to  fit  a  corresponding  groove  in  the  eye  of  a  wheel.  A  sniall 
steel  slip  inserted  in  a  shaft  and  projecting  so  as  to  fit  the  groove  in 
the  eye  of  a  wheel.  One  of  two  pieces  of  metal  placed  in  a  hole  in  a 
stone,  which  is  to  be  split  by  drivmg  a  "plug"  or  steel  wedge  between 
them.    The  stone  is  said  to  be  split  by  "plug  and  feather." 

Peatber-edEe. — A  very  thin  edge. 

Feather-Joint. — A  joint  between  boards  consisting  of  a  small  strip,  bead  or 
feather  fitting  into  the  opposite  mortises  on  the  edges  of  the  boards. 

Feeders. — In  a  system  of  distribution  by  constant  potential,  as  in  incan- 
descent electric  lighting,  the  conducting  wires  extending  between  the 
bus-wires  or  bars,  and  the  junction  boxes. 

Feller—fellinf -machine. — A  machine  for  cutting  standing  timber. 

FelllfiK-MW. — The  saw  in  a  felling-machine     (See  Feller?) 

Felloe— felly. — The  wooden  rim  of  a  cart  wheel,  into  which  the  outer  ends 
of  the  spokes  are  driven,  and  around  the  outer  circumference  of  which 
the  iron  tire  is  fitted. 

Digitized  by  VjOOQ IC 


1500  GLOSSARY. 

FtiL — A  coarse  fabric  of  hair,  wool,  or  wool  and  fur.  matted  togeUw^  by 

moisture,  heat  or  pressure,  but  not  woven  like  cloth. 
Fender. — A  bundle  of  rope  or  pie<»  of  timber  hung  over  the  side  of  a  vessel 
to  protect  it  from  injury  bv  rubbing  against  another  vessel  or  wharf, 
etc.    A  giuud  post  at  the  edge  of  a  pier  or  wharf. 
Feiideni>ile. — One  of  a  series  of  piles  driven  to  protect  a  structure  or  wock 

from  injury  by  concussion  resulting  from  moving  bodies. 
Ferro. — Relating  to  some  compound  ofwhich  iron  is  a  constituent  element. 
Ferrtde. — A  metal  ring  around  anything  to  prevent  it  from  splitting  or 
breaking.    A  bushing  for  expanding  the  end  of  a  flue  of  a  steam-bmler. 
Many  things,  in  the  nature  of  a  ring  for  protection.    A  sleeve. 
Ferrv-bndge. — ^The  landing-stage  of  a  ferry. 

Field*  Altematiag. — An  electrostatic  or  magnetic  field,  the  positive  direction 
of  the  lines  of  force  in  which  is  alternately  reversed  or  changed  ia 
direction. 
Filler. — Anything  to  fill  a  space  or  void,  as  a  long  narrow  plate  between  the 
web-plate  of  a  girder  and  its  vertkal  angle-iron  stinener,  8ometixn« 
called  fUkr-platt.    Washers  are  often  used  as  fillers.    A  separator,  as 
one  of  the  cast-iron  spools  near  the  ends  of  wooden  bridge-strin|Kxs  to 
space  them  one  or  two  inches  apart  so  the  air  can  circulate  and  keep 
tnem  seasoned.    In  painting,  the  prime  coat  for  filling  in  between  the 
fibers  of  the  bare  wood. 
Fillet. — A  small  fiat  molding,  as  in  a  cornice. 
Flr^-damp. — ^The  dangerous  and  explosive  gas  from  coal  in  a  mine.     See 

Datyv. 
Fish. — A  long  piece  of  timber  or  iron  secured  alongside  of  another  to 
strengthen  it;  or  at  a  joint  to  give  stiffness,  as  one  of  two  fish-plates  to 
stiffen  a  rail-Joint. 
Flag. — A  broad  nat  stone  (flagstone)  used  for  paving.    A  flag-pole  used  by 

surveyors. 
Flange — A  projecting  edffe  or  rim,  as  the  flange  of  a  car-wheel,  or  of  cast- 
iron  flange-pipe  (the  flanges  being  bolted  together  when  laid). 
Flap. — A  heavy  valve  to  prevent  back  tidewater  into  a- sewer,  etc. 
Flap-valve. — See  Clack-vahe. 

Flashing. — Sheets  of  lead,  copper,  zinc,  tin,  etc.,  used  on  roofs  aaad  other 

places,  at  the  junction  of  roof  and  chimney,  and  at  comers,  to  prevent 

the  rain  from  leaking  through.     At  a  chimney,  the  upper  edge  of  the 

sheet  of  metal  is  inserted  into  the  joints  of  the  brickworic,  so  the  rain 

cannot  get  beneath  the  flashing,  and  the  rest  of  the  sheet  is  flatta^d 

down  against  the  chimney  and  passes  between  two  coxines  of  ahingW 

Flask  »  molding-flask. — ^A  wooden  or  iron  mold  used  in  foundries  to  hoki  the 

sand  and  patterns  employed  in  molding  and  casting.    May  be  in  one  or 

two  parts,  a  lower  and  an  upper. 

Flatting-coat. — ^The  last  of  four  or  five  coats  of  paint  prepared  so  as  to  dry 

without  gloss;  it  is  of  pure  white  lead  diluted  with  spirits  of  turpentine. 

Flier. — One  of  several  steps,  called    fii^rs^  in  a  strain  flight  ox  stairs. 

Opposed  to  winding  stairs. 
Rint-glass. — Glass  in  which  the  silica  is  combined  with  oxid  of  lead  in  vmrvras 
proportions,  and  also  containing  potash.     The  lead  gives  it  a  hi^ba' 
specific  gravity  and  refractive  power,  and  greater  brilliancy. 
Flood-gate. — A  gate  designed  to  open  on  the  rising  tide  to  allow  water  to 
fill  a  basin,  and  to  close  at  the  flood  tide  to  prevent  it  from  flowing  oat 
at  that  point.     A  gate  designed  to  allow  water  to  escape  at  floods. 
Various  uses. 
Floor-hanger. — A  bearing-bracket  fastened  to  the  floor  and  used  for  snp- 

F>ortinff  shafts  and  countershafts. 
Flume. — ^^  artificial  channel  for  a  stream  of  water;  used  in  goM-minnig. 

logging,  irrigation,  etc. 
Flush. — To  drench  plentifully  with  water,  as  flushing  a  sewer,  gutter,  etc.; 

having  the  idea  of  fullness.  Bven  with  the  suriace. 
Flush-^x « flush-tank. — A  rectangular  box  in  a  water-closet  for  fiu^ixng 
out  the  bowl.  The  outlet- valve  is  opened  by  pulling  a  cord  attachea 
to  a  lever.  As  the  water  in  the  box  lowers,  the  inkt-valve,  consssting 
of  a  ball-valve  or  ball-and-lever  valve,  opens  allowing  the  box  to  fifi; 
and  when  full  the  valve  closes  automatically  through  the  rise  of  the 
ball  float. 
PJux*— -Any  substance  or  mixture  that  will  assist  the  welding  or  adhimnc 
of  two  metals  by  preventing  the  formation  of  rustr^hichis  very  mpiji 
at  such  times.  og^ed byL-OOglc 


FELT.  FUSE.  1601 

Fly«wlie«l. — ^A  wheel  with  a  heavy  rim  placed  on  a  revolvin^r  shaft  of  a 
machine  for  equalizing  the  motion  of  the  machinery. 

Follower. — Any  cog-wheel,  or  other  part  of  a  machine,  which  ia  driven  or 
which  follows  the  motion  of  another  part  called  the  Itadtr. 

Foolscap. — A  folded  writing-paper  12x  loto  13x  16  inches  in  sise.  making 
the  sheet  about  8  x  12i 

Foot-board  "-foot-plate. — ^The  platform  on  which  the  engineer  and  fireman 
of  a  locomotive  stand. 

Foot-poundal. — ^The  unit  of  energy,  equal  to  a  foot-pound -i-£  ("33.2±)<" 
421402  ergs. 

Force,  Electromotive. — ^Thcpressure  which  tends  to  move  electricity  from 
one  place  to  another.    The  unit  of  E.  M.  P.  is  the  volt,  V. 

Force,  Lines  of. — ^A  term  applied  to  the  strength  of  a  magnetic  or  electro- 
magnetic circuit.  They  reach  between  the  opposite  poles  which  produce 
l^m,  and  never  intersect.  They  lie  at  right-angle  with  the  direction  of 
ether  waves. 

Fofceps. — ^Tongs,  pincers  or  pliers  for  seizing  and  manipulating  things 
wnich  it  woiila  be  impracticable  to  handle  with  the  fingers. 

Forebay. — ^That  part  of  a  mill-race  (channel  where  the  water  flows  from  the 
dam  to  the  mill-wheel)  where  the  water  flows  upon  the  wheel.  The 
penstock. 

Forge. — An  open  furnace  provided  with  a  bellows  for  heating  metal  to  be 
hammered  or  forged  into  shape.  Portable  forges  are  used  for  heating 
rivets  in  bridge-erection.  A  hearth  or  furnace  for  making  malleable 
iron  by  the  "direct  process."  A  forging-machine  is  called  a  drop-press 
and  operates  with  a  hammer,  by  power. 

Forge-nrfl.— -One  of  a  series  of  rolls  for  rolling  slabs  or  blooms  into  puddled 
bars. 

Forging-nucliine. — A  machine  for  for^ng  metal,  usually  heated. 

Foundry  Iron. — Iron  containing  sufficient  carbon  for  casting. 

Four-way  cock. — A  cock  or  valve  with  four  passages:  two  in  the  plug  and 
four  for  delivery. 

Foxtail —fox-wedge. — A  wedge  inserted  into  the  end  of  a  pin  or  bolt  so  that 
when  the  latter  is  driven  to  the  bottom  of  the  hole  the  wedge  will  be 
forced  into  the  pin,  spreading  the  end  of  the  pin  and  making  it  secure 
against  withdrawal. 

Ffmme. — Any  construction  composed  of  parts  fitted  together  and  designed 
to  support  itself  or  other  things. 

Friability. — ^The  quality  ot  being  friable,  i.  e..  easily  broken  or  crumbled. 

Friction. — ^The  resistance  to  the  relative  motion  ot  surfaces  of  bodies  in 
contact:  sliding  friction  if  one  body  tends  to  slide  on  another;  and' 
rolling  friction  if  th«  body  is  on  wheels  or  rollers,  as  the  rolling  friction 
of  a  train  is  say  7  or  8  lbs.  per  ton.  The  angle  of  friction,  called  the 
anglt  of  re^se,  is  the  angle  of  inclination  (with  the  horizontal)  of  a  sur- 
face at  which  a  body  will  just  tend  to  overcome  the  frictional  resistance 
and  begin  to  slide,  by  the  force  of  gravity.  The  coefffieru  of  friction  is 
the  tangent  of  the  an^le  of  repose.  The  friction  of  liquids  is  more  or 
less  associated  with  viscositv. 

FrlcHon-balls. — Balls  used  to  reduce  friction  of  moving  parts,  as  in  bicycles 
and  some  movable  bridges;   such  bearings  are  callea  ball-bearings. 

Friction-lMrake. — A  brake  acting  by  friction. 

Friction-gearing. — A  gearing  of  wheels  imparting  motion  one  to  another 
by  the  friction  of  contact  alone.  'They  can  be  thrown  in  and  out  of 
contact  readily;   when  in  gear  or  contact  they  are  called  frictkm-tight. 

Friction-rollers. — Cylinders  used  to  reduce  friction  of  moving  parts,  as  the 
rollers  of  a  movable  land  pile-driver. 

Friction-wlieeU. — Wheels  especially  designed  to  reduce  friction  of  moving 
parts:  or  to  provide  for  excess  of  stress  in  machinery,  as  dredging, 
by  allowing  the  outer  rim  ot  wheel  to  give  way  to  all  stress  in  excess  of 
the  frictional  resistance  on  the  inner  section  of  the  rim. 

Fricse. — In  architecture,  the  decorative  feature  ot  an  entablature  between 
the  architrave  and  cornice:   also  similar  decorative  features  elsewhere. 

Frustum. — ^That  part  next  to  the  base  when  the  top  is  cut  off,  as  of  a  cone. 

Ftdcnim. — ^The  point  of  rest  or  support  of  a  lever  when  lifting  a  body.  The 
support  itself. 

Furring.— Strips  nailed  on  to  a  wall  for  subsequent  lathing  and  plastering; 
or  to  the  bottoms  of  joists  and  rafters  to  bring  them  to  a  level  surface. 
The  placing  of  said  strips. 

Fusc-fuxe.--A   sk)w-buming   tube-like   or   rope-like   attachment   to   an 


1602  GLOSSARY. 

explosive  charge.  A  time -fuse  is  one  which  will  explode  the  charge  it 
a  certain  time.  Electric  fuses  (fired  bv  a  spark  caused  by  a  break  k 
the  electric  circuit)  are  most  frequently  used  for  blasting,  in  work  at 
magnitude.     To  fus€  is  to  melt  and  blend  together. 

Fnsible-pliif . — A  plug  of  fusible  metal  placed  in  the  shell  of  a  boiler  of  a 
steam-engine,  and  intended  to  melt  and  allow  the  steazn  to  escape 
when  a  dangerously  high  temperature  is  reached. 

Fusioa-poiiit. — ^The  temperature  at  which  a  substance  melts. 

a 

QaMe. — ^The  rertical  end  of  a  triangular-  or  pitched  roof;    the  triaxiguhr 

canopy  over  a  window.    The  gable-end  of  a  house  is  the  end-wall. 
Qad. — ^A  |x>inted  steel  bar  or  shorter  tool  for  driving  into  anjrthizig  axai 

loosening  it. 
Qaddinf-machiiM""  gadder. — In  quarrying,  a  movable  platform  on  whkh  a 

steam-drill  is  motmted. 
Qage  — gauge. — An    instrument  for  determining  the  dimensions,  qaantity. 

distance,  force,  capacity,  etc..  of  anything;   or  the  measurement  itse'i 

The  gage  of  a  wire  is  its  diameter;  in  shingling,  it  is  the  exposed  length 

of  the  slate,  tile,  etc.,  below  the  lap:  in  gunnery,  the  bore  of  a  gun. 
Qace-«aw. — ^A  saw  with  a  gage-bar  to  determine  the  depth  of  kerf. 
Oage-stuff  — gaged^tufff. — m   plastering,   a   plaster  of   Paris   mixture  iot 

quick-setting,  in  making  moldings,  etc. 
Qallon. — Four  quarts.     U.  S.  ffallon  — 231  cu.  ins.  — 3.7863  liters— capacity 

of  a  cylinder  7'dia.  and  6  high;  more  accurately,  such  a  cylinder  hss 

a  capacity  of  230.90706  cu.  ins.,  or  0.9006  gallon,  or  almost  exactly  ooc 

part  in  2^0  too  small. 
Qallows-frame. — ^The  frame  for  supporting  the  beam  of  a  beam-engine. 

The  structure  for  supporting  the  pullevs  and  cage  in  a  mine  shaft. 
Qang-drlU. — A  machine  containmg  a  number  of  vertical  drills  in  the  sax» 

head. 
Oang-pUok— gang-board. — A  plank  with  cleats  nailed  on  transversely  far 

steps  and  used  as  an  inclined  stair. 
Qap-window. — A  long  narrow  window, 
Qas-compressor. — A  pump  for  compressing  coal-gas  into  reservoirs  for  rail- 

road-cars.etc. 
Qasket. — Any  fibrous  or  soft  substance  used  for  packing,  in  machinerr- 

The  circular  collar  used  when  pouring  lead  aroimd  lead-pipe  jotnts. 
Qas-meter. — An  apparatus  for  measuring  the  flow  of  illummating  gas  ia 

pipes,  etc. 
Qate. — A  valve.     When  placed  at  the  headworks  of  a  water  supply  it  is 

called  a  head-gate. 
Qate-house. — A  small  house  in  which  the  gate  of  a  reservoir  is  sittaated  aor. 

operated. 
Qauss. — The  imit  of  intensity  of  magnetic  field. 
Generator,  Dynamo-Electric. — An  apparatus  for  producing  electricity  b? 

the   mechanical  movement  of  conductors  through  a  magnetic  neH 

cutting  lines  of  force. 
Gear. — ^The  connecting  parts  in  machinery  for  transmitting  motion. 
Qearing. — A  train  of  toothed  wheels,  or  worms,  belts,  ropes,  etc..  in  ma- 
chinery. 
Qenerator,  Motor. — A  generator  driven  by  electricity  instead  of  by  steam- 
water-,  or  other  power. 
Qib. — A  wooden  support  tmder  the  roof  of  a  coal-mine.    An  iron  clasp  used 

in  connection  with  a  key  for  clasping  pieces  together.     The  arm  of  a 

crane.    A  fixed  wedge  used  with  the  driving  wedge  to  hold  together  ll» 

brasses  at  the  end  of  a  connecting-rod  of  an  en^e. 
Qin. — One  of  the  two  main  uprights  of  a  pile-dnver,  between  which  the 

hammer  operates.     A  machine  for  sepsuating  the  seeds  frxun  cotu». 

also  called  a  cotton-gin.     A  machine  with  a  drum  and  windJhog  rope, 

for  various  purposes  as  moving  houses  in  streets,  etc. 
Oin-Mock. — A  tackle-block  over  which  a  rope  runs,  and  suspended  by  a  hock 

attached  to  it. 
Qin«tackle. — A  double  and  a  single  block  used  as  a  system  of  puDeys  for 

hoisting. 

u'* — ^  simple  or  composite  beam  of  larger  dimensions  than  an  ordiaai>' 

beam.    Thus,  6tfam-girder.  6oa;-girder,  p7a(f-girder,  etc 


FUSIBLE-PLUG.  HALVING.  1503 

Qlacte. — In  fortifications,  a  gentle  slope  over  which  the  advancing  enemy 

is  brought  into  a  direct  line  of  fire. 
Oland— fluid-box. — ^A  stuffing  box.     A  joint  tightly  packed  and  capable 
of  retaining  lubricants  for  a  period  of  time. 
ize. — A  vitnable  substance,  as  salt,  applied  to  the  surface  of  brick,  tile. 
etc..  and  giving  it  a  transparent  coating.     An  enamel  is  an  opaque 
coating. 
Qliae. — ^A  substance  having  cement  properties;   the  common  gelatin  boiled 

out  of  the  hides  and  hoofs  of  animals. 
Qooseneck. — A  flexible  coupling,  or  a  pipe  shaped  like  the  letter  5.  A 
nozzle  with  a  universal  joint  similar  to  that  used  on  the  stand-pipe  of 
a  fire-engine. 
Qovemor. — An  automatic  regulator  for  controlling  the  supply  of  steam, 
water  or  gas.  The  compass-shaped  two-ball  apparatus  on  an  engine: 
the  supply-valve  is  connected  to  the  levers  which  are  operated  by  the 
radial  movement  of  the  balls,  as  the  latter  revolve  faster  or  slower. 

Qrapael— i^ppla. — One  or  more  hooks  in  a  cluster  for  grasping  hold  of 
things  in  deep  water:  a  grappling-iron. 

QravinsHlock. — A  dry-dock  tor  graving  or  cleaning  the  bottoms  of  ships. 

QrUlafe. — ^Two  or  more  courses  of  heavy  timbers  laid  parallel  and  at  ri^ht 
angle  (sometimes  notched  at  their  intersections)  and  xisually  dnft- 
bolted  together,  to  serve  as  a  foundation  resting  on  piles  or  on  the  bot- 
tom, and  supporting  a  masonry  pier  or  other  structure. 

Qrille. — A  grating  or  open  work  of  metal,  usually  of  wrought-iron,  for  orna- 
mental work. 

Qroln. — ^The  intersection  of  simple  vaults  or  arches  crossing  each  other  at 
right  angle.  A  breakwater  constructed  across  a  beach  to  form  a  protec- 
tion from  the  waves  and  prevent  the  drifting  and  washing  of  sand  and 
mud.    Sometimes  spelled  Groyne, 

Groove. — ^A  long  narrow  channel  as  if  made  by  a  tool,  for  something  to  fit 
into. 

Qrouiid-ic«— ancbor-ice. — Ice  formed  at  the  river  bottom,  prior  to  surface- 
freezing. 

Qround-swdl. — A  deep  swell  of  the  sea  caused  by  a  distant  or  late  storm. 
The  surface  of  a  rolling  country. 

Qroot. — Thin  mortor  poured  or  forced  in  joints  of  masonry. 

Qroyoe. — See  Groin. 

QmbMiw-hoe. — ^A  long-handled  instrument  for  digging  up  or  cutting  roots; 
used  in 'drubbing."    A  mattock. 

QtMJ^K^on. — ^The  metal  journal  of  a  horizontal  shaft,  or  that  part  which  turns 
m  the  collar. 

Qnide-lMU'. — One  of  the  two  parallel  sides  fitted  on  the  cross-head  of  a  steam- 
engine,  on  which  the  cross-head  slides. 

Qnncottoa.— Cotton  or  other  cellulose  substances  digested  in  a  mixture  of 
nitric  and  sulphuric  acids,  or  in  nitric  acid  alone.  Explodes  violently 
by  percussion. 

Qtm-inetal. — A  bronze  for  making  cannon;  now  supplanted  by  cast  iron, 
and  more  frequently  by  steel. 

QuD-penduliifn. — An  apparatus  for  determining  th^  strength  of  gtmpowder. 

Qunwale. — ^The  upper  edge  of  a  ship's  side. 

Qioset— ftissct-plate. — A  triangular  or  trapezoidal  plate  riveted  to  box- 
girders  to  stiffen  them  transversely:  or  used  to  connect  the  ends  of 
steel  floor-beams  with  the  web  of  plate-girders,  the  gtisset  extending 
usually  the  full  height  of  the  girder  or  nearly  so  in  order  to  give  trans- 
verse stiffness.     In  general:  alarge  steel  connecting-plate. 

Qity. — ^A  rope,  rod  or  chain  fastened  to  anything  to  keep  it  from  swinging, 
as  the  guy  of  a  derrick. 

Qyrate. — To  whirl  or  revolve  about  a  point  or  axis. 

H. 

Hacking. — In  masonry,  the  cutting  up  of  large  courses  into  smaller  ones  for 
expediency  when  the  stones  run  small. 

Hackofron. — A  miners'  pick  or  hack.   A  chisel  for  cutting  nails. 

Half-trap. — A  sinking  bend  in  a  sewer-pipe. 

Halving. — ^The  notching  of  two  timbers  of  eaual  thickness  together,  either 
crossing  each  other  or  at  the  ends,  so  the  thickness  of  johit  will  be  equal 
to  that  of  one  of  the  timbers.  Digitized  by  GoOglc 


1504  GLOSSARY, 

HmmmitpAitam, — A  short  beam  projection  £rom  the  foot  of  a  pfindpil 

rafter,  outward  toward  the  center  of  the  truss  but  not  reaching  a 
similar  one  from  the  opposite  rafter:  xased  in  church  roof-trcunes. 

HammeiHlressed. — In  stone-cutting,  dressed  with  a  pick  or  pointed  hamnxr. 

Hand-lew. — In  a  steam-engine,  the  lever  for  starting,  stopping  or  revetsiog 
the  engine. 

Handscrew. — A  jack,  or  machine  for  raising  heavy  weights. 

Handspike. — ^A  wooden  lever  for  raising  weights  or  working  a  windlass  or 
capstan. 

Hand-wheeL — A  form  of  circular  crank,  as  the  hand-wheel  of  a  car^nake. 

Hanger. — A  bracket  from  the  ceiling  or  wall,  or  a  stand  from  the  floor, 
with  a  box  and  oiling  device,  for  supporting  a  line  of  shafting.  Use 
plates,  straps  or  yokes  at  the  ends  of  floor  beams,  for  suniendiag 
them  to  brioge-trusses.  Yoke-hang9rs  are  used  in  connection  with  wood- 
en floor-beams  and  consist  of  sqtiare  iron  bent  over  the  pin  of  lower 
truss,  the  ends  passing  down  through  the  floor  beam  and  an  iron  f^te. 
using  a  nut  and  checkout  at  each*  end  of  hanger.  Plate-koMgfrs  ast 
riveted  directly  to  the  ends  of  steel  floor-beams,  a  hole  being  drflled  in 
upper  end  for  the  truss-pin  to  pass  through.  A  hangar-board  is  a  board 
for  supporting  electric  arc-lamps,  making  easy  connection  poles  of 
lamp    and    Ime-circuit. 

Hasp. — A  metal  clasp  as  for  a  door,  with  a  slot  for  folding  it  over  a  staple. 
and  fastened  by  a  pin  or  padlock.  A  metal  hook  for  the  same  pur- 
pose. 

Hatch. — ^The  opening  in  a  ship's  deck  leading  to  the  hold;  usually  termed 
hatchway.    The  cover  of  such  an  opening. 

Hannch. — ^The  part  of  one  side  of  an  arch  between  the  crown  and  springing. 

Headbav. — The  water  space  just  above  a  canal  lock. 

Head*4»lock. — ^The  forward  carriage  for  supporting  logs  being  sawed  in  a 
mill.   Any  block  for  supporting  a  pillow-block. 

Header. — A  stone  or  brick  with  its  longest  dimension  at  right  angle  to 
the  face  of  the  wall. 

Heading. — A  small  passage  or  opening  or  driftway  excavated  in  advance  in 
the  line  of  a  tunnel  to  facilitate  the  work. 

Head-valve. — The  delivery  valve  in  a  steam-engine. 

Headway  =  headroom. — ^Tne  clear  height  of  space  overload.  In  ratlroading. 
the  clear  height  above  rail  to  the  lower  part  of  an  overhead  bridge  or 
other  structure.  Advance  or  progress  in  work. 

Heart-cam  —  heart-wheel. — A  cam-wheel  with  a  heart-shaped  channel  oo 
face  of  disk  in  which  a  guide-wheel  travels  at  the  end  of  an  arm,  and  used 
for  converting  rotary  into  reciprocal  motion. 

Heart-shake. — Defects  in  timber,  consisting  in  cracks  or  shakes  extending 
from  the  center  outward. 

Heat-anit. — (6.T.U.)  The  amount  of  heat  required  to  raise  1  lb.  of  water 
through    1*»   Fahr.     See  page  1347. 

Hectrogam. — 100  grams,  equal  to  1543.235  grains. 

HectolKer.— 100  liters,  equal  to  26.4  U.  S.  gallons. 

Hectometer. — 100  meters,  equal  to  328*  T. 

Helve. — ^The  handle  of  an  ax.  hatchet  or  ads. 

Helver. — The  handle  of  a  mining  tool. 

Hematite. — One  of  the  most  valuable  of  iron  ores;  red  oxid  of  iron,  Pe»  Oj. 
Pound  in  large  quantities  in  the  Lake  Superior  region. 

Hemp. — ^The  fibre  of  a  plant;  used  for  makuig  hemp  rope. 

Hennr*  A. — ^The  practical  unit  of  self-induction. 

Herring-bone  bridging  ^bridglnf. — ^The  diagonal  pieces  nailed  between  the 
floor-joists  to  give  stiffness,  by  distributing  the  resistance  to  the  floor 
loads  over  several  joists. 

Highway. — A  road  or  way  of  common  right  for  all  to  pass. 

Hlige. — A  device  for  joinmg  two  pieces  in  such  a  manner  that  one  may  be 
tiimed  or  swung  around  or  upon  the  other,  as  the  hinipe  of  a  door  or  oi 
a  trunk.  A  common  hinge  consists  of  two  straps  or  leaves,  joined  by 
the  pin  or  pintle  passing  through  the  knuckle.  A  rising  kiner  is  one 
which  rises  when  the  door  opens,  to  clear  the  carpet,  and  usually 
closing  itself.  A  butt  hinge  is  a  common  door  hinge  where  the  leaves 
butt   against   each   other. 

Hinge-pin. — ^The  pin  or  pintle  of  a  hinge. 

Hip. — The  external  angle  or  comer  formed  at  the  junction  of  two  sk>pii9 
roof  faces,  and  supported  by  a  hip-rafter.  Opposed  to  vaUey^  whk^  is 
the  internal  angle,  and  supported  by  a  valley-rafter. 


HAMMER-BEAM.  IDLE-WHEEL,  1566 

Hip-roof —hipped-roof. — A  roof  with  four  sloptnpr  faces,  risixig  immediately 
from  the  wall-plates  and  with  the  same  inclmations. 

Hip-Cile. — The  tile  which  saddles  the  hip  of  a  roof. 

Hitch. — A  kind  of  knot  used  in  making  one  rope  fast  to  another  or  to  a  spar, 
boom,  post  or  timber.    See  p.  668. 

Hoarding. — ^An  English  term  for  a  fence  for  enclosing  a  building  or  mater- 
ials while  buildtng  work  is  in  progress;  a  board  fence  used  as  an  en- 
closure. 

Hold-beam. — One  of  the  transverse  beams  in  the  lowest  tier  of  beams  in  a 
ship's  hold. 

HoMing-plate— anclior-plate. — The  plate  at  the  anchorage  of  a  cable  or 
guy.  through  which  the  cable  passes  or  is  secured;  the  plates  t>eing 
backed  with  masonry,  or  loose  rocks,  earth,  etc. 

Hook. — A  bent  iron  for  holding  a  link,  or  suspending  anything.  A  pulUy- 
suspension  hook  is  an  S-hook  which  can  be  hung  over  a  beam,  and  sup- 
port a  pulley  from  below. 

Hooik-Moclc. — A  pulley-block  fitted  with  a  hook  for  suspending  it,  or 
weights  to  it.  The  standing  part  of  the  hook  is  that  part  attached  to 
the  block. 

Hook-bolt. — A  bolt  with  one  end  in  the  form  of  a  hook;  used  in  fastening 
the  wooden  floor  of  a  bridge  to  the  iron  stringers. 

Hoop. — A  circular  band  or  clasp.  Hoops  around  wooden  tanks  are  often 
adjustable. 

Horizon. — The  astronomical  or  ceUstial  horizon  is  the  great  circle  of  the 
celestial  sphere  whose  plane  is  perpendictilar  to  gravity  at  any  station. 

Horse. — ^A  wooden  frame  with  tour  legs  for  supporting  staging;  many 
similar  things. 

Horse-slioveL — A  road  scraper. 

Honinc-iron— iron. — A  long-handled  calking-iron  held  by  one  man  and 
driven  by  another. 

Honr^ircle. — A  circle  perpendicular  to  a  north  and  south-axis,  and  graduat- 
ed un-clockwise  mto  24  radial  divisions.  Any  great  circle  which 
passes  through  the  two  poles.    See  Hour  Angle,  page  021. 

How,  Kilo-Watt. — ^A  tmit  of  electrical  power  equal  to  a  kilo-watt  main- 
tained   for   one   hour. 

Hoar.  Watt. — A  unit  of  electrical  work— one  watt  for  one  hour. 

HouBingd —  A  niche  in  a  wall  for  a  statue.  The  jaw  of  a  frame  which  holds  the 
journal-box  or  housing-box. 

Honsing^^ranie. — ^The  frame  which  holds  the  rollers,  in  a  rolling-mill. 

Hob. — -The  center  of  a  wagon-wheel  from  which  the  spokes  radiate  and 
through  which  the  axle-tree  passes;  or,  in  car-wheels,  the  metal  part  in 
the  center  to  which  the  paper  web  is  clamped.    The  bell-end  of  a  pipe. 

Hy<faant— fire-pluf. — An  apparatus  with  a  valve  and  with  hose-connec- 
tions for  drawmg  water  from  a  main.  • 

Hydratrilc  iialance. — A  water-wheel  regulator. 

Hydraulic  Jack. — A  jack  operated  by  a  plunger  or  piston  against  some 
liquid   as  oil. 

Hydraulic  main. — In  gas-works,  a  lar^re  pipe  containing  water  into  which 
the  raw  gas  is  brought,  and  servmg  as  a  purifier  and  to  convey  the 
crude  gas  to  the  condenser. 

Hydrocarbon. — ^A  compotmd  of  hydrogen  and  carbon,  alone. 

Hydrometer. — An  instrument  for  determining  the  specific  gravity  of  fluids. 

Hysromet^. — ^An  instnunent  for  determinmg  the  hiunidity  of  the  at- 
mosphere. 

Hygroacope. — An  instrument  for  determining  the  approximate  humidity 
of  the  atmosphere. 

Hysteresis. — Molecular  friction  due  to  magnetic  change  of  stress. 


I. 

ice-breaker. — A  structure  built  in  the  water  to  protect  bridge-piers  &om 
moving  ice. 

ice-maclrine. — ^A  machine  for  producing  ice.  Anhydrous  ammonia  is  the 
solution  most  used,  and  is  most  efficient. 

idle>wlieel. — In  toothed  gearing,  a  wheel  placed  between  two  others  to 
preserve  the  same  direction  of  motion  in  both  of  them.  In  rope  trans- 
mission of  power,  a  wheel  to  make  the  cable  sag  and  preserve  its  tension. 


1506  GLOSSARY. 

Impedance. — Opposition  to  current  flow. 

Impedance  —  N/(Ohmic  resistance)*  +  (inductance  resistance)*! 

Impost. — ^The  upper  part  of  a  wall  or  colun^n  from  which  an  arch  springs. 

Inch. — 2.54  centimeters.  One  meter— 39.37  inches. 

Inductance. — ^The  induction  of  a  circuit  on  itself,  or  on  other  cixcuxts.  Self* 
induction.  The  practical  imit  is  the  henry.  The  coefficient  of  inductance 
is  a  constant  quantity  which,  multiplied  by  the  current  strengfth  passing 
in  any  coil  or  circuit  will  give  the  induction  due  to  that  current.  The 
practical  unit  of  inductance  is  1,000.000,000  centimeters.    (See  Ohm.) 

Induction,  Electro-Dynamic. — Electromotive  forces  set  up  by  induction  in 
conductors  which  are  either  actimlly  or  practically  moved  so  as  to  cot 
the  lines  of  magnetic  force.  Flemings'  rule: 


Induction-pipe. — In  a  steam-engine,  the  pipe  through  which  the  live  steam 
passes  to  the  steam-chest.  The  induaicn-port  is  the  opening  from  the 
steam -chest  into  the  cylinder.  The  induaion-wUve  is  tnie  valve  oontxoll- 
ing  the  steam  into  the  cylinder. 

Indurate. — ^To  harden,  as  with  indurated  clay. 

Infusorial  earth. — Pine  white  earth  composed  of  minute  nUaoas  shells 
and  resembling  magnesia.  Used  as  an  absorbent  in  making  dynamite 
(with  nitroglycerin). 

Ingot. — ^A  cast  of  metal  from  a  mold  (ingot-mold),  as  pig  iron. 

Injector. — An  apparatus  for  forcing  water  into  a  steam-boiler. 

Inscribe. — In  geometry,  to  draw  within,  as  a  sqtiare  within  a  circle.  Oppc^ed 
to  circumscribe. 

Insulator,  Oil. — A  fluid  insulator  filled  with  oil. 

Insulator,  fiingle-Shed. — An  insulator  with  a  single  inverted  cup. 

Insulator,  Telegraphic  or  Telephonic. — A  non-conductizig  support  of  tele- 
graphic, telephonic,  electric  light  or  other  wires.  Insulators  are  generally 
made  of  glass,  porcelain  or  hard  rubber,  and  assume  a  variety  of  forms. 

Interlocking  system  of  sijt^als. — In  railroading,  a  system  of  operatxnc 
switches  and  signals  jointly  by  means  of  locking  mechanism,  operated 
from  a  central  station,  so  trainmen  can  tell  the  position  of  the  switches 
from  a  distance. 

Interpolate. — To  find  the  missing  number  of  a  series.  In  many  mathemati- 
cal tables  it  is  desirable  to  find  (usually  by  simple  proportion,  but 
not  alway^)  intermediate  values  to  those  given,  and  this  is  done  by 
interpolation. 

Intrados. — ^The  inner  line  of  an  arch;  the  outer  line  is  called  the  ejctrado^ 

Invert. — An  inverted  arch,  as  the  floor  of  the  lock-chamber  of  a  x^anal. 
or  the  lower  part  of  the  brick  sewer,  or  the  inverted  arches  used  in  the 
foundation  walls  of  buildings  in  order  to  distribute  the  pressure  more 
uniformly. 

Ion. — One  of  the  elements  of  an  electrolyte;  anions  are  evolved  at  the 
anode,  and  cations  at  the  cathode. 

Isobar, — A  contour-like  line  on  a  map,  connecting  places  at  which  the 
barometric  pressure  is  the  same. 

lsochime»isocheim. — A  contour-like  line  on  a  map,  connecting  places  bav> 

-^*"8  the  same  mean  winter  temperature. 

iSSii     i*7r^"  geology,  strata  having  the  same  inclination  or  dip. 

isoclinal  lines. — In  magnetism,  contour-like  lines  on  a,^nap,  through  points 
at  which  the  dip  of  the  needle  is  the  same.        tized  by  CoOgTC 


IMPEDANCE.  JOURNAL-BOX.         1607 

Isometric. — In  crystalloprraphy,  that  s^tem  which  is  characterized  by 
three  equal  axes  at  right  angles,  and  includes  the  cube. 

Isotherm, — A  contour-like  line  on  a  map,  connecting  points  having  the  same 
mean  temperature. 

J. 

Jack. — An  instrument  for  raising  weights:  "jacking  them  up".  A  scrtw* 
jack  consists  of  a  screw  or  worm  working  in  a  thread;  a  iwer-jack  is 
a  kind  of  a  ratched-jack.  Various  forms.  See  Hydraulic  jack. 

Jack-engine. — A  donkey-engine. 

Jack-rafter. — A  short  lafter,  usual  in  hip-roofs.  A  sort  of  sub-rafter  or 
secondary  rafter,  parallel  with  the  mam  rafters  and  supported  on  the 
main  purlins;  used  for  supporting  directly  the  sub-purUns  or  sheathing 
of  the  roof. 

Jack-rib. — ^A  rib  in  a  framed  arch  or  dome  shorter  than  the  others. 

Jack-timber. — A  framing  timber  shorter  than  the  others  as  in  the  floor  of 
a   bay. 

Jad. — In  quarrving,  a  long  deep  gash  pr  hole  made  in  quarrying  soft  rock, 
as  a  sort  of  heading  for  wedging  or  blasting  the  balance.  In  coal-mining, 
a  "holing"  or  "benching"  so  the  mass  of  coal  may  fall  or  be  loosened  by 
wedging  or  blasting. 

Jadding-pick. — A  sort  of  pick  for  cutting  a  jad  in  a  quarry  or  coal-mine. 

Jag-bolt. — A  bolt  with  a  barbed  shank. 

Jamb. — The  vertical  side  of  an  opening  or  recess  in  a  wall,  as  of  a  door  or 
window,  serving  to  support  m  part  the  weight  above,  as  a  lintel.  A 
door-jamb,  or  window-jamb,  or  flreplace-jamb. 

Jamb-post. — ^The  upright  post  or  timber  at  the  side  of  an  opening  or  jamb. 

Jam-nut. — A  sort  of  lock  nut,  or  a  nut  screwed  down  on  a  bolt  hard  against 
another  nut  to  prevent  the  latter  from  working  loose.  Used  under 
wooden  floor-beams  of  bridges  when  suspended  by  iron  hangers. 

Jaw. — Anything  in  the  shape  or  use  of  a  common  jaw,  as  the  jaws  of  a  vice, 
or  wrench,  or  stone-crusher. 

Jaw-bit. — A  bar  imder  a  journal-box  for  uniting  the  two  pedestals  in  a  car- 
truck. 
_Jaw-lx>lt. — A  bolt  with  a  U-shaped  head  perforated  to  carry  a  pin. 

Jetty. — A  sort  of  pier  or  arm  constructed  m  the  water  to  divert  the  current 
and  protect  banks  from  washing  away,  or  to  scour  out  the  channel, 
or  to  cause  slack-water  and  deposit  of  mud  in  any  place.  A  pier  in  the 
ordinary  sense  of  a  wharf. 

Jews'-liarp. — A  shackle,  or  partly-closed  link  in  the  shape  of  a  horse-shoe 
and  with  eyes  and  bolt,  for  connecting  the  ring  of  an  anchor  with  the 
chain   or   cable. 

Jib. — ^The  projecting  arm  of  a  crane. 

Jig-pin. — In  mining,  a  pin  to  prevent  the  turn-beams  from  turning. 

Jig-saw. — A  vertical  reciprocating  saw  with  a  narrow  blade  for  sawing 
scroll-work  in  boards.  • 

Jimmy. — A  short  crow-bar. 

Joggle. — A  sub-tenon  at  the  end  of  a  framed  timber  to  prevent  it  from 
moving  laterally.  A  notch  or  mortise  in  a  piece  of  stone  or  timber,  or  a 
key  engaging  such  a  notch,  to  prevent  a  corresponding  piece  or  counter- 
part  from  movement. 

Jog^e-piece. — A  piece  like  the  kin^-post  of  a  truss. 

Jogglework. — In  masonry,  stones  mtemotched  or  keyed  together,  as  in 
light-house    construction. 

Jofftduig-table. — A  table  or  machine  for  dressing  or  concentrating  ore. 

JoK.— -One  of  the  spaced  beams  supporting  the  boards  of  a  floor,  as  floor- 
joist;  or  a  ceiling,  as  ceiling- joist;  or  the  floor  of  a  bridge,  as  bridge- 
joists;  etc.  Where  beams  act  singly  or  independently  they  are  called 
'rders,  especially  if  larger  than  common  joists. 

— ^The  unit  of  electric  energy  or  work.  A  volt-coulomb.  One  joule 
—  0.7373  foot-pound.  One  joule  per  second ■=  1  watt. 

Journal. — ^The  part  of  an  axle  or  shaft  which  rests  in  the  bearings. 

Jotimal-bearing. — ^The  bearing-support  of  an  axle  or  shaft.  In  general, 
it  consists  of  the  brasses,  resting  in  the  pillow-block  and  inclosed  in 
the   ioumal-box.  . 

Jonmal-box— housing-box. — ^The  box  (cast-iron)  which  contains  the  Toumal 
(of  the  car-axle  or  shaft),  the  journal-bearing  and  key,  and  the  oil- 
packing  for  lubricating  tne  journal. 


gird( 

joi£r— 


1508  GLOSSARY, 

Joiini«I4»ras8. — ^The  bearing  of  the  journal.  (Metals  of  different  lands 

while  in  nibbing  contact  will  not  wear  as  rapidly  as  thoee  of  the  saae 

kind.) 
Jump. — A  step  in  a  masonry  course  to  accommodate  a  rise  or  fall  in  grcrasd 

level,  or  slope.   Used  in  buildings. 
Jiiinp-coupliiiK<-thiinUe-coiipliiig->  riiig^<oiiplliig. — ^A  coupling  with  a  ooop- 

Img-box  consisting  of  a  rmg  or  thimble  over  the  two  connected   ends  of 

the  shaft,  the  connection  being  made  by  pins  thsough  thimble  and  shaft 

or  by  parallel  keys  feather  bedded. 
Jumper. — A  drill  used  for  drilling  holes  in  stone:  a  short  drill  woxlced  by 

a  hammer;  a  long  drill,  weighted,  raised  by  hand  and  let  fall,  and  titit 

worked  by  a  hammer. 
Jmction-box. — ^A  chamber  connecting  lines  of  pipes  or  wires. 
Jnta. — ^A  plant  producing  jute-fiber;  swells  with  moisture  and  is  xnferior 

for   rope. 


Kadiiid — ^A  fine  variety  of  clay  or  decomposed  feldspar. 

Kedge. — A  small  anchor  with  an  iron  stock. 

Keeper. — A  key  which  may  be  inserted  in  a  stationary  or  sliding  bolt  or 

other  piece,  to  keep  it  in  place.   An  armature  of  a  magnet,  or  a  piece  c^ 

soft  iron  across  the  poles  of  a  magnet  when  not  in  use  to  maintain  (or 

increase)  the  power. 
Karf. — A  channel  or  cut  made  as  by  a  saw.  A  saw-kerf. 
Key. — Anything  that  locks  or  holds  fast. 

Key-bed -key-seat. — A  groove  for  a  key  for  locking,  as  a  wheel  to  a  shaft. 
Key-bolt— cotter-bolt. — A  bolt  with  a  key  or  cotter,  instead  of  a  nut. 
Keystone^^ — ^The  center  stone  of  an  arch  nng,  at  the  apex  or  crown. 
Kibble. — ^The  bucket  of  a  shaft  or  mine  for  hoisting  material;  the  hoisting 

chain  is  called  the  kibble-chain. 
Kiln. — A  furnace  or  large  oven  for  baking,  burning  or  drjring.  as  a  brick  kih 

for  burning  or  baking  brick. 
Kiln-dried. — Anything,  as  timber,  deprived  of  moisture  by  treatment  in  a 

kiln  or  furnace. 
Kllognun. — 1.000  grams  in  weight,  equal  to  2.20463  lbs. 
KUogrammeter. — A  unit  of  work,  equal  to  7.233  ft. -lbs. 
KUoliter. — ^A  imit  of  capacity,  equal  to  1.000  liters. 
KUometer. — 1000  meters. 
Kilowatt. — 1000  watts. 

Kinetic  energv. — Energy  in  some  form  of  motion. 
King-post -klng^iece. — ^The  vertical  post  in  a  truss  with  two    sloping 

chords  meeting  the  top  of  post  and  framed  into  it.  The  two  chords  may 

be  rafters.  The  middle  vertical  member  of  a  king-post  truss. 
King-rod. — A  rod  used  in  place  of  a  Idng-post.  in  a  king-truss. 
King-truss— king-post  truss. — A  truss  framed  with  a  king-post. 
Knee. — A  piece  ot  wood  or  metal  having  an  angle  and  used  to  join  two 

pieces  together,  giving  support  and  stiffness;  as  the  beam  of  a  ship  to  a 

side  timber. 
Knee-strap. — ^An  iron  strap  used  in  connection  with  a  knee-timber. 
Knot. — A  fastening  with  a  rope.  See  page  668. 
Knuckl^ioint. — ^A  flexible  joint,  as  with  two  adjoining  links. 
K.  W. — A  contraction  for  kilo-watt. 


Laboratory. — ^A  place  with  suitable  apparatus  for  conducting  investiga- 
tions or  experiments. 

Labyrinth. — A  maze,  or  combination  of  passages  mBking  exit  difficuh- 

Lacauer*- lacker. — An  opaque  varnish  containing  lac. 

Ladder-dredge. — A  dredge  with   buckets  carried  on  a  ladder-like  chain. 

Lagging. — Palling  behind.  Narrow  strips  of  wood  or  planking  placed  oat- 
side  of  and  between  the  ribs  of  an  arch  or  tunnel  to  give  support  to  ex- 
traneous material.  Used  in  ttmnel  construction.  The  outer  wooden  cas- 
ing of  boilers,  or  the  wooden  strips  placed  on  the  periphery  of  a  winding 
dnim.   Also  used  in  the  sense  of  shifting. 

Lag-screw. — ^An  iron  bolt  with  a  flat  square  or  hexagonal  head  and  witfe 
the  other  end  sharp  and  threaded  like  a  wood-screw;  used  in  fastening 
small  wooden  guard-rails  to  the  ties.       Digitized  by  LjOOQIC 


JOURNAL-BRASS,  UNK,  1600 

Lamp!  Arc— An  electric  lamp,  the  source  of  whose  light  is  the  voltaic  arc. 
formed  between  two  or  more  carbon  electrodes. 

Lamp,  Incandescent. — ^An  electric  lamp  in  which  the  light  is  produced  by 
the  electric  incandescence  of  a  strip  or  filament  of  some  refractory 
substance,  generally  carbon. 

Lancet-window. — A  long  narrow  window  crowned  with  an  acutely-pointed 
arch. 
nding. — A  rratini^-place  or  platform  at  the  end  of  a  flight  of  stairs,  or  in- 
terrui>ting  a  series  of  steps.  A  place  on  shore  for  discharging  passengers 
or  freight  from  water-craft,  usually  called  landing-place. 

Landlocked. — Protected  from  the  wind  and  waves,  as  a  small  body  of  water 
nearly  shut  in  by  land. 

Landmark. — ^A  prominent  object  locating  a  line  or  comer  of  the  boundary 
of  a  tract  of  land. 

Lantern-wheel— lantern-pinion— trundle-wheel. — A  sort  of  drum-like  wheel 
with  two  parallel  heads  joined  near  their  peripheries  by  parallel  rods 
or  spindles  and  so  spaced  as  to  engage  the  cogs  of  a  spur-wheel. 

Lap. — ^The  length  or  width  of  expoBed  stirface  partly  covered  by  another, 
as  the  lap  of  shingle  or  slate  in  roofing. 

Lap-joint.— Opposed  to  butt- joint.  A  joint  formed  by  the  leaves  overlap- 
ping as  in  the  chord  of  a  Howe-truss  bridge.  If  each  piece  is  composed 
of  only  one  leaf,  the  ends  are  halved  to  form  the  lap-joint. 

Lap-weld. — Opposed  to  butt-weld.  A  weld  made  by  lapping  two  metals 
before  hainimering. 

Larboard. — In  navigation,  the  left-hand  or  port  side.  Opposed  to  starboard 
or  right-hand  side. 

Latch. — A  sort  of  self-locking  device  which  may  be  disengaged  usually 
without  the  use  of  a  key. 

Lattice-girder. — A  girder  with  web  consisting  of  diagonal  pieces  crossing 
like   latticework. 

Laad  (pronounced  leed). — Opposed  to  lag.  In  earthwork,  the  distance  from 
c.  of  g.  of  cut  to  c.  of  g.  of  fill.  The  pay-lead  may  be  less  than  this  dis- 
tance. In  steam-en^es,  the  advance  of  a  valve  or  valves  so  that  the 
steam  is  admitted  m  front  of  the  piston,  or  allowed  to  escape  behind 
it,  before  the  end  of  the  stroke. 
ider. — In  mining,  the  leading  vein.  A  pipe  leading  from  the  roof  to  con- 
duct rain-water.  The  principal  wheel  in  a  mechanism,  and  giving 
motion  to  the  follower. 

Leading-Mock. — A  block  for  simply  keeping  a  rope  in  a  certain  lateral 
--ution,  without  transmitting  any  of  its  power. 
„_^-whe^ — In  a  locomotive,  one  of  the  smaller  wheels  ahead  of  the 
driving-wheels. 

Leaf. — ^A  tooth  of  a  small  pinion. 

Leaf-bridge. — A  small  draw  with  leaves  swinging  vertically. 

Leaf-valve— flap-valve— clack-valve. — ^A  hinged  or  pivoted  valve  in  a 
pumping  engine. 

Lean-to. — ^A  roof  or  building  whose  rafters  pitch  against  another  structure. 

Ledge.— A  shelf  or  something  projecting,  as  a  small  horizontal  molding,  or 
the  side  of  a  rebate  against  which  a  window  or  door  is  stopped. 

Lewis. — A  contrivance  for  securing  a  hold  in  a  vertical  wedge-«iaped  hole 
in  a  block  of  stone,  for  hoisting  it;  consists  of  two  side  pieces  of  metal 
wedging  a  center  piece  (called  lewis-bolt)  firmly  and  to  which  the  hoist- 
ing tacKle  is  attached. 

Lewlt-bolt. — A  wedge-shaped  bolt  fastened  in  a  hole  drilled  in  a  stone, 
by  pouring  lead  arotmd  it  or  by  inserting  metal  wedges.  If  used  for 
liltino:  the  stones  it  is  provided  with  an  eye  and  is  an  eye-bolt. 

Lewis-hole. — ^The  hole  drilled  in  a  stone  for  a  lewis. 

Lift. — ^The  rise  in  a  canal-lock.  The  vertical  distance  from  one  level  to 
another  in  a  mine,  or  a  set  of  pumps.  A  machine  for  lifting. 

Lift-bridge. — ^A  bridge  which  is  raised  to  accompiodate  cross-trafiic,  as  in 
a  canal. 

Uft-pnmp. — Opposed  to  force-pump. 

Lift-wall. — The  cross-wall  of  a  canal-lock  chamber. 

Lighter. — A  water-craft  or  barge  tised  for  unloading  or  loading  cargoes  of 
vessels  while  anchored  in  the  harbor. 

Light-ship. — A  vessel  at  anchor  used  as  a  sort  of  light-house. 

Linch-hoop. — A  ring  on  a  carriage-axle  fastened  by  a  linch-pin. 

Linch-pln. — A  pin  on  the  end  of  a  carriage-axle  to  hold  the  wheel  on. 

|jj,k._One  of  the  rings  or  separate  pieces  of  a  cham.     In  surveying,  tue 


positi 
Leading-^ 


1510  GLOSSARY, 

httndredth  part  of  a  chain;   equal  to  12  inches  in  an  engineer's  diaai. 

or  7.92  inches  in  a  surveyor's  or  Gunter's  chain.     In  a  steam-enstae. 

the  links  or  parts  forminf^  the  link-motion. 
Unk-lever. — In  a  steam-engine,  the  reversing  lever  contxoUins  the  link  d 

the  link-motion  valve-gear. 
Unk-moCton. — In  a  steam-engine,  a  system  of  levers  for  contxollinc  the 

valves  in  starting  and  reversing  the  engrine.  and  for  cut-off. 
Uatd. — A  horizontal  beam  for  supporting  a  wall  over  a  door  or  window  or 

other  similar  opening  of  moderate  span;  termed  a  brtastsummttr  wbea 

the  opening  is  large. 
Listw — In  architecture,  a  square  molding,  fillet  or  lisUl.     A  narrow  stnp 

from  the  edge  of  a  board.    The  first  or  thin  coat  of  tin  on  iron  plates. 

to  be  followed  by  a  heavier  coat.    The  tipping  of  a  vessel  due  to  unequal 

loading. 
Liter. — A  unit  of  capacity,  equal  to  l.OM  U.  S.  quarts. 
Lithari*. — ^A  protoxid  of  lead  {Ph  O),  used  in  the  composxtioa  of  flint-glass. 

varnishes  and  drying-oils. 
Load. — In  mechanics,  the  pressure  upon  any  part  of  a  structure. 
Load-line. — ^The  line  around  a  vessel  to  show  the  allowable  load:  when  she 

sinks  in  the  water  to  that  marie. 
Loam. — In  fotmdry-work,  a  mixture  of  clay,  sand,  sawdust,  etc.  used  in 

making  the  molds  for  castings  of  iron  and  brass. 
Lock. — A  device  for  fastening  doors,  gates,  etc.;  composed  of  a  bolt,  wards 

(for  guarding  against  the  entrance  of  a  kev  not  of  the  right  ipattem). 

tumbler  (to  nold  the  bolt  in  position  ana  render  the  operation  of  s 

wrong  key  difficult),  and  a  spring.    A  mortise-lock  is  one  concealed,  as 

in  a  b:>u8e-door.    An  enclosure  or  chamber  in  a  canal  with  gat^  at  each 

end.  for  allowing  boats  to  pass  from  one  level  to  another. 
Lock-not— cbeck-nnt— Jam-nut —pinch-oaL — A    nut    screwed    down    on 

another  to  keep  it  in  place. 
Log^beam. — ^A  traveling  frame  for  supporting  and  feeding  logs  to  the  saw. 

in  a  saw-mill. 
Log-scale^ — ^A  table  showing  the  quantity  of  lumber^  in  B.  M..  procurable 

from  a  log  when  sawed;   the  length  of  log  and  its  diam.  Doieath  the 

bark  being  given. 
Loaver= louvre. — ^A  long  window,  usually  at  tops  of  roofs  of  ^ops,  depots. 

etc..  with  the  opening  traversed  with  broad  slats  sloping  downward  and 

outward,  like  the  slats  of  a  window-blind,  to  provide  for  ventilation  axid 

exclude  rain. 
Lozenge. — A  plane  figure  shaped  like  a  rhomb  or  diamond,  having  four 

equal  sides  with  two  acute  and  two  obtuse  angles.    In  art.  the  loseoge 

pattern  is  a  pattern  with  diamond-shaped  figures,  or  lines  meeting  or 

crossing  each  other  at  regular  intervals  but  not  at  ri^ht  angle. 
Lug. — ^A  short  fiange  or  projecting  piece  on  anything,  as  m  a  casting,  by  or 

to  which  something  is  fastened  or  supported  or  icept  rigid,  etc 
Lug-bolt— strap-bolt. — A  bolt  terminating  in  a  long  flat  extension  or  bar 

which  takes  the  place  of  a  head ;  made  oy  welding  a  flat  bar  to  a  commoo 

bolt .   The  bar  often  contains  holes  for  bolts  or  screws  to  fasten  to  timber. 

There  are  various  forms. 
Lumber<ar. — A  railroad  car  for  carrying  lumber;  usuallv  34  ft.  long. 
Lumber4dhi. — ^An  artificially  warmed  diiamber  in  which  lumber  is  placed 

to  deprive  it  of  its  moisture.    The  heat  is  often  furnished  by  coils  of 

steam-pipes,  and  the  moisture  in  the  air,  from  the  wood,  is  condensed. 

as  on  cold-water  pipes  hung  in  the  room,  and  the  drippings  oondactod 

out  of  the  chamber.    The  green  lumber  may  be  run  into  a  kiln  on  cars 

and  remain  on  them  until  dried. 
Machine-bolt. — ^A  threaded  bolt  with  a  square  or  hexagonal  head. 
Machine-tool— engine-tool. — A  machine  operated  by  power  (water  or  steam, 

etc.)  for  performing  operations  which  may  be.  or  which  formeriy  were. 

accomplished  by  the  use  of  hand-tools,  as  drilling,  planing,  etc 
Magnet,  Electro. — A  magnet  produced  by  a  pass- 
age of  an   electric   current   through  a  coil  of 

insulated  wire  surrounding  a  core  of   magne- 
tizable material.  The  directions  of  the  < 

required  to  produce  N  and  S  poles,  re^ 

ly,   are   shown   in   the  accompanying  a 

tions.    A  magnetizing  coil  is  called 

solenoid. 
Main. — ^The  chief  pipe-line  in  a  system 


UNK'LEVER.  MEANDER,  Iftll 

distributing  system  tapped  for  domestic  supply.  Water-main.  Simi- 
larly with  gas.  as  gas-main. 

JHain-liiik. — ^The  bar  that  coxmects  the  piston-rod  with  the  beam  of  the 
engine. 

JHalleaoiUty. — ^The  property  of  bein^  malleable,  i.  e.,  of  being  shaped,  by 
hammering  or  rolling,  without  fracture,  as  malleable  brass  or  iron. 

Mallet. — ^A  wooden  hammer  or  small  beetle  used  by  stonecutters,  carpenters, 
etc. 

JHandreL — A  bar  or  spindle  inserted  in  any  work  to  hold  it  or  shape  it,  as 
in  a  lathe.  The  spindle  of  a  turning  lathe:  the  arbor  or  axis  of  any 
tool,  as  a  circular  saw  or  cutter:  a  rod  for  shaping  the  inside  or  hollow 
of  anything,  as  the  plug-core  ot  a  metal  casting. 

Mandrel-collar. — A  collar  formed  on  the  mandrel  of  a  lathe,  against  which 
the  chucks  abut. 

MandreMathe. — A  lathe  for  turning  long  hollow  work;  the  material  is 
clasped  by  a  chuck  on  the  end  of  the  mandrel. 

Manhole. — An  opening  in  a  sewer,  culvert,  drain,  cesspool,  steam-boiler, 
tank,  etc.,  through  which  a  man  may  enter  for  the  purpose  of  inspecting, 
repairing,  cleaning,  etc. 

MarMe-saw. — One  or  more  thin  iron  blades,  set  in  a  frame  and  reciprocated 
on  a  block  of  marble  to  be  sawed,  the  kerfs  being  fed  with  sand  and 
water. 

Mark. — ^A  German  coin  of  the  value  of  $0,288. 

Markins-safe. — A  small  graduated  rod  with  a  steel  point  on  one  end  for 
scratching  a  line  on  the  wood,  and  with  an  adjustable  block  for  gaging 
the  line  from  the  edge  of  the  board. 

Marl-brick —mari-ctock. — A  superior  brick  for  the  fronts  of  buildings  and 
for  arches. 

Marlinespike. — ^A  pointed  iron  tool  used  by  riggers  to  separate  the  strands 
of  rope  in  splicing. 

Marsb-cas. — Carburetted  hydrogen:  a  constituent  of  firt-damp. 

Masonry. — Generally  defined  as  anything  constructed  of  the  materials  used 
b^  masons,  as  stonework,  brickwork,  tile  work,  etc.;  but  now  it  is  con- 
sidered as  including  concrete,  cyclopean  masonry  (which  see)  or  rubble- 
concrete  masonry,  and  rein  forced-concrete  masonry.  Drv  masonry 
comprises  masonry  built  without  mortar.  See  subject  o!  Masonry, 
Section  25. 

Mass. — ^The  weight  of  a  body  divided  by  the  gravity  acceleration  at  the 
place  where  the  weight  is  measured. 

Mas»<enter— center  of  mass. — A  point  through  which  if  a  plane  is  passed 
in  any  direction,  the  sum  of  the  products  of  all  the  minute  masses  or 
particles  on  one  side  of  the  plane  each  multiplied  by  its  respective  dis- 
tance from  that  plane,  will  be  equal  to  the  sum  of  similar  products  of 
particles  and  distances  on  the  other  side  of  the  plane. 

Mass,  Ma^etic. — A  quantity  of  magnetism  which  at  unit  distance  produces 
an  action  equal  to  unit  force. 

Master-wheel. — The  chief  wheel  or  the  driving-wheel  of  a  mechanism  or 
machine. 

Mat-boat « matting-boat. — A  sort  of  framework  on  scows  for  making  and 
launching  mats  to  protect  river-banks  from  scour. 

Match-board. — A  board  with  a  tongue  on  one  edge  and  a  groove  on  the  other 
for  constructing  partitions,  floors,  etc.,  of  match-boarding  or  matched- 
boarding. 

Match-plane. — One  or  two  planes  for  preparing  the  edges  of  matched- 
boards. 

Mathook. — A  long  pole  with  an  iron  hook  used  in  the  construction  of  mats 
for  river-bank  protection. 

Mattock. — A  kind  of  pick  for  digging,  but  having  the  edges  broad  instead 
of  pointed. 

Maul. — A  heavy  wooden  hammer. 

Maximum. — ^The  greatest  value  or  upper  limit.  The  greatest  of  several 
maxima  is  termed  the  absolute  maximum,  or  maximum  maximorum. 
Opposed  to  minimum. 

Mean. — An  intermediate  value  in  a  series,  from  which  it  is  derived.  Artth- 
matical  mean  is  the  sum  of  n  quantities  divided  by  n.  Geometrical  mean 
is  the  square  root  of  the  product  of  two  numbers.  Mean  error  is  the 
quadratic  mean  of  the  errors  of  observation.  .... 

Meander. — A  series  of  transit  or  compass  lines  in  a  surve^r,  with  distances, 
angles  or  bearings,  and  perhaps  levels.  Digitized  by  GoOglc  , 


U12  GLOSSARY, 

Metader-Uae. — ^A  part  or  the  whole  of  a  fmantUr, 

Mean  proportloaal. — Geometrical-mean.    See  M^an. 

Mcfohm. — A  larse  measure  of  electrical  resistance:  one  million  ohzns. 

Mett. — ^The  charge  of  metal  in  a  cupola  or  pot,  for  melting  or  after  being 
melted. 

Meltteg-pot. — ^A  pot  for  melting.    A  crucible. 

Membor. — A  subordinate  part  of  a  structure,  as  a  post  or  a  diagonal  of  a 
truss. 

Mercury-funuice. — ^A  furnace  for  roasting  cinnabar  so  the  mercurial  fumes 
will  arise,  to  be  condensed  in  a  series  of  vessels. 

Meridian. — Noon.  A  north  and  south  line,  on  the  earth,  or  on  the  oelestal 
sphere. 

Meter. — A  unit  of  length;   39.37  ins.  by  U.  S.  law. 

Meter,  Watt. — An  instrument  for  measuring  ctxrrent  flow  in  watts  (volt- 
amperes). 

Mica. — A  mineral  substance  employed  as  an  insulator,  as  for  instance  of 
commutator  bars. 

Micro. — ^The  one-millionth. 

Micrometer. — An  instrument  for  measuring  exceedingly  small  lengths  and 
angles. 

MIL — ^The  unit  of  length  equal  to  the  tAq  of  an  inch,  or  .001  inch,  used  in 
measuring  the  diameter  of  wires. 

Mil,  Circular. — ^A  tmit  of  area  employed  in  measuring  the  areas  of  cross- 
sections  of  wires;  equal  to  0.7854  square  mil.  One  circular  miJ» 
.000000785  square  incdi. 

