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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> ^**®
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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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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
Digitized by VjOOQ IC
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
Digitized by VJOOy IC
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
tized by Google
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
tizedbyUOOgle
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
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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
d by Google
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
d by Google
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
by Google
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 . ■
EoooooofcSo
gs
6wa
b o o 6f : fi o o
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
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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
( ''
d by Google
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
•10
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
795
910
m^
138
252
365
478
591
704
816
928
040
151
262
373
483
594
704
813
923
012
141
518
642
765
888
011
138
255
376
497
618
739
859
979
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
'.81
.82
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
.26130
.26413
286
284
284
283
.28093 .
.28371 1
.28647 1
.28923 ;
.29198 ^
r
.29473 .
9tktAC ^
281
281
279
279
278
278
276
276
275
275
.29746 g*
.30019 g*
1.30291 g;
i .30563 ^^^
270
.30833 270
.31103 £J
.31372 ;JJ
.31641 |fi»
.31909 ^^
267
.32176 »-.
.32442 III
.32707 III
.32972 ;55
.33237 2*5
263
.33500 -R-
.33763 ;g
.34025 ;"
.34286 il\
.34547 ^®^
260
.34807 ,j5n
.35067 ;52
.35325 258
.35584 ,^;
.35841 ^^'
257
.36098 ,-.
.36354 ;?X
.36609 III
.36864 iZ
.37118 ^^
254
.37372 ,„
.37624 iti
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
572
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
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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
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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.
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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
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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
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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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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 '
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- 1 6oritoe.
Oouuiff
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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
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Cosine.
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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.
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.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
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NATURAL SINES, ETC. 167
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(Versed sixie —1 — coeine; coversed eine^l— sine.)
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9.— PLANE TRIGONOMETRY.
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1.857201
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1.781979
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1.855908
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41
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1.780765
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41
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1.854615
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40
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1.779662
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40
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1.777130
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37
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35
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1.846892
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1.772302
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34
27
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1.845609
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33
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1.771098
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33
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1.844328
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32
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1 .769895
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33
29
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1.843049
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1.841770
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1 .767494
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30
31
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1.840494
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29
31
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1.766295
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29
32
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1.839218
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28
32
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1.766097
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28
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27
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1.763900
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27
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1.762705
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1.761611
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1.760318
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1.832861
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1.831593
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1.830327
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21
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1.756747
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21
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1.829062
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30
40
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1.766669
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30
41
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1.827799
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19
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1.754372
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1.826537
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1.763186
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1.825276
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17
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1.752002
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17
44
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1.824017
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1.760819
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1.749637
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1.821502
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14
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1.748466
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160 9.-'PLANE TRIGONOMETRY.
3.— Natnrml Sines, Tanobnts, Cotangbnts. Cosinbs. — (Contintted.)
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NATURAL SINES, ETC. 161
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%^PLANE TRIGONOMETRY.
S.— Nataral Siaet, Tanobkts, CoTANCBKTt, Cosinbs. — (Continiaed.)
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Note. — Secant —l-»- cosine.
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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
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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"
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1 II ' 1 Sine.
Tang. I Ootang.l Cosliie. i
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1.191753
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1.150368
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1.191049
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1.149692
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51
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1.190346
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2
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1.189643
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3
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1
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1.176382
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1.135608
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1
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1.175688
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13
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1.134942
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1.174996
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1.134277
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35
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1.133612
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3
26
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1.173612
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16
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1.132947
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27
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29
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1.130294
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31
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1.170160
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1.129632
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32
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1.169471
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12
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1.128970
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33
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1.168782
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13
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1.128308
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34
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1.168094
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14
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1.127647
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35
6505533
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: 5
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1.126987
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86 .6507742
! 857 103
1.166720
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16
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1.126327
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37
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1.166033
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17
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1.125667
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38
.6512158
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1.165347
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18
.6643612
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1.125008
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39
.6514366
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1.164661
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19
.8645785
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1.124349
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40
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: 0
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41
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1.162607
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1.121061
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1.160557
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1 15
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1.120405
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46
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1.159874
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47
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1.159192
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17
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48
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1.158511
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18
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1.118439
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49
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1.157830
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19
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1.117784
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50
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1 O
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1.117130
. 7450681
51
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1.116476
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52 .6543010
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53
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54
.6547408
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.75!i8&35
>4
.6678326
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1.114518
.7448115
55
.6549607
.86673611.153753
.7556630
5
.6680490
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1.113866
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56
.6551804
.867246 1.153075
.7554724
>6
.6682655
.898299
1.113214
.7430229
57 .6554002
.8677 55 1.1 52397 .7552818
)7
.6684818
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1.112563
.7437385
58
.6556198
.868265 1.151 721 .755091 1
>8
.6686981
.899351
1.111912
.7436340
59
.6558395
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i9
.6889144
.899877 1.111262
.7433304
60 .6560590 1.869286
1.160368 .7547096
0|. 6691306
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.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
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900404
1.110612
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60
0
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1.072368
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60
1
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1.109963
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59
1
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1.071743
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59
2
IgJ^IQ