Mill-f urnace. — A  furnace  for  re-heating  metals  to  be  rolled  into  shapes  or 
welded  under  the  hammer. 

Milligram. — One  thousandth  of  a  gram,  equal  to  about  1/65  of  a  grain. 

Milliliter. — One  thousandth  of  a  liter,  equal  to  about  0.061  cu.  in. 

Millimeter. — One  thousandth  of  a  meter,  equal  to  0.0S937  inch. 

Mil,  Square. — A  imit  of  area  employed  in  measuring  the  areas  of  cross- 
sections  of  wires;  equal  to  .001 X. 001 ». 000001  square  inch.  One 
square  mil  =  1.2732  circular  mil. 

Miner's  Inch.— See  page  1313. 

Minimum. — The  smallest  or  least  quantity.    PI.,  mtnima. 

Miter » mitre— mkcr-joint. — A  joint  whose  line  makes  an  angle  of  45*  with 
each  of  the  two  pieces  joined  together  at  right  angle.  A  btvel-joint  is 
one  whose  line  makes  any  angle  greater  or  less  than  45*  with  two  pieces 
joined  together  at  any  angle. 

Miter-siU. — ^A  raised  sill  against  which  the  bottom  of  the  canal-lock  gates 
shut  on  the  floor  of  the  lock-bav. 

Miter^wheel. — One  of  two  wheels  of  a  mechanism  whose  teeth  engage,  the 

Jslanes  of  the  wheels  being  at  right-angle  with  each  other. 
ulus— coefficient. — A  constant  or  positive  number  used  as  a  measure  of 
some  function,  as  the  modulus-  or  coeificient  of  elasticity  of  a  znaterial, 
the  modulus  depending  upon  the  material  and  the  method  of  testing, 
etc. 

Moment — ^The  product  of  a  force  into  its  shortest  leverage  distance.  See 
page  805. 

Monkey— ram. — ^The  hammer  of  a  pile  driver. 

Monkey-engine. — A  pile-driver. 

Monkey-wrench. — A  common  wrench,  with  one  jaw  adjiistable  by  a  screw, 
for  screwing  on  nuts,  etc. 

Monnment. — An  artificial  landmaric  used  by  surveyors  to  fix  a  point  or  a 
comer  on  an  instrument-  or  a  property  line.  Granite  monuments, 
6'  square  at  top  and  3  to  5  ft.  long  are  serviceable.  Small  gas-pipes  are 
frequently  usea  in  surbtirban  districts  for  semi-permanent  work. 

Mooring. — That  to  which  a  ship  or  anything  is  secured. 

Moorinf-swivel— mooring-shackle. — A  swivel  used  to  connect  two  anchor- 
chains  together  just  above  the  water,  say  at  the  forward  end  of  the  ship, 
when  both  anchors  are  out. 

Mortise. — ^A  part  of  a  mortise-and-tenon  joint;  the  hole  in  timber  to  receive 
the  tenon,  and  made  by  a  carpenter's  mortise-chisel. 

Motor,  Electric. — A  device  for  transforming  electric  power  into  mechanical 
power.  Electric  motors  are  specially  designed  tor  continuous  current 
or  for  alternating  current  or  for  rotating  current. 

M-roof. — A  double  pitch-roof  forming  an  inverted  W. 

Muck-bar. — An  iron  bar  which  has  been  passed  through  the,  muck-roUs 
only,  of  a  roUing-mill.  tized  by  GoOg  Ic 


MEANDER-UNE.  OGEE.  1613 

Mack-rolb. — The  first  pair  of  rolls  for  rolling  iron;  the  bars  are  finished  by 
passing  them  throiigh  the  merchant  train  or  puddU'bar  train  of  rolls. 

Mollioii. — ^A  vertical  division  between  the  lij^hts  of  windows,  screens,  etc. 

Mnnnioo. — In  ship-building,  a  vertical  division  or  piece  between  the  panels 
of  framed  bulkheads. 

Muntln  -"  mmitiiig. — ^The  central  vertical  piece  dividing  the  panels  of  a  door. 

Motiile. — A  fiat  block  projecting  tmder  the  carona  of  the  Doric  cornice;  a 
sort  of  modillion. 

N. 

Nadir. — ^The  point  in  the  heavens  vertically  below  any  station  on  the  earth. 
Opposed  to  zenith,  which  is  a  point  vertically  above. 

Nail-plate. — A  metal  plate  of  the  proper  thickness  for  cutting  up  into  nails. 

Naphtha. — A  colorless  liquid  distilled  from  petroleum.  Largely  used  in  the 
manufacture  of  illimunating  gas,  and  for  light  and  power  in  general. 

Nave. — ^The  long,  main,  central  interior  part  of  a  church,  including  the 
central  aisle.    The  hub  of  a  wheel. 

Nave-box. — ^The  metallic  ring  inserted  in  the  nave  or  hub  of  a  wheel,  to 
reduce  the  wear. 

NeedlCNbfMm. — ^The  fioor-beam  of  a  bridge.  A  transverse  bolster  placed 
beneath  the  sills  of  a  car  and  between  the  bolsters. 

Nest. — A  ffroup  of  parallel  steel  rollers  in  a  frame  and  used  at  the  expansion 
end  of  a  truss.    A  connected  series  of  pulleys  or  cog-wheels.  • 

Net-masonnr. — Masonry  with  joints  like  the  meshes  of  a  net. 

Neutivl  feeder. — ^The  feeder  that  is  connected  with  the  neutral  or  interme- 
diate terminal  of  the  dynamos  in  a  three-wire  system  of  distribution. 

NeweL— An  upright  pillar  from  which  the  steps  of  a  winding  stair  radiate; 
or  the  laise  ornamental  post  supporting  the  hand-rail  at  the  head  or 
foot  of  a  flight  of  stairs;  or  a  round  pillar  at  the  end  of  the  wing-wall 
of  a  bridge.    Sometimes  called  neweUpost, 

Niche. — A  nook  or  recess  in  a  wall  for  a  statue. 

Nippers. — ^A  tool  like  isincers  or  tongs  for  grasping  hold  of  small  objects* 
sometimes  with  cutting  edges  for  cutting  wire  and  small  pieces  ot 
metal.  In  engineering,  two  toothed  jaws  attached  to  gearing,  for  cut- 
ting off  piles  under  water. 

NoD-Condiictors. — Substances  that  offer  so  great  resistance  to  the  passage 
of  an  electric  current  through  their  mass  as  to  practically  exclude  a 
discharee  passing  through  them.    Insulators. 

Normal. — Perpendicular;  at  ri^ht-angle  to  the  tangent  to  a  curve  at  the 
point  of  tangency.    Accordmg  to  the  rule  or  right  principle. 

Noee-piece. — ^The  nozzle  of  a  hose. 

B. — ^The  nozzle  of  a  blast-pipe  inside  the  twyer  of  a  blast-furnace. 


Nosing. — ^The  projecting  edge  of  a  molding,  or  of  a  tread  or  step  of  a  stair. 

NuUed-work. — In  wood -turning,  pieces  or  wood  turned  to  form  a  series  of 
connected  beads  or  knobs,  as  in  the  rounds  of  cheap  chairs  and  bed- 
steads. 

Nut. — A  sort  of  adjustable  head  to  a  screw-bolt.  A  short  piece  of  iron  with 
a  central  female  screw  to  fit  the  screw  of  a  bolt. 

Nut-coal.— Chestnut-coal . 

Nat-lock  — BUt-fastenlng— lam-nut. — ^A  device  for  fastening  the  nut  on  a 
bolt  so  it  will  not  work  loose. 

Not-machine. — A  nmchine  for  making  (cutting,  stamping  and  swaging) 
iron  nuts  from  a  heated  bar  fed  to  it. 


Oakam. — ^The  coarse  part  of  hemp  or  flax,  removed  in  combing  or  hackling. 

Obelisk. — A  Large  rectangular,  monumental  shaft,  tapering  from  the  base 
upward,  and  with  a  pointed  top.  Many  abound  in  Egypt.  One  in 
Central  Park,  New  York  City,  near  Metropolitan  Museum  of  Art. 

Octastyle. — An  architectural  feature  of  a  portico  with  eight  columns  in  front. 

OdooMter. — ^An  instrument  to  be  attached  to  a  wheeled  vehicle  for  measur- 
ing distances  traveled ;  useful  in  preliminary  surveys  in  connection  with 
the  compass,  and  especially  for  making  maps  of  country  roads. 

Ofee—O.  G. — A  reverse  curve,  as  in  a  sectional  outline  of  some  molding, 
or  of  a  cast-iron  washer;  hence  ogee  washer  or  O.  G.  washer.    A  cyma. 


1514  GLOSSARY. 

Ohm. — ^The  unit  of  electric  resistance.  It  really  expresses  a  velocitir.  nanK^r. 
1.000.000,000  centimeters  per  second.  Thus,  the  formula  for  resistasce 
in  electro-magnetic  tmits  (see  Units,  Electro-Masnetic.  DimensEkms  oO 

Ohm,  British  Board  of  Trade. — The  resistance  of  a  column  of  mercurr 

100.3  centimeters  in  len^ith  and  one  square  millimeter  area  of  cross- 
section  at  0*  C. 
Olim,  British  Association. — ^The  resistance  of  a  column  of  mercury  104.1 

centimeters  in  length  and  one  square  millimeter  area  of  crosa-sectioa 

at  0^  C.    (Not  used.) 
Olim,  L«d. — ^The  resistance  of  a  column  of  mercury  100  centimeters  xc 

length  and  one  square  millimeter  area  of  I  cross-section  at  0^  C.  or  S3*  P. 

(Never  legalized.)    One  ohm  - 1.00112  B.  A.  Units. 
Ohm,  Standard. — A  length  of  wire  having  a  resistance  of  the  vahae  of  the 

true  or  legal  ohm.  employed  in  standardizing  resistance  coils. 
Ohmmeter. — A  commercial  galvanometer  for  meastuing  ohmic  resxstanoe. 
Oil-cellar. — A  metal  box  containing  oil  for  oiling  the  crank-pin.  and  attacJied 

to  the  tmder  side  of  the  strap  of  the  connecting-rod  of  the  engine. 
Oil-pump. — A  pump  for  discharging  oil  upon  a  iotimal. 
Oil-tefflperinf. — ^The  tempering  of  steel  with  oil  (not  water). 
Oil-well. — A  boring  made  for  petroleum. 
O.  K.— Correct;  e^  right.    (Oil  Korrect.) 

Opaque. — Dark;  shady;  obscure;  not  transparent;  impervious  to  light. 
Open4ieai%h  furnace. — A  furnace  tised  in  making  steel  by  the  Siemen*- 

Martin  process,  with  certain  late  improvements. 
Openworic  —  open-cast. — Relates  to  mining  or  quarrying  done  in  the  opeo 

air,  i.  e.,  not  covered. 
Ordinate. — An   offset   from  a  base  line  to  any  given  point.     In  analytic 

geometry,  one  of  the  coordinates  locating  a  point  on  a  curve  &om  two 

co-ordinate  axes.    See  Abscissa. 
Oscillator. — ^Anything  which  has  or  produces  a  rapid  reciprocating  tnottoo 

within  a  limited  range  of  distance,  as  a  power-hammer,  the  shuttle  of  a 

sewing-machine,  the  piston  of  a  steam-engine,  etc. 
Osier. — ^A  specie  of  willow,  much  used  in  liver-bank  protection. 
Outfall. — ^The  discharge  end  of  a  river,  sewer,  culvert,  drain,  etc. 
Outfail-«ewer. — ^That  portion  of  a  laige  sewer  which  receives  the  aew&ge 

from  one  or  more  districts  and  discharges  it,  as  into  a  river  or  ocean. 
Out  of  wind. — Not  winding;  straight.    Specifications  calling  for  timber  out 

of  wind,  mean  that  the  faces  shall  not  be  warped. 
Overshot-wlieel. — A  mill-wheel  with  blades  or  buckets  aroimd  the  periphery. 

and  designed  to  operate  by  water  shot  over  the  top  on  the  descent. 
Ovolo  ■=- quarter-round. — A  convex  molding  forming  a  quarter  of  a  ctrde. 

In  Greek  architecture  the  moldings  are  a  quarter^llipse,  like  an  egg. 

instead  of  a  quadrant  of  a  circle. 
Ozone. — Modified  oxygen;  its  density  is  one  and  one-half  times  that  of 

oxygen.    It  exists  in  cold  regions  and  in  country  districts.    Can  be 

froduced  by  an  electric  spark  passing  through  air  or  throu^  oxjrgen. 
t  is  a  great  purifier  and  oleacher. 

P. 

Packing. — In  machinery,  material  stuffed  arotmd  moving  parts,  as  la  a 

stumng-box,  to  prevent  leakage  of  steam,  water,  etc. 
Packing-ring. — A  metal-  or  rubber-ring  tised  as  seat  for  a  coupHng-valre  of 

a  car,  to  make  an  air-tight  joint. 
Pack-train. — Pack-animals  with  their  loads. 
Pallet-molding. — In  brick-making,  a  process  in  which  the  mold  is  sanded 

after  each  using. 
Panel. — Any  area  slightly  sunk,  or  raised,  or  more  or  less  distinct,  as  the 

panel  of  a  door.    The  panel  of  a  truss  is  the  vertical  area  embraced 

between  the  chord-joints  or  ffoor-beams;  the  length  of  a  panel  timet 

the  niunber  of  panels  is  equal  to  the  span. 
^nel-strip. — A  narrow  strip  on  the  edge  of  a  panel  or  between  two  paneb. 
Pantile  — pan-tile. — ^A  tile  with  surfaces  curved  transversely,  and  overiapping 

and  underlapping  adjacent  tiles,  thus: 

and  laid  on  a  roof  sningle-fashion. 


d  by  Google 


OHM,  PHOTOMETER.         1515 

Pantographd — A  lever-like  instrument  with  arms  for  reproducing  a  sketch 

to  the  same  scale  or  to  another  scale. 
Paraffin  »  paraffine. — ^A  substance  obtained  by  the  dry  distillation  of  wood, 
wax.  peat,  bituminous  coal,  etc. 

Piu«llax. — In  an  object  glass,  an  apparent  lateral  movement  of  the  cross- 
hairs as  the  eye  changes  position:  occurs  when  the  hairs  are  not  co- 
incident with  the  focal  plaoie. 

Parapet. — ^A  top  wall  of  a  masonry  structure,  forming  a  sort  of  breastwork. 
The  parapet  of  an  abutment  is  the  long  transverse  wall  on  the  back  edge 
of  the  coping,  rising  nearly  to  sub-grade,  to  protect  the  bridge-seat 
from  the  earth  embankment  of  the  roadbed. 

Paicel. — ^To  wind  anything,  as  a  rope,  with  strips  of  canvas. 

PargfiL — ^To  cover,  gloss  over,  or  smooth  over,  the  surface  of  anything 
with  paiget  or  plaster. 

Parthenon.— ^he  temple  of  Athene  Parthenos.  at  Athens. 

Paity-wall. — A  building-wall  centrally  located  on  a  property-line  or  party- 
line,  for  joint  tase;  it  may  belong  to  one  or  to  both  property  owners. 

Passimeter. — ^A  watch-like  pocket-odometer  for  registenng  walking-  or 
running  distance. 

Patent  hammw, — A  hammer  for  dressing  stone,  and  having  sharp  knife- 
like ridges  on  the  face. 

Pattern. — ^An  original,  or  model,  or  mold  for  anything.  Patterns  for  castings, 
as  chord-blocks  of  Howe  trusses  and  combination  trusses,  are  made  of 
wood,  and  due  allowance  must  be  made  for  shrinkage  of  mqtal. 

PawL — A  short  iron  bar  or  ratchet  to  engage  the  saw-like  teeth  of  a  ratchet- 
wheel  to  prevent  a  windlass  or  capstan  from  turning  back. 

Pay. — On  a  ship,  to  cover  with  a  coat  of  tar  or  pitch,  as  a  seam,  or  a  rope. 

Pay  oat. — ^To  slacken  rope,  as  a  cable  or  main  sheet. 

Peak. — ^The  upper  comer  of  a  sail.  Farepeak  is  the  forward  elttremity  of 
a  ship's  hold,  as  opposed  to  afier-p^ak.    Peak  load  means  maximum  load. 

Peat-charcoaL--Charcoal  made  by  carbonizing  peat. 

Pediment. — ^The  triangular  front-end  of  a  building  included  between  the 
portico  and  the  sloping  edges  of  the  roof. 

Peen  —  pean. — ^The  end  of  the  head  of  a  peen  hammer  (pean-hammer). 

Peeo-taanuner. — A  pean-hammer.  or  hammer  with  two  opposite  cutting 
edges  for  dressing  stone.  A  hammer  with  a  chisel  edge,  used  foi 
straightening  iron  plates. 

Pendentlve. — In  architecture,  a  triangular  segment  of  a  hemispherical 
dome  rising  from  four  supports  formed  by  two  intersecting  arches. 

Penstock. — ^A  channel  or  conduit  supplying  water  from  the  race  to  the 
gate,  through  which  the  water  flows  to  the  wheel  of  the  mill  or  power- 
plant. 

Percussion-cap. — A  small  metal  cap  or  cup  containin«r  fulminating  (deto- 
nating or  exploding)  powder,  for  exploding  dynamite  or  gunpowder. 

Perihelion. — A  point  in  the  orbit  of  a  planet  or  comet  in  which  it  is  nearest 
to  the  sun.     Opposed  to  aphelion,  in  which  it  is  farthest  from  the  stm. 

Perimeter. — Circumference  or  outer  boundary. 

Perlodictty. — ^The  rate  of  change  in  the  alternations  or  pulsations  of  an 
electric  current. 

Periphery. — Circumference  of  a  circle;  arc. 

Peristyle. — In  architecture,  columns  arranged  around  an  enclosure,  or  any 
part  of  same,  as  a  court,  or  cloister. 

Permeability,  Magnetk;. — Conductibility  for  lines  of  magnetic  forces.  The 
ratio  existing  between  the  magnetization  produced,  and  the  magnetizing 

force  producing  it.    Permeability.   ^— ^  • 


I. — In  architecture,  a  flight  of  steps  to  a  building  in  which  the  principal 
floor  is  raised  considerably  above  the  grotmd  level. 

Pestle.— One  of  the  vertical  moving  bars  in  a  stamp-mill  for  crushing  ore. 

Petroleum^iU. — ^A  still  for  separating  the  hydro-carbons,  in  the  cwrdcr  of 
their  volatility,  from  crude  petroleum. 

Phase,  Angle  of  Difference  of,  between  Alternating  Currents  of  Same  Period. — 
The  angle  which  measures  the  shifting  of  phase  of  a  simple  periodic 
current  with  respect  to  another  due  to  lag  or  other  cause. 

Phase,  Shifting  of,  of  Alternating  Current. — A  change  in  phase  of  current 
due  to  magnetic  lag  or  other  causes. 

Photometer. — An  instrument  for  measuring  the  intensitjroAJigJ^I/oOr  com- 
paring one  with  another.  °'9' '^^^  byVjOOglC 


1510  GLOSSARY, 

Pick. — A  pointed  instniment  with  a  handle  used  in  loosening  any  nuKtena] 
by  vertical  swinging.  The  comnxm  pick  for  k>osening  ee^rth.  The 
stone-pick. 

Pickax —pickaxe.^ — A  sort  of  combinatk>n  of  pick  and  mattock:  with  esse 
end  pointed  and  the  other  flat. 

Pier. — One  of  the  supports  of  a  bridge ;  generally,  one  of  the  central  supports 
of  two  or  more  spans,  the  end  supports  b^ng  termed  abutments.  The 
solid  support  from  which  two  or  more  arches  spring.  The  support  of  a 
wall,  between  openings.  A  structure  built  out  into  the  water,  to  mp- 
port  something,  as  freight,  txaffic,  warehouses,  eto.  Usually  conveys 
the  ideas  of  length  and  support. 

Pierre  perdne. — Masses  of  stone  thrown  into  the  water  to  serve  as  a  sob- 
fotmdation.  as  for  a  breakwater. 

Pig. — A  cast  of  metal  in  compact  form,  as  iron  irom  a  blast-furnace. 

Pigment. — Any  substance  used  by  painters  to  give  the  desired  color. 

Pilaster. — A  sort  of  ouartet^  or  half -pillar  projectixig  from  the  face  of  a 
wall,  and  having  the  prDportional  parts  of  capitafand  base. 

Pile. — ^y  kmg  piece  dnven  or  planted  in  the  ground  to  serve  as  a  sub- 
foundation.    May  be  of  wood,  iron,   concrete,  reinforoed-concrete,  etc 

Pne-hoop. — ^An  iron  ring  driven  over  the  head  of  a  pile  to  prevent  it  from 
splitting,  in  driving. 

Pile-pl*nk. — Planks  dnven  into  the  ground  like  piles,  as  the  sheet-pQmg 
of  a  coffer-dam. 

PUe-shoe. — An  iron  point  fitted  to  the  lower  end  of  a  pile  so  it  will  penetrate 
more  easily  and  not  burr  at  the  end. 

PWar. — A  column. 

PHlow^rtock-  piumber-block. — The  metal  case  or  support  for  the  end  of  a 
revolving  uiaft  or  journal. 

Pin,  Insulator. — A  bolt  by  means  of  which  an  insulator  is  attached  to  the 
telegraphic  support  or  arm. 

PIncb-bar— pinchfng-bar. — An  iron  bar  with  a  small  lever-like  anotxt  at 
the  foot,  for  working  heavy  masses  sideways. 

Pinion. — ^A  small  cog-wheel  or  gear-wheel  geared  to  a  larger  one,  and  usually 
giving  it  motion. 

Plnnade. — ^A  relatively  small  structure  rising  from  the  roof  or  walls  of  a 
larger  one. 

Pin,  Switch. — A  metallic  pin  or  plug  provided  for  insertion  in  a  telegraphic 
switchboard. 

Pln-6wltcta. — An  electrical  switohboard  by  which  connections  are  made  by 
means  of  pins  inserted  in  hol^  between  plates  insulated  from  each  other. 

Pintle. — A  pin  or  dowel  or  long  bolt  upon  which  anything  turns  or  revolves, 
as  the  cylindrical  pins  on  which  a  blind  or  a  rudder  swings,  the  bolt  on 
which  the  forward  axle  of  a  carnage  swings  under  the  body,  ete. 

Pipei<oupling. — A  sort  of  sleeve  which  screws  on  the  ends  of  two  abutting 
pipes. 

Pipe-cutter. — A  sort  of  chisel-tool  for  cutting  iron  pipes  by  forcing  it  down 
on  the  pipe  and  arotmd  it. 

Pipe-line. — ^A  pipe-conduit. 

Pipe-tongs. — A  pair  of  tongs,  one  projection  being  sharp  for  pushing  and 
the  other  one  hooked  for  ptillmg,  tised  in  screwing  pipe  together,  or 
into  their  coupling. 

Piston. — A  movable  piece  operated  reciprocally  by  the  steam  in  the  cirHnder 
of  an  engine;  consists  of  the  piston-head  which  fits  the  inside  diameter 
of  the  cylinder,  and  the  piston-rod  which  connects  with  the  mecfaanisn 
outside. 

Pitch. — Inclination.  In  mechanlcsj  the  distance  center  to  center  (c.  to  c 
or  c.-c.)  of  two  adjacent  teeth  of  a  cog-wheel,  or  of  rivets  when  the 
measurement  is  along  some  base  line,  or  of  the  threads  of  a  screw,  etc 
The  residuum  of  tar.  The  sap  from  the  bark  of  pines. 

Pitch-board. — ^A  fruide  or  pattern  for  carpenters  in  framing  the  strings  of 
stairs,  the  rignt-angled  notches  for  the  treads  and  risers. 

Pitch^ircle » pitch-line. — In  toothed-wheels,  a  circle  intersecting  all  the 
teeth  near  the  middle  of  their  lenffth,  and  which  is  tangent  to  a  sunilar 
circle  of  a  wheel  geared  to  it;  outlines  the  theoretical  size  of  a  toothed- 
wheel. 

Pitch-wheel. — One  of  two  toothed-wheels  geared  together. 

Pitman. — A  connecting-rod  between  a  rotary  and  a  reciprocatinff  part. 

■^*"***''-7A  laige  saw  operated  by  two  men  one  of  whom  is  below  in  the 

pit.'*  Digitized  by  LjOOgle 


PICK,  POTENTIAL,  DIFF,      1617 

Pivot — ^That  upon  which  something  turns,  as  the  center-pin  or  pivot-pin 
of  a  center-oearing  drawbridge  or  turntable. 

Place-brick -sandel- samel-brick.— In  brickmaking.  a  soft  brick,  insuffi- 
ciently burned. 

Planimeter. — An  instrument  for  measuring  the  plane  area  of  any  object 
or  drawing  of  zxiy  irrefi[ular  outline;  it  can  be  adjusted  to  the  scale  of 
the  drawing.    It  is  an  mtegrator  and  is  mathematically  correct. 

Planish. — ^To  make  smooth  or  polish.  A  planish^  or  flat-headed  tool  is 
used  by  tinners;  a  pianishing-hamnwr  is  used  by  metal  workers,  also  a 
phnishing-roUer, 

Plant. — Machinery,  tools,  and  general  outfit  used  in  any  mechanical  opera- 
tion or  construction  work.  etc. 

PlatlMUid. — A  wide  fillet.  A  fiat  molding.  A  lintel  formed  with  voussoirs 
but  with  intrados  horizontal,  as  anarch  with  infinite  radius. 

Plate,  Arrester,  of  Lightning  Pn>tector. — ^That  plate  of  a  lightning  protector 
which  is  directly  connected  With  the  circxxit  to  be  protected,  as  dis- 
tingtiished  from  the  F>late  that  is  connected  with  the  grotmd. 

Plat»«n'der. — ^A  girder  with  a  web  composed  of  steel  plate. 

Plate,  Qround,  off  Uglitning  Arrester. — ^That  plate  of  a  comb  lightning 
arrester  which  is  connected  with  the  earth  or  grotmd. 

Pliers. — Small  pinchers  with  long  jaws  for  handling  and  bending  small 
pieces  of  metal. 

Plinth. — The  flat  square  member  at  the  base  of  a  column. 

Plii^. — ^A  piece  to  stop  a  hole.  A  cast-iron  cap  leaded  in  the  end  of  a  cast- 
iron  water  main.    A  cap  screwed  into  the  end  of  a  pipe. 

Ploc  and  featliers. — An  iron  wedge  or  plug  inserted  in  one  of  a  series  of 
holes  in  a  stone,  and  between  two  semi-cylindrical  pieces  of  iron  called 
feathers,  all  the  holes  being  similarly  treated,  in  order  to  split  the  stone 
on  the  line  of  the  holes,  by  striking  the  plugs  with  a  sledge-hanuner. 

Plnmb. — Vertical,  as  in  the  direction  of  gravity. 

Plumlnbob  — plumb. — A  top-shaped  metallic  instrument,  with  the  lower 
end  pointed,  suspended  by  a  cord  or  plumb-line  and  used  in  surveying, 
carpentry,  mason-work,  etc.,  to  obtain  vertical  lines.  There  are  various 
kinds  and  shapes,  suited  to  different  classes  of  work. 

Plumber-Mock. — See  pillow-block. 

PInmb-Joint. — A  soldered  lap-joint,  the  edges  of  the  metal  not  being  bent 
or  seamed. 

Plumb-level -pendulum-level. — A  board  with  a  line  perpendicular  to  its 
edge,  used  in  connection  with  a  plumb  for  obtaining  levels. 

Plumb-rule. — A  narrow  board  with  parallel  edges  and  with  a  straight  line 
drawn  through  the  middle,  used  m  connection  with  a  plumb,  for  obtain- 
ing verticals,  in  bricklaying,  carpentrv.  etc. 

Plummer-block  —  plumber-Mock  »  pulow-block. — See  Pillow-block. 

Plummet. — A  plumb  or  plumb-bob  used  by  carpenters,  masons,  etc. 

Plummet-level  —  masons*-level. — Similar  to  plumb-level,  preceding. 

Plunger. — A  solid  piston,  as  that  of  a  Cornish  pump;  one  without  a  valve. 

Pockets,  Armature. — Spaces  provided  in  an  armature  for  the  reception  of 
the  armature  coils. 

Point. — A  pointed  chisel  for  dressing  stone.  To  point  is  to  dress  masonry 
with  a  point;  or  to  finish  the  outer  joints  with  mortar. 

Pole-plate. — ^A  small  wall-plate  resting  on  the  ends  of  the  tie-beams  of  a 
roof,  for  supporting  the  lower  ends  of  the  common-  or  jack-rafters. 

Polygon. — A  figure  with  numerous  sides  and  angles. 

Pontoon* — One  of  a  series  of  flat-bottomed  boats  or  floating  structures, 
used  in  the  construction  of  a  temporary  bridge  across  a  stream,  or  for 
support  of  a  pipe-line  in  hydraulic  dredging,  etc. 

Pontoon-bridfe. — A  bridge  or  roadway  supported  on  pontoons. 

Port. — One  of  two  passages  leading  from  the  steam-chest  to  the  inside  of 
the  cylinder  of  an  engine,  above  and  below  the  piston,  and  controlled 
by  valves  so  that  the  steam  enters  and  exhausts  at  the  proper  time. 

PortaL — ^A  door.  gate,  opening,  entrance,  etc.,  to  a  passage,  as  to  a  tunnel 
or  cathedral. 

Post. — A  compression  member  connecting  the  two  chords  of  a  truss.  An 
end-^ost,  or  an  intermediate-post,  of  a  truss. 

Potential,  Attemating. — A  potential,  the  sign  or  direction  of  which  is  alter- 
nately changing  from  positive  to  negative. 

Potential,  Constant. — ^A  potential  which  remains  constant  under  all  condi- 

PotentUdi  Difference  of.- -A  term  employed  to  denQfeidl?iG®OS4e  of  the 


1518  GLOSSARY. 

electromotive  force  which  exists  between  anv  two  points  in  a  ciicaiL 
In  a  battery  or  dvnamo  it  is  the  total  B.  M.  P.  that  is  avaikdile.  k 
mav  be  measured  by  "method  of  weighing,"  by  "use  of  electcocnetem" 
or  by  "use  of  galvanometers." 

Potontiai,  Drop  of.—Pall  of  potential. 

FoCcotial,  Electric. — ^The  power  of  doing  electric  woik.  Comparing  wiU 
flow  of  water,  it  is  the  "pressure"  or  "head." 

Power. — ^The  rate  of  work.    (Energy  is  capacity  for  work.) 

Power,  Hone,  Electric — Such  a  rate  of  doing  electrk  woik  as  is  equal  to 
740  watts  or  746  volt-coulombs  per  second. 

Pressure. — ^A  force  in  equilibrium,  i.  e..  cmposed  by  an  equal  and  opposite 
force.  Presstue  is  usually  stated  in  lbs.  per  so.  in.  or  in  lbs.  per  so.  ft 
The  pressure  on  bridge  masonry,  under  tne  peaestals,  is  txsualTy  lixmted 
to  about  260  lbs  per  sq.  in.,  depending  upon  the  quantity  of  the  stcaie. 
etc. 

Prime. — First  of  anjrthing,  as  the  primt  coat,  in  painting.  To  prime  means 
to  charge,  as  to  potu*  water  into  a  pump^tube  to  start  suction. 

Principal.— -{This  word  may  be  used  in  various  branches  of  mecfaanics  to 
denote  the  chief  or  motn  of  anything  where  there  are  also  »*^^t  bat 
subordinate  parts,  as  principal  axis,  principal  rafter,  etc) 

Profiaos. — An  open  vestibule  or  portico. 

Pro  rata. — In  proportion. 

Proscenium. — ^Thatpart  of  a  theater  between  the  drop-scene  or  curtain  and 
the  orchestra.  Thus  we  have  the  proecenium-arch  and  the  i 


box. 

Pro  ten.  — pro  tempore. — ^Temporary;  for  the  time  being. 

Prow. — The  bow  of  a  vessel. 

Prox.— proximo. — In  or  of  the  next  or  coming  month. 

Pud<fle4Mir. — Bar-iron  from  the  puddle-rolls  of  a  mill. 

Puddle-rolls,— Orooved  iron-rollers  for  rolling  iron  as  it  comes  £rofn  the 
pudd  ling-furnace  and  forge. 

Puddling. — The  process  of  ramming  plastic  clay  into  a  structure  to  prevent 
leakage,  as  m  making  the  puddle-core  of  an  earth-dam.  Aao,  the 
converting  of  pig-iron  (cast-iron)  into  wrought-iron  in  a  puddling- 
ftunace  (rcverberatory  fiunace). 

Pngginff. — Mixing  clay  for  bricks.  The  deadening  of  sound  through  a  floor 
or  partition  by  mterposing  some  composition  or  constructioD;  the 
construction  itself. 

Puf-mill. — ^A  machine  for  mixing  and  tempering  clay  for  bricks,  etc 

Pug-pUing. — Dovetailed  piling,  the  piles  being  mortised  into  one  anothw 
with  a  dovetailed- joint. 

Pulley. — A  mechanism  consisting  of  a  shell  (blodc)  containing  one  or  more 
grooved  wheels  (sheaves)  over  which  a  rope  runs  for  hoisting.  One  or 
more  pulleys  together  with  the  hoisting  rope  comprise  what  is  called 
a  tackle.  Also,  a  sort  of  drum  over  which  a  belt  or  cable  or  rope  runs, 
without  winding  arotmd  it. 

Pulsometer. — A  kind  of  pump  without  a  piston;  operates  by  steam-con- 
densation and  partial  vacuum. 

Punt. — ^A  small  boat,  square-ended  and  with  a  flat  bottom. 

Puppet. — ^The  head-  or  tail-stock  of  a  lathe. 

Puppet-valve. — A  valve  which  lifts  bodily  from  its  seat  when  open. 

Purlin  —  purline.^-One  of  a  series  of  parallel  timbers  laid  honsontaify  on 
the  main  or  principal  rafters  of  a  roof  to  support  the  common  or  jadc- 
rafters.  PL — Horizontal  shapes,  as  tees,  um*  supporting  any  zoofinf 
material,  as  tiling. 

Put-log. — One  of  several  pieces  of  timber  used  in  forming  the  floor  of  a 
scafTold;  one  end  being  inserted  into  a  ptU-kole  in  the  side  ci  tbe  Imfld- 
ing  and  the  other  end  supported  by  a  horiiontal  string  secured  to  poles 
erected  from  the  ground. 

Putty. — A  mixture  of  soft  carbonate  of  lime  or  whiting,  with  linseed-oiL 

Pyx. — ^The  metallic  box  in  which  the  nautical  compass-card  is  suspcauled. 

Q. 

Quadrangle. — A  court,  square  or  rectangular,  nearly  or  quite  surrounded 

by  buildings. 
""■g™**c. — In  algebra,  an  equation  in  which  the  highest  powder  of  the  un« 

Known  quantity  is  the  second  power.  Digitized  by  dOOglC 


POTENTIAL,  DROP.  RA  TUNE.  U19 

Quadrature  of  the  drde. — ^The  0xact  determination  in  square  measore  of 
the  area  of  a  circle.  Never  been  solved  exactly,  either  arithmetically 
or  geometrically,  by  any  limited  expression. 

Qoaiitity,  Unit  of  Electric — A  definite  amount  or  quantity  of  electricity 
called  the  coulomb. 

Quay. — ^A  landing  place  for  vessels;  a  wharf. 

Queen-post  truss. — A  truss  with  two  upright  intermediate  posts  meeting 
the  end-posts  at  their  tops.  Used  as  roof-trusaes.  The  posts  are  adled 
queen-posts.  Queen-post  stajrs  are  the  long  rods  running  below  the 
two  queen-posts  which  support  the  body  of  the  car  between  the  trucks. 

Qulrked-moMinc— qniclcmolding. — A  form  of  molding  having  an  abrupt 
re-entrant  angle  at  its  extreme  projection. 

Quoin. — Blocks  of  stone  at  the  comers  of  buildings  and  projecting  some- 
what from  the  face  of  the  wall :  the  subordinate  corners  of  the  stones 
being  chamfered  off,  usually.  The  recess  into  which  the  heel-post  of  a 
lock-gate  is  fitted. 

Quoin-post. — ^The  heel-poet  of  a  lock-gate,  on  which  the  latter  turns. 


Rabbet. — A  groove,  channel,  halving  or  other  cut  along  the  edge  of  a  board 
to  fit  a  corresponding  cut  on  another  t>oard  to  fit  it.  A  joint  so  formed 
by  two  boards  is  called  a  rabbtP-joitu.  Rabbet-saws  and  rabbet-planes 
are  used  in  preparing  the  cuts  or  grooves. 

Race. — Htad-raci  is  a  channel,  canal  or  watercourse  from  a  dam  to  a  water- 
wheel;   tail-ract  is  such  a  watercourse  after  it  leaves  the  wheel. 

Rack. — One  or  more  long  metal  bars  fitted  end  to  end,  forming  either  a 
straight  or  a  circular  piece,  and  having  teeth  on  one  of  its  sides  or 
edges  to  engage  or  work  into  the  teeth  of  a  wheel,  pinion  or  screw. 
If  the  rack  is  curved  it  is  a  sigtnent-rack;  if  it  is  a  circle  it  is  called  a 
circular-rack  and  is  usually  composed  of  segments,  as  the  cast-iron  rack 
in  the  turntable  of  a  drawbridge. 

Rack-and-Pinion. — A  small  cog-wheel  or  pinion  geared  to  a  rack. 

Rack-and-phiion-Jack. — ^A  liftmg-jack  operated  by  a  straight  rack  and 
pinion. 

Rack-and-worm. — A  rack  geared  to  a  worm  or  screw  instead  of  to  a  pinion. 

Rack-railway. — A  railway  operated  by  a  gear-wheel  of  the  car  or  locomo- 
tive engaging  the  teeth  of  a  rack-rail — a  rail  laid  along  the  track  and 
provided  with  teeth  or  cogs.  Used  on  inclined  planes,  as  up  the  sides 
of  motmtains. 

Rack-saw. — A  saw  with  wide  teeth. 

Raft-dog. — An  iron  bar  with  ends  pointed  and  bent  at  right-angle  with 
body  of  bar;  used  for  securing  logs  together  in  a  raft. 

Rag-bolt -barb-bolt -sprig-bolt. — A  sort  of  pag-spike,  or  iron  spike  or  pin 
with  its  shank  barbed  so  as  to  make  it  difficult  to  withdraw  after  being 
driven. 

Rag-wbed- chain-wheel— sprocket-wheel. — A  wheel  with  teeth  on  the  rim 
to  engage  the  links  of  a  chain. 

Rafl-bender— rail-bending  machine. — A  machine  for  applying  lateral  pres- 
sure on  a  rail  supported  against  a  bearer,  for  the  purpose  of  straight- 
ening or  curving  it. 

Rail-saw. — A  portable  saw  for  sawing  steel  rails. 

Ram. — ^The  hammer  of  a  pile-driver.  The  steel  hammer  used  in  forming 
a  bloom,  in  metal-working. 

Rammer. — An  instrument  for  ramming;  thus,  pavers'  rammers,  founders' 
rammers,  gunners'  rammers,  etc. 

Random  stone. — Rip-rap;  stone  dumped  but  not  evenly  placed,  as  for 
slope  protection  or  for  the  sub-foundation  of  a  breakwater. 

Random  stonework— random  work. — A  masonry  construction  formed  of 
stone  laid  in  irregular  courses. 

Rasp. — A  coarse  file;   various  forms  for  the  trades. 

Ratchet— ratchet  and    pawl. — A  bar  or  wheel  furnished  with  teeth  which 


Ratk>,  Velocity. — A  ratio,  in  the  nature  of  a  vekx:ity,  that  exists  between 
the  dimensions  of  the  electro-static  and  the  electro-magnetic  units. 

Ratline- ratlin  — ratling  — rattling. — One  of  the  small  horizontal  ropes 
forming  steps  to  the  shrouds  of  a  vessel,  for  going  aloft. 


1520  GLOSSARY, 

Reamer^ — ^A  tool  with  sharp  lateral  edges  or  fluted  sides  for  smoothing 
ptmched  holes  in  plates  of  metal,  or  for  enlarging  them.  They  may  be 
reamed  tapered  by  using  a  reamer  with  tapered  flutes. 

Rtenmiir's  scale. — ^A  thermometer  with  the  freezing-point  sero.  and  the 
boiling-point  80.  Superseded  by  the  centigrade  scale,  0  and  IM, 
respectively. 

Rebate  »  rabbet  -  rabate.— See  Rabbrt. 

Reciprocal. — ^The  reciprocal  of  a  number  is  1  divided  by  that  niamber. 
the  result  being  expressed  usually  in  decimal  form.  Reciprocal  rootioa 
is  alternating  motion. 

Reconn  s  isssnrr — reconnoissance. — ^A  critical  eTamination  of  a  country  or 
territory  prior  to  the  preliminary  survey. 

Reducer. — A  short  pipe  ot  variable  diameter  for  connecting  two  pipes  of 
different  diameters.    Also  called  an  increastr. 

ReteteriBf-an^— reentrant  anale. — An  angle  or  comer  pointing  inward. 

Reflux. — Plowmg  back.  A  refiuX'Valve  is  one  designed  to  prevent  bade- 
flow;  a  back-pressure  valve. 

Refraction. — Deflection  or  change  of  direction  of  rays  of  light;  due  to  the 
rays  passing  through  a  medium  of  varying  density,  as  the  air,  or  from 
one  medium  to  another,  as  air  to  water  or  water  to  air.  Witness  the 
blade  of  an  oar  in  the  water;  it  stems  to  bend  at  the  surface.  When 
rays  pass  into  a  denser  medium  they  are  refracted  toward  the  perpec- 
dicular  to  the  surface,  and  vic9  vtrsa. 

Refrigerating-machioe. — ^A  machine  for  absorbing  heat  or  converting  it 
into  work,  and  hence  producing  cold. 

Reluctance,  Magnetic — Magnetic  resistance. 

T,  I  ^  The  magneto-motive  force 

Keiuctanoe  ■• =?r —. — 3 . 

The  magnetic  flux 

Reptacing-«wltcii. — A  device  for  replacing  rolling-stock  on  the  track. 

n    «^  CI  _L_i        n     .  X  .1-  r»      -S     ElectTomotive  force 

Resistance,  Electric. — Resistance  m  ohms  —  /?  —  ^  —  • Current " 

Volts 


Amperes* 

Retaining-wall— reCain-wall—revetmeot^ — ^A  (steep)  wall  (of  masonry) 
built  to  prevent  a  bank  of  earth  from  sliding  or  washing  away.  Astroe- 
ture  designed  to  resist  lateral  pressure  of  loose  material,  as  earth.  See 
Retaining  Walls,  Section  48. 

Revetment — See  Rttaining-wall  above,  but  applies  particularly  to  fortifi- 
cations, the  protection  of  river-banks,  etc. 

Revolution. — ^Turning  through  360°,  or  a  complete  circle*  a  cycle. 

Rheostat. — An  adjustable  resistance.  A  rheostat  enables  the  current  to 
be  brought  to  a  standard,  i.  e.,  to  a  fixed  value,  by  adjusting  the  resist- 
ance. 

Rheostat,  Dynamo-Balancing. — An  adjustable  resistance  whose  range  is 
sufficient  to  balance  the  current  of  one  dynamo  against  another  with 
which  it  is  required  to  run  in  parallel. 

Rheostat,  Water. — A  rheostat  the  resistance  of  which  is  obtained  by  means 
of  a  mass  of  water  of  fixed  dimensions. 

Rib. — One  of  the  curved  pieces  of  iron  or  timber,  as  of  a  dome,  an^  vault, 
vessel,  etc..  to  which  the  outer  shell  is  secured. 

Ridge. — ^The  highest  part  of  a  roof;  the  line  of  meeting  of  the  upper  ends  ol 
the  rafters. 

Ridge-pole— ridge-piece —rid^e-plate. — ^The  timber  or  iron  piece  akMig  the 
ridge  of  the  roof  into  which  the  rafters  are  secured. 

Right  and  left, — In  the  frame  of  structures,  certain  members  are  rights 
.  and  their  counterparts  are  lefts,  some  small  details  being  on  opposite 
sides  of  the  members  otherwise  alike,  as  the  end-posts  of  a  brif^e. 
In  such  a  case  it  is  necessary  to  make  onlv  one  drawing  and  call  it  the 
right,  accompanied  by  explanatory  notes  describing  the  Uft^  Similariy, 
we  have  right-and-left  spring-frogs,  switches,  door-locks,  screws,  etc 

Riglit  iMmk  of  a  river  is  the  bank  on  the  right-hand  side  in  descending  a 
stream. 

Rjglit  solid. — ^A  solid  with  axis  perpendicular  to  base. 

Rim-saw. — A  saw  with  a  central  circular  dak  over  which  is  fitted  a  central 

n.    "^d  of  teeth  lying  in  the  plane  of  the  disk. 

R  ng.bolt»eye-bolt.--See  Eye-bolt. 

King-chock. — A  chuck  to  a  lathe  fitted  with  a  ring  01 


REAMER.  SACK-HOIST,  1521 

RlnCHlog. — ^Two  iron  doss  for  driving  into  and  hauUns  timber,  and  con- 
nected by  a  rinff;  called  a  sli$ie-dog  when  connected  by  ropes  or  chains. 
Riparian. — Maifrin^J  or  bordering  on,  as  relating  to  the  shore  of  an  ocean, 

a  bay,  or  a  stream. 
Riparian  owner —riparian  propriator. — One  who  has  vested  control  in  the 

soil  to  the  thread  of  a  stream  or  to  some  line  in  the  water  established 

by  law. 
Riparian  rights. — ^The  rights  of  a  riparian  owner,  as  fishing,  ferriage,  wharf 

or  other  construction,  filling  in.  etc. 
Riprap— rip-rap. — Broken  stone  loosely  dumped;    tised  for  walls,  founda* 

tion-beds.  bank  protection,  etc. 
Rip-saw— ripping-saw. — A  saw  used  in  sawing  wood  in  the  direction  of  the 

grain,  by  hand. 
Rising-main. — ^The  vertical  column  of  pipe  through  which  water  is  ptunped 

from  a  mine. 
RisiM-rod. — The  valve-rod  of  a  Cornish  pumping-^ngine. 
Rivetrng-machine. — A  power  machine  for  driving  and  heading  rivets;  may 

be  operated  bv  steam,  hydraulics,  electricity,  etc.    Many  are  portable. 
Road-nncUne. — A  large  scraper  motmted  on  wheels  and  used  for  scrapmg, 

transporting  and  dumping  earth;   used  in  road-  making,  shaping  and 

repairing. 
Road-plow. — ^A  strong  plow  for  loosening  earth,  etc. 
Road-roiler. — A  heavy  roller  for  compacting  the  surfaces  of  roads;  operated 

by  steam-power  usually. 
Road-scraper. — A  scraper  for  handling  earth  which  is  fairly  loose  or  has 

previously  been  loosened. 
Roadstead  —  road . — An  unsheltered  place  where  vessels  can  anchor;  not  a 

sheltered  harbor. 
Roadway. — ^The  width  of  roadway  in  excavation  or  embankment  is  the 

width  at  sub-grade  between  edges  of  slopes. 
Rock^msher. — A  machine  for  breaking  rock  into  suitable  sizes,  as  for 

concrete.    A  stone-breaker. 
Rock-drill. — A  machine-drill  for  quarries,  mines,  rock-excavation,  etc. 
Rocker,  Brush. — In  a  dynamo-electric  machine  or  electric  motor,  any  device 

for  shifting  the  position  of  the  brushes  on  the  commutator  cylinder. 
Rock-jfaced  — quarry-faced. — ^The  natural  face  of  the  stone,  without  dressing. 
Roddng-ter. — ^A  bar  supporting  a  furnace-grate  so  that  the  grate  can  be 

tipped  when  desired. 
Rockmg'-fliu. — A  bridge-pier  hinged  at  the  bottom,  to  accommodate  the 

change  in  length  of  span,  i.  e.,  the  expansion  and  contraction,  due  to 

temperature  changes.     Sometimes  used  in  suspension  bridges. 
Rock-oil. — Petroleum. 
Rock*«haft- rocker-shaft— rocklng-shaft. — ^A    shaft    that    rocks    on    its 

journals  but  does  not  revolve  entirely. 
Rockworic— qnarry-faced   masonry  —  rock-faced  masonry. — See  Rock-factd. 

Squared  masonry  with  the  face  of  stones  left  undre^ed. 
RoU-Joint.^ — A  metal  joint  made  by  rolling  one  edge  over  the  other  and 

pressing  the  joint.     Used  in  tinning  roofs. 
Rooff-plate- watt-plate. — A  plate  on  which  the  lower  ends  of  the  rafters  of 

a  roof  rest. 
Ropei<lamp. — ^The  metal  attachment  on  the  end  of  a  rope  or  cable  and 

forming  a  part  of  it. 
Ropewalk. — A  long  shed  in  which  rope  is  made. 

Rosin  (and  Resin. )--The  residutun  ot  distilled  turpentine.    {See  page  481.) 
Rotary  pump. — A  pump  having  rotary  parts  as  fans  to  force  the  liquid  ahead. 

A  centrifugal  pump  is  a  rotary  ptunp. 
RnbMe. — Rough  stones  used  in  rubble-masonry  or  rubble-work;   irregular, 

for  common  rubble-masonry,  and  squared  for  ranged  rubble-work. 
RabMe-Concrete  masonry.— -See  Cvclop^an  Masonry, 
Rundle. — ^The  rung  or  round  of  a  ladder. 
Runninc-trap.^-A  depressed  U-shaped  section  of  a  pipe,  to  contain  water 

at  all  times  and  guard  against  ttie  escape  of  jjases. 
Rustic.— Various  classes  of  facings  for  masonry  mcluding  rockwork. 


Sack-hoist. — An  endless-chain  device  for  hoisting  filled^sacks,.  as  grain, 
cement,  etc.  ized  by  LjOOQ  IC 


1622  GLOSSARY. 

Saddle. — ^Ansrthing  resembling  a  common  saddle.  A  block  resting  on  roSka 
on  top  of  the  pier  of  a  suspension  bridge  to  give  the  prooer  relief  for 
expansion  and  contraction  of  cables;  in  such  a  case  the  resoltaat 
pressure  is  vertical.  A  chair  for  rails.  The  ridge-tile  of  a  roof  is  oftea 
saddle-shaped  and  hence  called  saddle-tile. 

Saddie-Joint. — In  tizming,  etc.,  a  joint  made  thus        fTI       between  t^io 

metal  plates.  '" 

S«ddl»-pUte  — crown-sheet — In  locomotive  boilers,  the  bent  plate  fonciag 

the  arch  of  the  furnace. 
Safety^age. — A  mining  cage  or  elevator  car  provided  with  a  parachute  or 

a  safety  clutch  in  case  of  breakage  and  too  rapid  descent. 
Safety-catch— sofety^op. — A  catch  to  hold  an  elevator  in  case  of  breakage 

ot  cable. 
Safety-lamp.  — A  lamp  used  in  coal  mining  and  safe  when  even  the  inflam- 
mable coal-gas  is  present,  from  igniting  the  latter. 
Safety-valve. — A  relief  valve  in  a  steam-boiler. 
Sag. — ^A  downward  curved  bend,  or  depression. 
SaUent. — Projecting  outward.    A  salient  angle  is  one  pointing  outward,  as 

in  a  common  polygon;  opposed  to  reentrant. 
Saltern. — A  salt-works,  or  plao:  where  salt  is  obtained  by  boiling  or  evapora- 
tion. 
Saltpeter— saltpetre. — Potassium  nitrate,  or  nitrate  of  potash.     Commoa 

name,  nitsr. 
Sand-bag. — A  bag  of  sand  or  earth,  used  for  repairing  leaks  or   breaks  in 

foundation  work  imder  water. 
Sand-blast. — A  stream  of  sand  driven  through  a  tube  onto  iron-work  for 

the  purpose  of  removing  paint,  scale,  rust.  etc..  preparatory  to  repainting 

or  welding.    Used  in  portable  form  in  weldmg  rail-joints.    The  sand  is 

forced  by  a  sand-blower. 
Sand-pump. — A  sludger  used  to  remove  the  pulverized  rock  in  rope-drillizig 

in  the  oil  regions.     A  sand -ejector  used  in  caisson-work  for  bridge 

foundations. 
Sand-trap. — A  device  consisting  of  a  kind  of  pocket  or  chamber  for  ooQectxiig 

sand  and  the  heavy  sediment  from  water  in  pipes,  etc. 
Saw^et- saw-wrest. — A  tool  for  springing  the  teeth  of  a  saw  altematdy 

to  right  and  left  in  order  that  the  kerf  will  be  wide  enough  not  to  band 

the  blade. 
ScabUe. — ^To  dress  oft  the  rough  projections  of  a  stone  with  a  broad  chisel 

or  stone-axe  or  heavy  pointed  pick  preparatory  to  finer  dressing. 
Scale. — A  flake  or  crust  on  iron  due  to  oxidation,  when  hammered  or  rolled 

(milled) ;  hence  hammer-scale,  mill-scale,  etc.    A  flux  is  used  to  prevent 

scale. 
Scaling-hammer. — A  hammer  used  to  remove  scale. 
Scantling. — A  small  stick  of  timber  not  over  say  5x6  ins.  in  section. 
Scarf » scarf-Joint. — A  joint  for  splicing  the  ends  of  two  timben  together 

so  as  to  make  a  continuous  stick;    may  be  reinforced  by  iron  stiapt 

and  bolts,  and  also  be  keyed.    A  usual  form  is: 


Scarp. — In  fortifications,  the  inner  slope  of  the  ditch.    A  slope. 

Scoring. — In  founding:  The  cracking  of  a  casting  when  unequal  cooling 

takes  place ;  frequently  happens  to  pipes  and  cylinders  when  the  core 

does  not  give  way  to  the  contraction  of  the  surroimding  metal. 
Scotia. — A  receding  or  concave  molding,  as  at  the  base  of  a  column. 
Scoifter. — In  stone-working,  one  who  removes  large  projections  by  boring 

slanting  or  transverse  holes  and  using  the  necessary  tools  for  spUttix^ 

as  wedges,  etc. 
Screed. — One  of  several  strips  of  plaster  6  or  8  ins.  wide  and  a  few  feet 

apart  dividing  a  stuiace  to  be  plastered,  into  bays;    the  screeds  are 

flushed  out  to  the  same  plane  and  serve  as  guides  in  bringing  the  whole 

surface  to  that  plane. 
Scr^. — One  of  the  six  mechanical  powers  or  simple  marhince,  namely, 

iever,  wedge,  wheel  and  axle,  pulley,  screw,  and  inclined  plane. 
Screw-bolt. — A  bolt  headed  at  one  end  and  provided  with  a  screw-tliread 

and  nut  at  the  other  end.  izedbyCjOOQEC 


tizedbyLjOOgr 


SADDLE,  SHANK.  1528 

Scfw^ctfw — ^An  endlew  screw  workixig  in  the  teeth  of  a  pinion;  a  wonn- 

screw  workinff  in  a  worm-wheel. 
Screw-pile* — A  pile  with  a  screw  at  the  lower  end. 
Screw-pin. — A  cylindrical  pin  with  a  screw  (and  nut)  at  the  end  to  hold  it 

in  position. 
Screw-wheel. — ^A  wheel  which  gears  with  an  endless  screw. 
Screw-wrench. — ^A  wrench  having  one  or  both  jaws  operated  by  a  screw. 
Scribe. — ^A  pointed  instrument  for  marking  lines  on  wood,  brick,  metal,  etc., 

as  guides  for  cutting  or  scribing. 
Scroll. — A  convolved   or  spiral  ornament   resembling   a   partly   imrolled 

sheet  of  paper  or  the  letter  S.    The  spiral  ajutage  around  a  reaction 

water-wheel. 
Scupper— scupper^hde. — One  of  several  openings  in  the  side  of  a  vessel  at 

the  deck  level,  for  the  escape  of  water. 
Scapper-natt« — A  short  nail  with  a  broad  head,  for  nailing  canvas,  etc. 
Scuttler. — ^A  small  hatchway  in  a  vessel's  deck;  a  hole  in  the  side  of  a  ship; 

a  hole  for  sinking  or  scuttling  a  ship. 
Sea-breeze. — A  breeze  from  the  sea  toward  the  land. 
Season. — ^To  dry,  as  timber. 
Seat-earth -8e«t««tooe-iinder<lay. — In    coal-mining,    the    bed    of    clay 

which  characteristically  underlies  coal-seams. 
Sea-wall. — A  wall  (generally  artificial,  but  sometimes  thrown  up  by  the 

waves)  to  prevent  encroachment  of  the  sea. 
Second,  Ampere. — One  ampere  flowing  for  one  second. 
Second,  Watt. — A  unit  of  electrical  work.    A  volt  -coulomb. 
Secret. — Covered  up  or  hidden;   thus,  secret  block,  secret  dovetail,  secret 

nailing.  , 

Sectlon-Unerd — ^An  instrument  for  drawing  parallel  lines  at  certain  distances 

apart,  and  consisting  of  triangle,  straight-edge,  scale  and  set-screw. 
Sector. — A  toothed  gear  comprising  only  an  arc  of  a  circle,  for  reciprocating 

motion;    s^ctor^ear.     An  astronomical  instrument  for  measuring  6xL- 

ferences  in  declination.    Sector  of  a  circle  is  the  area  between  two  radii 

and  the  included  arc. 
Seguient. — ^A  distinct  part  of  anything.    Segment  of  a  circle  is  the  area  in- 
cluded between  arc  and  chord. 
Segment-gear. — ^A  gear  extending  over  an  arc  only,  for  reciprocating  motion. 
Segment-rock. — A  rock  or  cogged  arc  oscillating  on  a  center. 
Senmograph— seismometer. — An    instrument    for    recording    earthqtiake 

phenomena. 
Seize. — ^To  fasten  together  with  small  rope,  cord  or  twine,  by  winding  around 

it,  as  the  end  oia  large  rope,  etc. 
Semi-colamnar. — ^Like  a  semi-column  or  half  column  appearing  on  the  face 

of  an3rthing,  as  on  a  wall. 
Semi-dome. — A  half  dome  abutting  a  surface. 
Semi-ffiised.~Half  melted. 
Septangular. — Having  seven  angles. 
Smrated. — Notched  or  toothed,  as  a  saw. 
Serve. — ^To  bind  or  wind  aroUnd  with  twine,  cord  or  marlin,  as  a  rope,  in 

order  to  protect  it  from  rubbing  and  wearing. 
Service-pipe. — A  pipe  for  suppljring  water,  or  gas,  etc.,  to  a  building,  from 

a  main. 
Set. — The  lateral  bend  of  a  saw-tooth.    The  last  coat  of  plaster  on  a  wall 

preparatory  to  papering. 
Set-screw. — A  screw  for  binding  two  or  more  things  together,  as  in  a  cramp. 

A  screw  acting  in  a  collar  and  with  a  point,  tor  pressing  into  the  metal 

of  a  shaft  or  other  member  to  bind  them  together. 
Sextant. — An  instrument  for  measuring  angular  distances  between  objects. 

Used  in  navigation  for  obtaining  latitude  and  longitude. 
Shackle. — An  unclosed  link  at  the  end  of  a  chain,  consisting  of  a  U-shaped 

piece  of  iron  fitted  with  a  bolt  (shackle-bolt)  across  the  mouth,  the 

shackle-bolt   being   held    in    place    by   a   pin    called    a   shackle-pin. 

A  sort  of  clevis. 
Shaft. — In  mining  and  tunnelin«:,  a  vertical  hole,  int  or  well  from  the  ground 

surface.    The  main  body  of  a  column.    The  interior  of  a  blast-furnace 

above  the  hearth.     In  machinery,  a  large  axle  supporting  something 

which  revolves  or  oscillates. 
Shank. — ^The  long  part  of  anything  as  the  stem  of  a  kev  or  of  an  anchor, 

the  shaft  of  a  column,  the  holding  part  of  a  drill,  the  body  of. a  bolt, 

etc.  Digitized  by  dOOgle 


2ft24  GLOSSARY. 

Slwr.^-The  tnmsverse  stress  in  a  gixder  at  any  cross-flection. 

make  that  part  of  the  girder  on  the  left  (or  ri^ht)  of  the  section  i 

along  the  i>lane  of  the  cross-section.    A  shear  m  any  direction  has  ■= 

accomi>anying  and  equal  shear  at  right  angle  to  it;    thus  we  han 

longitudinal  diear  in  a  beam.    Rivets  may  be  in  single  shear  or  double 

shear,  the  latter  when  connecting  three  bars  the  middle  one  of  whidi  is 

pulling  in  a  direction  opposite  to  that  of  the  two  outside  l^rs. 
Shsart  (formerly  sheers). — ^Two  or  more  poles  fastened  together  near  thdr 

tops,  with  their  lower  ends  or  legs  spread  apart  as  a  base,  and  sappotist^ 

hoisting  tackle.    Called  shtar-legs. 
Shear^steel. — Blister-steel   especially   prepared   and    suitable    for    makiag 

shears,  knives,  etc.    When  re-worked,  it  is  called  daubk  simar  ssetl. 
Siieathfaif . — ^A  thin  covering,  as  with  plates,  boards,  etc 
Sheave. — A  grooved  wheel,  as  the  wheel  of  a  pulley. 
Sheeting -sheet-pillnc—slMet-tiaiberiiic. — ^Timber  or  metal  p>ile8. sheeU of 

boarding  driven   to   form  a  more  or  less  water-tight  lining,  and  used 

in  connection  with  the  construction  of  foundations  under  water,  tunnd 

lining,  etc. 
Shellac. — A  resinous  substance  possessing  valuable  insulating  j;>ropert]es, 

which  is  exuded  from  the  roots  and  branch^  of  certain  tropacal  plants. 
Shim. — A  sort  of  flat  wedge  to  separate  the  surfaces  of  two  adjacent  bodies 

by  wedging  them  or  holding  them  apart.    Wooden  or  iron  shims  axe 

used  in  spacing  rail-joints  m  track-laying.    Heavy  machinery  is  oftea 

shimmed  up  from  the  floor. . 
Shingle. — Stones  on  the  sea-shore,  a  little  coarser  than  gravel. 
Ship-worm— teredo  (T.  nrvaiis). — A  worm  that  bores  into  and  honeycombs 

timber  and  piling  tmder  water. 
Shoe. — A  metallic  piece  usually  shaped  to  fit  the  end  of  various  thii^ 

as  the  shoe  or  metallic  point  of  a  pile,  or  the  malleable  or  cast  fitting 

at  the  connecting  ends  of  the  bands  or  wood-stave  pipe,  etc. 
Shore. — A  prop  or  temporary  support  for  bracing  up  anything,  as  a  ship, 

or  the  weeting  in  a  sewer-trench,  etc. 
Shot.— A  blast. 
Shroud. — One  of  the  ropes  from  the  side  of  a  ship  to  the  mast-head,  to 

support  the  mast. 
Sbunt. — ^To  establish  an  additional  path  for  the  passage  of  an  electxkal 

current  or  discharae. 
Shuttle. — A  gate  to  allow  water  to  flow  on  a  water-wheel.    A  sectioo  of  a 

shuttle-dam. 
Side-beam. — dhie  of  the  two  beams  of  a  side-beam  engine. 
Side-hatchet — A  hatchet  with  onlv  one  side  of  the  blade  diamfered. 
Skiing. — A  short  piece  of  railroad-track  lying  along  the  main  track  and 

used  for  passing  of  trains,  etc.    The  boarding  of,  or  for,  the  side  of  a 

building. 
Silt. — ^An  earthy  sediment,  or  deposit  of  fine  soft  mud  from  standing  water 

or  a  running  stream. 
Sink. — ^To  excavate  downward,  as  a  shaft. 
Sinusoid. — A  curve  of  sines,  the  angles  being  laid  off  as  abscissas,  and  the 

sines  as  ordinates. 
Siphon. — ^A  bent  tube  like  an  inverted  V  but  with  unequal  legs,  the  shorttr 

leg  inserted  in  the  basin  of  water.    When  the  tube  is  thus  placed  and  is 

filled  with  water,  the  water  in  the  basin  will  be  discharged  through  the 

tube  unless  air  collects  in  the  latter  and  stops  the  siphonic  action. 
Siphon,  Electric. — A  siphon  in  which  the  stoppage  of  flow,  due  to  the  gradnal 

accumulation  of  air.  is  pyre  vented  by  electrical  means. 
Sister-hooks— clip-hooks— clove-hooks. — A    pair    of    hooks  which    dost 

together  like  the  jams  of  tongs  and  fit  together  side  by  side. 
Size. — A  gelatin  wash  used  by  painters,     y^  y^ 
S-jolnt.— A    metal    joint,    thus  J^^>\ 

Skew. — Opposed  to  right-angled.    Oblique.    W^e  have  skew  gearing,  skev 

bridges,  skew  abutments,  skew  arches,  etc. 
Skewback. — The  inclined  stone  or  surface  which  takes  the  thrust  of  the 

arch. 
Skid.— Any  simple  arran^ment  of  one  or  more  (generally  two)  poks  or 

timbers  placed  on  an  incline  (usually),  for  sliding  or  rolling  freignt  upon 
_. , jn  nnloading  from  a  car  or  vessel,  etc. 
akirting-board  -  baseboard  »  mop-board — wasb-board.-?-A     narrow     board 

placed  around  the  walls  of  a  room  next  the  floor.  jOOQIC 


SHEAR.  SPANDREL,  1625 

Sledge. — ^A  large  heavy  hammer;  a  sledge-hammer. 

Sleeper. — A  piece  of  wood  or  metal  laid  on  the  ground  to  support  various 
classes  of  construction  as  rails  of  a  track,  floors  of  houses,  etc.    A  tie. 

Sleeve. — A  hollow  pipe,  tube,  or  thimble,  slid  over  the  ends  of  two  cylinders 
to  be  joined  together. 

Slide-bar. — A  bar  which  is  slid  over  the  draft-opening  of  a  furnace.  One  of 
the  guides  for  the  cross-heads  of  a  piston-rod. 

Slide-box. — ^The  slide-valve  chest  of  a  steam  engine. 

Slide-rod. — ^The  rod  which  operates  the  slide-valve  of  a  steam-engine. 

Slide-valve. — ^A  valve  which  slides  two  and  from  its  seat. 

Slipe. — A  sledge*  or  skip  without  wheels;   used  in  coal-minixig. 

Slinf . — A  short  rope  or  chain  placed  around  anything  to  be  hoisted. 

Slip. — ^A  docking  place  for  vessels. 

Slope-wan. — A  wall  built  along  a  stream  to  prevent  the  bank  from  wash. 

Sludge. — In  mining,  the  finely  powdered  stone,  mixed  with  water,  in  a  drill- 
hole. Refuse  from  coal-washing  and  other  operations  in  mining,  and 
in  the  refining  of  crude  petroleum.  The  deposited  sediment  in  sewage 
tanks  after  the  sewage  is  treated  with  chemicals. 

Slug. — In  mining,  a  loop  in  a  rope  through  which  a  man  puts  his  leg  when 
being  raised  or  lowered  in  a  shaft. 

Sioice. — ^A  wooden  trough  which  miners  use  in  washing  gold  from  gravel 
and  sand.  An  artificial  channel.  A  body  of  water  held  in  check  or 
flowing  through  a  flood-gate  or  sluice-gate.  The  injection-valve  to  a 
condenser. 

Slnice-gate^  flood-gate. — ^The  gate  of  a  sluice. 

Smoke-box. — A  chamber  through  which  smoke  and  gases  pass  from  the 
furnace  to  the  chimnejr. 

Snap. — ^A  tool  used  in  riveting,  to  form  the  new  head. 

Snap-hook. — ^A  metal  hook  with  a  spring-mousing  to  prevent  the  object 
hooked  from  slipping  off. 

Snatch-block. — A  pulley-block  with  an  opening  on  the  side  so  that  the  bite 
of  a  rope  can  oe  passed  over  the  sheave;  when  in  use,  the  opening  is 
coverea  by  a  strap. 

Snip. — To  cut  off.  In  carpentry,  to  cut  off  nearly  or  quite  at  right-angle 
with  the  length  of  the  timber.    But  see  Snipe. 

Snipe. — ^To  cut  off  on  a  long  bevel.  In  caxpentry,  to  make  long  beveled 
cuts  at  the  end  of  a  timber,  in  framing  the  end  to  smaller  section  than 
the  main  timber. 

Snub. — ^To  check  qtiite  suddenly,  as  the  speed  of  a  boat;  the  checking  is  done 
bv  a  snubbing-Une,  passed  around  a  post  called  a  snubbing-post. 

Soaking-plt. — A  pit  in  which  cast  ingots  are  placed  so  the  mass  may  cool 
to  a  uniform  temperature  suitable  for  rollmg. 

Socket-bolt. — A  bolt  that  passes  through  a  thimble  placed  between  the 
parts  connected  by  the  bolt. 

Socket-chisel. — A  form  of  heavy  chisel  for  mortising. 

Socket-drill. — ^A  drill  for  enlargmg  or  countersinking  drilled  holes. 

Socket-|obit. — An  articulated-,  flexible-.,  or  ball-and-socket  joint,  as  a 
flexible  joint  in  a  pipe-line.  Flexible-joint  pipes  arc  used  as  water-  and 
gas  mains  across  streams:  they  are  jomted  together  on  a  scow  and  sunk 
m  a  continuous  line  as  fast  as  connected,  the  last  joint  being  always 
out  of  water. 

Soffit. — ^The  lower  surface  of  an  arch;  extended  also  to  include  the  lower 
surface  of  a  span  over  a  door  or  window  opening. 

SoMer. — A  fusible  alloy  for  uniting  metal  surfaces  or  joints.  There  are  a 
great  variety  of  solders  for  different  metals.  Hard  solders,  composed 
of  copper  and  zinc,  and  called  sptlUr,  are  used  for  uniting  iron,  copper 
and  brass.  Soft  solders,  composed  of  lead  and  tin,  are  used  for  unitmg 
tin  or  lead. 

Sole. — Anything  resembling  in  function  the  sole  of  a  shoe.  The  foundation- 
plate  of  a  marine-engine.    The  lower  edge  of  a  turbine. 

Solenoid. — ^A  cylindrical  coil  of  wire  the  convolutions  of  which  are  circular. 

Sounding. — ^To  measure  the  depth  of  water,  soft  mud,  etc.  In  shallow  water 
this  may  be  done  with  a  graduated  rod  or  pole.  In  deep  water,  various 
kinds  of  apparatus  are  used;  some  of  them,  in  addition  to  measuring 
the  depth  of  water,  are  provided  with  a  device  for  bringing  to  the  surface 
sampl^  of  mud  from  the  bottom  of  the  sea. 

Spall. — A  piece  chipped  from  a  stone,  as  with  a  spalling-hammer. 

SpAndrd. — ^Thc  triangular-like  portion  or  space  of  an  arch  lying  above  or 
outside  the  extrados,  and  below  the  roadway. 


15M  GLOSSARY. 

SpMidrel"fllliiig« — ^The  filling  of  earth,  or  masonry,  etc.,  in  ihm  spandrel  of 
an  arch. 

Spandrel-wall. — ^A  wall  built  on  the  extrados  of  an  arch  in  the  ^>axidrel; 
used  to  give  rigidity  to  the  arch,  or  to  support  the  roadway,  etc. 

^HUiner* — A  sort  of  lever-wrench  with  a  hole  or  with  movable  jaws  to  fit 
over  a  nut  for  tightening  it;  or  any  instrument  for  clasping  and  tighten- 
ing a  nut  or  screw  or  wheel,  etc.  A  rod  connecting  two  parts  having 
parallel  motion. 

Spar. — A  round  stick  of  timber  used  for  various  purposes,  as  the  jib  or  boom 
of  a  derrick,  the  masts,  booms  and  yards  of  a  ship,  the  poles  or  comznoc 
rafters  of  a  roof,  etc. 

Spark-arrester. — A  netting  or  device  placed  over  or  in  the  smoke-stack  to 
prevent  the  escape  of  the  sparks. 

Spectroscope. — An  instnunent  for  producing  a  spectrum  from  rays  of  light, 
and  for  studying  it. 

Spectrum. — ^The  continuous  and  successive  colors  in  a  band  of  light  seen 
when  rays  of  light  are  deflected  through  a  prism. 

Speculum-metal. — An  alloy  consisting  of  ten  parts  copper  and  one  part  tic: 
used  as  a  mirror  or  speculum. 

Speed-pulley. — A  sort  ot  cone-pulley,  but  stepped;  different  ^>eeds  are 
obtained  by  placing  the  belt  over  different  steps  or  faces  of  tne  pulley. 

Spelter. — Zinc.    Spelter  solder  is  hard  solder  composed  of  copper  and  ainc^ 

Spider,  Armature. — A  light  framework  or  ^eleton  consisting  of  a  cectral 
sleeve  or  hub  keyed  to  the  armature  shaft,  and  provided  with  a  number 
of  radial  spokes  or  arms  for  fixing  or  holding  the  armatuxe  core  to  the 
dynamo-electric  machine. 

Spiegeleisen— spiegd-iron — A  pig-iron  containing  from  ^  toHor  more  of 
manganese;  used  in  the  manufacture  of  Bessemer  steel. 

Spigot. — A  plug  with  a  hole  in  it  and  used  as  a  faucet.  The  end  of  a  cast- 
iron  pipe  which  fits  into  the  bell-end  of  an  adjoining  pipe;  such  a  joint 
is  called  a  spigot-joint. 

Spike. — ^A  large  metal  nail;  may  be  pointed,  chisel-pointed,  barbed,  grooved, 
or  split,  etc.;  the  head  also  may  be  variously  shaped. 

Spile. — A  pile. 

Spillway. — A  sort  of  weir  or  gap  or  passage  for  surplus  water  frona  a  reser- 
voir; located  near  one  end  of  the  dam  or  at  the  dam  itself. 

Spindle. — A  thin  axle  or  shaft.  A  solid  generated  by  a  curve  about  its 
chord;  may  be  circular,  parabolic,  elliptkal,  etc.,  depending  upon  the 
ciu^e. 

Splay. — ^The  flaring  or  widening  at  the  mouth  of  anything.  The  wings  of 
a  culvert  when  they  spread  back  from  the  center  line  are  aaui  to  be 
splayed. 

Splice. — The  joining  of  two  pieces  together  by  overlapping. 

Spoil-bank-* waste-bank. — A  refuse  bank  in  mining  and  in  general  excava- 
tion. 

Springer. — ^The  lowest  voussoir  or  arch-stone  of  an  arch. 

Sprlnging-line. — ^The  lower  face-line  of  the  springers  of  an  arch;  the  Ux» 
from  which  the  arch  springs  or  rises  or  b^ns. 

Spring-pole  drillinf. — In  rock-boring,  a  simple  method  of  usinga  spring- 
pole  on  the  outer  end  of  which  is  stispcnded  the  drill-rod.  The  sprix« 
of  the  pole  raises  the  rod,  the  down  motion  being  effected  by  hand. 

Sprocket-wheel. — A  rag-wheel  or  wheel  with  projections  that  engage  the 
links  of  a  chain  passing  over  it.  The  projections  may  be  pins,  teeth  or 
lugs,  etc. 

Spur-gear— spttr-gearing. — Gearing  in  which  spur-wheels  are  used. 

Spur-wheel. — A  common  cog-wheel,  the  cogs  being  on  the  periphery  of  the 
wheel,  and  radial. 

Square. — An  in^ttrument  for  laying  off  right  angles.  In  roofing  and  £kx>ring. 
an  area  equal  to  ten  feet  square  —  lOO  sq.  ft. 

Square-headed. — Straight,  as  the  upper  edge  of  the  opening  of  a  door  or 
window  not  arched  or  curved. 

Stack. — One  or  more  main  flues,  funnels,  or  chimneys  grouped  together  for 
the  passage  of  smoke.    A  smoke-stack. 

Staff-angle. — In  plastering,  a  square  rod  of  wood  flush  with  the  wall  at  the 
external  angle  of  a  room,  to  protect  the  plastering. 

Staging. — A  temporary  structure,  including  the  flooring  and  supports,  used 
m  building  operations. 

Stamp-mill — stamplog-miU — A  mill  for  crushing  ore  by  the  use  of  vertically- 
actmg  stamps;  may  be  operated  by  any  kind  of  power. 


SPANDREL-FJLUNG.  STRIKING-PLATE.       1527 

Stanchion. — A  vertical  support,  as  a  coltuno,  post  or  strut  used  as  a  support 

to  a  vessel's  deck,  or  part  of  a  roof,  etc. 
Standing. — Anything  quite  permanent,  as  standing-rigging  or  the  shrouds 

and  stays  of  a  ship.    Anything  rigidly  fastened  to  and  projecting  from, 

as  a  standing-bolt,  or  stud-bolt. 
Stand-pipe. — A  vertical  water-pipe  used  as  a  reservoir;    or  inserted  in  a 

main  to  show  the  hydraulic  grade  line  or  to  act  as  an  air^valve;  and 

for  other  purposes  as  in  a  steam-engine. 
Staple. — A  U-shaped  loop  of  metal  driven  into  a  door  or  other  object,  the 

projecting  ends  being  bent  or  clinched  on  the  inside,  to  receive  a  nook 

or  hasp  and  form  a  kind  of  lock. 
Starboard. — ^The  right  side  of  a  vessel  facing  her  bow.     Opposed  to  larboard 

or  port. 
Starling. — ^A  pile  structure  around,  or  up-stream  or  down-stream  from,  a 

bridge-pier  for  protection  or  support.    One  of  such  piles. 
Static— statical. — Pertaining  to  weight,  without  motion;    as  static  equili- 
brium, static  load,  static  pressure,  etc. 
Stay. — ^A  rope,  tie,  brace,  or  strut,  etc.,  for  keeping  anything  in  place  or 

making  it  "stay"  in  position. 
Stay-bolt. — A  bolt  used  to  prevent  two  opposite  plates  or  parts  from  being 

pressed  or  pulled  apart  further,  as  a  stay-bolt  in  a  steam-boiler. 
Stay-rod. — Same  as  stay-bolt  but  longer,  and  used  for  various  purposes  as 

in  btiilding-construction. 
Staam-box— steam-chest — A  reservoir  or  chamber  for  steam  to  be  used; 

situated  above  the  boiler,  in  a  locomotive.    Prom  this  chamber  the 

steam  passes  to  the  cylinders. 
Steam-chest. — [The  common  name.]  Same  as  St4am-box,  above. 
Steam-pipe. — A  pipe  which  leads  from  the  boiler  to  the  engine  or  from  the 

boiler  to  the  steam-chest.    Various  pipes  conveiring  steam. 
Stem* — A  projecting  part,  as  the  stem  of  a  gate-valve. 
Step. — In  mechanics,  ansrthing  resembling  a  step  of  a  stair*  as  an  offset  on  a 

cone-pulley.    The  foot  or  bearing  of  a  vertical  shaft. 
Stile«— One  of  the  main  frames  of  a  door  to  which  the  secondary  or  central 

frames  are  secured.    The  outer  frame  or  main  frame  of  anjrthing. 
Stilted-arch. — In  architecture,  an  arch  apparently  raised  above  its  springing 

as  if  stilted. 
Stlrmp. — In  carpentry,  an  iron  loop  or  strap  for  supporting  one  beam 

butting  another,  or  a  rafter,  etc. 
Stock  and  die. — ^A  die  and  its  holder,  for  cutting  screws. 
Stoker. — A  fireman.    A  imchanical  stoker  is  an  automatic  device  for  feeding 

fuel  in  a  furnace  and  attending  to  the  ashes,  etc. 
Stone-brealcer. — See  Rock-crusfur. 
Stonei«iw. — ^A  blade  made  to  reciprocate  in  its  kerf  while  sand  is  fed  by  a 

stream  of  water.    Used  for  sawing  marble,  etc. 
Stope. — ^An  (horizontal)  excavation  in  a  mine,  from  a  shaft  or  tunnel  or  drift, 

to  remove  the  ore  laid  bare,  or  to  pile  the  ore.  or  to  receive  refuse,  etc. 
S-trap. — An  S-bend  in  a  waste  pipe  to  prevent  gases  from  rising  above  the 

point  of  bend. 
Strap. — ^A  long  narrow  strap-like  piece  of  metal,  either  straight  or  looped, 

and  bolted  to  two  pieces  to  hold  them  together,  as  in  an  iron  strap  used 

in  a  timber  splice,  etc. 
Stratified. — Depcraitea  in  lajrers  or  strata.     One  of  the  layers  is  called  a 

stratum.    In  geology,  stratified  rock  or  earth;  bed  rock. 
Ctien. — A  force  producing;  strain;  measured  in  lbs.  per  sq.  in.  or  per  sq.  ft. 

on  the  member  to  which  it  is  applied.     Within  the  elastic  limit  of  the 

material,  strtss  is  proportional  to  strain — Hook's  Law. 
Stress-sheet— straln^sheet. — A  diagram  of  a  structure,  as  a  bridge,  giving 

stresses  and  sizes  of  members  and  other  information  which  will  determine 

the  character  of  the  structure  to  be  built. 
Stretcher. — In  masonry,  a  brick  or  stone  laid  horizontally  in  the  direction 

of  the  face  of  the  wall;  distinguished  from  header  which  heads  onto  the 

face  of  the  wall. 
Stretclierwbond. — Bricks  or  stones  all  laid  as  stretchers  in  continuous  courses, 

no  two  joints  being  opposite  transversely. 
Stria. — A  fillet  between  tne  flutes  (base  moldings)  of  columns. 
Strike. — ^The  direction,  by  the  compass,  of  a  stratified  formation;   at  right 

angle  to  the  dip. 
Striking-plate. — In  arch-centers,  one  of  a  series  of  compound  wedges  on 

which  the  centering  rests  while  the  masonry  arch  is  being  built;   and 


16S8  GLOSSARY. 

wbm  the  wwSget  are  ■truck,  tl&e  centering  lowers  and  the  ax^  becooH 

aelf-eupportang. 

Striae. — ^A  string-ooune.  A  line  of  pieces  used  in  construction,  as  txa^Mi; 
stone,  etc. 

8triaf«<oiirse. — In  architecture,  a  projecting  molding  or  other  prominent  os 
distinct  band. 

Stflager. — A  string-board  or  string-pint  of  a  stair,  or  one  of  the  skstfax 
pieces  supporting  the  treads  cund  risers;  or  an  ornamental  piece  fhted 
outside  the  supporting  stringer.  A  longitudinal  piece  for  soppcating 
anything  such  as  the  ties  or  planking  on  a  bridge. 

Stripping. — In  a  quarry,  mine  or  gravel-pit,  the  useless  material  stripped  or 
removed  preparatory  to  openmg  the  quarry,  mine  or  pit. 

Stmt. — A  member  acting  in  compression.  Opposed  to  lt#  whi^  acts  is 
tension.    A  prop  or  brace. 

Stub. — ^A  short  end  or  blimt  end. 

Stnlnand. — ^The  enlarged  end  of  a  connecting-rod  or  pitman,  to  which  the 
strap  is  fastened. 

Stnd. — One  of  the  vertical  pieces  of  scantling  in  a  partition  azKl  to  whidx 
the  laths  are  nailed. 

Stod-bolt.— See  Standing-boU, 

Stadding. — In  carpentry,  material  to  be  used  as  studs  or  joists. 

Stufflag-box. — A  sort  of  cast-iron  box  or  chamber  arranged  arouxMl  a 
movable  rod  to  secure  a  tight  ioint  against  water,  steam,  or  air,  etc, 
passing  along  the  rod  through  the  wall  which  the  rod  pierces.  The  box  is 
packed  with  greased  hemp,  or  india-rubber,  etc.,  and  the  riiig<ap 
screwed  or  bolted  on. 

ctioa. — ^The  removal  or  the  lessening  of  the  atmospheric  pressure  on  any 
part  of  a  liquid  so  as  to  disturb  its  eqmlibritun  and  cause  it  to  flow,  the 
atmospheric  pressure  still  remaining  on  some  other  suriace  of  the  liquki. 
The  exhaustion  of  a  gas  or  liquid  from  a  chamber. 

Soctioii-pipe. — ^A  pipe  connected  with  the  bottom  of  a  pump-barrel  and 
leadmg  down  mto  a  well  or  body  of  water  to  be  raised.  A  pipe  leading 
from  beneath  a  water-wheel  downward  to  the  level  of  the  tail-race  in 
order  to  make  the  total  head  or  fall  available  for  power;  the  pipe  must 
be  air-tight. 

Soction^ump. — ^A  pump  with  a  barrel  or  cylinder  standing  on  and  fastened 
to  a  suction-pipe  leading  to  a  well;  at  the  junction  oi  barrel  and  pipe 
is  a  flap- valve  raising  upward  to  allow  water  to  enter  from  below,  Irat 
which  closes  down  tight  against  any  back  pressure;  the  barrel  itself 
being  fitted  with  a  piston-rod  operating  a  piston-head  containing  a 
flap-valve  which  also  raises  in  the  same  manner  as  the  other  valve.  At 
the  down -stroke  of  the  piston  the  lower  valve  closes  and  the  upper  ooe 
opens:  at  the  up-stroke  they  reverse.   Other  kinds  of  valves  may  oe  used. 

Suction-valve. — ^The  lower  valve  of  a  suction-pump;  the  one  below  the  piston. 
See  Suction-pump, 

Sump. — ^A  depression  in  which  water  collects,  as  at  the  head  of  a  bnd- 
uide;  a  kind  of  pool.  A  reservoir  in  a  mine  or  other  woricing  into  which 
drainage  water  is  led  and  from  which  it  is  pumped  out  of  the  working; 
a  sump-pump  is  used  for  this  purpose,  ana  the  shaft  through  which  it 
is  pumped  is  called  a  sump-shaft. 

Surbase. — An  upper  molding  above  a  base,  as  that  above  the  wainscoting 
or  at  the  top  of  a  pedestal. 

Surd. — In  mathematics,  a  qxiantity  which  cannot  be  expressed  definitely. 

as  vr. 

Sorface-condeoser. — A  condenser  in  which  the  exhaust-steam  is  condensed 

on  metal  surfaces  which  are  cooled  by  flowing  cold  water  in  contact 

with  the  opposite  faces. 
Surface-tension. — ^The  adhesion  or  tension  of  the  surface-ddn  of  a  UqukL 

as  when  anything  is  made  to  touch  it  and  is  then  zaised.    A  kind  of 

capillary  attraction. 
Swage. — A  sort  of  die  for  giving  shape  to  a  piece  of  metal   being    hana- 

mered. 
Swage-Mock. — A  block  with  various  holes,  grooves,  and  other  shapes  for 

swaging  or  shaping  pieces  of  metal,  as  for  heading  bolts,  etc. 
Sway-brace, — A  brace  used  to  cut  a  four-sided  panel  of  a  structure  into  rigid 

triangles.    A  sort  of  diagonal  member  or  brace  (strut  or  rod)  between 
lilT^  °PP<^**«  posts  of  bridge  trusses. 
Swing-saw. — A  circular  saw  suspended  from  a  frame  and>whlch|Can  be  used 

m  sawmg  large  bulky  pieces  at  rest.  Digitized  by  LiOOglC 


STRING.  TERNE-PLATB.         1520 

Switch. — ^Any  device  for  connecting  or  disconnecting,  aa  a  track,  a  ctiment 

of  electricity,  etc. 
SwMchlNick. — ^A  sort  of  zig-zag  location  of  a  railway,  for  gaining  a  gradual 

grade  over  a  mountain. 
SwlvcL — A  fastening  comprising  an  axis  which  may  be  turned  around  freely 

in  the  other  part,  the  end  of  the  axis  being  headed  like  a  bolt,  to  sustain 

tension. 
Ssfachroolze. — ^To  cause  to  occur  or  act  simultaneously. 
SsmdUud. — In  geokwy,  the  dipping  of  strata  toward  each  other  and  forming 

valley  shapes.    Opposed  to  anticlinal.    A  synclinal  axis  is  a  line  foUow- 

ing  along  the  lowest  points  of  the  depression. 
Syiteiii,  Thne-Wire. — A  system  of  electric  distribution  for  lamps  or  other 

translating  devices  connected  in  multiple,  in  which  three  wires  are  used 

instead  of  two  usually  emplo^d.    In  such  a  system  two  dynamos  are 

usually  emploved,  connected  m  series. 


T— tee. — ^Anything  resembling  the  letter  T,  as  a  T-rail,  T-square,  T-iron.  etc. 

Table. — In  mechanics,  the  table-like  part  of  a  machine  on  which  the  work 
is  placed.  In  architecture,  a  horizontal  molding  or  a  projecting  portion 
from  a  wall. 

Tackle. — ^A  rope  operating  in  one  or  more  pulleys  for  hoisting  or  hauling. 

TaU-nicfr. — ^A  channel  and  stream  of  water  leading  from  the  water-wheel. 

Talus « batter. — Slope,  as  of  a  parapet  or  rampart,  in  fortifications. 

Tamp. — ^To  force  down  with  strokes  or  pressures,  as  tamping  a  charge  of 
powder  in  a  hole,  or  tamping  earth,  concrete,  etc 

Tampliic-bar— tamping-iron. — In  blasting,  an  iron  bar  for  forcing  the  tamp- 
ing (material)  on  the  charge  of  explosive  in  the  hole. 

TaaipiiiffHrfiig. — A  form  of  cast-plug  used  instead  of  tamping  material  in  a 
bbMt-hole. 

Tangent-screw. — ^A  sort  of  slow-motion  screw  for  revolving  circtilar  disks 
sk>wly. 

Taak-engine. — ^A  locomotive  that  carries  its  coal  and  water  without  a  tender. 

Tank-Iron. — Plate  iron  whose  thickness  is  between  that  of  boiler-plate  and 
sheet-iron,  the  latter  being  the  thinnest  and  about  the  same  as  stove- 
pipe iron. 

Ta^* — A  tool  with  an  external,  tapered,  and  longitudinally-grooved  screw 
for  cutting  the  internal  screws  of  nuts,  etc.  As  a  verb,  to  make  a  tap 
as  in  a  pipe  (pipe-tap) ;  to  bore  or  cut  into;  to  poimd  as  with  a  hammer 
in  testing  rivets  or  cast-iron  pipe. 

Tap4M>lt— tap-screw. — A  bolt  screwed  into  a  tapped  hole,  as  in  a  plate, 
the  plate  acting  as  a  nut. 

Tapping-drill  — tapping^fliachlne. — ^A  drill  or  machine  for  tapping  holes  in 
street-mains,  or  iron  pipes. 

Tappet.^ — A  projection  or  arm  on  a  revolving  shaft,  which  strikes  or  taps 
something  at  each  revolution. 

Tee  "T.— See  T. 

Tecth.-^Plural  of  tooth;  see  Tooih. 

Telfofd  pavement— telford.-^A  rocul  pavement  consisting  of  a  foundation 
of  small  stones  laid  by  hand;  on  top  of  and  in  the  crevices  of  these 
stones  are  i>acked  smaller  pieces:  upon  this,  is  broken  stone.  The 
whole  mass  is  rolled  until  the  sur6u:e  becomes  compact  and  smooth. 

Temper. — ^To  modify.  To  bring  metal  to  a  proper  degree  of  hardness 
by  first  heating  to  a  high  temperature,  and  then  suddenly  cooling  in  a 
bath  of  oil.  or  water,  etc.  To  mix  mortar  to  the  right  consistency  for 
bricklaying,  etc. 

Templet— template. — An  outline  of  anything,  used  as  a  guide  or  model  in 
snaping  it,  as  the  edge  of  a  board  cut  to  shape  a  molding,  or  a  board 
or  plate  with  holes  spaced  for  punching  other  plates,  etc. 

Tender* — That  which  tenders  or  waits  upon,  as  an  engine  tender,  or^a  vessel 


supplying  freight,  provisions,  etc,  to  another, 
■on.— Thefi 


Tenon. — The  framed  projection  at  the  end  of  a  timber,  to  fit  into  a  mortise; 

such  a  joint  is  called  a  mortise  and  tenon  joint. 
Tefedo— ship-worm. — A  sea-worm  which  bores  into  and  honeycombs  piling 

and  timoer. 
Tsrn»iplate. — An  inferior  tin-plate,  or  a  plate  of  sheet-iron^ 

coated  with  tin  which  is  largely  alloyed  with  lead. 


15S0  GLOSSARY. 

Terrace — ^A  tort  of  long  horizontal  step  in  an  embankment;    used  on  the 

slopinff  up-stream  and  down-stream  faces  or  slopes  of  earthen  dams. 

A  Kind  of  bench  or  level,  on  the  side  of  a  hill. 
Terra-cotta. — A  fine  quality  of  clay  baked  very  hard;    used  for  brii^ 

roofing  tile,  pipes,  etc. 
Test-piunp. — A  force-pump  used  for  testing  the  strength  or  tightxiess  dt 

pipes,  cylinders,  etc.    it  is  provided  with  a  pressure-gage. 
Theodolite. — A  surveying  instrument,  something  like  a  transit  btxt  whose 

telescope  is  not  reversible. 
Thannometer. — An  instrument  for  measuring   temperatures.     C^nsigradt 

th€TtHcmgt4r  reads  sero   at   freezing  and +  100^  at  boiling.      D^psti 

ihtrmomgUr  used  to  record  the  temperature  of  the  water  at  any  depti 

in  the  sea.    DiH^rwntial  thirmomeur  is  used  to  record  small  diiferencsi 

in  temperature.    Fahrenheit  thermometer  reads  +32**  at  freezing  9xA 

+  212^  at  boiling.    Maximum  thermometer  registers  the  maximum  tec- 

perature.    AftMtmMm /A#rmo»fU/tfr  registers  the   minimum   tempexatuxt. 

tteamur  thermometer  reads  zero  at  freezing  and  +80^  at  boillx^. 
ThimMe. — ^A  sleeve  or  tube  used  to  join  the  ends  of  pipes  or  rods.    A  carcnhtr 

ring,  concave  outside,  to  form  the  inside  protection  to  a  loop  of  xo7t 

when  suspended  on  a  hook  or  other  contrivance. 
Tlilnbl»-Joint. — A  sleeve  or  thimble  slipped  over  a  pipe-joint  and  jH^r^*^ 

to  prevent  leakage  during  expansion  and  contraction. 
Thread. — ^The  spiral  ndge  or  worm  of  a  screw. 
Three-ply. — ^Three  thicknesses,  as  three-ply  roofing  felt. 
Throat. — The  narrow  part  of  an  opening,  not  always  near  the  end,  as  the 

throat  of  a  ventun-meter. 
Throagh-mortlse. — A  mortise  cut  entirely  through  a  timber. 
Through-stone  «-thorotigh<4toiM — ^A  header  extending  entirely  through  & 

wall. 
Throw. — ^The  distance  moved,  as  the  throw  of  a  railroad  switcli  is  fror 

6  to  6  inches.    The  extreme  movement  of  a  slide-valve.    The  doobk- 

radius  of  a  crank. 
Thrust. — ^The  crushing  of  the  pillars  in  a  coal-mine. 
Thrust-box. — A  box-bearing  sustaining  a  vertical  shaft. 
Tide-gate. — ^A  gate  through  which  water  passes  into  a  basin  when  the  tide 

flows  in,  and  which  is  shut  to  retain  the  water  from  flowing  ba<^  at  ebb. 
Tie. — Any  beam  or  rod  used  in  construction  to  hold  certain  parts  tceetber 

bv  tension  or  pull.    One  of  the  sleepers  or  supports  to  the  rails. 
TI*H>uite. — ^A  metal  plate  resting  on  a  tie  and  supporting  the  rail;    t»ed  to 

prevent  the  flange  of  the  rail  from  sinking  into  the  woodm  tie. 
Tie>4t>d. — Any  rod  used  as  a  tie  to  sustain  tension  or  pull. 
Tile. — A  thin  shape  of  baked  clay,  used  for  covering  roofs,  floors,  walls,  etc,; 

also  for  pipe,  drains  and  sewers. 
Tire. — ^An  outside  ring  aroimd  the  periphery  of  the  wheel  of  a  vehicle.    la 

common  wagons,  the  metal  tire  is  heated  so  as  to  expand  and  t>ywi 

shrunk  over  the  wooden  felloe. 
Tit. — A  small  projection,  as  like  the  end  of  a  bolt  on  the  stufisce  of  a  casting. 
Toe. — ^The  sharp  end,  or  front  end,  or  moving  end  of  many  devices.    The 

toe  of  a  switch,  or  of  a  frog,  etc.  « 

Toggte-Joint. — ^A  joint  formed  bv  two  bars  hinged  ' 

together  at  an  obtuse  angle  so  that  when 
direct  pressure  or  pull  is  applied  at  the  joint 
the  lateral  force  is  greatly  augmented. 

Tongue. — ^Many  things  pointed  or  projecting,  as  the  bead  or  tongue  along 
one  edge  ot  a  board  to  fit  into  the  groove  of  an  adjacent  board ;  called 
tonguf  and  groove^  and  used  for  flooring,  etc.  The  pointed  part  c^  a 
crossing-frog. 

Tooling. — In  masonry,  dressing  with  a  chisel  so  the  face  shows  the  parallel 
marks  of  the  tool  with  uniformity. 

Tooth. — One  of  the  teeth  or  cogs  of  a  wheel.  Also  applies  to  other  tooth- 
like  projections  as  in  a  saw. 

Toms.— ;-A  large  convex  molding,  used  at  the  base  of  a  oolunin.  Opposed  to 
scotia,  a  concave  molding. 

Tower,  Electric. — A  high  tower  provided  for  the  support  of  a  number  o€ 
electric  arc  lamps,  employed  m  systems  of  general  illumination. 

Tower,  Electric-Transmission. — ^A  tower  on  a  trazismission  lane,  for  sup- 
porting long-span  wires.  Digitized  by  LjOOg IC 


TERRACE.  TUBE-VALVE.  1681 

Traction-wlied. — A  wheel  which  by  friction  on  its  circumference  draws  a 
vehicle,  as  the  driver  of  a  locomotive. 

TractioiK«iiCine. — ^A  steam-enfidne  for  drawing  loads  on  common  roads. 

TraiUns-wheel. — One  of  the  wheels  situated  just  behind  the  driving-wheels 
of  a  locomotive  to  support  the  rear  weight. 

Train. — ^A  set  of  wheels,  as  cog-wheels,  woridng  in  series,  i.  e.,  connected 
together  in  a  train. 

Trammel. — An  instrument  for  drawing  an  ellipse;  consists  of  a  horisontal 
arm  with  a  vertical  pencil  at  one  end,  two  points  of  the  arm  working 
along  lines  which  cross  each  other  at  right  angle. 

Transformer. — ^An  induction  coil  used  for  raising^or  hwtring  the  electro- 
motive force  at  any  point  of  a  circuit.  The  B.  M.  F.  is  raised  by  the 
step-up  transformer,  and  lowered  by  the  step-down  transformer. 
Other  terms  are:  Commuting-,  Constant-current-,  Core-.  Hedgehog-, 
Lightning-arrester-,  Multiple-,  Oil-,  Open-iron-circuit-,  Pilot-,  Kotary- 
current-.  Rotary-phase-,  Series-,  etc. 

Transom. — One  of  the  horizontal  framing  timbers  across  the  stem  of  a  ship. 
A  horisontal  beam  across  the  opening  for  a  door.  The  opening  above  a 
door.    A  horizontal  beam  of  timber  or  stone  across  a  window. 

Trap. — A  pipe  with  a  depressed  bend  to  hold  water  and  thus  form  a  water- 
seal  against  the  passage  of  gases;  usually  U-  or  S-shaped;  used  in 
closets  in  connection  with  soil-pipes,  and  elsewhere. 

Trap-valve— clack-valve. — See  Clack-valve. 

Travene. — In  surveying,  a  polsrgonal  base-line  around  a  piece  of  land  to  be 
stirveved,  showing  distances  and  angles. 

Tread. — ^The  horizontal  part  of  a  step,  the  vertical  part  being  the  ristr. 

TreaiUe. — A  foot-lever,  for  operating  a  sewing  machine,  grindstone,  or 
lathe,  etc. 

Treenail. — A  long  wooden  pin  (hard  wood)  for  fastening  planks  and  timbers; 
used  in  ship-building.    Auger-holes  are  first  bored ,  and  the  pins  driven  in. 

Tresdework. — A  stilted  framework  for  supporting  the  floor  of  a  bridge  or 
other  structure. 

Trimmer. — In  carpentry,  a  short  cross-joint  inserted  at  right  angle  between 
two  lines  of  joists  and  butting  against  them;  and  in  turn  supporting 
the  ends  of  other  joists  parallel  with  the  main  ones.  The  ends  may  be 
supported  by  iron  stirrups,  or  mortised  into  the  other  joists.  Used  at 
floor-  and  roof -openings,  at  chimnevs  and  stairwasrs. 

Trip-gear. — ^A  gear  that  trips  the  valve-closing  mechanism  in  a  steam- 
engine  when  the  piston  reaches  a  certain  definite  position. 

Trip-hammer— titt-hammer—tiltinf-liammer. — A  hammer  operated  by  a 
cam  which  trips  a  lever  and  allows  the  hammer  to  fall;  used  for  heavy 
work. 

Tripod. — ^A  three-legged  support,  as  for  surveying-instruments,  screw-jacks, 
drills,  etc. 

Tripper. — A  part  of  a  machine  which  causes  another  part  to  be  released, 
as  the  tnpper  of  a  pile-driver  hammer. 

Trippet. — ^Any  projecting  part  of  a  machine  that  trips. 

Truck. — A  framework  with  two  or  more  pairs  of  wheels  for  supporting  one 
end  of  a  car  or  locomotive.  A  bogie-truck  is  used  forward  of  the  drivers 
and  is  carried  by  the  bogie-wheels;  this  name  also  applies  to  street-car 
trucks.    Also,  a  wagon  with  a  solid  platform  for  hauling  heavy  material. 

Trttndi»-wheei  —  lantem-plnlon  —  lantern-wheel  -  wallower. — See  Lantern- 
wheel. 

Trunk. — A  long  trough  or  box  for  convejring  water,  as  from  a  race' to  a  water- 
wheel;  a  penstock  or  flume. 

Trunnion. — One  of  the  cylindrical  projections  on  the  side  of  a  cannon, 
which  support  it  in  its  carriage  and  on  which  it  revolves  in  a  vertical 
plane.  A  hollow  gudgeon  on  either  side  of  an  oscillating  cylinder,  for 
supporting  the  cylinder  and  through  which  steam  enters  and  is  ex- 
hausted. 

Trunnion-valve. — A  valve  of  an  osciUating-cylinder,  and  operated  by  its 
'  oscillating  motion. 

Truss. — A  framework  acting  as  a  beam  or  girder. 

Truss-beam. — A  simple  or  compound  (wooden)  beam  reinforced  by  one  or 
more  tie-rods  (or  in  some  cases,  A-shaped  struts). 

Tube,  Crookes*. — A  tube  containing  a  high  vacuum  and  adapted  for  showing 
any  of  the  phenomena  of  the  ultra-gaseous  state  of  matter. 

Tub^valve. — A  tube  pressed  against  a  seat  at  outlet,  the  other  end  pro- 
jecting above  the  surface  ofthe  water;  operated  in  various  ways.. 


1632  GLOSSARY, 

Tudor  ityle. — ^A  style  of  English  architecture  of  the  16th  century. 

TumUw. — ^A  kind  of  lever  which  drops  intp  a  notch  at  a  certain  definite 
position  in  the  movement  of  a  mechanism,  and  locks. 

Tombler-taiik. — ^A  tank  which  automatically  discharges  its  contents  wbec 
filled;  if  two  tanks,  they  alternate  in  filling  and  emptying. 

TumbUog-bay— waste-weir — ^That  part  of  the  outlet  or  waste  from  a  canal 
or  other  body  of  water  at  which  the  water  falls  rapidly. 

T«mblinff*box. — A  box  pivoted  at  opposite  ends  or  comers  and  made  tc 
revolve.    A  cubical  concrete-mixer  is  a  tumblin|(-box. 

Tiimbling^4liaft — A  shaft  used  in  stamping  mills,  m  the  link-motion  of  s 
locomotive,  in  thrashing-machines,  etc.;  a  sort  of  a  cam-shaft. 

TurMne. — In  the  broadest  sense:  A  motor  with  vanee  (usuallv  curved)  and 
acted  upon  by  the  pressure  or  velocity  (or  both)  of  fluids,  as  air,  gas. 
water,  etc.  (as  ventilating  fans,  turbine  water  wheels,  etc.);  or  actat 
upon  fluids  (as  in  the  case  of  the  centrifugal  pump).  In  a  restrkXM 
sense:  A  motor  with  curved  vanes  acted  upon  by  fluids  (water  or  steam), 
as  the  hydraulic  turbine  and  steam  turbine  (see  below). 

TurMne,  HydraHlic-Tarbine  Water  Whed-Tuftine.— A  turbine  deriving  its 
motive  power  from  the  pressure  and  velocity  of  water.     See  pa8el3ft2. 

Turbine,  Steam. — A  turbine  deriving  its  motive  power  from  the  Telocxty 
and  expansive  force  of  steam. 

Turn,  Ampere. — A  single  turn  or  winding  in  a  coil  of  wire  through  which 
one  ampere  passes. 

Tumbttckle. — ^A  double-nut  with  right  and  left  threads,  used  for  connec^cs 
the  ends  of  two  rods  or  bars,  making  one  adjustable  member. 

Tuming-point. — In  leveling,  a  temporary  bench-maik. 

Turn-table— turntable. — A  sort  of  deck-drawbridge  swinging  in  a  horisontal 
circle,  for  turning  locomotives;  tased  at  terminal  points  and  at  shops, 
round-houses,  etc.  There  is  a  central  pin  or  pivot-pin  supportix«  the 
table,  and  the  outer  ends  are  steadied  by  wheels  on  a  circular  tra(£. 

Turpentine. — An  oleoresinous  substance  obtained  from  the  baxk  and  wood 
of  coniferous  trees.    The  oil  of  turpentine  is  obtained  by  distiUataoct. 

Tuscan  Order. — In  architecture,  one  of  the  five  Orders;  similar  to  the  Romaa 
Doric. 

Tusk-tenon. — A  tenon  stepped  or  shouldered  into  a  mortise,  to  gire  addi- 
tional strength  to  the  connected  beams. 

Two-ply. — Havmg  two  thicknesses,  or  double  thickness. 

Twyer. — One  of  the  tubes  through  which  air  enters  a  blast-furnace. 

U. 

U-bolt. — ^A  U-shaped  rod  with  nut  and  thread  at  each  end. 

Unctuous. — Oily;  greasy,  soapv.    Having  the  nature  of  an  unguent. 

Underdrain. — A  sub-dram,  or  drain  under  ground. 

Undermine. — ^To  render  imstable  by  weakening  the  fotmdation.  To  exca- 
vate beneath,  as  by  digging  or  washing. 

Underpinning. — A  support  or  new  foundation  placed  under  a  wall  oat 
properly  supported;  it  may  be  either  temporary  or  permanent,  and 
may  consist  m  merely  projecting  the  wall  downward.  The  act  of  intro- 
ducing such  a  support.  The  term  uruUrsttting  may  be  used,  especially 
with  reference  to  machinenr,  pedestals,  etc. 

Undershot  wheeL — A  water-wheel  operated  by  the  force  of  the  stream 
acting  upon  the  blades  or  paddles  as  they  fall  below  the  level  of  the 
center  or  axis  of  the  wheel. 

Undertow. — A  sub-surface  cturent  moving  in  a  direction  different  £rom  the 
stu-face-current. 

Unguent. — Any  soft  substance  or  composition  used  for  lubrication. 

UnicUnai—monoclinal. — In  geology,  dipping  in  one  direction:  a  monocHnal 
fold  is  half  an  anticlinal  fold. 

Unit. — A  standard  of  quantity  in  any  sjrstem,  as  unit  of  measure,  capacity, 
weight,  force,  etc. 

Upset. — The  end  of  a  rod,  or  bar,  etc..  which  has  been  thickened  by  shorten- 
ing its  length,  for  the  purpose  of  connecting  it  with  some  other  member 
so  that  the  joint  will  not  be  weaker  than  the  body  of  the  rod  or  bar; 
as  for  forming  the  head  of  an  eye-bar.  or  the  upset-end  on  a  rod  for 
cutting  a  screw-thread.  The  machine  tor  making  upsets,  or  upeettiaf . 
IS  called  an  uffsetting-machine.  The  shaping  <^  eye-bar  heads  is  called 
fo^gtngi  weldmg  a  separate  head  on  the  body  of  the  bar  is  not  afio«* 
able  m  a  good  class  of  structural  work. 


TUDOR  STYLE.  VALVE.  1638 


Vacuum-brake. — A  device  for  stopping  a  train  by  the  operation  of  brakes 
through  partial  vacuum  created  in  a  pipe  connected  with  the  locomo- 
tive;   the  vacuum  being  created  by  a  steam -jet  escaping  through  an 
ejector,   and  the  brakes  being  operated  by  the  drawing  of  the  brake- 
rods  which  are  joined  to  collapsing  bellows  connected  with  the  pipes. 
Vacuum-gase. — A  gage  for  indicating  the  pressure   (or  the  amoimt  of 
vacuum)  in  any  chamber,  as  in  the  receiver  of  an  air-pimip,  a  steam- 
condenser,  etc. 
Vacuum-valve. — A  safety-valve  opening  inward  in  a  steam-boiler  to  give 
relief  from  collapse  when  the  partial  vacuum  in  the  boiler  reduces  the 
internal  pressure  below  the  point  of  safety  in  ressting  the  external 
atmospheric  presstue. 
Valve. — Any  device  for  controlling  the  flow  of  liqmd,  vapor  or  gas  through 
a  pipe  or  passage.    Valve-chest,  in  a  steam-engine,  is  the  steam-chest; 
it  is  the  chamber  in  which  the  valve  works.    Valve  face,  that  part  of  the 
surface  of  the  valve  which  comes  in  contact  with  the  valve  seat.    Valve 
«of  — valve  motion,  the  system  which  gives  motion  to  a  valve,  as  the 
link  motion  of  a  locomotive  for  regulating  the  supply  and  exhaust  of 
steam  to  and  from  the  cylinder.     Valve  seal,  the  fixed  surface  or  piece 
on  which  a  valve  presses  and  rests.     Valve  stem,  a  rod  attached  to  a 
valve  to  operate  it.    Valve  yoke,  a  strap  to  hold  a  valve. 
Air  valve;  a  valve  to  regulate  flow  of  air.  as  in  a  steam-boiler. 
Automatic  valve;  a  valve  that  works  automatically,  as  a  clack-valve. 
Back-pressure  valve;  a  valve  to  prevent  back-flow  when  the  direction 

or  pressure  of  fluid  is  reversed. 
Balance -valve;  a   valve  admitting  fluid  to  both  sides  tmder  nearly  equal 

pressure. 
Bait-cock  valve;  a  sort  of  ball  float  valve,  as  used  it.  water-closet  tanks. 
Ball  valve;  a  valve  formed  by  a  ball  resting  upon  a  seat. 
Blow-through  valve;   a  valve   situated   in  the  opening  through  which 

steam  enters  a  condensing  steam-engine,  for  blowing  through. 
Brake-shoe  valve;   in  an   air-  or  vacuum-brake,  a  valve  to  reheve  the 

excessive  pressure  upon  the  wheel. 
Butterfly  valve;  a  double  clack-valve,  used  in  pumps. 
C^cA;-t^tw;  a  valve  placed  in  a  pipe-line,  or  boiler,  to  prevent  back-flow. 
Clack  valve;  a  trai>-flap,  or  clapper,  hinged  to  allow  flow  in  one  direc- 
tion only. 
Cone-valve;  a  valve  with  a  conical  face  and  seat. 
Conical  valve;  a  T-valve  or  puppet  valve — a  circular  metal  plate  with 

beveled  edge  and  seat. 
Cup-valve;  a  valve  cup-shaped,  and  becoming  a  balance-valve  if  con- 
sisting of  two  cups  connected  by  a  stem  tlut>ugh  the  opening. 
Double-beat  valve;  a  double-seat  valve. 
D-valve;   a  valve  resembling  the  letter  D.  used  in  the  induction  and 

eduction  passages  of  a  steam-engine  cylinder. 
Eauilibrium  valve;  a  balance  valve  (see  above). 
Flap-valve;  a  clack-valve  (see  above). 
Globe-valve;  a  valve  with  a  globular  casing. 
Hinged  valve;  a  butterfly-valve  or  clack-valve  (see  above). 
Key-valve;  an  air  valve-plug. 

Lifting  valve;  a  ball-,  cone-,  poppet-,  or  safety-valve. 
Long-slide  valve;    a    long-valve,    governing  parts  of  both  ends  of  a 

steam-engine  cylinder,  especially  of  the  (Romish  type  of  engine. 
Long-valve;  a  long-slide  valve  (see  above). 
Low-water  valve;  a  valve  which  allows  the  steam  to  escape  when  the 

water  in  the  boiler  is  too  low. 
Oscillatine  valve;  a  valve  that  oscillates. 
Piston-valve;  a  reciprocating  valve,  alternately  opening  and  closing  the 

port  of  a  steam-engine  cylinder. 
Pocketed-valve;  a  valve  flttea  into  the  depression  of  a  pocket. 
Poppet-valve;  a  valve  which  lifts  bodily  from  the  seat. 
Pot-lid  valve;  a  cap  valve  used  at  the  end  of  a  pipe,  or  the  cover  of 

an  air-pump  of  a  steam-engine. 
Puppet-vcuve'  a  conical  valve  or  poppet  valve  (see  above). 
Regulator-valve;  a  throttle  valve.  ^  i 

Relief -valve;   a  valve  through  which  fluids  escape  at  a^^BflnC  deter- 
mined high  pressure. 


1584  GLOSSARY, 

Rnmst  valvt  or  rtv^rsing  vah«:  the  valve  of  a  revening  cylinder,  ^tea 
a  plain  slide-valve. 

Rotary  valv0;  a  rock  valve  which  acts  by  partial  rotatioa. 

Saf0ty-wiive;  a  valve  to  relieve  excessive  pressure,  as  in  a  steam-boiler. 

Scrtw-vaivt:  a  screw  with  a  point  forming  a  small  valve,  for  regxxlattx^ 
flow. 

Slidt-vaim:  a  valve  which  slides  over  a  seat. 

Snifting-vaUM;  the  tail  valve  or  blow  valve  in  the  cylinder  of  a  steam- 
engine,  for  the  escape  or  admission  of  air. 

Sph^rxcal  valvt;  a  ball  valve. 

Tkrottk'Valve:  a  valve  in  the  steam  pipe  of  a  boiler  for  coatrolltng  the 
flow  of  steam,  as  to  a  cylinder. 

Trap^vaiut;  a  clack-valve  or  flap-valve  (see  above). 

Twxn-valve;  a  double-connecton  valve  or  gate. 

UtuUrshut  vaht;  a  valve  beneath  the  sole-plate  of  a  pomp,  etc.,  and 
which  closes  by  upward  pressure  from  below. 
Vapor. — A  gaseous  form  of  a  substance  which  ordinarily  exists  in  solid  or 

liquid  form,  and  while  it  is  in  this  gaseous  form  it  is  phjrsically  a  real 

gaSt  which  may  be  defined  as  a  substance  which  at  ordinary  tempera- 
tures and  pressures  exists  in  the  gaseous  state;   hence,  all  vapors  are 

gases  but  all  gases  are  not  vai>ors.     A  satwraUd  vaM  is  a  vapor  whidi 

IS  on  the  point  of  condensation.     A  Hon-saiutaUd  vapor  is  one  whkh 

obeys  the  laws  of  gases,  as  superheated  steam. 
Variable  gear. — Geared  wheels  or  sectors  which  impart  altematins  changes 

in  speed. 
VauH. — A  long  arch  (not  in  span  but  in  the  direction  of  the  axis),  or  one 

whose  length  is  great  in  proportion  to  its  span.    The  space  enclosed  by 

or  beneath  such  a  vault. 

Conical  vault;  a  vault  formed  as  upon  part  of  the  surface  of  a  cone. 

Compound  vanity  a  vault  composed  of  two  or  more  simple  vaxilts. 

Cross  vault;  a  vault  which  crosses  another. 

Cylindrical  vault;  a  vault  of  cylindrical  form. 

Double  vault;  a  vault  placed  above  or  enclosing  another  vault. 

Elliptical  vault;  a  vault  of  elliptical  form. 

Grotned  vault;  a  vault  formed  by  two  intersecting  vaults. 

Pointed  vault;  a  vault  pointed. 

Rampant  vault;  a  vault  which  springs  from  planes  not  horizontaL 

Simple  vault;  an  ordinary  vault  with  one  axis. 

Single  vault;  one  vault. 

Spherical  vault;  a  vault  of  spherical  form. 

Surbased  vault;  a  circular  vault  whose  height  is  less  than  half  the  anao. 

Surmounted  vault;  a   circular  vattlt  whose  height  is  greater  than  "Wtt 
the  span. 
Vaulting-shah. — A  shaft  to  receive  the  spring  of  a  roof- vault  rib;    may 

extend  downward  to  the  floor  or  to  the  capital  of  a  pier. 
Vaulting-tile. — ^A  tile  tised  in  vaulting:  hollow  and  of  various  forms. 
Vault-light. — A  vault  cover  set  with  glass  for  the  admission  of  light. 
Vault-shell. — ^The  masonry,  skin,  plate  or  thin  filling  between  the  riba  of  a 

vault. 
Veneer. — A  thin  layer  of  costly  or  ornamental  wood  glued  over  the  sarCacr 

of  a  cheaper  variety  composing  the  frame. 
Venetian  blind. — A  hanging  blind  operated  with  cords,  the  slats  being  he!^ 

together  by  some  flexible  material. 
Vermicular  work. — ^The  surface  of  architectural  stone  so  dressed  or  woricz- 

as  to  appear  thickly  covered  or  indented  with  worm  tracks  or  shapes. 
Vernier. — A  small  movable  scale  sliding  parallel  with  a  fixed  scale,  xim 

number  of  subdivisions  varying  by  1,  in  order  to  obtain  ~ 

readings;  as  the  vernier  of  a  transit  instrument. 
Viaduct. — A  series  of  (masonry)  arches  supporting  a  roadway. 
Viscosity. — Internal  fnction  in  the  movement  of  liquids  and  gases.      VtaexrM 

fluids  are  those  in  which  viscosity  is  strongly  present. 
Vise »  vice. — A  tool  with  two  gripping  jaws  that  may  be  opened  or  doarJ 

by  a  screw  worked  with  a  lever;  used  by  carpenters  and  machinists  tx 

gripping  pieces  to  be  worked. 
Vitreous. — ^Resembling  glass;   glassy. 
Vitrified. — ^The  whole  body,  or  the  suriace  only,  converted  into  gJBS 

glazed,  as  vitrified-  or  glazed-brick,  tile,  terra  CQtta.  pipes,  etc,     Ti« 
\t  i^^^S?^^*®**  ^  performed  by  the  action  of  heat.  ^OOQ IC 
volt.— The  practical  unit  of  electromotive  force.  ^ 


i 


VAPOR.  WATER-MAIN.  153d 

Volt-AiBmeter. — ^A  watt-meter. 

VoU-Ampere. — A  watt. 

Vott-Coiuomb. — ^The  unit  of  electrical  work.    The  joule. 

Voltas®. — Electromotive  force  or  differential  of  potential. 

Vottmeter. — ^An  instrument  for  nMasuring  the  aifference  of  potential. 

W. 

IValnscot. — ^A  wooden  lining  or  paneling  of  the  walls  of  a  room,  and  reaching 

upward  three  feet  or  more  above  the  floor. 
'Waim  *  wale-piece. — ^A  lon^tudinal  timber  fastened  to  a  row  of  piles  to  keep 
them  more  rigid  and  m  position;  or  fastened  along  a  ship,  cofferdam, 
caisson,  whan,  quay,  or  jetty,  etc. 
IValL — In  mining,  one  of  the  rock  surfaces  enclosing  a  vein  or  lode. 
Wallow. — To  wabble,  as  a  water-wheel  revolving  unevenly  on  its  journals. 
IVallower— lantern-wheel. — See  Lantgm-wlugl. 

Wan-plate. — In  building,  a  horizontal  timber  placed  on  top  of  the  wall  to 
bind  it  together  and  stiffen  it:  and  to  receive  the  ends  of  girders,  joists, 
rafters,  roof-trusses,  etc.,  and  distribute  their  pressures  over  the  wall. 
In  minins^,  the  two  long  pieces  of  timbers  of  the  four  comprising  a  set 
of  timbering  in  a  shaft. 
Waro. — ^A  twist  or  bend  as  in  a  piece  of  timber  which  in  drying  has  twisted. 
A  rope  smaller  than  a  cable  and  used  in  towing  or  warping  a  vessel. 
Sediment. 
Warped  surface. — ^A  surface  which  looks  as  though  it  had  been  twisted 
nom  a  true  plane;   applies  to  the  surface  of  Doards,  stones,  soffits  of 
arches,  etc. 
Warplng-banic — A  ridge  of  earth  raised  around  an  area  of  land  for  holding 

water  let  in  to  enrich  the  land  with  warp  or  sediment. 
Wash-board— mopboard— skirting  board. — ^A  board  around  the  walls  of  a 

room  next  to  the  floor.  A  base-board. 
Washer. — An  annular  piece  of  metal,  leather,  or  rubber,  etc.,  placed  at  a 
joint  to  prevent  leakage,  or  tmder  a  nut  to  distribute  pressure,  etc. 
Flat  washes  are  stamped  out  of  plate  (metal) ;  cast  wasfurs  are  thicker 
and  mostly  of  the  O.  G.  pattern,  a  section  of  the  edge  describing  a  re- 
versed curve. 
Washout. — Excavation  of  a  bank  or  hillside  bv  the  erosive  action  of  water; 

the  cutting  or  washing  away  of  a  road-bed  by  rains  or  floods;  etc. 
Waste-gate. — -A  gate  placed  at  the  waste-outlet  of  a  reservoir,  pond,  or 

lake,  etc.    See  Tide  gai4. 
Waste-pipe. — ^A  pipe  for  discharging  waste  water;  an  overflow-pipe. 
Waste-trap. — ^A  device  in  a  pipe  to  allow  the  surplus  water  to  escape  and 

yet  prevent  gases  from  returning. 
Waurway. — ^An  opening  or  passage  lor  waste  water  or  overflow. 
Waste-weir. — A  cut  in  the  side  of  a  reservoir,  pond,  or  canal,  etc.,  for  the 

discharge  of  surplus  water. 
Wast^well. — ^A  well  into  which  surplus  water  is  discharged;  should  have  a 

permeable  bed,  as  gravel. 
WateNbutt. — A  Utrge  cask  used  as  a  reservoir  or  tank  for  water. 
W«ter-craft. — ^Vessels  and  boats  in  general. 
Watenfloat. — ^A  float  placed  in  a  tank,  boiler,  or  cistern,  etc.,  to  control  a 

valve. 
WAter^gage^ — A  device  for  indicating  the  height  of  water  in  tank,  boiler,  or 
reservoir,  etc.    A  connecting  glass  tube  may  be  used .  or  a  float  connected 
with  an  mdicator,  or  a  board  with  elevations  marked  upon  it;  various 
contrivances. 
WateiHAte. — A  gateway,  gate  or  valve  for  controlling  the  passage  of  water 

through  an  opening  or  pipe  or  channel. 
Wltefwhammer. — ^The  impact  of  water  when  its  volume  of  flow  is  checked 
suddenly  as  by  a  gate  in  a  water-pipe;   large  gates  in  long  pipes  are 
regulated  by  gearing  to  close  slowly  in  cases  where  the  combined  volume 
and  velocity  would  tend  to  produce  considerable  impact  if  checked 
suddenly,  pipes  often  bursting  from  this  cause. 
Wateri4aclu — ^The  quantity  of  water  which  will  discharge  through  a  circular 
hole  one  inch  in  diameter  in  24  hours,  the  surface  of  the  water  being  at 
top  of  hole;  about  600  cubic  feet. 
WatCMiialn.— One  of  the  main  pipes  in  a  system  of  water-works;    the 
main  pipe  in  each  street,  or  the  main  pipe  supplying  several  streets,  or 
the  main  pipe  leading  from  the  reservoir  or  headworks.  ^OOgLc 


1536  GLOSSARY. 

y/witirHO0Uir, — ^An  instrument,  device  or  apparatus  for  meaaorins  the 

velocity  or  rate  of  dischaxve  of  water. 
Water-motor. — A  water-wheel  or  turbine.    Any  motor  deriving  its  power 

from  the  pressure  and  flow  of  water,  either  for  direct  ptamping  or  ks 

the  transmission  of  power  to  any  kind  of  machinery. 
Water-pillar  «-water<raiie. — A  vertical  pipe  with  a  swinging  ann  or  goose- 
neck, acting  as  a  sort  of  hydrant  for  suppljring  water  to  locomotives. 
WateTiiWUie; — ^A  plane  passing  through  the  water  line  of  a  ship.  L  e^  the 

water-surface  plane;  hence  the  terms  li^  waUr-plattt  and  lead  wmtgr- 

plam. 
Water-ram. — A  hydraulic  ram,  for  raising  water. 
Watershed. — ^The  boundary  of  a  catckmnU  arta  or  basin,  i.  Om  the   high 

ridge  or  divide  which  surrounds  the  area  drained  bv  a  stream. 
Water^aMe. — In  architecture,  a  string-course  around  the  base  of  a  bniTdiwg. 

and  projecting  outward  for  ornament  and  as  if  to  throw  off  water  frcaa 

the  wall. 
Water-tower. — A  large  standpipe. 
Water-tube  boUer. — ^A  form  oi  boiler  containing  pipes  or  tubes  in  which  the 

water  circulates,  bein^  heated  by  the  surroimaing  flames 
Watt. — ^The  xmit  of  electric  power.    The  volt-ampere.    One  watt  is  equivm* 

lent  to  the  work  of  0.7373  foot-pound  per  second  —  rH  horae  power. 

Watts— volt-amperes— C5—Ci?—js ,  in  which  C— current  in  amperes. 

£— electromotive  force  in  volts,  /?— resistance  in  ohms. 

Watt-iH^er. — A  galvanometer,  for  measuring  simultaneously,  the  current 
and  the  difference  of  potential  at  any  point  of  a  circuit. 

Watt-second. — A  unit  of  electrical  work. 

Way-gate. — ^The  tail-race  of  a  mill. 

Ways.— The  inclined  timbers  on  which  a  ship  moves  in  latmching 

Weather-boardinK. — ^A  facing  of  boards  on  a  building:  the  boards  beins 
either  (1)  clapboards,  laid  horizontally  with  feather-edge  upward  and 
overlapping  each  other  like  shingles,  or  (2)  boards  nailed  vertically 
and  having  either  tongued  and  grooved  joints  or  else  nanower  boards 
nailed  over  the  joints,  or  (3)  ordmanr  shingling. 

Weather-tile. — Tile  used  as  a  substitute  tor  weather-boards. 

Wedg»-valve. — ^A  wedged  shaped  valve  operated  by  a  screw. 

Wedfing. — The  process  of  driving  a  wedge  into  a  saw-kerf  in  the  end  of  a 
tenon  which  just  passes  through  a  tturotwh-mortise,  in  order  to  expaxkd 
the  end  of  the  tenon  and  make  it  bind  firmly  against  the  sides  of  the 
mortise,  as  in  securing  the  helve  or  handle  or  an  ax  into  the  steel  head. 

Weir. — A  dam  across  a  stream,  over  which  the  water  flows.  A  measuring 
weir,  simply  called  a  weir  and  more  properly  a  standard  weir,  for  measur- 
ing the  flow  of  water. 

Weld. — ^To  unite  metallic  substances  by  hammering  or  compression,  with 
or  without  previous  heating;  if  heated  to  fusion,  a  flux  is  used  to  pre- 
vent oxidation  or  rapid  rusting.  Electric  welding  is  accomplished  by 
bringing  the  proposed  joint  into  a  circuit,  the  greater  resistance  at  the 
joint  causing  the  abutting  surfaces  to  become  mtensely  hot,  and  then 


applying  great  mechanical  pressure. 
Wdd-rron.— Wroui 


ought-iron  is  weld -iron. 

Weld-steel.— Puddled  steel. 

Well-boring. — ^The  process  of  sinking  or  driving  wells  by  drilling  or  bcwing 
through  rock,  often  to  great  depths;  percussion  drills  are  most  fre- 
quently employed .    A  form  of  weU-sinkini. 

Well-trap » sink-trap. — A  trap  which  allows  water  to  pass  down,  bat  pre- 
vents air  or  gases  from  passing  up;  such  as  an  S-trap 

Welt. — A  strip  of  metal  riveted  to  two  abutting  plates,  forming  a  butt- 
joint.  Similarly  in  carpentry,  a  strip  placed  over  a  seam  or  joint  to 
strengthen  it. 

Wharf. — A  platform  or  depot  for  vessels.    Plural  is  wharves  or  wharfs. 

Wheel. — ^A  circular  body  or  frame  revolving  on  an  axis.  The  wheel  and 
axle,  lever,  wedge,  pulley,  screw  and  inclined  plane  comprise  ttn  six 
simple  machines  or  mechanical  powers. 