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1.109314
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58
2
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1.071118
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58
S
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1.108665
.7426606
57
3
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1.070494
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57
4
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1.108017
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56
4
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1 .069870
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56
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1.107369
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S
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1.069246
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1.106721
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1.068623
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54
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53
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53
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1.106428
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52
8
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1.104782
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51
9
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1.066755
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51
M.67U8S5
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1.104136
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SO
10
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1.066134
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1.103491
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49
11
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1 .065512
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1.103846
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48
12
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1.064891
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48
la nitMi
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1.102201
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47
13
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1.064271
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47
M .6721515
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1.101557
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46
14
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I .063651
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46
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1.100914
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48
IS
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1.063031
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45
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1.100270
7400225
44
16
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1.062411
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1.099628
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43
17
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1.061792
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43
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1.098985
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42
18
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1.061174
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42
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1.098343
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41
19
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1.060556
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at
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1.097702
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40
20
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1.059938
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40
21
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39
21
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38
22
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1 .058703
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38
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37
23
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1.058086
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37
24
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36
24
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1 .057470
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36
28
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1.094000
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35
28
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1.056854
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35
26
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1.093881
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34
26
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1.056238
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34
V
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1 .093222
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33
27
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1.055623
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33
28
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1.092584
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32
28
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1.055008
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32
29
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1.001946
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31
29
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1 .054394
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31
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1.091308
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30
30
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1.053780
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30
21
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1.090671
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29
31
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1.053166
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29
22
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1.090034
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28
32
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1.052553
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28
22
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1.089398
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27
33
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1.051940
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27
24
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1.088762
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26
34
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1.051327
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26
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1.088126
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28
35
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1.050715
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28
86
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1.087491
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24
36
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1.050103
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24
27
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1.086857
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23
37
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1.049492
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23
18
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1.086222
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22
38
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1.048880
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22
26
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1.085588
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39
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1.048270
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21
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1 .084955
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20
40
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1.047659
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20
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1.084322
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41
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1.047049
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19
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1 .045222
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1 .044613
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46
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14
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1.080532
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47
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1.043397
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13
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48
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1.042790
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12
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m.6798881
U .6880813
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1.079271
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49
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1.042183
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11
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1.078642
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SO
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1.041576
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10
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1.078012
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51
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1.040970
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9
sl. 6882846
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1.0n384
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52
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1.040364
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8
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1.076756
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53
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1.039758
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7
S4t 6807209
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1.076128
.7325429
54
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1.039153
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6
is; .6889339
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1.075500
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55
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1.038548
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5
»l 6811488
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56
.6938209
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1.037944
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4
S7,.68ia5»8
98i.681f728
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.7319486
57
.6940304
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1.037340
.7199457
3
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1.073620
.7317503
58
.6942398
.964565 '1.036736
.7197438
2
». .6817866
.931971
1.072994
.7315521
59
.6944491
.965126|l. 036133
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1
88| .6819884
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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
.3047-
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
.75513
.80074
.84935
.90126
.95678
17
.56497
.59880
.63464
.67264
.71298
.75587
.80162
.85019
.90216
.96744
18
.56661
.69938
.63525
.67329
.71368
.75661
.80231
.85103
.90305
.96870
19
.56606
.69996
.63587
.67394
.71437
.75734
.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
.60112
.63710
.67525
.71576
.75882
.80467
.85355
.90576
.94158
22
.56771
.60171
.63772
.67691
.71646
.75956
.80546
.85439
.90665
.94265
23
.56826
.60229
.63834
.67656
.71715
.76031
.80625
.85523
.90755
.94351
24
.66881
.60287
.63895
.67722
.71785
.76105
.80704
.85608
.90845
.94448
35
1.56937
1.60346
1.63957
1.67788
1.71855
1.76179
1.80783
1.85692
1.90935
1.96544
24
.56992
.60404
.64019
.67853
.71925
.76253
.80862
.85777
.91026
.94441
27
.57047
.60463
.64081
.67919
.71996
.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
.97ir
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
.86627
.91936
.97415
87
.57603
.61051
.64706
.68582
.72698
.77077
.81740
.86713
.92027
.97713
88
.67659
.61111
.64768
.68648
.72769
.77152
.81820
.86799
.92118
.97811
39
.67715
.61170
.64831
.68716
.72840
.77227
.81900
.86885
.92210
.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
.98107
42
.57883
.61348
.65020
.68915
.73053
.77454
.82142
.87142
.92486
.982<»&
43
.57939
.61407
.65083
.68982
.73124
.77530
.82222
.87289
.92578
.98804
44
.57995
.61467
.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
.69655
.73840
.78291
.83034
.88096
.93505
.0029S
54
.58560
.62065
.65780
.69723
.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
.78521
.83280
.88357
.93785
.00598
67
.58731
.62246
.65972
.69926
.74128
.78598
.83362
.88445
.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
.45664
.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
.58888
42
.02559
.18479
.36276
.56294
.78970
.04860
.34689
.69417
.10344
.89277
43
.02810
.18759
.36590
.56649
.79374
.05322
.35224
.70044
.11088
.88174
44
.03062
.19040
.36905
.57005
.79778
.05786
.35761
.70678
.11835
.81072
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
.03821
.19886
.37854
.68076
.80996
.07184
.37380
.72569
.14087
.68790
48
.04075
.20169
.38171
.58434
.81404
.07652
.37923
.73205
.14842
.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
.75123
.17121
.87454
52
.05094
.21306
.39448
.59876
.83045
.09535
.40106
.75766
.17886
.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
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.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
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23
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23
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31
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184
^.— PLANE TRIGONOMETRY.
5. — Locarithmic Sines, Tanobnts. Cotanobnts. Cosimbs. — (Cont'd.)
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le^ ir
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37' .48094
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Ex.— Log sec le^'-aC- 10.01826
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LOGARITHMIC SINES, ETC.
185
6. — Locaritkmic Sliiet, Tanobnts, Cotanobnts. Cosinbs.— (Cont'd.)