Wheel-oase. — ^The  distance  between  centers  of  the  extreme  front  and  rear 
wheels  of  a  locomotive,  or  car,  etc. 

Wheel-window. — In  architecture,  a  special  circular  window. 

Whitewash. — (1)  common,  quicklime  and  water;  (2)  good,  whiting,  ose 
and  water. 

Whiting. — Chalk  specially  prepared  by  drying,  grinding,  etc. 


WATER-METER.  YARD.  1537 

Wicket. — A  small  gate,  dcK>r  or  opening  in  a  larger  one;  a  small  gate  in  the 
lock-^ate  of  a  canal,  by  which  the  chamber  can  be  emptied;  a  small 
gate  m  a  water-wheel  chute,  etc. 
Winch. — An  axle  with  one  or  two  bent  arms  or  cranks  for  ttiming,  as  a 
common  windlass  or  a  grindstone.  The  axis  may  be  geared  to  a  sepcuute 
drum,  thus  giving  more  power  for  hoisting. 
Wind  [Pronounced  with  long  i]. — A  t\im,  twist  or  bend.  Out  of  wind  means 
free  from  turns,  twists,  bends,  etc.;  used  in  specifications  for  timber, 
stone,  etc. 

Windage,  of  Dynamo. — A  term  proposed  for  the  air  gap  between  the  arma- 
ture and  the  pole-  pieces  of  a  dynamo. 

Wlnd4>eam— collar-beam. — A  beam  joining  together  the  rafters  of  a 
pitched  roof. 

Wind-bore. — ^The  end  of  the  suction-pipe  of  a  pump,  and  covered  with  a 
strainer  to  exclude  foreign  material. 

Wind-bracing. — Any  system  of  braces  to  stiffen  a  frame  against  the  pres- 
sure of  the  wind. 

Winder.— One  of  the  steps  in  a  stair  where  the  staircase  winds  or  turns. 

Wind-gage ->  anemometer. — An  instrument  for  determining  the  velocity  and 
pressxire  of  the  wind. 

Wind-liatch. — The  opening  where  ore  is  taken  out  of  a  mine. 

Winding-engine  —  drawing-engine  —  holstlng-en^ne. — An  engine  used  in 
turning  a  drum  arotind  which  is  wound  a  hoisting-  or  winding-rope. 

WIndlaM. — A  large  axle  bulging  into  a  drum  at  the  center,  or  a  modified 
wheel  and  axle,  used  with  a  winding  rope  in  hoisting  or  hauling  weight 
or  loads,  raising  anchors,  etc.;  the  ends  of  the  axle  are  pier^d  with 
radial  holes  in  which  handspikes  are  inserted  as  levers  or  cranks  in 
winding,  and  the  drum  is  fitted  with  ratchet  and  pawls.  Also  operated 
by  steam,  as  the  suantr-windlass. 

Wing. — A  prefix  used  with  certain  names  of  structures  which  fiare  out  like 
a  wing. 

Wing-dam. — ^A  dam  projecting  out  from  the  shore  so  as  to  divert  the  cur- 
rent;  used  to  deepen  channels,  protect  river-banks  from  wa^  etc. 

Wing-gudgeon. — A  short,  winged  metal-shaft  used  as  a  journal  for  wheels 
having  wooden  axles. 

Wlng-waU. — One  of  the  lateral,  flaring  walls  of  an  abutment,  and  acting  as 
a  sort  of  retaining-wall. 

Winze. — In  mining,  a  vertical  or  inclined  shaft  which  does  not  reach  the 
surface  but  usually  connects  one  level  with  another,  for  ventilation, 
passages,  etc. 

Wiper. — hi  machinery,  a  sort  of  lever-cam  attached  to  a  (horizontal)  shaft 
for  the  purpose  of  pressing  against  the  toe  or  projection  from  another 
(vertical)  shaft  and  raising  it  so  it  may  fall  again  by  its  own  weight; 
used  in  connection  with  marine-engines,  stamp-mills,  etc. 

Wood-screw. — A  common  metal  screw  for  fastening  metal  or  wood  to  wood. 
But  see  Lag-screw. 

Wofk,  Unit  ofElectrlcal.— The  eig. 

Wortc,  Units  of.— (See  pages  00,91.) 

Wofking-beam— walking-beam  "beam. — ^The  large  beam  of  a  steam-engine, 
usually  the  marine  or  pumping  type,  and  used  as  an  oscillating  lever  in 
connecting  the  piston-rod  and  crank-shaft  or  pump-rod. 

Wofidng-polnt. — ^The  part  of  a  tool  or  machine  producmg  the  desired  effect 
or  work. 

Worrn^ — A  shaft  with  a  screw-thread  which  in  revolving  engages  the  teeth 
of  a  wheel  and  turns  it;  the  worm  is  called  an  endless  screw,  and  the 
wheel  a  worm-wheel. 

Wrecking-pump. — A  steam-pump  of  great  capacity  used  in  pumping  water 
from  wrecked  or  damaged  vessels. 

Wrench. — A  tool  with  a  lever  arm  and  with  jaws  for  holding  or  turning 
pipe,  rods,  bolts,  heads,  nuts,  etc. 

Wroufht-lron. — Iron  that  has  been  forged  or  rolled,  and  may  be  forged, 
rolled  or  welded. 

Y. 

Yard. — ^A  round  spar  with  tapering  end  or  ends.  In  railroading,  the  space 
set  aside  for  handling  and  making  up  trains,  and  general  switching; 
and  by  extension  it  includes  the  space,  tracks,  buildings,  etc.,  at  railway 
stations.  C  r\r\ci\o 

Digitized  by  VjOOv  Ic 


1588  GLOSSARY. 

Yard-llmK. — ^The  extreme  end  of  *  yard,  at  whldi  a  tign  usualljr  cantioet 
extreme  care  or  slower  speed  in  running  trains. 

Y-level. — Common  engineers  spirit-level. 

Yoke. — Any  sort  of  a  U-shaped  strap  or  coupHn^. 

Yoke,  Multiple-Pair  Bmslu — A  device  for  holdmg  a  number  of  p«irB  o< 
brushes  of  a  dynamo  electric  machine  in  such  a  manner  that  taey  can 
readily  be  moved  or  rotated  on  the  commutator  cylinder.  Alsoe 
Multiple-pcdr-brush-,  Single-brush-.  Single-pair-^  Single-piairbrosh-.  etc. 

Y-tnick. — A  Y-shaped  arrangement  of  tracks  leadmg  from  another  txack, 
and  often  used  instead  of  a  tumtable  m  tormng  engitw,  cats,  or 
whole  trains. 


d  by  Google 


INDEX. 

(See.  also.  Glossary,  page  1485;  and  Contents,  page  V.) 


Abbreviation  of  a  decimal  by  sub- 
script, 96. 
Abrasion  test  of  bricks,  1116. 
Abscissa  and  ordinate  defined,  256. 
Absorption   process,  for  ties,  cost, 

375. 
Abutments  (R.  R.  ),  masonry,  quan- 

tities  in.  table,  436,  437. 
Accelerated    motion,  equations  of, 

279.  280.  281. 
Acceleration, 
gravity, 
equation  of.  287. 
formu]a,450. 
table,  288. 
in  nuch.,  defined,  278. 
metric  and   English  equivalents, 

table,  89. 
problem,  289. 
A^tic  acid  from  wood.  846. 
Acetylene  flame  for  cutting  steel- 
work, 833. 
Add 
bessemer  process,  394. 
combinations,  321. 
in  chem.,  defined.  821. 
open^iearth  process,  394,  395. 
•proof  compositions,  418 
Acre,  acres, 
and  hectars, 
equivalents,  88. 

sauare,  eqtiiv.  (1-10),  table,  80. 
equivalent  in  vans,  81. 
metric  equivalents,  68.  81. 
per  station  (100-ft.)  and  per  mile, 
(R.  R.).  tables.  1015. 
Acreage,  square,  dimensions  of,  131 3. 
Acre-^t, 
and  cubic  feet,  equivalents,  88. 
per  day  and  cu.  ft.  per  second, 

equivalents.  90. 
per   day,    irrigation    equivalents, 

table.  1314. 
per  month,  irrigation  equivalents, 
table.  1315. 
Addition  and  subtraction,  in  alge- 
bra. 100. 
Adulterants,  cement.  407. 
Aerating  fountain  in  reservoir,  1206. 
Awregate,  concrete,  416. 
Air. 
compressed-,  reference  data.  1482. 
dry.  weight  of.  1145. 
friction  of,  in  small  pipes,  formu- 
la. 1180. 
necessary  for  combustion,  calcula- 
tion, 1871. 


Air. — Oint'd. 
physical  properties  of,  table.  514. 
xelief  valves.  1270. 
valves,  1270. 

weight   of,   at   various  tempera* 
tures,  table.  463. 
Alabaster,  defined.  339. 
Alcohol, 
boilinp;  point  of,  514. 
capacity  and  weight  equivalents, 

table.  1376. 
fuel, 
properties  of ,  1370,  1375. 
tests  of  internal-combustion  en- 
gines on,  1368-1370,  1874. 
melting  point  of,  515. 
physical  properties  of.  table,  514. 
vapor  pressure  of  saturation  for, 

1372:  table.  1373. 
wood-,  a  tree  product,  346. 
Algebm,  100-103. 
Algebraic  ftmctions,  differentiation 

of.  267. 
Alinement  of  tunnels,  935. 
Alkali,  in  ch^m.,  defined.  321. 
Alligation  and  center  of  gravity,  57. 
Alloy,  alloys, 
alzene.  308. 
antimony-tin,  tensile  strength  of, 

499. 
bismuth,  330. 
copper.  329. 
copper-gold,   tensile  strength  of, 

497. 
lead.  329. 
lead-base.  398. 
manganese,  329. 
metal.  396. 
nickel,  329. 
platinum-iridium,  composition  of, 

516. 
tin,  330. 
tin-base,  398. 
vanadium  steel,  399. 
Alternate-current  dynamos, 
classification  of.  1383. 
principle  of,  1382. 
Alternating  current  and  continuous 

current,  compared,  1386. 
Alternating  stresses,  denned,  487. 
Alternations,  in  tltc,  defined,  1485. 
Altitude, 
in  astron..  defined,  947. 
of  cone,  defined,  134. 
of  pyramid  (gtomX  defined,  133. 
of  sUr,  defined,  201. 
AluminumjAl.),  318. 
bronze,  3»7.  alp 

composition  of.  496o 


IMO 


INDEX. 


Aluminum-^Cont'd. 
bronse^ — Cont'd, 
physical  properties  of.  table,  496. 
weight  of,  478. 
expansion  coefficient  of.  616. 
in  metal  castings,  330. 
melting  point  of,  515. 
minerals,  330. 
nickel-, 
composition  of,  496. 
physical  properties  of,  table,496. 
paint,  how  made,  356. 
physical  properties  of,  table,  496. 
wire  as  conductor,  compared  with 

copper.  496. 
wire  compared  with  coppei*  wire, 

in  transmission.  1386. 
wire,  use  of.  in  transmission,  1386. 
Alzene  (alloy),  398. 
Amal^mation,  357. 
American    equivalents    of    Foreign 
weights  and  measures,  table. 
92-54. 
Ammeter,  defined,  1485. 
Ampere, 
as  a  current  unit,  1379. 
defined.  1485. 
Analysis  of  fuels,  1350. 
Analytic  Geometry.  256. 
Anchon^    for   suspension    bridge. 

Anchorages  of  suspension  bridges. 

Anchor-bolts,  618. 

holding  power  of,  (ref.),  890. 
Aneroid  barometer,  998. 
Angle,  angles, 

and  lines.geometric  definitions,  128. 

arcs  and  chords,  relation  of.  130. 

between  two  planes,  to  find.  265. 

circular  and  time  measure,  equiva- 
lents. 99. 

dihedral,  261. 
defined,  132. 

flange-,  of    plate  girders,  proper- 
ties of,  table,  572. 

^eometric^  planes  and  lines,  132. 

mscribed  in  a  semicircle,  130. 

methods  of  plotting,  969. 

minutes  ana  seconds  to  decimals 
of  a  degree,  table.  1010. 

natural  ftmctions  of,  in  the  four 
quadrants,  138. 

of  fnction  for  various  substances. 
517-621. 

of  polygon,  sum  of  interior  and 
exterior.  129. 

of  quadrilateral,  sum  of  interior 
and  exterior,  128. 

of  repose  for  various  substances, 
517-621. 

of  triangle,  sum  of  interior  and 
exterior,  128. 

rolled,  properties  of,  538. 

skeleton   section,    properties   of, 
630,  631. 

steel. 
.  properties  of.  tables.  648-553. 

^  nvet  gages  for.  614. 


Angle,  angkfl — Oont'd. 
supplement  and  cotnplexnent  of. 

139. 
to  lay  off,  (90^.  60».  45*.  SCP).  130. 
(ic—0°— 360°),  trigonometric    val- 
ues, 139. 
(*+y).  trig,  values  of,  139. 
(x—y),  trig,  values  of,  139. 
(H).  trig,  values  of.  140. 
(2br),  trig,  values  of.  140. 
(3x),  trig,  values  of,  140. 
(4x),  trig,  values  of,  140. 
Animals,  clarification  of.  847. 
Anions  (in  electrolysis),  357. 
Annealing,  steel.  396. 
Annuities,  various  kinds  of.  63. 
Annuity, 
and  sinking  fund  tables,  64-6& 
final  value  of,  formula,  63. 
present  or  initial  value  of,  fbrmula, 
63. 
Anode  pole,  357. 
Anthracene,  from  creosote,  367. 
Anti-logarithm, 
defined.  104. 
of  numbers,  to  find.  105. 
Antimony  (Sb),  318. 
cast,  tensile  strength  of,  496. 
minerals,  330. 

-tin  alloy,  tensile  strength  of.  490. 
uses  of.  830. 
Antiseptic,  borax  as,  330. 
Apex, 
of  cone.  134. 
of  pyramid.  133. 
Apothecaries 
measure  (fluid) .  metric  eqmvalents, 

table,  83. 
weight,  metric  equivalents,  table, 
86. 
Apothem  of  polygon,  129,  204. 
Apparatus,  electrical-, 
classification  of,  1462. 
definitions,  1461. 
Apparent  solar  day,  defined,  202. 
Approach,  velocity  of,  in  weirs,  bow 

measured,  1177. 
Aqueduct,  aqueducts, 
masonry,  1208. 
New  Croton,  mte  of.  1208. 
reinforced  concrete,  1208. 
tunnel,  Los  Angeles,  cost  data.  939. 
Arabic 
numbers,  abstract,  table.  95. 
svBtem  ol  numbers,  1. 
Arbitration  bar.  mold  for.  498. 
Arbor  vites,  ckissifiGation  of.  342. 
Arc.  arcs, 
angles  and  diords.  relation  o£,  1 90. 
circular, 
cen.  of  grav.  of,  207. 
defined,  129. 
mensuration  of.  207. 
skeleton  properties  of,  532. 
table  of  lengths  to  ebon)  1.  210. 
tables  of  lengths  to  radios  1.  20S, 
209. 
flat,  dnnilar,  formulas  and  tables, 
211.  212.  213. 


INDEX. 


1641 


Arc,  arcs — Cont'd, 
-lampe, 

elec.  code  rules,  1442. 
in  series,  elec.  axle  rules,  1405. 
on   constant  -  potential  circuits, 
elec.  code  rules.  1414. 
of  a  great  circle,  defined,  1 36. 
parabolic,  to  chord  1,  table.  238. 
semicircular,  skeleton  section, 

properties  of.  531.  632. 
semi-elliptic,  lengths  of ,  table.  241. 
Arch,  arches,  761. 
brick-,  764. 
bridges,  reinforced  concrete,  cost 

of.  V84. 
catenarian-,  761. 
centers  for.  770. 
camber  of.  773. 
loads  on.  771. 
nomenclature  of.  770. 
striking.  773. 
types  of.  772. 
classification  of.  763,  764. 
curve  of  intrados.  764. 
dimensions,  etc.,  of,  tables.  774- 

781. 
groined,  in  filter  and  reservoir  con- 
struction, (ref.),  1202. 
ideal.  761. 
kinds  of.  763. 
masonry-,  763. 
forces  acting  on,  767. 
lines  of  resistance  of.  768. 
specifications,  436. 
thickness  of  rings,  tables,   766, 
767. 
no-hinged.  782. 
nomenclature  of,  763. 
parabolic-,  761. 
parts  of  an.  768. 
reference  data,  784. 
ring,  thickness  of,  765. 

tables,  766,  767. 
steel  and  combination.  782. 
stone,  stonecutter's  plan.  457,  458. 
three-hinged.  783. 

stress  diagram.  315. 
transforraed-catenarian-,  761. 
two-hinged-,  steel,  782.  783. 
Archimedes,  spiral  of.  equation.  260. 
Area,  areas, 
artesian-,  defined.  1190. 
equivalents  (1-10).  English  and 

metric,  table,  80. 
metric  and   English  equivalents. 

table.  88. 
of  circle.  120. 

of  curved  surfaces,  by  calculus,  276. 
of  curves,  by  calculus,  275. 
of  pipes  for  given  diameters.  1157. 
of  plane  surfaces,  tables,  524. 
of  r»ular  polygon.  129. 
of  triangle.  128. 

by  calculus.  273. 
stress  per.   metric  and   English 

equivalents,  table,  89. 
to  cu.  yds.  per  station,  earthwork, 

tables.  1021-1027. 
units  of,  equivalents.  66. 


Ar^on  (chem.),  818. 
Arithmetic, 
elementary,  1-18. 
practical,  55-65. 
Arithmetical 
mean,  57. 

series  of  progression,  57. 
Arizona  land  measure,  English 

equivalents,  81. 
Armatures.  1486. 

of  magnet.  1382. 
Armored  cable, 
table.  1427. 
elec.  code  rules.  1411. 
Arrester,  lightning,  defined.  1486. 
Arroba  (Philippine  weight),  English 

equivalent,  81. 
Arsenates,  in  mss.,  classification  of. 

327. 
Arsenic, 
chtm.,  318. 
minerals.  390. 
white.  330. 
Artesian 
area,  defined,  1100. 
basin,  defined,  1190. 
definitions,  1190. 
nomenclature.  1190. 
pressure,  defined,  1190. 
principle,  defined.  1190. 
slope,  denned,  lllN). 
system,  defined,  1190. 
well,  defined.  1100. 
Artificial  stone,  described,  415.  417. 
Asbestos, 
for  paint,  355. 
uses  of,  331. 
Ascension  (right),  of  a  star,  defined 

202. 
Ashes, 
coal,  weight  of.  478. 
(trees),  classification  of,  346. 
Ashlar  masonry,  defined,  432. 
Asphalt,  asphalts, 
and  bituminous  rock  deposits,  of 

U.  S..  1141. 
as  protection  for  iron  and  steel, 

358. 
block     pavement,     specifications, 

1122?^ 
cement,  defined,  405. 
coatings  for  waterproofing,  418. 
concrete,  defined.  405 . 
described.  404. 

for  pavements,  kinds  of,  1 1 28. 
gravel  roofing.  802. 
mastic,  defined,  405. 
paints  for  iron  and  steel.  372. 
pavement, 
construction  of,  1100. 
specifications.  1104,  1110.  1125. 
1128. 
paving, 
weight  of,  478. 
blocks,  1100. 
properties  of,  405. 
rock-,  experiments,  on  roads,  costs; 

1138.1139  -.oOQie 

specifications.  1116.  o 


154S 


INDEX. 


Asphaltic 
cement,  specifications,  1126. 
flux, 
specifications,  1126. 
use   of.   for  coating   macadam 
roads,  cost.  1142. 
Asphalting  iron  and  steel,  858. 
Asphaltum. 
liquid,  specifications.  1113. 
mmeral,  substances  related  to.  8  tS. 
natural,  weight  of,  478. 
Astronomical  time,  elements  of,  202. 
Atmoei^heric  pressure,  1146. 
Atom,  in  matter,  317. 
Atomic 
svmbols.  table,  318. 
theory,  316. 
weights,  table.  818. 
Attachments,  pressure  pipe,  1269. 
Atwood's  machine,  problem.  288. 
Austro-Hungarian  money,  U.  S.  val- 
ues, 96. 
Automatic 
drcuit-breakeis,  dec.  code  rules, 

1406. 
cut-off  engines,  performance  of, 

1966. 
cut-outs.  elec.  code  rules.  1406. 
fuses,  elec.  code  rules.  1406. 
high-speed    engines,    performance 
of.  1366. 
Autumnal  equinox,  defined.  202. 
Avagadro's  law  of  gases,  1372. 
Avenarius  carbolineum,  for  timber, 

361. 
Avoirdupois  weight, 
Oong    ton),    metric    equivalents, 
4  table.  86. 

(short  tons),  metric  equivalents, 
table,  86. 
Axe,  stone-,  described,  429. 
Axes, 
coordinate.  266. 
of  ellipse.  268. 
Axis, 
inclined,  moment  of  inertia  about, 

535-538. 
of  celestial  sphere,  defined,  201. 
Axles,  steel,  specifications,  504. 
Azimuth,  azimuths, 
and  offsets  for  parallels  of  latitude, 

tables.  978-975. 
observation  of  polaris  for,  949. 
of  polaris.  at  elongation,  table,  950. 
of  star,  defined,  201. 

B 

Babbitt-metal,  398. 

Backfilling  and  trenching,  for  sewer, 

cost,  table.  917,  918. 
Backing,  masonry,  defined,  431. 
Backstays  and  towers  of  suspension 

bridges,  764. 
Bacteria,  removed  by  slow  sand  fil- 

tration,  1204. 
Bag  of  cement,  weight  of,  474. 
Bale,  paper  measure,  95. 


Ballast.  1078. 

amount  required  per  mile  of  toA 
1073. 

brick  and  gravd,  weight  q£,  471 
Ballasting  blasting,  923. 
Ball-mill,  for  cement  making,  401 
Bands,  steel,  for  wood  stave  pipe. 

1209-1214. 
Bar,  bais, 

moment  of  inertia  ol.  902. 

omnibus-,  defined,  1487. 

steel, 
areas  and  weights,  table,  544. 
weights  an(f  areas,  table.  644. 

weight  of,  &om  specific  sravxty. 
table,  484. 
Barium,  ch^m.,  318. 
Barometer,  anercnd,  998. 
Barometric 

correction,  table.  1000. 

elevations,  table,  999. 
Barrels, 

liquid,  and  liters,  eqtiivalents,  88. 

liquid,  equivalents,  83. 

of  cement,  weight  of,  474. 
Barshall  process,  for  timber.  96L 
Basalt, 

composition  of,  table,  338. 

defined,  340. 

rock,  properties  of,  400. 
Bascule  bridges, 

highway  (ref.),  739. 

weight  of.  749. 
Base, 

in  chtm.,  defined.  321. 

lines  and  meridians  of  U.  S.  sar- 
vey.  table.  972. 
Basic 

bessemer  process.  394,  305. 

open  hearth  process,  394,  306. 
Basin,  artesian-,  defined,  1100. 
Basket-handle  sewers  and  oooduita. 

properties  of.  table,  1302. 
Batter,  masonry,  defined.  431. 
Batteries,  storage  or  primary,  elec. 

code  rules.  139& 
Bauxite  ore,  330. 
Badn's 

hydraulic  formula,  1180. 

weir  formula,  1178w 
Beam,  beams, 

and  ^rdeis,  properties  of,  tables 

as  Orders,  tor  buildings,  require- 
ments of,  820. 
box  girdeis,  steel, 

problem,  569. 

properties  <^,  table,  568. 
calculation  of.  examples.  664. 
cast  separators  for,  table.  623. 
circular, 

moment  of  inertia  of,  SOO. 

radius  <^  gyratiofi  of,  300 

and  rectangular,  resistance  cxm 
pared   SOL 
concrete,  sUp  of  rods  in,  fref  ).  45fc 
Cooper's  loading,  table,  708. 
deflection 

and  slope  of,  formulas.  562, 


INDEX. 


1543 


Beam,  beams,— Cont'd. 
deflection—Cont'd. 

and  span  for  plastered  ceiling, 
664. 
electric-car  loadings  for,  tables, 

717-719. 
fiber  stress  in,  299. 
formtUas.  562. 
girder   (single    I),    properties  of, 

table.  688. 
Idnds  of  loading,  formulas,  662. 
loads  on,  formulas,  662. 
longitudinal   shear   in,    formulas, 

566. 
moments  and  shears,  various  load- 
ings, 688. 
moment  of  inertia  of,  formula,  299. 
moments  of  resistance  of,  formu- 
las, 562. 
rectangular,  loads  on,  table,  666. 
reinforced  concrete-, 

bending  moment,  828,  825,  827, 

829,  832. 
formulas,  444,  447. 
table,  446. 

tests,  formulas,  (ref.).  586. 
Thacher's  computation,  686. 
time  element  effect  in  loading, 

(ref.),  686. 
working  stresses,  686. 
resisting  and  bending  moments  of, 

298. 
resisting   moments   of,    formulas, 

662. 
shear  (longitudinal)  in.  formulas, 

666. 
slope  and  deflection  of,  formulas, 

662. 
special  I-.  properties  of,  table,  684. 
standard   connection   angles   for, 

616. 
steel, 
properties  of,  654. 
rivet  gages  for,  614. 
stresses  in,  formulas,  662. 
stringers,  wooden-,  bending  mo- 
ments, table,  791. 
submergea,  formulas  for  presstux} 

ana  moments  in,  (ref.),  1189. 
wooden, 
for  buildings,  819. 
loads  on,  table.  666. 
problems  in.  667. 
working  stresses,  table.  495. 
working  loads,  formulas.  562. 
working  stresses,  formulas,  562. 
Bearing  value  of  concrete  in  beams. 

585. 
Beaume's  hjrdrometer,  461. 
Becquerel  rav,  316. 
Bed  plates,  tor  bridges,  pressure  on 

masonry,  705. 
Beds,  masonry,  defined,  432. 
Beeches,  clasoncation  of,  344. 
Belgian  block  pavement,  described, 

1100. 
Bell 
and  spigot  joint  pipe,  1215. 
holes  for  pipe  in  rock  trenches,  923. 


Bell— Cont'd, 
of  cast  iron  pipe  and  special  cast- 
ings, dimensions,  etc.,  of,  ta- 
bles, 1220.  1221.   1223.   1243. 
1245. 
wires,  elec.  code  rules,  1448. 
Belt  conveyor,  in  screening  gravel, 

419. 
Belting, 
cotton,  strength  of,  512. 
flax,  strength  of.  612. 
leather,  friction  of.  617.  618,  519. 
Bending 
and  resting  moment  of  beams.  298. 
extreme  fiber,  values  of  concrete 

in  beams.  686. 
in  building  materials,  safe  fiber 

stress,  822. 
modulus  of  elasticity,  of  timber. 

table.  493. 
moments 
and  chord  stresses.  307. 
and  shears  for  engine  loading. 

table,  692. 
of  pins,  table,  630. 
problem  in.  637. 
strength  of  metals,  table,  496. 
tests  of  timber,  table.  492,  493. 
Bends, 
in  cordage,  669. 

in  pipe  fines,  loss  of  head  in,  1160. 
Bents, 
grass-hopper,  789. 
trestle-.  788-792. 
Bemouilli,  lemniscate   of,  equation 

of.  260. 
Beryllium,  chtm.^  318. 
Bessemer 
processes,  804,  395. 
steel,  defined.  1487. 
Beton-Coignet.  manufacture  of.  417. 
Bevel  siding  lumber  (fir),  classified, 

389. 
Binder,  asphalt  pavement,  specifi- 
cations, 1110. 
Binomial  formula.  101. 
cube  root  by.  102. 
square  root  by.  102. 
Bins  and  bunkers,  reference  data, 

1481. 
Birches,  classification  of.  344. 
Bismuth  (Bi.).  318. 
alloys,  330. 
minerals,  330. 
tensile  strength  of,  496. 
uses  of,  330. 
Bitulithic  pavement 
patents.  1127. 
specifications,  1105.  1126. 
Bitumastic  enamel,  coating,  359. 
Bitumen, 
described.  404. 
weight  of.  478. 
Bitimiinized -brick, 
specifications.  1116. 
^tters,  spedncations,  1116. 
Bitimiinous 
and  asphalt  rock  deposits  of  U.  S.. 
1141. 


1544 


INDEX, 


Bituminous— Cont'd . 

oompotmds,  grouping  of,  1141. 

rock  pavement,  1100. 
BUck^or^galvam^    pipe.  iaMe. 

Blast-funutce,  302. 
Blasting^ 

and  drilling  in  tunneling,  934. 

ballasting-.  023. 

gelatin,  362. 
oles,  drilled  with  well-driUer, 
cost,  026. 
in  rock,  drill  holes  for.  022. 
mat,  woven,  023. 
powder,  composition  of,  360. 
stimips,  cost  daU,  016. 
submarme,  cost,  026. 
Block,  blocks, 
pavmg,  size  of,  1120. 
shapes,  properties  of,  633. 
stone,  kmds  of,  417. 
Blow-off,  blow-offs, 
described,  1280. 
branches, 
cast  iron  pipe,  table,  1230.  1267. 
with   manhole,   cast  iron   pipe, 
tables.  1231,  1268. 
Blowpipe  characteristics,  328. 
Bluestone, 
composition  of,  331. 
defined.  t402. 

physical    properties    of,   table, 
607. 
Board,  boards, 
classification  of,  388. 
measure.  370. 
table,  380 
Booster,  defined,  1380. 
Boat, 
drill-,  for  submarine  woric,  026. 
spikes,  table.  028. 
Bodies, 
falling,  table,  283. 
impact  effect,  804. 
Boiler,  boilers, 
cement,  402. 

staybolts.  etc.,  in,  (ref.).  1378. 
plate  steel  (open  hearth),  specifi- 
cations. 601. 
power  required  for  channeling  ma- 
chines, 421. 
steam.  1361-1363. 
efficiency  and  rating.  1361. 
horse-power  of,  demied,  1361. 
settings,  notes,  1362. 
tests  of  coal  as  fuel,  table.  1353. 
Boiling-point, 
absolute,  defined,  613. 
defined,  613. 

of  chemical  elements,  table,  318. 
of  liquids,  table,  614. 
of  substances,  tables,  614. 
Bolsters,  for  bridges,  specifications, 

706. 
Bolts 
and  nuts,  tables.  018-621. 
rail-.  1060. 

standard,  for  fastenings.  618. 
Bomb  colorimeter,  described,  1362. 


Bond, 
between  concrete  and  ste^  teso. 

(re£.),  686-686. 
English,  defined.  437. 
Flemish,  defined,  437. 
masonry,  defined.  432. 
value  ot  concrete  in  beanuw  585. 
in  brickwork,  764. 
of  concrete  to  steel.  82  3w 
Boneblack  for  paint,  356. 
Borates.  380. 

in  min.,  classification  of,  327. 
Borax,  uses  of,  330. 
Boron 
dmn,,  318. 
minexuls,  330. 
Borings, 
diamond  drill,  cost  data,  017 
in  soil,  866. 

wash  drill,  oost  data,  016. 
Bosses  on  cast  iron  pipe.  1280L 
Botanical  materials,  340. 
Boulder 
foundation,  865. 
pavement,  specifications,  1107. 
Bow's  notation  for  trusses,  900 
Box-girder, 
steel  beam* 
problem,  560. 
properties  of,  table,  568L 
Boxes, 
gate,  teble,  1288. 
outlet-,  elec.  code  rules  1420. 
resistance  •,  elec  code  rules,  1440. 
switch-,  elec.  code  rules,  1420. 
Braces,  rail-,  1071. 
Bracing, 
lateral-,  cf  bridges,  problem,  007. 
portal-,  of  bridges,  608. 
vertical-,  of  brtdges,  608 
Brake  horsepower  (B.  H.  P.),  forma- 

la,  13W 
Branches, 
blow-off, 
cast  iron  pipe,  table,  ISM.  1257. 
with  manhole^  cast  ixxm   pipe, 
tables,  1231,  1258. 
hydxant,  cast  iron  pipe,  table.  1 220. 
pipe,  cast  iron, 
L's.   T's.   crosses,   taUe.    1225. 

1260-1264. 
Y's.    table,    1227,    1228»    1255. 
1256. 
Brass, 
cast, 
physical  properties  of,  table.  406l 
sheet,  wire,  etc.,  weight  of.  table, 
478. 
expansion  coefficient  of,  516. 
friction  of,  618.  510. 
melting  point  cf,  615. 
tablel07. 

wire,  physical  properti^  of.  496i. 
Brazing-metal,  307. 
Breakers,  circuit-,  elec.  code  rules, 

1484. 
Breakwaters,  001 
cost  data.  002-004. 
materials  for  concrete  of,  904. 


INDEX, 


1546 


Breakwaten— Cont'd . 
notable,  table  of.  903. 
reaction-.  905. 

reinforced  concrete    caissons   for, 
cost  data.  904. 
Breast  wheel,  described.  1886. 
Brick,  bricks, 
abrasion  test,  1116. 
arches,  764. 
bittumnized-. 

gutters,  specifications.  1115. 

specifications.  1116. 
bonding  of,  764. 
block 

paving  specifications,  1105. 

pavement  specifications,  1105. 
clinker.  415. 

common,  manofacture  of,  415. 
crushing  tests,  522. 
expansion  coefficient  of,  516. 
face-,  415. 
friction  of,  518. 

S lazed,  415. 
ard.  415. 
kinds  of,  described,  415. 
manufacture  of.  415. 
masonry,  437. 

compressive  strength  of,  511. 

quantities  of  bride  ana  mortar 
in.  table.  438. 
pavement, 

described,  1100. 

cost.  (ref.).  1142. 

spnedfications,  1109,  1129. 
paving.  415. 

grout  filling.  1109. 

handling  and  piling,  1109. 

manner  of  iaymg,  1109. 

of  country  road.  cost.  1141. 

rolling  and  tamping,  1109. 

size  of.  1129. 

specifications,  1124. 

tar  filling,  1109. 
piers. 

compressive  strength  of,  51 1. 

crushing  tests,  table,  522. 
pressed,  size  of.  488. 
rattler  test,  507.  1116. 
sand-,  manufacture  of.  417. 
sewer-,  415. 

walls,     thickness    of,    formula, 
1306. 

66-in..  cost,  1310. 
sidewalks,  specifications,  1103. 
size  of.  415. 
soft.  415. 

specific  gravities  of.  table.  474. 
specifications,  1116. 
street  pavements,  proper  construc- 
tion of.  1106. 
temperature  stress  for  1 00^  P.. 523. 
terra  cotta.  manufacture  of.  415. 
tesu  of.  507. 
various  kinds,  physical  properties 

of.  507. 
vitrified.  415. 

pavement,  specifications,    1121. 
1128. 
weights  of,  table,  474. 


Brickwork,  437. 
bonds  in,  764. 
friction  of.  521. 
in  buildings, 

safe  loads  for.  821,  826. 

weight  of.  821. 
lime  mortar  for.  408. 
mortar,  kinds  used,  488. 
Bridge,  bridges,  688. 
arch-, 

(see  also  Arches).  774-784. 

dimensions,  etc..  of.  tables.  774- 
781. 

reference  data.  784. 

reinforced  concrete-,  cost  of.  784. 
basciUe-.  weight  of.  749. 
cantilever-.  740. 

references.  741. 
clearance.  699. 

combination    highway-,   and    de- 
tails. 729. 
concrete,  surface  finish,  454. 
economic  length  of  spans,  683. 
electric-car  loadings  for,  716. 
electric  railway,  716. 
estimating  weights  of.  685. 
ferry-,  and  details,  898. 
floor. 

specifications.  700. 

trestle.  788-790. 
highway-.  720. 

live  load  daU  for.  table,  728. 

nickel  and  carbon  steel,  specifi- 
cations. 737:  table,  788. 

references,  739. 

typical  loading  for.  727. 

umt  stress  sheets,  720. 
impact  for.  table.  709. 
masonry,  specifications,  484. 
movable.-. 

references,  749. 

weights  Of  steel  in,  748. 
nickel-steel  and  carbon-«teeI,  787. 

738. 
piers. 

contents  of.  889. 

masonry,  889. 
pins.  629. 

portals,  types  of,  098. 
references.  687. 
railroad.  688. 

proportion  of   parts,   specifica- 
tions. 702. 

references,  713. 

stresses  allowable  in,  specifica- 
tions,  702. 

types  of.  009. 
railway,  electric,  716. 
reinforced  concrete,  highway,  cost 

data.  738. 
steel  of  nigh  grades  used  in.  499. 
steel,  railroad. 

compression  formulas,  table.  710. 

compressive   stresses,    specifica- 
tions, 703. 

specifications  for,  699. 

tensile  stresses,  specifications. 
702. 


weight  ^jigoogle 


1546 


INDEX, 


Bridge,  bridges— Cont'd, 
steel, 
specifications.  500. 
weight  of,  formulas,  680. 
suspension-,  750. 
details  and  specifications,  756- 

700. 
miscellaneous  data,  760. 
weights  of  materials  in,  table. 
758. 
swing-,  742. 
timber  framing.  780. 
wind  pressure  for,  607. 
Briggs  logarithms,  defined,  104. 
Briquette,  briquettes, 
cement, 
form  of,  410. 
tesUof.  411. 

mortar,  amount  of  water  to  use, 
408. 
molds,  form  of.  410. 
storage  tank  (ref.).  418. 
British  thermal  unit  (B.  T.  U.), 
defined.  1847. 
equivalents  of.  00. 
table.  01. 
British-French  thermal  unit  (Lb.- 

Col.).  defined.  1847. 
Broach 
channeling,  described.  410. 
machine,  m  quarrying.  410. 
Broken -stone, 
pavement,  construction  of.  1000. 
size  for  concrete,  417. 
voids  in  concrete,  416. 
Bromides,  mtn.,  classification  of.  325. 
Bromine,  dbtfm.,  318. 
Bronze, 
aluminum,  807. 
composition  of.  496. 
physical  properties  of.  table,  406. 
etc.,  weighu  of,  table.  478. 
expansion  coefficient  of.  516. 
gun    (metal),   physical   properties 

of.  table.  407. 
manganese-,  307. 
physical  properties  of,  table.  407. 
(ref.).  800. 
melting  point  of,  515. 
paint,  how  made,  357. 
phosphor-,  307. 
phvsical  properties  of,  table, 

siUcon-*  307. 
tensile  strength  of.  407. 

table,  397. 

tobin-,  307. 
physical   properties  of.  table, 
407. 
Brownstone, 

composition  of,  table,  884. 

formation  of,  table,  334. 
Brush-holaers,  defin^.  1480. 
Building,  buildings,  812. 

bearing  power  of  soils  for,  867. 

codes.  819-829. 

construction,  references,  880-834. 

fireproot-,  requirements  for,  819. 

foundaUon  loads  for,  866. ' 


Btiilding,  buildings.— Cont'd, 
materials, 
fire  tests  on.  523. 
heat  effect  on,  523. 
temperature  stresses  in.  6SS. 
regulations  for  reinforced  ooa 
construction,  by  Nat'l 
Cem.  Users,  831. 
stone, 
and  cement,  400. 
artificial.  415. 

physical  properties  of,  table,  507. 
safe  loads  for.  821. 
nedfic  gravities  of,  table,  474. 
thickness  of  joints.  457. 
weights  of.  table.  474. 
wall,  stonecutter's  plan,  457. 
Bucket  dredges.  028. 
Bulkhead  and  pierhead  lines.  802. 
Bumping  posts  (ref.).  1092. 
Bunkers  and  bins.ref  erence  data,  1481. 
Boojrancy.  1152. 
center  ot,  1153. 
Burden,  in  tmtruling,  defined,  033. 
Bumetisii\g 
process,  for  ties,  cost,  875. 
timber,  860. 
cost.  875. 
Bundle,  paper  measure,  05. 
Bushel,  bushels, 
and  cubic  feet,  equivalents  (1-0). 

table.  485. 
and    gallons,    equivalents    (1-0). 

taUe.  485. 
and  hectoliters,  equivalents(l-10). 

table,  84. 
and  yards-inch,  equivalents  (1-0), 

table.  485. 
(dollars  per) 
and  francs  per  hectoliter.  e<iuiv- 

alents  (1-10),  table.  08. 
and  marks  per  hectoliter.  equiv> 
alents  (1-10),  table,  08. 
(dollars  per  U.  S.)  and  shillings 
per  British  bushel,  equivalenu 
U-10).  table.  0& 
equivalents.  67. 
heaped,  measure  of,  84. 
metric  equivalents,  68. 
of  produce, 
weight  ot.  table.  478. 
weighu  of.  482. 
per  acre  and  hectoUters  per  hectar, 

equivalents  (1-10).  table.  84. 
(shillsngs  per  Br.)  and  dollars  per 
U.  S.  bushel,  equivalents  (1- 
10).  table.  08. 
struck,  metric  equivalent.  84. 
Bush  hammer,  described,  430. 
Bushings  and  tubes,  elec.  code  rules. 

table,  1480. 
Butt  (liquid)  or  pipe,  equiv.,  88. 
Butternut  tree,  343. 
By-pass,  defi  ed,  1480. 


C  and  A^  in  Kutter's  formula,  experi- 
mental determination  of,118& 

Digitized  by  VjOOQ  IC 


INDEX. 


1547 


Caban   (Philippine  meastire),  Eng- 
lish eauivalent.  81. 
Oabinet.  cabinets. 

cut-out-,  elec.  code  rules,  1439. 
projection,  261. 
Cable,  cables, 
armored-, 
elec.  code  niles.  1411. 
table.  1427. 
catenarian,  lengths  of.  table   752. 
length,  equivalents.  68. 
suspension  bridge-,  curves  of.  750. 
telephone,  676. 
wrappings.  755. 
Cableways  and  conveyors,  reference 

data.  1481. 
Cadmium 
chem.,  318. 
minerals,  329. 
Caesium,  chsm.,  318. 
Caisson 

disease,  prevention  of,  (ref.)  890. 
method  of  ttmneling,  936. 
open-,  876. 
pneumatic,  880. 

reinforced  concrete-,  for  break- 
waters, cost  data,  904. 
Calcimine,  355. 

Calcination,  in  cement  making,  405. 
Calcined  magnesite,  380. 
Calcium. 

cement,  properties  of,  403. 
ckem.,  318. 
chloride, 
cost,  1138. 

experiments  on  roads,  costs,  1 1 38 
minerals.  329. 
oxide,  408. 
Calculating  machine,  Thatcher,  127. 
Calculus.  266. 
Differential,  266. 
Integral,  272. 
CaUfomia    land    measure,    English 

equivalents,  81« 
Cak>mel,  329. 

Cakme  (Cal.).  defined,  1347. 
Calorimeter  test,  described.  1352. 
Camber 

in  bridges,  705. 
in  cantilever  bridges,  741. 
of  arch  centers,  7/3. 
Canadian  canal  systems,  table,  1323. 
Canal,  canals, 

Chicago,  material,  work,  costs,  923 
commercial,  of  the  U.  S.,  table, 

1329.  1330. 

earth-,  experimental  values  of  N 

in  Kutter's  formula  for  flow  in, 

1188. 

evaporation  and  seepage  in.  1199. 

flow,  surface  and  mean  velocity  of, 

1183. 
for  water  supply,  1207. 
irrigation, 
kxatting,  (ref.).  1318. 
miscellaneous  daU,  (ref.),  1318. 
velocity  in.  1317. 
large  irrigation,  dimensions  and 
grades  of.  Uble,  1317. 


Canal,  canals,— Cont'd, 
maintenance  and  operation,  cost 

data,  1329. 
miscellaneous  data,  (ref.),  1331. 
navigable,  1320. 
Panama, 
distance  between  Atlantic  and 

Pacific  ports,  table.  1328. 
excavation,  cost  data  916. 
steam  shovel  work,  cost  data, 
919. 
proportioned   for  maximum   dis- 
charge, 1161. 
seepage  and  evaporation  in,  1200 
Cannon  ball,  energy  of,  294. 
Cantilever  bridges,  740. 
camber  in,  741. 
references,  741. 
Canvas,  strength  of,  512. 
C^aoutchouc,  weight  of,  480. 
Otpacities, 
dry, 
equivalents,  67. 
equivalents  (1-10),  English  and 

metric,  table.  84. 
metric.  English  equivalents, 
table.  84. 
in  gallons,  of   pipes,  table,  246- 

247. 
hquid, 
equivalents,  67. 
eqtuvalents  (1-10),  English  and 

metric,  table,  83. 
metric,  English  equivalents, 
table.  82. 
liquid  and  dry,  metric  and  English 

equivalents,  tables,  88. 
of  wires,  elec.  code  rules,  table, 

1448. 
overload-,  in  tkc,  1469. 
volumes  and  weights,  equivalents 
(1-9);  tables,  485. 
Capitalization  of  annuity,  table,  65. 
Caps, 
castiron  pipe,  tables,  1234,  1266. 
wooden  trestle,  788. 
Car 
axles,  specifications,  504. 
gondola-,  large  capacity,  (ref.). 

1091. 
hottses,  elec.  code  rules.  1421. 
wiring  and  equipment,  elec.  code 
rules,  1411 
Otrbolic  acid,  from  creosote,  367. 
C^bolineum  avenarius,  for  timber. 

361. 
Carbon 
chem.,  318. 

Lb.  of,  oxidized  with  perfect  effi- 
ciency, equivalents  of.  table, 
91. 
minerals,  330. 
Otrbonates 
in  min.,  classification  of,  327. 
of  lime,  403. 
Carbonic  acid,  boiling  point  of,  514. 
Carburetters,  for  vaporizing  liquid 

fuels.  1371. 
Card  process,  for  ties^< 


1148 


INDEX. 


Cardinal  points  of  celestial  sphere, 

defined.  201. 
Carrying  capacities  of  copper  wires, 

talle,  1404. 
Cartridge  enclosed  fuses,  elec.  code 

rules,  table.  1438. 
Castings, 
aluminum  in.  330. 
iron  (gray),  specMcations.  408. 
malleable,  893. 
steel, 
physical  properties  of,  604; 

table,  400. 
specifications,  393,  508. 
test  pieces,  504. 
^     testing,  604. 
Cast-iron, 
columns,  loads  on.  tables,  606,  607. 
details   for   combination  bridge, 

732. 
drilling,  392. 

expansion  coefficient  of.  516. 
flange  pipe,  table,  1236. 
for  buildmgs.  819. 
friction  of.  518.  519. 
haid.  392. 

in  buildings,  safe  stresses.  826. 
melting  pohit  of.  515. 
physical  properties  of,  table,  497. 
properties  of,  892. 
puddling,  392. 
refining.  392. 
separators,  Uble,  623. 

use  of,  623. 
temperature  stress  for  160**  P.,  523. 
washers,  weights  and  dimensions, 

Uble.  624. 
weight  of,  480. 
Cast-iron  pipe,  1214. 

and  specials,  weights  and  dimen- 
sions of,  tables,  1219.  1267. 
bells  of,  dimensions,  etc.,  tables, 

1220.  1221.  1223.  1243,   1245. 
curves,  table.  1244.  1248,  1249. 
forvarious  pressures,  table,  1216. 
formulas  for  designing,  1216. 
friction  heads  in.  table.  1217. 
lead  reqmred  per  joint.  1216; 

table.  1222. 
jute   required   per  joint,  table. 

1222. 
specials,  described.  1280. 
sp)ecifications,  1239. 
standard  length  of.  1215. 
variation  allowed.  1222. 
weights  and  dimensions,  tables, 

1220.  1222.  1243-1246. 
weight  of.  table,  1216. 
Cast  separators  for  wooden  string- 

crs,  623. 
Cast-steel, 
expansion  coefficient  of,  516. 
open  hearth.  396. 
specifications  for.  398. 
Cast-tm. 
physical  properties  of,  499. 
weight  of;  679. 
Cast-zinc,  physical  properties  of. 499. 
Catch  basins,  sewer,  1308. 


Catenarian 

arch,  761. 

arcs,  lengths  of.  table,  752. 

cable  of  su^)enaion  bridge,  751. 
Catenary, 

graphical  solution  of.  753. 

length  of.  by  calculus.  276. 

parameter  of,  values  of.  table,  751 

sewers  and  conduits,  properii»  o4 
Uble.  1301. 

transformed,  753. 
Cathode  pole,  357. 
Cations  (m  electrolysis),  S57. 
Catty  (Philippine  weight).   Kngh<^ 

eqmvalent,  81. 
Caulking  pipe  joints.  1215. 
Cavil,  described.  427. 
Odar,  cedars. 

classification  of,  342,  343. 

grading  rules.  388,  300. 
Cedar   block    pavement,    specifica- 
tions. 1110.  1128. 
(filing 

construction.  818. 

lumber  (fir),  classified.  389. 

plastered,  beam  calculatiana.  564. 
Celestial  sphere,  elements  of.   201- 

202. 
Cellulose  nitrate,  351. 
Cement,  cements,  402. 

adulterants,  407. 

and  lutes,  useful  to  engixMCfs,  418. 

as  protection  for  iron  axKl  steeL 
358. 

asphalt.  405. 
described.  404. 

asphaltic.  specifications.  1125. 

barrel  of,  weight.  474. 

bitumen.  404. 

briquette, 
form  ot,  410. 
molds,  form  of.  410. 


storage  of.  410. 
buildeTs.  403. 


chemical  composition,  400. 
clinker,  grinding.  405. 
crucible,  (ref.),  418. 
elastic,  (ref.).  418. 
endurance  of.  406. 
expansion  coefficient  of.  516. 
filler  in  brick  pavement,  1107. 
final  set  of,  deifined,  406. 
fineness  of.  discussed.  406. 
fineness  test.  407. 
foreign,  weights  per  barrel,  47«. 
gravel, 

defined,  389. 

roofing,  802. 

swellage  when  loosened.  911. 
grout,  injected  in  sab-fotmdatao«; 

442. 
hardening  or  set,  406. 
hydraulic,  described.  404. 
in  concrete,  economy  in.  416. 
initial  set  of.  defined,  406. 
iron,  (ref.),  418. 
leather,  (ref.).  418. 
miscellaneous.  402. 
mixing,  for  testing.  410 


INDEX. 


1640 


Cement,  cements.— Cont'd, 
molding,  for  testing.  410. 
mortar 

briquettes,  amount  of  water  to 
use.  409. 

defined.  408. 

for  buildings.  819. 

mix  for  concrete,  417, 

strength  of.  607.  608. 

weight  of,  table,  475. 
natural-, 

constancy  of  volume,  specifica- 
tions, 412. 

defined.  412. 

fineness  ^>ecifications,  412.  414. 

hydraulic,  manufacture  of.  404. 

spec.  grav.  specifications.  412. 

specincations. 
(A.  S.  T.  MO.  411. 
(Engrs.  U.  S.  A.).  414. 

strength  of.  607.  608. 

tensile    strength    specifications, 
412.  414. 

time   of  setting,   specifications, 

412.  414. 

weight  per  barrel,  414. 
nonnal  consistency  test,  408. 
petste.  defined,  408. 
pats,  412.  413.  414. 

for  testing,  411. 

tests  of.  411. 
pavement,  described.  1099. 
paving,  specifications.  1121. 
physical  properties  of,  607. 
plaster  ot  pans.  404. 
Portland-. 

constancy  of  volume,  specifica- 
tions. 413. 

cost.  418. 

defined.  412.  413. 

fineness  specifications.  412.  413. 

impurities  in,  413. 

manufacture  of,  404,  406. 

spec.  grav.   specifications,   412, 
413. 

sotmdncss  specifications,  413. 

specifications. 
(A.  S.  T.  MO.  412. 
(Engrs.  U.  S.  A.),  413, 

strength  of.  607,  608. 

temperattire  stress  for  160*  P., 
623. 

tensile    strength,  specifications, 

413,  414. 

time  of    setting,  specifications, 
412.  414. 
preservative  qxialities  of.  444. 
Fuzzolan-, 
fineness  specifications,  414. 
soundness  specifications.  414. 
spec.  grav.  specifications,  414. 
specincations,  (Engrs.  U.  S.  A.), 

414. 
tensile    strength,  specifications, 

416. 
time  of  setting,   specifications, 
416. 
quick-setting,  406. 
requirements  of  good,  406. 


Cement,  cements, — Cont'd. 
Rosendale-,  manufacture  of,  404. 
-sand  mix  for  concrete,  417. 
sea-water-proof,  418. 
set  or  hardening,  406. 
setting,  rate  of,  406. 
sidewalk, 

described.  1099. 

specifications,  1117. 
sieve,  for  fineness  test.  407. 
slag,  manufactiue  of,  404. 
slow-setting.  406. 
solvents.  402. 
sotmdness  of.  406.  407. 
specific  gravity 

of.  apparatus  for  finding.  407. 

of.  table,  474. 

test,  407. 
specifications, 

(A.  S.  T.  MJ.  411. 

(Engrs.  U.  S.  A.).  413. 
stone,  (ref.).  418. 
strength  ratios  of  compression  and 

tension.  608. 
testing.  406. 

specific  gravity.  407. 

standard  methods.  407. 

standard  sand.  409. 

standard  sieve.  407. 

time  of  setting,  409. 
tesu 

for  constancy  of  volume.  411. 

on  specimen  cylinders,  608. 

tensile  strength,  411. 

Vicat  needle  test.  408. 

weights  of.  table.  474. 

Cementation  process,  396. 

Cementing  materials.  402. 

in  rocks,  table.  334. 
Cent,  U.  S.  money,  96. 
Center,  centers, 
for  arches,  770. 

camber  of,  773, 

loads  on,  771. 

nomenclature  of,  770. 

striking.  773. 

types  of,  772. 
of  celestial  sphere,  defined,  201. 
of  gravity 

by  Alligation.  67. 

of  distributed  force,  296. 

of  parallel  forces,  296. 

of  plane  figure,  formulas.  301. 

of  plane  surfaces,  table,  624. 

of  solids.  303. 

of  trapezoid.  847. 
of  gyration.  303. 
of  oscillation.  303. 
of  pendulum.  287. 
of  percussion.  303. 
of  pressure.  846.  847.    • 

formulas,  1160. 

on  vertical  orifices  and   weirs, 
table.  1161. 
Centigrade  and   Fahrenheit  scales, 

equivalents,  table,  466. 
Centigram.  English  equivalents,  86. 
Centiliter.  English  equivalents,  81, 
82,  84.         jOOgle 


1660 


INDEX. 


Centimeter.  centimetcfB, 
and  inches, 
cubic, 
eqiiivalenU  (1-10).  table,  82. 
equivalent.  88. 
equivalents  (1-10),  table.  70. 
equivalents,  88. 
square, 
equivalenU.  (1-10).  table.  80. 
equivalents,  88. 
cubic, 
and   liquid  ounces,  equivalents 

(1-10).  Uble.  83. 
English  equivalenU.  68.  81. 
Engl^  equivalenU,  68.  70. 
•grams  and  inch-pounds,  equiva- 
lents. 80. 
square.  English  equivalenU,  68,79. 
Centrifugal 
force, 
formulas,  207. 
of  train  on  curve,  specifications, 

702. 
of  train,  problem,  207. 
pumps,J3o7. 
steam  pumps,  1867. 
Century,  time  measure.  00. 
Cerium,  chem.,  318. 
Cesspools.  1206. 
Chains,  967. 
and  meters.  equivalenU,  88. 
steel  hoisting-,  formulas.  1484. 
surveyors',  eqtdvalent,  68. 
Chalk, 
-rock,  401. 
weight  of,  478. 
Channel,  channels, 
block,  properties  of.  633.  684. 
columns, 
properties  and  safe  loads,  tables, 

601-603. 
standard  dimensions  of.  506. 
rolled,  properties  of.  637. 
skeleton  section,  properties  of .  630. 
standard    connection   angles   for, 

616. 
steel, 
properties  of.  table.  666. 
rivet  gages  for,  614. 
(Channeling  machines, 
air  used.  420. 
boiler  ;)ower  for,  421. 
dimensions,  etc..  table,  421. 
in  canal  excavation,  024. 
in  quarrying,  420. 
in  tunneling,  934. 
weighu,  etc.,  table.  421. 
Chapman  valve  with  wedge-shaped 

gate,    nomenclature,  1286. 
Characteristic  and  mantissa,  of  log- 
arithms. 104-106. 
Charcoal,  birch,  oak.  etc.,  table,  47«. 
C^eck  valves, 
described.  1288. 
horizontal,  table,  1278. 
vertical,  table,  1279. 
Warinff's,  1206. 
Chemical 
analysis  of  fuete.  1360. 


Chemical— Cont'd, 
compounds.  321. 
elements,  Uble,  818. 
eneiKy.  examples  of,  1346. 
equivalents,  Uble,  318. 
substances,   common   names  of, 
324. 
Chemistry  of  materials,  316. 
ChestnuU,   classification    of,    trees, 

344. 
Chezy's  hydraulic  formula,  1167. 
Chicago  drainage  canal, 
daU,  1324. 

material,  work,  costs,  023. 
Chimneys,  reference  daU,  14M. 
Chisel, 
splitting,  described.  427. 
stone,  described.  427. 
tooth,  described.  427. 
Chlorate  explosives,  361. 
Chloride,  chlorides, 
in  min.  classification  of,  825. 
of  zinc, 
cost.  375. 
for  timber,  361. 
Chlorine.  ch»m.,  318. 
Chord,  chords, 
angles  and  arcs,  relation  of,  130. 
lengths  of  curved  rails,  tables. 

1066.  1067. 
of  circle,  defined.  129. 
(or  circular  arc),  mensuration  of. 

207. 
(of  flat  circular  arc),  formulas  and 

Ubles.  211.  212.  213. 
of  truss,  stress  in.  305. 
platting  angles  by.  050. 
stresses 
and  bending  moments,  307. 
in  Pratt  truss,  concentrated 

loads.  606. 
in   Warren   truss,  concentxuted 
loads,  606. 
to  radius  1.  Uble  of,  050. 
Chrome 
steel,  306. 

-vanaditmi  steel,  300. 
Chromium,  chem.t  318. 
Cinder  concrete 
cubes,  tests  of.  510. 
for  buildings,  831. 
physical  properties  of.  510. 
proportions,  tests,  510. 
weight  of.  475. 
Circle,  circles, 
and  octagon,  inscribed  and  circum- 

scribed.  131. 
and  square, 
inscribed  and  circumscribed,  131 
relations.  220.  221.  222. 
and  triangle,  inscribed  and  circnm* 

scribed.  180. 
areas  in  sq.  ft.  for  diameters  in  ft. 

and  ins..  Uble.  1157 
area  of.  129. 
center  of,  to  find,  130. 
diameter 
(in  fractions)  to  ciitnim  (in  deci- 
mals). Uble,  236-220. 


INDEX. 


15fil 


Circle,  dxtsle«r-Cont*d. 
diameter— Cont'd, 
to  area, 
in  decimals,  table.  232.  233. 
in  inches,  table.  230,  231. 
(ft  and  ins.)  to  area  (sq.  ft.), 

table.  234.  285. 
to  circum.   in  decimals,  table. 
224.  226. 
equation  of.  257. 
normal  to,  257. 
tangent  to.  257. 
hollow,  properties  of,  528. 
tntenection 
with  parabola.  ^58. 
with  straight  line,  solution,  257. 
mensuration  of,  204. 
properties  and  parts  of,  120. 
properties  of,  528. 
(semi-),  properties  of,  528. 
skeleton   section,  properties  of, 
531. 
Circular 
arc.  skeleton  section,  properties  of, 

532. 
beam, 
moment  of  inertia  of,  300. 
radius  of  gyration  of,  300. 
cell,  skeleton,  properties  of.  531. 
conduits 
and  sewers,  properties  of.  table. 

1300. 
best    for   maximum    discharge, 
1161. 
cylinder,  moment    of    inertia  of. 

302. 
measure  (}r),142;  table.  99. 
motion,  286. 
orifices,  center  of   pressure   on, 

formulas.  1151. 
pendulum.  287. 

plate,  moment  of  inertia  of,  302. 
ring,  moment  of  inertia  of.  302. 
sector,  properties  of,  528. 
segment  (half-),  properties  of ,  528. 
sewers  and  conduits,  properties  of, 
table.  1297. 
Circumference, 
circular  measure,  99. 
of  circle,  ratio  to  diameter.  129. 
(semi-),  circular  measure,  99. 
Circtiit-breakers. 
automatic-,  elec.  code  rules,  1406. 
elec.  code  rules.  1404.  1434. 
Circuits,   grounding,    low-potential, 

elec.  code  rules,  1401. 
Cities,  population  of.  in  U.  S..  1202, 
Qty-k>t  surveying.  966. 
C^mp  fastenings  lor  wire  rope,  675. 
Clam-«hell  bucket  dredge.  928. 
(Classification  of  yellow  pine  lumber. 

387.  388. 
Clay, 
composition  of^  331. 
dry,  friction  of,  521. 
foundation.  864.  865. 
moist,  friction  of,  521. 
tiles,  for  roofs,  800. 
weiffht  of.  table.  478. 


(bearing 
and  grubbing,  906. 
cost  data,  916. 
reference  data,  920. 
road  specifications,  1101. 
Cleats,  elec.  code  rules.  1430. 
Clevices,  dimensions  ot,  table,  682. 
Clinker,  cement,  grinder.  405. 
C^p  fastening  for  wire  rope.  675. 
0>agulants  used  in  settling  basins, 

1204. 
Coal, 
anthracite,  etc.,  weight  of,  478. 
boiler  test  of,  table.  1353. 
classified  for  heating  value,  table, 

1350. 
consumption 
per  boUer  hoisepower,  1362. 
per  h.-p.  hour.  1363. 
heating  value  of,  tables.  1350-51. 
mineral,  classification  of,  328. 
mines,  explosives  permissible    in, 

854. 
storage  of,  in  salt  water,  (ref.), 
1378. 
Coal-tar, 
coatings.  301. 

composition  and  source.  365. 
for  roads,  specifications,  1135. 
manufacture  of,  1 131. 
paints,  (ref.).  374. 
production  of,  table,  366. 
properties  of .  1131. 
Coating, 
bitumastic-enamel.  359. 
protective,  for  dry-dock,  359. 
0>balt, 
blue,  329. 
clum,  318. 
minerals,  829. 
O>bblestone 
gutters.  1099. 

pavement,  construction  of,  1099. 
Ckxles. 
building-,  819-829. 
electric,  1393. 
Coefficient,  coefficients. 
c,  in  Kutter's  formula,  1168-1172. 
of  contraction  of  jet.  1 175. 
differential-,  defined.  266. 
of  discharge 
of  jet,  1175. 

through  circular  orifices,  (ref.), 
1189. 
of  elasticity,  defined,  486. 
of  expansion, 
formulas.  516. 
of  gases,  table,  464. 
of  liquids,  table.  468. 
of  substances,  table.  516. 
of  heat  resistance,  1377. 
of  impact,  for  bridges,  table,  709. 
of  restitution.  304. 
of  roughness  A^,  values  of.  1168. 
of  velocity  of  jet,  1175. 
temperature-,  in  eUc,  table.  1475. 
0>exsecants, 
natural,  table.  167-175. 
triconometric.  defined.  136- 


1662 


INDEX. 


Coffer-dams, 
kinds  of,  described,  868. 
leakage  in,  870. 
pneumatic  foundation-,  882. 
Coils, 
in  gkc.,  kinds  of,  defined,  1403. 
economy-,  elec.  code  rules.  1414. 
Coins  (Foreign) 
and     paper    notes,    equivalents. 
(1-10,-60-100)  in  U.  S.  money, 
table.  07. 
value  of,  in  U.  S.  money,  table, 
06. 
Coke 
concrete,  strength  of.  (ref.),  466. 
weight  of.  table,  478. 
0>ld  rolling,  for  mill  scale,  368. 
C:ollecton.  in  $Uc.,  defined.    1383. 

1408. 
Collector  rin^,  defined,  1383. 
Collision  (or  impact),  formulas.  303. 
Colors, 
by  mixing,  366. 
conventional,  for  maps,  066. 
Columbium,  cfUm.,  318. 
Columns, 
cast  iron,  loads  on,  table,  606,  607. 
channel-, 
properties  and  safe  loads,  tables 

601-603. 
standard  dimensions  of.  606. 
concrete,   plain  and   reinforced, 

tests,  610. 
eccentric  loading  on,  688. 
for  buildings,  requirements  of.  820. 
formulas,  687-600. 
Gordon's  formula  for,  602. 
H-,  properties  of.  tables,  608. 
ideal-,  formulas.  688. 
in  buildings,  formulas,  821,  824. 

826. 
nickel  and  carbon  steel,  tests.  609. 
Phoenix-,  properties  and  safe  loads, 

tables.  604-606. 
properties  and  tables  of.  687-610. 
reinforced -concrete, 
formulas,  440. 
in  buildings.  823.  826.  827.  820. 