(SbCANTS. CO8BCANT8.)*
*\ able. 1
Twag. 1 Ootoag. I Cootne. | || ' | Sine. |
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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
.54794
.45206
.97448
33
28
.50072
.52368
.47632
.97704
32
28
.52278
.54835
.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
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33
27
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33
281 .58223
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.88349
.96672
32
28
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.96251
32
29 .58153
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.38313
.96667
31
29
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.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
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29
31
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.96234
29
32 .58345
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.96661
28
82
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.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
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.96625
23
37
.60273
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23
38
.58SX7
.62008
.37993
.96530
22
38
.60302
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.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
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.96504
41
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42
.56648
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18
42
.60417
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.35767
.96174
43
.58678
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.r8l6
.96493
43
.60446
.64278
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.96168
44
.58709
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.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
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.35619
.96151
47
.58799
.62327
.37673
.96472
47
.60561
.64415
.35585
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48
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LOGARITHMIC SINES, ETC.
189
Tanobnts, Cotangbhts. Cosinbs. — (Cont'd.)
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27»
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190
9.— PLANE TRIGONOMETRY.
6. — Locarithniic Sines, Tanobnts, Cotanobnts, Cobinss. — (Cont'd.)
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28«
JJ sine.
1 Tang. 1 Cotang. 1 Coelne. | 11 ' | Sine. I Tang. | Cotang. | Ocalne. |
0
9.67161
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10.27280
9.94660
55
5
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9.74524
10.26476
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6
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64
6
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9
7
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53
7
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3
8
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62
8
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1
9
.67374
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61
9
.68762
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10
9.67398
9.72872
10.27128
9.94526
50
10
9.68784
9.74673
10.25327
9.94112
S
11
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49
11
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A
12
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48
12
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4
13
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47
13
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4
14
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14
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15
9.67515
9.73023
10.26977
9.94492
45
15
9.68897
9.74821
10.26179
9.94076
4
16
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44
16
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4
17
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43
17
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10.26825
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21
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21
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22
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3
23
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37
23
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24
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35
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35
35
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26
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34
26
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27
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28
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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
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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
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10.24589
9.9S»4
;
36
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24
36
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23
37
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38
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22
38
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21
39
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40
9.68098
9.73777
10.26223
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30
40
9.69456
9.76568
10.24442
9.98896
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19
41
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42
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18
42
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43
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17
43
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44
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16
44
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45
9.68213
9.73927
10.26073
9.94286
15
45
9.69567
9.75706
10.24295
9.93862
46
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14
46
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47
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13
47
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12
48
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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
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9
61
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52
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8
52
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53
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7
53
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64
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6
54
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55
9.68443
9.74226
10.25774
9.94217
5
55
9.69787
9.75998
10.24002
9.93789
56
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4
56
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67
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3
57
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58
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2
58
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69
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1
59
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60
9.68657
9.74375
10.25626
9.94182
0 60
9.69897
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Oodne. Gotane.
Tang.
Sine.
1 Cwdne.
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Tsng.
SIlMS. f
*Log
secant "-colog cosine— 1
61" <
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l~loRsinc
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x>gsec
28«»-80'-
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10.
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GARITHMIC SINES,
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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.
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0
9.72421
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9.92842
60
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10.20281
9.92803
55
5
9.73708
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10.18610
9.92318
6
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64
6
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7
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9.92763
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10
9.72805
9.81628
10.18472
9.92277
11
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11
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15
9.72723
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10.20000
9.92723
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15
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9.92236
16
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17
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18
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41
19
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9.72823
9.80140
10.19860
9.92683
40
ao
9.739OT
9.81803
10.18197
9.92194
21
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22
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23
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24
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36
24
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35
9.72922
9.80279
10.19721
9.92643
35
35 9.74093
9.81941
10. 18059
9.921S2 3
26
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34
26
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27
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33
27
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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
9.73022
9.80419
10.19581
9.92603
30
30
9.74189
9.82078
10.17922
9.92111
31
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29
31
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32
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28
32
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33
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27
33
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34
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26
34
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35
9.73121
9.80558
10.19442
9.92563
35
35
9.74284
9.82215
10.17785
9.92069
36
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24
36
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37
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23
37
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22
38
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39 .73200
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21
39
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.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
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19
41
.74398
.82380
.17620
.92018 1
42
.73269
.80753
.19247
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18,
42
.74417
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.17593
.92010 1
43
.73278
.80781
.19219
.92498
171
43
.74436
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.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
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47
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! 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
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.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
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.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
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3
67
.76870
.86046
.13954
.90823
8
58
;;is?
.84469
.15531
.91354
2
58
.76887
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.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
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. 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
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33
^ .793«
2»J .793M
.90009
.09991
.89375
32
28
.80320
.91559
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32
.90035
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.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
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21
««.799?3
«j!.79n9
9.90820
10.09680
9.89254
ao
40
9.80504
9.91868
10.08132
9.88636
20
.90348
.09654
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19
41
.80519
.91893
.08107
.88626
«3 .79108
^i .79821
.90371
.09629
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18
42
.80534
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.88615
.90397
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17
43
.80650
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.88605
0^1 .7968
^H.788S2
.90423
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16
44
.80565
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9.90449
10.09551
9.89203
15
45
9.80580
9.91996
10.08004
9.88584
■el .79888
^2 79884
.90475
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.89193
14
46
.80596
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.88573
.90601
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13
47
.80610
.92048
.07952
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M .79889
51 .Tins
.90527
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12
48
.80625
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11
49
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»<«.T9731
a^ .79748
9.90978
10.09422
9.89152
10
50
9.80656
9.92125
10.07875
9.88531
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9
61
.80671
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i», .79782
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8
52
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7
53
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itff '79781
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6
64
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»*«.79a89
9.90708
10.09293.
9.89101
5
55
9.80731
9.92253
10.07747
9.88478
m -7968
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4
66
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ri -79840
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3
67
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m -798BC
.90785
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2
58
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0 '79871
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1
59
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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
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69
1
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.Wm 51
.80837
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58
2
.81723
.93967
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.80852
.92458
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.88394
57
3
.81738
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.80867
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.88383
56
4
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!06988
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9.80882
9.92510
10.07490
9.88372
S5
6
9.81767
9.94044
10.05956
9.87721 5!
.80897
.92636
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54
6
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.80912
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53
7
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.80927
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52
8
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.80942
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51
9
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9.80957
9.92638
10.07362
9.88319
50
10
9.81839
9.94171
10.05829
9.87668 «
.80972
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49
11
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48
12
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47
13
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.81017
.92740
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46
14
.81897
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9.81032
9.92766
10.07234
9.88266
45
15
9.81911
9.94299
10.05701
9.87618 4
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44
16
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43
17
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42
18
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41
19
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9.87657 4
20
9.81106
9.92894
10.07106
9.88212
40
20
9.81983
9.94426
10.05574
21
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39
21
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22
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88
22
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23
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87
23
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24
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36
24
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25
9.81180
9.93022
10.06978
9.88158
35
25
9.82055
9.94654
10.05446
9.87501 J
26
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34
26
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27
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33
27
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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
9.81254
9.93150
10.06850
9.88105
30
30
9.82126
9.94681
10.05319
9.87446 J
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31
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29
31
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32
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28
32
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S3
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27
33
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34
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26
34
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359.81328
9.93278
10.06722
9.88051
25
35
9.82198
9.94808
10.05192
9.87290 7
36
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24
36
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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
9.81402
9.93406
10.06594
9.87996
20
40
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9.87224 :
41
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19
41
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42
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18
42
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43
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17
43
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44
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16
44
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45
9.81475
9.93533
10.06467
9.87942
15
45
9.82340
9.95062
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9.87277
46
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14
46
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47
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13
47
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48
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12
48
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49
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11
49
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50
9.81549
9.93661
10.06339
9.87887
10
50
9.82410
9.95190
10.04810
9.87211
51
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9
51
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52
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8
52
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53
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7
53
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54
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6
54
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65
9.81622
9.93789
10.06211
9.87833
6
55
9.82481
9.95317
10.04683
9.271M
56
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4
66
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67
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3
57
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58
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2
58
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59
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1
59
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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
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59
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59
V .8tf7f
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58
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58
i{ .asm
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57
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67
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66
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56
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9.06671
10.04439
9.87050
55
9.83446
9.97092
10.02908
9! 86354
68
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54
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54
71 .et49
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53
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53
s ato
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52
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53
» .82in
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51
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51
ll».8Mtl
9.05098
10.04303
9.86993
50
9.83513
9.97219
10.02781
9.86295
50
li .«706
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49
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49
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48
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48
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47
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47
14 .«747
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46
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46
U<9.eK761
9.95825
10.04175
9.86836
45
9.83581
9.97345
10.02656
9.86235
45
11 .8S77S
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44
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44
171 .S7tt
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43
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43
u .szsn
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42
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43
1» .SUA
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41
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41
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10.04048
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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.
I ^ §
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322
11.— MENSURATION.
i II
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3 II
I
^
H
i ^
> 7
I I I
I
■ § I
^ I U
I
'^h^h 'i -u'>kl'M'>
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f
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U I 0
x^jiBiiba
I I >
I I D
I I
i<Ni„ i
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d by Google
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
4551.4
i
5558.3
6665.7
7873.6
9182.1
■
•_o
4566.4
5574.8
6683.8
7893.3
9203.3
g°
i
4581.3
5591.4
6701.9
7913.0
9224.6
4596.3
5607.9
6720.1
7932.7
9245.9
4611.4
5624.5
6738.2
7952.5
9267.2
4626.4
5641.2
6756.4
7972.2
9288.6
4641.5
6657.8
6774.7
7992.0
9309.9
H '
77
85
93
101
109
gg
4656.6
5674.5
6792.9
8011.8
9331.3
.
4671.8
•
5691.2
6811.2
8031.7
9352.7
»'P
4686.9
5707.9
6829.5
8051.6
9374.2
*^z
4702.1
1
5724.7
6847.8
8071.4
9395.6
7i
4717.3
6741.5
6866.1
8091.4
9417.1
■
4732.5
5758.3
6884.5
8111.3
9438.6
B-K
4747.8
5775.1
6902.9
8131.3
9460.2
S2
4763.1
5791.9
6921.3
8151.3
9481.7
78
86
94
103
110
^P
4778.4
5808.8
6939.8
8171.3
9503.3
H'*
4793.7
5825.7
6958.2
8191.3
9524.9
gs
4809.0
5842.6
6976.7
8211.4
9546.6
4824.4
5859 6
6995.3
8231.5
9568.2
Si"
4839.8
5876.5
7013.8
8251.6
9589.9
4855.2
5893.5
7032 4
8271.7
9611.6
•
4870.7
5910.6
7051.0
8291.9
9633.3
; ,
4886.2
5927.6
7069.6
8312.1
9655.1
?
79
87
95
103
111
4901.7
5944.7
7088.2
8332.3
9676.9
a.
4917.2
5961.8
7106.9
8352.5
9698.7
^
1
4932.7
5978.9
T125.6
8372.8
9720.5
4948.3
5996.0
7144.3
8393.1
9742.4
s.
4963.8
6013.2
7163.0
8413.4
9764.3
4979.5
6030.4
7181.8
8433.7
9786.2
to
s
4995.2
6047.6
7200.6
8454.1
980S.1
5010.9
6064.9
7219.4
8474.5
9830. I 1 t 1 "^
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.