832. 
working  stresses  for,  600. 
Ritter's  formxila  for,  680. 
shearing  effect  on,  687. 
steel-, 
discussion,  506. 

moment  of  inertia  of.  problem 
.  in.  637. 

standard  sections.  606. 
ultimate  strength  of,  table.  697. 
straight-line  formulas  for,  693. 
wooden-, 
safe  loads  on,  table,  694. 
Smith's  formula  for.  693. 
working  stresses,  table.  495. 
Z-bar.  dimensions  and  safe  loads, 
tables.  698-600. 
Combination 
and  permutation.  66. 
highway  bridge  and  details,  729. 
roof  truss,  design  of,  806-810. 


Combined  stresses,  tests,  (ref.)  SSX 
Combustion, 
air.  necessary  for,  calculation,  1971. 
of  fuels,  cakulations.  1362. 
Commutators,  defined.  1383.  1494. 
0>mp]ement  and  supplement  of  an 

angle.  130. 
0>mplementary  angles,  dctfined.  12& 
Composition  and  gravel  filling    for 
wood  block  pavement,  specifi- 
cations. 1128. 
Comoound 
ana  simple  units,  equiv..  table,  88. 
chemical,  321. 
curves.  (R.  R.).  1011. 
engines,  performance  of.  1366. 
interest, 
methods.  60-62. 
table.  62. 
(}ompressed-air 
painting,  with  cost,  374. 
process,  879. 
quarrying  by,  423. 
reference  data.  1482. 
Compression 
in  steel  bridge  members,  table. 

710. 
of  earth,  how  estimated,  010-91 3. 
tests  of  timber,  table.  400. 
strength  of  metals,  table,  406. 
Compressive  strength  value  of  con- 
crete in  beams,  686. 
Concrete 
aggregate,  416. 
asphalt-,  defined,  406. 
beams,  slip  of  rods  in,  (ref.)  456. 
bk>ck.  blocks,  450. 
hollow,  building, 
specifications,  460. 
testing,  461. 
hollow,  safe  loads  on,  820. 
masonry,  460. 
bonding  new  to  old.  (ref.)  466. 
bridges,  highway,  cost  data.  738 
broken-stone,  voids  in.  416. 
cement-sand  mix,  417. 
cinder- 
and  stone-,  weight  of.  455. 
corrosion  of  steel  in,  374. 
for  btiildings,  831. 
physical  properties  of,  610. 
proportions,  tests,  510. 
tests  on  cubes,  table,  610. 
weight  of.  476. 
coke-,  strength  of,  466. 
columns, 
tests,  508. 
formulas,  508. 
corrosion  of  iron  in,  (ref.)  466. 
cubes, 
compression  tests  of  j  500. 
trap"  rock,  compression  tests  of. 

curbing,  specifications.  1108. 
curbs,  specifications,  1111. 
defined  J  416. 

depositin|i  in  water,  methods.  441. 
dry,  medium  and  wet,  440. 
economy  of  cement  in,  416. 


INDEX, 


1653 


Concrete— Cont'd. 

elastic   limit   under  compression, 

509. 
expansion  coefficient  of.  610.  616; 

table,  516. 
expansion  joints  in,  464. 
fire-resisting  qualities  of,  444. 
for  buildings,  819. 
forms,  costs,  (ref.),  1298. 
frost-resisting,  economical.  416. 
German  specincations,  442. 
gravel  voids  in,  416. 
gutters,  specifications^  1111. 
heat  effect  on,  510. 
in  buildings,  safe  loads  for,  821. 
in  sea-water,  tests  of,  (ref.)  891. 
in  sub-foundations,  442. 
kinds  of,  416. 

laying,  imder  water,  (ref.)  891. 
masonry,  439. 

material    for,   of    Buffalo   break- 
water. 904. 
matrix,  416. 

mix,  to  determine  proportions,  416. 
mixers,  439. 
efficiency  of,  458. 
traveling,  (ref.)  455. 
mixing.  416,  440. 
modulus  of  elasticity  of,  510. 
natural,  physical  properties  of.  510. 
new  layer  on  old,  440. 
oil-mixed,  for  waterproofing,  455. 
paints  for,  (ref.)  376. 
pavement,  specifications,  1128. 
paving  for  streets,  cost,  etc.,  (ref.) 

1142. 
permeabUity  of,  under  water  pres- 
sure, 453. 
physical  properties  of ,  508-510. 
piles,  876. 

metal-shell,  875. 
piles, 
reinforced-,  675. 
water-jet,  875. 
pile  piers  for  steamship  terminal, 

(ref.)  900L 
placmg  and  ramming,  440. 
proportions,  416,  440. 

of  mix  for  bridge,  45^. 
rammers,  440. 
reinforced-,  443. 
aqueduct.  1208. 
arch  bridges,  cost  of,  784. 
beams, 
formula,  444.  447. 
table,  446. 

tests,  formula,  (ref.)  585. 
Thacher's  computation,  585. 
working  stresses,  585. 
bridges,  railroad,  712. 
columns, 
formulas,  449. 
working  stresses  for.  609. 
construction  for  buildings.  822- 

834. 
design,  office  methods,  (ref./  455. 
formulas  of  A.  S.  C.  E.,  446. 
French  Gov't  rules,  (ref).  454. 
oroDortions.  444. 


(Concrete— Cont'd . 
reinforced- ,— Omt'd. 
references,  456. 
strength  of.  445. 
trestles,  792. 
use  of,  (ref.)  455. 
sand  voids  in,  416. 
sidewalks,  specifications,  1111, 

1129. 
size  of  broken  stone  for.  417. 
slabs,  fiat,  calculation  of,  (ref.)  455. 
spreading  and  ramming,  440. 
-steel 

adhesion  tests,  (ref.)  454. 
construction,  tor  buildings,  822- 

834. 
ties,  1072. 
stone-,  weight  of,  475. 
subaqueous-,  placing,  440. 
surface  finish.  454. 
surfaces, 
scrubbed,  specifications,  (ref.) 

455. 
treatment  of,  (ref.)  455. 
telegraph  poles,  147/. 
tension  test  of  Portland,  509. 
various  mixtures.  Portland,  tests, 

508. 
voids 
determined  for,  440. 
in,  formula,  1118. 
waterproofing 

data  for.  453,  455. 
work,  Chicago  rules  for  measuring, 
891. 
Condensers  and  reactive  coils,  elec 

code  rules,  1443. 
(Condensing  engines,  performance  of, 

1866. 
Conductivity 
in  tUc,  1494. 
of  copper,  standard,  1466. 
Conductors, 
aluminum  and  copper  wire  com- 
pared, 1386. 
elec.  code  rules,  1 394. 
portable,  elec.  code  rules.  1448. 
size  of  wire,  in  transmission,  1386. 
underground-,    elec.    code    rules, 
1404. 
Conduits, 
and  fiumes,  irrigation,  1317. 
and  sewers,  hydraulic  properties 

of;  tables,  1296-1306. 
expenmental  values  of  A^  in  Kut- 
ter's  formula  for  fk>w  in,  1188. 
for  water  supply,  1207.  ' 

ideal  sections  tor  maximum  dis- 
charge, 1161. 
interior-,  elec.  code   rules.    1412, 

1450;  table,  1428, 
miscellaneous  data,    (ref.)    1291- 
1294. 
Conduit  wire,  elec.  code  rules,  1427. 
Cone,  cones. 
g9om.,  134. 

altitude  of  {g$om.),  defined,  134. 
and  spheres,  relations,  250. 
frustum  of  (g«om.),  defined.  134. 


liH 


INDEX, 


Cone,  coneS; — Cont'd. 

znenstiiution  of,  248. 

of  sphere,  defined.  135. 

volume  of  (from.),  134. 
Conglomerate. 

composition  of,  table,  334. 

formation  of.  table.  334. 
Conic  frustum,  mensuration  of,  248. 
Conical  noxzle.  1177. 

sections,  256. 

wedge  and  frustum.  240. 
Conjugate  angles,  denned.  128. 
Connections, 

of  wood  stave  with  cast  iron  pipe, 
1280. 

standard,  for  I-beams  and  chan- 
nels, 615. 
Canoid.  parabolic-,  mensuration  of. 

Construction, 
of  geometric  figures.  130. 
railroad.  1016. 
Consumption  of  water,  1202. 

in  cities,  table.  1203. 
Continuous-current 
and  alternating-current,  ocmi- 

pared.  1386. 
dynamos, 
classification  of,  1884. 
principle  of.  1884. 
Contraction, 
coefficient  of.  1175. 
of  earth,  how  estimated,  910-913. 
Ccotracts  and  specifications,  refer- 
ence data.  1484. 
Convective,  electric-,  defined,  1494. 
Converse   pipe,   patent   lock  joint, 

table.  1282. 
Converter,  rotary,  defined,  1380. 
Conveyors 
and  cableways,  reference  data,1481. 
systems,  for  earth.  007. 
Coordinate,  coordinates, 
axes.  256. 

planes,  132.  261-265. 
rectangular,  defined,  256. 
Coping,  masonry,  defined,  432. 
Copper  (Cu).  318, 
alloys.  320. 

cast,  wire,  etc.,  weight  table.  479. 
conductivity  of,  standard.  1466. 
expansion  coefficient  of.  516. 
friction  of.  519. 

-gold  alloy,  tensile  strength  of,  497. 
melting  point  of,  515. 
minerals,  ores.  £20. 
physical  properties  of,  table,  407. 
sheeting,  for  timber,  861. 
uses  of,  320. 
wire, 
as  conductor,  compared  with 

altmiintun,  406. 
as  conductor,  compared  with 

silicon-bronze.  407. 
carrying  capacity  of.  table.  1404. 
compared  with  aluminum  wire, 

m  transmission.  1386. 
table,  electric.  1388-1301. 
weight  of,  table.  470. 


Coppersmith's  cement,  402. 

in  cordage,  668. 

flexible-,  elec  code  roles.    14IIL 
1426. 

foot,  of  wood,  metric  equiv..  82. 

of  wood,  metric  equivalent.  82. 
Cordage.  668. 

terms,  technical,  668. 
Corduroy  roads,  described.  lOfS. 
Core 

drills,  rock,  922. 

for  dams 
and  reservoir  embankment,  zna- 

cadam  as—.  850. 
concrete  a*—,  860. 
Cores,  in  wUc.,  defined.  1495. 
Corinth  canal,  data.  1320. 
Cork,  weight  of.  478. 
Corliss  engine,  cylinder  of,  1364. 
Corpuscles  in  atoms,  316. 
Corpuscxilar  theory.  116. 
Corrosion 

of  iron  in  concrete,  (ref.)  455. 

of  steel,  in  cinder  concrete,  374. 
Corrosive  sublimate,  for  timber.  3iSL 
Corrugated 

metal,  properties  of.  532. 

sheet,  properties  of,  532. 

sheeting,  strength  of,  (ref.)  561. 

steel, 
roofing.  801. 
stren^  of,  801. 
Corrugations,   cydoidal,    properties 

of,  532. 
(Cosecant,  cosecants, 

defined,  136. 

logarithmic,  table,  176-198. 

natural,  table.  167-175. 
0>sine.  cosines, 

defined,  186. 

logarithmic  table.  170-198. 

natural,  table.  144-166.- 
Costs  (see  items  in  question). 
Cotangent,  cotangents. 

defined.  186. 

k)garithmic,  table.  176-19& 

natural.  Uble.  144-166. 
Cotter  pins,  629. 
Cotton, 

belting,  strength  of,  512. 

tensile  strength  of,  512. 
Cottonwood  tree,  348. 
0>uk>mb,  1495. 

-volt.  1495. 
Coimter  rods,  634. 
0>unterBttnk  rivets.  616. 
(bourse,  masonry,  defined.  481 
Conversed  sine,  -sines, 

defined,  136. 

natural,  table,  144-160. 
Cramps,  masonry,  defined,  4^. 
Crandall  described.  428w 
Cranes  and  derricks,  xefcreoce  data 

1480. 
Creosote, 

commctfcial.  867. 

composition  and  manu&u:t\xre,86& 

cost  of.  366.  ^OOgle 


INDEX, 


1556 


CreoBOte,— Cont'd, 
extracted  from  timber. 

analysis  of.  367;  Uble,  368. 
for  timber,  best  oils  to  use,  372. 
from  coal  tar,  366. 
injected  in  timber,    inspection  of 

treatment,  (ref.)  374. 
in  ties  and  timber,  analysis  of.  370. 
in  timber  well  preserved.  366. 
oil, 
cost,  376. 

from  timber,  analysis  of.  371. 
in  ties.  861. 
weight  of.  479. 
production  and  importation,  table, 

366. 
treatment  of  wood  paving  block, 

1126. 
well  or  tank,  367. 
Creosoted 
poles,  effect  on  linemen,  374. 
wood  block   pavement,    specifica- 
tions, 1126. 
Creosoting 
plant,  (lef.)  360,  874. 

for  poles,  374. 
timber.  360. 
cost,  876. 
wooden  poles,  378. 
worics  in  Prance,  (ref.)  874. 
Crib 
coffer-dams,  869. 
ferry-,  and  details.  894. 
piers,  877. 

pneumatic  foundation-,  880. 
Cntical 
point  of  a  gas,  defined,  612. 
pressure, 
defined,  613. 
of  gases,  table,  614. 
of  Uquids,  table,  614. 
temperature 
of  a  gas.  defined.  612. 
of  gases,  table.  614. 
of  liquids,  table,  61 4. 
volume,  denned,  613. 
Cronstadt  and  St.  Petersburg  Canal, 

data,  1320. 
Cross, 
block,  properties  of,  633. 
skeleton  section,  properties  of.  680. 
Crosses, 
cast  iron  pipe,  table.  1226,  1260- 

1264. 
Matheson  pipe,  table.  1281. 
Crossover  tracks,  frog  spacing,  table, 

1089. 
Cross-sections  of  tunnels,  934, 936. 939. 
Cross  ties,  railroad,  1069. 
Crosswalks,  flagging.  1108. 
Croton  (New)  aqueduct,  size  of .  1208. 
Crown  (Austrian),  equiv.  (1-10,-60- 
idO)  in  U.  S.  money,  table,  97. 
Crowning  streets, 
formula  and  Uble.  1123. 
in  (^icago,  formula,  1143. 
Crucible 
.cast  steel,  manufacture  of,  396. 
cements,  (ref.)  418. 


Crude 
oils, 
and  residuums,  compared,  1134. 
products  from,  in  refining,  1133. 
petroleums,  test  properties,  1134. 
Crushed-stone    sidewalk,    specifica- 
tions, 1106. 
Cube,  cub^, 
and  sphere,  relations.  260. 
and  squares,  tables  of,  uses,  636. 
and  square  roots,  by  slide  rule,  126. 
defined,  133. 
roots 
and  square  roots,  common  tables, 

31-60. 
by  binomial  formula,  102. 
engineers'  tables,  21-24. 
to  find,  20. 
squares  and  xoots,''common  tables, 

31-43. 
tables  of,  for  structural  detailing, 
639-642. 
Cubic 
centimeters  (m  1.), 
and  liquid  otmces,  equiv.  (1-10), 

table.  88. 
English  equivalents,  81. 
equations,  143. 
feet 
and  bushels,  equivalents  (1-9), 

table.  486. 
and  gallons,  equivalents  (1-9), 

table,  486. 
and  meters,  equivalents,  88. 
and  tons,  equiv.  (1-9),  table.  486. 
and   yards-inch,    equiv.    (1-9), 
.    table,  486. 

per  minute,  discharge,  equiva- 
lent, 90. 
per  second,  discharge,  equiva- 
lent. 90. 
per  second,   irrigation   equiva- 

lento.  table,  1814. 
per  time,  discharge,  equiv.,  90. 
foot,  metric  equivalent.  82. 
inch,  metric  equivalent,  82. 
inches  and  centimeters,  equiv.,  88. 
measure. 
English,  metric  equiv.,  table,  82. 
metric.  English  equiv..  table,  81. 
parabola,  1013. 
yards 
and  meters,  equivalents,  88. 
in  pipes,  table,  246,  247. 
metnc  equivalent,  82. 
per  station,  for  areas,  earth woric, 

tables,  1021-1027. 
weight  of,  from  specific  gravity, 
table.  484. 
Culminations  of  polaris.  949. 
Culvert,  culverts, 
concrete-,  782. 
masonry,  specifications,  436. 
pipe,  tables,  1307. 
Curb,  •curbs, 
cement  mortar,  (ref.)  1142. 
concrete,  specifications.  1111. 
on  concrete  foundation.  1122. 
trench,  specifications,  1108. 


16(6 


INDEX. 


Curbing, 
concrete,  specifications,  1108. 
stone,  spedfic^tions.  1108. 
vitrined  clay,  tor  roads  and  streets, 
1143. 
Current,  currents^ 
electrical-,  definitions,  1451. 
breaker,  in  «^c..  defined,  1406. 
mctere  (water),  1186. 
use  of.  1186. 

use  and  care  of,  by  U.  S.  G.  S., 
(ref.)  1180. 
wheel  (water),  described.  13S6. 
Curvature 
and  refraction 
corrections  in  leveling,  087. 
table.  088. 
earthwork  correction  for,  1060. 
head,  in  pipe  lines,  1160. 
radius  of.  of  ellipse,  765. 
railroad,  economic  considerations, 
007. 
Curved 
pipe,  cast  iron,  tables,  1224,  1248, 

1240. 
rails, 
chord  lengths  of,  tables,   1066, 

1067. 
middle  ordinatesof,  tables,  1064- 
1067. 
surfaces,  areas  of.  by  calculus,  276. 
track, 
to  find  degree  of  ciu^re  of,  1066. 
turnouts  from,  1084. 
Curves, 
analysis  of,  (plane-).  266. 
areas  of.  by  calculus.  276. 
centrifu^l  force  of  train  on.  207; 

specifications,  702. 
cycloidal,  motion  on,  286. 
easement-,  (R.  R.),  1013. 
elevation  of  outer  rail  on.  208. 
finding  intersection  of.  103. 
in  pipe  lines,  loss  of  head  in.  1160. 
lengths  of.  by  calctilus,  276. 
of  projectile.  285. 
parabolic  oval-,  (ref.)  766. 
railroad,  1005. 
problems.  1011. 
radii  of,  table.  1007. 
reversed-,  1011.  1012. 
tangents  and   externals  to    P. 
table.  1000. 
spiral-,  (R.  R.)  1013. 
to  lay  out,  130. 
track  gage  on,  1073. 
turnout-,  formula.  1083. 
vertical  (R.  R.),  1005. 
Cut-out,  cut-outs, 
cabinets,  elec.  code  rules,  1430. 
automatic-,  elec.  code  rules,  1406. 
elec.  code  rules,  1404.  1434.  1440. 
Cutters  for  hydraulic  dredges,  (ref.) 

032. 
Cycloid, 
equation  of,  260. 
normal  to,  260. 
properties  of,  236. 
radius  of  curvature  of.  260. 


Cycloidal 
corrugations,  properties  of.  632. 
curve,  motion  on,  286. 
spindte.  264. 
poidulum.  287. 
Cyclopean  masonry, 
dam.  860. 
defined.  1407. 
Cylinder,  cylinders,  gf&m.^  184. 
and  sphere,  relations,  260. 
area,  volume.  244 
hoUow.  dia.  to  area,  capadtv,  noear. 
raaius.  volume,  weight  (water) . 
table,  246-247. 
maximum,  inscribed  in  sphere,  261 
moment  of  inertia  of.  d02. 
of  Corliss  engine,  1364. 
piers.  878. 
frictional  resistance  of.  878. 
platform-.  870 
pneumatic.  870. 
volume  of,  g0om.,  134. 
wind  prenure  on.  707. 
Cypresses.  cla^i6cation  of,  342.  343. 


Dalton's  atomic  theory.  316. 
Dam.  dams.  844. 
arched  masonry,  (ref.)  861. 
backwater  of,  height,  (ref.)  860. 
buttressed-,  design  of.  (ref.)  8G0. 
Cyclopean  masonry.  860. 
earth-v 

auantities  in,  table,  868. 

shrinkage  data.  014. 
fixed,  tjrpes  of.  844. 
foundation  of.  pressure  oo.   848- 

861. 
gravity-. 

design  of,  852. 

staUlity  of.  846. 
high,    masonry,    dimensions     of 

eight,  table.  860. 
hydraulic  fill,  cost  data,  010. 
hydrostatic  pressure  on.  845. 
masonry. 

design  of.  852. 

quantities  in,  tables.  866,  856. 
movable,  (ref.)  861. 
multiple-arch,  described,  860. 
profile  effect  on,  864. 
reference  data,  860-862. 
rock  fill,  quantities  in,  table,  867. 
rubble  concrete.  860. 
safety  factor  against  overttimins, 

850. 
shear  in.  860. 
steel-,  (ref.)  850. 
surchaived.  (ref.)  850. 
triangular-,  847. 
Day.  days, 
number  of.   between   two   datcs^ 

table,  61. 
sidereal-,  defined.  202. 
solar. 

defined,  202. 

and  degrees  (longitude),  equi-va- 
lent8.00.   Google 


INDEX, 


1657 


Dead-men  piles,  874. 
Dead  oil  of  coal  tar,  367. 
Decagon, 
inscribed  in  circle,  131. 
mensuration  of,  204. 
Decay  of  timber,  359. 
Decimm,  English  equivalents,  85. 
Deciliter,   English  equivalents,    81. 

83.  84. 
Decimal,  decimals, 
abbreviation  of,  by  subscript.  95. 
and  fractions,  short  methods    of 
multiplication    and    division. 
11-13. 
to  find  root  of.   by  logarithms, 
105. 
Decimeter. 

English  equivalents,  70. 
square,  English  eqmvalents,  79. 
Deck  cantilever  bridges,'  741. 
Declination, 
in  astron.,  defined,  947. 
of  a  star,  defined,  202. 
Decorative   lighting   systems,   elec. 

code  rules,  1414. 
Deflection 
and    slope   of   beams,    formulas, 

562. 
angle,  of  railway  curve,  130. 
Decree,  degrrees, 
circular  and  time  measure,  equiva- 
lents 99. 
(lon^tude)  and  time,  equiv.,  99. 
marmers*.  equivalents,  68. 
of  curve  of  laid  track,  to  find,  1066. 
or  hour,  decimals  of,  for  minutes 
and  seconds,  table,  1010. 
Dekagram,  English  equivalents,  85. 
Dekaliters, 
and  pecks  (U.  S.),  equiv.  (1-10), 

table,  84. 
English  equivalents,  81,  82,  84. 
Dekameter, 
English  equivalents,  70. 
square,  English  equivalents,  79. 
Delta-metal.  397. 
composition  of,  479,  497. 

and  weight,  479. 
tensile  strength  of,  table,  497. 
Density, 
defined,  460. 
of  steam,  defined,  1356. 
of  water,  metric,  67. 
relative,  of  gases  to  air  and  water, 
table.  464. 
Dependent  variables,  defined,  256. 
Depreciation  diagrams  and  tables, 

(ref.)  1293. 
Depth 
of  plate  girder,  economic,  684. 
of  trusses,  economic,  684. 
Derrick,  derricks, 
and  cranes,  reference  data,  1480. 
used   in   sewer  excavation,    cost 
data,  916. 
Descriptive  geometry,  261. 

problems  of  construction,  263-5. 
Design  of  sewers,  modem  procedure 
in,  (ref.)  1311. 


Details, 

combination  bridge,  730. 

structxiral,  611. 
Detonation  of  explosives,  352. 
Dew-point,  defined,  1190. 
Diagrams, 

load  line,  in  stntc.,  311. 

stress,  general  rules,  310. 
Diameter 

and  radius,  circular  measure,  99. 

of  circle, . 
defined,  129. 

ratio  to  circumference,  129. 
Diamond  drill  borings,  cost  data. 

table,  917. 
Dicken's  run-off  formula,  1198. 
Dielectric  strength,  1463. 
Differential 

calctUus,  266. 

coefficient,  defined,  266. 

defined,  266. 
Differentiation, 

defined,  266. 

of  algebraic  functions,  267. 

of  expotential  functions,  270. 

of  inverse  trigonometric  functions, 
271. 

of  logarithmic  functions,  270. 

of  trigonometric  functions,  270. 

rules  for.  267.  270,  271. 

successive.  271. 
DihedriU  angles,  261. 

defined,  132. 
Dime,  U.  S.  money,  95. 
Dimension 

stones  defined,  4  33. 

stuff,  (lumber) .  claadfication  of,  388 
Dipper  dredge,  928,  931. 
Dipping  tank,  pipe,  1282. 
Directnx,  of  parabola,  258. 
Dirt  roads,  described,  1098. 
Discharge 

and  velocity  of  sewers  and  con- 
duits, tables.  1296-1306. 

coefficient  of,  1175. 
through  circular  orifices,  (ref.) 
1189. 

(cu.  ft.,  galls.,  liters,  etc.)  per  time, 
equivalents,  table,  90. 

from  nozzles,  1175. 

from  orifices,  1175;  table,  1176. 

from  tubes,  1175. 

in    circular   brick   sewexs.    table, 
1299. 

of  water  through  a  pipe,  formula. 
1156. 

pipe  of  dredge,  981. 

through  small  pipes,  table,  1284. 

through  wood  stave  pipe,  table, 
lTlO-1214. 
Discount  and  interest,  59. 
Disk  piles,  874. 
Distance 

between  points  on  Earth's  surface, 
to  find,  201. 

polar,  of  a  star,  defined,  202. 
Distributing 

reservoirs,  1205.  *"^^^T^ 

system,  1280.      ^OOglC 


1668 


INDEX. 


Division  and  roots,  algebraic,  102. 
Docks, 

kinds  of.  892. 

wharves  and  piers.  802. 
Dodecagon, 

inscribed  in  circle.  131. 

mensuntion  of,  204. 
Dodecahedron,  defined.  132. 
Dollar.  U.  S.  money,  06. 
Dolomite. 

compression  tests  of,  61 1. 

properties  of,  401. 
Dolphin,  feny-.  and  details.  896. 
Dote,  in  lumber,  defined,  387. 
Double  integration  for  polar  moment 

of  inertia,  686.  636. 
Dowels,  masonry,  defined,  432. 
Dozen,  equivalent  of.  06. 
Drachm  (see  also  dram). 

apoth.,  fluid,  metric  equiv.,  83. 
Drafted  stone,  defined.  427. 
Drain  pipes,  1206. 
Drains,  storm  water,  design  of,  (ref .) 

1311. 
Drainage 

of  irrigated  lands,  costs,  1310. 

road  specifications,  1101. 
Drams 

(apoth.)   and   milliliters    (c   c), 
eauivalenU  (1-10),  table,  88. 

(apoth..  fluid),  metric  equiv.,  83. 

(apoth.),  metric  equivalents,  86. 

(avoir.),  metric  equivalents.  86. 
Drawbridges,  742. 

calculation  of.  746.  748. 

center-bearing,  three  supports, 746. 

jack-knife,  748. 

moments  and  reactions,  table,  746. 
747. 

reactions,  tables,  744,  746,  747. 

rim-bearing,  four  supports,  743. 

stress-diagrams  for,  746. 
Drawings,  snop-,  for  structural  steel, 

cost  of,  066. 
Dredge,  dredges, 

discharge  pipe  of,  031. 

hydraulic-,  cutters  for,  (ref.)  082. 

types  of,  027,  031. 
Dredged  material,  methods  of  meas- 
uring. 927,  931. 
Dredging,  927. 

Detroit  river,  cost  data,  929-980. 

gold.  030,  082. 

method  of  tunneling,  036. 

Panama  canal,  cost  data.  010. 
Drift 

and  heading  methods  of  tunneling. 
033. 

bolts.  618. 

in  tunneling,  defined,  033. 
DriU,  drills, 

boat,  for  submarine  work,  926. 

compressed-air,  for  rock  excava- 
tion, 923. 

diamond-,  borings,  cost  data,  917. 

holes  in  rock,  spacing,  922. 

m  quarrying,  422. 

percussion,  described,  422. 

rock-,  922. 


DriU.  drills.— Omfd. 
used  in  ttmneling,  934. 
wash-,  borings,  cost  data.  016. 
Drilling 
and  blasting  in  tunneling.  034. 
bkwting   holes    with   well-driUer. 

cost,  026 
cast  iron.  802. 

holes  for  rock  excavation.  022. 
in  tuimel,  cost  data.  030. 
machine-,  in  rock  cuts,  economy 

of.  023. 
submarine,  cost.  026.  080. 
Drop 
(apoth.)  or  minim,  metrk  equiva- 
lent, 83. 
siding  lumber  (fir),  claaaified.  880. 
test  for  steel 
castings,  604* 
raihTm 
Dry 
and  liquid  capacities,  metric  «nd 
English  equivalents.  table8,88. 
capacities, 
equivalents.  67. 
equivalents  (1-10),  English  and 

metric,  Uble,  84. 
metric  and  English  equivalents. 
Uble.  84. 
quarts  (U.  S.)  and  liters,  equiva- 
lents (1-10).  table.  84. 
Dry-dock,  -docks, 
coating  for,  860. 

concrete  expansion  joints  in.  464. 
steel,  floating,  (ref.)  000. 
Dry- 
masonry,  specifications.  486. 
measure,  English  (U.  S.)  metric 

equivalents,  table.-  84. 
process,  in  cement  making.  406. 
rubble  work,  road  specifications, 
1101. 
Dulong's  formula  for  combostaon, 

1862. 
Duodecimo  numbexs.  table,  06. 
Dust 
preventives 
for  road  surftuxs,  1131. 
road  experiments,  costs,  1186. 
suppression  on  N.  J.  roads,  cost, 
1148. 
Duty 
6f  pumps,  formula,  1867. 
of  water  in  irrigation,  tables.  1316- 
1817. 
Dynamics,  288. 
Dimamite, 
cartridges,  863. 
charge,  how  prepared.  863. 
commercial,  ust  of,  364. 
defined.  361. 
for  submarine  blasting.  030; 

cost  026. 
grades  of.  368. 
handling  and  use  of.  863. 
in  quarrying,  410. 
in  tunnels,  cost  data.  080. 
kinds  of.  862. 
properties  of,  368.     gle 


INDEX. 


1569 


Dyoamite,— Cont'd, 
thawing.  353. 
used  in  tunneling,  034. 
Dynamos, 
alternate-current. 

classification  of.  1388. 

prmciple  of,  1382. 
continuous-current , 

classification  of,  1384. 

defined.  1384. 
defined,  i870 . 
foundations  for.  867. 

B 

Eagle  and  double  eagle.  U.  S.  money. 

05. 
Earth,  earths, 
canals,  experimental  values  of  N 
in  Kutter's  formula  for  flow 

.    in.  1188. 
compression   of.   how   estimated. 

010-013. 
contraction     of.   how   estimated. 

010-013. 
dams. 

quantities  in,  table.  858. 

saturization  of.  800. 

shrinkage  data.  01 
defined.  000. 
embankment, 

rolling.  000. 

shrinkage  vertical  in.  015. 

tisual  slopes  of,  000. 
excavation. 

labor  item  in,  008. 

Panama  canal,  cost  data.  010. 
fiU. 

e^ect  of  water  on.  010. 

jarring  effect  on.  010. 

puddmig  effect  on.  010. 

shrinkage  recommendations.  01 4. 

temperature  effect  on,  010. 
friction  of.  521. 
frozen-,  excavation  by  machine. 

cost  data,  021. 
Puller's,  uses  of.  331. 
inftisorial.  uses  of,  331. 
loading  and  conveying,  007. 
kxrsenmg.  007. 
methods  of  handling.  006. 
pressure, 

Rankine's  theory.  830-840. 

theories,  835-840. 
roculs,  application  of  oils  to,  1135. 
shrinkage  of.  000. 

how  estimated.  010-013. 
surface  of,  distance  between  points 

on,  to  find,  201. 
swellage  of,  how  estimated.  010-013. 
voidsm,  010. 

table.  Oil. 
weight  of,  475. 
Earthwork.  006. 
calculations,  1010. 

for  sround  slopes.  1030. 
classification 

in  Chicago  drainage  canal.  023. 

(R.  R.),  010, 


Earthwork,— Cont'd, 
computation,  1055. 
correction  for  curvature,  1050. 
cost  data,  015. 
"haul,"  1050. 
reference  data,  020.  > 
shrinkaffe. 
experiments,  013. 
railroad  specifications  for,  013. 
tables, 
formulas  for  extending,  1042. 
list  of.  1017. 

methods  of  cakulating,  1028. 
Easement  curves,  (R.  R.),  1018. 
Bast  point,  of  celestial  sphere,  de- 

^ed,  201. 
Economy  coils,  elec.   code   rules, 

1414. 
Economic 
depth 
of  plate  girders,  684. 
of  trusses,  684. 
length  of  spans,  684. 
problems  in  calculus,  260. 
Edge   ^ain  (in  lumber),  defined, 

Ed^estones,  specifications,  1102. 
Efficiencies  of  turbines,  1343. 
Egg-shaped  sewers 
and  conduits,  properties  of.  table, 

1304. 
velocities  in.  table,  1305. 
Elastic 
bodies,  impact  effect.  804. 
limit 
affected  by  stresses.  487. 
defined.  487. 
of  metals,  table,  406. 
Elasticity, 
coefficient  of.  defined,  486. 
modulus  of,  defined,  486. 
Elbe  and  Trave  canal,  data.  1322. 
Electric 
apparatus,  cost  data,  1477. 
car  loadings,  for  bridges,  716. 
code,  1303. 

heaters,  elec.  code  rules,  1407. 
horse-power,  equivalents  of,  00. 
hydraulic  problem,  1370. 
lighting,  cost  data,  table,  1478. 
line  poles,  373. 

creoeoting,  373. 
motors, 
railway.  1471. 
speed  classification,  1452. 
power 
and  lighting,  1370. 
cost  data,  table,  1478. 
plants,  costs,  1477. 
sources  and  uses  of.  1385. 
units,  1370. 
railway  bridges.  716. 

steel,  weiffht  of.  formulas.  686. 
resistance,  formula,  1520. 
steam-,  problem,  1370. 
transmission  of  power,  1385. 
waves.  1380. 

wires,    attraction    and    repulsion 
between.  1381. 


IMO 


INDEX. 


Electrical 
apparatus,  clawificatkm  of,  1452. 
conductivity 
of  aluminum  and  copper  com- 
pared. 490. 
of  copper   and    silicon  -  bronze, 
compared.  407. 
currents,  definitions.  1461. 
definitions  and  technical  data, 

1451. 
efficiency,  1455. 
energy .  examples  of,  1340. 
insulation.  1402. 
machinee. 
classification  of,  1452. 
cost  daU,  1477. 
defined.  1370. 
mechanical  and  heat  units,  eqtdva* 

lenu.  table.  01. 
notation  signs.  1471. 
rating.  14M. 
regxilaticn.  1461. 
rptatixig     machines,     definitions, 

standardization  rules.  1451. 

stationary  apparatus,  definitions, 
1451. 
Electricity 

and  magnetism,  principles  of.  1360. 

as  a  form  of  energy.  1370. 

composition  of.  817. 

source  of,  1380. 
Electro-chemistry,  357. 
Electrolysis,  defined,  357.  14M. 
Electrolytes,  367. 
Electro- 
magnet, 1381. 

metallurgy,  defined.  867. 
Electromotive  force,  defined,  1882. 
Electron,  defined,  817. 
Electro-plating.  367.  368. 
Elements. 

metallic,  table,  818. 

(the),  of  matter,  317. 
Elevating-s^rader  tised  in  railroad  ex- 
cavation, cost  data.  016. 
Elevation  of  outer  rail  on  curves, 

formula,  208. 
Elevator  bucket  dredge.  028. 
Elimination,  in  algebra,  108. 
Ellipse. 

axes  of.  258. 

circumference,  length  of,  230. 

equation  of.  258. 
(calculus),  268. 
normal  to,  250. 
Ungent  to.  250.  268. 

false,  or  oval,  250. 

foci  {sing,  focus)  of,  258. 

hollow,  properties  of.  520. 

how  to  draw,  238. 

properties  of.  238.  520. 

radius  of  curvature  of,  250.  765. 
Ellipsoid,  mensuration  of.  255. 
Elliptic 

arcs^formulas  for  lengths  of,  230, 

cone,  defined.  134. 
cylinder,  g^om.,  134. 


Elliptic— Coot'd. 

segment, 
area  of.  242. 
chord  of.  length,  242. 
Elm,  elms, 

friction  of,  510. 

classification  of,  345. 
Elongations  of  polaris,  040. 
Emanation  of  matter,  317. 
Emery,  weight  of,  470. 
Enamel  (bitumastic)  coating.  350. 
Enclosed  fuses, 

cartridge  type.  elec.   code  rules 
Uble.  1488. 

elec.  code  rules,  1436. 

cut-outs,  elec.  code  rules,  1436. 
Energy, 

ana  matter,  phenomena  of.  1486. 

electrical,  dennitions,  1870. 

equation  of,  208. 

forms  of,  examples.  1846. 

heat  a  form  of.  1346. 

kinds  of.  1846. 

law  of  the  conservation  of.  1846. 

lost  during  impact.  304. 

of  cannon  ball,  204. 

of  flowing  water,  (ref.)  llSa 

of  moving  mass,  formula.  1346. 

transformation  of,  1846. 
Engine,  engines, 

axles,  specifications,  504. 

Corliss,  cylinder  of,  1864. 

load  diagrams,  600,  601.  701. 
Cooper's,  707. 

internal-combustion,  tests  o£,  on 
alcohol  fuel,  1368-1370,  1374. 

moment  diagram,  601. 

steam-,  1368-1866. 
diagrams,  described.  1864. 
horsepower,  problem,  1868. 
principle  of,  1863. 


and  metric 
approximate  equiv..  table,  68. 
areas,  equiv.  (1-10).  table,  80. 
dry   capacities,    equiv.    (1-10) 

table,  84. 
fundamental  unitequivalents,61 
lengths,  equiv.  (1-10).  table.  70. 
liquid  capacities,  equiv.  (1-10). 

table.  83. 
system  of  weights  and  measom. 

66-01. 
volumes,  equiv.  (l-10).table.81 
weights,  equiv.  (l-10).table,  85. 
bond,  defined.  487. 
cubic  measure,  metric  equivaknts. 

table,  82. 
dry  measure,  metric  equivalents. 

table.  84. 
land  measure,  square,  metric 

equivalents,  table,  81. 
liquid  measure,  metric  equiva- 
lents, table.  83. 
money.  U.  S.  Value,  05. 
Entropy 
diagrams,  defined,  1866. 
of  the  liquid,  formula,  1366. 
Entry  head,  defined,  1160. 


INDEX, 


1561 


Bphemeris  (solar)  tables,  reference 

to.  202. 
Equilateral    triangle,    inscribed    in 

circle.  131. 
Equalizers,  elec.  code  rules,  1395. 
Equation,  equations, 

algebraic,  defined,  100. 

of  Payments,  61. 

of  time  (astronomical) .  202. 

quadratic,  squaring,  102. 

smiultaneous, 
examples  in.  108. 
graphical,  256. 
Equator,  of  celestial  sphere,  defined, 

201. 
Equilateral  hyperbola,  260. 
Equilibrium, 

kinds  of.  1152. 

of  floating  bodies.  1153. 

of  forces,  in  imch.,  204. 

three  laws  of.  1158. 

unstable.  803. 
Equinox. 

autumnal,  defined,  202. 

vernal,  defined,  202. 
Equivalents  (see  units  in  question). 
Erbium,  chem.,  318. 
Estimating  weights  of  bridges,  685. 
Ether 

and  ether  waves,  1380. 

boiling  point  of,  514. 
Evaporation,  1199. 

ettect  on  gases,  513. 

from  ice,  1199. 

from  land  surface.  1199. 

from  rtmning  water,  1199. 

from  snow,  1199. 

from  water  surface,  1199. 

in  the  U.  S..  table.  1199. 

of  1  lb.  water  from  and  at  212*  P., 
equivalents  of,  table,  91. 
Excavating 

by  machme.  cost  data.  915. 

granite  in  open  cuts  (R.  R.),  cost, 

^  925. 

Chicago  rules  for  measuring,  891. 

earthwork-,  cost  data,  915. 

for  buildings,  819. 

of  Chicago  drainage  canal,  mate- 
rial, work,  costs.  923. 

Panama  canal,  cost  data.  916. 919. 

railroad-,  cost  data.  916. 

road  specifications.  1101. 

rock,  922. 
by  channeling  machines,  924. 

sewer-,  cost  data,  916. 

subway  ,  cost  data.  916. 
Exciter  in  wise,  defined,  1888. 
Expanded  metal,  814. 
Expansion 

bolts,  618. 

by  heat,  516. 

coefficient  of, 
formulas,  516. 
of  gases,  table.  464. 
of  llquias,  table.  468. 
of  substances,  table,  516. 

joints  in  concrete.  454. 

linear,  surface  and  volumetric.  5 16. 


Expansion— Cont'd. 
o£  functions.  271. 
of  gases,  513. 
of  metals  in  cooling,  380. 
rollers, 
for  bridges,  pressure  on,  705. 
segmental-,  table,  685. 
Expert  valuations  and  reports,  refer- 
ence data,  1484. 
Explosion  pumj>,  direct-acting,  1378. 
Explosives,  360. 
detonation  of,  352. 
in  quarrying,  422. 
in  timnels.  cost  data,  989. 
permissible  in  coal  mines,  list,  354. 
unmixed.  353. 
Exponential   functions,   differentia- 
tion of,  270. 
Exponents,  algebraic,  examples  in. 

Exsecant,  exsecants. 
defined,  136. 
natural,  table,  167-175. 
Externals  and  tangents  to  a  1*  curve, 

table,  1009. 
Eye-bars, 
bending  stresses  in,  formula,  686. 
in  bridges,  specifications,  706. 
length  to  form  heads  of,  formula, 

686. 
properties  of,  631. 
Eye-bolt  fastenings  for  wire  rope, 
675. 


Pace  brick,  strength  of.  507. 
Pactor,  factors, 
algebraic-,   of  equation,  defined. 

100. 
greatest  common,  to  find.  6. 
of  safety, 
defined.  487. 
for  timber,  496. 
in  buikiing,  821. 
prime,  of  numbere,  table,  3-5. 
Fahrenheit  and  Centigrade  scales, 

equivalents,  table.  465. 
Pahrenheifs  hydrometer,  462. 
Pallacy  (apparent)  in  algebraic  solu- 
tions. 103. 
Palling  bodies,  tables.  283. 
Palse  ellipse  or  oval,  259. 
Farm  surveying,  964. 
Farraday's  ring,  1882. 
Fascines.  905. 
Fastenings,  wire-rope.  676. 
Fat,  beet;  etc.,  weight  of,  table,  479. 
Fathom,  equivalents.  68. 
Feathers,  plug  and,  described,  426. 
Feet, 
and  chains,  equivalents,  table.958 
and  meters, 
cubic,  equivalents,  88. 
cubic,  equiv.  (1-10).  table.  82. 
equivalents,  88. 
equivalents  (1-10),  table.  70. 
square,  equivalents,  88. 
square,  equiv.  (1-10).  table.  80. 


1M2 


INDEX. 


Feet,— Cont'd, 
cubic  and  acre-,  equivalents,  88. 
per  minute  and  miles  per  hour, 

equivalents,  89. 
per  second 
and  meters  per  sec.,  equiv.,  80. 
and  miles  per  hour,  equiv.,  80. 
and  miles   per  minute,  equiv., 
80. 
per  sec.  per  sec.  and  meter*  per  sec. 

per  sec.,  equivalents,  80. 
to  meters  <  1-1000).  equivalents, 
table.  71-74. 
Feldspar,  uses  of,  881. 
Felsite, 
composition  of,  table,  888. 
formation  of.  table,  838. 
Fencing,  road  specifications,  1101. 
Fender  piles,  803. 
Fermentation  of  timber,  850. 
Ferric  structures,   protection  from 

corrosion,  372. 
Feny 
bridge  and  details.  808. 
crib  and  details,  804. 
dolphin  and  details.  806. 
house,  D.  L.  &  W.,  Hoboken, 

(lef .)  000. 
slips  ana  bridge  aprons,  803. 
Fertiliser, 
greensand  as  a,  840. 
marl  as  a.  340. 
Fifth  powers 
and  fifth  roots,  engineers'  table, 

26-27. 
square  roots  of,  engineers'  table. 
25. 
Filling,  fillings, 
for  woods. block  pavement,  specifi- 
cation. 1128. 
masonry,  defined.  431. 
Filters,  mechanical.  1204. 
Filtratwn, 
mechanical,  1204. 
of  water,  cost,  1201. 
rapid  sand,  1204. 
slow  sand,  1204. 
Fire 
hydrants,  table.  1200. 
plugr.  described.  1288. 
streams,  effect  of  long  lengths  of 

hose  on.  (ref.)  1187. 
tests  on  building  materials,  523. 
tube  boilers,  described.  1362. 
Fireproof 
buildings,  requirements  for,  810. 
cement,  402. 
fioors.  818. 
requirements  for,  820. 
Fir,  grading  rules.  388,  380. 
Firs  (trees),  classification  of.  342. 
Fitting  and  materials  of  construc- 
tion, elec.  code  rules,  1423. 
Fixtures,  elec.  code  rules.  1413. 1440. 
Fixture  wire.  elec.  code  rules.  1427. 
Flagging  crosswalks,  1103. 
Flagstone, 
defined,  402. 
quarrying,  410. 


Flange 

angles  of  plate  gixders,  properties 
of,  table.  5727      "•  *'     *~ 

block,  prooesties  of,  638. 

pipe,  cast  iron,  table,  123G. 

plates  of  plate  girders,  pxoperties 
of,  table,  588. 
Flashing,  defined,  1500. 
Plat  plates.  Grashof's  analysis  of. 

(ref.)  586. 
Flax 

belting,  strength  c^,  512. 

tensile  strength  <^.  512. 

yam  fiber,  strength  of.  512. 
Flemish  bond,  de&ied,  437. 
Flexible 

cord,  elec.  code  rules,  1413.  1426. 

joint  pipe,  cast  iron,  1238. 

tubing,  elec.  code  rules,  1431. 
Flitch  (lumber),  classification  of  ,388. 
Floating  dry-dock,  steel,  (ref.)  MO. 
Floats, 

hydraulic,  described,  1183. 

rod-.  1188. 

sub-surface-,  1183. 

surface-,  1183. 
Floor,  floors, 

and  ceiling  constructioa.  817.  818. 

bridge-,  specifications,  700. 

building-,  construction,    tyctes  oL 
817,  818. 

fireproof,  818. 
requirements  for  820. 

live  loads  on,  table,  815. 

loads, 
for  buildings,  820. 

of  building,  live  loads  for,  824. 

plates,  reinforced  concrete,  bend- 
iM  moment,  823,    835.   827, 

reinforeisd   concrete,   instruction 

sheet  for  placing,  (ref.)  586. 
slabs,  reinforced  concrete,  plaok 

flooring  for,  831. 
trestle  bridge,  788-700. 
wooden-,  framing,  817. 
Floorbeam,  floorbeams, 
effect  of,  on  bending  moments.  605. 
end  cotmections  of.  700. 
reactions. 
Ox>per  s  loading,  table,  708. 
for  concentrated  loads,  table, 

604. 
from  electric  cars,  tables,  717, 

718. 
for  highway  bridges,  table,  728. 
Flooring, 
classification  of,  388. 
glass,  physical  properties  of,  512. 
lumber  (nr).  classified    380. 
Ftorin   (Dutch),  equiv.    (1-10.-50- 
100)  in  U.  S.  money,  table,  07. 
Flotation, 
depth  c»,  formula.  1152. 
of  bodies,  1152. 
Flour  cement,  402. 
Flow 
in  cu.  ft.  per  sec.  reduced  to  bofse- 
power.  table.  1888. 


INDEX. 


IMS 


low — Cont'd. 

in  open  channels,  suiiace  and  mean 
velocity  of,  1183. 

of  air  in  small  pipes,  friction  form- 
ula. 1180. 

of  liquids,  theory  of,  UM. 

of  steam 

through  pipes  formula  and  table, 

1361. 
through  orifices,  (ref.)  1377. 

of  water 

in  open  channels,  diagram,  (ref.) 

1189. 
in  pipes,  measurement  of.  1183. 
in  wood  pipes,  (ref.)  1187. 
through  submerged  tubes,  (ref.) 
1189. 

lowing  water,  energy  of,  (ref.)  1 188. 

lue  boilers,  described.  1302. 

luid 

drachm  (apoth.),  metric  equiv.,83. 

measure  (apoth.),  metric  equiva- 
lenU.  table,  83. 

ounce  (apoth.),  metric  equiv..  83. 

lume.  flumes. 

and  conduits,  irrigation,  1317. 

for  water  supply,  1207. 

measuring-,    uistructions    for   in- 
stalUng.  (zef.)  1187 

proportioned   for   maximum   dis- 
chaige,  1161. 

semicircular,  merit  of,  1317. 

steel,  for  water  supply,  1207. 

valves,  table,  1279. 

luorine,  chtm.,  818. 

lush  hydranU,  table,  1290. 

lux. 

asphaltic,  specifications,  1125. 

borax  as,  330. 

lywhecl.  tension  in  rim,  problem, 
297. 

ocus  (pi.  fod) 

of  ellipse.  258. 

of  parabola.  258. 

oot, 

cord  (wood),  metric  equiv..  82. 

cubic, 
equivalents,  67. 
metric  equivalents,  68,  82. 

decimals  of,  to  inches  and  frac- 
tions, table,  223. 

equivalents,  68. 

metric  equivalent  of.  66.  68. 

.pounds 

and  meter-ldlograms,  equiv.,  89. 
equivalents  of,  90. 
table.  01. 

per  hour,  equivalents  of,  90. 

per  minute,  equivalents  of,  90. 

per  second,  equivalents  of,  90. 

square,  metric  equivalents.  68,  81. 

valves,  vertical,  tabic,  1279. 

ootings,  foundation-.  867,  868. 

orce  and  motion,  equations  o  f, 
mech.,  278. 

arce.  forces, 
centrifugal,  297. 
componeiit,  305. 
defined,  278. 


Force,  forces. — Owit'd. 
distributed-. 

center  of  gravity  of,  296. 

resultant  of.  296. 
electromotive,  defined.  1382. 
equations  of.  in'mechanics.  288. 280. 
equilibrium  of,  in  nmch..  294. 
lines  of.  electric,  defined.  1382. 
outer  and  inner,  in  structures.  305. 
parallel,  center  of  gravity  of.  295, 
parallelogram  of,  294. 
polygons.  295. 

at  joints  of  truss.  310. 
resolution  of.  294. 
tractive  problem.  288. 
triangle  of,  294 
unbalanced,  formulas,  288. 
Foreign 
coins  and  paper  notes,  equiv.  (1- 
10,-50-100)  in  U.  S.  money, 
tables.  96   97. 
money,  tables.  95-97. 
weights  and  measures,  American 
eqmvalents.  table.  92-94. 
Forest  sttmipage  in  the  U.  S.   376. 
Forgings, 
carbon  and  nickel  steel,  chemical 

properties  of,  505. 
nickel  steel,  physical  properties  of. 

table.  499. 
steel. 

physical  properties  of .  table,  499. 

specifications,  505. 

testing.  506. 
Forms  for  concrete,  costs,  (ref .)  1293, 
Foundation,  foundations,  863. 
beds. 

bearing  pressures,  863-865. 

classification  of.  863. 
coffer-dams  for,  869. 
concrete.  867. 
footings.  867,  868. 
for  buildings,  819. 
gravel  and  sand,  864.  865. 
hard-pan,  864. 
I-beam.  867. 
indurated  clay.  864.  865. 
k>ads,  for  buildings,  866. 
loads  on.  estimating.  866. 
loam,  865. 

of  dams,  pressure  on.  848-851. 
pile,  871. 
pneumatic,  880. 
references.  890. 
road  specifications,  1101. 
sand-,  864.  865. 
sewer,  1306. 
sheet  piling  for,  869. 
soils. 

bearing  power  of,  for  buildings, 
867. 

tests  of,  865. 
solid  rock,  863,  864. 
spread-,  reinforced  concrete,  (ref.) 

890. 
sub-. 

concrete  for.  442. 

cement  grout  injected  in,  442. 
walls,  waterproofing  for,  418. 


1M4 


INDEX. 


Poxuidry  work,  892. 

Fountain,   aerating-,   in   reservoir 

1206. 
Fractions 
and   decimals,    s^ort  methods  of 
multiplication     and   division, 
U-13. 
kinds  of,  7. 

reduced  to  decimals,  tables,  0-10. 
reduction  of,  7-10 
(12ths)  reduced  to  decimals  table, 

0. 
(04ths)  reduced  to  decimals,  table. 
10. 
Fractional  distillation   of  gasoline, 

table,  1376. 
Franc  (French),  equiv.   (1-10,-60- 
100)  in  U.  S.  monev,  table.  97. 
Francis'  weir  formulas,  1178. 
Freezing 
mixtures,  513. 
point,  defined,  513. 
point  of  liquids,  table,  514. 
process,  in  foundation  work,  882. 
test  for  sandstone,  402. 
weather,  laying  masonry  in,  488. 
French 
money,  U.  S.  values,  05. 
thermal  unit  (Cal.)  defined.  1847. 
Frequencies  and  voltages,  in  eUc, 

1470. 
Friction.  617. 
angle  of,  for  various  substances, 

tables.  617-521. 
head,  in  pipe  lines,  1160. 
heads   in   cast  iron  pipe,   table, 

1217. 
in  machines,  table,  521. 
laws  of,  517. 

losses  in  pipes,  defined.  1161. 
Morin's  experiments,  617. 
of  air  in  small  pipes,  formulas, 

1189. 
of  journals  on  their  pillows,  table. 

520. 
of  plane  surfaces,  table,  517. 
of  various  substances,  tab]e,  521. 
rolling,  521. 
sliding,  517-621. 
sliding-,  of  train,  702. 
Frictional  resistance  of  cylinder 

piers.  878. 
Frictionless  orifices,  experiments  on, 

(ref.)  1187. 
Frog,  frogs,  1076. 
and  switches,  tables,  1079-1082. 
angles,  properties  of,  table,  1076. 
crossing-,  1078. 
kinds  of,  1075. 
manganese  steel,  1075. 
movable-point,  M)76. 
number,  formula,  1075. 
spacing 
on  crossover  tracks,  table.  1089. 
on  ladder  tracks,  table,  1089. 
spring  rail.  1076. 
Frost  boxes  for  gate  valves,  table. 

1288. 
Fruhling  suction  dredge,  (ref.)  932. 


Frustum 
of  circular  spindle.  254. 
of  cone.  248. 

defined.  134. 
of  conic  wedge,  249. 
of  cylinder  or  prism,  area,  voloxoe. 

244. 
of  parabolic  spindle,  264. 
of  pyramid,  248. 
defined,  184. 
Fteley  and  Steams'  weir  fonnulas. 

1180.  1181. 
Fuel,  fuels, 
chemical  analvsis  of,  1360. 
heat  of  combusUon   of.   cakiila' 

tions,  1362. 
heating  power  of,  1369. 
liquid,  properties  of,  1870. 
solid,    chemical    composition    of. 

table,  1362. 
vaporization  of.  1871. 
wood  as,  value  of.  1803. 
Fuller's  earth,  uses  of.  831. 
Fulminate  of    mercury  for  percus- 
sion, 352. 
Fungus  in  timber,  369. 
Furlong,  equivalents,  68, 
Fuses, 
automatic-,  elec.  code  rules,   1401 
cartridge  enclosed,  elec.  code  rules 

table.  1438. 
elec.  code  rules,  1436. 
Fusible 
metal 
(Rose's),  melting  point  of.  615. 
(Wood's),  melting  point  of,  61  i- 
plug,  398. 
Fusion, 
latent  heat  of.  defined.  513. 
temperature  of.  defimcd,  613. 
vitreous,  of  glass  and  irtm,  616. 


Gadolinium,  chtm.^  318. 
Cv£>ge.  gxiges, 
hook-,  1182,  1188. 
metal-,  tables,  666,  667. 
of  track  and  wheels  railroad.  107] 
rain-,  standard,  1196. 
sheet  metal,  tables,  667. 
standard  wheel-,  1078L 
wire,  tables,  666,  671. 
GalUum,  dum.,  318. 
Gallon,  gallons, 
apoth.,  metric  equivalents.  88. 
and  bushels,    equivalents    (1-f). 

table.  486. 
and  cubic  feet,  equivalents  (1-91, 

table,  485. 
and  liters. 
equivalenU  (1-10).  table.  S3 
equivalents.  88. 
and  yards-inch,  equivalents  f  1-Ji 

table.  485. 
(dollars  per  U.  S.) 
and  francs  per  liter,  eqiuv.  (1* 
10).  table.  98. 


INDEX. 


1565 


Gallon,  gallons, — Cont'd, 
(dollars  per  U.  S.)— Cont'd, 
and  marks  per  liter,  equiv.  (1- 

10).  table.  08. 
and  shillings  per  Br.  Imp.  gallon, 
equivalents  (1-10),  table,  98. 
eqtiivalents.  67. 
metric  equivalents.  68,  83. 
of  liquid,  weight  of,  47D. 
per  minute  (discharge)  and  liters 

per  minute,  equiv..  90. 
(shillings  per  Br.  Imp.)  and  dollars 
per  U.  S.  gallon,  equiv.  (1-10), 
Uble,  98. 
Galvanized 
iron  covering  for  bridges,  861. 
or  black  pipe,  table.  1284. 
Galvanizing.  357. 

Gantah  (Philippine  measure),  Eng- 
lish equivalents,  81. 
(garbage  disposal,  1295. 
Gas.  gases, 
and  steam  power,  1346. 
Avasadro's  law  of,  1372. 
coefficient  of  expansion  of,  table, 

464. 
critical  point  of  a,  defined,  512. 
critical  temperature  of  a,  defined, 

512. 
defined.  512. 
engine  principlesand  management, 

(ref.)  1377. 
engineering,    problems    in,    (ref.) 

1378. 
evaporation  eflfect  on,  513. 
expansion  of.  513. 
heat  effect  on  a.  512. 
lighting,  electric-,  elec.  code  rules, 

liquefaction  of,  how  accomplished, 

513. 
physical  properties  of,  table,  514. 
-producer  ana  water-gas  process, 

1377. 
proof  compositions,  418. 
specific  gravities  of, 
Uble.  464. 
to  determine,  462. 
standards  for  specific  gravity.  462. 
standard 
pressure  of,  defined,  462. 
temperature  of,  462. 
weights  and  specific  gravities   of, 
table,  464. 
Gasfitters'  cement,  402. 
Gasket,  gaskets, 
compositions,  (ref.)  418. 
pipe,  1215. 
Gasoline, 
capacity  and  weight  equiv.,  1 376 . 
fractional   distillation   of.    table, 

1376. 
fuel,  properties  of .  1370,  1375. 
vapor  pressure  of  saturation  for, 
table.  1373. 
Gate,  gates,   1271-1279,  1285-1287. 
and  valves,  Ludlow,  tables,  1274- 

1279.  1286.  1287. 
boxes,  table.  1288. 


Gate,  gates. — Cont'd, 
sluice, 
stand  and  wheel,  1270. 
Uble.  1279. 
valves,  1271-1279.  1285-1287. 
Chapman,  nomenclature,  1285. 
dimensions  and  weights  of,  1273. 
vertical,  geared  and  ungeared, 
1273. 
Gearing  and  mechanism,  reference 

data,  1480. 
Generators  (see  also  Dynamos), 
defined.  1379. 

elec.  code  rules,  1394,  1447. 
Geometrical 
figures, 
areas  of,  Uble,  524. 
center  of  gravity  of,  Uble.  524. 
construction  of,  130. 
moments  of  inertia  of,  Uble,  524. 
neutral  axis  of,  Uble,  524. 
properties  of,  Uble,  524. 
radius  of  gyration  of,  Uble,  524. 
section  modulus  of.  Uble,  524. 
mean.  57. 

series  or  progression,  57. 
Geometry, 
Analjrtlc,  256. 
Descriptive.  261. 

problems  of  construction,  263. 
Plane,  128-181. 
Solid.  132-135. 
German 
money,  U.  S.  value,  95. 
-silver.  397. 
Germanium,  ch^m.,  318. 
Gill,  liquid,  metric  equivalent,  83. 
Girder,  girders  (see  also  Beams), 
and  beams,  properties  of,  Ubles, 

562. 
beam  box,  steel, 
problem.  569. 
properties  of.  Uble,  568. 
Cooper's  k>ading,  Uble.  708. 
deck,  plate-,  spacing  of.  700. 
electric-car    loadings   for,    Ubles, 

717-719. 
for  buildings,  requirements  of,  820. 
moments  and  shears,  various  load- 
ings, 688. 
plate  and  lattice,  section-modulus 

diagrams,  (ref.)  586. 
plate-, 
economic  depth  of,  684. 
specifications.  704. 
steel,  properties  of,  Uble,  570- 

railroad,  weight  of,  710. 
(single  I)  beams,    properties  of, 
Uble.  583. 
Glass, 
expansion  coefficient  of,  516. 
flooring, 

physical  properties  of,  512. 

strength,  of,  512. 
melting  point  indefinite,  515. 
physical  properties  of,  512. 
sizes  and  weights,  Uble,  4J!|9, 
strength  of,  512.  g^^ 


ISW 


INDEX. 


GIam.— Cont'd, 
tiles,  800. 

vitreous  fusion  of,  515. 
window,  cost  prices,  470. 
Glased 
brick.  415. 

pipe,  for  water  supply,  1207. 
Glucinum,  cfum.,  818. 
Glue, 
cement,  402. 
marine,  (ref.)  418. 
Gneiss, 
and  granite,  weights  of.  475. 
composition  of,  table.  336. 
compression  tests  of.  511. 
compressive  strength  of,  511. 
defined,  340. 

transverse  strength  of.  511. 
Gold, 
cast, 
physical  properties  of,  407. 
etc.,  weight  of,  480. 
ckgm.,  319. 
-copper  alloy,  tensile  strength  of, 

497. 
dredging,  080,  982. 
meltmg  point  of,  515. 
minerals,  ores,  828. 
plating,  358. 

wire,  tensile  strength  of,  407. 
Gondola  cars,  large  capacity,  (ref.) 

1001. 
Gothic  sewers  and  conduits,  proper- 
ties of.  table.  1303. 
Government  land  surveying,  067. 
Grade,  grades, 
angles 
and   %   of,   equivalents,   table, 

1002. 
and  rates  per  mile,  equivalents, 
table.  1003. 
cost  of  haul  on,  table,  906. 
economic  considerations,  992. 
feet  per   100  ft.  and    per    mile, 

tables,  1001.  1003. 
limiting-,  092. 

locomotive  traction  on,  002. 
problem,  008. 
table,  004. 
of  large  irrigating  canals,  table, 

1317. 
of  sewers,  1206. 
of  timnels,  035. 
on  profiles,  railroad,  1004. 
reduction   (R.  R.).  allowable  ex- 
pense for,  095. 
ruling-,  992. 

determination  of,  996. 
traction  on,  1007. 
Grader,  elevating-,  used  in  railroad 

excavation,  cost  data,  916. 
Gradients,  raihx»d-,  991. 
Grading, 
for    street    pavement,    specifica- 
tions, 1127. 
lumber,  387. 

railroad,  economic  problem,  269. 
with  wheeled  scrapers,  cost  data. 


Grain,  grains, 
and  grams,  equiv.  (1-10)  .table.  85. 
(apoth.)  metric  equivalent,  86. 
(avoir.),  metric  equivalents,  86. 
metric  equivalents,  68. 
troy, 

equivalents,  67. 

metric  equivalents,  86. 
Gram,  grams, 
and  grains,  equiv.  (1-10),  tab]e,85. 
and  ounces, 

equivalents,  89. 

equivalents  (1-10),  table.  85. 
English  equivalents,  68.  8&. 
per  cu.  centimeter  and  pounds  per 

cu.  in.,  equivalents,  89. 
standard,  equivalents,  67. 
Granite, 
block  pavement, 

described.  1100. 

specifications,  1102.  1105.  1119. 
block  paving,  specxficatioas,  1105. 
building,  400. 
compontion  of,  381. 

table,  887. 
compression  tests  of,  51 1. 
compressive  strength  o£,  511. 
excavation,  in  open  cuts  (R.  R.). 

cost,  925. 
expansion  coefficient  of.  516. 
heat  effect  on.  400. 
high  compression  tests.  511. 
Idnds  of,  400. 
paving  blocks,  1102. 
properties  of.  400. 
temperature  stress  for  160*  P.,  523L 
tenfloon  tests,  (ref.)  511. 
transverse  strength  of.  51 1. 
weight  of.  table,  475. 
Graphical 
methods,  in  stmc,,  906,  SIO. 
solution 

of  catenary,  753. 

of  Pratt  truss,  812. 

of  truss,  810. 
Graphite, 
for  paint,  855. 
paint,  359. 
weight  of.  480. 
Grashofs   analysis  of    flat    plates 

(ref.)  586.  ^ 

Grasshopper  b^ts,  789. 
Gravel 
and  composition  filling  for  wood 
block  pavement,  specifications, 
1128. 
foundation,  864,  865. 
friction  of,  521. 
quarrying,  419. 
roads, 

application  of  oils  to.  11 34. 

construction  of,  1(^8. 
screening.  419. 

sidewalks,  construction  of.  1008. 
streets,  oiled,  specifications.  1114. 
swellage  when  Kx>sened,  Oil. 
voids  m.  911. 

concrete.  416.     ^T^ 
weight  of.  475.      8^^ 


INDEX. 