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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
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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):
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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.
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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.
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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
Digitized
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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
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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
316
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318
n.^NATURAL HISTORY OF MATERIALS.
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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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1:
1 :
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1:
3:
2:
3:
max.
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,
823
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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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n.— NATURAL HISTORY OF MATERIALS.
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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.
d by Google
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
d by Google
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
d by Google
CREOSOTE OILS I
d by Google
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.
d by Google
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
d by Google
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.
Digitized by VjOOQ LC^ y»^^
d by Google
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.
d by Google
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 ^ ,
Digitized by VjOOQ IC
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."
d by Google
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.
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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.
421
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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
by Google
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
d by Google
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
d by Google
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.
d by Google
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.)
d by Google
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.
d by Google
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.
d by Google
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.
d by Google
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 " "
d by Google
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
by Google
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. ^
Digitized by VjOOQ IC
d by Google
^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-
d by Google
d by Google
d by Google
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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).
by Google
d by Google
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
Digitized by V^OOQLC
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«,«
d by Google
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
d by Google
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 ^
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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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?
a
z-
b
s
S5
s
n
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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).
d by Google
d by Google
d by Google
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
d by Google
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
d by Google
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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d by Google
d by Google
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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d by Google
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.
d by Google
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.
t 26 feet or less.
d by Google
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.
d by Google
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.)
d by Google
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
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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.
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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
d by Google
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
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1.0000000
1.0314941
4.0000000
4.0627441
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9.093994
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1.0634766
4.1259766
9.188477
16.250977
25.313477
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1.0959473
4.1896973
9.283447
16.377197
25.470947
8/64
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1.1289063
4.2539063
9.378906
16.503906
25.628906
1/18
5/64
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1.1623535
4.3186035
9.474854
16.631104
25.787364
5/64
3/32
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1.1962891
4.3837891
9.571289
16.758789
25.946289
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1.2307129
4.4494629
9.668213
16.886963
26.105713
7/64
1/8
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1.2656250
4.5156250
9.765625
17.015625
26.265625
1/8
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1.3010254
4.5822754
9.863552
17.144775
26.426025
9/64
5/32
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1.3369141
4.6494141
9.961914
17.274414
26.586914
5/32
11/64
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1.8732910
4.7170410
10.060791
17.404541
26.748291
11/64
3/16
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1.4101563
4.7851563
10.160156
17.535156
26.910156
3/16
13/64
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1.4475098
4.8537698
10.260010
17.666260
27.072510
13/64
7/32
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1.4853516
4.9228516
10.360352
17.797852
27.235352
7/32
15/64
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1.52S6816
4.9924316
10.461182
17.929932
27.898682
16/64
1/4
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1.5625000
5.0625000
10.562500
18.062500
27.562500
1/4
17/64
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1.6018066
6.1330566
10.664307
18.195657
27.726807
17/64
9/32
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1.6416016
5.2041016
10.766602
18.329102
27.891602
9/32
lt/64
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1.6818848
6.2756348
10.869385
18.463135
28.056885
19/64
6/16
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1.7226563
5.3476563
10.972656
18.597656
28.222656
.6/16
21/64
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1.7639160
5.4201660
11.076416
18.732666
28.388916
21/64
11/32
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1.8056641
5.4931641
11.180664
18.868164
28.555664
11/32
23/64
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1.8479004
5.6666504
U. 285400
19.004150
28.722900
23/64
8/8
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1.8906250
5.6406250
11.390625
19.140625
28.890625
3/8
23/64
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1.9338379
6.7150879
11.496338
19.277588
29.058838
25/64
13/32
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1.9775391
5.7900391
11.602539
19.415039
29.227539
13/32
27/64
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2.0217285
5.8654785
11.709229
19.552979
29.396729
27/64
7/16
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2.0664063
5.9414063
11.816406
19.691406
29.566406
7/18
29/64
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2.1115723
6.0178223
11.924072
19.830322
29.736572
29/64
15/32
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2.1572266
6 0947266
12.032227
19.969727
29.907227
15/32
31/64
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2.2033691
6.1721191
12.140869
20.109619
30.078369
31/64
1/2
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2.2500000
6.2500000
12.250000
20.250000
30.250000
1/2
33/64
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2.2971191
6.3283691
12.359619
20.390869
30.422119
38/64
17/32
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2.3447266
6.4072266
12.469727
20.532227
30.594727
17/32
35/64
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2.3928223
6.4865723
12.580322
-fS. 691406
20.674072
30.767822
35/64
9/16
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2.4414063
6.5664063
20.816406
30.941406
9/16
37/64
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2.4904785
6.6467285
12.802979
20.959229
31.115479
37/64
19/3^
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2.5400391
6.7275391
12.915039
21.102539
31.290039
19/32
39/64
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2.5900879
6.8088379
13.027588
21.246338
31.465088
39/64
5/8
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2.6406250
6.8906250
13.140625
21.390625
31.640625
5/8
41/64
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2.6916504
6.9729004
13.254150
21.535400
31.816650
41/64
21/32
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2.7431641
7.0556641
13.368164
21.680664
31.993164
21/33
48/64
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2.7951660
7.1389160
13.482666
31.826416
82.170166
43/64
11/16
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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
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2.9541016
7.3916016
13.829102
22.266602
32.704102
23/32
«?/»4
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3.0080566
7.4768066
13.945557
22.414307
32 883057
47/64
3/4
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3.0625000
7.5625000
14.062500
22.562500
33.062500
3/4
49/64
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3.1174316
7.6486816
14.179932
22.711182
33.242432
49/64
25/32
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3.1728516
7.7353516
14.297852
22.860352
33.422852
25/32
51/64
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3.2287598
7.8225098
14.416260
23.010010
33.603760
51/64
13/16
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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
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3.5156250
8.2656250
15.015625
23.76.1625
34.515625
7/8
S7/64
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3.6744629
8.3557129
15.136963
23.918213
34.699463
67/64
29/32
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3.6337891
8.4462891
15.258789
24.071289
34.883789
29/33
59/64
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3.6936035
8.5373535
15.381104
24.224854
35.068604
69/64
15/16
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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
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3.8759766
8.8134766
15.750977
24.688477
35.625977
31/32
63/64
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8.9377441
8.9064941
15.876244
24.843994
35.812744
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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.
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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
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411
414
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429
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3436
440
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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
{.OOi
.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
,220l 512
,191 518
,165 524,
1419530,
118 536.
098' 542.
079 548,
063 9555
OlS 561.
035 567.
024, 573.
01619579.
009| 585.
004 591.
001 597.
844
163 9850
,642, 856
,723 862
806 869.
891 9875
,978 881
066 887
157| 894
25019900
345j 906
441 912
5401 918
64119925
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.
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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.*
&
Dhicknets in Dectmals of an
Inch.
1
t
1
u^
.!s!ll
'-S3||l
1884
British
Imperial
l-f
II
h
7*
500
.46875
.4375
.40625
.500
.464
.432
.400
.49
.46
.43
.3938
««»
6*
*!45
.40
4-
Ask"
".W
S*
.425
409M
.375
.372
.3625
.36
r
.380
!3648
.34376
.348
.3310
.33
0
.340
.32486
.3125
.324
.3066
.306
1
.300
.2893
.28125
.300
.2830
.285
.237
2
.284
.25763
.265625
.276
.2625
.265
.219
8
.259
.22942
.25
.252
.2437
.245
.212
4
.238
.20431
.234375
.232
.2253
.225
.207
6
.220
.18194
.21875 ■
.212
.2070
.206
.204
e
.203
.16202
.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
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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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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.
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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
d by Google
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
d by Google
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). ^ *
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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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d by Google
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
d by Google
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, •<>»
d by Google
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
d by Google
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
d by Google
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
d by Google
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 *■
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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~ ^^^^^ "^
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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
d by Google
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-
d by Google
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^
d by Google
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
d by Google
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.
d by Google
d by Google
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
1 The I
mmonia |
as the J
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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
iSHSJ ofWallat
1 • Cor of Top Section
* Section
•'-^'^ of Walled-
CorMlddleSed
ofWollot
I CocBottomSec
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.
"*W
•I /W7
/Wt'
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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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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001 "^
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
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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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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.
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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.
labor roB. Tliere wen N JoIm In an, and theM are nuintMr
by **Mde aod U»p'* method. Tbe foUow1n« Infomuuioa to
p— dlA.of plp«. mina.: l» Hie of trench, widtb by dq^: d
yard tor dintnc trench, d— cost In cents per euMc yard fo
18 eta. per hour.
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920 6i— EARTHWORK.
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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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
d by Google
d by Google
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^
d by Google
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
d by Google
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
d by Google
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.
d by Google
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
d by Google
L
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 '
d by Google
t&e'Amf"*' ^Kmuller. 1881
^ A«encan Ephemerii or Nkutical Atoaiuc
d by Google
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^ "^
Digitized
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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.
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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
2 43.9
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
0 35.4
6 36.4
24.0
5
8 31.4
2 30.5
46J
6
0 31.5
6 32.5
24.4
6
8 27.5
2 26.5
Mi
7
0 27.6
6 28.5
24.8
7
8 23.5
2 22.6
44.7
8
0 23.6
6 24.6
25.2
8
8 19.6
2 1&,6
8 if 7
4T.6
9
0 19.7
6 20.7
26.6
9
8 15.7
4T.S
10
0 15.8
6 16.7
25.9
10
8 11.7
2 10.8
4T.«
11
0 11.8
6 12.8
26.3
11
8 7.8
1 6.8
47.1
12
0 7.9
6 8.9
26.6
12
8 3.8
8 2.9
4S.3
13
0 4.0
E.E. 6 5.0P.M.
27.0
13
7 59.9
1 58.9
4S.4
»{
0 0.1 A.M.
11 56.2 P.M.
|W.E.5 55.2 A.M.
f 27.4
27.8
14
15
7 55.9
7 52.0
1 55.0
1 51.0
4SI
4S,I
15
11 52.2
^ 5 51.3
^28.2
16
7 48.0
1 47.1
49.1
16
11 48.3
8 47.3
38.6
17
7 44.1
1 43.1
4».3
17
11 44.4
6 43.4
29.1
18
7 40.1
1 39.1
49 S
18
11 40^4
6 39.5
29.5
19
7 36.2
1 35.2
OS
19
11 36.5
6 35.5
29.9
20
7 32.3
1 31.3
4».>
20
11 32.6
5 31.6
30.2
31
7 28.3
1 27.4
Sll
21
11 28.6
5 27.7
30.6
22
7 24.4
1 23.4
MJ
22
11 24.7
6 23.7
31.0
23
7 20.4
1 19.5
ai.4
23
11 20.8
6 19.8
31.3
24
7 16.5
1 15.5
S6J
24
11 16.8
6 15.9
31.7
25
7 12.6
1 11.6
56 J
26
11 12.9
5 11.9
32.0
26
7 8.6
1 7.6
SIJ
26
11 9.0
• 6 8.0
32.4
27
7 4.6
1 3.7
»J
27
>i 5.0
6 4.1
32.8
28
7 0.7
0 59.7
»>
28
JA Ai
5 0.1
33.2
29
6 66.7
0 55.8
H.I
H
s
4 56.2
33.6
30
6 62.8
0 51.8
g.l
4 52.3
34.0
31
6 48.8
0 47.9
10 49.3
10 45.4
4 48.3
4 44.4
34.4
34.9
82
6 44.9
tizpd hv \^T
0 48.9
51.1
d by Google
d by Google
TABLB
4c. — Polaris. 191
(To accoi
d by Google
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. !
d by Google
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.
d by Google.