1567 


Graving  dock,  892. 
Gravity 

acceleration, 
formtda,  459. 
equation  of,  287. 
table.  283. 

center  of,  of  trapezoid,  847. 

force  of,  278. 

specific,  (see  specific  gravity). 

yards,  (rcf.)  1091. 
Gray  iron  castings,  specifications, 

498     * 
Great-circle, 

arc  of,  denned.  135. 

of  sphere,  defined,  134 
Greensand,  337. 

use  of,  340. 
Greenstone, 

composition  of,  338. 

properties  of,  400. 

trap,  weight  of,  480. 
Greatest  common  factor,  to  find.  6. 
Groined  arch  in  filter  and  reservoir 

construction,  (ref.)  1292. 
GrosSj 

eqmvalent  of,  05. 

great-,  equivalent  of,  95. 
Grounding   low-potential   circuits, 

elec.  code  rules.  1401. 
Groiand-slope  quantities. 

formulas  for.  1030. 

correction  table.  1039.  1041. 
Grout, 

cement,  in  sub-foundation,  442. 

filling, 
for  wood  block  pavement,  speci'* 

fications.  1128. 
in  brick  paving,  1109. 
Grubbing    and  clearing.  900. 

cost  data.  916. 

refemece  data,  920. 
Guard  rails. 

specifications,  700. 

timber,  789. 
Gum 

trees,  classification  of,  345. 

arabic,  weight  of.  480. 
Gtmcotton 

explosives.  351.  352. 

manufacture  of,  351. 
Gunmetal.  bronze. 

weight  of.  478.  480. 

physical  properties  of,  table.  497. 
Gunpowder.  350. 

weight  of,  480. 
Gusset  plates,  705. 
Guttapercha, 

expansion  coefficient  of,  516. 

wcoght  of.  480. 
Gutters, 

bituminized -brick,  specifications, 
1115. 

cobblestone,  1099. 

concrete,  specifications,  1111. 

plank,  described.  1098. 
Gypsum.  329.  404. 

defined,  339. 

variety  of,  336. 

weight  of.  480. 


Gyration, 

center  of,  303. 

radius  of,  problem  in,  637. 
Gyroscope,  theory  of,  (ref.)  1095. 


H 

H 
columns,  properties  of,  tables,  608. 
skeleton  section,  properties  of ,  530. 
Halite,  composition  of,  336. 
Hammer-dnll,  422. 
Hammers,  stone,  described,  426-7. 
Hanger  boards  for  series  arc  lamps, 

elec.  code  rules,  1442. 
Hard  pan 
excavation,  by  use  of  dynamite, 

923. 
foundation,  864. 
Harlem  River  ship  canal,  cost  data, 

1329. 
Harveyized  steel  396. 
Haskell  current-meter,  1185. 
Haul, 
earthwork-,  1059. 
on  various  grades  (R.  R.),  cost  of, 
table,  M6. 
Hawser,  in  cordage,  668. 
Head,  heads, 
curvature-,  in  pipe  lines,  1160. 
entry-,  denned,  1160. 
friction-,  in  pipe  lines,  1160. 
of  eye-bars,  added  length  formula, 

086. 
of  water, 
forgiven  pressures,  table,  1147. 
reduced  to  equivalent  velocities, 

table.  1155. 
reduced  to  equivalent  pressures, 
tables.  1148,  1149. 
pressure-,  in  pipe  lines,  1160. 
various  hydraulic,  defined,  1160. 
velocity-,  in  pipe  lines,  1160. 
Header,  masonry,  defined,  432. 
Heading 
and  drift  methods  of  tunneling, 

933. 
in  tunneling,  defined,  933. 
Heaped  bushel,  measure  of,  84. 
Heat, 
and  power,  problems,  1350. 
as  energy,  1346. 

conductivity  and  resistance  of  ma- 
terials, table,  1377. 
effect 
on  building  materials,  523. 
on  concrete,  510. 
on  various  substances,  512. 
engines    (internal    combustion), 
tests  of,  on  alcohol  fuel,  1 368- 
1370.  1374. 
equivalent 
of  external  woik,  formula,  1356. 
of  internal  work,  formula,  1355. 
expansion  by,  516. 
mechanical 
and  electrical  units^equivalents, 
table,  Oi.izedbyVjOC 


1568 


INDEX. 


Heat,— Cont'd, 
mechanical — Cont'd, 
equivalent  of, 
defined.  1347. 
equiv.  (1-10),  table.  1340. 
of  combustion 
of  fuel,  calculations.  1362. 
of  liquid  fuels.  1870.  1375. 
of  the  ]i<^uid,  formula,  1355. 
of  vaporization,  formulas,   1355. 

1356. 
resistance.    • 
and  conductivity  of  materials. 

table,  1877. 
coefficients  of.  1377. 
imits, 
defined,  1347. 
equivalents  of.  table.  01. 
equivalents  (1-10).  Uble,  1348. 
per  sq.  ft.  per  minute,  equiva- 
lents. Ubfe,  91. 
waves,  1380. 
Heaters,  electric-,  elcc.  code  rules. 

1407. 
Heating 
and    ventilation,   reference   data. 

1482. 
power  of  fuels.  186(1 
values  of  coals,  tables.  1360,  1861. 
Heavy  oil  (creosote),  367. 
Hectar.  hcctars, 
and  quarter  section,  equiv..  88. 
and  town^p.  equivalents,  8iB. 
English  eqmvalents,  68. 
Hectogram.  English  equivalents,  85. 
Hectoliter,  hectoliters, 
and  bushels  (U.  S.),  equiv.  (1-10), 

table.  84. 
English  equivalents.  81.  82,  84. 
(francs  per)  and  dollars  per  bushel, 

equivalents  (1-10).  table,  98. 
(Germ,  marks  per)  and  dollars  per 
bushel,  equiv.  (1-10).  table.98. 
per  hectar  and  bushels  per  acre. 
equivalents  (1-10),  table,  84. 
Hectometer, 
English  equivalents,  70. 
square,  English  eqmvalents,  79. 
Height,  slant-,  defined,  133. 
Helical  springs,  formulas,  1482. 
Helium, 
chem.,  319. 

gas  never  been  liquified,  518. 
Helix  or  screw.  260. 
Hemlock,  hemlocks, 
classification  of.  342. 
grading  rules,  388,  890. 
Hemp, 
friction  of,  518^  519. 
required  per  joint  of  cast  iron  pipe, 
1216. 
Hept€igon, 
defined.  129. 
mensuration  of,  204. 
Herschel's  weir  formula.  1181. 
Hertzian  ray.  316. 
Hesselmann  prcx:ess  for  timber,  861, 
Hexagon, 
defined,  129. 


Hexagon,— Cont'd, 
hollow-,  properties  of,  527. 
inscribed  in  circle.  131. 
mensuration  of,  204. 
regular^,  properties  of.  526. 
Hexahedron,  defined,  132. 
Hickories,  classification  of.  343. 
Highway,  highways.  1097. 
bridges.  720. 
combmation-,  with  details,  729. 
live  k)ad  data  for,  728. 
nickel  and  carbon  steel,  specifi- 
cations, 737;  table,  738. 
references.  739. 
typical  loading  for,  727. 
unit  stress  sheets,  720. 
with   solid    floors,    weight    of, 

formulas.  686. 
With  wooden  fioors,  weight  of, 
formulas.  686. 
History  (Natural)  of  materiaK  316. 
Hitches  and  knots,  in  cordagt,  668-9. 
Ho|prshead  (liquid).  equivalenU,  83w 
Hoisting, 
rope,  tension  in.  290. 
work  formula,  290. 
Hollow 
circle,  properties  of,  628: 
concrete  blocks,  safe  loads  on,  829. 
ellipse,  properties  of,  629. 
hexagon,  properties  of,  527. 
octagon,  properties  of,  527. 
rectangle,  properties  of,  525. 
square, 
diagonal  axis,  properties  of.  626. 
properties  of,  526. 
tile  partitions,  813. 
Hook 
bolts.  618. 

fastenings  for  wire  rope,  676. 
gage.  1182.  1183. 
Horizon,  of  celestial  sphere,  defined, 

201. 
Horizontal  check  valves,  table,  1278. 
Horse,  power  of  a,  1097. 
Horsepower, 
brake-,  (B.  H.  P.),  formula.  1371. 
electric, 

energy  value  of,  90, 91. 
equivalents  of,  90. 

Uble,  91. 
from  flow  of  one  ca.  ft.  per  sec 

table.  1333. 
hours, 
equivalents  of,  table,  91. 
from   storage  of  one  acre-ft. 

table,  1835. 
from  storage  of  1,000,000  cu.  ft., 
table,  1384. 
indicated,  (I.  H.  P.),  formula.1871 
mechanical,  eauxvaknts  of,  90. 
metric,  equivalents  of,  90. 
of  locomotives,  problem,  291. 
of  steam  boiler,  defined.  1361. 
of  turbines,  theoretic,  femnii^ 

1844. 
unit,  291. 
Hose,  effect  of  long  lengths  of.  oc 
fire  streams,  (ref.)  1187. 


INDEX, 


1569 


Hour 
angle,  of  a  star,  defined.  202. 
circle,  of  celestial  sphere,  defined, 

262. 
or  degree,  decimals  of,  for  minutes 

and  seconds.  1010. 
(time)    and    degrees    (longitude), 
equivalents,  90. 
House,  nouses, 
car-,  elec.  code  rules,  1421. 
drainage.  1296. 
paints.  356. 
Howe  truss 
and  details,  711. 
brace  problem.  635. 
Human  oody.  weight  of.  480. 
Hundred    weight    (avoir.),    metric 

equivalent.  86. 
Hydrant,  hydrants, 
branches,  cast  iron  pipe,  table, 

1229. 
described,  1288. 
Ludlow,  weight  of.  table.  1290. 
nomenclattire.  1289. 
Hydraulic,  hydraulics.  1154. 
cements,  described.  404. 
di«dges.  928.  931. 
fill  dams,  cost  data,  919. 
formulas,  1161. 
Basin's.  1189. 
Chezy's.  1167, 
Kuttcr's,  1167. 
grade  line.  1159. 
Ume,  manufacture  and  use  of, 

^4. 
limestone^  properties  of,  401. 
mean  radii  of  pipes,  table,  246>7. 
measurements,  1182. 

of  streams,  (ref.)  1187. 
method  of  earth  excavation,  908. 
notation,  1154. 
problems.  1167,  1172.   1219.  1298, 

1306. 
properties  of  conduits  and  sewers, 

tables.  1296-1306. 
shield  used  in  sewer  tunnel,  cost 
data.  916. 
Hydrocarbons, 
m  min.,  classificaton  of.  828. 
natural,  classification  of,  1141. 
Hydrodynamics,  defined,  1154. 
Hydro-electric  problem,  1879. 
Hydrogen, 
boiling  point  of,  514. 
chem.,319. 
corpuscles  in,  816 
melting  point  of,  515. 
minersus.  330. 
•  -oxygen  flame,  317. 

physical  properties  of,  table,  514. 
Hydrokinctics,  1154. 
Hydrometers.  461.  462. 
Hydrostatics.  1146. 
head  and  pressure, 
equiv.  (1-10).  1146. 
tables.  1146-1149. 
pressure, 
for  lead  pipe.  679. 
formulas,  1146. 


Hyd  rostatlcs.— 0>nt*d . 
pressure. — Ojnt'd. 
in  pipes  and  tanks,  1152. 
on  dams.  845. 

on  submerged  surfaces.  846,  847. 
units.  1146. 
Hydroxide,  in  ch»m.,  defined.  321. 
Hyperbola, 
equation  of,  259. 
normal  to.  259. 
tangent  to.  259. 
equilateral.  260. 
Hyperbolic 
logarithms,  defined.  104. 
example  in.  106. 
table.  108. 
spiral,  equation  of,  260. 


block,  properties  of.  533,  534. 
skeleton  section,  properties  of,  530, 
631. 
I-beam,  -beams, 
block,  properties  of,  533,  534. 
cast  separators  for,  table,  623. 
rivet  gages  for,  614. 
skeleton,  properties  of .  530,  531. 
special,  properties  of.  table,  584. 
standard    connection    angles   for, 

615. 
steel,  properties  of,  554. 
Ice.      - 
evaporation  from,  1199. 
expansion  coefficient  of,  516. 
hardj  compressive  strength,  512. 
melting  point  of,  515. 
weight  of.  480. 
Icosahedron.  defined.  132. 
Impact, 
coefficient  of,  for  bridges,  table, 

709 
effect  of,  489. 
formulas.  303. 

railroad  bridges,  effect  of,  701. 
Impedance  and  inductance  in  trans- 
mission line.  1387.  1392. 
Impulse 
and  momentum.  298. 
water  wheels,  1386. 
Ion,  positive  and  negative,  317. 
Incandescent   lamps,   in  series  cir< 

cuits.  elec.  code  rules.  1406. 
Inch,  inches, 
and  centimeters, 
cubic, 
equivalents  (1-10).  table,  82. 
equivalents.  88. 
equivalents  (1-10),  table,  70. 
equivalents,  8S. 
square, 
equivalents  (1-10),  table,  80. 
equivalents,  88 
and  millimeters, 
cubic,  equiv.  (1-10).  table   §2. 
equivalenU  (1-10).  Uble.  70. 
sqxiaro.  equiv.  ('-10).  table.  80. 


1570 


INDEX. 


Inch,  inches, — Cont'd, 
cubic, 
equivalents,  67. 
metric  equivalents.  68.  82. 
decimals  of,  to  millimeters,  table, 

69. 
equivalents,  68. 
fractions  of, 
and  millimetexs.  equivalents,  88. 
to    decimals    and    millimeteis, 
Uble.  69. 
metric  equivalent  of,  66,  68. 
miner's,  table,  1313. 
-potmds    and    centimeter-grams, 

equivalents.  89. 
square,  metric  equivalents,  68,  81. 
to  decimals  of  a  toot,  table.  223. 
(1-12)  to  meters,  equiv..  table,  71. 
Inclined 
plane, 
in  tiuch.,  formula,  292. 
motion  on,  286. 
velocities  on,  286. 
railway,  (ref.)  1091. 
Increasers. 
cast  iron  pipe,  tables.  1238,  1259- 

1264. 
Matheson  pipe,  table.  1281. 
India  rubber,  weight  ot,  480. 
Indicated   horsepower   (I.    H.   P.), 

formula,  1376. 
Indium,  ch^m.,  319. 
Inductance  and  impedance,  in  trans- 
mission line.  1387,  1892. 
Induction,  electric,  defined,  1381. 
Inductive  load,  in  eUc,  1453. 
Inelastic  bodies,  impact  effect,  304. 
Inertia, 
moment  of, 
about  inclined  asds,   formulas, 

636-538. 
about  parallel  axis.  524. 
of  rectangles,  table,  599-540. 
of  rolled  shapes,  537. 
polar  moment  of,  535-538. 
maximum  and  minimum  values, 
537. 
Infusorial  earth,  uses  of,  331. 
Insect  larvae  in  timber,  359. 
Inspection  of  yellow  pine  lumber, 

387,  388. 
Insulated  wires,  table,  1423. 
Insulating  joints,  elec.  code  rules, 

1442. 
Insulation, 
electrical.  1462. 
resistance, 
elec  code  rules,  1396. 
tables,  1447.  1450. 
Intake,  mouthpiece  (bell-shaped)  at, 

1177. 
Integral  calculus,  272. 
Integration, 
definite,  273. 

double,  for  polar  moment  of  iner- 
tia, 535.  536. 
formulas  for,  274,  276 
method  of  udng  current  meters. 
1186. 


Interest, 
compotmd, 
methods.  59-62. 
table.  62. 
simple, 
common  and  exact^methods,  5^ 

59. 
table,  60. 
Interior  conduits,  elec.  code  rcles. 

1412.  1450;  table,  1428. 
Interlocking  plant,   nulroad,    (refJ 

1093. 
Internal  combustion  engines.  UaXs 
of.  on  alcohol  fuel,  1968-1370. 
1374. 
Intersection  of  curves,  to  find,  Itl. 
Intrados  of  arch,  curve  of.  764. 
Inverse  trigonometric  fuiictloDS,140L 
Iodides,  in  min.,  classification  oC.3S5u 
Iodine,  dmn,,  319. 
Ions,  in  electrolysis.  357. 
Iridium, 

minerals.  328. 
-platinum,  expansion  coefficient  of. 

516. 
Iron. 
cksm.,  319. 
cast, 

expansion  coefiScient  of.  516. 

for  buildings.  819. 

melting  pomt  of,  516. 

pipe,  1214. 

physical  properties  of, .table.  497. 

properties  of,  392. 

temperature  stress  for  160^  F., 
523. 

weight  of,  480. 
cement,  402. 

(ref.)  418. 
corrosion  of.  in  concrete,  (ref.)  455. 
friction  of.  518,  519. 
^ray,  castings,  specifications.  498. 
u  btiildings.  stresses  for,  824. 
malleable  cast, 

high  tensile  strenvth  of,  398. 

tensile  strength  of.  497. 
melting  point  of.  394. 
minerals,  ores,  329. 
molten,  weight  of.  480. 
ore, 

treatment  of,  392. 

uses  of,  329. 
oxide  (s) 

for  paint,  855. 

paints  for  iron  and  steel.  372. 
physical  properties  of,  table.  497 
pig. 

manufacture  of.  392.  ' 

uses  of,  392. 
pipe. 

cast,  specifications.  1239. 

wrought,  1268. 
preservation  of.  358. 
slag  block  pavement,  spedfica* 

tions,  li21. 
vitreous  fusion  of.  515. 
weight  of.  480. 
wire,  physical  properties  of.  498. 


1 


INDEX. 


1671 


Iron, — Cont'd, 
-wrought, 
expansion  coefficient  of,  610. 
for  buildings.  819 
in  buildings,  safe  stresses,  820. 
nuinufacture  of,  393. 
melting  point  of,  616. 
phvsical   properties  of    table, 

weight  of.  480. 
Irrigated  lands,  dxainage  of,  costs, 

(ref.)  13li. 
Irrigation,  1313. 
caif&.l8, 
large,  dimensions  and  grades  of, 

table,  1317. 
locating,  (ref.)  1818. 
miscellaneous  data,  (ref.)  1318. 
velocity  in,  1317. 
duty  of  water  in .  tables.  1316-17. 
flumes  and  conduits,  1817. 
units.  1313. 
of  flow.  1313. 
of  volume,  1814. 
works  of  Southern  Oalifomia,  (ref.) 
131& 
Isometric  projection*  201. 
of  stonewonc.  467,  468. 
Isosceles  triangle,  defined,  128. 
Isthmian  canal,  proposed  American, 

data,  1324. 
Italian  money,  U.  S.  values,  96. 
Ivory, 
weight  of,  480. 
-black,  for  paint,  366. 


,  ack-knife  drawbridge,  748. 

.  apan  varnish,  367. 

/apanning,  367. 

,  arring  effect  on  earth  fill.  910. 

,  ets  and  nozzles.  1176. 

,  etties,  906. 

kinds  of.  906. 
Jetty-head,   reinforced   concrete, 

(ref.)  906. 
Joint,  joints, 

cast  iron  pripe.  kinds  of,  1216. 

Converse  pipe.  1282. 

fleidble-.  pipe.  1238. 

insulating-,  elec.  code  rules.  1442. 

masonry,  defined.  432. 

Matheson  pipe,  1281. 

pipe,  locking-bar,  1269. 

rail-,  kinds  of.  1068. 
Joist  lumber  (fir),  classified.  389. 
Joule  Q.),  joules. 

defined.  1347. 

equivalents  of,  90. 
table.  91. 

per  second,  equivalents  of.  90. 
Journals,  friction  of,  on  their  pillows, 

table,  620. 
Jumper-drill.  422. 

Jute  required  per  joint  of  pipe,  table, 
1222. 


K 

Kaiser  Wilhelm  canal,  data.  1322. 
Kalamein  pipe,  tables.  1281,  1282. 
Kaolin,  weight  of,  480. 
Kaolimte,  uses  of,  331. 
Keene's  marble  cement,  403. 
Kerosene, 
capacity  and  weight  equivalents, 

fuel,  properties  of.  1370.  1376. 
obtained  from  crude  petroleum, 
1133. 
Kieaelguhr.  368. 
Kiln 
drying,  of  timber,  368. 
rotary,  for  cement  making,  406. 
Kilograms 
and  pounds  (avoir.), 
equivalents.  89. 
equivalents  (1-10),  table,  86. 
and  tons  (U.  S.),  equivalents,  89. 
English  equivalents,  68,  86. 
(francs  per)  and  dollars  per  pound, 

equmlents  (1-10),  table.  98. 
(Gennan  marks  per)  and  dollars 
ner  pound.equiv.  (l-10),table, 

per  CO.  meter  and  pounds  per  cu. 

ft.,  equivalents,  89. 
per  sq.  centimeter  and  pounds  per 

sq.  in.,  equivalents,  89. 
per  sq.  meter  and  pounds  per  sq. 

ft.,  equivalents,  89. 
pounds  and  tons,  equivalents,  (1- 

10),  table.  87. 
standard,  equivalents.  67. 
-degree  (C^t.).  equivalents,  90. 
-meter,    -meters    (see    Meter-kilo- 
grams), 
and  foot-pounds,  equiv.,  89. 
equivalents  of.  table,  91. 
Kiloliter,  English  equiv.,  81,  82,  84. 
Kilometers, 
and  miles, 
equivalents  (1-10),  table,  70. 
square,  equiv.  (1-10),  table,  80. 
equivalents,  88. 
English  equivalents,  68.  70. 
per  hour  and  miles  per  hour, 

equivalents.  89. 
per  nunute  and  mUes  per  minute, 

equivalents,  89. 
square,  English  equivalents,  79. 
Kinetic  energy,  defined.  1346. 
Kilowatt, 
energy  value  of.  1379. 
equivalents  of.  table.  91. 
per  second,  equivalents.  90. 
•hour, 

energy  value  of,  1379. 
equivalents  of.  table,  91. 
Knife   switches,  elec.   code  rules, 

1431. 
Knot.  British  Admiralty,  68. 
Knots 
and  hitches,   in  cordage,  668-669. 
in  lumber,  defined, -887.  ^j^ 
Krypton,  chem.,  319^00gle 


1572 


INDEX. 


Ktitter's 
formtila^ 
experimental  detennination 
of//.  1187. 
of  A^andC.  1188. 
hydraulic  formula,  1167. 
Kyaniztng.  for  timber.  361. 


L's.  cast  iron   pipe,  tables,    1226, 

126&-1264. 
Ubor 
item  in  earth  excavation.  008. 
(square),  Texas  land  measure,  in 
acres.  81. 


for  bridge  members,  table.  706. 

for  steel  compression  members, 
weight  of.  (ref .)  609. 
Lacquers,  367. 
Lacauering.  367. 

dredge,  (ref.)  932. 
tracks,  frog  spacing,  table.  1089. 
Lag-screws, 
table.  622. 
use  of.  622. 
Lake  Boigue  (La.)  canal.  daU.  1323. 
I^mps. 
ana  photometry,  in  tUc,  1473. 
arc-, 
elec.  code  rules,  1442. 
on   constant-potential   circuits, 
elec.  code  rules,  1414. 
incandescent,  in  scries  circuits, 

elcM:.  code  rules,  1406. 
in  series,  elec.  code  rules.  1423. 
series  arc,  elec.  code  rules.  1406. 
Lampblack  for  paint,  366. 
Land, 
clearing  and  grubbing,  cost  data. 

Government-,  surveying.  967. 

measure, 
of  Texas,  Mexico,  etc.,  table,  81. 
square,  English,  metric  equiva- 
lents, table,  81. 
Lanthanum,  chem..  319. 
Lap-welded  pipe,  1269. 
Larches,  classification  of,  341. 
Lard,  weight  of.  480. 
Latent  heat 

of  fusion,  defined.  613. 

of  vaporization,  defined.  513. 
Lateral 

bracing,  of  bridges,  problem,  697. 

pins.  629. 
Laths, 

diamond.  814. 

expanded  metal,  814. 

metal.  812. 

wooden,  812. 
Lathing. 

and  plastering,  812. 

building,  812. 
Latitude 

and  longitude  (spher.  trig.).  201. 

lengths  of  a  degree  of,  table,  979. 


Latltttde—Cont'd. 

to  determine,  with  solar.  946u 
Lattice  and  plate  girders,  section- 
modulus  diagrams,  (ref.)  686l 
Latus  rectum  of  parabola.  257. 
Lava, 
denned.  340. 
weight  of.  480. 
Law  of  the  conservation  of  enezsT. 

1846. 
Laying  brick  pavement.  1107. 
L/h.-Cal.     (potmd   calorie.)    defined. 

1347. 
Lead,  ckem.,  319. 
alloys  of.  329. 
-base  alloys,  398. 
expansion  coefficient  of.  616. 
^oielting  furnace,  portable,  1280. 
melting  point  of,  515. 
minoais,  ores,  329. 
physical  properties  of,  498. 
pipe,  tables,  679. 
red-, 
for  paint,  866. 
weight  of,  481. 
required  per  joint 
of  cast  iron  pipe.  1216. 
of  pipe,  table,  1222. 
sheet.  679. 

effect  of,  on  masonry.  687. 
tubing.  679. 
uses  of.  329. 
weight  of,  679; 

table.  480. 
white-, 
for  pcunt,  355. 
paint,  329. 
wire,  tensile  strength  of,  498. 
wool,   pneiunatic  calking   with, 
(ref.)  1293. 
League, 
equivalents,  68. 

square,  Texas    land   measure,  in 
acres,  81. 
Leakage  in  coffer-dam.  870. 
Lean-to  roof  trusses,  unit  stresses  in 

806,  806. 
Leap  year,  time  measure,  99. 
Least  common  multiple,  to  6nd,  6. 
Leather, 
cements,  {tel.)  418. 
friction  of.  517.  518.  619. 
ox, 
modulus  of  elasticity.  612. 
strength  of.  512. 
Le  C^telier's  apparatus  for  find- 
ing   spec.   grav.  of    cements, 
407. 
Lemniscate  of  Bemouilli,   equatkin 

of,  260. 
Length,  lengths, 
equiv.  (1-10),  BngUsh  and  metric. 

table,  70. 
metric  and  English,  equivalents, 

table.  88. 
of  curves,  by  calculus,  275. 
of  spans,  economic,  683. 
units  of,  equivalents.  66. 
Lentinus  lepidens,  in  timber,  362. 


INDEX, 


1678 


adjustment  of,  Ml. 
sections,  earthwork,  list  of  tables, 
1017. 
Leveling.  987. 
allowable  errors  in,  table,  989. 
correction  for  earth's  curvature 

and  refraction,  987. 
sources  of  errors  in,  987. 
Levelman,  duties  of,  in  preliminary 

sxirvey  (R.  R.).  1004. 
Lever, 
compound,  formulas,  292. 
simple,  formulas,  291. 
Leverage,  in  mech.,  formulas,  291. 
Libra  (Philippine  weight),  English 

equivalents.  81. 
Light-waves.  1380. 
Lights,  signal,  elec.  code  rules,  1450. 
Lighting, 
and  electric  power,  1379. 
electric-,  cost  data,  table.  1478. 
systems,    decorative-,    elec.    code 
rules.  1414. 
Lightning  arresters,  elec.  code  rules, 

1396.  1444. 
Lignite,  weight  of,  480. 
Lignum  vitse  journals,  friction  of,  520. 
Lime, 
(cement),  properties  of,  403. 
(common,)  properties  of,  403. 
fat,  403. 
hydratilic,  manufacture  and  use, 

404. 
mortar,  403. 
for  brickwork.  403. 
for  buildings.  819. 
weight  of,  475. 
plaster,  403. 
quick-,  403. 
slacked,  403. 
specific  gravity  of.  403 
weight  of,  table,  475. 
Limestone, 
building,  400. 

composition  of,  table.  335. 
compressive 
strength  of,  511. 
tests  of,  511. 
defined^  339. 
formation  of.  table.  335. 
hydraulic  properties  of ,  401. 
in  ntin.,  329. 
kinds  of.  401. 
properties  of.  400. 
quarrying,  419. 
tensile  strength  of,  511. 
tension  tests,  (ref.)  511. 
transverse  strength  of,  511. 
travertine  401. 
weights,  of,  table.  475. 
Limnoria,  in  timber,  3ftO. 
Line,  lines, 
and  angles,  geometric,  definitions, 

128. 
of  force,  electric,  defined,  1382. 
of  resistance  of  masonry  arches, 

768. 
polC'i  elec.  code  rules,  1 400. 


Line,  lines, — Cont'd, 
right-,  projection  of,  262.  263. 
skeleton-,  properties  of,  529,  531. 
straight-, 
defined,  132. 
equation  of,  256. 
intersection  with  circle,  solution, 
257. 
transmission-,  1386. 
Linea  (Philippine  measure),  English 

equivalent,  81. 
Lining, 
reservoir,  1206. 
tunnels,  934,  939. 
Link 
-fuse  cut-outs,   elec.    code    rules, 

1434. 
fuses,  elec.  code  rules,  1436. 
surveyor's,  equivalents,  68. 
Linseea  oil, 
boiling  point  of,  514. 
for  iron  and  steel,  372. 
for  steel,  358. 
manufacture  and  use,  356. 
weight  of.  480. 
Lintels,  for  buildings,  requirements 

of.  820. 
Live  load  data  for  highway  bridges, 

table,  728. 
Liquefaction  of  gases,  how  accom- 
plished, 513. 
Liquid,  liquids, 
and  dry  capacities,  metric  and 
English  equivalents,  table,  88. 
boiling  point  of,  table,  514. 
capacities, 
equivalents,  67. 

equiv.  (1-10),  English  and  met- 
ric, table.  83. 
metric,  English  equiv.,  table,  82. 
defined,  512. 
freezing  point  of,  514. 
gallons  (U.  S.)  and  liters,  equiva- 
lents (i-10),  table,  83. 
measure,  English  (U.  S.),  metric 

equivalents,  table,  83. 
ounces  and  milliliters  (c.c.) 

equivalents  (1-10).  table,  83. 
physical  properties  of,  table,  514. 
quarts  (u.  S.)  and  liters,  equiva- 
lents (1-10).  table,  83. 
specific  gravities  of, 
table.  468.  469. 
to  find.  461. 
weights  of,  table,  468.  469. 
Lira  (Italian),  equiv.  (1-10.-50-100) 

in  U.  S.  money,  table,  97. 
Liter,  liters, 
and  barrels  (liquid),  eqmv..  88. 
and  gallons 
(U.  S.  ).  equivalents,  88. 
(U.  S.  liqmd),   equiv.    (1-10), 
table,  83. 
and  pecks  (U.  S.).  equiv.  (1-10), 

table,  84. 
and  quarts 
(U.  S.),  equivalents,  88. 
(U.  S.  Uquid),  equiv.   (1-10), 
table,  83. 


1674 


INDEX. 


Liter.  Htcre.— Cont'd. 

English  equivalents,  68,  81,  82.  84. 

(francs  per)  and  dollars  per  gallon, 
equivalents  (1-10),  table,  98. 

(Cjerman  marks  per)  and  dollars 
per  gal..equiv.  (1-10),  table, 98. 

of  water,  weight  of,  67. 

per  minute  (discharge),  equiv.,  90. 

standard,  equivalents.  66. 
Lithium, 

ch€in.,  319. 

minerals,  328. 
Lithology,  331. 
Live  loaas  on  floors  and  roofs,  table, 

816. 
Load,  loads. 

data  for  highway  bridges,  table, 
728. 

factor,  in  eke.,  1463. 

floor-,  for  buildings,  820. 

from  safes,  816. 
-line  diagrams,  in  stntc  ,  311. 

of  crowd  of  people,  816. 

on  floors.  814. 
and  roofs,  table.  815. 

on  railroad  bridges,  specifications, 
700. 

on  structures,  306. 

snow-,  on  roofs,  797,  798. 
Loading, 

rock  on  cars  by  steam  shovel,  924. 

sudden,  effect  of,  489. 
Loam  (earth), 

weight  of,  475. 

foundation,  866. 

voids  in,  911. 
Lobnitz  rock  breaker  for  rock  exca- 
vation, (ref.)  926. 
Locating 

engineer,  duties  of,  in  preliminary 
survey  (R.  R).  1000. 

irrigation  canals,  (ref.)  1318. 
Location, 

railroad-,  998. 
filing  with  State,  1013. 

survey  (R.  R.).  1004. 
Locking-bar  joint  pipe,  1269. 
Locomotive,  locomotives, 

horsepower  of ,  291. 

oil  fuels  in,  use  of,  (ref.)  1378. 

traction  force  of,  992. 
Log,  logs, 

(mill),  lengths  of,  878. 

rules.  (r«fT)  391. 

sawing,  379. 

scales,  (ref.)  391. 

scaling.  379. 

transportation  of,  378. 
Logarithm,  logarithms, 

(anti-),  defined,  104. 
of  numbers,  to  find.  106. 

(common),  table.  108-125. 

(Hyperbolic),  table,  108-126. 

mathematical  operations  by,  105- 
106. 

(Naperian).  table.  108-125. 

of  numbers.  104-127. 
table.  108-126. 

systems  of,  104. 


Logarithmic 
bases,  defined,  104. 
(common)  tables,  explanation  oi, 

104-106. 
cosecants,  table,  176-198. 
cosines,  table.  176-198. 
cotangents,  table,  176-198. 
equivalentflL  104. 

functions,  defferentiation  of.  270. 
secants,  table.  176-198. 
sines,  table,  176-198. 
spiral,  equation,  260. 
tangents,  table,  176-198. 
Logging.  378. 
Long 
-distance  transmission,  1386. 
measure, 
English,  metric  equiv.,  table.  68. 
surveyors',  metric  equiv.,  table, 

68. 
metric  EngUsh  equiv.,  table.  70. 
Longitude, 
and  latitude  (spher.  trig.).  201. 
and  time  measure,  table,  99. 
lengths  of  a  degree  of,  981. 
to  determine,  with  solar.  946. 
Longitudinal  shear  in  beauns,  £or> 

mulas.  565. 
Loomis  water-gas  and  producer-gas 

process,  (ref.)  1377. 
Loop  heading,  in  tunneling,  defined, 

933. 
Loose  rock  classification  (R.  R.).919. 
Loss,  losses, 
in  friction  in  cast  iron  pipe,  table. 

1217. 
of  energy  in  turbines,  1343L 
of  head 
due  to  friction  in  pipe  lines,  1 1 60. 
during  flow  in  pipe  lines.  1159. 
Lowry  process,  for  ties,  cost,  375. 
Ludlow 
double-gate  valves, 
dimensions,   table,    1274.    127S. 

1286.  1287. 
nomenclature,  1272. 
gates  and  valves,  tables.   1274- 

1279,  1286,  1287. 
hydrants,  weight  of,  table.  129GL 


187. 


d  by  Google 


INDEX. 


1670 


Lumber.— Cont'd. 

rot  in,  defined,  387. 

rotagh.  379. 

saWtag.  879. 

saws.  Idnds  of,  879. 

seasoning,  879. 

shakes  in.  defined,  887. 

sizing,  879. 

steam  seasoning,  379. 

stumpage  of  Pacific  coast.  377. 

supplym  U.  S-876. 

tniae  weights.  391. 

trees,  best,  346. 

wane  in.  defined,  387. 

yellow  pine, 
classification  of.  387.  388. 
inspection  of.  387.  388. 
Lune, 

circular-,  mensuration  of,  220. 

of  sphere,  defined,  135. 
Lutes  and  cements,  useful  to  engi' 
neers,  418. 


M 

Macadam 
and  telford  roads,  specifications, 

nil. 

roads, 
specifications,  1116. 
construction, 
application  of  oilin,  1134. 
inverted.  1142. 
roadway,  specifications.  U  06. 1 1 29. 
surfaces,  application  of  oils  to, 

Uachine,  machines, 
drilling  in  rock  cuts,  economy  of, 

electrical-, 
clarification  of,  1452. 
defined.  1379. 
definitions,  1451. 
excavation  of  trenches,  cost  data, 

921. 
excavator,  916. 
Icnindations  for,  867. 
friction  in,  table,  521. 
quarrying,  419. 
reference  data,  1481. 
work,    in    bridges,    specifications, 
706. 
Maclauren's  theorem,  271. 
Magnesia,  weight  of,  480. 
Magnesite,  calcined,  330. 
Magnesium,  chem.,  319. 

minerals,  330. 
Magnet, 
electro-,  1381. 
horse-shoe,  1382. 
permanent,  1382. 
Magnetic 
field,  induced,  1380. 
reluctance,  formula,  1520. 
Magnetism  and  electricity,  princi- 
ples of.  1380. 
Mahler's  formula  for  combustion, 
1352. 


Maintenance  and  operation  of  can- 
als, cost  data,  1329. 
Malleable 
castings,  393. 
cast-iron, 
high  tensile  strength  of,  398. 
specifications,  497. 
iron,  physical  properties  of,  497. 
Mallet,  stone-,  described.  428. 
Manchester  ship  canal,  data,  1320. 
Manganese,  cMm.,  319. 
alloys,  839. 
bronze.  897. 
physicalDropertiesof,  table,  497. 
(ref.)  999. 
in  cast  iron,  effect  of,  398. 
minerals,  ores,  329. 
steel.  396. 

weight  of,  toble,  480. 
Maintenance-of-way,  cost  data,(ref .) 

1092. 
Manhattan  suspension  bridge,  de- 
tails and  specifications,   766* 
760. 
Manhole,  manholes, 
sewer,  1306. 

pipes,  cast  iron,  tables,  1232.  1259. 
Manila  rope.  009. 
weight  and  strength  of,  tables,  609. 
670. 
Manometer,  1174. 

Mantissa  and  characteristic,  of  loga- 
rithms, 104-105. 
Mantle  of  Welsbach  lamps.  330. 
Maples  (trees),  classification  of,  346. 
Mapping,  906. 
in  preliminary  survey  (R.  R.). 
1004. 
Marble, 
cement.  Keene's,  403. 
compressive 
strength  of,  511. 
tests  of,  611. 
defined,  339. 

expansion  coefficient  of,  516. 
forei^,  401. 
tn  9MtK.,  339. 
prop^ties  of,  401. 
quarried  where,  401. 
quarrying,  419. 

temperature  stress  for  160°  F..523. 
tensile  strength  of.  511. 
transverse  strength  of,  611. 
weight  of,  table,  476. 
Bfarine  engmeering,  reference  data. 

1480. 
Mariners'  measure,  metric  equiva- 
lents, table,  68. 
Mark  (German),  equiv.  (1-10,-60- 
100)  in  U.  S.  money,  table.  97. 
Marks  and  Davis  equation  for  total 
heat  of  steam,  dry  and  satu- 
rated, 1378. 
Mari, 
for  cement,  405. 
properties  of,  401. 
use  of,  340.  ^  , 

weight  of.  480.      ^OOQ Ic 
Marline,  m  cordage,  668.    ^ 


1576 


INDEX. 


Masonry.  481. 
abutments,   quantities  in,   table, 

430.  437. 
aqueducts,  1208. 
arch,  -arches,  763. 

forces  acting  on,  767. 

line  of  resistance  of,  768. 

specifications,  435. 

thickness  of  rings,  tables,  766-7. 
ashlar,  defined,  432. 
brick,  437. 

compressive  strength  of,  611. 

quantities  in.  table.  438. 

weight  of.  table,  476. 
bridge,  specifications,  434. 
classification,  434. 
compressive  strength  of,  511. 
concrete,  (see  Concrete), 
concrete,  430. 

•block.  450. 

cinder,  weight  of,  table.  476. 

stone,  weight  of,  table,  476. 
culvert,  specifications.  435. 
Cyclopean-,  defined,  1497, 
dams,  quantities  in,  tables.  856. 856. 
dressed,  weight  of.  table.  476. 
dry,  specifications.  435. 
expansion  coefficient  of,  516. 
friction  of,  521. 
^cranite,  weight  of.  table.  476. 
m  buildings,  safe  loads  on,  826.  - 
kinds  of,  431,  432. 
laying  in  freezing  weather,  433. 
limestone,  weight  of,  table,  476. 
marble,  weight  of.  476. 
mixed.  449. 
piers.  888. 

pitch-faced,  defined,  432. 
ixjinting,  specifications,  434. 
pressure  on,  allowable,  826. 
quarry-faced,  defined,  432. 
railroad,  classification  of,  431. 
random -work,  defined.  432. 
range- work,  defined,  432. 
retaining-wall,  specifkations,  434. 
rubble, 

defined,  432. 

weight  of,  table,  476. 
sandstone,  weight  of,  476. 
squared-stone,  defined,  432. 
stone-. 

compressive  strength  of,  511. 

described.  431. 

in  buildings,  weight  of,  821. 

laying,  specifications,  433. 

Rpecincations,  433. 
wall,  parts  of,  defined,  431. 
work,  in  buildings,  safe  kxuis  for. 
821. 
Mass. 
and  weight,  of  water,  metric,  67. 
defined,  459. 
in  mech..  defined,  278. 
moving,  energy  of,  formula,  1346. 
unit  of.  defined.  469. 
Masses  (weights), 
metric.  English  equiv..  table.  86. 
metric  and  English,  equiv.  (1-10), 
table.  85. 


Mastic, 
asphalt,  defined,  405. 
(resin),  weight  o£^  480. 
Materials, 
chemistry  of^  816. 
(genex&l),  weight  and  specific  grav- 
ities of.  table,  478. 
miscellaneous,  physical  properties 

of,  512. 
Natuzal  Historv  of,  316. 
qtaality  of.  for  buildings.  819. 
resistance  of ,  486. 
roofinj;-.  weight  of.  802. 
specific  gravities  of,  450. 
strength  ot.  486. 
weight  of,  469. 
Matheson    pipe,    patent    k>ck-joxnt, 

tablesTlMl. 
Matter, 
and  energy,  phenomena  of.  1346. 
composition  of,  316. 
defined,  459.  1346. 
in  meek.,  denned,  278. 
radio-activity  of.  316. 
states  of  existanoe  of.  1346. 
the  elements  of,  817. 
Matrix,  concrete,  416. 
Maxima  and  minima  (calculus),  to 

find,  268. 
Maximum  and  minimum  polar  mo- 
ments of  inertia.  587. 
McMurtrie  stone,  manufacture  of.  417 
Mean, 
arithmetical,  57. 
effective   pressure    (m.   e.   p.)    of 

steam  engines,    1365,  1366. 
geometrical-,  67. 
proportional,  56. 

in  semicircle,  131. 
solar 
and  siderial  time,  equivalents. 

table.  202. 
day,  defined,  202. 
Measure,  measures, 
and  weii^hts 

(Foreign).  American  eqtiivalents 

table.  92-94. 
of  Philippines,  English  equiv.. 81. 
English  long,  metric  equivalents. 

table,  CiS. 
lineal,  surveyors',  metric  equiva- 
lents, table,  68. 
mariners  ,  metric  equiv.,  table.  68. 
weights  and  money,  66-99. 
Measurements,  hydraulic,  1182. 
Measuring 
-flumes,  instructions  for  installing. 

(ref.)  1187. 
vekxaty  of  approach  in  weirs,  1 1 77. 
Mechanical, 
electrical  and  heat  units,  equiva 

lents,  table.  91. 
energy,  example  of,  1346. 
equivalents  of  heat  (J.), 
defined,  1347. 
equiv.  (1-10),  uble.  1349. 
filters,  1204. 
filtration,  1204. 
horse-power,  equivalents  of,  90. 


INDEX. 


W7 


Mechanics.  278. 

Mechanism  and  gearing,  reference 

data.  1480. 
Melaphvr.   composition    of.   table. 

Melting  point. 

defined.  613. 

of  chemical  elements,  table,  318. 

of  iron  and  steel,  394. 

of  substances,  table,  615. 
Members 

in  algtb.,  of  equation,  defined,  100. 

in  struc.,  active,  cutting  of.  306. 
Mensuration. 

of  lines,  203. 

of  solids.  243. 

of  surfaces,  203. 
Mercury, 

boiling  point  of,  614. 

chem.,  310. 

melting  point  of,  515. 

minerals.  329. 

uses  of,  329. 

weight  of.  table,  480. 
Menptel  (marl),  for  cement,  406. 
Meridian,  meridians, 

and  base  lines  of  U.  S.  surveys, 
table.  072. 

from  north  star,  to  determine,  948. 

in  cuiroH.,  defijied,  947. 

in   surv.,  convergency   of.   table, 
977. 

of  celestial  sphere,  defined,  201. 

to  determine  with  solar.  946. 
Metacenter,  defined,  1163. 
Metal,  metals. 

alloys.  396. 

bending  strength  of.  table,  496. 

compressive  strength  of.  table, 490, 

elastic  limit  of.  table.  496. 

expanded-,  814. 

expansion  of,  table.  510. 

friction  of,  621. 

^ages.  tables.  666^  667. 

m  machines,  friction  of,  521. 

journals,  friction,  table,  520. 

melting  point  of.  615. 

modulus  of  elasticity  of.  table.  496. 

moldings,  elec.  code  rules,  1412. 

physical  properties  of.  table,  496. 

resistance  (strength)  of,  table,  496. 

shearing  strength  ot.  table.  496. 

springs,  formulas,  1482. 

strength  of,  table.  496. 

surfa^.  varnishing.  367. 

tensile  strength  of,  table,  496. 
Metallic 

elemento.  table,  318. 

tiles,  800. 
Metallurgy,  392. 

of  steel,  (ref.)  399. 
Meter,  meters, 

and  chains,  equivalents.  88. 

and  feet, 
cubic, 
equivalent,  88. 
equiv.  (1-10).  table.  82. 
equivalents.  8$. 
equiv.  (I-IO).  table,  70. 


Meter,  meters, — Omt'd. 
and  feet,— Cont'd, 
square, 
equiv.  (1-10).  table.  80. 
equivalents,  o8. 
and  rods, 
equivalents,  88. 
square,  equi\^ents,  88. 
and  stations  (100  ft.),  equiv.,  88. 
and  vards. 
cubic, 
equivalents.  88. 
equiv.  (l-lO),  table,  82. 
equivalents.  88. 
eqxiiv.  (1-10),  table.  70. 
square, 
equivalents.  88. 
equiv.  (1-10),  table,  80. 
cubic,  English  equivalent.  68. 
current  (water),  1186. 
English  equivalents,  68.  70. 
(francs  per)  and  dollars  per  yard, 

equivalents  (1-10),  table.  98. 
(Germ,  maiks  per)  and  dollars  per 
yard,  equiv.  (1-10),  table,  98. 
per  second 
and  feet  per  second,  equiv..  89. 
and  miles  per  minute,  equiv..  89. 
per  sec.  and  feet  per  sec.  per  sec 
equivalents.  89. 
Pitottube,  1183.  1184. 
register.  1174.  1186. 
square.  English  equiv.,  68.  79. 
standard,  equivalents.  66. 
(1-1,000)  to  feet,  equiv.,  table.  76- 

78. 
Venturi.  1173. 
-kilograms 

and  foot-pounds,  equiv..  89. 
eqtiivalents  of.  90; 

Uble.  91. 
per  hour,  equivalents  of,  90. 
per  minute,  equivalents  of,  90. 
per  second,  equivalents  of,  90 
Method 
of  moments,  in  siruc.^  stresses  by. 

306. 
of  shears,  in  struc.,  stresses  by.  306. 
Metric 
and  English 
approximate  equiv..  tabic,  68. 
areas,  eqxiiv.  (1-10).  table,  80. 
curves,  tables,  100/. 
fundamental  tmit  equiv.,  66. 
lengths,  equiv.  (1-10),  table,  70. 
systems  of  weights  and  meastires 

66-91. 
volumes,  equiv.  (1-10).  table. 82. 
weights,  equiv.  (1-10),  table,  86. 
and  United  States    ' 
dry    capacities,    equiv.    (1-10), 

table.  84. 
liquid  capacities,  equiv.  (1-10), 
table.  83. 
capacities 
(dry),  English  equiv..  table.  84. 
(liquid),  English  equiv.,  table.  82 
cubic    measure.    English   equiva- 
lents, table.  81. 


1578 


INDEX. 


Metric— Cont'd, 
horaepower,  eouivalents  of,  90. 
long  measure,  English  equivalents, 

table.  70. 
square  measure,  English  equiva* 

lents,  table.  79. 
volumes,  English  equiv.,  table, 

81. 
weights  (masses),  English  equiva- 
lents, table.  86. 
Mexico  land  measure.  English  .equiv- 

alents.  table,  81. 
Mica 
schist,  oompositton  o£,  886. 
uses  of,  331. 
weight  of,  480. 
Middle  ordinate  of  curved  fails, 
formulas,  1068. 
tables,  1064-1067. 
Mils, 
and  miUimeters, 
equivalents^  88. 
square,  equivalents  88. 
areas  of  wire  in,  tables,  671. 
Mile,  miles, 
and  IdlometerSj^ 
equivalents,  88. 

square,  eqmv.  (1-10),  table.  80. 
equivalents  (1-10),  table.  70. 
and  stations  (100-ft.),  equivalents, 

table,  1001. 
equivalent  in  varas,  81. 
land.  68. 

metric  equivalents,  68. 
nautical,  equivalents,  68. 
per  hotir 
and  feet  per  minute,  equiv.,  80. 
and  feet  per  second,  equhr.,  89. 
and  Idlometers  per  hour,  equiva- 
lents. 89 
per  minute 
and  feet  per  second,  equiv.,  89. 
and     kilometers    per    minute, 

eqtuvalents.  89. 
and  meters  per  second,  equiv., 89. 
square, 
and  nectars,  equivalents,  88. 
metric  equivalent,  81. 
statute,  equivalents,  68. 
-stones,  road  specifications,  1102. 
U  S.  C.  S.  nautical,  68. 
Milk,  weight  of,  480. 

Mm 

buildings, 
cost  data,  (ref .)  833. 
wind  loads  on,  883. 
scale,  removing,  358. 
U.  S.  money,  96. 
Miller  or  tonncau  (metric),  English 

equivalents,  86. 
Milligram,  English  equivalents,  86. 
Millifiter,  millSiters  (c.  c), 
and  drams  (U.  S.  apoth.),  equiva- 
lents (1-10).  table.  83. 
and  liquid  ounces,  equiv.   (1-10). 

table,  83. 
and  scruples  (U.  S.  apoth.),  equiv- 

aJents  (1-10),  table.  83. 
English  equivalents,  81.  82.  84. 


MiUimeters 
and  inches, 
cubic,  equiv.  (1-10).  table.  82. 
equivalents.  SB. 
equiv.  (l-lO).  table.  70. 
square,  equiv.  (1-10),  table,  80. 
and  mils, 
equivalents.  88. 
square,  equivalents,  88. 
English  equivaletns,  68,  70. 
of  water,  weijght  of,  67. 
square.  English  eoxuvalents,  79. 
to  decimals  of  an  idxAl,  table,  70. 
Mine,  mines,  steel  timbering  tn.(fcCJ 

989. 
Miner's  inch,  table.  1313. 
Mineral,  minerals, 
chemical  composition,  table,  332. 
classification  cL  325. 
color,  table,  332. 
defined,  324. 
hardness  of,  324; 

table.  332. 
oils,  for  roads,  spedficatims.  1 136. 
physical  characteristics  <xE.  3M. 
rock-forming,  table,  332. 
species,  table,  332. 
spedfic  gravity,  table,  332. 
Mineralogy.  324. 
Minim  or  drop  (apoth.).  metric 

equivalents,  83. 
Minima  and  maxima  (calculus),  to 

find.  266. 
Mining,  reference  data,  1482. 
Minium,  for  paint.  355. 
Minute,  minutes, 
and  seconds  to  decimals  kA  a  de> 

gree  or  hour,  table.  1010. 
drcxilar  and  time  measure,  equiva- 
lents. 99. 
time  and  longitude,  equiv.,  09. 
Mixed  masonry,  449. 
Mixing  process,  in  cement  nmking. 

Mixtures,  explosive,  350. 
Modulus 
of  elasticity, 
bending,  of  timber,  table.  403. 
concrete  and  steel,  445. 
defined.  486. 
of  metals,  table,  496. 
of  steel  and  concrete,  ratio.  823. 
826,  832. 
of  resilience,  defined.  488. 
section-,  of  plane  surfaces.  taUes, 
524. 
Moisture    in  timber,  effect  on 

strength.  490-494. 
Moldings, 
elec  code  rules.  1429. 
metal-,  elec.  code  rules,  1412. 
wooden-,  elec.  code  rules,  1450. 
Molybdenuzn.  cA#in.,  319. 
in  steel.  330. 
minerals.  330. 
Moment,  moments, 
and  reactions, 
drawbridge-,  table,  745,  747. 
of  forces,  295. 


INDEX. 


1579 


Moment,  momentt, — Cont'd, 
and   ahean  for  engine   loadings, 

table.  092. 
arm,  in  struc,,  to  find.  806. 
bending, 
and  chord  stresses,  307. 
problem  in.  637. 
diagram  for  engine  loads,  091. 
in  beams  and  girders,  various  load- 
ings, 088. 
in  Btructtires,  method  of,  306. 
In  trusses,  various  loadings,  093. 
maximum-. 
Cooper's  loading,  table,  708. 
for  highway  bridges,  table,  728. 
from  electric  cars,  table,  717,  718. 
position  of  load  on  truss  for.  096. 
metric  and  English,  equivalents, 

table^  89. 
of  forces  m  structures,  to  find,  305. 
of  inertia 
about  inclined  axis,  300. 

formulas,  535-538. 
about  pcuallel  axis,  300. 
of  beams,  formula.  299. 
of  circular  beam.  300. 
of  figure  about  parallel  axis,  524. 
of  plane  surfaces,  298. 

tables,  524. 
of  rectangles, 
(ref.)  580. 
table.  539-540. 
of  rolled  shapes.  537. 
of  solids,  table,  302. 
of  steel  column,  problem  in.  037. 
polar.  535-538. 
maximum  and  minimum  val- 
ues. 537. 
origin  of,  290,  305. 
parabola,  to  draw,  088. 
resisting-,  problem  in,  037. 
Momentum, 
and  impulse  293. 
train-,  coefficient  of  sliding  fric- 
tion. 702. 
Money, 
Austro-Hungarian.  U.  S.  values, 

95. 
English,  U.  S.  values.  95. 
Poieign,  tables.  95-97. 
French.  U.  S.  values,  95. 
German,  U.  S.  values.  95. 
Italian.  U.  S.  values.  95. 
Russian,  U.  S.  values,  95. 
U.  S..  table.  95. 
Monomials,  examples  in.  101. 
Mortar, 
brickworic.  kinds  used.  438. 
cement. 
for  concrete,  417. 
strength  of.  507,  508. 
strength  ratios  of  compressoin 

and  tension,  508. 
weight  of.  480. 
Uble.  476. 
for  buildings,  819. 
lime,  403. 

•  for  brickworic,  403. 
,  weight  of,  476.  480. 


Mortar,— Cont'd, 
quantities  in  brick  masonry,  table, 

438. 
stone  masonry,  specifications,  433. 
Motion, 
accelerated, 
equations  of,  270,  280,  281.  282. 
table,  283. 
and    force,    equations  of,  tmch., 

278. 
circular.  280. 

formulas,  summary  of.  284. 
in  ni4ch.,  defined,  278. 
of  projectile.  285. 
on  cycloidal  curve,  280. 
on  inclined  plane,  280. 
uniform,  equations  of,  279. 
Motor,  motors, 
elec.  code  rules,  1397.  1450. 
electric, 
defined.  1380. 
railway.  1471. 
speed  classification.  1452. 
water,  described.  1330. 
Mouthpiece,  bell-shaped,  at  intake, 

1177. 
Movable  bridges.  742. 
references.  749. 
weight  of  steel  in.  748. 
Moving  picture  machines,  elec.  code 

rules.  1440. 
Muck,  in  tunnslnig,  defined.  933. 
Mud.  weight  of.  480. 
Mueller  tapping  machine.  1283. 
Multiple,  least  common,  to  find,  0. 
Multiplication 
and  powers,  algebraic,  examples 

in,  101. 
tables,  1018-1020. 
Mtmtz-metal,  397. 
Mushroom  floor,  analysis  of,   (ref.) 

580. 
Myriagram,  English  equivalents,  85. 
Myrialiter,  English  equivalents,  81. 

82.  84. 
Myriameter. 
English  equivalents,  70. 
square.  English  equivalents,  79. 


N 

N, 
coefficients  of  roughness,  values  of, 

1108. 
experimental  determination  of,  in 

Kutter's  formula,  1187. 
and  C,  in  Kutter's  formula,  experi- 
mental determination  of.  1188. 
Nadir,  of  celestial  sphere,  defined, 

201. 
Nails, 
slating,  402. 

steel,   weights  and    dimensions, 
tables.  025-028. 
Naperian  logarithms, 
defined.  104. 

examples  in,  100.  ><^  i 

table.  108.     izedbyLjOOgle 


1580 


INDEX. 


NaphthaUn. 
boiling  point  of.  514. 
from  creosote.  367. 
National  electric  code,  1193. 
Natural 
cement,  hydraulic,  manufacture  of 

404. 
coexsecants,  tables,  167-176. 
cosecants,  table.  167-175. 
cosines,  table,  144-166. 
cotangents,  table.  144-166. 
ooversed  sines,  table,  144-166. 
exsecanU,  table,  167-175. 
secants,  table.  167-175. 
sines,  table,  144-166. 
tongents,  table,  144-166. 
versed  sines,  table,  144-166. 
Nautical  almanac,  reference  to,  202. 
Navigable  canals,  1320. 
Neodymium,  cfrnn.,  319. 
Neon,  chem.,  319. 
Neutral  axis  of  plane  surfaces,  table. 

524. 
New  Mexico  land  measure.  English 

equivalents,  table,  31. 
Nicaragua  and  Paifama  routes  com- 
pared, 1824-1328. 
Nicholson's  hydrometer,  462. 
Nickel 
alloys.  329. 
-aluminum, 

composition  of,  496. 
physical  properties  of,  table,  496. 
expansion  coefficient  of,  516. 
in  ch^m.,  319. 
minerals,  329. 
steel.  396. 
annealed,  physical  properties  of. 

table,  499. 
forged,  oil-tempered,  phvsical 

properties  of,  table,  499. 
forgings, 
chemical  properties  of,  505. 
physical  properties  of,  505. 
manufacture  of.  398. 
properties  of,  398. 
spans,  compared  with  carbon 

steel.  737.  738. 
specifications  for  Manhattan 
bridge,  758. 
-vanadium  steel.  899. 
weight  of,  480. 
Niobium,  chtm.,  318. 
Nitrate  explosives,  850. 
Nitric  acid 
compounds,  351. 
treatment  of  cellulose,  351. 
Nitro-explosives,  351. 
Nitroglycerin,  manufacture  of  ,351,352 
Nitrogen, 
boihng  point  of,  514. 
in  ch4m.,  319. 
melting  point  of,  515. 
physical  properties  of,  table,  514. 
Nonagon,  mensuration  of,  204. 
Non- 
condensing  engines,   performance 

of.  1365. 
mductive  load,  in  eke,  1453. 


Normal 
and  tangent  (calcolua).  equatfeoxxs 

to  circle,  equation  of,  257. 
to  cycloid,  260. 
to  ellipse,  equation  of.  259. 
to  hyperbola,  equation  of,  259. 
to  parabola,  equation  of,  258. 
North 
point,  of  celestial  8(^>ere,  defined, 

20l. 
star  (see  also  Polaris), 
to  determine  meridian  from,  94S. 
to  find,  948. 
Notation,  Bow's,  for  trusses,  309. 
Nozzle,  nozzles, 
conical.  1177. 
dischange  from.  1175. 
Numbers, 
abstract,  Arabic  notation,  table, 

95. 
Arabic  system  of,  1. 
duodecimo,  table,  95. 
logarithms  of,  104-127. 
primes,  multiples  and  factors,  3. 
Roman  sirstem  of,  1. 
short   methods  of   multiplication 
and  division.  11-13. 
Nuts 
and  bolts.  Ubles.  618-621. 
pilot-.  629. 
pin-,  table.  629. 
sleeve-.  634. 
weights  and  dimensions,  table, 
633. 


Oak,  oaks, 
expansion  coefficient  of,  516. 
classification  of,  344. 
friction  of,  518-520. 
Obsidian, 
composition  of.  table,  338. 
defined.  340. 
Ochre  for  paint.  855. 
Octagon, 
and  circle,  inscribed  and  circum- 
scribed, 181. 
hollow,  properties  of,  527. 
mensuration  of,  204. 
regular,  properties  of,  527. 
Octs^edron.  defined,  132. 
Offsets,  cast  iron  pipe,  tables.  1235 

1249. 
Ohm.  defined,  1514. 
Oil.  oils, 
as  road  dust  preventives.  1181. 
crude-,  products  from,  in  refining, 

1133. 
experiments  on  roads,  cosu.  1139, 

ri40. 
fields  of  the  17.  S..  1183. 
for  graveled  streets,  qiecifications, 

1115. 
for  roads.  j 

best  kinds,  11S8.  gLC 


INDEX. 


1681 


Oil.  oils.— Cont'd. 
for  roads, — Cont'd, 
classification  of,  1 1 33. 
properties  of ,  1133. 
fuels  in  locomotives,  use  of,  (ref.) 

1378. 
heavy, 

application  to  roads,  1134. 
application  to   road    surfaces, 
1134. 
linseed,  manufacture  and  use,  356. 
mineral,   for  roads,  specifications 

1136. 
-proof  compositions,  418. 
refining  crude-,  1133. 
semi-asphaltic,  1133. 
Oiling 
graveled  streets,  specifications, 

1114. 
iron  and  steel,  368. 
roads,  cost  of,  (ref.)  1142. 
electronic  theory,  317. 
Omnibus  bars,  defined,  1487. 
Onzo   (Philippine  weight).   English 

equivalent,  81. 
Open 
-cut  tunneling,  033. 
hearth 
cast  steel.  396. 
process,  394.  395. 
steel  (boiler  plate),  specifica- 
tions. 501. 
Operation  and   maintenance  of  ca- 
nals, cost  data.  1 329. 
Orange-peel  bucket  dredge,  928. 
Ordinate  and  abscissa,  defined,  256. 
Ore,  ores, 
amalgamation,  357. 
extraction.  357. 
iron,  treatment  of,  392. 
of  minerals,  328. 
smelting.  357. 
weighto  of,  480. 
Orifice,  orificek, 
and  tubes,  compared.  1176. 
center  of  pressure  on,  table,  1151. 
coefficient    of   discharge    through 

circular,  (ref.)  1189. 
discharge  from,  1175. 

table,  1176. 
flow  of  steam  through,  (ref.)  1377. 
frictionless-,  experiments  on.  (ref.) 

1187. 
standard.  1176. 


Oriffin, 
of  cm 


oTcurves,  defined,  256. 
of  moments.  296,  305. 
Orthographic  projection.  261. 
Osbom  rivet  code,  61 1. 
Oscillation, 
center  of.  303. 
of  pendulum,  287. 
Osmium,  chem.,  319. 
Ounce,  ounces, 
and    grams,    eqtiivalents    (1-10), 

table,  85. 
apothecary, 
fluid,  metric  equivalents,  83. 
metric  equivalents,  86. 


Ounce,  ounces, — Cont'd* 
avoirdupois, 
and  grams,  eqtiivalents,  89. 
and  troy,  equivalents,  67. 
metric  equivalent,  86. 
liqtiid,  and  milliliters  (c.  c),  equiv. 