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.
d by Google
•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.
d by Google
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
6Sr.68
60
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
6S
d by Google
!NG, MAPPING AND LE
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d by Google
980
Si.— SURVEYING, MAPPING AND LEVELING.
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d by Google
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
d by Google
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
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*^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
d by Google
i018 SH.— RAILROADS.
d by Google
d by Google
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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
jrardafl
e (
P. P.c
-H^.
.4-_
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d by Google
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.
i
8=
I
I-
S-
■g."
2*0
52
a
.8:
I R
3 *^ C
o f2o
.s :2
§ 8
< o
gs.
^1' •
i'ai
MS"
U
S Q
If
ii
H H
+ I
at Jt
§xix§x
§1
II
5 8
+
<»».
•«x
1
ss
Jl
ii
+
s +
•c
i2*
g
o
D^zed by Google^
rHWORK-^GROUND-SljOPE QUANTITIES.
1081
llxll^l
0
+
S? 8
+ I
s ^
IT
9 **
& n Q
"I
i-r
a
« +
§1
J.*;
a Q Q
l|xl!>
tl
« «
8
M
li
d
5 s
-^
1 ■*
o
<io
+
s +
^
-5
00 '
el«
tl
«(
1
8
O
+
n
00
00
o
o
32
:s?
• mm
■§•3
il
•SI
a!
s"
^8
r.
?.§
b*y (google
1032
Bi.—RAILROADS,
"S g 3
"2 •«
•2 tJ
1 1
ir
^iss
51*
o gji-6'
O E^ ■»;
CO 8 S a
5 «-a ■ ^
0*0
■ .".2
« o
O V
J3 >
O
Ouan.inCu. Yds.
ForalOO-ft. Stan
On One Side of
Center.
I
CI
as ^|a» n; o
xg|xg X
t
CO ^
3X9
100^4 ••
3X9
i
eo *^
1
A
■11
8
c
2
+
5-
i
L +
« +
§ I
:: 8
+ 1
i
+
0
II
T a
o +
1
« +
1 !
*h 1
»s
I
+
• i.
c '^ a
•••
c
a
+
§8i o
<••
§
+
0
if
Si
1 o
+
5
1
+
S 5
+
•*
is
Ground
Slope.
Case.
r:^ Q Q
::5 cj Q
:d Q Si
i
;^ = '
** 5
d
^
4
^
■* tizec
byGoC
'gT
4
1
e
■-
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 <■
.
a. 8.-5:10.
^!;-
a-
-26«».6
sy
ro
+ Up
— Down
1 31 17
46
26
79
29
123
31
185
31
3 38 30
66
37
96
49
149
66
224
59
3, 30 34
67
44
114
62
178
75
267
83
41 34 »
78
62
134
72
• 208
89
313
104
8/ 40 S3
91
60
156
84
242
104
863
121
41 44 38
104
69
179
96
278
119
417
139
7| 03 43
119
79
203
109
316
135
474
158
91 09 49
134
89
329
124
357
153
535
178
)| 07 06
150
100
257
138
400
171
600
200
1/74 61
167
111
387
164
446
191
669
223
1 S3 67
185
123
317
171
494
212
741
247
/ 91 73
204
136
350
188
544
233
817
371
1 100 81
224
149
384
207
697
266
896
299
1 100 89
245
163
420
226
653
280
980
327
1 119 97
267
178
457
246
711
305
1067
856
139 106
289
193
496
267
771
331
1157
886
139 1 114
313
209
537
289
834
358
1252
417
100 123
338
225
579
812
900
386
1350
450
161 132
363
242
622
835
968
415
1452
484
173 142
389
260
667
859
1038
445
1557
519
186 162
417
278
714
386
nil
476
1667
556
198 162
445
297
763
411
1186
608
1780
593
211 172
474
316
813
438
1264
543
1896
632
224 183
604
836
864
465
1344
676
2017
672
238 196
635
357
917
494
1427
612
2141
714
262 206
567
378
971
534
1512
648
2269
756
267 218
600
400
1029
654
1600
686
2400
800
282 230
634
423
1087
565
1690
724
2535
846
297 243
669
446
1146
617
1783
764
2674
891
313 286
704
469
1207
650
1878
805
2817
939
$29 369
741
494
1270
684
1975
847
2963
988
M6 283
778
619
1334
718
2075
889
3113
1038
163 297
817
644
1400
754
2178
933
3267
1089
SO I 311
856
671
1467
790
2283
978
3424
1141
98 320
896
698
1537
827
2390
1024
3585
1196
17 1 341
938
626
1607
865
2500
1071
3750
1250
?5| 3M
980
653
1679
904
2612
1120
3919
1306
» 1 872
1023
682
1753
944
2727
1169
4091
1364
'5 1 388
1067
711
1829
985
2844
1219
4267
1422
A 1 404
1112
741
1906
1026
2964
1270
4446
1482
4 / 431
1157
772
1984
1068
3086
1323
4630-
1543
5 438
1204
803
2064
1112
3211
1376
4817
1606
S 1 455
1252
835
2146
1156
3338
1431
5007
1669
i I 473
1300
867
2229
1200
3468
1486
5201
1734
) 1 491
1350
900
2314
1246
360O
1543
5400
1800
1 1 609
1400
934
2401
1293
3734
1601
5602
1867
1 618
1452
968
2489
1340
3871
1659
5807
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
3353
1806
5216
2235
7824
2608
783
2017
1344
3457
1862
6378
2305
8067
2689
756
2078
1385
3563
1918
5543
2375
8313
2771
778
2141
1427
3670
1976
5708
2447
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
d by Google
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 ]
d by Google
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.]