(1-10).  table,  83. 
metric  equivalents,  68. 
troy,  metric  equivalents,  86. 
Outlet 
boxes,  elec.  code  rules,  1429. 
pipe  from  reservoir,  how  arranged, 
1205. 
Oval, 
or  false  ellipse,  259. 
parabolic-,  curve  of,  (ref.)  765. 
Overload  capacities,  in  elec,  1469. 
Overshot  wheel,  described,  1336. 
Oxidation  of  1  lb.  carbon  with  per- 
fect eflficiency,  equivalents  of, 
table,  91. 
Oxide,  in  chem..  defined,  321. 
Oxy-acetylene  name  for  cutting  steel- 
work, 833. 
Oxygen, 
boiling  point  of,  514. 
ckem.,Zl9. 
compounds,  in  min.,  classification 

of,  326. 
physical  properties  of.  table,  514. 
Oxy -hydrogen  flame,  317. 
Osone,  chsm.,Zl9. 


Paint,  paints.  355. 

adulterants.  355. 

aluminum,  how  made.  356. 

bronze,  how  made,  357. 

coal  tar,  (ref.)  374. 

driers,  356. 

for  concrete,  (ref.)  375. 

house,  356. 

iron  ground  for,  329. 

solvents,  356. 

vehicles,  355. 

white  lead,  329. 

zinc  white,  329. 
Painting 

and  sand-blast  cleaning,  373. 

by  compressed  air,  with  cost,  374. 

iron  ana  steel,  358. 

metal  work,  for  buildings,  820. 

steel  at  the  mill,  373. 
Palladium,  chem.,  319. 
Panama 

and  Nicaragua  routes  compared. 
1324-1828. 

canal, 
distance  via.,  between  Atlantic 
and  Pacific  ports,  Uble.  1328. 
excavation,  cost  data,  916. 
steam  shovel   work,   cost   data, 
919. 
Panclastite  explosives.  353. 
Panel  boards,  elec.  code  rules,  1489. 
Paper 

measure,  table,  96.^^^!^ 

weight  of,  480.    -^OOglC 


1582 


INDEX. 


PappuB't  theorem,  34S. 
Parabola, 
any  base  and  altitude,  to  draw. 

268. 
area  of.  by  calctUtis.  275. 
cubic-.  1013. 
equation  of,  257. 
normal  to,  258. 
Ungent  to.  258. 
intersection  with  circle,  258. 
moment-,  to  draw,  688. 
properties  of,  287. 
radius  of  curvature  of,  258. 
to  draw,  288. 
Paraboloid, 
mensuration  of,  254. 
volume  of,  by  calculus,  277. 
Parabolic 
arch,  761. 

arcs,  lengths  of.  table.  288. 
cable  of  stxspension  bridge,  750. 
conoid,  mensuration  of.  254. 
motion  (of  projectile),  285. 
oval,  curve  of.  (ref.)  765. 
segment,  287. 

(half-),  properties  of,  629. 
spandrel,  237. 

properties  of.  529. 
vertical  curves,  (R.  R.).  106. 
Paraffin, 
compounds,  obtained  from  petro- 
leum. 1133. 
expansion  coefficient  of,  516. 
weight  of.  480. 
Parallelogram, 
area  and  dennition,  203. 
defined.  128. 
properties  of.  525. 
Parallelopipeds.  defined,  133. 
Parameter  of  catenary,   values  of, 

Uble,  762. 
Paris  green,  330. 
Parmley's  weir  formula,  1180. 
Partial  payments,  63. 
Partitions, 
building,  812. 
expanded  metal,  814. 
hollow-tile.  813. 
lumber  (fir),  classified,  389. 
plaster  board.  813. 
wire  lath.  813. 
wooden.  813. 
Paste,  flour,  402. 
Patent  hammer,  described,  429. 
Pavement, 
asphalt, 
construction  of,  1100. 
specifications,  1104.  1110.  1125, 

1128, 
block,  specifications,  1122. 
rock,  specifications,  1126. 
sheet,  refined  .specifications,  1126. 
Belgian  block,  described.  1100. 
bitulithic.    specifications.  1106, 

1126. 
bituminous-rock,  1100. 
boulder,  specifications.  1107. 
bnck, 

-block,  specificatiors.  1105. 


Pavcmentj— Orat'd. 
brick,— Cont'd, 
cost,  (ref.)  1142. 
described,  1100. 
specifications.  1109.  1129. 
street,   proper  constnsctsoci    oC 

uoA. 

broken-stone,  constractkm  of, 

1099. 
cedar  block,  specifications.  1116, 

1128. 
cement,  described,  1099. 
cobblestone,  construction  of.  1099. 
concrete,  specifications,  1128. 
grading  for  street,  specifications, 

1127. 
granite-block,  specifications,  1 102. 

1108.  1119. 
petrolithic.  specifications.  1112. 
reinforced  concrete  base  for,  (ref.) 

1112. 
sandstone    block,    spedficatsona, 

1124. 
dag  (iron)  block,  specifications, 

1121. 
specifications,  1101. 
traction  on.  1097. 
vitrified  brick,  specifications.  1121. 

1128. 
wood  block, 
construction  of,  1099. 
creosoted.  specifications,  1126. 
specifications.  1120. 
Paving 
a  country  road  with  brick,  cost, 

1141. 
blocks, 
asphalt.  1100. 

specifications,  1122. 
cedar,  «>ecifications,  1128. 
granite.  1102. 

iron  slag,  tpecificatkms,  1121. 
sandstone,  specifications.  1124. 
sise  of.  1129. 
vitrified   brick,  specifications, 

1121. 
wood, 
creosoting  treatment,  1126. 
grooved,  1120. 
specifications.  1120. 
brick.  415. 
-block.  «)ecifications,  1105. 
specifications,  1124. 
stse  of.  1129. 
strength  of.  507. 
cedar  block,  specifications.  1138. 
cement,  specifications,  1121. 
concrete,   for  streets,    cost,  etc^ 

(ref.)  1142. 
granite-block,  specifications.  1105. 
practice  m  (Chicago,  crowning,  IMl. 
Payments, 
equation  of.  61. 
partial,  68 
Pean  hammer,  described.  429 
Peat,  pressed,  weight  of,  480. 
Peck,  pecks. 
(U  S.),  and  dekaliters,  eqmv  (I- 


S.). 
10). 


Uble. 


S^ogle 


INDEX. 


15S3 


Peck,  pecks,— Cont'd. 

(U.  S.),  and  liters,  equiv.  (1-10). 

table,  84. 
equivalents.  67. 
metric  equivalents.  68.  84. 
Pecul  (Philippine  weight).  English 

equivalent.  81. 
Pelton  water  wheels, 
qulntex  nozzle,  table.  1342. 
single  nozzle,  table.  1338-1341. 
Pendulum, 
circular,  287. 
compound  drctilar,  287. 
cycloidal,  287. 
simple  circular,  287. 
Pennyweight  (troy),  metric  equiva- 
lent, 86. 
Penstock  design,  economic,  1332. 
Pentagon, 
defined,  129. 
inscribed  in  circle.  131. 
mensuration  of,  204. 
to  construct,  131. 
People,  load  of  crowd  of.  815. 
Percentage,  interest  and  discount, 

68. 
Percussion 
caps,  368. 

fulminate  of  mercury  in.  352. 
center  of.  808. 

of  pendulum,  287. 
driU,  described,  422. 
rock-drills, 
dimensions,  etc..  table.  424. 
weights,  etc.,  table.  424. 
Perimeter 
of  ellipse,  289. 
of  polygon.  129.  204. 
of  triangle,  defined,  128. 
Periodic  law.  in  chsm.,  322.  323. 
Permutation  and  combination.  56. 
Perspective,  261. 

Peso  (Mexican),  equiv.   (1-10.-60- 
100-)  in  17.  S.  money,  table.  97. 
Petroleum, 
crude-, 
products  from,  in  refining.  1133. 
test  properties.  1134. 
heat  of  combustion  of.  1370. 
residuums.  test  properties^  1 1 34. 
Petrolithic  pavement,  specifications, 

1112. 
Pewter.  398. 
expansion  coefficient  of,  516. 
weight  of.  480. 
Phase,  single-,  alternator,  defined. 

1384. 
Philippines,  weights  and  measures, 

English  equivalents,  81. 
Philoriers  mixture  or  freezing.  613. 
Phcenix  columns,  properties  and 

safe  loads,  tables.  004.  605. 
Phosphates,  in  tmn.,  classification 

of.  327. 
Phosphor  bronze.  397. 

physical  properties  of.  table,  497. 
Phosphorus.  CMm.,  319. 

weight  of.  480. 
Photometry  and  lamps,  in  eUc.,li7Z. 


Pi  («). 
circular  measure,  99. 
table  of  combinations  of,  with  logs, 

206,  206. 
times    any  number,  tables,  224- 
229 
Pick,  stone-,  described,  428. 
Pickling,  for  mill  scale,  368. 
Pie   (Philippine   measure),   English 

equivalents,  81. 
Pier,  piers, 
concrete  pUe.  for  steamship  termi- 
nal, (ref .)  900. 
construction,  893. 
crib,  877. 
cylinder,  878. 

frictional  resistance  of,  878. 
docks  and  wharves,  892. 
masonry,  888. 

contents  of,  889. 
pile,  877. 

platform  cylinder,  879. 
pneumatic  cylinder,  879. 
reinforced  concrete,  (ref.)  890. 
river,  889. 

steel,  in  Africa,  (ref.)  900. 
tubular.  877. 
Pierhead  and  bulkhead  lines.  892. 
Piezometer  tubes,  1174. 
Pig  iron, 
manufacture  of,  892. 
use  of,  392. 
Pigments  for  paints,  866. 
Pile,  piles. 

-and-timber  trestles.  790. 
bearing  power  of.  819. 

in  various  materials.  890. 
concrete.  876. 

creosote  in,  analysis  of,  370. 
cutting  off,  874. 
dead-men-,  874. 
disk,  874. 
drivers.  871. 
derrick.  873. 
droi>-hammer,  872. 
portable,  873. 
power  for.  873. 
steam-hammer,  872. 
tilting-,  (ref.)  890. 
driving, 
formulas.  871. 
water  jet  in.  873. 
false.  788. 
fender-.  898. 
foundations,  871. 
iron.  874. 

maximum  load  on.  787. 
metal-^ell,  concrete,  876. 
piers.  877. 
concrete,  for  steamship  terminal , 
(ref.)  900. 
planted.  874.  • 

-pulling  machines,  (ref.)  871. 
reinforced  concrete,  875. 
safe  bearing  power  of,  table,  872. 
sand.  875. 
screw.  874. 
shoes.  874. 
supporting^^w^^^gj^ 


1584 


INDEX. 


Pile,  piles,— Cont'd, 
spadng  and  driving,  874. 
spli^.  874. 
trestles,  787. 
water-jet  ooncxete,  876. 
Piling, 
cost  of  creoflottng,  S60. 
preservation  of,  860. 
sheet-.  860. 
Pillars,  (see  Colvimns). 
Pilot-nuts.  629. 
Pin,  pins, 
bending  moments  of,  table.  630. 
bending  stresses  on,  specifications, 

704. 
bridge-,  620. 
colter-,  620. 
lateral-.  629. 
-nuts,  table.  620. 
plates,  for  bridges,  706. 
steel-j  properties  of.  table,  630. 
Pine,  pines, 
expansion  coefficient  of,  516. 
classification  of,  341. 
Pint, 
(apoth),  metric  equivalents,  83. 
(dry),  metric  equivalent,  84. 
(liquid),  metric  equivalent,  83. 
metric  equivalents,  68. 
Pipe,  pipes, 
or  butt  (liquid),  equivalents,  83. 
and  tubes,  677. 

references,  682. 
areas  of.  forgiven  diameters,  table, 

1157. 
bell  and  spigot,  1215. 
black  or  galvanized,  table,  1284. 
block  tin,  679. 
branches,  cast  iron, 
L's,  T's,  crosses,  tables,  1225, 

1250-1254. 
Y's,  tables,  1227.  1228.  1255. 
1256. 
cast  iron,  1214. 
and  specials,  weights  and  dimen- 
sions of .  tables,  1219-1267. 
flange,  table,  1236. 
for  various  pressures,  table,  1216. 
formulas  for  designing,  1215. 
friction  heads  in,  table,  1217. 
hemp  required  per  joint,  1216. 
jute  required  per  joint,  table, 

1222. 
lead  required  per  joint,  1216; 

table,  1222. 
specifications,  1239. 
variation  allowed,  1222. 
weights  and  dimensions,  tables, 

1220,  1222.  1243-1246. 
weight  of.  table,  1216. 
caulking  with  lead  wool,   (ref.) 

1293. 
coating,  Sabin  process,  358. 
Converse  patent  lock  joint,  table. 

1282. 
crosses,  Matheson,  table.  1281. 
culvert,  tables,  1307. 
curves,  cast  iron,  tables,    1224, 
1248,  1249. 


Pipe,  pipes, — Cont'd, 
diameters  and  equivalent  i 

table.  1157. 
dia.  to  area,  capacity,  mean  radius, 
volume,  weight  (water),  table 
246-247. 
dipping  tank.  1282. 
dischaxge  through  small,  table, 

1284. 
drain-,  1296. 
flexible  joint,  cost,  1238. 
flow  of  steam  through,  fonntila 

and  table.  1361. 
fk>w  of  water  in.  measurement  oC. 

1183. 
for  water  worics,  cost.  1293. 
friction  losses  in.  defined,  1161. 
friction  of  air  in  small,  formulsi. 

1189. 
glazed  (salt-),  for  water  supply. 

1207. 
increasers,  Metheaon,  table,  1281. 
iron-,  cement.  402. 
joints, 
caulking.  1216. 

mortar  required  for,  table.  1 309. 
sewer, 
cement  and  sand  required  for, 

table.  1309. 
sulphur  and  sand  required  for, 
table.  1310. 
kalamein.  tables.  1281.  1282. 
lap-welded.  1269. 
-laying.  1215. 
notes,  1219. 
lead, 
hydrostatic  pressure  for.  679. 
tables,  679. 
line, 
economic  size  of.  for  power  in- 

sUllation.  1189. 
gains  and  losses  in.  1154. 
hydraulic  notation  used  in,  1 154. 
hydraulic  terms  used  in.  1154. 
losses  in  during  flow.  1 158. 
practice    of   increasing  the  dia- 
meter. 1156. 
locking-bsir  joint,  1269. 
Matheson  patent  lock-joint,  tables. 

1281. 
plugs.  Matheson,  table.  1281. 
pressure-, 
attachments.  1269. 
in.  hydrostatic.  1 152. 
reducers,  Matheson.  table,  1281. 
riveted  steel,  design  of.  1268. 
sewer,  tables,  1307. 
soil-.  1295. 

specials,  cast,  described,  1280. 
spiral  riveted,  1269. 

steel,  680-682. 
steel.  1268. 
experimental  values  of  N  in  Kut- 
ter's  formula  for  flow  in.  1188, 
tees.  Matheson^  table.  1281. 
theoretic  velocities  of  flow  in, 

table.  1155. 
velocity  ratios  to  area  and  diam- 
eter, 1158.^  ^ 

Digitized  by  UOOgle 


INDEX, 


1586 


Pipe,  pipeB,— Cont'd, 
waste-.  1296. 

wood-,  bored  and  banded.  1208. 
wooden  (bored),  for  water  supply. 

1207. 
wood  stave, 

and  cast  iron  connection.  1280. 
and  details,  table.  1210. 
details  of.  1208. 
durability  of.  1187. 
flow  of  water  in.  (ref.)  1187. 
wrought  iron,  1268. 
welded,  standard,  tables,  677. 678. 
Pitch 
and  tar  for  waterproofing,  418. 
of  screw  thread,  618. 
weight  of,  480. 
-fac^  masonry,  defined,  432. 
Pitot-tube 
meter.  1183.  1184. 
rating,  (ref.)  1180. 
Plane,  planes, 
coordhiate,  182,  261-266. 
geometric, 
angles  and  lines.  132. 
determination  of,  132. 
geometry,  128-181. 
inclined, 
in  ntech.,  formulas,  202. 
motion  on,  286. 
velocities  on,  286. 
revolved,  261,  262.  266. 

volumes  of.  by  calculus,  277. 
-table,  (ref.)  lioO. 
the,  projection  of,  268,  264. 
trigonometry.  136-108. 
two,  to  find  angle  between,  265. 
Planing, 
in  bndge  work,  706. 
lumber,  379. 
cost  of,  379. 
Plank, 
classification  of.  888. 
gutters,  described.  1098. 
roads,  described.  1098. 
sidewalks,  described.  1098. 
Planking,  classification  of.  388. 
Plaster, 
expansion  coefficient  of.  516. 
gypsum,  weight  of.  table,  481. 
lime.  403. 
of  paris.  404. 
how  made.  389. 
manufacture  and  use,  404. 
physical  properties  of,  512. 
weight  of.  480. 
ordinary,  481. 
Plastered  ceiling,  beam  calculation, 

564. 
Pktstermg,  building,  812. 
Plate,  plates, 
bearing  value  of  pins,  table.  630. 
circular,  moment  of  inertia  of,  302. 
fiange,  of  plate  girders,  properties 

of.  table,  580. 
flat, 
(jirashof's  analvsis  of,  (ref.)  586. 
washers,  weignts  and  dimen- 
sions, table,  624. 


Plate,  plates.— Cont'd, 
girders, 
economic  depth  of.  684. 
steel,  properties  of,  table,  570- 

spedfications.  704. 
steel, 
areas  and  weights,  table,  544. 
ga^e  and  weight,  table,  067. 
weight  and  areas,  table,  544. 
web,  of  plate  girders,  properties  of, 
table.  5757 
Platform  cylinder  piers.  879. 
Plating.  367,  858. 
Platinum,  ehem.,  819. 
cast,  etc.,  table,  481. 
expansion  coefficient  of,  516. 
-iridium, 

alloy,  composition  of.  516. 
expansion  coefficient  of,  516. 
melting  point  of,  515. 
minerals.  328. 

wire,  tensile  strength  of.  498. 
Platting  angles,  methods  of,  959. 
Plenum  process,  879. 
Plug,  plugs, 
and  feathers,  described.  426. 
cast  iron  pipe,  tables,  1234.  1267. 
Metheson  pipe,  table,  1281. 
Plumbago,  weight  of,  481. 
Pneumatic 
caissons,  880. 
caulking  of  mains  with  lead  wool, 

costs,  (ref.)  1293. 
cylinder  piers,  879. 
foundations.  880. 
process.  879. 

stone-dressfaig  machine,  (ref.)  430. 
Point, 
stone-,  described.  428. 
(the),  projection  of,  262. 
Pointing,  masonry, 
defined.  432. 
specifications,  484. 
Pokr 
distance, 
of  a  circle,  defined,  135. 
of  a  star,  defined,  202. 
of  Polaris  for  latitude  (f^,  949. 
moment  of  inertia.  535-538. 
maximum  and  minimum  values. 
637. 
Polaris, 
azimuth  of, 
at  elongation.  950. 
tables.  954-955f . 
how  to  find.  948. 
observations  of,  951. 

for  azimuth.  949. 
polar  distances  of.  for  latitude  (P, 

table.  949. 
time  of  upper  culmination  of,  table 

953. 
to  determine  meridian  from,  948. 
Pole,  poles, 
concrete  telegraph,  1477. 
cost  of  creosoting.  374. 
(geom.)  of  a  circle^  define<l.  134. 
iro"'  373.     tized  by  Google 


1586 


INDEX. 


Pole,  poles,— Cont'd, 
lines,  elec.  code  rules,  1400. 
of  celestial  sphere,  defined,  201. 
preservation  of,  373. 
reinforced  concrete,  (ref .)  1 142. 
wooden, 
for  electric  line,  373. 
life  of.  373. 
PolyKon,  polygons, 
definitions  of,  120. 
(seneral),  properties  of.  120. 
€i  forces,  206. 
regular, 
area  of,  120. 
formulas  and  table,  204. 
prooerties  of,  120. 
Polyhearons. 
(geom.),  132. 
regular,  table,  243. 
Polyphase  alternator,  defined.  1384. 
Poplars,  classification  of,  348. 
Population  of  cities  in  U.  S..  1202. 
Porcelain,  expansion  coefficient  of, 

616. 
Porch  decking  lumber  (fir),  classi- 
fied, 380. 
Portable  conductors,  elec.  code  rules, 

1448. 
Portalj  portals, 
bracmg,  of  bridges,  608. 
bridge-,  types  of.  608. 
skew-,  detailing,  (ref.)  666. 
Portland  (dement  (sec,  also,  Cement, 

Portland). 
Portland 
cement, 
cost,  418. 

manufacture  of,  404.  406 
concrete  (sec  Omcretc,  Portland), 
stone,  manufacture  of,  417. 
Posts,  wooden, 
preserving,  361. 
trestle,  788. 
Position  line,  of  an  arch,  782,  783. 
Potash,  weight  of,  481. 
Potassium,  chem.,  310. 
minerals,  328. 
weight  of,  481. 
Potential  energy,  defined,  1346. 
Pound,  pounds, 
and  kilograms,  equiv.  (1-10), 

table,  86. 
fapoth.),  metric  equivalents,  86. 
(avoir.),  and  kilograms,  equiv., 

80. 
avoirdupois  and  troy,  equiv^  67. 
(avoir.),  metric  eqtuvalent,  o6. 
-calorie  (Lb.-Cal.),  defined,  1347. 
-<iegree  (Fahr.),  equivalents  of,  00. 
(dollars  per) 
and  francs  per  kilogram,  equiva- 
lents (1-10),  table,  08. 
and  marks  per  kilogram,  equiva- 
lents (1-10),  Uble,  08. 
kilograms  and  tons,  equiv.  (1-10), 

table.  87. 
metric  equivalents,  68. 
per  cu.  ft.  and  kilograms  per  cu. 
meter,  equivalents,  80. 


Pound,  pounds,^— Cont'd, 
per  cu.  in.  and  grams  per  ca. 

centimeter,  equiyalents,  80L 
per  sq.  ft.  ana  lajognuns  per  aq. 

meter,  equivalents,  89. 
per  sq.  in.  and  Idlograms  per  sq. 

centimeter,  equivalents,  80. 
(troy),  metric  equivalent,  86. 
i£)  sterling  (British),  equivalents 

(1-10,-60-100)  in  U.  S.  mcney. 

Uble,  07. 
Powder, 
Aetna,  364. 
AUas,  362.  864. 
black,  360. 
blasting. 


Power 
and  heat  problems,  1360. 
and  work  equivalents,  metric  and 

English,  table,  00. 
comparative   cost   of   electricity, 
gas.  gasoline  and  steam   for, 
(ref.)  1378. 
electric-, 
and  lighting,  1370. 
cost  data,  table.  1478. 
sources  and  uses  of.  1886. 
transmission  of,  1 385. 
-factor,  in  0l»c.,  1463. 
horse-,  (see,  also.  Horsepower), 
mechanical,  equivalents  of.  M. 
electric,  equivalents  of,  90. 
metric,  equivalents  of,  00. 
equivalents  of,  01. 
in  fH€ch.t  equations  of,  201. 
of  a  horse,  1007. 
plants, 
electric  and  steam,  costs,  1477. 
railway,  elec.  code  rules,  1308. 
solar-,  reference  data,  1484. 
steam  and  gas,  1346. 
steam-  and  water-,  compared,  1 885. 
uniu  of.  201. 

electrical,  1370. 
water-  installation,  economic  «Be 
of  pipe  line  for,  1180. 
Powexs, 
and  multiplication,  algebraic,  ex- 
amples in,  101. 
fifth,  engineers'  table.  26-27. 
of  numbers,  by  logarithms,  106L 
roots  and  reciprocals  of  mimb«rL 
14-64. 
Pxaseod3rmiiim,,^fc^m.,  310. 

tizedbyLiOOgTe 


INDEX. 


1587 


Pratt  trtiss, 
calculation  of.  306. 
chord  stresses  in.  concentrated 

loads.  696. 
graphical  solution  of.  312. 
Precipitation, 
average  monthly,  in  United  States, 

1101. 
defined.  1190. 
high  intensities  of,  formulas,  1196' 

1197. 
in  U.  S.,  for  driest  years.  1194, 
1196. 
Preliminary  siu-«^y  (R.  R.),  1000. 
Preservation 
of  iron  and  steel,  368. 
of  timber,  369. 
Preservatives,  366. 
Pressure, 
artesian-,  defined,  1190. 
atmospheric,  1146. 
center  of.  846,  847. 
formulas,  1160. 

on   vertical  orifices  and   weirs, 
table,  1151. 
critical, 
defined.  618. 


of  gases,  table.  614. 
of  uquids,  table.  614. 


uqiut 
earth-. 

Rankine's  theory.  839-840. 
theories.  836-840. 
head  in  pipe  lines,  1160. 
hydrostatic-, 
for  lead  pipe.  679. 
formulas,  1146. 
on  dams.  846. 
in  pipes,  hydrostatic.  1162. 
in  tanks,  hydrostatic,  1162. 
of  train  on  curve,  problem.  297. 
of  water, 
for  given  heads,  tables,  1148, 

1149. 
reduced  to  equivalent  heads, 
table.  1147. 
on  masonry, 
allowable.  826. 
for  bridges.  706. 
on  submerged  planes,  846.  847. 
-pipe  attachments.  1269. 
relief  valves,  described.  1288. 
units,  hydrostatic.  1146. 
wind-,  794. 
Price  current-meter,  1186. 
Prices  per  imit  weights  and  meas« 
ures  (metric  and  English)  .com- 
parison of,  equivalents  (1-10), 
table.  98. 
Primary  or  storage  batteries,  elec. 

code  rules.  1398. 
Prime,  primes, 
vertical,   of  celestial   sphere,   de- 
fined, 201. 
multiples  and  factors,  table,  3-6. 
Prism,  prisms, 
area,  volume,  224. 
g9om.,  133. 

truncated,  defined.  133. 
volume  of.  133. 


Prismoidal 

correction 
formula,  earthwork.  1066. 
table,  earthwork,  1067. 

formula, 
earthwork,  1066. 
for  contents  of  piers,  889. 
general.  243. 
Principle,  artesian-,  defined,  1190. 
Produce,  weight  of.  478.  482. 
Profiles  and  grades,  railroad,  1004. 
Proerression. 

Arithmetical.  67. 

Geometrical,  67. 
Projectiles, 

motion  of,  286. 

velocity  and  height  of,  table.  288. 
Projection, 

Cabinet.  261. 

Isometric,  261. 

of  right  lines,  262,  263. 

of  the  plane,  363.  264. 

of  the  point.  262. 

Orthopnntphic,  261. 
Properties  of  plane  surfaces,  tables. 

624. 
Proportion 

and  ratio,  66-66. 

by  segments  of  chords  of  circle, 
131. 
Proportional,  mean-,  66. 

in  semicircle,  131. 
Proximate  analysis  of  fuels,  1360. 
Puddling, 

cast  iron,  392. 

effect  on  earth  fill,  910. 
Pulley^  in  nutch.,  formulas,  292. 
Pulsation   and    variation,    in   eiec, 

1453. 
Pulverizer,  for  cement  making.  406. 
Pulverizing  process,  in  cement  mak- 


Pumice  stone,  weight  of.  481. 
Pump,  pumps, 

duty  of.  formula.  1367. 

explosion-,  direct-acting.  1378. 

steam-.  1366.  1367. 
Pmification  of  water,  1204. 
Purlins,  roof-,  weight  of  steel  in,  810, 

811. 
Pyramid,  pyramids. 

altitude  of,  defined.  133. 

frustum  of.  defined.  134. 

gtom.,  133. 

mensuration  of.  248. 

of  sphere,  defined,  136. 

spherical,  solution  of,  199. 

volume  of,  133. 
Pyramidic  frustum,  mensuration  of, 

248. 
Pyroxylin,  manufacture  of.  361. 


Quadrant,  quadrants, 

geom.,  defined.  136. 

of  circle,  defined,  129. 

trig.,  the  four.  137. 
Quadratic  equations,  squaring,  102. 


1688 


INDEX, 


OuadriUterals, 

defined.  128. 

mensuration  of,  203. 
Ouarry-faced 

masonry,  defined.  432. 

stone,  defined.  427. 
Ouarrying,  419. 

block  stone.  419. 

by  compressed  air,  423. 

channelmg  machines  in,  420. 

cost  of.  423. 

drills  used  in.  422. 

explosives  in,  422. 

flagstones.  419. 

gravel  and  sand.  419. 

machines  used  in,  419. 
Inprap.  419. 

sand  and  gravel.  419. 

stone,  building.  419. 

tools  used  in.  419. 
Quart,  quarts. 

and  liters,  equivalents.  88. 

dry. 
and  liters,  equiv.  (1-10).  table, 

84. 
metric  equivalents,  84. 

equivalents,  67. 

liquid, 
and  liters,  equiv.  (1-10),  table, 

83. 
metric  equivalent.  83. 

metric  eqmvalents.  68. 
Quarter 

(avoir,  wt.),  metric  equiv.,  86. 

section  (16(ki.)  and  hectars,  equiv- 
alents. 88. 
Quartz, 

cnrstal,  weight  of,  481. 

uses  of,  331. 
Quicklime, 

made  how.  408. 

specific  gravity  of,  408. 
Qtuntal  (metric),  English  equiv.,  86. 
Quire,  paper  measure.  96. 
Quoin,  masonry,  defined.  432. 


Rack  railways,  (ref .)  1095. 
Radian  (>r).  circular  measure.  142. 
Radii  of  curves  (R.  R.),  tables,  1007. 
Radio-activity  of  matter.  316. 
Radium,  cfunn,,  319. 
corpuscles  in,  316. 
energy  of,  316. 
from  uranites,  830. 
Radius 
and  diameter,  circular  measure,90. 
of  circle,  defined,  129. 
of  curvature 
of  cycloid.  260. 
of  ellipse.  269,  766. 
of  parabola.  268. 
of  gyration 
of  circular  beam.  300. 
of  plane  section,  299,  300. 
of  plane  surfaces,  table,  524. 
of  solids,  302. 
problem  in,  687. 


Radius— Cont'd. 

of  polygon,  129. 
Rail.  raUs, 

and  fastenings,  (R.  R.).  1060. 

braces,  1071 

elevation  on  curves,  formula.  29& 

joints,  kinds  of,  1068. 

manganeae-fiteel,  oo  ciirves,  inL), 
r094.  -.V*     / 

secrtions,  standard.  1060-1063. 
steel. 

chemical  properties  of.  603. 

dimensions  and  weights,  table. 
560. 

properties  of,  table,  560. 

specifications,  503. 

testing,  503. 

traction  on,  1097. 

weights  and  dimensions,    table, 

T-,  for  street  railway  tracks,  (ref.) 

1142. 
weight  of,  per  mile,  table.  1063. 
Railroad,  railroads.  991. 
bridges,  688. 

references,  713. 

reinforced  concrete,  712. 

steel-, 
specifications  for.  600. 
weight  of,  710. 
construction.  1016. 
curves.  1005. 

problems,  1011. 
excavation,  cost  data,  916. 
grading, 

economic  problem.  269. 

with  wheeled  scrapers,  cost  data 
917. 
k>cation.  998. 

filing  with  State.  1013. 
masonry,  classification  of,  431. 
mileage  tn  U.  S..  991. 
projection  of,  991. 
reconnoissance,  998. 
right-of-way,  1018. 
spikes, 

table.  627. 

wei^t  per  mile  of  track,  table 

ties.  1060. 
trestles,  787. 
cost  of,  793. 
Railway 
bridges,  steel-,  weight  of.  forma- 

las.  686. 
curvcj  to  lay  out,  130. 
electric  motors,  1471. 
embankments,  shrinkage  vertical 

in.  916. 
inclined-,  1001. 
location,  tables,  (ref.)  1092. 
power  plants,  elec.  code  rulessl3^ 
rack-,  (ref.)  1095. 

trestles,  steel-,  weight  of,  formnSa, 
686. 
Rainfall, 
and  runoff  in  storm  sewers,  fortm.- 


lasj  diagraaug^Uibleft,  (ret' 


1310. 


INDEX. 


1689 


Rainfall,— Cont'd 
average  monthly,  in  U.  S.,  tabic, 

1191. 
data  most  useful  to  engineers,  1 1 90. 
distribution  of,  1190. 
high  intensities  of,  formulas,  1 195-- 

1197. 
in  U.  S.,  for  driest  years,   1194, 

1196. 
relation  of,  to  runoff,  in  California, 
(ref.)  1201. 
Rain-gage,  standard,  1196. 
Rain-water,  weight  of,  482. 
Randoms,  in  surv.t  correction   of, 

976. 
Random-work  masonry,  defined  .432. 
Range-work  masonry,  defined,  432. 
Rankine's  theory  of  earth  pressure, 

83(K840. 
Ransome  stone,  manufacture  of,417. 
Rapid  sand  filtration.  1204. 
Rating, 
electrical-,  1464. 
pitot-tube,  (ref.)  1189. 
Ratio  and  proportion,  66-66. 
Rattler  test  for  bricks,  607,  1116. 
Reaction,  reactions, 
and  moments,  296. 
breakwater,  906. 

drawbridge-,  tables.  744,  746,  747. 
floorbeam-. 
for  concentrated  loads,  table. 

694. 
for  highway  bridges,  table.  728. 
from  electric  cars,  tables.  717, 
718. 
in  stTuc.,  in  any  direction,  314. 
of  forces,  296. 
to  find.  306. 
Reactive 
coils  and   condensers,   elcc.   code 

rules.  1443. 
-factor,  in  ei^c.,1453. 
Ream,  paper  measure.  96. 
Reaming,  in  bridge  work,  706. 
Reciprocals, 
by  slide  rule.  126. 
common  tables.  61-64. 
engineers'  tables,  28-29. 
powers  and  roots  of  nxmibers,  14- 

64. 
to  find,  30. 
Reconnoissance  survey.  (R.  R.),  998. 
Rectangle,  rectangles, 
angular  axis,  properties  of,  625. 
area  and  cen.  of  grav.,  203. 
axis  at  base,  properties  of,  626. 
defined,  128. 

diagonal  axis,  properties  of,  626. 
holfow-,  properties  of.  626. 
moments  of  inertia  of,  table,  639- 

640. 
properties  of,  626. 
skeleton  section,  properties  of ,  630. 
Rectangular 
beams, 
formulas,  663. 
loads  on,  table.  666. 
cell,  skeleton,  properties  of,  530. 


Rectangular — Cont'd, 
conduits,  proportioned  for  maxi- 
mum discnarge,  1161. 
orifices,  center  of  pressure  on, 
formulas,  1151. 
Red 
heart,  in  lumber,  defined,  387. 
lead 
for  paint,  366. 
paint.  369. 
weight  of,  481. 
oxide  for  paint,  366. 
rays,  length  of,  1380. 
Reducers, 
cast  iron  pipe.  Ubles.  1233.  1259- 

1264. 
Matheson  pipe,  table,  1281. 
Redwoods,  classification  of,  342. 
Refraction, 
defined.  1520. 
and  curvature,  table,  088. 
Refuse  disposal,  1296. 
miscellaneous  data,  (ref.)  1309- 
1312. 
Regenerative  method  of  liquefying 

gases.  613. 
Register  current-meter.  1186. 
Relation,  electrical-.  1461. 
Reinforced  concrete,  443. 
aqueduct.  1208. 
arch  bridges,  cost  of,  784. 
arches,  reference  data,  784. 
beam,  beams, 
diagram,  (ref.)  686. 
formulas.  444.  447. 
table.  446. 

tests,  formulas,  (ref.)  585. 
Thacher's  computation.  586. 
time  element  effect  in  loading. 

(ref.)  586. 
working  stresses.  586. 
bridges, 
highway,  cost  data,  738. 
ranroad,  712. 
piers,  (ref.)  890. 
buildings,  tmit  stresses  used.  831 
caissons,  for  breakwaters.  904. 
columns, 
formulas,  449. 
working  stresses  for,  009. 
construction, 
building  regulations  for,  by  Nat'l 

Assn.  of  Cem.  Users,  831. 
for  buildings,  822,  834. 
design,  office  methods,  (ref.)  466. 
economic  design  of.  (ref.)  586. 
flat  plates,  methods  of  computing 

(ref.)  586. 
floors,  instruction  sheet  for  plac- 
ing, (ref.)  586. 
formulas  of  A.  S.  C.  E.,  446. 
French  Gov't  rules,  (ref.)  454. 
in  buildings,  references,  830-834. 
jetty-head,  (ref.)  905. 
members  separately-molded,  cost 

data,  (ref.)  831. 
piles,  875. 

proportions  of  mixT'««.o 


1600 


INDEX. 


Reinforced  concrete,— Cont'd, 
references,  4M. 

retaining  waUs.  (ref.)  841-843. 
roadway  base,  (ref.)  1112. 
slabs,  slide  rule  for.  (ref.)  686. 
T-beam  and   column   tests,  (ref.) 

686. 
trestles.  702. 
use  of,  (ref.)  466. 
wharf,  (ref.)  000. 
Reinforcement,  steel,  in  beams,  ten- 
sile stress  value,  686. 
Relief  valves,  pressure-,  described. 

1288. 
Reluctance,  magnetic-,  formula.  1620. 
Repeated  stresses,  defined,  487. 
Reports  and  valuations,  expert, 

reference  data,  1484. 
Repose,  angle  of.  for  various  sub- 
stances. 617-621. 
Reservoir,  reservoirs,  1206. 
aerating  fountain  in,  1206. 
concrete  expansion  j<»nts  in.  464. 
distributing,  1206. 
linings,  1206. 
miscellaneous  data,    (ref.)    1201- 

1204. 
outlet  pipe  from,  how  arranged, 

storage-.  1206. 

walls,  waterproofing  for,  418. 

waterproofing,  1208. 
Residuums  from  refining  crude  oil, 

1133. 
Resilience,  488. 

elastic,  defined,  488. 

formulas,  488. 

modulus  of,  defined,  488. 
Resin, 

a  tree  product,  346. 

defined,  481. 

mastic,  weight  of.  480. 

weight  of,  481. 
Resistance 

boxes,  elec.  code  rules,  1306,  1440. 

electric-,  formula,  1620. 

insulation-,  elec.  code  rules,  tables, 
1447.  1460. 

line  of,  of  masonry  arches,  768. 

of  materials,  486. 
Resisting 

and  bending  moment  of  beams,  298. 

moments,  problem  in,  637. 

forces,  in  mech.,  204. 
Resultant 

of  a  distributed  force.  206. 

of  two  velocities,  284. 

velocities.  284. 
Restitution,  coefficient  of,  804. 
Retaining 

plank,  street,  specifications,  1111. 

stone,  street,  specifications,  1100. 

walls.  835. 
dimensions  of,  table.  842. 
dry,  specifications,  436. 
masonry,  specifications,  434. 
qmntitxes  in,  table,  841. 
reference  data,  841-843. 
•tandard  type,  841. 


Return  wires,  elec.  code  rules,  1400. 
Reversed  curves,  (R.  R.).  1012. 
Revetments,  reference  data,  148L 
Revolved  planes.  261,  262,  265. 
Rheostats,  elec.  code  rules,  1308, 

1443. 
Rhodium,  ctmn.,  310. 
Rhomboid, 
defined,  120. 

area  and  cen.  of  grav.,  203. 
properties  of,  626. 
Rhombus, 
defined,  120. 
and  area,  203. 
RhyoHte. 
composition  of,  table,  338. 
defined.  340. 
formation  of,  table,  338. 
Right 
angle,  circular  and  time  meastire. 

equivalents,  00. 
ascension,  of  a  star,  defined,  202. 
-of-way, 

purchase  and   condemnation. 

1014. 
railroad-.  1013. 

required  widths  of,  table.  1014. 
tabkA,  1014,  1016. 
Ring,  rings, 
circxilar, 
mensuration  of,  210. 
moment  of  inertia  of,  302. 
segmental,  mensunition  of,  2S3. 
collector-,  defined,  1383. 
regular  circular,  mensuration   of. 

263. 
revolving,  tension  in;  207. 
Riprap,  quarrying,  410. 
Rise  of  temperature,  in  «/#c..  1406. 
River,  rivers, 
mean  velocity  depth  of  thread  in. 

1187. 
spans,  economic  layout  of.  68S. 
Rivet,  rivets.  611. 
button  head.  616. 
countersunk,  616. 
gages  for  standard  steel  shapes, 
table,  614.  ^^ 

shearing  and  bearing  values,  table, 

612. 
signs,  Osbom  code,  611. 
spacing  and  clearance  of,  table. 

613. 
weights  and  dimensions  of,  table. 
616. 
Riveted 
joints, 
application  of  polar  moment  ai 

inertia  to.  (reO  638. 
net  areas  of,  table,  617. 
problem,  612. 
sprrral-,  steel  pipe,  680-682.  1260. 
steel  pipe,  design  of,  1268. 
work,  in  bridges,  specifications, 
706. 
Rivet-steel, 
extra  soft,  specifications,  602. 
Ttre-box.  specifications,  602. 
flange  or  boiler,  spedficatkms.  502 


INDEX. 


1691 


Rivct-stecl,— Cont'd, 
open  hearth,  specifications,  501. 
test  pieces,  602. 
testing.  502. 
Road,  roads, 
and  streeU.  1098. 
application  of  oils  to.  1 1 34. 
construction,  tise  of  tar  in,  1132. 
corduroy,  described.  1098. 
dirt-,  described,  1098. 
dust   preventives,   experiments, 

costs,  1136. 
gravel-,  construction  of.  1098. 
graveled,  oiled,  specifications.  1114. 
macadam 
and  telford.  specifications.  1111. 
specifications,  1116. 
oils  for. 
best  kinds,  1138. 
classification  of,  1138. 
properties  of ,  1133. 
oiling,  cost,  (ref.)  1142. 
plank,  described,  1098. 
sampittic  surfacing  of,  (ref.)  1142. 
specifications,  UOl. 
surfaces, 
application  of  oils  to,  1134. 
application  of  tars  to,  1 1 32. 
care  of.  1131. 
dust  preventives,  1131. 
tars  for,  1131. 
traction  on,  1097. 
surfacing  materials,  tests  of,  table, 

1144. 
tar  macadam,  cost,  1142. 
Roadbed.  sUndard-,  (R.  R.).  1069. 
Roadway, 
board  bed,  specifications.  1128. 
concrete  base,  specifications,  1102, 

1109. 
crushed-stone  base,  specifications, 

1106. 
gravel  base,  specifications.  1102. 
macadam,   specifications.    1106. 

1129. 
reinforced  concrete  base,  (ref.)  1112. 
Rock,  rocks, 
-asphalt,  experiments  on  roads, 

costs.  1138.  1139. 
-breaking  machines,   for  rock  ex- 
cavation, (ref.)  926. 
calcareous,  400. 

cementing  material  in.  table,  334. 
common,, 
notes  on,  339. 
table   334. 
crushed,  voids  in,  911. 
crushers,  capacity,  cost,  etc.,  439. 
crysUl  (haute),  weight  of.  481. 
crystalline,  siliceous.  400. 
cuts, 
open-,  excavation  of,  922. 
side  slopes  for.  922. 
drills,  922. 
in  quarrying.  422. 
Little  Giant.  425. 
percussion, 
dimensions,  etc.,  table.  424. 
weights,  etc.,  table,  424. 


Rock,  rocks, — C  ont'd. 
excavation.  922. 
by  channeling  machines,  924. 
by    Lobnitz    rock  breaker  and 

other  machines,  (ref.)  926. 
Chicago  canal,  924. 
costs,  926. 
methods,  926. 

Panama  canal,  cost  data,  919. 
•fill  dams,  quantities  in,  table.  867. 
formations,  331. 
fragmentary,  401. 
granite,  excavation,  in  open  cuts. 

(R.  R.),  cost.  926. 
loading  on  cars,  by  steam  shovel. 

iMi. 
k>ose.  classification  (R.  R.),  919. 
loosened,  voids  in,  911. 
salt,  composition  of,  336. 
solid, 
classification  (R.  R.),  919. 
foundation,  863.  864. 
swellage  when  broken,  table,  911. 
trench  excavation,  estimating. 92  3. 
trenching  in,  92Z. 
Rod,  rods, 
and  meters, 
equivalenut,  88. 
square,  eouivalents,  88. 
coimter-,  634. 
equivalents,  66. 
floats,  for  hydraulic  measurements, 

li83. 
or  bar,  moment  of  inertia  of.  302. 
square,  metric  equivalent,  81. 
steel. 
areas  and  weights,  table,  542. 
weights  and  areas,  table,  642. 
RoUed 
angle,  properties  of.  638. 
channel,  properties  of.  637. 
T-beam,  properties  of.  537. 
tee,  properties  of,  538. 
shapes,  properties  of,  536-638. 
Z-bar,  properties  of.  538. 
Rollers,  segmental-,  table.  636. 
Rolling 
brick  pavement.  1107. 
friction,  521. 
Roman 
numerals,  table   1. 
system  of  numbers,  1. 
Rdntgen  ray.  316. 
Rood,  metric  equivalent,  81. 
Roof,  roofs.  794. 
angles  and  pitches  of.  table.  796^ 

797. 
coverings.  798. 
live  loads 
for,  824. 
on,  toble.  816. 
pitches  and  angles  of.  tables,  796, 

797. 
reference  data  ,811. 
snow  loads  on,  797,  798. 
tile-,  specifications.  800. 
trusses, 
combination-,  design  of,   806- 
810. 


1602 


INDEX. 


Roof.  roof8,--Cont*d. 
tnisses. — Con  t'd. 
four  cases.  314. 
stress  diagrams 
for.  803-804. 
of.  314.  315. 
timber  for.  819. 
types  of.  803. 

unit  stresses  in.  tables.  804.  806. 
weight  of  steel  in.  810.  811. 
wind  pressure  on.  tables.  796.  797. 
Roofing, 
asphalt-gravel.  802. 
cement-gravel.  802. 
corrugated  steel,  801. 
materials.  798. 

weight  of.  Uble.  802. 
patented.  802. 
sheet-steel-.  801. 
shingle.  790. 
slag-.  802. 
slate, 
laying  of.  402. 
tables,  m.  800. 
tar-gravel.  801. 
tile    800. 
tin-,  800. 
Root,  roots, 
ana  division,  algebraic,  102. 
by  slide  rule.  136. 
cube, 
engineers'  tables.  21-24. 
to  find.  20. 
of  decimals,  by  logarithms,  106. 
of  numbers,  by  logarithms,  106. 
powers  and   reciprocals  of  num- 
bers, 14-64. 
square 
and  cube,  common   tables,   31- 

60. 
engineers*  tables,  16-19. 
of  fifth  powers,  engineers'  table. 

26. 
to  find,  14. 
Rope, 
hoisting,  tension  in,  290. 
in  cordage,  668. 
manila,  660. 
weight  and  strength  of,  tables, 
669-670. 
tension  in  traction,  280. 
wire-,  673. 
fastenings.  675. 
tables,  674. 
Rosendale  cement  (sec,  also,  Ce- 
ment, natural), 
manufacture  of,  404. 
Rose's  fusible  metal,  melting  point 

of.  515. 
Rosettes,  elec.  code  rules,  1430. 
Rosin, 
a  tree  product,  346. 
definecf,  481. 
weight  of,  481. 
Rosseau's  hydrometer.  461. 
Rot.  in  lumber,  defined,  387. 
Rotary 
furnace,  for  cement  making,  406 
pumps,  1367. 


Rotating  machines,  electrical-,  dc^ 

nittons,  1461. 
Rotting  of  timber.  369. 
Rough 
edge  (lumber),  classification  oC, 

388. 
lumber  (fir),  classified,  389. 
Roughness  iv.  values  of.  116& 
Rubber 
-covered  wire,  tables.  1424. 
India,  weight  of,  480. 
vulcanizer,  330. 
Rubble 
concrete  dam.  860. 
masonry,  defined.  432. 
stoneworic.  in  buildings,  safe  loada 
for.  821. 
Rubidium,  ch$m.,  319. 
Ruble  (Russian,  gold),  equivalents 
(1-10,-60-100)  in  U.  S.  money, 
table,  97. 
Rtieping  process,  for  ties,  cost,  376. 
Runoff, 
distribution  of.  1190. 
formulas  for.  1197.  1198. 
in  storm  sewers,  formulas,  dia- 
grams and  tables,  (ref.)  1310. 
relation  of  rainfall  to.  (ref  J  1901. 
relation  of.  to  rainfall,  in  (Jalifor^ 
nia.  (ref.)  1201. 
Rupture  (bending)  tests  of  timber. 

table.  492. 
Russian  money.  U.  S.  values.  05. 
Rustic  lumber  (fir),  classified.  389. 
Rutgen's  process,  for  timber,  36 !• 
Ruthenium,  c^irm..  819. 


S-trap.  1295. 

Sabin  process  for  pipe  coating,  3M. 
Safes, 
loads  from.  816.  817. 
weight  of.  table,  816. 
Safety  factor, 
defined,  487. 
for  timber,  496. 
in  building,  821. 
Salt, 
a,  in  chem.,  defined.  321. 
and  ice  for  freezing,  613. 
solutions,  as  roacT  dust  prerent- 

ives,  1131. 
(rock),  composition  of.  336. 
weights  of.  table.  481. 
Saltpetre,  weight  of.  481. 
Samarium,  chem.,  319. 
Sampittic  surfacing  of  roads,  (ref.) 

1142. 
Sand 
-blast 
cleaning 
and  painting,  373. 
(ref.)  874. 
with  cost,  874. 
for  mill  scale.  358. 
bricks,  manufacture  of,  417. 
filtration  of  water,  methods,  WA, 
foundation.  864,  865. 


INDEX. 


1693 


Sand, — Cont'd. 

impurities  in,  for  concrete,  (ref.) 
455. 

Ottawa,  in  cement  testing,  400. 

piles,  875. 

quarrying,  419. 

sieve  m  cement  testing,  409. 

standard,  in  cement  testing,  409. 

voids  in,  911. 
concrete,  416. 

weight  of.  table,  476. 
Sandstone, 

best  kind  of,  401. 

building,  401. 

block  pavement,  specifications, 
1134. 

blocks,  paving,  specifications,  1 1 24. 

composition  of,  881. 
Uble,  334. 

compression  tests  of.  512. 

compressive  strength  of.  512. 

defined.  339. 

expansion  coefficient  of.  516. 

formation  of,  table.  334. 

freezing  test.  402. 

frost  action  on.  401. 

kinds  of.  401. 

physical  properties  of,  512. 

qtmrrying,  419. 

temperature  stress  for  160*  F.,523. 

tensile  strength  of,  512. 

test  for  frost  action.  402. 

transverse  strength  of,  512. 

water  absorbed  by,  401. 

weight  of.  476. 
Sanitary 

disposal,  miscellaneous  data,  (ref.) 
1309-1312. 

works,  designs,  (ref.)  1311.  1312. 
SaniUtion.  1295. 
Saturated  steam, 

formulas,  1355. 

tables,  1355-1360. 
Saturation-factor,  in  the,  1453. 
Saturization  of  earth  dams,  860. 
Sault  Ste.  Marie  canals,  data.  1322. 
Saws,  lumber,  kinds  of,  379. 
Sawing 

logs.  379. 

lumber,  379. 
Scalene  triangle,  defined,  128. 
Scaling  logs,  879. 

(ref.T  391. 
Scandium.,  chem.,  819. 
Scantling, 

classification  of.  388. 

lumber  (fir),  classified,  389. 
Schist,  schists, 

composition  of,  table,  337. 

defined.  340. 

mica-,  composition  of,  336. 
Score,  equivalent  of,  95. 
Scrapers,  wheeled-,  grading  with, 

cost  data.  917. 
Screening. 

gravel.  419. 

water  for  domestic  use,  1204. 
Screw,  screws, 

bolts.  618. 


Screw,  screws. — 0>nt*d. 

in  mtch.,  formulas,  292. 

lag-, 
table.  622. 
use  of.  622. 

or  helix.  260. 

pUes.  874. 

threads,  standard.  618. 

wood-,  table.  622. 
Scruple,  scruples, 

rtn.),  metric  eauivalents,  86. 
S.  apoth.)  and  milliliters, 
equiv.  (I-IO),  table.  83. 
Seasoning, 
lumber,  379. 
steam-,  of  lumber,  379. 
of  timber,  361. 
described,  362. 
Sea-wall,  at  Havana,  (ref.)  904. 
Sea-water  at  great  depths,  density 

of.  1145. 
Sea-worms,  in  timber.  360. 
Secant,  secants, 
logarithmic,  table,  176-198. 
natural,  Uble.  167-175. 
to  circle,  defined.  129. 
(trig.),  defined,  136. 
Second,  seconds, 
and  minutes  to  decimals  of  a  de- 
gree or  hour,  table,  1010. 
circular  and  time  measure,  equiva- 
lents. 99. 
time  and  longitude  equivalents.99. 
Section,  sections, 
conic.  256. 
Government  land,  subdivision  of, 

970. 
-modulus  of  pkme  surfaces,  table, 

524. 
quarter-,  and  hectars.  equiv..  88. 
Sector, 
circular, 
center  of  gravity  of.  220. 
mensuration  of.  220. 
properties  of.  528. 
of  circle,  defined.  129. 
Sedimentation,  in  settling  basins, 

1204. 
Seepage.  1200. 

distribution  of,  1190. 
Segment,  segments, 
circular, 
area,  formulas  for,  215. 
areas,  etc..  tables.  216.  217.  218. 
(half-), 
circular,  properties  of,  528. 
parabohc.  properties  of,  529. 
of  circle, 
cen.  ot  grav.  of.  214. 
defined.  129. 
mensuration  of.  214,  215. 
of  circular  spindle,  254. 
of  ellipse  area  of,  242. 
of  parabola,  237. 
of  sphere, 
defined.  135. 
mensuration  of,  252. 
Segmental  rollers,  table,  636 
Selenium,  c/»rm.,  319.     glc 


1694 


INDEX, 


Semicircle, 
axis  at  base,  properties  of,  628. 
axis  through  cen.  of  grav.,  proper- 
ties of,  628. 
defined.  129. 
Semicircular 
arc,  skeleton  section,  properties  of, 

631.  682. 
cell,  skeleton,  properties  of,  631. 

632. 
orifices,  center  of  pressure  on, 
formulas,  1161. 
Semi-tangents  and  externals  to  a  1^ 

curve,  table,  lOW. 
Separators, 
cast  iron. 
Uble.  628. 
use  of.  628. 
steel  diaphragm-,  628. 
Series 
arc  lamps,  elec.  code  rules,  1406. 
lamps,  elec.  code  rules.  1423. 
Serpentine.  337. 
defined,  881. 
weight  of,  481. 
Settling  basins,  sedimentation  in, 

^4. 
Sewage  disposal,  12M. 
miscellaneous  data,    (ref.)    1300- 
1312. 
Sewer,  sewers.  1206. 
and  conduits, 
circular,   properties  of,  table, 

1300. 
hydraulic  properties  of,  tables, 
1206-1306. 
basket-handle,  properties  of,  table, 

1302. 
brick.  416. 

66-in..  cost  of.  1310. 
catch  basins,  1306. 
catenary,  properties  of,  table,  1301. 
circular 
and  other  sections  compared. 

1206   1300. 
brick,  vekxnties  in,  table.  1200. 
construction,   illustrated,    (ref.) 

1306. 
design,  modem  procedure  in,  (ref.) 

1311. 
egg-shaped, 
properties  of,  table,  1304. 
velocities  in,  table.  1306. 
excavation,  cost  data,  016. 
foimdations,  1306. 
Gothic,  properties  of,  table,  1303. 
^rade  of.  1296. 
mverts.  wear  of .  1310. 
kinds  of.  1307. 
location  of.  1308. 
manholes,  1308. 
pipe 
Ubles,  1307. 
joints, 
cement  and  sand  required  for, 

table.  1309. 
mortar  required  for.  table,  1309. 
sulphur  and  sand  required  for, 
table.  1810. 


Sewer,  sewers. — Cont'd, 
runoff  in.  formulas,  dia^rn^ns  and 

Ubles,  (ref.)  1310. 
size  of.  1296. 
trench,  cost  data,  916. 
trenching  and  backfilling,   cost 

data,  917,  918. 
tunnel  work,  cost  data,  918. 
walls,  brick,  thickness  of,  foraxnla, 
1306. 
Shackle  fastenings  for  wire  rope.  67S. 
Shaft,  in  tUMn*Ung,  defined.  0S3. 
Shakes,  in  luhiber,  defined.  387. 
Shale    . 
rock,  quarrying,  419. 
weight  of.  481. 
Shapes, 
block,  properties  of,  639. 
rolled,  properties  of,  635-638. 
skeleton,  properties  of,  629. 
steel. 
list  of  tables.  641. 
properties  and  tables  of.  541. 
Shear,  shears, 
and  web  stresses.  307. 
and  moments  for  engine  loadtns. 

table.  692.  ^^ 

end-. 
Cooper's  loading.  Uble.  708. 
for  highway  bridges,  Uble.  728. 
from  electnc  cars,  Ubles«717. 719. 
in.beams  and  girders,  various  kied- 


txigs. 
buildii 


in  building  materials,  safe'streaaes. 

822. 

in  struc.,  method  of.  306. 
in  trusses,  various  loadings,  603. 
longitudinal,  in  beams,  formal  " 

666. 
-steel.  395. 
Shearing 
effect  on  columns.  687. 
strengths  of  metals,  uble.  496. 
tesU  of  timber,  with  grain,  t-""*^ 

494.  ^ 

values  of  concrete  in  beams,  Ihx 
Sheet,  sheets, 
asphalt  pavement,  spedficat-     i, 

1110. 
lead.  679. 
metal, 
weight  of,  from  specific  brevity, 

table,  484. 
gages,  Ubles.  667.        , ' 
paper  measure,  96.  * 

piling,  869.  *,': 

steel,  870.  '■' 

Sheeting,   corrugated,   strength  od 

(reh)  661. 
Shield, 
hydraulic-,  used  in  sewer^  'mnel, 

cost  daU,  916.  *   - 

method  of  tunneling.  93^^.. 
Shims,  track-,  thickness  o:,  iw9. 
Shingle,  shingles, 
dimensions  of.  390. 
grading  of,  390. 
roofing,  799. 
wooden,  Uble,  TOflble 


INDEX, 


1696 


Shipping  weights  of  lumher,  891. 
Shoes, 
cast-,  for  wood  stave  pipe,  1209. 
pile-,  874. 
Shop  drawings  for  structural  steel, 

cost  of.  666. 
Shrinkage, 
earthwork,  reference  data,  930. 
in  earth  dams,  914. 
.  of  earth,  909. 

how  estimated.  910-913. 
fills,  recommendations,  914. 
of  earthwork, 
experiments,  918. 
rsulroad  specifications  for,  91 8. 
vertical  in  earth  embankments,  916. 
Shroud  laid,  in  cordagt,  668. 
Sidereal 

and  mean  solar  time,  equivalents, 

table,  202. 
day,  defined.  202. 
Sidewalk,  sidewalks, 
areas,  surfacing.  1116. 
brick,  specifications,  1108. 
cement, 
described;  1099. 
specifications,  1117. 
concrete, 
specifications.  1111,  1129. 
base  for,  specifications.  1129. 
crushed -stone,  specifications,  1106. 
gravel,  construction  of.  1098. 
part  cement,  part  gravel.  1116. 
plank-,  described.  1098. 
practice  in  Chicago,  costs.  1148. 
Sienite.  composition  of,  337. 
Sit  nna  for  paint,  366. 

e.  sand-,  in  cement  testing,  409. 
signs, 
^cular  and  time  measure,  equiva- 
lents. 99. 
electrical  notation.  1471. 
-. -^ues  (trig.).  137. 
S)         lights,  elec.  code  rules,  1460. 
Si%    iling  systems,  elec.  code  rules, 

SiK 

3.A.i^rals,  331. 
weight  of.  481. 
Silicates, 
in  min.,  classification  of,  826. 
most  important.  331. 
Silicic  a'^ia.  weight  of.  481. 
Silico*      'i^m.,  319. 
-bn  397. 

ie^    J  strength  of,  497. 
-wire  as  conductor,  compared 
with  copper,  497. 
Sills,  wooden  trestle,  788. 
Silver,    hem.,  320. 
casf       nsile  strength  of.  498. 
ex  on  coefficient  of,  616. 

meiwA  K  point  of.  615. 
minerals,  ores.  328. 
weight  of,  481. 
Simple 
and  compound  units,  equivalents, 

table.  88. 
interest  tables.  60. 


Simultaneous  equations, 

examples  in,  108. 

graphical.  266. 
Sine,  sines, 

bgarithmic,  table.  176-198. 

natural,  table.  144-166. 

(trig.),  defined,  136. 
Single-^ase    alternator,    defined. 

Sinking  fund,  63. 
and  annuity  tables,  64-66. 
formula,  66. 

diagrams  and  tables,  (ref.)  1298. 
Sizing  lumber,  879. 
Skeleton  figures,  properties  of,  629. 
Skew  portals,  detailing,  (ref.),  666. 
Slabs, 
concrete,  calculation  of,  (ref.)  466. 
floor-,  reinforced  concrete,  bending 
moment,  828,  826»  837.  829, 
,  883. 
reinforced  concrete, 
sUde  rule  for.  (ref.).  686. 
Thacher's  computation,  686. 
Slag 
block  pavement  specifications, 

1121. 
cement,  manufacture  of,  404. 
roofing,  802. 
weight  of.  481. 
Slant  height,  defined.  188. 
Slate, 
composition  of,  381. 

table.  384. 
defined.  339. 

expansion  coefficient  of,  616. 
formation  of.  table,  384. 
formed  how,  402. 
physical  properties  of,  612. 
quarried  where,  402. 
roofing,  402.  799. 
temperature  stress  for  160*  P., 

628. 
weight  of.  477. 
Sleeve,  sleeves, 
cast  iron  pipe,  tables,  1282,  1266. 
nuts,  634. 
w^hts  and  dimensions,  table, 
688. 
Slide 
rules, 
described,  126-127. 
problems.  126-127. 
for  reinforced  concrete  slabs,  (ref.) 

686. 
-valve  engines,  performance  of, 
1866. 
Sliding  friction,  617-621. 
Slip, 
in  cement  making,  406. 
of  rods  in  concrete  beams,  (ref.) 
466. 
Slope  4 

and  deflection  of  beams,  formulas. 

662. 
artesian-,  defined.  1190. 
side-,  for  rock  cuts,  922. 
•staking.  1055. 
walls,  dry,  specifications,  480. 


IMd 


INDEX. 


Slow  ,' 

sand  filtration,  1?"  'm  ' 

-btiming  wire    ir  ^^ustion,    table, 
1425. 
Sludge,  defined.  1525. 
Sluice  sate,  -gates, 

stand  and  wheel,  1270. 

table.  12^9. 
Slurry,  in  cement  making,  405. 
Smelting.  357. 

Smith's  durable  metal  coating,  358. 
Smokeless  powders,  352. 
Snap  switcnet,  elec.  code  rules,  1433. 
Snow, 

evaporation  from,  1190. 

k)ads  on  roofs,  707,  708. 

weight  of,  481. 
Soapstone,  840. 

weight  of,  481. 
Sockets, 

elec.  code  rules.  1413.  1440.  1400. 

fastenings  for  wire  rope,  075. 
Sodium.  cJUm.,  320. 

chloride,  use  of,  840. 

minerals.  828. 
Soil,  soils, 

bearing  capacity  of.  810. 

bearing  power  of,  for  buildings,  867. 

borings  in,  806. 

defined,  OuO. 

density  of.  900. 

for  foundation,  tests  of,  885. 

pipes,  1295. 

seepage  in,  various,  1200. 
Solar 

and  sidereal  time,  equivalents, 
table,  202. 

attachment,  044. 
adjustment  of.  947. 

dav.  defined,  202. 

ephemeris  tables,  reference  to,  202. 

instrument,  uses  of.  946. 

observations  with  transit   alone, 
947. 

power,  reference  data,  1484. 
Solder.  896. 

kinds  of,  1525. 
Soldering  fluid,  elec.  code  formula. 

Solid,  solids, 

center  of  gravity  of,  802. 

coefficient  of  expansion  of,  table, 
516. 

defined,  512. 

determming  specific  gravity  of, 
460. 

Geometry,  182-135. 

melting  points  of.  515. 

mensuration  of.  243. 

moments  of  inertia  of,  table,  302. 

radius  of  gyration  of,  302. 

rock  classmcation  (R.  R.),  919. 
Solvents,  cement,  402. 
Sorel  stone,  manufacture  of,  417. 
South  point,  of  celestial  sphere,  de- 
fined, 201. 
Space, 

Analytic  Geometry  of,  256. 

m  tmch.,  defined,  27a 


Spans,  bridge-,  aconomic  length  oC 

688. 
Spandrel,  parabolic,  properties  of, 

237,  529. 
Spar,  weights  of,  481. 
Spark  arresten,  elec.  code  rules, 

1442. 
Sparking  daitancen,  in  eltc.,  1474. 
Specials, 
pipe,  described,  1290. 
pipe-casttngs,  bells  of,  dinaecsioos. 
etc..  tables.  1221.  1223.  1241. 
1245. 
Specific 
gravity,  gravities, 
by  displacement  method.  400. 
defined,  460. 
equivalents  for  any  weight,  tabk 

474. 
methods  for  determining,  400. 
of  brkk.  Uble,  474. 
of  building  stoneSitable^  474. 
of  cement  bv  LaChatelxer's  ap- 
paratus, 407. 
of  granular  substances,  to  find. 

of  liquids,  Uble.  468.  469. 
of  materials^  450. 

general  table,  478. 
of  porous  substances,  to  find, 400. 
of  tars.  1132. 
of  woods,  toble.  47(M78. 
reduced  to  weight,  table,  481. 

484. 
standards  for  determinins,  460. 
heat  oi  the  liquid,  formula,  1856. 
volume 
of  saturated  steam,defined .  1 866w 
of  the  water,  formula,  1356. 
Specifications  (see  specific  items). 
Specifications  and  contracts,  refer- 
ence data,  1484. 
Spelter,  weight  of.  481. 
Sphere,  spheres, 
area  sreat  circle  of,  equivalents. 

area  of  surface  of,  by  calculias.276. 
Celestial,  elements  of,  201-302. 
circumference  of  J  eqmvalenta,  251. 
cylinder  (max.)  inscribed  in.  269. 
diameter  of,  equivalents,  251. 
diameter 
(ft.  and  ins.) 
to  surface  (sq.  ft.),  table.  284. 

235. 
to  volume(  in  ft.),  table.  234. 
235. 
(in  fractions)  to  surface  (in  deci- 
mals), table.  226-229. 
to  surface, 
in  decimals,  table,  324,  225. 

882,  283. 
in  inches,  table,  280,  831. 
to  volume, 
in  decimals.  tal>le,  383.  388. 
in  inches,  Uble,  280,  231. 
geometry  of ,  134-135. 
hollow,  mensuration  of,  253. 
moment  of  inertia  of,  803. 


INDEX, 


1M7 


Sphere,  spheres, — Cont'd, 
properties  of.  240. 
radius  of.  equivalents,  251. 
relations  of  area,  diameter,  surface. 

volume,  etc,  250. 
relations  to  cone,  cube  and  cylin- 
der. 250. 
surface  measure,  in  radii,  186. 
surface  of, 
equivalents.  250. 
table.  251. 
tables  listed.  251. 
volume  of, 
equivalents.  250. 
measure,  in  radii,  186. 
.  table.  252. 

tables  listed,  252. 
wind  pressure  on,  797. 
Spherical 

cone,  defined,  186. 
pyramid, 
defined,  135. 
solution  of,  190. 
segment, 
defined,  135. 
mensuration  of.  252. 
triangles,  solution  of,  199-201. 
trigonometry,  199-202. 
zone, 
area  of.  hy  calculus.  276. 
mensuration  of,  253. 
Spindle, 

circular,  mensuration  of,  258. 
cycloidal.  mensuration  of,  254. 
oil,  weight  of,  481. 
parabouc,  mensuration  of,  254. 
Spikes, 
railway, 
effect  of  creosote  oil  on,  361. 
weight  per  mile  of  track,  table, 
1068. 
steel,  weights  and  dimensions. 

tables.  626-628. 
street  railway,  table,  628. 
Spiral. 

common,  260. 
curves  (R.  R.).  1013. 
hyperbolic,  equation  of.  260. 
kmrithmic.  equation  of,  260. 
ot  Archimedes,  equation.  260. 
riveted    steel    pipe,    680-682. 
1269. 
Spirit,  rectified,  weight  of,  481. 
Splices, 
in  cordage,  669. 
rail-.  1060. 
Split  switches.  1084,  1088. 

turnouts  for.  tables.  1085-1088. 
Splitting  chisel,  described,  427. 
Spot  method  of  using  current  meters, 

1186. 
Spread-foundation,   reinforced  con- 
crete, (ref.)  890. 
Spring,  springs, 
metal-,  formulas.  1482. 
steel. 

physical    properties   of.    499. 
-  1884. 
tests  of,  table,  1484. 


Spruce,  sprcces, 

classifica;ic       ^.  341. 

grading  rules.  cd8,  390. 
Square,  squares. 

acreage,  dimensions  of,  1318. 

and  circle,  inscribed  and  circum- 
scribed, 131. 

and  cubes,  tabl^  of,  uies,  686. 

and  cube  roots,  by  slide  rule.  126. 

axis  at  base,  properties  of,  526. 

cell,  skeleton,  properties  of,  580. 

centimeters.  English  equiv..  79. 

cubes  and  roots,  common  tables, 
31-43. 

decimeter,  English  equiv..  79. 

dekameter.  English  eouiv.,  79. 

diagonal  axis,  properties  of.  526. 

feet  and  meters,  equivalents.  88. 

foot,  metric  equivalent,  81. 

yards  and  meters,  equivalents,  88. 

geometric,  defined,  l28. 
ectometer,  English  equiv.,  79. 
hollow-, 
properties  of,  526. 
diac[onal  axis,  properties  of,  626. 
inch,  inches, 
metric  equivalent.  81. 
and  centimeters,  eqtiivalents,  88. 
kilometers.  English  equiv..  79. 
land  measure.  English,  metric 

equivalents,  table,  81. 
measure,  metric.  English  equiva- 
lent, table,  79. 
mensuration  of.  203. 
meter.  English  equivalents.  79. 
miles  and  nectars,  equivalents,  88. 
mile,  metric  equivalent.  81. 
millimeter.  English  equiv.,  79. 
mils  and  millimeters,  equiv..  88. 
myriameter.  English  equiv.,  79. 
properties  of,  525. 
rod.  metric  equivalent.  81. 
rods  and  meters,  equivalents,  88. 
root,  roots, 
and  cube  roots,  common  tables, 

31-50. 
by  binomial  formula.  102. 
ennneers'  tables,  16-19. 
of  nfth  powers,  engineers'  tables, 

25. 
to  find,  14. 
skeleton  section,  properties  of. 530. 
tables  of.  for  structural  detailing, 

643-664. 
yard,  metric  equivalent,  81. 
Squared-stone  masonry,  defined.  432. 
Squaring  quadratic  equation,  exam- 
ples, 102. 
Stadia 
reduction  table,  984. 
surveying,  983. 
surveys,  cost  data.  990. 
Standard 
connection  angles,  for  I-beams  and 

channels.  615. 
orUice.  1176. 
rain  gage,  1196. 
tube.  1176.  /^___T^ 

weir,  1177.     izedbyLjOOgle 


1508 


INDEX. 


Standardization,  electrical-,  1451. 
Stand  pipes.  1271. 
miscellaneous  data,  (ref.)  1202- 

1294. 
steel,  design  of.  1206. 
Star, 
altitude  of.  defined.  201. 
azimuth  of.  defined.  201. 
hour  angle  of.  defined.  202. 
polar  distance  of.  defined.  202. 
right  ascension  of.  defined.  202. 
zenith  distance  of.  defined.  202. 
Static 
equilibrivim,  in  struc.,  principles  of. 

306. 
stress,  defined.  487. 
Stations  (100  ft.) 
and  meters,  equivalents.  88. 
and  miles.equivalents.  table.  1001. 
Stave,  wood-,  pipe, 
and  details,  table.  1210. 
details  of,  1206. 
Staybolts  (iron),  tensile  strength  of. 

407. 
Steam 
and  gas  power.  1346. 
apparatus,  cost  data,  1477. 
boUers.  1361-1368. 
efficiency  and  rating.  1361. 
horsepower  of,  defined.  1361. 
kinds  of.  1362. 
-electric  problems,  1379. 
engines,  1363-1366. 
consumption  of  coal  per  h.-p. 

hour,  1363. 
economic  performance  of,  1365. 

1366. 
effect  of  load  upon  economy  of, 

1366. 
efficiencies  of ,  1363. 
horsepower,  problem.  1363. 
mean  effective  pressure  of.  1365. 

1366. 
principle  of,  1363. 
flow  through  orifices,  (ref.)  1377. 
flow  through  pipes,   formula  and 

Uble,  1361. 
ideal,  weight  and  specific  gravity 

of,  464. 
joints,  waterproofing  for.  418. 
kinds  of,  defined.  1354. 
pipe  cement.  402. 
pipes,  connections  of,  etc.,   (ref.) 

1377. 
plants,  cost  data,  table.  1478. 
power 
and   water  power  compared. 

1385. 
plants,  costs,  1477. 
problems  solved  by  the  use  of  dia- 
grams, (ref.)  1378. 
pumps^  1366,  1367. 
seasoiung  of  lumber.  379. 
saturated, 
formulas,  1355. 
tables.  1355-1360. 
shovel  work 
at  Panama,  cost  data,  919. 
cost  data,  916. 


Steam— 0»t'd. 
shovels  used  in  loading    rock  oe 

cars.  924. 
superheated-,  formulas.  13^. 
total  heat  of,  new  and  old  torma- 
las.  1378. 
Steams  and  Pteley's  weir  formulas 

1180.  1181. 
Steel, 
acid  open  hearth  process,  394.  39i 
angles,  properties  of.  tables.  MS* 

553. 
annealing,  395. 
arches.  782. 

axles,  specifications,  504. 
bars, 
areas  and  weights,  table.  544. 
for  drills.  922. 

weights  and  areas,  table.  544. 
basic  open  hearth  process.  395. 
beam  box  girders,  properties  of. 

table,  568. 
beams,  properties  of,  table.  554. 
carbon-, 
aimealed,  physical  pxx>perties  of. 

Uble.  500. 
oD-tempered.  physical  properties 
'    of,  table,  500. 
ast. 

expansion  coefficient  of.  516. 
open  hearth.  396. 
specificatioi^  for.  393. 
castings, 
physical  properties  of,  504. 
table.  499. 
.     specifications.  503. 
test  pieces.  504. 
testing,  504. 
cementation  process.  805. 
channels.  porip>eTties  of.  table.  556. 
chemical  properties  of.  500. 
chisel-.  896. 
chrome.  396. 

-vanaoium.  899. 
corrugated-,  roofing.  801. 
cost  of  cleaning.  378. 
crucible.  395. 

details  of  combination  bridge.  7M. 
die-.  396. 

expansion  coefficients  of,  516. 
flumes,  for  water  supply.  1207. 
for  bridges,  specifications,  706. 
forbuildLo^    819. 
for  mine  timbering,  use  of.  (ref.) 

939. 
forgings. 
physical  properties  of.  506; 

table.  499. 
specifications,  505. 
testing.  506. 
girder  beams  (single  I),  propertirs 

of,  toble.  583. 
grades  of,  used  in  structures,  499. 
harveyized,  396. 
I-beams, 
properties  of,  table.  554. 
special,  properties  of,  table,  584 
in  cinder  concrete.  corroGion  oi. 

Digitized  by  VjOOQ  IC 


INDEX, 


1609 


Steel,— Cont'd. 

in  concrete,  adhesion  tests,  (ref.) 

454. 
in  buildings, 

safe  stresses.  826. 

stresses  for,  824. 
kinds  of,  306. 
manganese-,  396. 
manufacturer's  standard.  499. 
melting  point  of,  394,  616. 
metallurgy  of,  (ref.)  399. 
molybdenum  in.  330. 
nickel-   396. 

manufacture  of,  398. 

properties  of.  398. 

specifications   for   Manhattan 
bridge.  768 

annealed,  physical  properties  of, 
499. 

forged,  oil-tempered,  physical 
properties  of.  table   499. 

-vanadium,  399. 
open  hearth. 

boiler  plate,  specifications,  601. 

rivet,  specifications.  601. 
physical  properties  of,  600. 

table.  499. 
pipe,  1268. 

experimental  values  of  N  in  Kut- 
ter's  formula  for  flow  in,  1188. 

for  water  works,  costs,  1292. 

riveted,  design  of.  1268. 

spiral  riveted,  680-682. 
plate,  -plates. 

areas  and  weights,  table,  644. 

-girders,   properties    of,    table, 
670-682 

weights  and  areas,  table,  644. 
preservation  of.  368. 
rails, 

chemical  properties  of.  603. 

dimensions  and  weights,  table, 
600. 

properties  of.  table,  660. 

specifications,  603. 

testing.  603. 

weights  and  dimensions,  table, 
660. 
railroad  bridges,  specifications,  699. 
.razor-.  396, 
reinforcement, 

for  buildings,  specifications,  (ref.) 
826. 

in  beams,  tensile  stress  value, 
686. 
rivet-. 

open  hearth,  specifications,  601. 

test  pieces,  602. 

testing,  602. 
rods, 

areas  and  weights,  table.  642. 

weighu  and  areas,  table.  642. 
saw-file-.  396. 
set.  396. 
shapes, 

list  of  tables,  641. 

properties  and  tables  of.  641. 
shear-,  396. 
sheet-,  roofing,  801. 


Steel.— Cont'd, 
specifications   for   Manhattan 

bridge,  table,  768. 
spindle-,  396. 
spring-, 

physical  properties  of,  1484 
springs. 

physical  properties  of,  499. 

tests  of.  table,  1484. 
structural, 

analysis  of   394. 

manufacture  of,  394. 

(bridge),  specifications,  600. 
tees,  properties  of,  tablet  668. 
temper  of,  396. 

temperature  stress  for  160°  P.. 623. 
tempering,  396. 
test  specimens,  601. 
testing,  specifications,  601. 
ties,  1072. 
tool-.  396. 
trestles.  791. 

elevated  railroad,  (ref.)  792. 
tungsten-,  396. 
uranium  in.  330. 
vanadium-,  396.  399. 

alloys,  399. 
weights  of,  481. 
welding,  396. 
wire, 

Physical  properties  of,  table.  499. 
loebling.  properties  of.  672. 
weight  of.  481. 
Z-bars,  properties  of.  table.  667. 
Steelwork, 
cleaning  by  sand  blast,  with  cost, 

374. 
cutting  with  oxy-acetylene  flame, 
833. 
Stepping  lumber. 
cliEUMification  of,  388. 
(fir),  classified.  389. 
Stereotomy,  467« 
Stone, 
-arch,  stonecutter's  plan,  467,  468. 
artificial,  described,  416.  417. 
-axed,  defined.  429. 
block-,  kinds  of,  417. 
bolts.  618. 
building-.  400. 
physical  properties  of,  table,  607. 
quarrying.  419. 
safe  loads  for.  821. 
specific  gravities  of.  table,  474. 
thickness  of  joints,  467. 
weights  of,  table.  474. 
bush-hammered,  defined,  430. 
-cements,  (refJ  418. 
chisels,  described,  427. 
classified  finish.  426. 
crandalled.  defined.  428. 
curbing,  specifications.  1108. 
cut.  defined.  428. 
cutting.  426. 

diamond-paneled,  defined,  480. 
dimension-,  defined.  433. 
drafted,  defined,  427. 
dressing,  ale 

specifications,  433.     o 


1600 


INDEX. 


Stone, — Cont'd, 
dressing, — Cont'd, 
tools  employed  il26. 
machines  pneumatic,  (ref.)  430. 
expansion  coefficient  ot,  616. 
fine>poined  defined.  428. 
friction  of   518-521. 
hammers,  described,  426,  427. 
masonry, 
compressive  strength  of,  511. 
described.  431. 
in  buildings  weight  of.  621. 
specifications,  433. 
McMurtrie,  manufacture  of,  417. 
natural  biulding*.  400» 
patent'hammerea.  defined.  429. 
pean -hammered,  defined.  429. 
Portland,  manufacture  of,  417 
quarry-faced,  defined.  427. 
Rsmsome,  manufacture  of,  417. 
rough-pomted,  defined,  428. 
rubbed-,  defined,  430. 
soxel-.  manufacture  of.  417. 
squared,  defined,  427. 
tooth-axed,  defined.  429. 
unsquared,  defined,  426. 
Stonework,  m  buildings,  safe  loads 

on.  826. 
Storm-water  drains,  design  of,  (ref.) 

1311.  ^ 

Stop  valves.  1271  1270.  1285-1287. 
Storage 
in  acre-ft.  reduced  to  horsepower 

hours,  table,  1335. 
in  million  cu.  ft.  reduced  to  horse- 
power hours,  table,  1334. 
or  primary  batteries,  elec.  code 

rules.  1398. 
reservoirs,  1205. 
Straight 
angle,  defined.  128. 
line,  defined,  182. 
lines  (skeleton),  properties  of .  629, 
631. 
Strain,  defined,  486. 
Strand,  in  cordage,  668. 
Stream,  streams, 
flow,  surface  and  mean  velocity  of. 

1183. 
method  of  measuring  flow  in,  (ref.) 
1187. 
Street,  streets, 
and  roads,  1098. 

crowning,  formvila  and  table.  1123. 
grading  for  pavement,  specifica- 
tions. 1127. 
graveled,  oiled,  specifications.  1114. 
pavements,  1099. 
railway  tracks, 
and  paving,  1094,  1096; 

inL)  1142. 
T-rails  for.  (ref.)  1142. 
trackway  (steel),  experimental, 
cost.  1142. 
Strength 
of  materials,  486. 
ultimate,  defined,  487. 
Stress,  stresses, 
alternating,  defined,  487. 


Stress,  stresses, — Cont'd, 
chord-  and  bending  moments.  307. 
combined-,  tests,  (ref.)  622. 
defined,  486. 
•diagrams 

for  drawbridge,  746. 
genera]  rules,  310. 
of  Pratt  truss.  312.  313. 
of  roof  trusses.  803-804. 
effect  of, 
on  elastic  limit.  487. 
on  ultimate  strength,  487. 
in  beams,  formula,  299. 
in  structures,  theory  of.  306 
per  area,  metric  and  English  equiv 

table,  89. 
repeated,  defined.  487. 
sUtic.  defined.  487. 
ultimate,  defined,  487. 
unit-,  in  roof  trusses,  tables,  804. 

806. 
web-,  and  shears,  807. 
worldng-, 
defined,  487. 

for  reinforced  concrete  beams, 
586. 
Stretcher,  masonry,  defined.  432. 
Striking  the  arch  center,  773. 
String,  in  cordage,  668. 
Stringers, 
bridge-, 
moments  and  shears,  various 

loadings.  '688. 
spacing  of,  700. 
wooden-, 
bending  moments,  table.  791. 
cast  separators  for.  628. 
floor-,  789. 
Strontium,  chtm.,  320. 
Struck  bushel,  metric  equiv.,  84. 
Structural 
details  611. 

references,  665. 
steel, 
shop  drawings  for.  cost  of.  M6. 
specifications.  600. 
Structures,  theory  of   stresses  in. 

305. 
Struts,  see  Columns. 
Stub  switches,  1078. 
Stumpage.  forest. 
Pacific  (3oast.  377. 
U.  S..  376. 
Stumps,  blasting,  cost  data,  916. 
Subaqueous  concrete,  placing.  440. 
Sub-grade  shaping,  road   specifica- 
tions. 1101. 
Submarine  drilling  and  blasting, 

cost.  926. 
Submerged 
beams,  formulas  for  pre^ure  and 

moments  in.  (ref.)  1189. 
planes,  pressure  on,  846,  847. 
tubes,  flow  of  water  thro\xgh,  (ref.) 

1189. 
weirs,  1181. 
formulas,  1181. 
Subscript  abbrevatton  jof  a  decimal 

95.  tized  by  Google 


INDEXx 


1601 


Sub-surface  floats,  for  hydmtilic 

measurements,  1188. 
Subtraction  and  addition,  in  algebra, 

100. 
Subway  excavationj  cost  data,  016. 
Successive  differentiation,  271. 
Sudden  loading,  effect  of,  480. 
Suez  canal, 
dimensions  and  cost,  1320. 
traffic  data,  table,  1321. 
Sulphates,  in  min.,  classification  of, 

327. 
Sulphides,  in  min.,  classification  of, 

325. 
Sulphur,  ckem.,  320. 
melting  point  of,  515. 
minerals.  330. 
uses  of,  330. 
weight  of,  481. 
Sulphuric  acid,  weight  of,  481. 
Superheated  steam, 
formulas.  1355. 

in  locomotive  boilers,  use  of.  (ref .) 
1378. 
Superintendence  of  work,  value  of 

good,  908. 
Supplement  and  complement  of  an 

angle.  130. 
Supplementary  angles,  defined.  128. 
Surface,  stufaces, 
ctu^ed-,  areas  of,  by  calculus,  276. 
fioats,    ifor   hydraulic    measure- 
ments, 1183. 
of  sphere,  measure   of,  in  radii, 
135. 
Surfacing,  road  specifications,  1101. 
Survey,  surveys, 
location.  (R.  R.),  1004. 
preliminary,  (R.  R.),  1000. 
reconnoissance,  (R.  R.).  098. 
stadia-,  cost  daU,  990. 
traverse,  964. 
Surveying, 
city-lot,  966. 
farm-,  964. 

Government  land,  967. 
instruments,  care  of,  941. 
mapping  and  leveling,  941. 
stadia-.  983. 
Surveyors'   measure,   lineal,   metric 

equivalents,  table,  68. 
Suspension 
bridges,  750.        • 
anchorages  of^  756,  769. 
cables  vs.  chains^  754. 
details  and  specifications,  756- 

760. 
miscellaneous  data,  760. 
towers  and  backstays,  754. 
weights  of  materials  in,  tables, 
768. 
cables,  curves  of,  750. 
Swedge  bolts.  618. 
Sweet  gums  (trees),  classification  of, 

345. 
Swellage 
of  earth,  how  estimated,  910-913. 
of  rock  when  broken,  table.  911. 
Swing  bridges,  742. 


Switch,  switches, 
and  frogs,  tables.  1079-1082. 
and  turnouts,  1075. 
boxes,  elec.  code  rules,  1429. 
elec.  code  rules,  1404,  1407.  1431, 

1449. 
spUt-.  1084.  1088. 

turnouts  tor.  tables,  1085-1088. 
stub-.  1078. 

table  for  laying  out,  1078. 
ties,  bills  for.  tables,  1070. 
Wharton,  1088 
Switchboards,  elec.  code  rules,  1 395. 

1449. 
Swivel  hook  fastenings  for  wire  rope, 

675. 
Syenite,  composition  of,  337. 
Symbols,  atomic,  table,  818. 
System,  artesian-,  defined,  1190. 


T,  T's, 
-bar,  -bars, 

block,  properties  of,  583,  534. 

rivet  gages  for,  614. 

steel,  properties  of,  table,  558. 

-beam,  rolled,  properties  of,  537. 

block,  properties  of,  533,  534. 

cast  iron  pipe,  table,  1225.  1250- 

1254. 
-rails  for  street  railway  tracks, 
(ref.)  1142. 
Tables 
of  cubes 
and  squares,  uses  of,  636. 
for  structural  detailing.  639-642. 
of  squares,  for  structural  detailing, 
643-664. 
Tablet  and  panel  boards,  elec.  code 

rules,  1439. 
Tacks,  table,  627. 
Tael, 

(Chinese),   equiv.    (1-10,-50-100) 

in  U.  S.  money,  table,  97. 
(Philippine    weight),    English 
equivalent,  81. 
Talc 
schist,  337. 
uses  of,  331. 
weight  of,  481. 
Tallow, 
melting  point  of,  515. 
weight  of,  481. 
Tangent,  tangents, 
and  externals  to  a  1^  curve,  table, 

1009. 
and  normal  (calculus),  equations 

of,  267. 
logarithmic,  table,  176-198. 
natural,  table,  144-166. 
to  circle, 
defined,  129. 
equation  of,  257. 
to  ellipse,  equation  of,  259.  268. 
to  hyperbola,  equation  of,  259. 
to  parabola,  equation  of,  258. 
(tr&.),  defined,  136. 


1602 


INDEX. 


Tank,  tonks, 
dia.  to  area,  capacity,  volume, 
weight  (water),  table,  24&-7. 
-measurement  of  water,  1182. 
pipe-dipping-,  1282. 
presstire  in,  hydrostatic.  1152. 
water-, 
elevated.  1207. 

miscellaneous  data,  (ref.)  1292- 
1204. 
Tantalum,  diwm.,  320. 
Tapes.  056. 
sag  and  stretch  of,  056. 
temperature  corrections  for.  table, 
056. 
Tapping  machine,  Mueller,  1288. 
Tar.  tars, 
a  tree  product.  346. 
adds.  867. 

amount  and  cost,  in  road  construc- 
tion, 1133. 
and  pitch  for  waterproofing.  418. 
application  to  road  surfaces,  1 1 32 . 
as  road  dust  preventives.  1181. 
coal-,  for  roads,  specifications,  1 1 35. 
composition  of,  1132. 
dehydrated,  1131. 
experiments  on  roads,  costs.  1136. 

1137. 
filling, 
for  wood  block  pavement,  speci- 
fications. 1128. 
in  brick  paving,  1100. 
for  road  stirfaces,  1181. 
from  coke  ovens,  1131. 
from  gas  plants,  1131. 
-gravel  roofing,  801. 
macadam  roads,  cost.  1142. 
manufacture  of,  1131. 
properties  of,  1131,  1132. 
refined  coal-.  1131, 
specific  gravity  of,  1 1 32. 
use  of,  in  road  construction,  1132. 
water-gas.  1132. 

cost,  1130. 
weight  of.  481. 
Taylor's  theorem,  272. 
Tee,  Tees, 
Matheson  pipe,  table,  1281. 
rolled,  properties  of,  538. 
skeleton   section,  properties  of, 

630. 
steel-, 
properties  of,  table,  558. 
rivet  gages  for,  614. 
Telegraph  poles, 
preserving,  361. 
concrete,  1477. 
Telephone,  telephones, 
cable.  676. 
reference  data.  1482. 
Telford  and  macadam  roads,  specifi- 

cations.  1111. 
Tellurium,  cnent.,  320. 
minerals,  330. 
weight  of,  481. 
Temperature, 
absolute  zero  of.  462.  613. 
coefficients,  in  elec,  table,  1475. 


Temperature, — Confd. 
(C.  and  P.)  scales,  equivaletits, 

table.  465. 
critioil, 
defined,  513. 
of  gases,  table,  514. 
of  Bquids,  table,  514. 
effect  on  earth  fill.  010. 
low,  from  freezing  mixtuxes,  513. 
lowest  attained.  513. 
of  fusion,  defined,  513. 
provision  for  bridges,  705. 
•    reduced 

by  exaporation,  513. 
by  expansion.  613. 
by  freezing  mixtures,  519. 
regenerative  method.  513. 
rise  of,  in  #^r..  1466. 
stresses  in  bmlding  materials.  6%Z. 
Tempering^  steel,  306. 
Tension  (direct) 
in  building  materials,  safe  loads, 

822. 
in  hoisting  ropes,  200. 
of  rope  in  traction,  289. 
strength  of  metals,  table,  496. 
Terbium,  ch^m.,  320. 
Teredo  nevalis,  in  timber,  860. 
Term   (algebraic)   of  equation,  de- 
fined. 100. 
Teme  plate.  357.  800. 
Terra  cotta, 
brick.  415. 

compressive  strength  of.  512. 
piers,  crushing  tests.  522. 
tiles,  for  roofs,  800. 
Tests, 
bending,  of  timber,  table,  492.  493. 
compression,  of  timber, 
across  grain,  table.  404. 
table,  490. 
of  cement,  cylinders,  508. 
of  reinforced  concrete  beams. 

formula,  (ref.)  585. 
shearing,  of  timber,  with  srain, 
table,  494. 
Testing  cement,  406. 
Tetrahedron,  defined,  132. 
Texas  land  measure,  English  equiva- 
lents, table.  81. 
Texture  of  rocks,  table.  334. 
Thallium,  ckem.,  320. 
Theater  wiring,  eiec.  code  rules,  1414. 
Theorem, 
Maclauren's.  271. 
Taylor's,  272. 
Thermal 
energy, 
defined,  1847. 
examples  of,  1346. 
unit  (British), 
defined,  1347. 
equivalents  of,  90. 
equiv   (1-10).  table,  1348. 
Thermodynamics, 
first  law  of.  1847. 
references,  615. 
Thimble  fastenings  for  wire  rope,  671 
Thorium,  chgm.,  880. 


INDEX. 


1008 


Thread,  threads, 
in  cordag0,  668. 
of  mean  velocity  in  rivers,  depth 

of.  1187. 
screw-,  standard.  618. 
Three-hinged  arch,  stress  diagram, 

316. 
Thtilium.  dum.,  320. 
Thurston-meUl,  397. 
Tie.  ties, 
and  timber  preserving  plant,  (ref.) 

374. 
best  time  for  cutting,  1071. 
concrete-steel,  1072. 
cost  of  various  treatments,  376. 
creosote  extracted  from, 
analyses  of,  table,  368. 
table.  868. 
life  of  creosoted,  370. 
plates.  1071. 

for  bridges,  specifications,  706. 
railroad,  1069. 
steel-.  1072. 

switch-,  bills  for,  tables,  1070. 
wooden-, 
btuied  in  concrete,  (ref.)  1093. 
cubic  feet  in,  table.  1069. 
feet  B.  M.  in.  table,  1070. 
life  of.  1071. 
Tile,  tiles, 
glass.  800. 
metallic,  800. 
roof,  specifications,  800. 
roofing,  800. 
weight  of,  481. 
Timber, 
across  grain,  compression  tests  of, 

Uble.  494. 
air-drying.  362. 

and  tie  preserving  plant,  (ref.)  374. 
bending  modidus  of  elasticity  of, 

table.  493. 
bending  tests  of.  table.  492.  493. 
best  time  for  cutting.  378. 
best  to  use.  360. 
bumettizing,  cost.  375. 
checking  and  splitting,  to  prevent, 

363. 
compression  tests  of,  table,  490. 
cost  of  bumettizing,  360. 
cost  of  creosoting.  360. 
creosote  extracted  from,  table,  368. 
creosoting,  cost,  376. 
cut  in  U.  S.,  377. 
decay  due  to  presence  of  water, 

362. 
deca^r  of,  359. 

details  of  combination  bridge.  730. 
evaporation  of  water  from,  362. 
framing  for  bridge,  731. 


friction  of.  ^21 
galvanizea  iron 


iron  covering  for,  361. 
grtien.  compression  tests  of,  table, 

491. 
in  buildings, 
safe  loads  for,  821. 
safe  stresses,  825. 
stresses  for,  824. 
insect  larvae  in,  359. 


Timber, — Cont'd. 
Idln  drying,  363. 
life  of  creosoted,  370. 
moisture  in.  effect  on  strength, 

490-494. 
oil  seasoning,  364. 
old  vs.  new,  crushing  tests,  523. 
preservation,  359. 
preserving  methods,  360. 
relation  between  strength  and     - 

weight,  494. 
rotting  of.  869. 
safety  factors  for,  496. 
seasoning,  361.  364. 
advantages  of,  368. 
described,  362. 
effect  of,  363. 
methods,  368. 
recommendations.  365. 
shipping  weights.  391. 
standing-,  volume  of.  estimated, 

378. 
steam  seasoning,  364. 
steaming,  effect  of,  363. 
structuntl.-  safe  unit  stress  in,  718. 
stumpage  of  Pacific  Coast.  377. 
supply  of  the  U.  S..  376. 
treatments,    various    processes, 

costs,  375. 
trees,  best.  346. 
trestles.  787. 

railroad,  cost  of,  798. 
'water  in,  361. 
water  seasoning,  364. 
water-soaked-,  crushing  tests.  522. 
well-preservea-.  creosote  in,  865. 
with  grain,  shearing  tests,  table, 

494. 
working  stresses,  table,  495. 
Timbering, 
steel-,  in  mines,  use  of,  (ref.>  939. 
tunnels,  934. 
Time, 
and  longitude  measure,  table,  99. 
astronomical, 
and  civil,  compared,  952. 
elements  of,  202. 
equation  of,  202. 
between  two  dates,  tabic.  61. 
mean  local.  950. 

mean  solar  and  sidereal,  equiva- 
lents, tables.  202. 
minutes  and  seconds  to  decimals 

of  an  hour,  table,  1010. 
railway  standards.  952. 
to  determine,  with  solar.  946. 
Tin  ckem.,  320. 
allo^.  330. 
-antimony  alloy,  tensile  strength  of. 

499. 
-base  alloys,  398. 
cast-, 
physical  properties  of.  499. 
weight  of.  679. 
etc.,  weight  of,  481. 
expansion  coefficient  of,  516. 
lined  lead  pipe,  table.  679. 
melting  pomt  of,  i^l5.      , 
minerals,  380.      ^OOQIc 


1004 


INDEX. 


Tin,— Cont'd, 
molten,  weight  of.  481. 
plate,  367. 

rolled,  etc.,  weight  of,  481. 
roofing.  800. 
tubing,  679. 
uses  of,  380. 
Tinning,  367. 
Titanium,  diwm.,  820. 

minerals,  330. 
Tobin  bxonze,  307. 

physical  properties  of,  table,  407. 
Toggle, 
in  cordage.  668. 
in  nwck..  formulas,  303. 
-jointf  principle  of,  1530. 
Ton,  tons, 
and  cubic  feet,  eqtiiv.  (1-0),  table. 

486. 
(avoir.,  short),  metric  equiv.,  86. 
kilograms  and  pounds,  equiv.  (1- 

TO),  table.  87. 
long, 
and  short,  equiv.  (1-0).  table, 

486. 
metric  equivalents,  66. 
metric, 
and  U.  S..  ecjuivalents,  80. 
English  equivalents,  68. 
per  cu.  meter  and  U.  S.  tons 

per  cu.  yd.,  equivalents,  80. 
persq.  meter  and  U.  S.  tons 
per  sq.  ft.,  equivalents,  80. 
short-,  metric  equivalents,  68. 
U.  S., 
and  kilograms,  equivalents.  80. 
and  metric,  equivalents,  80. 
per  cu.  yd.  and  metric  tons  per 

cu.  meter,  equivalents,  89. 
per  sq.  ft.  and  metric  tons  per  sq. 
meter,  equivalents,  89. 
Toimeau  or  miller  (metric),  English 

equivalents.  86. 
Tools,  quarrying,  419. 
Tool-steel.  396. 
Tooth 
ax,  described.  429. 
chisel,  described,  427. 
Topographer,  duties  of,  in  prelimi- 

nary  survey  (R.  R.),  1004. 
Total 
head  (hjrdrostatic).  defined,  1160. 
heat, 
formuki,  1356. 

of  steam,  new  and  old  formulas. 
1378. 
Tower,  towers, 
and  backstays  of  suspension 

bridges.  764. 
water-,  1207. 
Township, 

and  hectars,  equivalents,  88. 
_  metric  equivalent.  81. 
Trachylite. 

comooaition  of,  table.  388. 
Trachyte^ 
composition  of,  table,  338. 
defined,  340. 
formation  of,  table,  338. 


Track,  tracks, 
and  paving  for  street  railways, 

1004.  1006. 
and  wheel  gage,  1073. 
construction 

for  tunnels  and  subwairs,  (r^.) 
1094. 

on  59  railroads,  (ref .)  1003. 
crossover-,  frog  spacing,  table,  1081. 
gage,  -gages. 

best  standard.  1074. 

increased  for  curves.  1(^8. 

table,  1074. 
ladder-,  frog  spacing,  table,  1080L 
shims,  thidcness  of.  1000. 
spikes, 

table.  627. 

wei^t  per  mile  of  trade,  table 

to  find  degree  of  curve  of.  1066. 
Trackway,  steel-,  for  street,  cost,  1142 
Traction 
force  of  locomotives.  902L 
on  grades.  1097. 
on  pavements.  1097. 
on  rails  (steel),  1097. 
on  railroad  grades, 
problem,  994. 
table.  994. 
on  roads.  1007. 
on  steel  rails,  1097. 
problem,  288. 

road-,  on  pavements,  1142. 
tension  on  rope,  289. 
Train 
momentum,  coefiKdent  of  sliding 

friction,  702. 
prewure  on  curve,  297. 
resistance  formulas,  (ref.)  1001. 
Transformed 
catenary,  763. 
-catenarian  arch,  761. 
Transformer,  transformers, 
defined.  1380. 
elec.  code  rules.  1398.  1401.  1422 

1443 
kinds  of.  1631. 
Transit, 
adjustment  of,  942. 
observation  of  polaris  for  azimuth 
949. 
Transitman.  duties  of,  in  prelimi- 
nary survey.  (R.  K.),  1000. 
Transmission, 
electric,  of  power.  1886. 
Une.  1386. 
cost  data.  1479. 
problems,  1387,  1392. 
wire  in,  kinds  and  properties  d 
1476. 
long-distance.  1386., 
Transmutation  of  matter.  317. 
Trap 
rock, 
composition  ofj  table,  337. 
greenstone,  wekht  of,  480. 
properties  of,  400. 
weight  of,  477.       J 
S-,  1295.        jOOgle 


INDEX. 


1605 


Trapezium,  defined.  129. 

and  area,  308. 
Trapezoid, 
center  ox  gravity  of,  847. 
defined.  129. 

and  area.  203. 
properties  of,  626. 
Trapezoidal  conduits,  proportioned 
for  maximum  discharge,  1161. 
Traverse, 
adjustment  of,  964. 
survey.  964. 
Travertine  limestone,  401. 
Trees, 
best  time  for  cutting.  378. 
classification  of,  341. 
•     how  they  grow.  378. 

interesting  facts  about,  346. 
life  of.  346. 
lumber,  best,  346. 
products  of.  346. 
rapid  growth  of,  346. 
tallest,  346. 
timber,  best,  346. 
Trench,  trenches, 
bracing  of,  formulas,  (ref.)  843. 
excavation, 
by  machine,  cost  data.  921. 
in  rock,  estimating.  923. 
sewer-,  cost  data,  916. 
Trenching 
and  backfilling  for  sewer,  cost 

data,  table,  917. 
in  rock,  923. 
Trestle,  trestles,  787. 
bents.  788-792. 
pile-.  787. 

and  timber.  790. 
railroad-,  cost  of.  793. 
reinforced  concrete,  792,  798. 
steel-.  791. 
elevated  railroad,  (ref.)  792. 
weight  of,  formulas.  686. 
timber.  787. 

railroad,  cost  of,  793. 
wooden-,  on  etudes,  790. 
Triangle,  triangles, 
and  circle,  circtunscribed  and  in- 
scribed. 130. 
area  of.  128. 

by  calculus,  273. 
center  of  gravity  of,  203. 
equilateral,  inscribed  in  circle,  131. 
geometric,  definitions.  128. 
menstiration  of,  203. 
properties  of,  624,  625. 
skeleton  section,  properties  of .  531. 
solution  of.  trigonometric.  141- 

142. 
solving,  by  table  of  squares.  638. 
spherical,  solution  of,  199-201. 
Triangular 
cell,  skeleton  properties  of,  631. 
dam,  847. 

orifices,  center  of  pressure  on, 
formulas,  1161. 
Trigonometric 
functions.  136-141. 
differentiation  of.  270 


Trigonometric — Cont'd, 
functions , ^-Cont'd, 
in  the  four  quadrants,  137. 
natural  and  logarithmic,  expla- 
nation of  tables,  141. 
(primary),   equivalents,    tables, 
136-137. 
inverse-,  fimctions,  140. 
differentiation  of,  271. 
operations  by  slide  rule,  127. 
Trigonometry, 
pkne,  136-198. 
spherical.  199-202. 
Trinidad  asphalt.  404. 
Trolley 
sjrstems.  cost  of.  table.  1479. 
wires,  elec.  code  rules,  1399. 
Tropical  year,  defined,  202. 
Troy  weight,  table,  86. 
Tnmcated 
cone,  defined,  134. 
prism,  defined,  138. 
pyramid,  defined,  134. 
Truss,  trusses, 
bridge-, 
electric-car  loadings  for,  tables, 

717-719. 
moments  and  shears,  various 
kMidings.  693. 
combination,  roof-,  design  of,  806- 

810. 
Cooper's  loading,  table.  708. 
diagonals,  economic  angle,  269. 
diagram.  729. 
economic  depth  of.  684. 
loading  on,  for  maximum  moment, 

696. 
Pratt-, 
calculation  of^  306. 
chord  stress  m.  concentrated 

loads,  695. 
graphical  solution  of.  312. 
railroad,  weight  of,  710. 
roof-, 
four  cases.  314. 
stress  diagrams  of,  314,  315, 

803,  804. 
timber  for,  819. 
types  of.  803. 

unit  stresses  in,  tables.  804,  805. 
weight  of  steel  in.  810.  811. 
spacing  of.  700. 

Warren-,  chord  stresses  in.  concen- 
trated loads.  696. 
Tube,  tubes, 
and  bushings,  elec.   code   niles, 

table.  1430. 
and  orifices  compared,  1176. 
and  pipes,  677. 

dia.  to  area,  capacity,  mean  radius, 
volume,  weight  (water),  table. 
246-7. 
discharge  from,  1176. 
meter.  Pitot,  1183,  1184. 
standard,  1176. 
Tubing, 
fiexible-,  elec.  code  rules,  1431. 

tSf  679.^'   tized  by  Google 


1606 


INDEX. 


Tubular  piers,  877. 

Tun  (liquid),  equivalents.  83. 

Tungstates,  an  min.,  classification  of, 

327. 
Tungsten,  ckmn,,  820. 

-steel.  806. 

weight  of,  481. 
Tunnel,  tunnels. 

alinement  ana  grade  of,  988. 

aqueduct-,  Los  Angeles,  cost  data, 
030. 

bracing  of,  formulas,  (ref.)  843. 

cross-sections  of,  084,  036,  030. 

kinds  of.  033. 

lining.  034,  030. 

list  of,  with  costs.  087. 

sewer-,  work,  cost  data,  016. 

timbering,  084. 

ventilation  of,  036. 
Tunneling.  038. 

caisson  method  of.  086. 

dredging  method  of,  086. 

methods, 
described,  088. 
and  cost  data,  037. 

shield  method  of.  036. 
Tiu-bine,  txu'bines, 

efficiencies  of.  1343. 

horsepower  ot.  theoretic,  1344. 

losses  of  energy  in,  1343. 

nomenclature  of.  1342. 

water  wheels,  described,  1342. 
Tumbuckle,  tumbuckles. 

fastenings  for  wire  rope,  675. 

weights  and  dimensions,  table,  633. 
Turnout,  tximouts. 

and  switches,  1075. 

curves,  formulas,  1088. 

for  split  switches,  tables,    1085- 
1088. 

from  curved  track,  1084. 
Turntable  pit,  (ref.)  1003. 
Turpentine, 

a  tree  product,  846. 

boiling  point  of,  614. 

for  p^t.  356. 

oil  of.  melting  point,  516. 

weight  of.  481. 
Tweddell's  hydrometer,  461. 
Type  metal,  cast,  weight  of,  481. 

U 

Ultimate 

analysis  of  fuels.  1 350. 

strength,  defined,  487. 

stress,  defined,  487. 
Ultra-violet  rays,  length  of,  1380. 
Umber  for  paint,  365. 
Undecagon,  mensuration  of.  204. 
Underground  conductors,  elec.  code 

rules,  1404. 
Undershot  wheel,  described,  1336. 
Un^la  (circular  cylindric-),  244. 
Uniform  motion,  equations  of,   278, 

IT     .       27*- 

Unit,  units, 
equivalents,  simple  and  compound, 
table,  88-01. 


Unit,  units,— Cont'd, 
heat  (B.  T.  U.).  equivalents  oL 

table,  01. 
heat,   mechanical   and    electrical, 

equivalents,  table.  01. 
heat,  per  sq.  ft.    per    nunute. 

equiv.  table.  01. 
of  electric  power.  1870. 
of  power,  defined,  201. 
stresses  in  roof  trusses,  tablea,  804. 

805. 
of  U.  S.  money,  05. 
United  States 
equivalents  of  foreign  weights  and 

measures,  tables,  02-04. 
money,  05. 
UfMet  screw  ends,  table,  634. 
Urine,  weight  of.  481. 
Uranite,  radium  from,  SSOl 
Uranium,  cJbtfm.,  320. 
in  steel,  330. 
minerals,  ore,  830. 
weight  of,  481. 


Vacuum  process,  870. 
Valency,  818. 

Valuations  and  reports,  exi)ert,  ref- 
erence data,  1484. 
Valve,  valves, 
air,  1270. 
and  gates,  Ludlow,  tables,  1274* 

1270,  12S6.  1287. 
boxes,  table  J  1288. 
Chapman,  with  wedge-shaped  gate, 

nomenclature.  1285. 
flume-,  table,  1279. 
gate-,  1271-1270,  1285-1287. 
described.  1288. 

dimensions  and  weights  of,  1273. 
vertical,  geared  and  ungeared, 
1278. 
horisontal  check,  table,  1278. 
kinds  of.  1533. 
Ludlow,  nomenclature.  1272. 
-metal.  307. 

pressure  relief,  described,  1288w 
vertical 
check,  table,  1270. 
foot,  table,  1270. 
Waring's  check.  1296. 
water.  1271-1279.  1285-1287. 
Vanadium,  chtm.t  320. 
•steel.  306.  300. 

alloys,  300. 
Vapor, 
defined.  1534. 

pressure  of  saturation  for  liquids, 
1372;  table,  1373. 
Vaporization, 
latent  heat  of.  defined,  618. 
of  fuel,  1371. 
Vaporizers  for  liquid  fuels.  1371. 
Vara, 
(Philippine    measure),    BngUsh 

equivalent,  81. 
(Texas  land  measure),  English 
equivalent,>81.      , 

Digitized  by  VjOOQ  IC 


INDEX. 


1007 


Vam,— Cont'd, 
square  (Texas  land  measure),  Eng- 
lish equivalents,  81. 
Variables,  dependent-,  defined.  250. 
Variation  and  pulsation,  in  0i4C., 

1463. 
Varnishes,  367. 
Vaults, 
fixed-,  loads  from,  817. 
kinds  of,  1634. 
Velocity,  velocities, 
and  discharee 
in  pipes,  theoretic,  table,  1166. 
of  sewers  and  conduits,  tables. 
1206-1306. 
coeflSdent  of ,  1176. 
duiins  impact,  304. 
head  m  pipe  lines,  1160. 
in  circular  brick  sewers,  table, 

1290. 
in  eg^-shaped  sewers,  table,  1306. 
in  irrigation  canals,  1317. 
in  meek.,  defined.  278. 
mean-,  depth  of  thread  of.  in  riv- 
ers, 1187. 
metric  and   English  equivalents, 

table.  80. 
of  approach,  1160. 

in  weirs,  how  measured,  1177. 
of  falling  bodies, 
from  various  heights,  table,  1 166. 
table;  283. 
on  inchned  plane,'  286. 
resultant  of,  284. 

surface  and  mean,  in  open  chan- 
nels. 1183. 
Ventilation 
and  heating,  reference  data,  1482. 
of  tunnels.  036. 
Venturi  meter,  1178. 
measurement  of  water,  1182. 
standard  proportions,  1176. 
(626  cu.  ft.  per  sec.)  in  India,  (ref.) 
1189. 
Verdigris  for  paint,  366. 
VermilUon.  329. 
Vernal  equinox,  defined,  202. 
Versed  sines, 
natural,  table,  144-166. 
(trig.),  defined,  136. 
Vertical 
angles,  defined.  128. 
bracing,  of  bridges.  698. 
check  valves,  table,  1279. 
circle,  of  celestial  sphere,  defined, 

261. 
curves,  parabolic,  1006. 
foot  valves,  table,  1279. 
line,  of  celestial  sphere,  defined, 
201. 
Viaduct,  reinforced  concrete,  793. 
Vibration  of  pendulum,  287. 
Vicat  needle  test  of  cement.  408. 
Violet  rays.  length  of.  1380. 
Vitreous  fusion  of  glass  and  iron, 

616. 
Vitrified  brick.  416. 
pavement,  specifications,    1121, 
1123. 


Voids, 

determined  for  concrete,  440. 

in  concrete,  formula,  1118. 

in  earth,  910. 

in  gravel,  911. 

in  loam,  911. 

in  loosened  earth  and  rock,  911. 

in  sand,  911. 
Volt,  as  a  pressure  unit^  1379. 
Voltages  and  frequencies,  in  tkc., 

1470. 
Volume,  voltmies. 

capaaties  and  weights,  eqtdv.  (1- 
9).  table.  486. 

critical,  defined,  613. 

cu.  yds.,  of  pipes,  table.  246-247. 

defined,  460. 

equivalents  (1-10),    English  and 
metric,  tables.  82. 

metric,  English  equlv..  table,  81. 

metric  equivalents,  table,  88. 

of  cone,  134. 

of  cylinder.  134. 

of  prism,  133. 

of  pyramid,  188. 

of  solids,  by  calculus,  277. 

of  sphere,  measure  of,  in  radii,  136. 

units  of,  equivalents,  66.  67. 

weight   per,   metric  and   English 
equivalents,  table.  89. 
Vulcamzer,  rubber.  330. 

w 

Wall,  walls, 
building-,  weights  of,  821. 
masonry,  parts  defined,  431, 
of  buildings, 
reinforcement,  831. 
stonecutter's  plan,  467. 
retaining-,  886. 
Walnuts  (trees),  classification  of. 

343. 
Wane,  in  lumber,  defined,  887. 
Waring's  check  valve,  1296. 
Warren  truss,  chord  stresses  in,  con- 
centrated loads,  696. 
Wash 
drill  borings,  cost  data,  916. 
mill,  in  cement  making.  406. 
Washers, 
cast  iron,  weights  and  dimensions, 

Uble,  624. 
flat  plate,  weights  and  dimensions, 

Uble.  624. 
use  of,  624. 
Waste  pipes,  1296. 
lead,  table,  679. 
Wasteway,  length  of,  formula,  (ref.) 

869. 
Water 
as  road  dust  preventive.  1131. 
at  maximum  density,  weight  of.  86. 
boiling  point  of,  614. 
capacity  and  weight  equivalents, 

table.  1376. 
consumption  of,  1202. 

in  cities,  table,  1203.    . 
cranes,  table,  1290.      Q[e 


1608 


INDEX. 


Water^-Cont'd. 
-current  meters,    1185. 
decompodtion  of,  810. 
density  of.  67. 
duty  of.  in  irrigation,  tables,  1315- 

13lV. 
effect  of.  on  earth  fill,  910. 
filtration.  1204. 

cost.  1291. 
gallons  per  capita  required  in  vari- 
ous cities,  table.  1208. 
-gas  and  gas-producer  process, 

(ref.)  1377. 
•gas  tar,  1132. 
heads 
forgiven  pressures,  table.  1147. 
reduced  to  equivalent  pressures, 
tables.  1148.  1149. 
hydrants,  table,  1290. 
-jet 

concrete  piles,  875. 
for  driving  piles,  (ref.)  890. 
in  pile  driving,  873. 
(Lb.  of)  evaporated  from  and  at 

212^  P..  equiv.  of.  toble.  91. 
measurement  of, 
byUnk,  1182. 
by  venturi  meter,  1182. 
by  weirs.  1182. 
meter,  Pitot  tube,  1183,  1184. 
metric  weight  of.  67. 
motors,  described,  1336. 
physical  properties  of.  table,  614. 
power 
and  steam  power  compared, 

1385. 
development,  miscellaneous  data 

(ref.)  1345. 
formulas,  1332. 

installation,  economic  sixe  of 
pipe  line  for,  1189. 
pressures, 
for  given  heads,  tables.  1148, 

1149. 
reduced  to  equivalent  heads, 
Uble.  1147. 
purification.  1204.  1292. 
rain-,  weight  of,  482. 
register,  1187. 
instructions  for  instalHng,  (ref.) 
1187. 
screening,  for  domestic  use,  1204. 
sea-, 
at  great  depths,  density   of, 

1145. 
-proof  cement,  418. 
weight  of.  481,  482. 
storage  ana  irrigation  works  of 

Southern  Cahfomia,  (ref.)  1318. 
supply,  1190. 

miscellaneous  data,  (ref.)  1201. 
surface,  evaporation  from,  1 109. 
tank,  elevated,  1207. 
tower,  1207. 

-tube  boilers,  described,  1362. 
under  pressure,  density  of ,  1145. 
valves.  1271-1279.  1286-1287. 
vapor  presstu^  of  saturation  for, 
table,  1373. 


Water— Cont'd, 
weight  of.  1145. 
table,  481. 
at  various  temperatures,  tab^ 

465. 
in  pipes,  table,  246-247. 
wheels, 
described,  1336. 
Pelton, 
<^uintex  noszle,  table,  1 342. 
single  nozzle,  table.  1338-1341. 
works,  1202. 
miscellaneous  data,  (ref.)  1291'- 
1294. 
Waterways,  1320. 
Waterproof  compositions,  418- 
Waterproofing 
a  reservoir.  1293. 
asphalt  for,  418. 
concrete,  455. 
data  for  concrete,  453. 
oil-mixed  concrete  for.  455. 
Watt,  watts, 
equivalent  of.  table,  91. 
-meter,  defined,  1536. 
per  second,  equivalents.  90. 
per  sq.  inch,  equiv.  of,  table.  91. 
units,  single  and  compound,  1879. 
Wave,  waves, 
shape,  in  §lic.,  1455. 
ether,  lengths  of.  1S80. 
Wax, 
bees-,  weight  of,  482. 
melting  point  of.  515. 
Weatherproof  wire,  table.  1428. 
Web 
plates 
of  plate  girders,  properties  of. 

table,  575. 
(vert,  line),  properties  of,  629. 
stresses  and  shears,  307. 
Wedge,  wedges, 
circular  cylindric-,  properties  of , 

245. 
common-,  volume  of.  249. 
in  mtdi.^  formulas.  292. 
of  cone.  249. 
Week  (time  measure),  99. 
Weight,  weights, 
and  dimensions  of  cast  iron  pipe 
and  spedaK  tables,    1219- 
1267. 
and  measures 
(Foreign),  American  eqmvalents, 

table,  92-94. 
of  Philippines,  English  equiva- 
lents. 81. 
and  mass  of  water,  metric.  67. 
apothecaries',  metnc  equivalents, 

table,  86. 
avoirdupois, 
long  ton,  metric  eguiv.,  table,  86. 
short  tons,  metnc  equivalents, 
table.  86. 
capacities  and   volumes,  equiva- 
lents (1-9),  table.  486. 
defined,  459. 

equivalent  for  any  specific  gravity, 
table.  488.  484. 


INDEX. 


1M9 


Weight,  weights,— Cont'd.   ^ 
in  m€ch.,  defined,  278. 
measures  and  money,  66-M. 
metric  and  English 
equivalents,  table,  89. 
equivalents  (1-10).  table.  85. 
metric.  English  equiv.,  table,  85. 
of  brick,  table.  474. 
of  building  stones,  table,  474. 
of  cast  iron  pipe,  table,  1216. 
of  cementa,  table,  474. 
of  concrete,  475. 

cinder-  and  stone-,  455. 
of  lime,  476. 

mortar.  476. 
of  limestone,  table,  475. 
of  liquids,  table,  468,  460. 
of  marble,  table.  476. 
of  masonry,  table,  476. 
of  materials.  450. 

general  table,  478. 
of  sand,  table,  476. 
of  water  at  maximum  density,  85. 
of  woods,  table.  470-473. 
per  cubic  foot,  equiv.  (1-9)  in  ca- 
pa^ties  and   volumes,   table, 
485. 
per  volume,  metric  and  English 

equivalenta^  table,  80. 
reduced  to  specific  gravities,  table, 

474. 
trade-,  of  lumber,  801. 
troy,  table,  86. 
Weir,  weirs,  1177. 
center  of  pressure  on,  table,  1151. 
contracted,  defined,  1177. 
formulas,  1178. 
Bazin's,  1178. 
Franci8\  1178. 

Pteley  and  Steams',  1180,  1181. 
Herschel's,  1181. 
Parmley's,  1180. 
instructions  for  installing,    (ref.) 

1187. 
measurement  of  water,  1182. 
sharp-crested,   surface,   formulas, 

1178. 
standard,  1177. 
submerged,  1181. 
formulas,  1181. 
suppressed-,  defined,  1177. 
triangular  and  trapezoidal,  1181. 
Weisenkalk  (marl)  for  cement,  405. 
Weld,  defined.  1586. 
WeU.  wells, 
artesian-,  defined,  1100. 
boring,  reference  data,  1481. 
dia.   to   area,   capacity,   volume, 

weight  (water),  table,  246-7. 
-driller  for  drilling  blasting  holes. 

cost,  026. 
Welded  (lap.)  pipe,  1260. 
Welding,  borax  for,  330. 
Welland  canal,  data.  1322. 
Wellhouse process,  forties,  cost. 875. 
West  point,  of  celestial  sphere,  de- 
fined. 201. 
Wet  process,  in  cement  making,  405. 
Wharton  switch,  1088. 


Wharf,  wharves, 
construction,  802. 
piers  and  docks,  802. 
reinforced  concrete,  (ref.)  000. 
Wheel  gage,  standard  M.  C.  B.,  1073. 
Wheels, 
Pelton, 
quintex  nozzle,  table,  1342. 
angle  nozzle,  table,  1388-1841. 
water,  described.  1336. 
Wheeled  scrapers,  grading  with,  cost 

data,  017. 
White 
lead  for  paint,  355. 
-metal,  308. 
zinc  for  paint,  355. 
Willow,  willows, 
classification  of,  344. 
weight  of,  482. 
Wind 
loads  on  mill  buildings,  838. 
pressure,  704. 
for  bridges.  607. 
for  buildings.  822. 
formulas.  704.  705. 
on  cyKnaers,  707. 
on  inclined  surfaces,  705-707. 
on  roofs,  tables.  706.  707. 
on  spheres,  707. 
railroad   bridges,   specifications. 

702. 
tables,  705.  706.  707. 
suction,  705. 
tension.  705. 

velocities  attained,  704.  705. 
Window  glass,  cost  prices.  470. 
Wire,  wires, 
aluminum  and  copper  compared, 

as  electrical  conductors,  406. 
bell-,  elec.  code  rules,  1448. 
brass,* 
physical  properties  of,  table.  406. 
weight  of,  478. 
brush,  for  mill  scale,  350. 
capacity  of,  elec.  code  niles,  table. 

1448. 
conduit-,  elec.  code  rules,  1427. 
copper, 
and  silicon-bronze  compared,  as 

electric  conductors.  407. 
carrjong  capacity  of ,  table,  1404. 
physical   properties  of,   table. 

table.'  1388-1301. 

weight  of.  478. 
delta-metal,    tensile   strength   of. 

table,  407. 
elec.  code  rules,  1300,  1403,  1405, 

1408,  1422,  1447. 
fixture-,  elec.  code  rules,  1427. 
gages,  tables,  666,  671. 
gold,  tensile  strength  of,  407. 
in  transmission  lines, 

kinds  and  properties  of,  1476. 

kind  and  size,  1386. 
insulated,  table.  1423. 
iron,  physical  properties  of,  table. 

408. 
lead,  tensile  strength  of.  408. 


1610 


INDEX. 


Wire,  wires,— Cont'd. 

platinum,  tensile  stienstfl  of,  498. 
Roebling  steel,  properOes  of,  673. 
rope.  673. 

fastenings.  676. 

toblesTMl. 
rubber-covered,  Ubles,  1424. 
silicon-bronze,  tensile  strength  of, 

407. 
slow-burning,  table,  1426. 
steel. 

physical  properties  of,  table,  499. 

wdght  of,  481. 
weatherproof,  table.  1426. 
weight  of,  from  specific  gravity, 

table,  484. 
caro,  ana  equipment,  elec.  code 

rules.  1417. 
theater-,  elec.  code  rules.  1414. 
Wood  (see.  also.  Timber), 
-alcohol,  a  tree  product,  346. 
as  fuel,  value  <A,  1363. 
-block  pavement, 

construction  of^  1099. 

creosoted,  specifications,  1126. 

specifications.  1108.  1120.  1128. 
compression  tests  of.  table.  490. 
expansion  coefficient  of,  616. 
friction  of,  617-521. 
(in  machines),  friction  of,  521. 
oil.  weight  of,  482. 
paving  blocks. 

grooved.  U20. 

treatment,  analjrsis  of,  1120. 

bored  and  banded.  1208. 
flow  of  water  in.  (ref.)  1187. 
screws,  table.  622. 
specific  gravities  of,   table.  470- 

478. 
stave  connection  with  cast  iron 

pipe,  1280. 
stave  pipe, 
and  details,  table.  1210. 
details  of,  1208. 
discharge  through,  table,  1210- 

1214. 
durabiUty  of,  1187. 
notes  on.  1214. 
vinegar.  346. 

weights  of.  table,  470-473. 
Wood^s  fusible  metal,  melting  point 

of,  515. 
Wolfram,  weight  of,  482. 
Wooden 
beams, 
for  buildings,  819. 
loads  on,  table/  566. 
problems  in,  567. 
working  stresses,  table,  495. 
columns,  working  stresses,  table, 

495. 
moldings,  elec.  code  rules,  1450. 
pipe,  bored-,  for  water  supply, 

.  1207. 
stringers,  bending  moments,  table. 


Wooden— Cont'd, 
structures,  methods  of  preaervisYs. 

361. 
ties, 
cubic  feet  in,  table,  1060. 
feet  B.  M.  in.  table,  1070. 
Work 
and  power  equivalents,  metric  and 

EngUsh,  table,  90. 
formula  for,  in  hoistingjJtOO. 
in  m4ch.,  equations  of,  290. 
Working  stress,  -stresses, 
defined.  487. 

for  reinforced  concrete  beams,  585. 
for  wooden  beams  and  oohmms, 
table.  495. 
WQrthington  steam  pump.  1367. 
Wrought  iron, 
expansion  coefficient  c^.  516. 
for  buildings.  819. 
in  buildings,  safe  stresses.  826. 
manufacture  of.  393. 
melting  point  o{^  515. 
physical  properties  of.  table,  498. 
pipe.  1268. 
standard,   welded,    tables.    677. 
678. 
weight  of.  480. 


X-ray.  316. 
Xenon,  chnn.,  320. 


Vs.  cast  iron  pipe,  tables.  1227. 1228. 

1255.  1256: 
Yard,  yards, 
ana  meters, 
cubic, 
equivalents.  88. 
equiv.  (1-10).  tabks.  82. 
eqmvalents.  88. 
equiv.  (l-lO),  table.  70. 
square, 
equivalents.  88. 
equiv.  (1-10).  table.  80. 
cubic, 
equivalents,  66-67. 
metric  eqmvalent,  68. 
metric  equivalent.  68,  82. 
(dollars  per) 
and  francs  per  meter,  equiva- 
lents (1-10).  table.  98. 
and  marks  per  meter,  98. 
equivalents,  68. 
^vity-,  (ref.)  1091. 
-mch  and  bushels,  equiv.  (1-9). 

table,  485. 
-inch  and  cubic  feet,  equiv.  (1-9) 

table.  485. 
-inch  and  gallons,  equiv.   (1-9), 

table,  485. 
metric  equivalents.  66,  68. 
square,  metric  equivalents,  68,  81 
Yam 
fiber,  fiax,  strength  of,  512. 
in  cordagf,  6^" 

Digitized  b 


d  by^OOgk 


INDEX. 


1811 


Year. 

common  and  leap-,  time  measure, 
M. 

tropical,  defined,  202. 
Yellow  pine  lumber, 

classihcation  of.  387.  388. 

inspection  of,  387.  388. 
Yen   (Japanese),  equiv.   (1-10,-60- 
100)  in  U.  S.  money,  table,  97. 
Yield  point,  defined.  487. 
Ytterbium.  chem.,Z2Q. 
Yttritmi,  dum.,  320. 


Z-bar,  -bars, 

block,  properties  of.  688.  634. 

columns,    dimensions   and   safe 
loads,  tables.  608-000. 

rivet  gages  forj  614. 

rolled,  properties  of,  638. 

steel,  properties  of.  table,  667. 
Z,  block,  properties  of,  633.  634. 
Zenith 

distance,  of  a  star,  defined,  201. 

in  astron.,  defined,  047. 

of  celestial  sphere,  defined,  201. 


ZmC;  clmn.,  320. 
boiling  point  of,  614. 
cast-,    physical   properties    of. 

409. 
cast,  etc.  weight  of,  482. 
chloride, 
cost.  376. 
for  timber,  361. 
expansion  coefficients  of.  616. 
melting  point  of,  616. 
minerals,  ores,  329. 
ores,  uses  of,  329. 
oxide  for  paint,  866. 
rolled-,  tensile  strength  of.  499. 
uses  ot,  329. 

•white  for  calcimining,  366. 
white  paint,  329. 
Zirconium,  dr#m.,  320. 
Zone, 
of  circle,  mensuration  of,  219. 
of  circular  spindle.  264. 
of  parabolic  sprindle.  264. 
of  sphere, 
area  of.  by  calculus,  276. 
defined.  136. 
mensuration  of.  263. 
Zook)gical  materials,  847. 


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