d by Google
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.]
d by Google
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
d by Google
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.!
d by Google
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.]
d by Google
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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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.
d by Google
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)
d by Google
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,
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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.
d by Google
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.
d by Google
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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^P ^ t ^ ^r^.-<
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9
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c
o
I
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t; T I '^ ? a
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♦* a
u
ig
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I I
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ts
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5si*o%[a'xj|c«'^i«
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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
Digitized
by Google
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-.
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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
-i
SS
o
G I
s
o
S
Ml I
o
2
B
S
|2
O
J
3^
2i
-III
II
m
111
©^55 S5
si
l|8|
4
3
m
In
&s
)igitized t
It
o
b^JGoogle
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.
d by Google
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
d by Google
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
d by Google
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.
d by Google
KUTTERS FORMULA—VALUES OF C. 1171
8.-<CoBvricxBNT8 c IN Kuttbr's FORMULA. Emolish Mbasurb — Cont'd.
S?:l Coeffldenti n of RoughneBS.
d by Google
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.
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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
If
11
5?
li
H
1*
*ft
1ft
1
H
5A
6
51
^.
**.
5X
H
2
A
ft
•
i
ft
ft
X
ft
8
iH
iH
i*
1 1
1*-
1*-
If-
ift
ift-
4
4r
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
33
7
1400
1500
1600
1700
1800
2000
210C
2200
2300
8
4 li'xfU
'*?/"
li-a#14
li-.#14
li1#14
1*'«#14
If'fU
li'«#14
1*'«#U
9
70
80
86
90
100
105
110
115
10
12
18
14
15
19
20
31
23
33
11
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
2254
14
16M
1656
1656
1656
3254
2254
2254
2254
2354
15
1
h 2*+
!i*
li
S
J*
J
2ft
It
It
16
17
41
443
608
399
^45
470
493
18
1101
ir3
1463
1666
1931
2162
2394
2651
2923
19
*
«
*
1
1
1
1
1
1
20
308
332
355
881
399
423
445
470
493
21
31
34
36
39
31
32
34
36
38
22
^' round.
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
3254
3944
25
2803
2049
2199
2254
2722
2888
2944
2944
2944
26
>^
\t
y^
1ft
1»
If
If
If
If
27
.^
3?r-
31
H
m
m
8ft
28
859
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
aA
2»
1
7A
7»
7I-.
7f+
7t-
7tT
7
7f-
2
2 -
2»-
i-
2*-
1*:
4-
24-
24-
2A-
tft-
3^
8
4
7+
7+
6i+
7i
7A
7A
74
7 -
7i?r
7A—
5
2*x«
^xs
2ix8
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
8
2
ir»#io
lf«/10
nwio
ir«#io
l|'s#10
ir«#io
ir-iio
14-«#1(^
2'«#10
2»«|10
9
120
125
130
130
135
140
145
150
155
160
10
61
63
64
67
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
1%
1*
11
11
It
U
11
2
2
2
3
16
21
5S4
'J
Ui
^
3iV
393
^1*
t^
tt!
'M
841
814
17
18
5762
6223
6614
7648
8084
8654
9080
9531
10031
10588
19
14
1*
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
9020
25
4608
6627
6627
6627
6627
6627
9020
9020
9020
9020
76
If
»*.
IJ
li
It
It
24
84
84
24
27
8*
IS
H
*kk
H
*^i
61
H
51
6VV
28
M8
245
253
265
273
281
213
217
224
231
?9
6845
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.
Us
" « b
0. ^ c
CO o «J
g ? &
«^|
IM^
«o«««»o«2S«aog;;^«9«;aog
^toooeioioeiAeotoeeeoooo
^ lo <o 00 M* V 00* -•' V »<I -^ t^ -4' lo ^ 9 d o
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C. I. PIPE— WEIGHT. DISCHARGE, LEAD. HEMP.
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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.
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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
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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.
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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.
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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.
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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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STANDARD CAST FLANGE PIPE.
1237
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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.
d by Google
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
d by Google
1S46
^—WATER WORKS.
^JS
22 2S28 ;$8S
Digitized by VjOOQ IC
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
1 1
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1274
^,— WATER WORKS.
o
P
I
V
•3
I
S)
^ X 3f
xx_
55II«S'*S7SS?:"7*
ll-8^8|gfl^y
oo«oio
ll'8*iiili^|^.
^h^^iU^p^
55 :
1
ifedbyQoOgle
ij
DOUBLE GATE LUDLOW VALVES,
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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
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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
d by Google
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.
d by Google
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
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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
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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
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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
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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.
d by Google
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
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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
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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*
d by Google
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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87.— tVArfiRWAKS.
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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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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."
d by Google
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.
d by Google
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.
d by Google
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.
d by Google
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
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4
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5760.
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£ . 46278
'^ .53985
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800
7200
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6.
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.010^90
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182000.
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300.
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9.
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4752x10*
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1440.
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9504x104
228096x10*
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4752000.
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8.
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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
by Google
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
d by Google
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.
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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.
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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
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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
d by Google
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.
d by Google
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.
d by Google
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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i
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.
d by Google
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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